From 0d7ef73cd818264a0bf2bae05868b478c70f2bcc Mon Sep 17 00:00:00 2001
From: gubaidulinvadim <gubaidulinvadim@gmail.com>
Date: Sun, 28 Apr 2024 20:10:35 +0200
Subject: [PATCH] Added sphinx documentation (to be tested with readthedocs)

---
 docs/Makefile                                 |    20 +
 docs/build/doctrees/environment.pickle        |   Bin 0 -> 655341 bytes
 docs/build/doctrees/index.doctree             |   Bin 0 -> 4947 bytes
 docs/build/doctrees/mbtrack2.doctree          |   Bin 0 -> 3686 bytes
 .../build/doctrees/mbtrack2.impedance.doctree |   Bin 0 -> 375662 bytes
 .../doctrees/mbtrack2.instability.doctree     |   Bin 0 -> 118275 bytes
 docs/build/doctrees/mbtrack2.tracking.doctree |   Bin 0 -> 791879 bytes
 .../mbtrack2.tracking.monitors.doctree        |   Bin 0 -> 366993 bytes
 .../build/doctrees/mbtrack2.utilities.doctree |   Bin 0 -> 273823 bytes
 docs/build/html/.buildinfo                    |     4 +
 docs/build/html/_modules/index.html           |   103 +
 .../html/_modules/mbtrack2/impedance/csr.html |   292 +
 .../mbtrack2/impedance/impedance_model.html   |   806 ++
 .../mbtrack2/impedance/resistive_wall.html    |   498 +
 .../mbtrack2/impedance/resonator.html         |   290 +
 .../_modules/mbtrack2/impedance/tapers.html   |   324 +
 .../mbtrack2/impedance/wakefield.html         |  1142 ++
 .../mbtrack2/instability/instabilities.html   |   511 +
 .../_modules/mbtrack2/instability/ions.html   |   393 +
 .../_modules/mbtrack2/tracking/aperture.html  |   245 +
 .../_modules/mbtrack2/tracking/element.html   |   591 +
 .../_modules/mbtrack2/tracking/feedback.html  |   382 +
 .../mbtrack2/tracking/monitors/monitors.html  |  1750 +++
 .../mbtrack2/tracking/monitors/plotting.html  |  1545 +++
 .../mbtrack2/tracking/monitors/tools.html     |   190 +
 .../_modules/mbtrack2/tracking/parallel.html  |   336 +
 .../_modules/mbtrack2/tracking/particles.html |  1136 ++
 .../html/_modules/mbtrack2/tracking/rf.html   |  1889 +++
 .../mbtrack2/tracking/synchrotron.html        |   667 +
 .../mbtrack2/tracking/wakepotential.html      |   964 ++
 .../mbtrack2/utilities/beamloading.html       |   487 +
 .../_modules/mbtrack2/utilities/misc.html     |   390 +
 .../_modules/mbtrack2/utilities/optics.html   |   865 ++
 .../mbtrack2/utilities/read_impedance.html    |   464 +
 .../_modules/mbtrack2/utilities/spectrum.html |   225 +
 docs/build/html/_sources/index.rst.txt        |    20 +
 .../html/_sources/mbtrack2.impedance.rst.txt  |    61 +
 .../_sources/mbtrack2.instability.rst.txt     |    29 +
 docs/build/html/_sources/mbtrack2.rst.txt     |    21 +
 .../mbtrack2.tracking.monitors.rst.txt        |    37 +
 .../html/_sources/mbtrack2.tracking.rst.txt   |    85 +
 .../html/_sources/mbtrack2.utilities.rst.txt  |    53 +
 .../_sphinx_javascript_frameworks_compat.js   |   134 +
 docs/build/html/_static/basic.css             |   930 ++
 docs/build/html/_static/doctools.js           |   264 +
 .../html/_static/documentation_options.js     |    14 +
 docs/build/html/_static/file.png              |   Bin 0 -> 286 bytes
 docs/build/html/_static/jquery-3.6.0.js       | 10881 ++++++++++++++++
 docs/build/html/_static/jquery.js             |     2 +
 docs/build/html/_static/language_data.js      |   199 +
 docs/build/html/_static/minus.png             |   Bin 0 -> 90 bytes
 docs/build/html/_static/nature.css            |   248 +
 docs/build/html/_static/plus.png              |   Bin 0 -> 90 bytes
 docs/build/html/_static/pygments.css          |    84 +
 docs/build/html/_static/searchtools.js        |   531 +
 docs/build/html/_static/underscore-1.13.1.js  |  2042 +++
 docs/build/html/_static/underscore.js         |     6 +
 docs/build/html/genindex.html                 |  1454 +++
 docs/build/html/index.html                    |   107 +
 docs/build/html/mbtrack2.html                 |   162 +
 docs/build/html/mbtrack2.impedance.html       |  1335 ++
 docs/build/html/mbtrack2.instability.html     |   484 +
 docs/build/html/mbtrack2.tracking.html        |  2921 +++++
 .../html/mbtrack2.tracking.monitors.html      |  1259 ++
 docs/build/html/mbtrack2.utilities.html       |   978 ++
 docs/build/html/objects.inv                   |   Bin 0 -> 3559 bytes
 docs/build/html/py-modindex.html              |   244 +
 docs/build/html/search.html                   |   103 +
 docs/build/html/searchindex.js                |     1 +
 docs/make.bat                                 |    35 +
 docs/source/Makefile                          |    20 +
 docs/source/conf.py                           |    60 +
 docs/source/index.rst                         |    20 +
 docs/source/make.bat                          |    35 +
 docs/source/mbtrack2.impedance.rst            |    61 +
 docs/source/mbtrack2.instability.rst          |    29 +
 docs/source/mbtrack2.rst                      |    21 +
 docs/source/mbtrack2.tracking.monitors.rst    |    37 +
 docs/source/mbtrack2.tracking.rst             |    85 +
 docs/source/mbtrack2.utilities.rst            |    53 +
 80 files changed, 41654 insertions(+)
 create mode 100644 docs/Makefile
 create mode 100644 docs/build/doctrees/environment.pickle
 create mode 100644 docs/build/doctrees/index.doctree
 create mode 100644 docs/build/doctrees/mbtrack2.doctree
 create mode 100644 docs/build/doctrees/mbtrack2.impedance.doctree
 create mode 100644 docs/build/doctrees/mbtrack2.instability.doctree
 create mode 100644 docs/build/doctrees/mbtrack2.tracking.doctree
 create mode 100644 docs/build/doctrees/mbtrack2.tracking.monitors.doctree
 create mode 100644 docs/build/doctrees/mbtrack2.utilities.doctree
 create mode 100644 docs/build/html/.buildinfo
 create mode 100644 docs/build/html/_modules/index.html
 create mode 100644 docs/build/html/_modules/mbtrack2/impedance/csr.html
 create mode 100644 docs/build/html/_modules/mbtrack2/impedance/impedance_model.html
 create mode 100644 docs/build/html/_modules/mbtrack2/impedance/resistive_wall.html
 create mode 100644 docs/build/html/_modules/mbtrack2/impedance/resonator.html
 create mode 100644 docs/build/html/_modules/mbtrack2/impedance/tapers.html
 create mode 100644 docs/build/html/_modules/mbtrack2/impedance/wakefield.html
 create mode 100644 docs/build/html/_modules/mbtrack2/instability/instabilities.html
 create mode 100644 docs/build/html/_modules/mbtrack2/instability/ions.html
 create mode 100644 docs/build/html/_modules/mbtrack2/tracking/aperture.html
 create mode 100644 docs/build/html/_modules/mbtrack2/tracking/element.html
 create mode 100644 docs/build/html/_modules/mbtrack2/tracking/feedback.html
 create mode 100644 docs/build/html/_modules/mbtrack2/tracking/monitors/monitors.html
 create mode 100644 docs/build/html/_modules/mbtrack2/tracking/monitors/plotting.html
 create mode 100644 docs/build/html/_modules/mbtrack2/tracking/monitors/tools.html
 create mode 100644 docs/build/html/_modules/mbtrack2/tracking/parallel.html
 create mode 100644 docs/build/html/_modules/mbtrack2/tracking/particles.html
 create mode 100644 docs/build/html/_modules/mbtrack2/tracking/rf.html
 create mode 100644 docs/build/html/_modules/mbtrack2/tracking/synchrotron.html
 create mode 100644 docs/build/html/_modules/mbtrack2/tracking/wakepotential.html
 create mode 100644 docs/build/html/_modules/mbtrack2/utilities/beamloading.html
 create mode 100644 docs/build/html/_modules/mbtrack2/utilities/misc.html
 create mode 100644 docs/build/html/_modules/mbtrack2/utilities/optics.html
 create mode 100644 docs/build/html/_modules/mbtrack2/utilities/read_impedance.html
 create mode 100644 docs/build/html/_modules/mbtrack2/utilities/spectrum.html
 create mode 100644 docs/build/html/_sources/index.rst.txt
 create mode 100644 docs/build/html/_sources/mbtrack2.impedance.rst.txt
 create mode 100644 docs/build/html/_sources/mbtrack2.instability.rst.txt
 create mode 100644 docs/build/html/_sources/mbtrack2.rst.txt
 create mode 100644 docs/build/html/_sources/mbtrack2.tracking.monitors.rst.txt
 create mode 100644 docs/build/html/_sources/mbtrack2.tracking.rst.txt
 create mode 100644 docs/build/html/_sources/mbtrack2.utilities.rst.txt
 create mode 100644 docs/build/html/_static/_sphinx_javascript_frameworks_compat.js
 create mode 100644 docs/build/html/_static/basic.css
 create mode 100644 docs/build/html/_static/doctools.js
 create mode 100644 docs/build/html/_static/documentation_options.js
 create mode 100644 docs/build/html/_static/file.png
 create mode 100644 docs/build/html/_static/jquery-3.6.0.js
 create mode 100644 docs/build/html/_static/jquery.js
 create mode 100644 docs/build/html/_static/language_data.js
 create mode 100644 docs/build/html/_static/minus.png
 create mode 100644 docs/build/html/_static/nature.css
 create mode 100644 docs/build/html/_static/plus.png
 create mode 100644 docs/build/html/_static/pygments.css
 create mode 100644 docs/build/html/_static/searchtools.js
 create mode 100644 docs/build/html/_static/underscore-1.13.1.js
 create mode 100644 docs/build/html/_static/underscore.js
 create mode 100644 docs/build/html/genindex.html
 create mode 100644 docs/build/html/index.html
 create mode 100644 docs/build/html/mbtrack2.html
 create mode 100644 docs/build/html/mbtrack2.impedance.html
 create mode 100644 docs/build/html/mbtrack2.instability.html
 create mode 100644 docs/build/html/mbtrack2.tracking.html
 create mode 100644 docs/build/html/mbtrack2.tracking.monitors.html
 create mode 100644 docs/build/html/mbtrack2.utilities.html
 create mode 100644 docs/build/html/objects.inv
 create mode 100644 docs/build/html/py-modindex.html
 create mode 100644 docs/build/html/search.html
 create mode 100644 docs/build/html/searchindex.js
 create mode 100644 docs/make.bat
 create mode 100644 docs/source/Makefile
 create mode 100644 docs/source/conf.py
 create mode 100644 docs/source/index.rst
 create mode 100644 docs/source/make.bat
 create mode 100644 docs/source/mbtrack2.impedance.rst
 create mode 100644 docs/source/mbtrack2.instability.rst
 create mode 100644 docs/source/mbtrack2.rst
 create mode 100644 docs/source/mbtrack2.tracking.monitors.rst
 create mode 100644 docs/source/mbtrack2.tracking.rst
 create mode 100644 docs/source/mbtrack2.utilities.rst

diff --git a/docs/Makefile b/docs/Makefile
new file mode 100644
index 0000000..d0c3cbf
--- /dev/null
+++ b/docs/Makefile
@@ -0,0 +1,20 @@
+# Minimal makefile for Sphinx documentation
+#
+
+# You can set these variables from the command line, and also
+# from the environment for the first two.
+SPHINXOPTS    ?=
+SPHINXBUILD   ?= sphinx-build
+SOURCEDIR     = source
+BUILDDIR      = build
+
+# Put it first so that "make" without argument is like "make help".
+help:
+	@$(SPHINXBUILD) -M help "$(SOURCEDIR)" "$(BUILDDIR)" $(SPHINXOPTS) $(O)
+
+.PHONY: help Makefile
+
+# Catch-all target: route all unknown targets to Sphinx using the new
+# "make mode" option.  $(O) is meant as a shortcut for $(SPHINXOPTS).
+%: Makefile
+	@$(SPHINXBUILD) -M $@ "$(SOURCEDIR)" "$(BUILDDIR)" $(SPHINXOPTS) $(O)
diff --git a/docs/build/doctrees/environment.pickle b/docs/build/doctrees/environment.pickle
new file mode 100644
index 0000000000000000000000000000000000000000..920fca3370fa44abd0701cd45faeae6769530a14
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diff --git a/docs/build/html/.buildinfo b/docs/build/html/.buildinfo
new file mode 100644
index 0000000..7c9c50a
--- /dev/null
+++ b/docs/build/html/.buildinfo
@@ -0,0 +1,4 @@
+# Sphinx build info version 1
+# This file hashes the configuration used when building these files. When it is not found, a full rebuild will be done.
+config: 05f20f44309c0b23df92472b9aade71e
+tags: 645f666f9bcd5a90fca523b33c5a78b7
diff --git a/docs/build/html/_modules/index.html b/docs/build/html/_modules/index.html
new file mode 100644
index 0000000..9822c3a
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+
+<!DOCTYPE html>
+
+<html lang="en">
+  <head>
+    <meta charset="utf-8" />
+    <meta name="viewport" content="width=device-width, initial-scale=1.0" />
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+            
+  <h1>All modules for which code is available</h1>
+<ul><li><a href="mbtrack2/impedance/csr.html">mbtrack2.impedance.csr</a></li>
+<li><a href="mbtrack2/impedance/impedance_model.html">mbtrack2.impedance.impedance_model</a></li>
+<li><a href="mbtrack2/impedance/resistive_wall.html">mbtrack2.impedance.resistive_wall</a></li>
+<li><a href="mbtrack2/impedance/resonator.html">mbtrack2.impedance.resonator</a></li>
+<li><a href="mbtrack2/impedance/tapers.html">mbtrack2.impedance.tapers</a></li>
+<li><a href="mbtrack2/impedance/wakefield.html">mbtrack2.impedance.wakefield</a></li>
+<li><a href="mbtrack2/instability/instabilities.html">mbtrack2.instability.instabilities</a></li>
+<li><a href="mbtrack2/instability/ions.html">mbtrack2.instability.ions</a></li>
+<li><a href="mbtrack2/tracking/aperture.html">mbtrack2.tracking.aperture</a></li>
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+<li><a href="mbtrack2/utilities/misc.html">mbtrack2.utilities.misc</a></li>
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new file mode 100644
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+            
+  <h1>Source code for mbtrack2.impedance.csr</h1><div class="highlight"><pre>
+<span></span><span class="c1"># -*- coding: utf-8 -*-</span>
+<span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">Define coherent synchrotron radiation (CSR) wakefields in various models.</span>
+<span class="sd">&quot;&quot;&quot;</span>
+<span class="kn">import</span> <span class="nn">mpmath</span> <span class="k">as</span> <span class="nn">mp</span>
+<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="kn">from</span> <span class="nn">scipy.constants</span> <span class="kn">import</span> <span class="n">c</span><span class="p">,</span> <span class="n">mu_0</span>
+<span class="kn">from</span> <span class="nn">scipy.special</span> <span class="kn">import</span> <span class="n">gamma</span>
+
+<span class="kn">from</span> <span class="nn">mbtrack2.impedance.wakefield</span> <span class="kn">import</span> <span class="n">Impedance</span><span class="p">,</span> <span class="n">WakeField</span><span class="p">,</span> <span class="n">WakeFunction</span>
+
+
+<div class="viewcode-block" id="FreeSpaceCSR"><a class="viewcode-back" href="../../../mbtrack2.impedance.html#mbtrack2.impedance.csr.FreeSpaceCSR">[docs]</a><span class="k">class</span> <span class="nc">FreeSpaceCSR</span><span class="p">(</span><span class="n">WakeField</span><span class="p">):</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    Free space steady-state coherent synchrotron radiation Wakefield element,</span>
+<span class="sd">    based on [1]. </span>
+<span class="sd">    </span>
+<span class="sd">    Impedance is computed using Eq. (A10) of [2].</span>
+
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">    time : array of float</span>
+<span class="sd">        Time points where the wake function will be evaluated in [s].</span>
+<span class="sd">    frequency : array of float</span>
+<span class="sd">        Frequency points where the impedance will be evaluated in [Hz].</span>
+<span class="sd">    length : float </span>
+<span class="sd">        Length of the impedacen to consider in [m].</span>
+<span class="sd">    radius : float </span>
+<span class="sd">        Dipole radius of curvature in [m].</span>
+<span class="sd">        </span>
+<span class="sd">    References</span>
+<span class="sd">    ----------</span>
+<span class="sd">    [1] : Faltens, A. N. D. R. I. S., &amp; Laslett, L. J. (1973). Longitudinal </span>
+<span class="sd">    coupling impedance of a stationary electron ring in a cylindrical </span>
+<span class="sd">    geometry. part. Accel., 4, 151-157.</span>
+<span class="sd">    [2] : Agoh, T., and K. Yokoya. &quot;Calculation of coherent synchrotron </span>
+<span class="sd">    radiation using mesh.&quot; Physical Review Special Topics-Accelerators and </span>
+<span class="sd">    Beams 7.5 (2004): 054403.</span>
+
+<span class="sd">    &quot;&quot;&quot;</span>
+
+    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">time</span><span class="p">,</span> <span class="n">frequency</span><span class="p">,</span> <span class="n">length</span><span class="p">,</span> <span class="n">radius</span><span class="p">):</span>
+        <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__init__</span><span class="p">()</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">length</span> <span class="o">=</span> <span class="n">length</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">radius</span> <span class="o">=</span> <span class="n">radius</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">Z0</span> <span class="o">=</span> <span class="n">mu_0</span> <span class="o">*</span> <span class="n">c</span>
+
+        <span class="n">Zl</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">LongitudinalImpedance</span><span class="p">(</span><span class="n">frequency</span><span class="p">)</span>
+        <span class="c1"># Wl = self.LongitudinalWakeFunction(time)</span>
+
+        <span class="n">Zlong</span> <span class="o">=</span> <span class="n">Impedance</span><span class="p">(</span><span class="n">variable</span><span class="o">=</span><span class="n">frequency</span><span class="p">,</span>
+                          <span class="n">function</span><span class="o">=</span><span class="n">Zl</span><span class="p">,</span>
+                          <span class="n">component_type</span><span class="o">=</span><span class="s1">&#39;long&#39;</span><span class="p">)</span>
+        <span class="c1"># Wlong = WakeFunction(variable = time, function = Wl, component_type=&quot;long&quot;)</span>
+
+        <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="n">append_to_model</span><span class="p">(</span><span class="n">Zlong</span><span class="p">)</span>
+        <span class="c1"># super().append_to_model(Wlong)</span>
+
+<div class="viewcode-block" id="FreeSpaceCSR.LongitudinalImpedance"><a class="viewcode-back" href="../../../mbtrack2.impedance.html#mbtrack2.impedance.csr.FreeSpaceCSR.LongitudinalImpedance">[docs]</a>    <span class="k">def</span> <span class="nf">LongitudinalImpedance</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">frequency</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Compute the free space steady-state CSR impedance.</span>
+<span class="sd">        Based on Eq. (A10) of [1].</span>
+<span class="sd">        </span>
+<span class="sd">        This formula is valid only if omega &lt;&lt; (3 * gamma^3 * c) / (2 * R).</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        frequency : float array</span>
+<span class="sd">            Frequency in [Hz].</span>
+
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        Zl : complex array</span>
+<span class="sd">            Longitudinal impedance in [ohm].</span>
+<span class="sd">            </span>
+<span class="sd">        References</span>
+<span class="sd">        ----------</span>
+<span class="sd">        [1] : Agoh, T., and K. Yokoya. &quot;Calculation of coherent synchrotron </span>
+<span class="sd">        radiation using mesh.&quot; Physical Review Special Topics-Accelerators and </span>
+<span class="sd">        Beams 7.5 (2004): 054403.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+
+        <span class="n">Zl</span> <span class="o">=</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">Z0</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">length</span> <span class="o">/</span> <span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span><span class="p">)</span> <span class="o">*</span> <span class="n">gamma</span><span class="p">(</span><span class="mi">2</span> <span class="o">/</span> <span class="mi">3</span><span class="p">)</span> <span class="o">*</span>
+              <span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="n">j</span> <span class="o">*</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="n">frequency</span> <span class="o">/</span>
+               <span class="p">(</span><span class="mi">3</span> <span class="o">*</span> <span class="n">c</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">radius</span><span class="o">**</span><span class="mi">2</span><span class="p">))</span><span class="o">**</span><span class="p">(</span><span class="mi">1</span> <span class="o">/</span> <span class="mi">3</span><span class="p">))</span>
+        <span class="k">return</span> <span class="n">Zl</span></div>
+
+<div class="viewcode-block" id="FreeSpaceCSR.LongitudinalWakeFunction"><a class="viewcode-back" href="../../../mbtrack2.impedance.html#mbtrack2.impedance.csr.FreeSpaceCSR.LongitudinalWakeFunction">[docs]</a>    <span class="k">def</span> <span class="nf">LongitudinalWakeFunction</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">time</span><span class="p">):</span>
+        <span class="k">raise</span> <span class="ne">NotImplementedError</span></div></div>
+
+
+<div class="viewcode-block" id="ParallelPlatesCSR"><a class="viewcode-back" href="../../../mbtrack2.impedance.html#mbtrack2.impedance.csr.ParallelPlatesCSR">[docs]</a><span class="k">class</span> <span class="nc">ParallelPlatesCSR</span><span class="p">(</span><span class="n">WakeField</span><span class="p">):</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    Perfectly conducting parallel plates steady-state coherent synchrotron </span>
+<span class="sd">    radiation Wakefield element, based on [1]. </span>
+
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">    time : array of float</span>
+<span class="sd">        Time points where the wake function will be evaluated in [s].</span>
+<span class="sd">    frequency : array of float</span>
+<span class="sd">        Frequency points where the impedance will be evaluated in [Hz].</span>
+<span class="sd">    length : float </span>
+<span class="sd">        Length of the impedacen to consider in [m].</span>
+<span class="sd">    radius : float </span>
+<span class="sd">        Dipole radius of curvature in [m].</span>
+<span class="sd">    distance : float</span>
+<span class="sd">        Vertical distance between the parallel plates in [m].</span>
+<span class="sd">        </span>
+<span class="sd">    Attributes</span>
+<span class="sd">    ----------</span>
+<span class="sd">    threshold : float</span>
+<span class="sd">        Shielding threshold in the parallel plates model in [Hz].</span>
+<span class="sd">        </span>
+<span class="sd">    References</span>
+<span class="sd">    ----------</span>
+<span class="sd">    [1] : Agoh, T., and K. Yokoya. &quot;Calculation of coherent synchrotron </span>
+<span class="sd">    radiation using mesh.&quot; Physical Review Special Topics-Accelerators and </span>
+<span class="sd">    Beams 7.5 (2004): 054403.</span>
+
+<span class="sd">    &quot;&quot;&quot;</span>
+
+    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">time</span><span class="p">,</span> <span class="n">frequency</span><span class="p">,</span> <span class="n">length</span><span class="p">,</span> <span class="n">radius</span><span class="p">,</span> <span class="n">distance</span><span class="p">):</span>
+        <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__init__</span><span class="p">()</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">length</span> <span class="o">=</span> <span class="n">length</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">radius</span> <span class="o">=</span> <span class="n">radius</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">distance</span> <span class="o">=</span> <span class="n">distance</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">Z0</span> <span class="o">=</span> <span class="n">mu_0</span> <span class="o">*</span> <span class="n">c</span>
+
+        <span class="n">Zl</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">LongitudinalImpedance</span><span class="p">(</span><span class="n">frequency</span><span class="p">)</span>
+        <span class="c1"># Wl = self.LongitudinalWakeFunction(time)</span>
+
+        <span class="n">Zlong</span> <span class="o">=</span> <span class="n">Impedance</span><span class="p">(</span><span class="n">variable</span><span class="o">=</span><span class="n">frequency</span><span class="p">,</span>
+                          <span class="n">function</span><span class="o">=</span><span class="n">Zl</span><span class="p">,</span>
+                          <span class="n">component_type</span><span class="o">=</span><span class="s1">&#39;long&#39;</span><span class="p">)</span>
+        <span class="c1"># Wlong = WakeFunction(variable = time, function = Wl, component_type=&quot;long&quot;)</span>
+
+        <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="n">append_to_model</span><span class="p">(</span><span class="n">Zlong</span><span class="p">)</span>
+        <span class="c1"># super().append_to_model(Wlong)</span>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">threshold</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Shielding threshold in the parallel plates model in [Hz].&quot;&quot;&quot;</span>
+        <span class="k">return</span> <span class="p">(</span><span class="mi">3</span><span class="o">*</span><span class="n">c</span><span class="p">)</span> <span class="o">/</span> <span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">radius</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">distance</span><span class="o">**</span><span class="mi">3</span><span class="p">)</span><span class="o">**</span><span class="mf">0.5</span>
+
+<div class="viewcode-block" id="ParallelPlatesCSR.LongitudinalImpedance"><a class="viewcode-back" href="../../../mbtrack2.impedance.html#mbtrack2.impedance.csr.ParallelPlatesCSR.LongitudinalImpedance">[docs]</a>    <span class="k">def</span> <span class="nf">LongitudinalImpedance</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">frequency</span><span class="p">,</span> <span class="n">tol</span><span class="o">=</span><span class="mf">1e-5</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Compute the CSR impedance using the perfectly conducting parallel </span>
+<span class="sd">        plates steady-state model.</span>
+<span class="sd">        </span>
+<span class="sd">        Impedance is computed using Eq. (A1) of [1].</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        frequency : float array</span>
+<span class="sd">            Frequency in [Hz].</span>
+<span class="sd">        tol : float, optinal</span>
+<span class="sd">            Desired maximum final error on sum_func. </span>
+
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        Zl : complex array</span>
+<span class="sd">            Longitudinal impedance in [ohm].</span>
+<span class="sd">            </span>
+<span class="sd">        References</span>
+<span class="sd">        ----------</span>
+<span class="sd">        [1] : Agoh, T., and K. Yokoya. &quot;Calculation of coherent synchrotron </span>
+<span class="sd">        radiation using mesh.&quot; Physical Review Special Topics-Accelerators and </span>
+<span class="sd">        Beams 7.5 (2004): 054403.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+
+        <span class="n">Zl</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">frequency</span><span class="o">.</span><span class="n">shape</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="nb">complex</span><span class="p">)</span>
+        <span class="n">constant</span> <span class="o">=</span> <span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">Z0</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">length</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">distance</span> <span class="o">*</span>
+                    <span class="p">(</span><span class="mi">2</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">radius</span><span class="p">)</span><span class="o">**</span><span class="p">(</span><span class="mi">1</span> <span class="o">/</span> <span class="mi">3</span><span class="p">))</span>
+        <span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">f</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">frequency</span><span class="p">):</span>
+            <span class="n">k</span> <span class="o">=</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">mp</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="n">f</span> <span class="o">/</span> <span class="n">c</span>
+
+            <span class="n">sum_value</span> <span class="o">=</span> <span class="n">mp</span><span class="o">.</span><span class="n">nsum</span><span class="p">(</span><span class="k">lambda</span> <span class="n">p</span><span class="p">:</span> <span class="bp">self</span><span class="o">.</span><span class="n">sum_func</span><span class="p">(</span><span class="n">p</span><span class="p">,</span> <span class="n">k</span><span class="p">),</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="n">mp</span><span class="o">.</span><span class="n">inf</span><span class="p">],</span>
+                                <span class="n">tol</span><span class="o">=</span><span class="n">tol</span><span class="p">,</span>
+                                <span class="n">method</span><span class="o">=</span><span class="s1">&#39;r+s&#39;</span><span class="p">)</span>
+
+            <span class="n">Zl</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="n">constant</span> <span class="o">*</span> <span class="p">(</span><span class="mi">1</span> <span class="o">/</span> <span class="n">k</span><span class="p">)</span><span class="o">**</span><span class="p">(</span><span class="mi">1</span> <span class="o">/</span> <span class="mi">3</span><span class="p">)</span> <span class="o">*</span> <span class="nb">complex</span><span class="p">(</span><span class="n">sum_value</span><span class="p">)</span>
+
+        <span class="k">return</span> <span class="n">Zl</span></div>
+
+<div class="viewcode-block" id="ParallelPlatesCSR.sum_func"><a class="viewcode-back" href="../../../mbtrack2.impedance.html#mbtrack2.impedance.csr.ParallelPlatesCSR.sum_func">[docs]</a>    <span class="k">def</span> <span class="nf">sum_func</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">p</span><span class="p">,</span> <span class="n">k</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Utility function for LongitudinalImpedance.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        p : int</span>
+<span class="sd">        k : float</span>
+
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        sum_value : mpc</span>
+
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="n">xp</span> <span class="o">=</span> <span class="p">(</span><span class="mi">2</span><span class="o">*</span><span class="n">p</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span> <span class="o">*</span> <span class="n">mp</span><span class="o">.</span><span class="n">pi</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">distance</span> <span class="o">*</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">radius</span> <span class="o">/</span> <span class="mi">2</span> <span class="o">/</span> <span class="n">k</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span><span class="o">**</span><span class="p">(</span><span class="mi">1</span> <span class="o">/</span>
+                                                                            <span class="mi">3</span><span class="p">)</span>
+        <span class="n">Ai</span> <span class="o">=</span> <span class="n">mp</span><span class="o">.</span><span class="n">airyai</span><span class="p">(</span><span class="n">xp</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span>
+        <span class="n">Bi</span> <span class="o">=</span> <span class="n">mp</span><span class="o">.</span><span class="n">airybi</span><span class="p">(</span><span class="n">xp</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span>
+        <span class="n">Aip</span> <span class="o">=</span> <span class="n">mp</span><span class="o">.</span><span class="n">airyai</span><span class="p">(</span><span class="n">xp</span><span class="o">**</span><span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
+        <span class="n">Bip</span> <span class="o">=</span> <span class="n">mp</span><span class="o">.</span><span class="n">airybi</span><span class="p">(</span><span class="n">xp</span><span class="o">**</span><span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
+        <span class="k">return</span> <span class="n">Aip</span> <span class="o">*</span> <span class="p">(</span><span class="n">Aip</span> <span class="o">+</span> <span class="mi">1</span><span class="n">j</span><span class="o">*</span><span class="n">Bip</span><span class="p">)</span> <span class="o">+</span> <span class="n">xp</span><span class="o">**</span><span class="mi">2</span> <span class="o">*</span> <span class="n">Ai</span> <span class="o">*</span> <span class="p">(</span><span class="n">Ai</span> <span class="o">+</span> <span class="mi">1</span><span class="n">j</span><span class="o">*</span><span class="n">Bi</span><span class="p">)</span></div>
+
+<div class="viewcode-block" id="ParallelPlatesCSR.LongitudinalWakeFunction"><a class="viewcode-back" href="../../../mbtrack2.impedance.html#mbtrack2.impedance.csr.ParallelPlatesCSR.LongitudinalWakeFunction">[docs]</a>    <span class="k">def</span> <span class="nf">LongitudinalWakeFunction</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">time</span><span class="p">):</span>
+        <span class="k">raise</span> <span class="ne">NotImplementedError</span></div></div>
+</pre></div>
+
+            <div class="clearer"></div>
+          </div>
+        </div>
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+    <meta charset="utf-8" />
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+        <li class="nav-item nav-item-this"><a href="">mbtrack2.impedance.impedance_model</a></li> 
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+          <div class="body" role="main">
+            
+  <h1>Source code for mbtrack2.impedance.impedance_model</h1><div class="highlight"><pre>
+<span></span><span class="c1"># -*- coding: utf-8 -*-</span>
+<span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">Module where the ImpedanceModel class is defined.</span>
+<span class="sd">&quot;&quot;&quot;</span>
+<span class="kn">import</span> <span class="nn">pickle</span>
+<span class="kn">from</span> <span class="nn">copy</span> <span class="kn">import</span> <span class="n">deepcopy</span>
+
+<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
+<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="kn">import</span> <span class="nn">pandas</span> <span class="k">as</span> <span class="nn">pd</span>
+<span class="kn">from</span> <span class="nn">matplotlib</span> <span class="kn">import</span> <span class="n">colormaps</span>
+<span class="kn">from</span> <span class="nn">mpl_toolkits.axes_grid1.inset_locator</span> <span class="kn">import</span> <span class="n">inset_axes</span>
+<span class="kn">from</span> <span class="nn">scipy.integrate</span> <span class="kn">import</span> <span class="n">trapz</span>
+<span class="kn">from</span> <span class="nn">scipy.interpolate</span> <span class="kn">import</span> <span class="n">interp1d</span>
+
+<span class="kn">from</span> <span class="nn">mbtrack2.impedance.wakefield</span> <span class="kn">import</span> <span class="n">WakeField</span><span class="p">,</span> <span class="n">WakeFunction</span>
+<span class="kn">from</span> <span class="nn">mbtrack2.utilities.misc</span> <span class="kn">import</span> <span class="p">(</span>
+    <span class="n">beam_loss_factor</span><span class="p">,</span>
+    <span class="n">double_sided_impedance</span><span class="p">,</span>
+    <span class="n">effective_impedance</span><span class="p">,</span>
+<span class="p">)</span>
+<span class="kn">from</span> <span class="nn">mbtrack2.utilities.spectrum</span> <span class="kn">import</span> <span class="p">(</span>
+    <span class="n">beam_spectrum</span><span class="p">,</span>
+    <span class="n">gaussian_bunch_spectrum</span><span class="p">,</span>
+    <span class="n">spectral_density</span><span class="p">,</span>
+<span class="p">)</span>
+
+
+<div class="viewcode-block" id="ImpedanceModel"><a class="viewcode-back" href="../../../mbtrack2.impedance.html#mbtrack2.impedance.impedance_model.ImpedanceModel">[docs]</a><span class="k">class</span> <span class="nc">ImpedanceModel</span><span class="p">():</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    Define the impedance model of the machine.</span>
+
+<span class="sd">    The model must be completed with successive add(...) and add_global(...)</span>
+<span class="sd">    calls, then compute_sum() must be run.</span>
+
+<span class="sd">    The transverse impedance and wake functions are beta weighted and divided</span>
+<span class="sd">    by the beta at the tracking location (ring.optics.local_beta).</span>
+
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">    ring : Synchrotron object</span>
+
+<span class="sd">    Attributes</span>
+<span class="sd">    ----------</span>
+<span class="sd">    wakefields : list of WakeField objects</span>
+<span class="sd">        WakeFields in the model.</span>
+<span class="sd">    positions : list of arrays</span>
+<span class="sd">        Positions corresponding the different WakeFields.</span>
+<span class="sd">    names : list of str</span>
+<span class="sd">        Names of the WakeField objects.</span>
+<span class="sd">    sum : WakeField</span>
+<span class="sd">        Sum of every WakeField in the model weigthed by beta functions.</span>
+<span class="sd">    sum_&quot;name&quot; : WakeField</span>
+<span class="sd">        Sum of the &quot;name&quot; Wakefield weigthed by beta functions.</span>
+<span class="sd">    sum_names : array</span>
+<span class="sd">        Names of attributes where the WakeFields are summed by name.</span>
+<span class="sd">    globals : list of WakeField objects</span>
+<span class="sd">        Globals WakeFields in the model.</span>
+<span class="sd">    globals_names : list of str</span>
+<span class="sd">        Names of the global WakeFields objects.</span>
+
+<span class="sd">    Methods</span>
+<span class="sd">    -------</span>
+<span class="sd">    add(wakefield, positions, name)</span>
+<span class="sd">        Add the same WakeField object at different locations to the model.</span>
+<span class="sd">    add_global(wakefield, name)</span>
+<span class="sd">        Add a &quot;global&quot; WakeField object which will added to the sum WakeField</span>
+<span class="sd">        but not weighted by beta functions.</span>
+<span class="sd">    sum_beta(wake, beta)</span>
+<span class="sd">        Weight a WakeField object by an array of beta functions.</span>
+<span class="sd">    compute_sum_names()</span>
+<span class="sd">        Compute the weighted WakeField for each WakeField object type.</span>
+<span class="sd">    compute_sum()</span>
+<span class="sd">        Compute the sum of all weighted WakeField into self.sum.</span>
+<span class="sd">    plot_area(Z_type=&quot;Zlong&quot;, component=&quot;real&quot;, sigma=None, attr_list=None)</span>
+<span class="sd">        Plot the contributions of different kind of WakeFields.</span>
+<span class="sd">    save(file)</span>
+<span class="sd">        Save impedance model to file.</span>
+<span class="sd">    load(file)</span>
+<span class="sd">        Load impedance model from file.</span>
+<span class="sd">    &quot;&quot;&quot;</span>
+
+    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">ring</span><span class="p">):</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">ring</span> <span class="o">=</span> <span class="n">ring</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">optics</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">optics</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">wakefields</span> <span class="o">=</span> <span class="p">[]</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">positions</span> <span class="o">=</span> <span class="p">[]</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">names</span> <span class="o">=</span> <span class="p">[]</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">globals</span> <span class="o">=</span> <span class="p">[]</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">globals_names</span> <span class="o">=</span> <span class="p">[]</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">sum_names</span> <span class="o">=</span> <span class="p">[]</span>
+
+<div class="viewcode-block" id="ImpedanceModel.add"><a class="viewcode-back" href="../../../mbtrack2.impedance.html#mbtrack2.impedance.impedance_model.ImpedanceModel.add">[docs]</a>    <span class="k">def</span> <span class="nf">add</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">wakefield</span><span class="p">,</span> <span class="n">positions</span><span class="p">,</span> <span class="n">name</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Add the same WakeField object at different locations to the model.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        wakefield : WakeField</span>
+<span class="sd">            WakeField object to add to the model.</span>
+<span class="sd">        positions : array, float or int</span>
+<span class="sd">            Array of longitudinal positions where the elements are loacted.</span>
+<span class="sd">        name : str, optional</span>
+<span class="sd">            Name of the element type. If None, the name of the WakeField object</span>
+<span class="sd">            is used. The default is None.</span>
+
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        None.</span>
+
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="k">if</span> <span class="n">name</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="n">name</span> <span class="o">=</span> <span class="n">wakefield</span><span class="o">.</span><span class="n">name</span>
+        <span class="k">if</span> <span class="n">name</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">&quot;Please give a valid name.&quot;</span><span class="p">)</span>
+        <span class="k">if</span> <span class="n">name</span> <span class="ow">not</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">names</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">names</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">name</span><span class="p">)</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">&quot;This name is already taken.&quot;</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">wakefields</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">wakefield</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">positions</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">positions</span><span class="p">)</span></div>
+
+<div class="viewcode-block" id="ImpedanceModel.add_global"><a class="viewcode-back" href="../../../mbtrack2.impedance.html#mbtrack2.impedance.impedance_model.ImpedanceModel.add_global">[docs]</a>    <span class="k">def</span> <span class="nf">add_global</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">wakefield</span><span class="p">,</span> <span class="n">name</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Add a &quot;global&quot; WakeField object which will added to the sum WakeField</span>
+<span class="sd">        but not weighted by beta functions.</span>
+
+<span class="sd">        To use with &quot;distributed&quot; elements, for example a resistive wall</span>
+<span class="sd">        wakefield computed from an effective radius (so which has already been</span>
+<span class="sd">        weighted by beta functions).</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        wakefield : WakeField</span>
+<span class="sd">            WakeField object to add to the model.</span>
+<span class="sd">        name : str, optional</span>
+<span class="sd">            Name of the element type. If None, the name of the WakeField object</span>
+<span class="sd">            is used. The default is None.</span>
+
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        None.</span>
+
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">globals</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">wakefield</span><span class="p">)</span>
+        <span class="k">if</span> <span class="n">name</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="n">name</span> <span class="o">=</span> <span class="n">wakefield</span><span class="o">.</span><span class="n">name</span>
+        <span class="k">if</span> <span class="n">name</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">&quot;Please give a valid name.&quot;</span><span class="p">)</span>
+        <span class="k">if</span> <span class="n">name</span> <span class="ow">not</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">globals_names</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">globals_names</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">name</span><span class="p">)</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">&quot;This name is already taken.&quot;</span><span class="p">)</span></div>
+        <span class="c1"># setattr(self, name, wakefield)</span>
+
+<div class="viewcode-block" id="ImpedanceModel.sum_beta"><a class="viewcode-back" href="../../../mbtrack2.impedance.html#mbtrack2.impedance.impedance_model.ImpedanceModel.sum_beta">[docs]</a>    <span class="k">def</span> <span class="nf">sum_beta</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">wake</span><span class="p">,</span> <span class="n">beta</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Weight a WakeField object by an array of beta functions.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        wake : WakeField</span>
+<span class="sd">            WakeField element object.</span>
+<span class="sd">        beta : array of shape (2, N)</span>
+<span class="sd">            Beta function at the locations of the elements.</span>
+
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        wake_sum : WakeField</span>
+<span class="sd">            WakeField object weighted by beta functions.</span>
+
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="n">wake_sum</span> <span class="o">=</span> <span class="n">deepcopy</span><span class="p">(</span><span class="n">wake</span><span class="p">)</span>
+        <span class="n">local_beta</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">optics</span><span class="o">.</span><span class="n">local_beta</span>
+        <span class="k">for</span> <span class="n">component_name</span> <span class="ow">in</span> <span class="n">wake_sum</span><span class="o">.</span><span class="n">components</span><span class="p">:</span>
+            <span class="n">comp</span> <span class="o">=</span> <span class="nb">getattr</span><span class="p">(</span><span class="n">wake_sum</span><span class="p">,</span> <span class="n">component_name</span><span class="p">)</span>
+            <span class="n">weight</span> <span class="o">=</span> <span class="p">((</span><span class="n">beta</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="p">:]</span><span class="o">**</span><span class="n">comp</span><span class="o">.</span><span class="n">power_x</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="n">beta</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="p">:]</span><span class="o">**</span><span class="n">comp</span><span class="o">.</span><span class="n">power_y</span><span class="p">))</span>
+            <span class="k">if</span> <span class="n">comp</span><span class="o">.</span><span class="n">plane</span> <span class="o">==</span> <span class="s2">&quot;x&quot;</span><span class="p">:</span>
+                <span class="n">weight</span> <span class="o">=</span> <span class="n">weight</span><span class="o">.</span><span class="n">sum</span><span class="p">()</span> <span class="o">/</span> <span class="n">local_beta</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
+            <span class="k">if</span> <span class="n">comp</span><span class="o">.</span><span class="n">plane</span> <span class="o">==</span> <span class="s2">&quot;y&quot;</span><span class="p">:</span>
+                <span class="n">weight</span> <span class="o">=</span> <span class="n">weight</span><span class="o">.</span><span class="n">sum</span><span class="p">()</span> <span class="o">/</span> <span class="n">local_beta</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span>
+            <span class="k">else</span><span class="p">:</span>
+                <span class="n">weight</span> <span class="o">=</span> <span class="n">weight</span><span class="o">.</span><span class="n">sum</span><span class="p">()</span>
+            <span class="nb">setattr</span><span class="p">(</span><span class="n">wake_sum</span><span class="p">,</span> <span class="n">component_name</span><span class="p">,</span> <span class="n">weight</span> <span class="o">*</span> <span class="n">comp</span><span class="p">)</span>
+        <span class="k">return</span> <span class="n">wake_sum</span></div>
+
+<div class="viewcode-block" id="ImpedanceModel.compute_sum_names"><a class="viewcode-back" href="../../../mbtrack2.impedance.html#mbtrack2.impedance.impedance_model.ImpedanceModel.compute_sum_names">[docs]</a>    <span class="k">def</span> <span class="nf">compute_sum_names</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Compute the weighted WakeField for each WakeField object type.</span>
+<span class="sd">        The new summed WakeField object are set to into self.sum_name.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="k">for</span> <span class="n">idx</span><span class="p">,</span> <span class="n">wake</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">wakefields</span><span class="p">):</span>
+            <span class="n">attribute_name</span> <span class="o">=</span> <span class="s2">&quot;sum_&quot;</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">names</span><span class="p">[</span><span class="n">idx</span><span class="p">]</span>
+            <span class="n">beta</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">optics</span><span class="o">.</span><span class="n">beta</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">positions</span><span class="p">[</span><span class="n">idx</span><span class="p">])</span>
+            <span class="n">wake_sum</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">sum_beta</span><span class="p">(</span><span class="n">wake</span><span class="p">,</span> <span class="n">beta</span><span class="p">)</span>
+            <span class="n">wake_sum</span><span class="o">.</span><span class="n">name</span> <span class="o">=</span> <span class="n">attribute_name</span>
+            <span class="nb">setattr</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">attribute_name</span><span class="p">,</span> <span class="n">wake_sum</span><span class="p">)</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">sum_names</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">attribute_name</span><span class="p">)</span></div>
+
+<div class="viewcode-block" id="ImpedanceModel.compute_sum"><a class="viewcode-back" href="../../../mbtrack2.impedance.html#mbtrack2.impedance.impedance_model.ImpedanceModel.compute_sum">[docs]</a>    <span class="k">def</span> <span class="nf">compute_sum</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Compute the sum of all weighted WakeField into self.sum.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">compute_sum_names</span><span class="p">()</span>
+        <span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">name</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">sum_names</span><span class="p">):</span>
+            <span class="k">if</span> <span class="n">i</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
+                <span class="bp">self</span><span class="o">.</span><span class="n">sum</span> <span class="o">=</span> <span class="n">deepcopy</span><span class="p">(</span><span class="nb">getattr</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">name</span><span class="p">))</span>
+                <span class="bp">self</span><span class="o">.</span><span class="n">sum</span><span class="o">.</span><span class="n">name</span> <span class="o">=</span> <span class="s2">&quot;sum&quot;</span>
+            <span class="k">else</span><span class="p">:</span>
+                <span class="n">wake2</span> <span class="o">=</span> <span class="nb">getattr</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">name</span><span class="p">)</span>
+                <span class="k">for</span> <span class="n">component_name2</span> <span class="ow">in</span> <span class="n">wake2</span><span class="o">.</span><span class="n">components</span><span class="p">:</span>
+                    <span class="n">comp2</span> <span class="o">=</span> <span class="nb">getattr</span><span class="p">(</span><span class="n">wake2</span><span class="p">,</span> <span class="n">component_name2</span><span class="p">)</span>
+                    <span class="k">try</span><span class="p">:</span>
+                        <span class="n">comp1</span> <span class="o">=</span> <span class="nb">getattr</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">sum</span><span class="p">,</span> <span class="n">component_name2</span><span class="p">)</span>
+                        <span class="nb">setattr</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">sum</span><span class="p">,</span> <span class="n">component_name2</span><span class="p">,</span> <span class="n">comp1</span> <span class="o">+</span> <span class="n">comp2</span><span class="p">)</span>
+                    <span class="k">except</span> <span class="ne">AttributeError</span><span class="p">:</span>
+                        <span class="nb">setattr</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">sum</span><span class="p">,</span> <span class="n">component_name2</span><span class="p">,</span> <span class="n">comp2</span><span class="p">)</span>
+        <span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">wake2</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">globals</span><span class="p">):</span>
+            <span class="n">name</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">globals_names</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
+            <span class="nb">setattr</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">name</span><span class="p">,</span> <span class="n">wake2</span><span class="p">)</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">sum_names</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">name</span><span class="p">)</span>
+            <span class="k">if</span> <span class="ow">not</span> <span class="nb">hasattr</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="s2">&quot;sum&quot;</span><span class="p">):</span>
+                <span class="bp">self</span><span class="o">.</span><span class="n">sum</span> <span class="o">=</span> <span class="n">deepcopy</span><span class="p">(</span><span class="n">wake2</span><span class="p">)</span>
+                <span class="bp">self</span><span class="o">.</span><span class="n">sum</span><span class="o">.</span><span class="n">name</span> <span class="o">=</span> <span class="s2">&quot;sum&quot;</span>
+            <span class="k">else</span><span class="p">:</span>
+                <span class="k">for</span> <span class="n">component_name2</span> <span class="ow">in</span> <span class="n">wake2</span><span class="o">.</span><span class="n">components</span><span class="p">:</span>
+                    <span class="n">comp2</span> <span class="o">=</span> <span class="nb">getattr</span><span class="p">(</span><span class="n">wake2</span><span class="p">,</span> <span class="n">component_name2</span><span class="p">)</span>
+                    <span class="k">try</span><span class="p">:</span>
+                        <span class="n">comp1</span> <span class="o">=</span> <span class="nb">getattr</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">sum</span><span class="p">,</span> <span class="n">component_name2</span><span class="p">)</span>
+                        <span class="nb">setattr</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">sum</span><span class="p">,</span> <span class="n">component_name2</span><span class="p">,</span> <span class="n">comp1</span> <span class="o">+</span> <span class="n">comp2</span><span class="p">)</span>
+                    <span class="k">except</span> <span class="ne">AttributeError</span><span class="p">:</span>
+                        <span class="nb">setattr</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">sum</span><span class="p">,</span> <span class="n">component_name2</span><span class="p">,</span> <span class="n">comp2</span><span class="p">)</span></div>
+
+<div class="viewcode-block" id="ImpedanceModel.group_attributes"><a class="viewcode-back" href="../../../mbtrack2.impedance.html#mbtrack2.impedance.impedance_model.ImpedanceModel.group_attributes">[docs]</a>    <span class="k">def</span> <span class="nf">group_attributes</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span>
+                         <span class="n">string_in_name</span><span class="p">,</span>
+                         <span class="n">names_to_group</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+                         <span class="n">property_list</span><span class="o">=</span><span class="p">[</span><span class="s1">&#39;Zlong&#39;</span><span class="p">]):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Groups attributes in the ImpedanceModel based on a given string pattern.</span>
+<span class="sd">        Args:</span>
+<span class="sd">            string_in_name (str): The string pattern used to match attribute names for grouping. If names_to_group is given, this is a name of a new attribute instead.</span>
+<span class="sd">            names_to_group (list, optional): List of attribute names to be explicitly grouped.</span>
+<span class="sd">                                            If not provided, attributes matching the string pattern will be automatically grouped.</span>
+<span class="sd">                                            Defaults to None.</span>
+<span class="sd">            property_list (list, optional): List of property names to be grouped for each attribute.</span>
+<span class="sd">                                            Defaults to [&#39;Zlong&#39;].</span>
+<span class="sd">        Returns:</span>
+<span class="sd">            int: Returns 0 indicating the successful grouping of attributes.</span>
+<span class="sd">        Notes:</span>
+<span class="sd">            - This method groups attributes in the ImpedanceModel class based on a given string pattern.</span>
+<span class="sd">            - If names_to_group is not provided, it automatically selects attributes from the existing sum_names that match the given string pattern.</span>
+<span class="sd">            - A new WakeField instance is created and assigned to the attribute named &#39;string_in_name&#39;.</span>
+<span class="sd">            - The specified properties from the first attribute in names_to_group are appended to the new WakeField instance.</span>
+<span class="sd">            - The values of the specified properties from the remaining attributes in names_to_group are added to the corresponding properties in the new WakeField instance.</span>
+<span class="sd">            - The names_to_group attributes are removed from the ImpedanceModel class.</span>
+<span class="sd">            - The new grouped attribute is added to sum_names, and the first attribute in names_to_group is removed from sum_names.&quot;&quot;&quot;</span>
+        <span class="n">attrs</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">sum_names</span>
+        <span class="k">if</span> <span class="n">names_to_group</span> <span class="o">==</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="n">names_to_group</span> <span class="o">=</span> <span class="p">[]</span>
+            <span class="k">for</span> <span class="n">attr</span> <span class="ow">in</span> <span class="n">attrs</span><span class="p">:</span>
+                <span class="k">if</span> <span class="n">string_in_name</span> <span class="ow">in</span> <span class="n">attr</span><span class="p">:</span>
+                    <span class="n">names_to_group</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">attr</span><span class="p">)</span>
+        <span class="nb">setattr</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">string_in_name</span><span class="p">,</span> <span class="n">WakeField</span><span class="p">())</span>
+        <span class="k">for</span> <span class="n">prop</span> <span class="ow">in</span> <span class="n">property_list</span><span class="p">:</span>
+            <span class="nb">getattr</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">string_in_name</span><span class="p">)</span><span class="o">.</span><span class="n">append_to_model</span><span class="p">(</span>
+                <span class="nb">getattr</span><span class="p">(</span><span class="nb">getattr</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">names_to_group</span><span class="p">[</span><span class="mi">0</span><span class="p">]),</span> <span class="n">prop</span><span class="p">))</span>
+        <span class="k">for</span> <span class="n">attr</span> <span class="ow">in</span> <span class="n">names_to_group</span><span class="p">[</span><span class="mi">1</span><span class="p">:]:</span>
+            <span class="k">for</span> <span class="n">prop</span> <span class="ow">in</span> <span class="n">property_list</span><span class="p">:</span>
+                <span class="n">old_values</span> <span class="o">=</span> <span class="nb">getattr</span><span class="p">(</span><span class="nb">getattr</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">string_in_name</span><span class="p">),</span> <span class="n">prop</span><span class="p">)</span>
+                <span class="n">new_values</span> <span class="o">=</span> <span class="nb">getattr</span><span class="p">(</span><span class="nb">getattr</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">attr</span><span class="p">),</span> <span class="n">prop</span><span class="p">)</span>
+                <span class="nb">setattr</span><span class="p">(</span><span class="nb">getattr</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">string_in_name</span><span class="p">),</span> <span class="n">prop</span><span class="p">,</span>
+                        <span class="n">old_values</span> <span class="o">+</span> <span class="n">new_values</span><span class="p">)</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">sum_names</span><span class="o">.</span><span class="n">remove</span><span class="p">(</span><span class="n">attr</span><span class="p">)</span>
+            <span class="nb">delattr</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">attr</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">sum_names</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">string_in_name</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">sum_names</span><span class="o">.</span><span class="n">remove</span><span class="p">(</span><span class="n">names_to_group</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
+        <span class="nb">delattr</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">names_to_group</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
+        <span class="k">return</span> <span class="mi">0</span></div>
+
+<div class="viewcode-block" id="ImpedanceModel.rename_attribute"><a class="viewcode-back" href="../../../mbtrack2.impedance.html#mbtrack2.impedance.impedance_model.ImpedanceModel.rename_attribute">[docs]</a>    <span class="k">def</span> <span class="nf">rename_attribute</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">old_name</span><span class="p">,</span> <span class="n">new_name</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Renames an attribute in the ImpedanceModel.</span>
+<span class="sd">        Args:</span>
+<span class="sd">            old_name (str): The current name of the attribute to be renamed.</span>
+<span class="sd">            new_name (str): The new name for the attribute.</span>
+<span class="sd">        Raises:</span>
+<span class="sd">            KeyError: If the old_name doesn&#39;t exist as an attribute in the ImpedanceModel.</span>
+<span class="sd">        Notes:</span>
+<span class="sd">            - This method renames an attribute in the ImpedanceModel class.</span>
+<span class="sd">            - The attribute with the old_name is removed from the class&#39;s dictionary (__dict__) using the pop() method.</span>
+<span class="sd">            - The attribute is then added back to the class&#39;s dictionary with the new_name using the __dict__ attribute.</span>
+<span class="sd">            - If the old_name doesn&#39;t exist as an attribute in the ImpedanceModel, a KeyError is raised.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="bp">self</span><span class="o">.</span><span class="vm">__dict__</span><span class="p">[</span><span class="n">new_name</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="vm">__dict__</span><span class="o">.</span><span class="n">pop</span><span class="p">(</span><span class="n">old_name</span><span class="p">)</span></div>
+
+<div class="viewcode-block" id="ImpedanceModel.plot_area"><a class="viewcode-back" href="../../../mbtrack2.impedance.html#mbtrack2.impedance.impedance_model.ImpedanceModel.plot_area">[docs]</a>    <span class="k">def</span> <span class="nf">plot_area</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span>
+                  <span class="n">Z_type</span><span class="o">=</span><span class="s2">&quot;Zlong&quot;</span><span class="p">,</span>
+                  <span class="n">component</span><span class="o">=</span><span class="s2">&quot;real&quot;</span><span class="p">,</span>
+                  <span class="n">sigma</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+                  <span class="n">attr_list</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+                  <span class="n">zoom</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Plot the contributions of different kind of WakeFields.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        Z_type : str, optional</span>
+<span class="sd">            Type of impedance to plot.</span>
+<span class="sd">        component : str, optional</span>
+<span class="sd">            Component to plot, can be &quot;real&quot; or &quot;imag&quot;. </span>
+<span class="sd">        sigma : float, optional</span>
+<span class="sd">            RMS bunch length in [s] to use for the spectral density. If equal</span>
+<span class="sd">            to None, the spectral density is not plotted.</span>
+<span class="sd">        attr_list : list or array of str, optional</span>
+<span class="sd">            Attributes to plot.</span>
+<span class="sd">        zoom : bool</span>
+<span class="sd">            If True, add a zoomed plot on top right corner.</span>
+
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="k">if</span> <span class="n">attr_list</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="n">attr_list</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">sum_names</span>
+
+        <span class="c1"># manage legend</span>
+        <span class="n">Ztype_dict</span> <span class="o">=</span> <span class="p">{</span>
+            <span class="s2">&quot;Zlong&quot;</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span>
+            <span class="s2">&quot;Zxdip&quot;</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span>
+            <span class="s2">&quot;Zydip&quot;</span><span class="p">:</span> <span class="mi">2</span><span class="p">,</span>
+            <span class="s2">&quot;Zxquad&quot;</span><span class="p">:</span> <span class="mi">3</span><span class="p">,</span>
+            <span class="s2">&quot;Zyquad&quot;</span><span class="p">:</span> <span class="mi">4</span>
+        <span class="p">}</span>
+        <span class="n">scale</span> <span class="o">=</span> <span class="p">[</span><span class="mf">1e-3</span><span class="p">,</span> <span class="mf">1e-6</span><span class="p">,</span> <span class="mf">1e-6</span><span class="p">,</span> <span class="mf">1e-6</span><span class="p">,</span> <span class="mf">1e-6</span><span class="p">]</span>
+        <span class="n">label_list</span> <span class="o">=</span> <span class="p">[</span>
+            <span class="sa">r</span><span class="s2">&quot;$Z_\mathrm</span><span class="si">{long}</span><span class="s2"> \; (\mathrm</span><span class="si">{k}</span><span class="s2">\Omega)$&quot;</span><span class="p">,</span>
+            <span class="sa">r</span><span class="s2">&quot;$\frac</span><span class="si">{1}</span><span class="s2">{\beta_0} \sum_</span><span class="si">{j}</span><span class="s2"> \beta_{x,j} Z_{x,j}^\mathrm</span><span class="si">{Dip}</span><span class="s2"> \; (\mathrm</span><span class="si">{M}</span><span class="s2">\Omega/\mathrm</span><span class="si">{m}</span><span class="s2">)$&quot;</span><span class="p">,</span>
+            <span class="sa">r</span><span class="s2">&quot;$\frac</span><span class="si">{1}</span><span class="s2">{\beta_0} \sum_</span><span class="si">{j}</span><span class="s2"> \beta_{y,j} Z_{y,j}^\mathrm</span><span class="si">{Dip}</span><span class="s2"> \; (\mathrm</span><span class="si">{M}</span><span class="s2">\Omega/\mathrm</span><span class="si">{m}</span><span class="s2">)$&quot;</span><span class="p">,</span>
+            <span class="sa">r</span><span class="s2">&quot;$\frac</span><span class="si">{1}</span><span class="s2">{\beta_0} \sum_</span><span class="si">{j}</span><span class="s2"> \beta_{x,j} Z_{x,j}^\mathrm</span><span class="si">{Quad}</span><span class="s2"> \; (\mathrm</span><span class="si">{M}</span><span class="s2">\Omega/\mathrm</span><span class="si">{m}</span><span class="s2">)$&quot;</span><span class="p">,</span>
+            <span class="sa">r</span><span class="s2">&quot;$\frac</span><span class="si">{1}</span><span class="s2">{\beta_0} \sum_</span><span class="si">{j}</span><span class="s2"> \beta_{y,j} Z_{y,j}^\mathrm</span><span class="si">{Quad}</span><span class="s2"> \; (\mathrm</span><span class="si">{M}</span><span class="s2">\Omega/\mathrm</span><span class="si">{m}</span><span class="s2">)$&quot;</span>
+        <span class="p">]</span>
+        <span class="n">leg</span> <span class="o">=</span> <span class="n">Ztype_dict</span><span class="p">[</span><span class="n">Z_type</span><span class="p">]</span>
+
+        <span class="c1"># sort plot by decresing area size</span>
+        <span class="n">area</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="nb">len</span><span class="p">(</span><span class="n">attr_list</span><span class="p">),</span> <span class="p">))</span>
+        <span class="k">for</span> <span class="n">index</span><span class="p">,</span> <span class="n">attr</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">attr_list</span><span class="p">):</span>
+            <span class="k">try</span><span class="p">:</span>
+                <span class="n">sum_imp</span> <span class="o">=</span> <span class="nb">getattr</span><span class="p">(</span><span class="nb">getattr</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">attr</span><span class="p">),</span> <span class="n">Z_type</span><span class="p">)</span>
+                <span class="n">area</span><span class="p">[</span><span class="n">index</span><span class="p">]</span> <span class="o">=</span> <span class="n">trapz</span><span class="p">(</span><span class="n">sum_imp</span><span class="o">.</span><span class="n">data</span><span class="p">[</span><span class="n">component</span><span class="p">],</span>
+                                    <span class="n">sum_imp</span><span class="o">.</span><span class="n">data</span><span class="o">.</span><span class="n">index</span><span class="p">)</span>
+            <span class="k">except</span> <span class="ne">AttributeError</span><span class="p">:</span>
+                <span class="k">pass</span>
+        <span class="n">sorted_index</span> <span class="o">=</span> <span class="n">area</span><span class="o">.</span><span class="n">argsort</span><span class="p">()[::</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
+
+        <span class="c1"># Init fig</span>
+        <span class="n">fig</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">()</span>
+        <span class="n">ax</span> <span class="o">=</span> <span class="n">fig</span><span class="o">.</span><span class="n">gca</span><span class="p">()</span>
+        <span class="n">zero_impedance</span> <span class="o">=</span> <span class="nb">getattr</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">sum</span><span class="p">,</span> <span class="n">Z_type</span><span class="p">)</span> <span class="o">*</span> <span class="mi">0</span>
+        <span class="n">total_imp</span> <span class="o">=</span> <span class="mi">0</span>
+        <span class="n">legend</span> <span class="o">=</span> <span class="p">[]</span>
+
+        <span class="k">if</span> <span class="n">sigma</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="n">legend</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="s2">&quot;Spectral density for sigma = &quot;</span> <span class="o">+</span> <span class="nb">str</span><span class="p">(</span><span class="n">sigma</span><span class="p">)</span> <span class="o">+</span> <span class="s2">&quot; s&quot;</span><span class="p">)</span>
+
+        <span class="c1"># Main plot</span>
+        <span class="n">colorblind</span> <span class="o">=</span> <span class="n">colormaps</span><span class="p">[</span><span class="s1">&#39;tab10&#39;</span><span class="p">]</span><span class="o">.</span><span class="n">colors</span>
+        <span class="k">for</span> <span class="n">index</span> <span class="ow">in</span> <span class="n">sorted_index</span><span class="p">:</span>
+            <span class="n">attr</span> <span class="o">=</span> <span class="n">attr_list</span><span class="p">[</span><span class="n">index</span><span class="p">]</span>
+            <span class="c1"># Set all impedances with common indexes using + zero_impedance</span>
+            <span class="k">try</span><span class="p">:</span>
+                <span class="n">sum_imp</span> <span class="o">=</span> <span class="nb">getattr</span><span class="p">(</span><span class="nb">getattr</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">attr</span><span class="p">),</span> <span class="n">Z_type</span><span class="p">)</span> <span class="o">+</span> <span class="n">zero_impedance</span>
+                <span class="n">ax</span><span class="o">.</span><span class="n">fill_between</span><span class="p">(</span><span class="n">sum_imp</span><span class="o">.</span><span class="n">data</span><span class="o">.</span><span class="n">index</span> <span class="o">*</span> <span class="mf">1e-9</span><span class="p">,</span>
+                                <span class="n">total_imp</span><span class="p">,</span>
+                                <span class="n">total_imp</span> <span class="o">+</span>
+                                <span class="n">sum_imp</span><span class="o">.</span><span class="n">data</span><span class="p">[</span><span class="n">component</span><span class="p">]</span> <span class="o">*</span> <span class="n">scale</span><span class="p">[</span><span class="n">leg</span><span class="p">],</span>
+                                <span class="n">edgecolor</span><span class="o">=</span><span class="n">colorblind</span><span class="p">[</span><span class="n">index</span> <span class="o">%</span> <span class="mi">10</span><span class="p">],</span>
+                                <span class="n">color</span><span class="o">=</span><span class="n">colorblind</span><span class="p">[</span><span class="n">index</span> <span class="o">%</span> <span class="mi">10</span><span class="p">])</span>
+                <span class="n">total_imp</span> <span class="o">+=</span> <span class="n">sum_imp</span><span class="o">.</span><span class="n">data</span><span class="p">[</span><span class="n">component</span><span class="p">]</span> <span class="o">*</span> <span class="n">scale</span><span class="p">[</span><span class="n">leg</span><span class="p">]</span>
+                <span class="k">if</span> <span class="n">attr</span><span class="p">[:</span><span class="mi">4</span><span class="p">]</span> <span class="o">==</span> <span class="s2">&quot;sum_&quot;</span><span class="p">:</span>
+                    <span class="n">legend</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">attr</span><span class="p">[</span><span class="mi">4</span><span class="p">:])</span>
+                <span class="k">else</span><span class="p">:</span>
+                    <span class="n">legend</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">attr</span><span class="p">)</span>
+            <span class="k">except</span> <span class="ne">AttributeError</span><span class="p">:</span>
+                <span class="k">pass</span>
+
+        <span class="k">if</span> <span class="n">sigma</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="n">spect</span> <span class="o">=</span> <span class="n">spectral_density</span><span class="p">(</span><span class="n">zero_impedance</span><span class="o">.</span><span class="n">data</span><span class="o">.</span><span class="n">index</span><span class="p">,</span> <span class="n">sigma</span><span class="p">)</span>
+            <span class="n">spect</span> <span class="o">=</span> <span class="n">spect</span> <span class="o">/</span> <span class="n">spect</span><span class="o">.</span><span class="n">max</span><span class="p">()</span> <span class="o">*</span> <span class="n">total_imp</span><span class="o">.</span><span class="n">max</span><span class="p">()</span>
+            <span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">sum_imp</span><span class="o">.</span><span class="n">data</span><span class="o">.</span><span class="n">index</span> <span class="o">*</span> <span class="mf">1e-9</span><span class="p">,</span> <span class="n">spect</span><span class="p">,</span> <span class="s1">&#39;r&#39;</span><span class="p">,</span> <span class="n">linewidth</span><span class="o">=</span><span class="mf">2.5</span><span class="p">)</span>
+
+        <span class="n">ax</span><span class="o">.</span><span class="n">legend</span><span class="p">(</span><span class="n">legend</span><span class="p">,</span> <span class="n">loc</span><span class="o">=</span><span class="s2">&quot;upper left&quot;</span><span class="p">,</span> <span class="n">ncol</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
+        <span class="n">ax</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="s2">&quot;Frequency (GHz)&quot;</span><span class="p">)</span>
+        <span class="n">ax</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="n">label_list</span><span class="p">[</span><span class="n">leg</span><span class="p">]</span> <span class="o">+</span> <span class="s2">&quot; - &quot;</span> <span class="o">+</span> <span class="n">component</span> <span class="o">+</span> <span class="s2">&quot; part&quot;</span><span class="p">)</span>
+        <span class="n">ax</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="n">label_list</span><span class="p">[</span><span class="n">leg</span><span class="p">]</span> <span class="o">+</span> <span class="s2">&quot; - &quot;</span> <span class="o">+</span> <span class="n">component</span> <span class="o">+</span> <span class="s2">&quot; part&quot;</span><span class="p">)</span>
+
+        <span class="k">if</span> <span class="n">zoom</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">:</span>
+            <span class="n">in_ax</span> <span class="o">=</span> <span class="n">inset_axes</span><span class="p">(</span>
+                <span class="n">ax</span><span class="p">,</span>
+                <span class="n">width</span><span class="o">=</span><span class="s2">&quot;30%&quot;</span><span class="p">,</span>  <span class="c1"># width = 30% of parent_bbox</span>
+                <span class="n">height</span><span class="o">=</span><span class="mf">1.5</span><span class="p">,</span>  <span class="c1"># height : 1 inch</span>
+                <span class="n">loc</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
+
+            <span class="n">total_imp</span> <span class="o">=</span> <span class="mi">0</span>
+            <span class="k">for</span> <span class="n">index</span> <span class="ow">in</span> <span class="n">sorted_index</span><span class="p">:</span>
+                <span class="n">attr</span> <span class="o">=</span> <span class="n">attr_list</span><span class="p">[</span><span class="n">index</span><span class="p">]</span>
+                <span class="c1"># Set all impedances with common indexes using + zero_impedance</span>
+                <span class="k">try</span><span class="p">:</span>
+                    <span class="n">sum_imp</span> <span class="o">=</span> <span class="nb">getattr</span><span class="p">(</span><span class="nb">getattr</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">attr</span><span class="p">),</span>
+                                      <span class="n">Z_type</span><span class="p">)</span> <span class="o">+</span> <span class="n">zero_impedance</span>
+                    <span class="n">in_ax</span><span class="o">.</span><span class="n">fill_between</span><span class="p">(</span><span class="n">sum_imp</span><span class="o">.</span><span class="n">data</span><span class="o">.</span><span class="n">index</span> <span class="o">*</span> <span class="mf">1e-3</span><span class="p">,</span>
+                                       <span class="n">total_imp</span><span class="p">,</span>
+                                       <span class="n">total_imp</span> <span class="o">+</span>
+                                       <span class="n">sum_imp</span><span class="o">.</span><span class="n">data</span><span class="p">[</span><span class="n">component</span><span class="p">]</span> <span class="o">*</span> <span class="mf">1e-9</span><span class="p">,</span>
+                                       <span class="n">edgecolor</span><span class="o">=</span><span class="n">colorblind</span><span class="p">[</span><span class="n">index</span> <span class="o">%</span> <span class="mi">10</span><span class="p">],</span>
+                                       <span class="n">color</span><span class="o">=</span><span class="n">colorblind</span><span class="p">[</span><span class="n">index</span> <span class="o">%</span> <span class="mi">10</span><span class="p">])</span>
+                    <span class="n">total_imp</span> <span class="o">+=</span> <span class="n">sum_imp</span><span class="o">.</span><span class="n">data</span><span class="p">[</span><span class="n">component</span><span class="p">]</span> <span class="o">*</span> <span class="mf">1e-9</span>
+                <span class="k">except</span> <span class="ne">AttributeError</span><span class="p">:</span>
+                    <span class="k">pass</span>
+            <span class="n">in_ax</span><span class="o">.</span><span class="n">set_xlim</span><span class="p">([</span><span class="mi">0</span><span class="p">,</span> <span class="mi">200</span><span class="p">])</span>
+            <span class="n">in_ax</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="s2">&quot;Frequency (kHz)&quot;</span><span class="p">)</span>
+            <span class="n">in_ax</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="sa">r</span><span class="s2">&quot;$[\mathrm</span><span class="si">{G}</span><span class="s2">\Omega]$&quot;</span><span class="p">)</span>
+
+        <span class="k">return</span> <span class="n">fig</span></div>
+
+<div class="viewcode-block" id="ImpedanceModel.effective_impedance"><a class="viewcode-back" href="../../../mbtrack2.impedance.html#mbtrack2.impedance.impedance_model.ImpedanceModel.effective_impedance">[docs]</a>    <span class="k">def</span> <span class="nf">effective_impedance</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span>
+                            <span class="n">m</span><span class="p">,</span>
+                            <span class="n">mu</span><span class="p">,</span>
+                            <span class="n">sigma</span><span class="p">,</span>
+                            <span class="n">M</span><span class="p">,</span>
+                            <span class="n">tuneS</span><span class="p">,</span>
+                            <span class="n">xi</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+                            <span class="n">mode</span><span class="o">=</span><span class="s2">&quot;Hermite&quot;</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Compute the longitudinal and transverse effective impedance.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        mu : int</span>
+<span class="sd">            coupled bunch mode number, goes from 0 to (M-1) where M is the</span>
+<span class="sd">            number of bunches</span>
+<span class="sd">        m : int</span>
+<span class="sd">            head-tail (or azimutal/synchrotron) mode number</span>
+<span class="sd">        sigma : float</span>
+<span class="sd">            RMS bunch length in [s]</span>
+<span class="sd">        M : int</span>
+<span class="sd">            Number of bunches.</span>
+<span class="sd">        tuneS : float</span>
+<span class="sd">            Synchrotron tune.</span>
+<span class="sd">        xi : float, optional</span>
+<span class="sd">            (non-normalized) chromaticity</span>
+<span class="sd">        mode: str, optional</span>
+<span class="sd">            type of the mode taken into account for the computation:</span>
+<span class="sd">            -&quot;Hermite&quot; modes for Gaussian bunches</span>
+
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        summary : DataFrame</span>
+<span class="sd">            Longitudinal and transverse effective impedance.</span>
+
+<span class="sd">        &quot;&quot;&quot;</span>
+
+        <span class="n">attr_list</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">sum_names</span>
+
+        <span class="n">eff_array</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="nb">len</span><span class="p">(</span><span class="n">attr_list</span><span class="p">),</span> <span class="mi">3</span><span class="p">),</span> <span class="n">dtype</span><span class="o">=</span><span class="nb">complex</span><span class="p">)</span>
+
+        <span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">attr</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">attr_list</span><span class="p">):</span>
+            <span class="k">try</span><span class="p">:</span>
+                <span class="n">impedance</span> <span class="o">=</span> <span class="nb">getattr</span><span class="p">(</span><span class="nb">getattr</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">attr</span><span class="p">),</span> <span class="s2">&quot;Zlong&quot;</span><span class="p">)</span>
+                <span class="n">eff_array</span><span class="p">[</span><span class="n">i</span><span class="p">,</span>
+                          <span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">effective_impedance</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="p">,</span> <span class="n">impedance</span><span class="p">,</span> <span class="n">m</span><span class="p">,</span> <span class="n">mu</span><span class="p">,</span>
+                                                   <span class="n">sigma</span><span class="p">,</span> <span class="n">M</span><span class="p">,</span> <span class="n">tuneS</span><span class="p">,</span> <span class="n">xi</span><span class="p">,</span> <span class="n">mode</span><span class="p">)</span>
+            <span class="k">except</span> <span class="ne">AttributeError</span><span class="p">:</span>
+                <span class="k">pass</span>
+
+            <span class="k">try</span><span class="p">:</span>
+                <span class="n">impedance</span> <span class="o">=</span> <span class="nb">getattr</span><span class="p">(</span><span class="nb">getattr</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">attr</span><span class="p">),</span> <span class="s2">&quot;Zxdip&quot;</span><span class="p">)</span>
+                <span class="n">eff_array</span><span class="p">[</span><span class="n">i</span><span class="p">,</span>
+                          <span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="n">effective_impedance</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="p">,</span> <span class="n">impedance</span><span class="p">,</span> <span class="n">m</span><span class="p">,</span> <span class="n">mu</span><span class="p">,</span>
+                                                   <span class="n">sigma</span><span class="p">,</span> <span class="n">M</span><span class="p">,</span> <span class="n">tuneS</span><span class="p">,</span> <span class="n">xi</span><span class="p">,</span> <span class="n">mode</span><span class="p">)</span>
+            <span class="k">except</span> <span class="ne">AttributeError</span><span class="p">:</span>
+                <span class="k">pass</span>
+
+            <span class="k">try</span><span class="p">:</span>
+                <span class="n">impedance</span> <span class="o">=</span> <span class="nb">getattr</span><span class="p">(</span><span class="nb">getattr</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">attr</span><span class="p">),</span> <span class="s2">&quot;Zydip&quot;</span><span class="p">)</span>
+                <span class="n">eff_array</span><span class="p">[</span><span class="n">i</span><span class="p">,</span>
+                          <span class="mi">2</span><span class="p">]</span> <span class="o">=</span> <span class="n">effective_impedance</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="p">,</span> <span class="n">impedance</span><span class="p">,</span> <span class="n">m</span><span class="p">,</span> <span class="n">mu</span><span class="p">,</span>
+                                                   <span class="n">sigma</span><span class="p">,</span> <span class="n">M</span><span class="p">,</span> <span class="n">tuneS</span><span class="p">,</span> <span class="n">xi</span><span class="p">,</span> <span class="n">mode</span><span class="p">)</span>
+            <span class="k">except</span> <span class="ne">AttributeError</span><span class="p">:</span>
+                <span class="k">pass</span>
+
+        <span class="n">eff_array</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">eff_array</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">omega0</span> <span class="o">*</span> <span class="mf">1e3</span>
+        <span class="n">eff_array</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="n">eff_array</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="mf">1e-3</span>
+        <span class="n">eff_array</span><span class="p">[:,</span> <span class="mi">2</span><span class="p">]</span> <span class="o">=</span> <span class="n">eff_array</span><span class="p">[:,</span> <span class="mi">2</span><span class="p">]</span> <span class="o">*</span> <span class="mf">1e-3</span>
+
+        <span class="n">summary</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">DataFrame</span><span class="p">(</span><span class="n">eff_array</span><span class="p">,</span>
+                               <span class="n">index</span><span class="o">=</span><span class="n">attr_list</span><span class="p">,</span>
+                               <span class="n">columns</span><span class="o">=</span><span class="p">[</span>
+                                   <span class="s2">&quot;Z/n [mOhm]&quot;</span><span class="p">,</span> <span class="s2">&quot;sum betax x Zxeff [kOhm]&quot;</span><span class="p">,</span>
+                                   <span class="s2">&quot;sum betay x Zyeff [kOhm]&quot;</span>
+                               <span class="p">])</span>
+
+        <span class="k">return</span> <span class="n">summary</span></div>
+
+<div class="viewcode-block" id="ImpedanceModel.energy_loss"><a class="viewcode-back" href="../../../mbtrack2.impedance.html#mbtrack2.impedance.impedance_model.ImpedanceModel.energy_loss">[docs]</a>    <span class="k">def</span> <span class="nf">energy_loss</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">sigma</span><span class="p">,</span> <span class="n">M</span><span class="p">,</span> <span class="n">bunch_spacing</span><span class="p">,</span> <span class="n">I</span><span class="p">,</span> <span class="n">n_points</span><span class="o">=</span><span class="mf">10e6</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Compute the beam and bunch loss factor and energy losses for each type </span>
+<span class="sd">        of element in the model assuming Gaussian bunches and constant spacing</span>
+<span class="sd">        between bunches.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        sigma : float</span>
+<span class="sd">            RMS bunch length in [s].</span>
+<span class="sd">        M : int</span>
+<span class="sd">            Number of bunches in the beam.</span>
+<span class="sd">        bunch_spacing : float</span>
+<span class="sd">            Time between two bunches in [s].</span>
+<span class="sd">        I : float</span>
+<span class="sd">            Total beam current in [A].</span>
+<span class="sd">        n_points : float, optional</span>
+<span class="sd">            Number of points used in the frequency spectrums.</span>
+
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        summary : Dataframe</span>
+<span class="sd">            Contains the beam and bunch loss factor and energy loss for the </span>
+<span class="sd">            full model and for each type of different component.</span>
+
+<span class="sd">        &quot;&quot;&quot;</span>
+
+        <span class="n">fmax</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">sum</span><span class="o">.</span><span class="n">Zlong</span><span class="o">.</span><span class="n">data</span><span class="o">.</span><span class="n">index</span><span class="o">.</span><span class="n">max</span><span class="p">()</span>
+        <span class="n">fmin</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">sum</span><span class="o">.</span><span class="n">Zlong</span><span class="o">.</span><span class="n">data</span><span class="o">.</span><span class="n">index</span><span class="o">.</span><span class="n">min</span><span class="p">()</span>
+
+        <span class="n">Q</span> <span class="o">=</span> <span class="n">I</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">T0</span> <span class="o">/</span> <span class="n">M</span>
+
+        <span class="k">if</span> <span class="n">fmin</span> <span class="o">&gt;=</span> <span class="mi">0</span><span class="p">:</span>
+            <span class="n">fmin</span> <span class="o">=</span> <span class="o">-</span><span class="mi">1</span> <span class="o">*</span> <span class="n">fmax</span>
+        <span class="n">f</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="n">fmin</span><span class="p">,</span> <span class="n">fmax</span><span class="p">,</span> <span class="nb">int</span><span class="p">(</span><span class="n">n_points</span><span class="p">))</span>
+
+        <span class="n">beam_spect</span> <span class="o">=</span> <span class="n">beam_spectrum</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="n">M</span><span class="p">,</span> <span class="n">bunch_spacing</span><span class="p">,</span> <span class="n">sigma</span><span class="o">=</span><span class="n">sigma</span><span class="p">)</span>
+
+        <span class="n">bunch_spect</span> <span class="o">=</span> <span class="n">gaussian_bunch_spectrum</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="n">sigma</span><span class="p">)</span>
+
+        <span class="n">attr_list</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">sum_names</span>
+
+        <span class="n">loss_array</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="nb">len</span><span class="p">(</span><span class="n">attr_list</span><span class="p">),</span> <span class="mi">2</span><span class="p">))</span>
+
+        <span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">attr</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">attr_list</span><span class="p">):</span>
+            <span class="k">try</span><span class="p">:</span>
+                <span class="n">impedance</span> <span class="o">=</span> <span class="nb">getattr</span><span class="p">(</span><span class="nb">getattr</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">attr</span><span class="p">),</span> <span class="s2">&quot;Zlong&quot;</span><span class="p">)</span>
+                <span class="n">loss_array</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">beam_loss_factor</span><span class="p">(</span><span class="n">impedance</span><span class="p">,</span> <span class="n">f</span><span class="p">,</span> <span class="n">beam_spect</span><span class="p">,</span>
+                                                    <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="p">)</span>
+                <span class="n">loss_array</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="n">beam_loss_factor</span><span class="p">(</span><span class="n">impedance</span><span class="p">,</span> <span class="n">f</span><span class="p">,</span> <span class="n">bunch_spect</span><span class="p">,</span>
+                                                    <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="p">)</span>
+            <span class="k">except</span> <span class="ne">AttributeError</span><span class="p">:</span>
+                <span class="k">pass</span>
+
+        <span class="n">loss_array</span> <span class="o">=</span> <span class="n">loss_array</span> <span class="o">*</span> <span class="mf">1e-12</span>
+        <span class="n">summary</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">DataFrame</span><span class="p">(</span><span class="n">loss_array</span><span class="p">,</span>
+                               <span class="n">index</span><span class="o">=</span><span class="n">attr_list</span><span class="p">,</span>
+                               <span class="n">columns</span><span class="o">=</span><span class="p">[</span>
+                                   <span class="s2">&quot;loss factor (beam) [V/pC]&quot;</span><span class="p">,</span>
+                                   <span class="s2">&quot;loss factor (bunch) [V/pC]&quot;</span>
+                               <span class="p">])</span>
+
+        <span class="n">summary</span><span class="p">[</span><span class="s2">&quot;P (beam) [W]&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="n">summary</span><span class="p">[</span><span class="s2">&quot;loss factor (beam) [V/pC]&quot;</span><span class="p">]</span> <span class="o">*</span> \
+            <span class="mf">1e12</span><span class="o">*</span><span class="n">Q</span><span class="o">**</span><span class="mi">2</span><span class="o">/</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">T0</span><span class="p">)</span>
+        <span class="n">summary</span><span class="p">[</span><span class="s2">&quot;P (bunch) [W]&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="n">summary</span><span class="p">[</span><span class="s2">&quot;loss factor (bunch) [V/pC]&quot;</span><span class="p">]</span> <span class="o">*</span> \
+            <span class="mf">1e12</span><span class="o">*</span><span class="n">Q</span><span class="o">**</span><span class="mi">2</span><span class="o">/</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">T0</span><span class="p">)</span><span class="o">*</span><span class="n">M</span>
+
+        <span class="k">return</span> <span class="n">summary</span></div>
+
+<div class="viewcode-block" id="ImpedanceModel.power_loss_spectrum"><a class="viewcode-back" href="../../../mbtrack2.impedance.html#mbtrack2.impedance.impedance_model.ImpedanceModel.power_loss_spectrum">[docs]</a>    <span class="k">def</span> <span class="nf">power_loss_spectrum</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span>
+                            <span class="n">sigma</span><span class="p">,</span>
+                            <span class="n">M</span><span class="p">,</span>
+                            <span class="n">bunch_spacing</span><span class="p">,</span>
+                            <span class="n">I</span><span class="p">,</span>
+                            <span class="n">n_points</span><span class="o">=</span><span class="mf">10e6</span><span class="p">,</span>
+                            <span class="n">max_overlap</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span>
+                            <span class="n">plot</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Compute the power loss spectrum of the summed longitudinal impedance </span>
+<span class="sd">        as in Eq. (4) of [1].</span>
+
+<span class="sd">        Assume Gaussian bunches and constant spacing between bunches.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        sigma : float</span>
+<span class="sd">            RMS bunch length in [s].</span>
+<span class="sd">        M : int</span>
+<span class="sd">            Number of bunches in the beam.</span>
+<span class="sd">        bunch_spacing : float</span>
+<span class="sd">            Time between two bunches in [s].</span>
+<span class="sd">        I : float</span>
+<span class="sd">            Total beam current in [A].</span>
+<span class="sd">        n_points : float, optional</span>
+<span class="sd">            Number of points used in the frequency spectrum.</span>
+<span class="sd">        max_overlap : bool, optional</span>
+<span class="sd">            If True, the bunch spectrum (scaled to the number of bunches) is </span>
+<span class="sd">            used instead of the beam spectrum to compute the maximum value of </span>
+<span class="sd">            the power loss spectrum at each frequency. Should only be used to </span>
+<span class="sd">            maximise the power loss at a given frequency (e.g. for HOMs) and </span>
+<span class="sd">            not for the full spectrum.</span>
+<span class="sd">        plot : bool, optional</span>
+<span class="sd">            If True, plots:</span>
+<span class="sd">                - the overlap between the real part of the longitudinal impedance </span>
+<span class="sd">                and the beam spectrum.</span>
+<span class="sd">                - the power loss spectrum.</span>
+
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        pf0 : array</span>
+<span class="sd">            Frequency points.</span>
+<span class="sd">        power_loss : array</span>
+<span class="sd">            Power loss spectrum in [W].</span>
+
+<span class="sd">        References</span>
+<span class="sd">        ----------</span>
+<span class="sd">        [1] : L. Teofili, et al. &quot;A Multi-Physics Approach to Simulate the RF </span>
+<span class="sd">        Heating 3D Power Map Induced by the Proton Beam in a Beam Intercepting </span>
+<span class="sd">        Device&quot;, in IPAC&#39;18, 2018, doi:10.18429/JACoW-IPAC2018-THPAK093</span>
+
+<span class="sd">        &quot;&quot;&quot;</span>
+
+        <span class="n">impedance</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">sum</span><span class="o">.</span><span class="n">Zlong</span>
+        <span class="n">fmax</span> <span class="o">=</span> <span class="n">impedance</span><span class="o">.</span><span class="n">data</span><span class="o">.</span><span class="n">index</span><span class="o">.</span><span class="n">max</span><span class="p">()</span>
+        <span class="n">fmin</span> <span class="o">=</span> <span class="n">impedance</span><span class="o">.</span><span class="n">data</span><span class="o">.</span><span class="n">index</span><span class="o">.</span><span class="n">min</span><span class="p">()</span>
+
+        <span class="n">Q</span> <span class="o">=</span> <span class="n">I</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">T0</span> <span class="o">/</span> <span class="n">M</span>
+
+        <span class="k">if</span> <span class="n">fmin</span> <span class="o">&gt;=</span> <span class="mi">0</span><span class="p">:</span>
+            <span class="n">fmin</span> <span class="o">=</span> <span class="o">-</span><span class="mi">1</span> <span class="o">*</span> <span class="n">fmax</span>
+            <span class="n">double_sided_impedance</span><span class="p">(</span><span class="n">impedance</span><span class="p">)</span>
+
+        <span class="n">frequency</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="n">fmin</span><span class="p">,</span> <span class="n">fmax</span><span class="p">,</span> <span class="nb">int</span><span class="p">(</span><span class="n">n_points</span><span class="p">))</span>
+        <span class="k">if</span> <span class="n">max_overlap</span> <span class="ow">is</span> <span class="kc">False</span><span class="p">:</span>
+            <span class="n">spectrum</span> <span class="o">=</span> <span class="n">beam_spectrum</span><span class="p">(</span><span class="n">frequency</span><span class="p">,</span> <span class="n">M</span><span class="p">,</span> <span class="n">bunch_spacing</span><span class="p">,</span> <span class="n">sigma</span><span class="p">)</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="n">spectrum</span> <span class="o">=</span> <span class="n">gaussian_bunch_spectrum</span><span class="p">(</span><span class="n">frequency</span><span class="p">,</span> <span class="n">sigma</span><span class="p">)</span> <span class="o">*</span> <span class="n">M</span>
+
+        <span class="n">pmax</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">floor</span><span class="p">(</span><span class="n">fmax</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">f0</span><span class="p">)</span>
+        <span class="n">pmin</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">floor</span><span class="p">(</span><span class="n">fmin</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">f0</span><span class="p">)</span>
+
+        <span class="n">p</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="n">pmin</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span> <span class="n">pmax</span><span class="p">)</span>
+        <span class="n">pf0</span> <span class="o">=</span> <span class="n">p</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">f0</span>
+        <span class="n">ReZ</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">real</span><span class="p">(</span><span class="n">impedance</span><span class="p">(</span><span class="n">pf0</span><span class="p">))</span>
+        <span class="n">spectral_density</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">spectrum</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span>
+        <span class="c1"># interpolation of the spectrum is needed to avoid problems liked to</span>
+        <span class="c1"># division by 0</span>
+        <span class="c1"># computing the spectrum directly to the frequency points gives</span>
+        <span class="c1"># wrong results</span>
+        <span class="n">spect</span> <span class="o">=</span> <span class="n">interp1d</span><span class="p">(</span><span class="n">frequency</span><span class="p">,</span> <span class="n">spectral_density</span><span class="p">)</span>
+        <span class="n">power_loss</span> <span class="o">=</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">f0</span> <span class="o">*</span> <span class="n">Q</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span> <span class="o">*</span> <span class="n">ReZ</span> <span class="o">*</span> <span class="n">spect</span><span class="p">(</span><span class="n">pf0</span><span class="p">)</span>
+
+        <span class="k">if</span> <span class="n">plot</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">:</span>
+            <span class="n">fig</span><span class="p">,</span> <span class="n">ax</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">()</span>
+            <span class="n">twin</span> <span class="o">=</span> <span class="n">ax</span><span class="o">.</span><span class="n">twinx</span><span class="p">()</span>
+            <span class="n">p1</span><span class="p">,</span> <span class="o">=</span> <span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">pf0</span><span class="p">,</span> <span class="n">ReZ</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s2">&quot;r&quot;</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s2">&quot;Re[Z] [Ohm]&quot;</span><span class="p">)</span>
+            <span class="n">p2</span><span class="p">,</span> <span class="o">=</span> <span class="n">twin</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">pf0</span><span class="p">,</span>
+                            <span class="n">spect</span><span class="p">(</span><span class="n">pf0</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">f0</span> <span class="o">*</span> <span class="n">Q</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span><span class="p">,</span>
+                            <span class="n">color</span><span class="o">=</span><span class="s2">&quot;b&quot;</span><span class="p">,</span>
+                            <span class="n">label</span><span class="o">=</span><span class="s2">&quot;Beam spectrum [a.u.]&quot;</span><span class="p">)</span>
+            <span class="n">ax</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="s2">&quot;Frequency [Hz]&quot;</span><span class="p">)</span>
+            <span class="n">ax</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="s2">&quot;Re[Z] [Ohm]&quot;</span><span class="p">)</span>
+            <span class="n">twin</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="s2">&quot;Beam spectrum [a.u.]&quot;</span><span class="p">)</span>
+            <span class="n">plots</span> <span class="o">=</span> <span class="p">[</span><span class="n">p1</span><span class="p">,</span> <span class="n">p2</span><span class="p">]</span>
+            <span class="n">ax</span><span class="o">.</span><span class="n">legend</span><span class="p">(</span><span class="n">handles</span><span class="o">=</span><span class="n">plots</span><span class="p">,</span> <span class="n">loc</span><span class="o">=</span><span class="s2">&quot;best&quot;</span><span class="p">)</span>
+
+            <span class="n">fig</span><span class="p">,</span> <span class="n">ax</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">()</span>
+            <span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">pf0</span><span class="p">,</span> <span class="n">power_loss</span><span class="p">)</span>
+            <span class="n">ax</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="s2">&quot;Frequency [Hz]&quot;</span><span class="p">)</span>
+            <span class="n">ax</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="s2">&quot;Power loss [W]&quot;</span><span class="p">)</span>
+
+        <span class="k">return</span> <span class="n">pf0</span><span class="p">,</span> <span class="n">power_loss</span></div>
+
+<div class="viewcode-block" id="ImpedanceModel.save"><a class="viewcode-back" href="../../../mbtrack2.impedance.html#mbtrack2.impedance.impedance_model.ImpedanceModel.save">[docs]</a>    <span class="k">def</span> <span class="nf">save</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">file</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Save impedance model to file.</span>
+
+<span class="sd">        The same pandas version is needed on both saving and loading computer</span>
+<span class="sd">        for the pickle to work.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        file : str</span>
+<span class="sd">            File where the impedance model is saved.</span>
+
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        None.</span>
+
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="n">to_save</span> <span class="o">=</span> <span class="p">{</span>
+            <span class="s2">&quot;wakefields&quot;</span><span class="p">:</span> <span class="bp">self</span><span class="o">.</span><span class="n">wakefields</span><span class="p">,</span>
+            <span class="s2">&quot;positions&quot;</span><span class="p">:</span> <span class="bp">self</span><span class="o">.</span><span class="n">positions</span><span class="p">,</span>
+            <span class="s2">&quot;names&quot;</span><span class="p">:</span> <span class="bp">self</span><span class="o">.</span><span class="n">names</span><span class="p">,</span>
+            <span class="s2">&quot;globals&quot;</span><span class="p">:</span> <span class="bp">self</span><span class="o">.</span><span class="n">globals</span><span class="p">,</span>
+            <span class="s2">&quot;globals_names&quot;</span><span class="p">:</span> <span class="bp">self</span><span class="o">.</span><span class="n">globals_names</span>
+        <span class="p">}</span>
+        <span class="k">with</span> <span class="nb">open</span><span class="p">(</span><span class="n">file</span><span class="p">,</span> <span class="s2">&quot;wb&quot;</span><span class="p">)</span> <span class="k">as</span> <span class="n">f</span><span class="p">:</span>
+            <span class="n">pickle</span><span class="o">.</span><span class="n">dump</span><span class="p">(</span><span class="n">to_save</span><span class="p">,</span> <span class="n">f</span><span class="p">)</span></div>
+
+<div class="viewcode-block" id="ImpedanceModel.load"><a class="viewcode-back" href="../../../mbtrack2.impedance.html#mbtrack2.impedance.impedance_model.ImpedanceModel.load">[docs]</a>    <span class="k">def</span> <span class="nf">load</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">file</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Load impedance model from file.</span>
+
+<span class="sd">        The same pandas version is needed on both saving and loading computer</span>
+<span class="sd">        for the pickle to work.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        file : str</span>
+<span class="sd">            File where the impedance model is saved.</span>
+
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        None.</span>
+
+<span class="sd">        &quot;&quot;&quot;</span>
+
+        <span class="k">with</span> <span class="nb">open</span><span class="p">(</span><span class="n">file</span><span class="p">,</span> <span class="s1">&#39;rb&#39;</span><span class="p">)</span> <span class="k">as</span> <span class="n">f</span><span class="p">:</span>
+            <span class="n">to_load</span> <span class="o">=</span> <span class="n">pickle</span><span class="o">.</span><span class="n">load</span><span class="p">(</span><span class="n">f</span><span class="p">)</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">wakefields</span> <span class="o">=</span> <span class="n">to_load</span><span class="p">[</span><span class="s2">&quot;wakefields&quot;</span><span class="p">]</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">positions</span> <span class="o">=</span> <span class="n">to_load</span><span class="p">[</span><span class="s2">&quot;positions&quot;</span><span class="p">]</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">names</span> <span class="o">=</span> <span class="n">to_load</span><span class="p">[</span><span class="s2">&quot;names&quot;</span><span class="p">]</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">globals</span> <span class="o">=</span> <span class="n">to_load</span><span class="p">[</span><span class="s2">&quot;globals&quot;</span><span class="p">]</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">globals_names</span> <span class="o">=</span> <span class="n">to_load</span><span class="p">[</span><span class="s2">&quot;globals_names&quot;</span><span class="p">]</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">compute_sum</span><span class="p">()</span></div></div>
+</pre></div>
+
+            <div class="clearer"></div>
+          </div>
+        </div>
+      </div>
+      <div class="sphinxsidebar" role="navigation" aria-label="main navigation">
+        <div class="sphinxsidebarwrapper">
+<div id="searchbox" style="display: none" role="search">
+  <h3 id="searchlabel">Quick search</h3>
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+  <h1>Source code for mbtrack2.impedance.resistive_wall</h1><div class="highlight"><pre>
+<span></span><span class="c1"># -*- coding: utf-8 -*-</span>
+<span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">Define resistive wall elements based on the WakeField class.</span>
+<span class="sd">&quot;&quot;&quot;</span>
+
+<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="kn">from</span> <span class="nn">scipy.constants</span> <span class="kn">import</span> <span class="n">c</span><span class="p">,</span> <span class="n">epsilon_0</span><span class="p">,</span> <span class="n">mu_0</span>
+<span class="kn">from</span> <span class="nn">scipy.integrate</span> <span class="kn">import</span> <span class="n">quad</span>
+
+<span class="kn">from</span> <span class="nn">mbtrack2.impedance.wakefield</span> <span class="kn">import</span> <span class="n">Impedance</span><span class="p">,</span> <span class="n">WakeField</span><span class="p">,</span> <span class="n">WakeFunction</span>
+
+
+<div class="viewcode-block" id="skin_depth"><a class="viewcode-back" href="../../../mbtrack2.impedance.html#mbtrack2.impedance.resistive_wall.skin_depth">[docs]</a><span class="k">def</span> <span class="nf">skin_depth</span><span class="p">(</span><span class="n">frequency</span><span class="p">,</span> <span class="n">rho</span><span class="p">,</span> <span class="n">mu_r</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">epsilon_r</span><span class="o">=</span><span class="mi">1</span><span class="p">):</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    General formula for the skin depth.</span>
+<span class="sd">    </span>
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">    frequency : array of float</span>
+<span class="sd">        Frequency points in [Hz].</span>
+<span class="sd">    rho : float</span>
+<span class="sd">        Resistivity in [ohm.m].</span>
+<span class="sd">    mu_r : float, optional</span>
+<span class="sd">        Relative magnetic permeability.</span>
+<span class="sd">    epsilon_r : float, optional</span>
+<span class="sd">        Relative electric permittivity.</span>
+<span class="sd">    </span>
+<span class="sd">    Returns</span>
+<span class="sd">    -------</span>
+<span class="sd">    delta : array of float</span>
+<span class="sd">        Skin depth in [m].</span>
+<span class="sd">    </span>
+<span class="sd">    &quot;&quot;&quot;</span>
+
+    <span class="n">delta</span> <span class="o">=</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">rho</span> <span class="o">/</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="n">frequency</span><span class="p">)</span> <span class="o">*</span> <span class="n">mu_r</span> <span class="o">*</span> <span class="n">mu_0</span><span class="p">))</span> <span class="o">*</span>
+             <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span>
+                 <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="mi">1</span> <span class="o">+</span> <span class="p">(</span><span class="n">rho</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="n">frequency</span><span class="p">)</span> <span class="o">*</span> <span class="n">epsilon_r</span> <span class="o">*</span>
+                              <span class="n">epsilon_0</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span> <span class="o">+</span>
+                 <span class="n">rho</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="n">frequency</span><span class="p">)</span> <span class="o">*</span> <span class="n">epsilon_r</span> <span class="o">*</span> <span class="n">epsilon_0</span><span class="p">))</span>
+    <span class="k">return</span> <span class="n">delta</span></div>
+
+
+<div class="viewcode-block" id="CircularResistiveWall"><a class="viewcode-back" href="../../../mbtrack2.impedance.html#mbtrack2.impedance.resistive_wall.CircularResistiveWall">[docs]</a><span class="k">class</span> <span class="nc">CircularResistiveWall</span><span class="p">(</span><span class="n">WakeField</span><span class="p">):</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    Resistive wall WakeField element for a circular beam pipe.</span>
+<span class="sd">    </span>
+<span class="sd">    Impedance from approximated formulas from Eq. (2.77) of Chao book [1].</span>
+<span class="sd">    Wake function formulas from [2].</span>
+<span class="sd">        </span>
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">    time : array of float</span>
+<span class="sd">        Time points where the wake function will be evaluated in [s].</span>
+<span class="sd">    frequency : array of float</span>
+<span class="sd">        Frequency points where the impedance will be evaluated in [Hz].</span>
+<span class="sd">    length : float </span>
+<span class="sd">        Beam pipe length in [m].</span>
+<span class="sd">    rho : float</span>
+<span class="sd">        Resistivity in [ohm.m].</span>
+<span class="sd">    radius : float </span>
+<span class="sd">        Beam pipe radius in [m].</span>
+<span class="sd">    exact : bool, optional</span>
+<span class="sd">        If False, approxmiated formulas are used for the wake function </span>
+<span class="sd">        computations.</span>
+<span class="sd">    atol : float, optional</span>
+<span class="sd">        Absolute tolerance used to enforce fundamental theorem of beam loading</span>
+<span class="sd">        for the exact expression of the longitudinal wake function.</span>
+<span class="sd">        Default is 1e-20.</span>
+<span class="sd">    </span>
+<span class="sd">    References</span>
+<span class="sd">    ----------</span>
+<span class="sd">    [1] : Chao, A. W. (1993). Physics of collective beam instabilities in high </span>
+<span class="sd">    energy accelerators. Wiley.</span>
+<span class="sd">    [2] : Skripka, Galina, et al. &quot;Simultaneous computation of intrabunch and </span>
+<span class="sd">    interbunch collective beam motions in storage rings.&quot; Nuclear Instruments </span>
+<span class="sd">    and Methods in Physics Research Section A: Accelerators, Spectrometers, </span>
+<span class="sd">    Detectors and Associated Equipment 806 (2016): 221-230.</span>
+
+<span class="sd">    &quot;&quot;&quot;</span>
+
+    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span>
+                 <span class="n">time</span><span class="p">,</span>
+                 <span class="n">frequency</span><span class="p">,</span>
+                 <span class="n">length</span><span class="p">,</span>
+                 <span class="n">rho</span><span class="p">,</span>
+                 <span class="n">radius</span><span class="p">,</span>
+                 <span class="n">exact</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span>
+                 <span class="n">atol</span><span class="o">=</span><span class="mf">1e-20</span><span class="p">):</span>
+        <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__init__</span><span class="p">()</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">length</span> <span class="o">=</span> <span class="n">length</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">rho</span> <span class="o">=</span> <span class="n">rho</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">radius</span> <span class="o">=</span> <span class="n">radius</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">Z0</span> <span class="o">=</span> <span class="n">mu_0</span> <span class="o">*</span> <span class="n">c</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">t0</span> <span class="o">=</span> <span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">rho</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">radius</span><span class="o">**</span><span class="mi">2</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">Z0</span><span class="p">)</span><span class="o">**</span><span class="p">(</span><span class="mi">1</span> <span class="o">/</span> <span class="mi">3</span><span class="p">)</span> <span class="o">/</span> <span class="n">c</span>
+
+        <span class="n">omega</span> <span class="o">=</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="n">frequency</span>
+        <span class="n">Z1</span> <span class="o">=</span> <span class="n">length</span> <span class="o">*</span> <span class="p">(</span><span class="mi">1</span> <span class="o">+</span> <span class="n">np</span><span class="o">.</span><span class="n">sign</span><span class="p">(</span><span class="n">frequency</span><span class="p">)</span> <span class="o">*</span> <span class="mi">1</span><span class="n">j</span><span class="p">)</span> <span class="o">*</span> <span class="n">rho</span> <span class="o">/</span> <span class="p">(</span>
+            <span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="n">radius</span> <span class="o">*</span> <span class="n">skin_depth</span><span class="p">(</span><span class="n">frequency</span><span class="p">,</span> <span class="n">rho</span><span class="p">))</span>
+        <span class="n">Z2</span> <span class="o">=</span> <span class="n">c</span> <span class="o">/</span> <span class="n">omega</span> <span class="o">*</span> <span class="n">length</span> <span class="o">*</span> <span class="p">(</span><span class="mi">1</span> <span class="o">+</span> <span class="n">np</span><span class="o">.</span><span class="n">sign</span><span class="p">(</span><span class="n">frequency</span><span class="p">)</span> <span class="o">*</span> <span class="mi">1</span><span class="n">j</span><span class="p">)</span> <span class="o">*</span> <span class="n">rho</span> <span class="o">/</span> <span class="p">(</span>
+            <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="n">radius</span><span class="o">**</span><span class="mi">3</span> <span class="o">*</span> <span class="n">skin_depth</span><span class="p">(</span><span class="n">frequency</span><span class="p">,</span> <span class="n">rho</span><span class="p">))</span>
+
+        <span class="n">Wl</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">LongitudinalWakeFunction</span><span class="p">(</span><span class="n">time</span><span class="p">,</span> <span class="n">exact</span><span class="p">,</span> <span class="n">atol</span><span class="p">)</span>
+        <span class="n">Wt</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">TransverseWakeFunction</span><span class="p">(</span><span class="n">time</span><span class="p">,</span> <span class="n">exact</span><span class="p">)</span>
+
+        <span class="n">Zlong</span> <span class="o">=</span> <span class="n">Impedance</span><span class="p">(</span><span class="n">variable</span><span class="o">=</span><span class="n">frequency</span><span class="p">,</span>
+                          <span class="n">function</span><span class="o">=</span><span class="n">Z1</span><span class="p">,</span>
+                          <span class="n">component_type</span><span class="o">=</span><span class="s1">&#39;long&#39;</span><span class="p">)</span>
+        <span class="n">Zxdip</span> <span class="o">=</span> <span class="n">Impedance</span><span class="p">(</span><span class="n">variable</span><span class="o">=</span><span class="n">frequency</span><span class="p">,</span>
+                          <span class="n">function</span><span class="o">=</span><span class="n">Z2</span><span class="p">,</span>
+                          <span class="n">component_type</span><span class="o">=</span><span class="s1">&#39;xdip&#39;</span><span class="p">)</span>
+        <span class="n">Zydip</span> <span class="o">=</span> <span class="n">Impedance</span><span class="p">(</span><span class="n">variable</span><span class="o">=</span><span class="n">frequency</span><span class="p">,</span>
+                          <span class="n">function</span><span class="o">=</span><span class="n">Z2</span><span class="p">,</span>
+                          <span class="n">component_type</span><span class="o">=</span><span class="s1">&#39;ydip&#39;</span><span class="p">)</span>
+        <span class="n">Wlong</span> <span class="o">=</span> <span class="n">WakeFunction</span><span class="p">(</span><span class="n">variable</span><span class="o">=</span><span class="n">time</span><span class="p">,</span> <span class="n">function</span><span class="o">=</span><span class="n">Wl</span><span class="p">,</span> <span class="n">component_type</span><span class="o">=</span><span class="s2">&quot;long&quot;</span><span class="p">)</span>
+        <span class="n">Wxdip</span> <span class="o">=</span> <span class="n">WakeFunction</span><span class="p">(</span><span class="n">variable</span><span class="o">=</span><span class="n">time</span><span class="p">,</span> <span class="n">function</span><span class="o">=</span><span class="n">Wt</span><span class="p">,</span> <span class="n">component_type</span><span class="o">=</span><span class="s2">&quot;xdip&quot;</span><span class="p">)</span>
+        <span class="n">Wydip</span> <span class="o">=</span> <span class="n">WakeFunction</span><span class="p">(</span><span class="n">variable</span><span class="o">=</span><span class="n">time</span><span class="p">,</span> <span class="n">function</span><span class="o">=</span><span class="n">Wt</span><span class="p">,</span> <span class="n">component_type</span><span class="o">=</span><span class="s2">&quot;ydip&quot;</span><span class="p">)</span>
+
+        <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="n">append_to_model</span><span class="p">(</span><span class="n">Zlong</span><span class="p">)</span>
+        <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="n">append_to_model</span><span class="p">(</span><span class="n">Zxdip</span><span class="p">)</span>
+        <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="n">append_to_model</span><span class="p">(</span><span class="n">Zydip</span><span class="p">)</span>
+        <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="n">append_to_model</span><span class="p">(</span><span class="n">Wlong</span><span class="p">)</span>
+        <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="n">append_to_model</span><span class="p">(</span><span class="n">Wxdip</span><span class="p">)</span>
+        <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="n">append_to_model</span><span class="p">(</span><span class="n">Wydip</span><span class="p">)</span>
+
+<div class="viewcode-block" id="CircularResistiveWall.LongitudinalWakeFunction"><a class="viewcode-back" href="../../../mbtrack2.impedance.html#mbtrack2.impedance.resistive_wall.CircularResistiveWall.LongitudinalWakeFunction">[docs]</a>    <span class="k">def</span> <span class="nf">LongitudinalWakeFunction</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">time</span><span class="p">,</span> <span class="n">exact</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="n">atol</span><span class="o">=</span><span class="mf">1e-20</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Compute the longitudinal wake function of a circular resistive wall </span>
+<span class="sd">        using Eq. (22), or approxmiated expression Eq. (24), of [1]. The </span>
+<span class="sd">        approxmiated expression is valid if the time is large compared to the </span>
+<span class="sd">        characteristic time t0.</span>
+<span class="sd">        </span>
+<span class="sd">        If some time value is smaller than atol, then the fundamental theorem </span>
+<span class="sd">        of beam loading is applied: Wl(0) = Wl(0+)/2.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        time : array of float</span>
+<span class="sd">            Time points where the wake function is evaluated in [s].</span>
+<span class="sd">        exact : bool, optional</span>
+<span class="sd">            If True, the exact expression is used. The default is False.</span>
+<span class="sd">        atol : float, optional</span>
+<span class="sd">            Absolute tolerance used to enforce fundamental theorem of beam loading</span>
+<span class="sd">            for the exact expression of the longitudinal wake function.</span>
+<span class="sd">            Default is 1e-20.</span>
+
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        wl : array of float</span>
+<span class="sd">            Longitudinal wake function in [V/C].</span>
+<span class="sd">            </span>
+<span class="sd">        References</span>
+<span class="sd">        ----------</span>
+<span class="sd">        [1] : Skripka, Galina, et al. &quot;Simultaneous computation of intrabunch and </span>
+<span class="sd">        interbunch collective beam motions in storage rings.&quot; Nuclear Instruments </span>
+<span class="sd">        and Methods in Physics Research Section A: Accelerators, Spectrometers, </span>
+<span class="sd">        Detectors and Associated Equipment 806 (2016): 221-230.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="n">wl</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros_like</span><span class="p">(</span><span class="n">time</span><span class="p">)</span>
+        <span class="n">idx1</span> <span class="o">=</span> <span class="n">time</span> <span class="o">&lt;</span> <span class="mi">0</span>
+        <span class="n">wl</span><span class="p">[</span><span class="n">idx1</span><span class="p">]</span> <span class="o">=</span> <span class="mi">0</span>
+        <span class="k">if</span> <span class="n">exact</span> <span class="o">==</span> <span class="kc">True</span><span class="p">:</span>
+            <span class="n">idx2</span> <span class="o">=</span> <span class="n">time</span> <span class="o">&gt;</span> <span class="mi">20</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">t0</span>
+            <span class="n">idx3</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">logical_not</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">logical_or</span><span class="p">(</span><span class="n">idx1</span><span class="p">,</span> <span class="n">idx2</span><span class="p">))</span>
+            <span class="n">wl</span><span class="p">[</span><span class="n">idx3</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">__LongWakeExact</span><span class="p">(</span><span class="n">time</span><span class="p">[</span><span class="n">idx3</span><span class="p">],</span> <span class="n">atol</span><span class="p">)</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="n">idx2</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">logical_not</span><span class="p">(</span><span class="n">idx1</span><span class="p">)</span>
+        <span class="n">wl</span><span class="p">[</span><span class="n">idx2</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">__LongWakeApprox</span><span class="p">(</span><span class="n">time</span><span class="p">[</span><span class="n">idx2</span><span class="p">])</span>
+        <span class="k">return</span> <span class="n">wl</span></div>
+
+<div class="viewcode-block" id="CircularResistiveWall.TransverseWakeFunction"><a class="viewcode-back" href="../../../mbtrack2.impedance.html#mbtrack2.impedance.resistive_wall.CircularResistiveWall.TransverseWakeFunction">[docs]</a>    <span class="k">def</span> <span class="nf">TransverseWakeFunction</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">time</span><span class="p">,</span> <span class="n">exact</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Compute the transverse wake function of a circular resistive wall </span>
+<span class="sd">        using Eq. (25), or approxmiated expression Eq. (26), of [1]. The </span>
+<span class="sd">        approxmiated expression is valid if the time is large compared to the </span>
+<span class="sd">        characteristic time t0.</span>
+<span class="sd">        </span>
+<span class="sd">        Exact expression (Eq. (25) from [1]) is corrected by factor (c * t0).</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        time : array of float</span>
+<span class="sd">            Time points where the wake function is evaluated in [s].</span>
+<span class="sd">        exact : bool, optional</span>
+<span class="sd">            If True, the exact expression is used. The default is False.</span>
+
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        wt : array of float</span>
+<span class="sd">            Transverse wake function in [V/C].</span>
+<span class="sd">            </span>
+<span class="sd">        References</span>
+<span class="sd">        ----------</span>
+<span class="sd">        [1] : Skripka, Galina, et al. &quot;Simultaneous computation of intrabunch and </span>
+<span class="sd">        interbunch collective beam motions in storage rings.&quot; Nuclear Instruments </span>
+<span class="sd">        and Methods in Physics Research Section A: Accelerators, Spectrometers, </span>
+<span class="sd">        Detectors and Associated Equipment 806 (2016): 221-230.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="n">wt</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros_like</span><span class="p">(</span><span class="n">time</span><span class="p">)</span>
+        <span class="n">idx1</span> <span class="o">=</span> <span class="n">time</span> <span class="o">&lt;</span> <span class="mi">0</span>
+        <span class="n">wt</span><span class="p">[</span><span class="n">idx1</span><span class="p">]</span> <span class="o">=</span> <span class="mi">0</span>
+        <span class="k">if</span> <span class="n">exact</span> <span class="o">==</span> <span class="kc">True</span><span class="p">:</span>
+            <span class="n">idx2</span> <span class="o">=</span> <span class="n">time</span> <span class="o">&gt;</span> <span class="mi">20</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">t0</span>
+            <span class="n">idx3</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">logical_not</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">logical_or</span><span class="p">(</span><span class="n">idx1</span><span class="p">,</span> <span class="n">idx2</span><span class="p">))</span>
+            <span class="n">wt</span><span class="p">[</span><span class="n">idx3</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">__TransWakeExact</span><span class="p">(</span><span class="n">time</span><span class="p">[</span><span class="n">idx3</span><span class="p">])</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="n">idx2</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">logical_not</span><span class="p">(</span><span class="n">idx1</span><span class="p">)</span>
+        <span class="n">wt</span><span class="p">[</span><span class="n">idx2</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">__TransWakeApprox</span><span class="p">(</span><span class="n">time</span><span class="p">[</span><span class="n">idx2</span><span class="p">])</span>
+        <span class="k">return</span> <span class="n">wt</span></div>
+
+    <span class="k">def</span> <span class="nf">__LongWakeExact</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">time</span><span class="p">,</span> <span class="n">atol</span><span class="p">):</span>
+        <span class="n">wl</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros_like</span><span class="p">(</span><span class="n">time</span><span class="p">)</span>
+        <span class="n">factor</span> <span class="o">=</span> <span class="mi">4</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">Z0</span> <span class="o">*</span> <span class="n">c</span> <span class="o">/</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">radius</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">length</span>
+        <span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">t</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">time</span><span class="p">):</span>
+            <span class="n">val</span><span class="p">,</span> <span class="n">err</span> <span class="o">=</span> <span class="n">quad</span><span class="p">(</span><span class="k">lambda</span> <span class="n">z</span><span class="p">:</span> <span class="bp">self</span><span class="o">.</span><span class="n">__function</span><span class="p">(</span><span class="n">t</span><span class="p">,</span> <span class="n">z</span><span class="p">),</span> <span class="mi">0</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">inf</span><span class="p">)</span>
+            <span class="n">wl</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="n">factor</span> <span class="o">*</span> <span class="p">(</span>
+                <span class="n">np</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="o">-</span><span class="n">t</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">t0</span><span class="p">)</span> <span class="o">/</span> <span class="mi">3</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="mi">3</span><span class="p">)</span> <span class="o">*</span> <span class="n">t</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">t0</span><span class="p">)</span> <span class="o">-</span>
+                <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span> <span class="o">/</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="n">val</span><span class="p">)</span>
+            <span class="k">if</span> <span class="n">np</span><span class="o">.</span><span class="n">isclose</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">t</span><span class="p">,</span> <span class="n">atol</span><span class="o">=</span><span class="n">atol</span><span class="p">):</span>
+                <span class="n">wl</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="n">wl</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">/</span> <span class="mi">2</span>
+        <span class="k">return</span> <span class="n">wl</span>
+
+    <span class="k">def</span> <span class="nf">__TransWakeExact</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">time</span><span class="p">):</span>
+        <span class="n">wt</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros_like</span><span class="p">(</span><span class="n">time</span><span class="p">)</span>
+        <span class="n">factor</span> <span class="o">=</span> <span class="p">((</span><span class="mi">8</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">Z0</span> <span class="o">*</span> <span class="n">c</span><span class="o">**</span><span class="mi">2</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">t0</span><span class="p">)</span> <span class="o">/</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">radius</span><span class="o">**</span><span class="mi">4</span><span class="p">)</span> <span class="o">*</span>
+                  <span class="bp">self</span><span class="o">.</span><span class="n">length</span><span class="p">)</span>
+        <span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">t</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">time</span><span class="p">):</span>
+            <span class="n">val</span><span class="p">,</span> <span class="n">err</span> <span class="o">=</span> <span class="n">quad</span><span class="p">(</span><span class="k">lambda</span> <span class="n">z</span><span class="p">:</span> <span class="bp">self</span><span class="o">.</span><span class="n">__function2</span><span class="p">(</span><span class="n">t</span><span class="p">,</span> <span class="n">z</span><span class="p">),</span> <span class="mi">0</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">inf</span><span class="p">)</span>
+            <span class="n">wt</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="n">factor</span> <span class="o">*</span> <span class="p">(</span>
+                <span class="mi">1</span> <span class="o">/</span> <span class="mi">12</span> <span class="o">*</span>
+                <span class="p">(</span><span class="o">-</span><span class="mi">1</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="o">-</span><span class="n">t</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">t0</span><span class="p">)</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="mi">3</span><span class="p">)</span> <span class="o">*</span> <span class="n">t</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">t0</span><span class="p">)</span> <span class="o">+</span>
+                 <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="mi">3</span><span class="p">)</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="o">-</span><span class="n">t</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">t0</span><span class="p">)</span> <span class="o">*</span>
+                 <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="mi">3</span><span class="p">)</span> <span class="o">*</span> <span class="n">t</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">t0</span><span class="p">))</span> <span class="o">-</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span> <span class="o">/</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="n">val</span><span class="p">)</span>
+        <span class="k">return</span> <span class="n">wt</span>
+
+    <span class="k">def</span> <span class="nf">__LongWakeApprox</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">t</span><span class="p">):</span>
+        <span class="n">wl</span> <span class="o">=</span> <span class="o">-</span><span class="mi">1</span> <span class="o">*</span> <span class="p">(</span><span class="mi">1</span> <span class="o">/</span> <span class="p">(</span><span class="mi">4</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">radius</span><span class="p">)</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">Z0</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">rho</span> <span class="o">/</span>
+                                                           <span class="p">(</span><span class="n">c</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span><span class="p">))</span> <span class="o">/</span>
+                   <span class="n">t</span><span class="o">**</span><span class="p">(</span><span class="mi">3</span> <span class="o">/</span> <span class="mi">2</span><span class="p">))</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">length</span>
+        <span class="k">return</span> <span class="n">wl</span>
+
+    <span class="k">def</span> <span class="nf">__TransWakeApprox</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">t</span><span class="p">):</span>
+        <span class="n">wt</span> <span class="o">=</span> <span class="p">(</span><span class="mi">1</span> <span class="o">/</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">radius</span><span class="o">**</span><span class="mi">3</span><span class="p">)</span> <span class="o">*</span>
+              <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">Z0</span> <span class="o">*</span> <span class="n">c</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">rho</span> <span class="o">/</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span><span class="p">)</span> <span class="o">/</span> <span class="n">t</span><span class="o">**</span><span class="p">(</span><span class="mi">1</span> <span class="o">/</span> <span class="mi">2</span><span class="p">)</span> <span class="o">*</span>
+              <span class="bp">self</span><span class="o">.</span><span class="n">length</span><span class="p">)</span>
+        <span class="k">return</span> <span class="n">wt</span>
+
+    <span class="k">def</span> <span class="nf">__function</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">t</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span>
+        <span class="k">return</span> <span class="p">((</span><span class="n">x</span><span class="o">**</span><span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span> <span class="o">*</span> <span class="p">(</span><span class="n">x</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span> <span class="o">*</span> <span class="n">t</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">t0</span><span class="p">))</span> <span class="o">/</span> <span class="p">(</span><span class="n">x</span><span class="o">**</span><span class="mi">6</span> <span class="o">+</span> <span class="mi">8</span><span class="p">))</span>
+
+    <span class="k">def</span> <span class="nf">__function2</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">t</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span>
+        <span class="k">return</span> <span class="p">((</span><span class="o">-</span><span class="mi">1</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span> <span class="o">*</span> <span class="p">(</span><span class="n">x</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span> <span class="o">*</span> <span class="n">t</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">t0</span><span class="p">))</span> <span class="o">/</span> <span class="p">(</span><span class="n">x</span><span class="o">**</span><span class="mi">6</span> <span class="o">+</span> <span class="mi">8</span><span class="p">))</span></div>
+
+
+<div class="viewcode-block" id="Coating"><a class="viewcode-back" href="../../../mbtrack2.impedance.html#mbtrack2.impedance.resistive_wall.Coating">[docs]</a><span class="k">class</span> <span class="nc">Coating</span><span class="p">(</span><span class="n">WakeField</span><span class="p">):</span>
+
+    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span>
+                 <span class="n">frequency</span><span class="p">,</span>
+                 <span class="n">length</span><span class="p">,</span>
+                 <span class="n">rho1</span><span class="p">,</span>
+                 <span class="n">rho2</span><span class="p">,</span>
+                 <span class="n">radius</span><span class="p">,</span>
+                 <span class="n">thickness</span><span class="p">,</span>
+                 <span class="n">approx</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        WakeField element for a coated circular beam pipe.</span>
+<span class="sd">        </span>
+<span class="sd">        The longitudinal and tranverse impedances are computed using formulas</span>
+<span class="sd">        from [1].</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        f : array of float</span>
+<span class="sd">            Frequency points where the impedance is evaluated in [Hz].</span>
+<span class="sd">        length : float</span>
+<span class="sd">            Length of the beam pipe to consider in [m].</span>
+<span class="sd">        rho1 : float</span>
+<span class="sd">            Resistivity of the coating in [ohm.m].</span>
+<span class="sd">        rho2 : float</span>
+<span class="sd">            Resistivity of the bulk material in [ohm.m].</span>
+<span class="sd">        radius : float</span>
+<span class="sd">            Radius of the beam pipe to consier in [m].</span>
+<span class="sd">        thickness : float</span>
+<span class="sd">            Thickness of the coating in [m].</span>
+<span class="sd">        approx : bool, optional</span>
+<span class="sd">            If True, used approxmiated formula. The default is False.</span>
+
+<span class="sd">        References</span>
+<span class="sd">        ----------</span>
+<span class="sd">        [1] : Migliorati, M., E. Belli, and M. Zobov. &quot;Impact of the resistive </span>
+<span class="sd">        wall impedance on beam dynamics in the Future Circular e+ e− Collider.&quot; </span>
+<span class="sd">        Physical Review Accelerators and Beams 21.4 (2018): 041001.</span>
+
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__init__</span><span class="p">()</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">length</span> <span class="o">=</span> <span class="n">length</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">rho1</span> <span class="o">=</span> <span class="n">rho1</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">rho2</span> <span class="o">=</span> <span class="n">rho2</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">radius</span> <span class="o">=</span> <span class="n">radius</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">thickness</span> <span class="o">=</span> <span class="n">thickness</span>
+
+        <span class="n">Zl</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">LongitudinalImpedance</span><span class="p">(</span><span class="n">frequency</span><span class="p">,</span> <span class="n">approx</span><span class="p">)</span>
+        <span class="n">Zt</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">TransverseImpedance</span><span class="p">(</span><span class="n">frequency</span><span class="p">,</span> <span class="n">approx</span><span class="p">)</span>
+
+        <span class="n">Zlong</span> <span class="o">=</span> <span class="n">Impedance</span><span class="p">(</span><span class="n">variable</span><span class="o">=</span><span class="n">frequency</span><span class="p">,</span>
+                          <span class="n">function</span><span class="o">=</span><span class="n">Zl</span><span class="p">,</span>
+                          <span class="n">component_type</span><span class="o">=</span><span class="s1">&#39;long&#39;</span><span class="p">)</span>
+        <span class="n">Zxdip</span> <span class="o">=</span> <span class="n">Impedance</span><span class="p">(</span><span class="n">variable</span><span class="o">=</span><span class="n">frequency</span><span class="p">,</span>
+                          <span class="n">function</span><span class="o">=</span><span class="n">Zt</span><span class="p">,</span>
+                          <span class="n">component_type</span><span class="o">=</span><span class="s1">&#39;xdip&#39;</span><span class="p">)</span>
+        <span class="n">Zydip</span> <span class="o">=</span> <span class="n">Impedance</span><span class="p">(</span><span class="n">variable</span><span class="o">=</span><span class="n">frequency</span><span class="p">,</span>
+                          <span class="n">function</span><span class="o">=</span><span class="n">Zt</span><span class="p">,</span>
+                          <span class="n">component_type</span><span class="o">=</span><span class="s1">&#39;ydip&#39;</span><span class="p">)</span>
+
+        <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="n">append_to_model</span><span class="p">(</span><span class="n">Zlong</span><span class="p">)</span>
+        <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="n">append_to_model</span><span class="p">(</span><span class="n">Zxdip</span><span class="p">)</span>
+        <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="n">append_to_model</span><span class="p">(</span><span class="n">Zydip</span><span class="p">)</span>
+
+<div class="viewcode-block" id="Coating.LongitudinalImpedance"><a class="viewcode-back" href="../../../mbtrack2.impedance.html#mbtrack2.impedance.resistive_wall.Coating.LongitudinalImpedance">[docs]</a>    <span class="k">def</span> <span class="nf">LongitudinalImpedance</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">f</span><span class="p">,</span> <span class="n">approx</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Compute the longitudinal impedance of a coating using Eq. (5), or </span>
+<span class="sd">        approxmiated expression Eq. (8), of [1]. The approxmiated expression </span>
+<span class="sd">        is valid if the skin depth of the coating is large compared to the </span>
+<span class="sd">        coating thickness. </span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        f : array of float</span>
+<span class="sd">            Frequency points where the impedance is evaluated in [Hz].</span>
+<span class="sd">        approx : bool</span>
+<span class="sd">            If True, used approxmiated formula.</span>
+
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        Zl : array</span>
+<span class="sd">            Longitudinal impedance values in [ohm].</span>
+<span class="sd">            </span>
+<span class="sd">        References</span>
+<span class="sd">        ----------</span>
+<span class="sd">        [1] : Migliorati, M., E. Belli, and M. Zobov. &quot;Impact of the resistive </span>
+<span class="sd">        wall impedance on beam dynamics in the Future Circular e+ e− Collider.&quot; </span>
+<span class="sd">        Physical Review Accelerators and Beams 21.4 (2018): 041001.</span>
+
+<span class="sd">        &quot;&quot;&quot;</span>
+
+        <span class="n">Z0</span> <span class="o">=</span> <span class="n">mu_0</span> <span class="o">*</span> <span class="n">c</span>
+        <span class="n">factor</span> <span class="o">=</span> <span class="n">Z0</span> <span class="o">*</span> <span class="n">f</span> <span class="o">/</span> <span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">c</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">radius</span><span class="p">)</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">length</span>
+        <span class="n">skin1</span> <span class="o">=</span> <span class="n">skin_depth</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">rho1</span><span class="p">)</span>
+        <span class="n">skin2</span> <span class="o">=</span> <span class="n">skin_depth</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">rho2</span><span class="p">)</span>
+
+        <span class="k">if</span> <span class="n">approx</span> <span class="o">==</span> <span class="kc">False</span><span class="p">:</span>
+            <span class="n">alpha</span> <span class="o">=</span> <span class="n">skin1</span> <span class="o">/</span> <span class="n">skin2</span>
+            <span class="n">tanh</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">tanh</span><span class="p">((</span><span class="mi">1</span> <span class="o">+</span> <span class="mi">1</span><span class="n">j</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sign</span><span class="p">(</span><span class="n">f</span><span class="p">))</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">thickness</span> <span class="o">/</span> <span class="n">skin1</span><span class="p">)</span>
+            <span class="n">bracket</span> <span class="o">=</span> <span class="p">((</span><span class="n">np</span><span class="o">.</span><span class="n">sign</span><span class="p">(</span><span class="n">f</span><span class="p">)</span> <span class="o">+</span> <span class="mi">1</span><span class="n">j</span><span class="p">)</span> <span class="o">*</span> <span class="n">skin1</span> <span class="o">*</span> <span class="p">(</span><span class="n">alpha</span><span class="o">*</span><span class="n">tanh</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span> <span class="o">/</span>
+                       <span class="p">(</span><span class="n">alpha</span><span class="o">+</span><span class="n">tanh</span><span class="p">))</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="n">valid_approx</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">thickness</span> <span class="o">/</span> <span class="n">np</span><span class="o">.</span><span class="n">min</span><span class="p">(</span><span class="n">skin1</span><span class="p">)</span>
+            <span class="k">if</span> <span class="n">valid_approx</span> <span class="o">&lt;</span> <span class="mf">0.01</span><span class="p">:</span>
+                <span class="nb">print</span><span class="p">(</span>
+                    <span class="s2">&quot;Approximation is not valid. Returning impedance anyway.&quot;</span><span class="p">)</span>
+            <span class="n">bracket</span> <span class="o">=</span> <span class="p">((</span><span class="n">np</span><span class="o">.</span><span class="n">sign</span><span class="p">(</span><span class="n">f</span><span class="p">)</span> <span class="o">+</span> <span class="mi">1</span><span class="n">j</span><span class="p">)</span> <span class="o">*</span> <span class="n">skin2</span> <span class="o">+</span> <span class="mi">2</span> <span class="o">*</span> <span class="mi">1</span><span class="n">j</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">thickness</span> <span class="o">*</span>
+                       <span class="p">(</span><span class="mi">1</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">rho2</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">rho1</span><span class="p">))</span>
+
+        <span class="n">Zl</span> <span class="o">=</span> <span class="n">factor</span> <span class="o">*</span> <span class="n">bracket</span>
+
+        <span class="k">return</span> <span class="n">Zl</span></div>
+
+<div class="viewcode-block" id="Coating.TransverseImpedance"><a class="viewcode-back" href="../../../mbtrack2.impedance.html#mbtrack2.impedance.resistive_wall.Coating.TransverseImpedance">[docs]</a>    <span class="k">def</span> <span class="nf">TransverseImpedance</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">f</span><span class="p">,</span> <span class="n">approx</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Compute the transverse impedance of a coating using Eq. (6), or </span>
+<span class="sd">        approxmiated expression Eq. (9), of [1]. The approxmiated expression </span>
+<span class="sd">        is valid if the skin depth of the coating is large compared to the </span>
+<span class="sd">        coating thickness. </span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        f : array of float</span>
+<span class="sd">            Frequency points where the impedance is evaluated in [Hz].</span>
+<span class="sd">        approx : bool</span>
+<span class="sd">            If True, used approxmiated formula.</span>
+
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        Zt : array</span>
+<span class="sd">            Transverse impedance values in [ohm].</span>
+<span class="sd">            </span>
+<span class="sd">        References</span>
+<span class="sd">        ----------</span>
+<span class="sd">        [1] : Migliorati, M., E. Belli, and M. Zobov. &quot;Impact of the resistive </span>
+<span class="sd">        wall impedance on beam dynamics in the Future Circular e+ e− Collider.&quot; </span>
+<span class="sd">        Physical Review Accelerators and Beams 21.4 (2018): 041001.</span>
+
+<span class="sd">        &quot;&quot;&quot;</span>
+
+        <span class="n">Z0</span> <span class="o">=</span> <span class="n">mu_0</span> <span class="o">*</span> <span class="n">c</span>
+        <span class="n">factor</span> <span class="o">=</span> <span class="n">Z0</span> <span class="o">/</span> <span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">radius</span><span class="o">**</span><span class="mi">3</span><span class="p">)</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">length</span>
+        <span class="n">skin1</span> <span class="o">=</span> <span class="n">skin_depth</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">rho1</span><span class="p">)</span>
+        <span class="n">skin2</span> <span class="o">=</span> <span class="n">skin_depth</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">rho2</span><span class="p">)</span>
+
+        <span class="k">if</span> <span class="n">approx</span> <span class="o">==</span> <span class="kc">False</span><span class="p">:</span>
+            <span class="n">alpha</span> <span class="o">=</span> <span class="n">skin1</span> <span class="o">/</span> <span class="n">skin2</span>
+            <span class="n">tanh</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">tanh</span><span class="p">((</span><span class="mi">1</span> <span class="o">+</span> <span class="mi">1</span><span class="n">j</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sign</span><span class="p">(</span><span class="n">f</span><span class="p">))</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">thickness</span> <span class="o">/</span> <span class="n">skin1</span><span class="p">)</span>
+            <span class="n">bracket</span> <span class="o">=</span> <span class="p">((</span><span class="mi">1</span> <span class="o">+</span> <span class="mi">1</span><span class="n">j</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sign</span><span class="p">(</span><span class="n">f</span><span class="p">))</span> <span class="o">*</span> <span class="n">skin1</span> <span class="o">*</span> <span class="p">(</span><span class="n">alpha</span><span class="o">*</span><span class="n">tanh</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span> <span class="o">/</span>
+                       <span class="p">(</span><span class="n">alpha</span><span class="o">+</span><span class="n">tanh</span><span class="p">))</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="n">valid_approx</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">thickness</span> <span class="o">/</span> <span class="n">np</span><span class="o">.</span><span class="n">min</span><span class="p">(</span><span class="n">skin1</span><span class="p">)</span>
+            <span class="k">if</span> <span class="n">valid_approx</span> <span class="o">&lt;</span> <span class="mf">0.01</span><span class="p">:</span>
+                <span class="nb">print</span><span class="p">(</span>
+                    <span class="s2">&quot;Approximation is not valid. Returning impedance anyway.&quot;</span><span class="p">)</span>
+            <span class="n">bracket</span> <span class="o">=</span> <span class="p">((</span><span class="mi">1</span> <span class="o">+</span> <span class="mi">1</span><span class="n">j</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sign</span><span class="p">(</span><span class="n">f</span><span class="p">))</span> <span class="o">*</span> <span class="n">skin2</span> <span class="o">+</span>
+                       <span class="mi">2</span> <span class="o">*</span> <span class="mi">1</span><span class="n">j</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">thickness</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sign</span><span class="p">(</span><span class="n">f</span><span class="p">)</span> <span class="o">*</span>
+                       <span class="p">(</span><span class="mi">1</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">rho2</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">rho1</span><span class="p">))</span>
+
+        <span class="n">Zt</span> <span class="o">=</span> <span class="n">factor</span> <span class="o">*</span> <span class="n">bracket</span>
+
+        <span class="k">return</span> <span class="n">Zt</span></div></div>
+</pre></div>
+
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new file mode 100644
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+
+<!DOCTYPE html>
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+  <h1>Source code for mbtrack2.impedance.resonator</h1><div class="highlight"><pre>
+<span></span><span class="c1"># -*- coding: utf-8 -*-</span>
+<span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">This module defines the impedances and wake functions from the resonator model </span>
+<span class="sd">based on the WakeField class.</span>
+<span class="sd">&quot;&quot;&quot;</span>
+
+<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
+
+<span class="kn">from</span> <span class="nn">mbtrack2.impedance.wakefield</span> <span class="kn">import</span> <span class="n">Impedance</span><span class="p">,</span> <span class="n">WakeField</span><span class="p">,</span> <span class="n">WakeFunction</span>
+
+
+<div class="viewcode-block" id="Resonator"><a class="viewcode-back" href="../../../mbtrack2.impedance.html#mbtrack2.impedance.resonator.Resonator">[docs]</a><span class="k">class</span> <span class="nc">Resonator</span><span class="p">(</span><span class="n">WakeField</span><span class="p">):</span>
+
+    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">time</span><span class="p">,</span> <span class="n">frequency</span><span class="p">,</span> <span class="n">Rs</span><span class="p">,</span> <span class="n">fr</span><span class="p">,</span> <span class="n">Q</span><span class="p">,</span> <span class="n">plane</span><span class="p">,</span> <span class="n">atol</span><span class="o">=</span><span class="mf">1e-20</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Resonator model WakeField element which computes the impedance and the </span>
+<span class="sd">        wake function in both longitudinal and transverse case.</span>
+<span class="sd">        </span>
+<span class="sd">        ! For transverse case, if Q &lt; 2, there is a kick factor mismatch </span>
+<span class="sd">        between time and frequency domain.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        time : array of float</span>
+<span class="sd">            Time points where the wake function will be evaluated in [s].</span>
+<span class="sd">        frequency : array of float</span>
+<span class="sd">            Frequency points where the impedance will be evaluated in [Hz].</span>
+<span class="sd">        Rs : float</span>
+<span class="sd">            Shunt impedance in [ohm] in longitudinal or [ohm/m] in transverse.</span>
+<span class="sd">        fr : float</span>
+<span class="sd">            Resonance frequency in [Hz].</span>
+<span class="sd">        Q : float</span>
+<span class="sd">            Quality factor.</span>
+<span class="sd">        plane : str or list</span>
+<span class="sd">            Plane on which the resonator is used: &quot;long&quot;, &quot;x&quot; or &quot;y&quot;.</span>
+<span class="sd">        atol : float, optional</span>
+<span class="sd">            Absolute tolerance used to enforce fundamental theorem of beam </span>
+<span class="sd">            loading for the exact expression of the longitudinal wake function.</span>
+<span class="sd">            Default is 1e-20.</span>
+<span class="sd">            </span>
+<span class="sd">        References</span>
+<span class="sd">        ----------</span>
+<span class="sd">        [1]  B. W. Zotter and S. A. Kheifets, &quot;Impedances and Wakes in High-Energy </span>
+<span class="sd">        Particle Ac-celerators&quot;, Eq. (3.10) and (3.15), pp.51-53.</span>
+
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__init__</span><span class="p">()</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">Rs</span> <span class="o">=</span> <span class="n">Rs</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">fr</span> <span class="o">=</span> <span class="n">fr</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">wr</span> <span class="o">=</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">fr</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">Q</span> <span class="o">=</span> <span class="n">Q</span>
+        <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">plane</span><span class="p">,</span> <span class="nb">str</span><span class="p">):</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">plane</span> <span class="o">=</span> <span class="p">[</span><span class="n">plane</span><span class="p">]</span>
+        <span class="k">elif</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">plane</span><span class="p">,</span> <span class="nb">list</span><span class="p">):</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">plane</span> <span class="o">=</span> <span class="n">plane</span>
+
+        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">Q</span> <span class="o">&gt;=</span> <span class="mf">0.5</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">Q_p</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">Q</span><span class="o">**</span><span class="mi">2</span> <span class="o">-</span> <span class="mf">0.25</span><span class="p">)</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">Q_p</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="mf">0.25</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">Q</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">wr_p</span> <span class="o">=</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">wr</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">Q_p</span><span class="p">)</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">Q</span>
+
+        <span class="k">for</span> <span class="n">dim</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">plane</span><span class="p">:</span>
+            <span class="k">if</span> <span class="n">dim</span> <span class="o">==</span> <span class="s2">&quot;long&quot;</span><span class="p">:</span>
+                <span class="n">Zlong</span> <span class="o">=</span> <span class="n">Impedance</span><span class="p">(</span><span class="n">variable</span><span class="o">=</span><span class="n">frequency</span><span class="p">,</span>
+                                  <span class="n">function</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">long_impedance</span><span class="p">(</span><span class="n">frequency</span><span class="p">),</span>
+                                  <span class="n">component_type</span><span class="o">=</span><span class="s2">&quot;long&quot;</span><span class="p">)</span>
+                <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="n">append_to_model</span><span class="p">(</span><span class="n">Zlong</span><span class="p">)</span>
+                <span class="n">Wlong</span> <span class="o">=</span> <span class="n">WakeFunction</span><span class="p">(</span><span class="n">variable</span><span class="o">=</span><span class="n">time</span><span class="p">,</span>
+                                     <span class="n">function</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">long_wake_function</span><span class="p">(</span>
+                                         <span class="n">time</span><span class="p">,</span> <span class="n">atol</span><span class="p">),</span>
+                                     <span class="n">component_type</span><span class="o">=</span><span class="s2">&quot;long&quot;</span><span class="p">)</span>
+                <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="n">append_to_model</span><span class="p">(</span><span class="n">Wlong</span><span class="p">)</span>
+
+            <span class="k">elif</span> <span class="n">dim</span> <span class="o">==</span> <span class="s2">&quot;x&quot;</span> <span class="ow">or</span> <span class="n">dim</span> <span class="o">==</span> <span class="s2">&quot;y&quot;</span><span class="p">:</span>
+                <span class="n">Zdip</span> <span class="o">=</span> <span class="n">Impedance</span><span class="p">(</span><span class="n">variable</span><span class="o">=</span><span class="n">frequency</span><span class="p">,</span>
+                                 <span class="n">function</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">transverse_impedance</span><span class="p">(</span><span class="n">frequency</span><span class="p">),</span>
+                                 <span class="n">component_type</span><span class="o">=</span><span class="n">dim</span> <span class="o">+</span> <span class="s2">&quot;dip&quot;</span><span class="p">)</span>
+                <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="n">append_to_model</span><span class="p">(</span><span class="n">Zdip</span><span class="p">)</span>
+                <span class="n">Wdip</span> <span class="o">=</span> <span class="n">WakeFunction</span><span class="p">(</span>
+                    <span class="n">variable</span><span class="o">=</span><span class="n">time</span><span class="p">,</span>
+                    <span class="n">function</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">transverse_wake_function</span><span class="p">(</span><span class="n">time</span><span class="p">),</span>
+                    <span class="n">component_type</span><span class="o">=</span><span class="n">dim</span> <span class="o">+</span> <span class="s2">&quot;dip&quot;</span><span class="p">)</span>
+                <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="n">append_to_model</span><span class="p">(</span><span class="n">Wdip</span><span class="p">)</span>
+            <span class="k">else</span><span class="p">:</span>
+                <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">&quot;Plane must be: long, x or y&quot;</span><span class="p">)</span>
+
+<div class="viewcode-block" id="Resonator.long_wake_function"><a class="viewcode-back" href="../../../mbtrack2.impedance.html#mbtrack2.impedance.resonator.Resonator.long_wake_function">[docs]</a>    <span class="k">def</span> <span class="nf">long_wake_function</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">t</span><span class="p">,</span> <span class="n">atol</span><span class="p">):</span>
+        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">Q</span> <span class="o">&gt;=</span> <span class="mf">0.5</span><span class="p">:</span>
+            <span class="n">wl</span> <span class="o">=</span> <span class="p">((</span><span class="bp">self</span><span class="o">.</span><span class="n">wr</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">Rs</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">Q</span><span class="p">)</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">wr</span> <span class="o">*</span> <span class="n">t</span> <span class="o">/</span>
+                                                        <span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">Q</span><span class="p">))</span> <span class="o">*</span>
+                  <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">wr_p</span> <span class="o">*</span> <span class="n">t</span><span class="p">)</span> <span class="o">-</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">wr_p</span> <span class="o">*</span> <span class="n">t</span><span class="p">)</span> <span class="o">/</span>
+                   <span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">Q_p</span><span class="p">)))</span>
+        <span class="k">elif</span> <span class="bp">self</span><span class="o">.</span><span class="n">Q</span> <span class="o">&lt;</span> <span class="mf">0.5</span><span class="p">:</span>
+            <span class="n">wl</span> <span class="o">=</span> <span class="p">((</span><span class="bp">self</span><span class="o">.</span><span class="n">wr</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">Rs</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">Q</span><span class="p">)</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">wr</span> <span class="o">*</span> <span class="n">t</span> <span class="o">/</span>
+                                                        <span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">Q</span><span class="p">))</span> <span class="o">*</span>
+                  <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">cosh</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">wr_p</span> <span class="o">*</span> <span class="n">t</span><span class="p">)</span> <span class="o">-</span> <span class="n">np</span><span class="o">.</span><span class="n">sinh</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">wr_p</span> <span class="o">*</span> <span class="n">t</span><span class="p">)</span> <span class="o">/</span>
+                   <span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">Q_p</span><span class="p">)))</span>
+        <span class="k">if</span> <span class="n">np</span><span class="o">.</span><span class="n">any</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">t</span><span class="p">)</span> <span class="o">&lt;</span> <span class="n">atol</span><span class="p">):</span>
+            <span class="n">wl</span><span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">t</span><span class="p">)</span> <span class="o">&lt;</span> <span class="n">atol</span><span class="p">]</span> <span class="o">=</span> <span class="n">wl</span><span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">t</span><span class="p">)</span> <span class="o">&lt;</span> <span class="n">atol</span><span class="p">]</span> <span class="o">/</span> <span class="mi">2</span>
+        <span class="k">if</span> <span class="n">np</span><span class="o">.</span><span class="n">any</span><span class="p">(</span><span class="n">t</span> <span class="o">&lt;</span> <span class="o">-</span><span class="n">atol</span><span class="p">):</span>
+            <span class="n">wl</span><span class="p">[</span><span class="n">t</span> <span class="o">&lt;</span> <span class="o">-</span><span class="n">atol</span><span class="p">]</span> <span class="o">=</span> <span class="mi">0</span>
+        <span class="k">return</span> <span class="n">wl</span></div>
+
+<div class="viewcode-block" id="Resonator.long_impedance"><a class="viewcode-back" href="../../../mbtrack2.impedance.html#mbtrack2.impedance.resonator.Resonator.long_impedance">[docs]</a>    <span class="k">def</span> <span class="nf">long_impedance</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">f</span><span class="p">):</span>
+        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">Rs</span> <span class="o">/</span> <span class="p">(</span><span class="mi">1</span> <span class="o">+</span> <span class="mi">1</span><span class="n">j</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">Q</span> <span class="o">*</span> <span class="p">(</span><span class="n">f</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">fr</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">fr</span> <span class="o">/</span> <span class="n">f</span><span class="p">))</span></div>
+
+<div class="viewcode-block" id="Resonator.transverse_impedance"><a class="viewcode-back" href="../../../mbtrack2.impedance.html#mbtrack2.impedance.resonator.Resonator.transverse_impedance">[docs]</a>    <span class="k">def</span> <span class="nf">transverse_impedance</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">f</span><span class="p">):</span>
+        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">Rs</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">fr</span> <span class="o">/</span> <span class="n">f</span> <span class="o">/</span> <span class="p">(</span><span class="mi">1</span> <span class="o">+</span> <span class="mi">1</span><span class="n">j</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">Q</span> <span class="o">*</span>
+                                        <span class="p">(</span><span class="n">f</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">fr</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">fr</span> <span class="o">/</span> <span class="n">f</span><span class="p">))</span></div>
+
+<div class="viewcode-block" id="Resonator.transverse_wake_function"><a class="viewcode-back" href="../../../mbtrack2.impedance.html#mbtrack2.impedance.resonator.Resonator.transverse_wake_function">[docs]</a>    <span class="k">def</span> <span class="nf">transverse_wake_function</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">t</span><span class="p">):</span>
+        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">Q</span> <span class="o">&gt;=</span> <span class="mf">0.5</span><span class="p">:</span>
+            <span class="n">wt</span> <span class="o">=</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">wr</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">Rs</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">Q_p</span> <span class="o">*</span>
+                  <span class="n">np</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span> <span class="o">*</span> <span class="n">t</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">wr</span> <span class="o">/</span> <span class="mi">2</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">Q_p</span><span class="p">)</span> <span class="o">*</span>
+                  <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">wr_p</span> <span class="o">*</span> <span class="n">t</span><span class="p">))</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="n">wt</span> <span class="o">=</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">wr</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">Rs</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">Q_p</span> <span class="o">*</span>
+                  <span class="n">np</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span> <span class="o">*</span> <span class="n">t</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">wr</span> <span class="o">/</span> <span class="mi">2</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">Q_p</span><span class="p">)</span> <span class="o">*</span>
+                  <span class="n">np</span><span class="o">.</span><span class="n">sinh</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">wr_p</span> <span class="o">*</span> <span class="n">t</span><span class="p">))</span>
+        <span class="k">if</span> <span class="n">np</span><span class="o">.</span><span class="n">any</span><span class="p">(</span><span class="n">t</span> <span class="o">&lt;</span> <span class="mi">0</span><span class="p">):</span>
+            <span class="n">wt</span><span class="p">[</span><span class="n">t</span> <span class="o">&lt;</span> <span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="mi">0</span>
+        <span class="k">return</span> <span class="n">wt</span></div></div>
+
+
+<div class="viewcode-block" id="PureInductive"><a class="viewcode-back" href="../../../mbtrack2.impedance.html#mbtrack2.impedance.resonator.PureInductive">[docs]</a><span class="k">class</span> <span class="nc">PureInductive</span><span class="p">(</span><span class="n">WakeField</span><span class="p">):</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    Pure inductive Wakefield element which computes associated longitudinal </span>
+<span class="sd">    impedance and wake function.</span>
+<span class="sd">    </span>
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">    L : float</span>
+<span class="sd">        Inductance value in [Ohm/Hz].</span>
+<span class="sd">    n_wake : int or float, optional</span>
+<span class="sd">        Number of points used in the wake function.</span>
+<span class="sd">    n_imp : int or float, optional</span>
+<span class="sd">        Number of points used in the impedance.</span>
+<span class="sd">    imp_freq_lim : float, optional</span>
+<span class="sd">        Maximum frequency used in the impedance. </span>
+<span class="sd">    nout, trim : see Impedance.to_wakefunction</span>
+<span class="sd">    &quot;&quot;&quot;</span>
+
+    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span>
+                 <span class="n">L</span><span class="p">,</span>
+                 <span class="n">n_wake</span><span class="o">=</span><span class="mf">1e6</span><span class="p">,</span>
+                 <span class="n">n_imp</span><span class="o">=</span><span class="mf">1e6</span><span class="p">,</span>
+                 <span class="n">imp_freq_lim</span><span class="o">=</span><span class="mf">1e11</span><span class="p">,</span>
+                 <span class="n">nout</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+                 <span class="n">trim</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">L</span> <span class="o">=</span> <span class="n">L</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">n_wake</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">n_wake</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">n_imp</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">n_imp</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">imp_freq_lim</span> <span class="o">=</span> <span class="n">imp_freq_lim</span>
+
+        <span class="n">freq</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="n">start</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">stop</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">imp_freq_lim</span><span class="p">,</span> <span class="n">num</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">n_imp</span><span class="p">)</span>
+        <span class="n">imp</span> <span class="o">=</span> <span class="n">Impedance</span><span class="p">(</span><span class="n">variable</span><span class="o">=</span><span class="n">freq</span><span class="p">,</span>
+                        <span class="n">function</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">long_impedance</span><span class="p">(</span><span class="n">freq</span><span class="p">),</span>
+                        <span class="n">component_type</span><span class="o">=</span><span class="s2">&quot;long&quot;</span><span class="p">)</span>
+        <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="n">append_to_model</span><span class="p">(</span><span class="n">imp</span><span class="p">)</span>
+
+        <span class="n">wf</span> <span class="o">=</span> <span class="n">imp</span><span class="o">.</span><span class="n">to_wakefunction</span><span class="p">(</span><span class="n">nout</span><span class="o">=</span><span class="n">nout</span><span class="p">,</span> <span class="n">trim</span><span class="o">=</span><span class="n">trim</span><span class="p">)</span>
+        <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="n">append_to_model</span><span class="p">(</span><span class="n">wf</span><span class="p">)</span>
+
+<div class="viewcode-block" id="PureInductive.long_impedance"><a class="viewcode-back" href="../../../mbtrack2.impedance.html#mbtrack2.impedance.resonator.PureInductive.long_impedance">[docs]</a>    <span class="k">def</span> <span class="nf">long_impedance</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">f</span><span class="p">):</span>
+        <span class="k">return</span> <span class="mi">1</span><span class="n">j</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">L</span> <span class="o">*</span> <span class="n">f</span></div></div>
+
+
+<div class="viewcode-block" id="PureResistive"><a class="viewcode-back" href="../../../mbtrack2.impedance.html#mbtrack2.impedance.resonator.PureResistive">[docs]</a><span class="k">class</span> <span class="nc">PureResistive</span><span class="p">(</span><span class="n">WakeField</span><span class="p">):</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    Pure resistive Wakefield element which computes associated longitudinal </span>
+<span class="sd">    impedance and wake function.</span>
+<span class="sd">    </span>
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">    R : float</span>
+<span class="sd">        Resistance value in [Ohm].</span>
+<span class="sd">    n_wake : int or float, optional</span>
+<span class="sd">        Number of points used in the wake function.</span>
+<span class="sd">    n_imp : int or float, optional</span>
+<span class="sd">        Number of points used in the impedance.</span>
+<span class="sd">    imp_freq_lim : float, optional</span>
+<span class="sd">        Maximum frequency used in the impedance. </span>
+<span class="sd">    nout, trim : see Impedance.to_wakefunction</span>
+<span class="sd">    &quot;&quot;&quot;</span>
+
+    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span>
+                 <span class="n">R</span><span class="p">,</span>
+                 <span class="n">n_wake</span><span class="o">=</span><span class="mf">1e6</span><span class="p">,</span>
+                 <span class="n">n_imp</span><span class="o">=</span><span class="mf">1e6</span><span class="p">,</span>
+                 <span class="n">imp_freq_lim</span><span class="o">=</span><span class="mf">1e11</span><span class="p">,</span>
+                 <span class="n">nout</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+                 <span class="n">trim</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">R</span> <span class="o">=</span> <span class="n">R</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">n_wake</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">n_wake</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">n_imp</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">n_imp</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">imp_freq_lim</span> <span class="o">=</span> <span class="n">imp_freq_lim</span>
+
+        <span class="n">freq</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="n">start</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">stop</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">imp_freq_lim</span><span class="p">,</span> <span class="n">num</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">n_imp</span><span class="p">)</span>
+        <span class="n">imp</span> <span class="o">=</span> <span class="n">Impedance</span><span class="p">(</span><span class="n">variable</span><span class="o">=</span><span class="n">freq</span><span class="p">,</span>
+                        <span class="n">function</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">long_impedance</span><span class="p">(</span><span class="n">freq</span><span class="p">),</span>
+                        <span class="n">component_type</span><span class="o">=</span><span class="s2">&quot;long&quot;</span><span class="p">)</span>
+        <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="n">append_to_model</span><span class="p">(</span><span class="n">imp</span><span class="p">)</span>
+
+        <span class="n">wf</span> <span class="o">=</span> <span class="n">imp</span><span class="o">.</span><span class="n">to_wakefunction</span><span class="p">(</span><span class="n">nout</span><span class="o">=</span><span class="n">nout</span><span class="p">,</span> <span class="n">trim</span><span class="o">=</span><span class="n">trim</span><span class="p">)</span>
+        <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="n">append_to_model</span><span class="p">(</span><span class="n">wf</span><span class="p">)</span>
+
+<div class="viewcode-block" id="PureResistive.long_impedance"><a class="viewcode-back" href="../../../mbtrack2.impedance.html#mbtrack2.impedance.resonator.PureResistive.long_impedance">[docs]</a>    <span class="k">def</span> <span class="nf">long_impedance</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">f</span><span class="p">):</span>
+        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">R</span></div></div>
+</pre></div>
+
+            <div class="clearer"></div>
+          </div>
+        </div>
+      </div>
+      <div class="sphinxsidebar" role="navigation" aria-label="main navigation">
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+<script>document.getElementById('searchbox').style.display = "block"</script>
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+        <li class="right" style="margin-right: 10px">
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+             >index</a></li>
+        <li class="right" >
+          <a href="../../../py-modindex.html" title="Python Module Index"
+             >modules</a> |</li>
+        <li class="nav-item nav-item-0"><a href="../../../index.html">mbtrack2 0.6.0 documentation</a> &#187;</li>
+          <li class="nav-item nav-item-1"><a href="../../index.html" >Module code</a> &#187;</li>
+        <li class="nav-item nav-item-this"><a href="">mbtrack2.impedance.resonator</a></li> 
+      </ul>
+    </div>
+    <div class="footer" role="contentinfo">
+        &#169; Copyright 2024, A. Gamelin et al.
+      Created using <a href="https://www.sphinx-doc.org/">Sphinx</a> 5.0.2.
+    </div>
+  </body>
+</html>
\ No newline at end of file
diff --git a/docs/build/html/_modules/mbtrack2/impedance/tapers.html b/docs/build/html/_modules/mbtrack2/impedance/tapers.html
new file mode 100644
index 0000000..ce74a42
--- /dev/null
+++ b/docs/build/html/_modules/mbtrack2/impedance/tapers.html
@@ -0,0 +1,324 @@
+
+<!DOCTYPE html>
+
+<html lang="en">
+  <head>
+    <meta charset="utf-8" />
+    <meta name="viewport" content="width=device-width, initial-scale=1.0" />
+    <title>mbtrack2.impedance.tapers &#8212; mbtrack2 0.6.0 documentation</title>
+    <link rel="stylesheet" type="text/css" href="../../../_static/pygments.css" />
+    <link rel="stylesheet" type="text/css" href="../../../_static/nature.css" />
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+    <script src="../../../_static/jquery.js"></script>
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+    <link rel="index" title="Index" href="../../../genindex.html" />
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+  </head><body>
+    <div class="related" role="navigation" aria-label="related navigation">
+      <h3>Navigation</h3>
+      <ul>
+        <li class="right" style="margin-right: 10px">
+          <a href="../../../genindex.html" title="General Index"
+             accesskey="I">index</a></li>
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+          <a href="../../../py-modindex.html" title="Python Module Index"
+             >modules</a> |</li>
+        <li class="nav-item nav-item-0"><a href="../../../index.html">mbtrack2 0.6.0 documentation</a> &#187;</li>
+          <li class="nav-item nav-item-1"><a href="../../index.html" accesskey="U">Module code</a> &#187;</li>
+        <li class="nav-item nav-item-this"><a href="">mbtrack2.impedance.tapers</a></li> 
+      </ul>
+    </div>  
+
+    <div class="document">
+      <div class="documentwrapper">
+        <div class="bodywrapper">
+          <div class="body" role="main">
+            
+  <h1>Source code for mbtrack2.impedance.tapers</h1><div class="highlight"><pre>
+<span></span><span class="c1"># -*- coding: utf-8 -*-</span>
+<span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">Module where taper elements are defined.</span>
+<span class="sd">&quot;&quot;&quot;</span>
+
+<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="kn">from</span> <span class="nn">scipy.constants</span> <span class="kn">import</span> <span class="n">c</span><span class="p">,</span> <span class="n">mu_0</span><span class="p">,</span> <span class="n">pi</span>
+<span class="kn">from</span> <span class="nn">scipy.integrate</span> <span class="kn">import</span> <span class="n">trapz</span>
+
+<span class="kn">from</span> <span class="nn">mbtrack2.impedance.wakefield</span> <span class="kn">import</span> <span class="n">Impedance</span><span class="p">,</span> <span class="n">WakeField</span>
+
+
+<div class="viewcode-block" id="StupakovRectangularTaper"><a class="viewcode-back" href="../../../mbtrack2.impedance.html#mbtrack2.impedance.tapers.StupakovRectangularTaper">[docs]</a><span class="k">class</span> <span class="nc">StupakovRectangularTaper</span><span class="p">(</span><span class="n">WakeField</span><span class="p">):</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    Rectangular vertical taper WakeField element, using the low frequency </span>
+<span class="sd">    approxmiation. Assume constant taper angle. Formulas from [1].</span>
+<span class="sd">    </span>
+<span class="sd">    ! Valid for low w</span>
+<span class="sd">    </span>
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">    frequency: frequency points where the impedance will be evaluated in [Hz]</span>
+<span class="sd">    gap_entrance : full vertical gap at taper entrance in [m]</span>
+<span class="sd">    gap_exit: full vertical gap at taper exit in [m]</span>
+<span class="sd">    length: taper length in [m]</span>
+<span class="sd">    width : full horizontal width of the taper in [m]</span>
+<span class="sd">    &quot;&quot;&quot;</span>
+
+    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span>
+                 <span class="n">frequency</span><span class="p">,</span>
+                 <span class="n">gap_entrance</span><span class="p">,</span>
+                 <span class="n">gap_exit</span><span class="p">,</span>
+                 <span class="n">length</span><span class="p">,</span>
+                 <span class="n">width</span><span class="p">,</span>
+                 <span class="n">m_max</span><span class="o">=</span><span class="mi">100</span><span class="p">,</span>
+                 <span class="n">n_points</span><span class="o">=</span><span class="nb">int</span><span class="p">(</span><span class="mf">1e4</span><span class="p">)):</span>
+        <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__init__</span><span class="p">()</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">frequency</span> <span class="o">=</span> <span class="n">frequency</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">gap_entrance</span> <span class="o">=</span> <span class="n">gap_entrance</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">gap_exit</span> <span class="o">=</span> <span class="n">gap_exit</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">length</span> <span class="o">=</span> <span class="n">length</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">width</span> <span class="o">=</span> <span class="n">width</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">m_max</span> <span class="o">=</span> <span class="n">m_max</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">n_points</span> <span class="o">=</span> <span class="n">n_points</span>
+
+        <span class="n">Zlong</span> <span class="o">=</span> <span class="n">Impedance</span><span class="p">(</span><span class="n">variable</span><span class="o">=</span><span class="n">frequency</span><span class="p">,</span>
+                          <span class="n">function</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">long</span><span class="p">(),</span>
+                          <span class="n">component_type</span><span class="o">=</span><span class="s1">&#39;long&#39;</span><span class="p">)</span>
+        <span class="n">Zxdip</span> <span class="o">=</span> <span class="n">Impedance</span><span class="p">(</span><span class="n">variable</span><span class="o">=</span><span class="n">frequency</span><span class="p">,</span>
+                          <span class="n">function</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">xdip</span><span class="p">(),</span>
+                          <span class="n">component_type</span><span class="o">=</span><span class="s1">&#39;xdip&#39;</span><span class="p">)</span>
+        <span class="n">Zydip</span> <span class="o">=</span> <span class="n">Impedance</span><span class="p">(</span><span class="n">variable</span><span class="o">=</span><span class="n">frequency</span><span class="p">,</span>
+                          <span class="n">function</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">ydip</span><span class="p">(),</span>
+                          <span class="n">component_type</span><span class="o">=</span><span class="s1">&#39;ydip&#39;</span><span class="p">)</span>
+        <span class="n">Zxquad</span> <span class="o">=</span> <span class="n">Impedance</span><span class="p">(</span><span class="n">variable</span><span class="o">=</span><span class="n">frequency</span><span class="p">,</span>
+                           <span class="n">function</span><span class="o">=-</span><span class="mi">1</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">quad</span><span class="p">(),</span>
+                           <span class="n">component_type</span><span class="o">=</span><span class="s1">&#39;xquad&#39;</span><span class="p">)</span>
+        <span class="n">Zyquad</span> <span class="o">=</span> <span class="n">Impedance</span><span class="p">(</span><span class="n">variable</span><span class="o">=</span><span class="n">frequency</span><span class="p">,</span>
+                           <span class="n">function</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">quad</span><span class="p">(),</span>
+                           <span class="n">component_type</span><span class="o">=</span><span class="s1">&#39;yquad&#39;</span><span class="p">)</span>
+
+        <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="n">append_to_model</span><span class="p">(</span><span class="n">Zlong</span><span class="p">)</span>
+        <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="n">append_to_model</span><span class="p">(</span><span class="n">Zxdip</span><span class="p">)</span>
+        <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="n">append_to_model</span><span class="p">(</span><span class="n">Zydip</span><span class="p">)</span>
+        <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="n">append_to_model</span><span class="p">(</span><span class="n">Zxquad</span><span class="p">)</span>
+        <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="n">append_to_model</span><span class="p">(</span><span class="n">Zyquad</span><span class="p">)</span>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">gap_prime</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+        <span class="k">return</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">gap_entrance</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">gap_exit</span><span class="p">)</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">length</span>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">angle</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+        <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">arctan</span><span class="p">(</span>
+            <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">gap_entrance</span> <span class="o">/</span> <span class="mi">2</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">gap_exit</span> <span class="o">/</span> <span class="mi">2</span><span class="p">)</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">length</span><span class="p">)</span>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">Z0</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+        <span class="k">return</span> <span class="n">mu_0</span> <span class="o">*</span> <span class="n">c</span>
+
+<div class="viewcode-block" id="StupakovRectangularTaper.long"><a class="viewcode-back" href="../../../mbtrack2.impedance.html#mbtrack2.impedance.tapers.StupakovRectangularTaper.long">[docs]</a>    <span class="k">def</span> <span class="nf">long</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">frequency</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
+
+        <span class="k">if</span> <span class="n">frequency</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="n">frequency</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">frequency</span>
+
+        <span class="k">def</span> <span class="nf">F</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">m_max</span><span class="p">):</span>
+            <span class="n">m</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">m_max</span><span class="p">)</span>
+            <span class="n">phi</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">outer</span><span class="p">(</span><span class="n">pi</span> <span class="o">*</span> <span class="n">x</span> <span class="o">/</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="o">*</span><span class="n">m</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span>
+            <span class="n">val</span> <span class="o">=</span> <span class="mi">1</span> <span class="o">/</span> <span class="p">(</span><span class="mi">2</span><span class="o">*</span><span class="n">m</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span> <span class="o">/</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">cosh</span><span class="p">(</span><span class="n">phi</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">tanh</span><span class="p">(</span><span class="n">phi</span><span class="p">)</span>
+            <span class="k">return</span> <span class="n">val</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
+
+        <span class="n">z</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">length</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">n_points</span><span class="p">)</span>
+        <span class="n">g</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">gap_entrance</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">gap_exit</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">n_points</span><span class="p">)</span>
+
+        <span class="n">to_integrate</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">gap_prime</span><span class="o">**</span><span class="mi">2</span> <span class="o">*</span> <span class="n">F</span><span class="p">(</span><span class="n">g</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">width</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">m_max</span><span class="p">)</span>
+        <span class="n">integral</span> <span class="o">=</span> <span class="n">trapz</span><span class="p">(</span><span class="n">to_integrate</span><span class="p">,</span> <span class="n">x</span><span class="o">=</span><span class="n">z</span><span class="p">)</span>
+
+        <span class="k">return</span> <span class="o">-</span><span class="mi">1</span><span class="n">j</span> <span class="o">*</span> <span class="n">frequency</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">Z0</span> <span class="o">/</span> <span class="p">(</span><span class="mi">2</span><span class="o">*</span><span class="n">c</span><span class="p">)</span> <span class="o">*</span> <span class="n">integral</span></div>
+
+<div class="viewcode-block" id="StupakovRectangularTaper.Z_over_n"><a class="viewcode-back" href="../../../mbtrack2.impedance.html#mbtrack2.impedance.tapers.StupakovRectangularTaper.Z_over_n">[docs]</a>    <span class="k">def</span> <span class="nf">Z_over_n</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">f0</span><span class="p">):</span>
+        <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">imag</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">long</span><span class="p">(</span><span class="mi">1</span><span class="p">))</span> <span class="o">*</span> <span class="n">f0</span></div>
+
+<div class="viewcode-block" id="StupakovRectangularTaper.ydip"><a class="viewcode-back" href="../../../mbtrack2.impedance.html#mbtrack2.impedance.tapers.StupakovRectangularTaper.ydip">[docs]</a>    <span class="k">def</span> <span class="nf">ydip</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+
+        <span class="k">def</span> <span class="nf">G1</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">m_max</span><span class="p">):</span>
+            <span class="n">m</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">m_max</span><span class="p">)</span>
+            <span class="n">phi</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">outer</span><span class="p">(</span><span class="n">pi</span> <span class="o">*</span> <span class="n">x</span> <span class="o">/</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="o">*</span><span class="n">m</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span>
+            <span class="n">val</span> <span class="o">=</span> <span class="p">(</span><span class="mi">2</span><span class="o">*</span><span class="n">m</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span> <span class="o">/</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">sinh</span><span class="p">(</span><span class="n">phi</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span> <span class="o">/</span> <span class="n">np</span><span class="o">.</span><span class="n">tanh</span><span class="p">(</span><span class="n">phi</span><span class="p">)</span>
+            <span class="n">val</span> <span class="o">=</span> <span class="n">x</span><span class="p">[:,</span> <span class="kc">None</span><span class="p">]</span><span class="o">**</span><span class="mi">3</span> <span class="o">*</span> <span class="n">val</span>
+            <span class="k">return</span> <span class="n">val</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
+
+        <span class="n">z</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">length</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">n_points</span><span class="p">)</span>
+        <span class="n">g</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">gap_entrance</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">gap_exit</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">n_points</span><span class="p">)</span>
+
+        <span class="n">to_integrate</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">gap_prime</span><span class="o">**</span><span class="mi">2</span> <span class="o">/</span> <span class="p">(</span><span class="n">g</span><span class="o">**</span><span class="mi">3</span><span class="p">)</span> <span class="o">*</span> <span class="n">G1</span><span class="p">(</span><span class="n">g</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">width</span><span class="p">,</span>
+                                                       <span class="bp">self</span><span class="o">.</span><span class="n">m_max</span><span class="p">)</span>
+        <span class="n">integral</span> <span class="o">=</span> <span class="n">trapz</span><span class="p">(</span><span class="n">to_integrate</span><span class="p">,</span> <span class="n">x</span><span class="o">=</span><span class="n">z</span><span class="p">)</span>
+
+        <span class="k">return</span> <span class="o">-</span><span class="mi">1</span><span class="n">j</span> <span class="o">*</span> <span class="n">pi</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">width</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">Z0</span> <span class="o">/</span> <span class="mi">4</span> <span class="o">*</span> <span class="n">integral</span></div>
+
+<div class="viewcode-block" id="StupakovRectangularTaper.xdip"><a class="viewcode-back" href="../../../mbtrack2.impedance.html#mbtrack2.impedance.tapers.StupakovRectangularTaper.xdip">[docs]</a>    <span class="k">def</span> <span class="nf">xdip</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+
+        <span class="k">def</span> <span class="nf">G3</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">m_max</span><span class="p">):</span>
+            <span class="n">m</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">m_max</span><span class="p">)</span>
+            <span class="n">phi</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">outer</span><span class="p">(</span><span class="n">pi</span> <span class="o">*</span> <span class="n">x</span><span class="p">,</span> <span class="n">m</span><span class="p">)</span>
+            <span class="n">val</span> <span class="o">=</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">m</span> <span class="o">/</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">cosh</span><span class="p">(</span><span class="n">phi</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">tanh</span><span class="p">(</span><span class="n">phi</span><span class="p">)</span>
+            <span class="n">val</span> <span class="o">=</span> <span class="n">x</span><span class="p">[:,</span> <span class="kc">None</span><span class="p">]</span><span class="o">**</span><span class="mi">2</span> <span class="o">*</span> <span class="n">val</span>
+            <span class="k">return</span> <span class="n">val</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
+
+        <span class="n">z</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">length</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">n_points</span><span class="p">)</span>
+        <span class="n">g</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">gap_entrance</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">gap_exit</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">n_points</span><span class="p">)</span>
+
+        <span class="n">to_integrate</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">gap_prime</span><span class="o">**</span><span class="mi">2</span> <span class="o">/</span> <span class="p">(</span><span class="n">g</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span> <span class="o">*</span> <span class="n">G3</span><span class="p">(</span><span class="n">g</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">width</span><span class="p">,</span>
+                                                       <span class="bp">self</span><span class="o">.</span><span class="n">m_max</span><span class="p">)</span>
+        <span class="n">integral</span> <span class="o">=</span> <span class="n">trapz</span><span class="p">(</span><span class="n">to_integrate</span><span class="p">,</span> <span class="n">x</span><span class="o">=</span><span class="n">z</span><span class="p">)</span>
+
+        <span class="k">return</span> <span class="o">-</span><span class="mi">1</span><span class="n">j</span> <span class="o">*</span> <span class="n">pi</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">Z0</span> <span class="o">/</span> <span class="mi">4</span> <span class="o">*</span> <span class="n">integral</span></div>
+
+<div class="viewcode-block" id="StupakovRectangularTaper.quad"><a class="viewcode-back" href="../../../mbtrack2.impedance.html#mbtrack2.impedance.tapers.StupakovRectangularTaper.quad">[docs]</a>    <span class="k">def</span> <span class="nf">quad</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+
+        <span class="k">def</span> <span class="nf">G2</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">m_max</span><span class="p">):</span>
+            <span class="n">m</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">m_max</span><span class="p">)</span>
+            <span class="n">phi</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">outer</span><span class="p">(</span><span class="n">pi</span> <span class="o">*</span> <span class="n">x</span> <span class="o">/</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="o">*</span><span class="n">m</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span>
+            <span class="n">val</span> <span class="o">=</span> <span class="p">(</span><span class="mi">2</span><span class="o">*</span><span class="n">m</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span> <span class="o">/</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">cosh</span><span class="p">(</span><span class="n">phi</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">tanh</span><span class="p">(</span><span class="n">phi</span><span class="p">)</span>
+            <span class="n">val</span> <span class="o">=</span> <span class="n">x</span><span class="p">[:,</span> <span class="kc">None</span><span class="p">]</span><span class="o">**</span><span class="mi">2</span> <span class="o">*</span> <span class="n">val</span>
+            <span class="k">return</span> <span class="n">val</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
+
+        <span class="n">z</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">length</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">n_points</span><span class="p">)</span>
+        <span class="n">g</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">gap_entrance</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">gap_exit</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">n_points</span><span class="p">)</span>
+
+        <span class="n">to_integrate</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">gap_prime</span><span class="o">**</span><span class="mi">2</span> <span class="o">/</span> <span class="p">(</span><span class="n">g</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span> <span class="o">*</span> <span class="n">G2</span><span class="p">(</span><span class="n">g</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">width</span><span class="p">,</span>
+                                                       <span class="bp">self</span><span class="o">.</span><span class="n">m_max</span><span class="p">)</span>
+        <span class="n">integral</span> <span class="o">=</span> <span class="n">trapz</span><span class="p">(</span><span class="n">to_integrate</span><span class="p">,</span> <span class="n">x</span><span class="o">=</span><span class="n">z</span><span class="p">)</span>
+
+        <span class="k">return</span> <span class="o">-</span><span class="mi">1</span><span class="n">j</span> <span class="o">*</span> <span class="n">pi</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">Z0</span> <span class="o">/</span> <span class="mi">4</span> <span class="o">*</span> <span class="n">integral</span></div></div>
+
+
+<div class="viewcode-block" id="StupakovCircularTaper"><a class="viewcode-back" href="../../../mbtrack2.impedance.html#mbtrack2.impedance.tapers.StupakovCircularTaper">[docs]</a><span class="k">class</span> <span class="nc">StupakovCircularTaper</span><span class="p">(</span><span class="n">WakeField</span><span class="p">):</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    Circular taper WakeField element, using the low frequency </span>
+<span class="sd">    approxmiation. Assume constant taper angle. Formulas from [1].</span>
+<span class="sd">    </span>
+<span class="sd">    ! Valid for low w</span>
+<span class="sd">    </span>
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">    frequency: frequency points where the impedance will be evaluated in [Hz]</span>
+<span class="sd">    radius_entrance : radius at taper entrance in [m]</span>
+<span class="sd">    radius_exit : radius at taper exit in [m]</span>
+<span class="sd">    length : taper length in [m]</span>
+<span class="sd">    &quot;&quot;&quot;</span>
+
+    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span>
+                 <span class="n">frequency</span><span class="p">,</span>
+                 <span class="n">radius_entrance</span><span class="p">,</span>
+                 <span class="n">radius_exit</span><span class="p">,</span>
+                 <span class="n">length</span><span class="p">,</span>
+                 <span class="n">m_max</span><span class="o">=</span><span class="mi">100</span><span class="p">,</span>
+                 <span class="n">n_points</span><span class="o">=</span><span class="nb">int</span><span class="p">(</span><span class="mf">1e4</span><span class="p">)):</span>
+        <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__init__</span><span class="p">()</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">frequency</span> <span class="o">=</span> <span class="n">frequency</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">radius_entrance</span> <span class="o">=</span> <span class="n">radius_entrance</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">radius_exit</span> <span class="o">=</span> <span class="n">radius_exit</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">length</span> <span class="o">=</span> <span class="n">length</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">m_max</span> <span class="o">=</span> <span class="n">m_max</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">n_points</span> <span class="o">=</span> <span class="n">n_points</span>
+
+        <span class="n">Zlong</span> <span class="o">=</span> <span class="n">Impedance</span><span class="p">(</span><span class="n">variable</span><span class="o">=</span><span class="n">frequency</span><span class="p">,</span>
+                          <span class="n">function</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">long</span><span class="p">(),</span>
+                          <span class="n">component_type</span><span class="o">=</span><span class="s1">&#39;long&#39;</span><span class="p">)</span>
+        <span class="n">Zxdip</span> <span class="o">=</span> <span class="n">Impedance</span><span class="p">(</span><span class="n">variable</span><span class="o">=</span><span class="n">frequency</span><span class="p">,</span>
+                          <span class="n">function</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">dip</span><span class="p">(),</span>
+                          <span class="n">component_type</span><span class="o">=</span><span class="s1">&#39;xdip&#39;</span><span class="p">)</span>
+        <span class="n">Zydip</span> <span class="o">=</span> <span class="n">Impedance</span><span class="p">(</span><span class="n">variable</span><span class="o">=</span><span class="n">frequency</span><span class="p">,</span>
+                          <span class="n">function</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">dip</span><span class="p">(),</span>
+                          <span class="n">component_type</span><span class="o">=</span><span class="s1">&#39;ydip&#39;</span><span class="p">)</span>
+
+        <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="n">append_to_model</span><span class="p">(</span><span class="n">Zlong</span><span class="p">)</span>
+        <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="n">append_to_model</span><span class="p">(</span><span class="n">Zxdip</span><span class="p">)</span>
+        <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="n">append_to_model</span><span class="p">(</span><span class="n">Zydip</span><span class="p">)</span>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">angle</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+        <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">arctan</span><span class="p">(</span>
+            <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">radius_entrance</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">radius_exit</span><span class="p">)</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">length</span><span class="p">)</span>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">radius_prime</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+        <span class="k">return</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">radius_entrance</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">radius_exit</span><span class="p">)</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">length</span>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">Z0</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+        <span class="k">return</span> <span class="n">mu_0</span> <span class="o">*</span> <span class="n">c</span>
+
+<div class="viewcode-block" id="StupakovCircularTaper.long"><a class="viewcode-back" href="../../../mbtrack2.impedance.html#mbtrack2.impedance.tapers.StupakovCircularTaper.long">[docs]</a>    <span class="k">def</span> <span class="nf">long</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">frequency</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
+
+        <span class="k">if</span> <span class="n">frequency</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="n">frequency</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">frequency</span>
+
+        <span class="k">return</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">Z0</span> <span class="o">/</span>
+                <span class="p">(</span><span class="mi">2</span><span class="o">*</span><span class="n">pi</span><span class="p">)</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">log</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">radius_entrance</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">radius_exit</span><span class="p">)</span> <span class="o">-</span>
+                <span class="mi">1</span><span class="n">j</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">Z0</span> <span class="o">*</span> <span class="n">frequency</span> <span class="o">/</span>
+                <span class="p">(</span><span class="mi">2</span><span class="o">*</span><span class="n">c</span><span class="p">)</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">radius_prime</span><span class="o">**</span><span class="mi">2</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">length</span><span class="p">)</span></div>
+
+<div class="viewcode-block" id="StupakovCircularTaper.Z_over_n"><a class="viewcode-back" href="../../../mbtrack2.impedance.html#mbtrack2.impedance.tapers.StupakovCircularTaper.Z_over_n">[docs]</a>    <span class="k">def</span> <span class="nf">Z_over_n</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">f0</span><span class="p">):</span>
+        <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">imag</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">long</span><span class="p">(</span><span class="mi">1</span><span class="p">))</span> <span class="o">*</span> <span class="n">f0</span></div>
+
+<div class="viewcode-block" id="StupakovCircularTaper.dip"><a class="viewcode-back" href="../../../mbtrack2.impedance.html#mbtrack2.impedance.tapers.StupakovCircularTaper.dip">[docs]</a>    <span class="k">def</span> <span class="nf">dip</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">frequency</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
+
+        <span class="k">if</span> <span class="n">frequency</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="n">frequency</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">frequency</span>
+
+        <span class="n">z</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">length</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">n_points</span><span class="p">)</span>
+        <span class="n">r</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">radius_entrance</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">radius_exit</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">n_points</span><span class="p">)</span>
+
+        <span class="n">to_integrate</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">radius_prime</span><span class="o">**</span><span class="mi">2</span> <span class="o">/</span> <span class="p">(</span><span class="n">r</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span>
+        <span class="n">integral</span> <span class="o">=</span> <span class="n">trapz</span><span class="p">(</span><span class="n">to_integrate</span><span class="p">,</span> <span class="n">x</span><span class="o">=</span><span class="n">z</span><span class="p">)</span>
+
+        <span class="k">return</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">Z0</span> <span class="o">*</span> <span class="n">c</span> <span class="o">/</span> <span class="p">(</span><span class="mi">4</span> <span class="o">*</span> <span class="n">pi</span><span class="o">**</span><span class="mi">2</span> <span class="o">*</span> <span class="n">frequency</span><span class="p">)</span> <span class="o">*</span>
+                <span class="p">(</span><span class="mi">1</span> <span class="o">/</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">radius_exit</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span> <span class="o">-</span> <span class="mi">1</span> <span class="o">/</span>
+                 <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">radius_entrance</span><span class="o">**</span><span class="mi">2</span><span class="p">))</span> <span class="o">-</span> <span class="mi">1</span><span class="n">j</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">Z0</span> <span class="o">/</span> <span class="p">(</span><span class="mi">2</span><span class="o">*</span><span class="n">pi</span><span class="p">)</span> <span class="o">*</span> <span class="n">integral</span><span class="p">)</span></div></div>
+</pre></div>
+
+            <div class="clearer"></div>
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+      Created using <a href="https://www.sphinx-doc.org/">Sphinx</a> 5.0.2.
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diff --git a/docs/build/html/_modules/mbtrack2/impedance/wakefield.html b/docs/build/html/_modules/mbtrack2/impedance/wakefield.html
new file mode 100644
index 0000000..2a1e6d5
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+++ b/docs/build/html/_modules/mbtrack2/impedance/wakefield.html
@@ -0,0 +1,1142 @@
+
+<!DOCTYPE html>
+
+<html lang="en">
+  <head>
+    <meta charset="utf-8" />
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+        <li class="nav-item nav-item-this"><a href="">mbtrack2.impedance.wakefield</a></li> 
+      </ul>
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+
+    <div class="document">
+      <div class="documentwrapper">
+        <div class="bodywrapper">
+          <div class="body" role="main">
+            
+  <h1>Source code for mbtrack2.impedance.wakefield</h1><div class="highlight"><pre>
+<span></span><span class="c1"># -*- coding: utf-8 -*-</span>
+<span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">This module defines general classes to describes wakefields, impedances and </span>
+<span class="sd">wake functions.</span>
+<span class="sd">&quot;&quot;&quot;</span>
+
+<span class="kn">import</span> <span class="nn">pickle</span>
+<span class="kn">import</span> <span class="nn">warnings</span>
+<span class="kn">from</span> <span class="nn">copy</span> <span class="kn">import</span> <span class="n">deepcopy</span>
+
+<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="kn">import</span> <span class="nn">pandas</span> <span class="k">as</span> <span class="nn">pd</span>
+<span class="kn">import</span> <span class="nn">scipy</span> <span class="k">as</span> <span class="nn">sc</span>
+<span class="kn">from</span> <span class="nn">scipy.constants</span> <span class="kn">import</span> <span class="n">c</span>
+<span class="kn">from</span> <span class="nn">scipy.integrate</span> <span class="kn">import</span> <span class="n">trapz</span>
+<span class="kn">from</span> <span class="nn">scipy.interpolate</span> <span class="kn">import</span> <span class="n">interp1d</span>
+
+
+<div class="viewcode-block" id="ComplexData"><a class="viewcode-back" href="../../../mbtrack2.impedance.html#mbtrack2.impedance.wakefield.ComplexData">[docs]</a><span class="k">class</span> <span class="nc">ComplexData</span><span class="p">:</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    Define a general data structure for a complex function based on a pandas </span>
+<span class="sd">    DataFrame.</span>
+
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">    variable : list, numpy array</span>
+<span class="sd">       contains the function variable values</span>
+
+<span class="sd">    function : list or numpy array of comp lex numbers</span>
+<span class="sd">        contains the values taken by the complex function</span>
+<span class="sd">    &quot;&quot;&quot;</span>
+
+    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span>
+                 <span class="n">variable</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="o">-</span><span class="mf">1e15</span><span class="p">,</span> <span class="mf">1e15</span><span class="p">]),</span>
+                 <span class="n">function</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">])):</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">data</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">DataFrame</span><span class="p">(</span>
+            <span class="p">{</span>
+                <span class="s1">&#39;real&#39;</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">real</span><span class="p">(</span><span class="n">function</span><span class="p">),</span>
+                <span class="s1">&#39;imag&#39;</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">imag</span><span class="p">(</span><span class="n">function</span><span class="p">)</span>
+            <span class="p">},</span>
+            <span class="n">index</span><span class="o">=</span><span class="n">variable</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">data</span><span class="o">.</span><span class="n">index</span><span class="o">.</span><span class="n">name</span> <span class="o">=</span> <span class="s1">&#39;variable&#39;</span>
+
+<div class="viewcode-block" id="ComplexData.add"><a class="viewcode-back" href="../../../mbtrack2.impedance.html#mbtrack2.impedance.wakefield.ComplexData.add">[docs]</a>    <span class="k">def</span> <span class="nf">add</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span>
+            <span class="n">structure_to_add</span><span class="p">,</span>
+            <span class="n">method</span><span class="o">=</span><span class="s1">&#39;zero&#39;</span><span class="p">,</span>
+            <span class="n">interp_kind</span><span class="o">=</span><span class="s1">&#39;cubic&#39;</span><span class="p">,</span>
+            <span class="n">index_name</span><span class="o">=</span><span class="s2">&quot;variable&quot;</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Method to add two structures. If the data don&#39;t have the same length,</span>
+<span class="sd">        different cases are handled.</span>
+<span class="sd">        </span>
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        structure_to_add : ComplexData object, int, float or complex.</span>
+<span class="sd">            structure to be added.</span>
+<span class="sd">        method : str, optional</span>
+<span class="sd">            manage how the addition is done, possibilties are: </span>
+<span class="sd">            -common: the common range of the index (variable) from the two</span>
+<span class="sd">                structures is used. The input data are cross-interpolated</span>
+<span class="sd">                so that the result data contains the points at all initial</span>
+<span class="sd">                points in the common domain.</span>
+<span class="sd">            -extrapolate: extrapolate the value of both ComplexData.</span>
+<span class="sd">            -zero: outside of the common range, the missing values are zero. In </span>
+<span class="sd">                the common range, behave as &quot;common&quot; method.</span>
+<span class="sd">        interp_kind : str, optional</span>
+<span class="sd">            interpolation method which is passed to pandas and to</span>
+<span class="sd">            scipy.interpolate.interp1d.</span>
+<span class="sd">        index_name : str, optional</span>
+<span class="sd">            name of the dataframe index passed to the method</span>
+<span class="sd">            </span>
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        ComplexData </span>
+<span class="sd">            Contains the sum of the two inputs.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+
+        <span class="c1"># Create first two new DataFrames merging the variable</span>
+        <span class="c1"># from the two input data</span>
+
+        <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">structure_to_add</span><span class="p">,</span> <span class="p">(</span><span class="nb">int</span><span class="p">,</span> <span class="nb">float</span><span class="p">,</span> <span class="nb">complex</span><span class="p">)):</span>
+            <span class="n">structure_to_add</span> <span class="o">=</span> <span class="n">ComplexData</span><span class="p">(</span>
+                <span class="n">variable</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">data</span><span class="o">.</span><span class="n">index</span><span class="p">,</span>
+                <span class="n">function</span><span class="o">=</span><span class="p">(</span><span class="n">structure_to_add</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">data</span><span class="o">.</span><span class="n">index</span><span class="p">))))</span>
+
+        <span class="n">data_to_concat</span> <span class="o">=</span> <span class="n">structure_to_add</span><span class="o">.</span><span class="n">data</span><span class="o">.</span><span class="n">index</span><span class="o">.</span><span class="n">to_frame</span><span class="p">()</span><span class="o">.</span><span class="n">set_index</span><span class="p">(</span>
+            <span class="n">index_name</span><span class="p">)</span>
+
+        <span class="n">initial_data</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">concat</span><span class="p">([</span><span class="bp">self</span><span class="o">.</span><span class="n">data</span><span class="p">,</span> <span class="n">data_to_concat</span><span class="p">],</span> <span class="n">sort</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
+        <span class="n">initial_data</span> <span class="o">=</span> <span class="n">initial_data</span><span class="p">[</span><span class="o">~</span><span class="n">initial_data</span><span class="o">.</span><span class="n">index</span><span class="o">.</span><span class="n">duplicated</span><span class="p">(</span>
+            <span class="n">keep</span><span class="o">=</span><span class="s1">&#39;first&#39;</span><span class="p">)]</span>
+        <span class="n">initial_data</span> <span class="o">=</span> <span class="n">initial_data</span><span class="o">.</span><span class="n">sort_index</span><span class="p">()</span>
+
+        <span class="n">data_to_add</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">concat</span><span class="p">([</span>
+            <span class="n">structure_to_add</span><span class="o">.</span><span class="n">data</span><span class="p">,</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">data</span><span class="o">.</span><span class="n">index</span><span class="o">.</span><span class="n">to_frame</span><span class="p">()</span><span class="o">.</span><span class="n">set_index</span><span class="p">(</span><span class="n">index_name</span><span class="p">)</span>
+        <span class="p">],</span>
+                                <span class="n">sort</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
+        <span class="n">data_to_add</span> <span class="o">=</span> <span class="n">data_to_add</span><span class="p">[</span><span class="o">~</span><span class="n">data_to_add</span><span class="o">.</span><span class="n">index</span><span class="o">.</span><span class="n">duplicated</span><span class="p">(</span><span class="n">keep</span><span class="o">=</span><span class="s1">&#39;first&#39;</span><span class="p">)]</span>
+        <span class="n">data_to_add</span> <span class="o">=</span> <span class="n">data_to_add</span><span class="o">.</span><span class="n">sort_index</span><span class="p">()</span>
+
+        <span class="k">if</span> <span class="n">method</span> <span class="o">==</span> <span class="s1">&#39;common&#39;</span><span class="p">:</span>
+            <span class="n">max_variable</span> <span class="o">=</span> <span class="nb">min</span><span class="p">(</span><span class="n">structure_to_add</span><span class="o">.</span><span class="n">data</span><span class="o">.</span><span class="n">index</span><span class="o">.</span><span class="n">max</span><span class="p">(),</span>
+                               <span class="bp">self</span><span class="o">.</span><span class="n">data</span><span class="o">.</span><span class="n">index</span><span class="o">.</span><span class="n">max</span><span class="p">())</span>
+
+            <span class="n">min_variable</span> <span class="o">=</span> <span class="nb">max</span><span class="p">(</span><span class="n">structure_to_add</span><span class="o">.</span><span class="n">data</span><span class="o">.</span><span class="n">index</span><span class="o">.</span><span class="n">min</span><span class="p">(),</span>
+                               <span class="bp">self</span><span class="o">.</span><span class="n">data</span><span class="o">.</span><span class="n">index</span><span class="o">.</span><span class="n">min</span><span class="p">())</span>
+
+            <span class="n">initial_data</span> <span class="o">=</span> <span class="n">initial_data</span><span class="o">.</span><span class="n">interpolate</span><span class="p">(</span><span class="n">method</span><span class="o">=</span><span class="n">interp_kind</span><span class="p">)</span>
+            <span class="n">mask</span> <span class="o">=</span> <span class="p">((</span><span class="n">initial_data</span><span class="o">.</span><span class="n">index</span> <span class="o">&lt;=</span> <span class="n">max_variable</span><span class="p">)</span>
+                    <span class="o">&amp;</span> <span class="p">(</span><span class="n">initial_data</span><span class="o">.</span><span class="n">index</span> <span class="o">&gt;=</span> <span class="n">min_variable</span><span class="p">))</span>
+            <span class="n">initial_data</span> <span class="o">=</span> <span class="n">initial_data</span><span class="p">[</span><span class="n">mask</span><span class="p">]</span>
+
+            <span class="n">data_to_add</span> <span class="o">=</span> <span class="n">data_to_add</span><span class="o">.</span><span class="n">interpolate</span><span class="p">(</span><span class="n">method</span><span class="o">=</span><span class="n">interp_kind</span><span class="p">)</span>
+            <span class="n">mask</span> <span class="o">=</span> <span class="p">((</span><span class="n">data_to_add</span><span class="o">.</span><span class="n">index</span> <span class="o">&lt;=</span> <span class="n">max_variable</span><span class="p">)</span>
+                    <span class="o">&amp;</span> <span class="p">(</span><span class="n">data_to_add</span><span class="o">.</span><span class="n">index</span> <span class="o">&gt;=</span> <span class="n">min_variable</span><span class="p">))</span>
+            <span class="n">data_to_add</span> <span class="o">=</span> <span class="n">data_to_add</span><span class="p">[</span><span class="n">mask</span><span class="p">]</span>
+
+            <span class="n">result_structure</span> <span class="o">=</span> <span class="n">ComplexData</span><span class="p">()</span>
+            <span class="n">result_structure</span><span class="o">.</span><span class="n">data</span> <span class="o">=</span> <span class="n">initial_data</span> <span class="o">+</span> <span class="n">data_to_add</span>
+            <span class="k">return</span> <span class="n">result_structure</span>
+
+        <span class="k">if</span> <span class="n">method</span> <span class="o">==</span> <span class="s1">&#39;extrapolate&#39;</span><span class="p">:</span>
+            <span class="nb">print</span><span class="p">(</span><span class="s1">&#39;Not there yet&#39;</span><span class="p">)</span>
+            <span class="k">return</span> <span class="bp">self</span>
+
+        <span class="k">if</span> <span class="n">method</span> <span class="o">==</span> <span class="s1">&#39;zero&#39;</span><span class="p">:</span>
+            <span class="n">max_variable</span> <span class="o">=</span> <span class="nb">min</span><span class="p">(</span><span class="n">structure_to_add</span><span class="o">.</span><span class="n">data</span><span class="o">.</span><span class="n">index</span><span class="o">.</span><span class="n">max</span><span class="p">(),</span>
+                               <span class="bp">self</span><span class="o">.</span><span class="n">data</span><span class="o">.</span><span class="n">index</span><span class="o">.</span><span class="n">max</span><span class="p">())</span>
+
+            <span class="n">min_variable</span> <span class="o">=</span> <span class="nb">max</span><span class="p">(</span><span class="n">structure_to_add</span><span class="o">.</span><span class="n">data</span><span class="o">.</span><span class="n">index</span><span class="o">.</span><span class="n">min</span><span class="p">(),</span>
+                               <span class="bp">self</span><span class="o">.</span><span class="n">data</span><span class="o">.</span><span class="n">index</span><span class="o">.</span><span class="n">min</span><span class="p">())</span>
+
+            <span class="n">mask</span> <span class="o">=</span> <span class="p">((</span><span class="n">initial_data</span><span class="o">.</span><span class="n">index</span> <span class="o">&lt;=</span> <span class="n">max_variable</span><span class="p">)</span>
+                    <span class="o">&amp;</span> <span class="p">(</span><span class="n">initial_data</span><span class="o">.</span><span class="n">index</span> <span class="o">&gt;=</span> <span class="n">min_variable</span><span class="p">))</span>
+            <span class="n">initial_data</span><span class="p">[</span><span class="n">mask</span><span class="p">]</span> <span class="o">=</span> <span class="n">initial_data</span><span class="p">[</span><span class="n">mask</span><span class="p">]</span><span class="o">.</span><span class="n">interpolate</span><span class="p">(</span>
+                <span class="n">method</span><span class="o">=</span><span class="n">interp_kind</span><span class="p">)</span>
+
+            <span class="n">mask</span> <span class="o">=</span> <span class="p">((</span><span class="n">data_to_add</span><span class="o">.</span><span class="n">index</span> <span class="o">&lt;=</span> <span class="n">max_variable</span><span class="p">)</span>
+                    <span class="o">&amp;</span> <span class="p">(</span><span class="n">data_to_add</span><span class="o">.</span><span class="n">index</span> <span class="o">&gt;=</span> <span class="n">min_variable</span><span class="p">))</span>
+            <span class="n">data_to_add</span><span class="p">[</span><span class="n">mask</span><span class="p">]</span> <span class="o">=</span> <span class="n">data_to_add</span><span class="p">[</span><span class="n">mask</span><span class="p">]</span><span class="o">.</span><span class="n">interpolate</span><span class="p">(</span>
+                <span class="n">method</span><span class="o">=</span><span class="n">interp_kind</span><span class="p">)</span>
+
+            <span class="n">initial_data</span><span class="o">.</span><span class="n">replace</span><span class="p">(</span><span class="n">to_replace</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">nan</span><span class="p">,</span> <span class="n">value</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">inplace</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
+            <span class="n">data_to_add</span><span class="o">.</span><span class="n">replace</span><span class="p">(</span><span class="n">to_replace</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">nan</span><span class="p">,</span> <span class="n">value</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">inplace</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
+
+            <span class="n">result_structure</span> <span class="o">=</span> <span class="n">ComplexData</span><span class="p">()</span>
+            <span class="n">result_structure</span><span class="o">.</span><span class="n">data</span> <span class="o">=</span> <span class="n">initial_data</span> <span class="o">+</span> <span class="n">data_to_add</span>
+            <span class="k">return</span> <span class="n">result_structure</span></div>
+
+    <span class="k">def</span> <span class="fm">__radd__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">structure_to_add</span><span class="p">):</span>
+        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">structure_to_add</span><span class="p">,</span> <span class="n">method</span><span class="o">=</span><span class="s1">&#39;zero&#39;</span><span class="p">)</span>
+
+    <span class="k">def</span> <span class="fm">__add__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">structure_to_add</span><span class="p">):</span>
+        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">structure_to_add</span><span class="p">,</span> <span class="n">method</span><span class="o">=</span><span class="s1">&#39;zero&#39;</span><span class="p">)</span>
+
+<div class="viewcode-block" id="ComplexData.multiply"><a class="viewcode-back" href="../../../mbtrack2.impedance.html#mbtrack2.impedance.wakefield.ComplexData.multiply">[docs]</a>    <span class="k">def</span> <span class="nf">multiply</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">factor</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Multiply a data strucure with a float or an int.</span>
+<span class="sd">        If the multiplication is done with something else, throw a warning.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">factor</span><span class="p">,</span> <span class="p">(</span><span class="nb">int</span><span class="p">,</span> <span class="nb">float</span><span class="p">)):</span>
+            <span class="n">result_structure</span> <span class="o">=</span> <span class="n">ComplexData</span><span class="p">()</span>
+            <span class="n">result_structure</span><span class="o">.</span><span class="n">data</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">data</span> <span class="o">*</span> <span class="n">factor</span>
+            <span class="k">return</span> <span class="n">result_structure</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="n">warnings</span><span class="o">.</span><span class="n">warn</span><span class="p">((</span><span class="s1">&#39;The multiplication factor is not a float &#39;</span>
+                           <span class="s1">&#39;or an int.&#39;</span><span class="p">),</span> <span class="ne">UserWarning</span><span class="p">)</span>
+            <span class="k">return</span> <span class="bp">self</span></div>
+
+    <span class="k">def</span> <span class="fm">__mul__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">factor</span><span class="p">):</span>
+        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">multiply</span><span class="p">(</span><span class="n">factor</span><span class="p">)</span>
+
+    <span class="k">def</span> <span class="fm">__rmul__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">factor</span><span class="p">):</span>
+        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">multiply</span><span class="p">(</span><span class="n">factor</span><span class="p">)</span>
+
+    <span class="k">def</span> <span class="fm">__call__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">values</span><span class="p">,</span> <span class="n">interp_kind</span><span class="o">=</span><span class="s2">&quot;cubic&quot;</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Interpolation of the data by calling the class to have a function-like</span>
+<span class="sd">        behaviour.</span>
+<span class="sd">        </span>
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        values : list or numpy array of complex, int or float</span>
+<span class="sd">            values to be interpolated.</span>
+<span class="sd">        interp_kind : str, optional</span>
+<span class="sd">            interpolation method which is passed to scipy.interpolate.interp1d.</span>
+<span class="sd">            </span>
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        numpy array </span>
+<span class="sd">            Contains the interpolated data.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="n">real_func</span> <span class="o">=</span> <span class="n">interp1d</span><span class="p">(</span><span class="n">x</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">data</span><span class="o">.</span><span class="n">index</span><span class="p">,</span>
+                             <span class="n">y</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">data</span><span class="p">[</span><span class="s2">&quot;real&quot;</span><span class="p">],</span>
+                             <span class="n">kind</span><span class="o">=</span><span class="n">interp_kind</span><span class="p">)</span>
+        <span class="n">imag_func</span> <span class="o">=</span> <span class="n">interp1d</span><span class="p">(</span><span class="n">x</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">data</span><span class="o">.</span><span class="n">index</span><span class="p">,</span>
+                             <span class="n">y</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">data</span><span class="p">[</span><span class="s2">&quot;imag&quot;</span><span class="p">],</span>
+                             <span class="n">kind</span><span class="o">=</span><span class="n">interp_kind</span><span class="p">)</span>
+        <span class="k">return</span> <span class="n">real_func</span><span class="p">(</span><span class="n">values</span><span class="p">)</span> <span class="o">+</span> <span class="mi">1</span><span class="n">j</span> <span class="o">*</span> <span class="n">imag_func</span><span class="p">(</span><span class="n">values</span><span class="p">)</span>
+
+    <span class="k">def</span> <span class="fm">__repr__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Return representation of data&quot;&quot;&quot;</span>
+        <span class="k">return</span> <span class="sa">f</span><span class="s1">&#39;</span><span class="si">{</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">data</span><span class="p">)</span><span class="si">!r}</span><span class="s1">&#39;</span>
+
+<div class="viewcode-block" id="ComplexData.initialize_coefficient"><a class="viewcode-back" href="../../../mbtrack2.impedance.html#mbtrack2.impedance.wakefield.ComplexData.initialize_coefficient">[docs]</a>    <span class="k">def</span> <span class="nf">initialize_coefficient</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Define the impedance coefficients and the plane of the impedance that</span>
+<span class="sd">        are presents in attributes of the class.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="n">table</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">name_and_coefficients_table</span><span class="p">()</span>
+
+        <span class="k">try</span><span class="p">:</span>
+            <span class="n">component_coefficients</span> <span class="o">=</span> <span class="n">table</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">component_type</span><span class="p">]</span><span class="o">.</span><span class="n">to_dict</span><span class="p">()</span>
+        <span class="k">except</span> <span class="ne">KeyError</span><span class="p">:</span>
+            <span class="nb">print</span><span class="p">(</span><span class="s1">&#39;Component type </span><span class="si">{}</span><span class="s1"> does not exist&#39;</span><span class="o">.</span><span class="n">format</span><span class="p">(</span>
+                <span class="bp">self</span><span class="o">.</span><span class="n">component_type</span><span class="p">))</span>
+            <span class="k">raise</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">a</span> <span class="o">=</span> <span class="n">component_coefficients</span><span class="p">[</span><span class="s2">&quot;a&quot;</span><span class="p">]</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">b</span> <span class="o">=</span> <span class="n">component_coefficients</span><span class="p">[</span><span class="s2">&quot;b&quot;</span><span class="p">]</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">c</span> <span class="o">=</span> <span class="n">component_coefficients</span><span class="p">[</span><span class="s2">&quot;c&quot;</span><span class="p">]</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">d</span> <span class="o">=</span> <span class="n">component_coefficients</span><span class="p">[</span><span class="s2">&quot;d&quot;</span><span class="p">]</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">plane</span> <span class="o">=</span> <span class="n">component_coefficients</span><span class="p">[</span><span class="s2">&quot;plane&quot;</span><span class="p">]</span></div>
+
+<div class="viewcode-block" id="ComplexData.name_and_coefficients_table"><a class="viewcode-back" href="../../../mbtrack2.impedance.html#mbtrack2.impedance.wakefield.ComplexData.name_and_coefficients_table">[docs]</a>    <span class="k">def</span> <span class="nf">name_and_coefficients_table</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Return a table associating the human readbale names of an impedance</span>
+<span class="sd">        component and its associated coefficients and plane.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+
+        <span class="n">component_dict</span> <span class="o">=</span> <span class="p">{</span>
+            <span class="s1">&#39;long&#39;</span><span class="p">:</span> <span class="p">{</span>
+                <span class="s1">&#39;a&#39;</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span>
+                <span class="s1">&#39;b&#39;</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span>
+                <span class="s1">&#39;c&#39;</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span>
+                <span class="s1">&#39;d&#39;</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span>
+                <span class="s1">&#39;plane&#39;</span><span class="p">:</span> <span class="s1">&#39;z&#39;</span>
+            <span class="p">},</span>
+            <span class="s1">&#39;xcst&#39;</span><span class="p">:</span> <span class="p">{</span>
+                <span class="s1">&#39;a&#39;</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span>
+                <span class="s1">&#39;b&#39;</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span>
+                <span class="s1">&#39;c&#39;</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span>
+                <span class="s1">&#39;d&#39;</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span>
+                <span class="s1">&#39;plane&#39;</span><span class="p">:</span> <span class="s1">&#39;x&#39;</span>
+            <span class="p">},</span>
+            <span class="s1">&#39;ycst&#39;</span><span class="p">:</span> <span class="p">{</span>
+                <span class="s1">&#39;a&#39;</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span>
+                <span class="s1">&#39;b&#39;</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span>
+                <span class="s1">&#39;c&#39;</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span>
+                <span class="s1">&#39;d&#39;</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span>
+                <span class="s1">&#39;plane&#39;</span><span class="p">:</span> <span class="s1">&#39;y&#39;</span>
+            <span class="p">},</span>
+            <span class="s1">&#39;xdip&#39;</span><span class="p">:</span> <span class="p">{</span>
+                <span class="s1">&#39;a&#39;</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span>
+                <span class="s1">&#39;b&#39;</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span>
+                <span class="s1">&#39;c&#39;</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span>
+                <span class="s1">&#39;d&#39;</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span>
+                <span class="s1">&#39;plane&#39;</span><span class="p">:</span> <span class="s1">&#39;x&#39;</span>
+            <span class="p">},</span>
+            <span class="s1">&#39;ydip&#39;</span><span class="p">:</span> <span class="p">{</span>
+                <span class="s1">&#39;a&#39;</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span>
+                <span class="s1">&#39;b&#39;</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span>
+                <span class="s1">&#39;c&#39;</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span>
+                <span class="s1">&#39;d&#39;</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span>
+                <span class="s1">&#39;plane&#39;</span><span class="p">:</span> <span class="s1">&#39;y&#39;</span>
+            <span class="p">},</span>
+            <span class="s1">&#39;xydip&#39;</span><span class="p">:</span> <span class="p">{</span>
+                <span class="s1">&#39;a&#39;</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span>
+                <span class="s1">&#39;b&#39;</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span>
+                <span class="s1">&#39;c&#39;</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span>
+                <span class="s1">&#39;d&#39;</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span>
+                <span class="s1">&#39;plane&#39;</span><span class="p">:</span> <span class="s1">&#39;x&#39;</span>
+            <span class="p">},</span>
+            <span class="s1">&#39;yxdip&#39;</span><span class="p">:</span> <span class="p">{</span>
+                <span class="s1">&#39;a&#39;</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span>
+                <span class="s1">&#39;b&#39;</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span>
+                <span class="s1">&#39;c&#39;</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span>
+                <span class="s1">&#39;d&#39;</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span>
+                <span class="s1">&#39;plane&#39;</span><span class="p">:</span> <span class="s1">&#39;y&#39;</span>
+            <span class="p">},</span>
+            <span class="s1">&#39;xquad&#39;</span><span class="p">:</span> <span class="p">{</span>
+                <span class="s1">&#39;a&#39;</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span>
+                <span class="s1">&#39;b&#39;</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span>
+                <span class="s1">&#39;c&#39;</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span>
+                <span class="s1">&#39;d&#39;</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span>
+                <span class="s1">&#39;plane&#39;</span><span class="p">:</span> <span class="s1">&#39;x&#39;</span>
+            <span class="p">},</span>
+            <span class="s1">&#39;yquad&#39;</span><span class="p">:</span> <span class="p">{</span>
+                <span class="s1">&#39;a&#39;</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span>
+                <span class="s1">&#39;b&#39;</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span>
+                <span class="s1">&#39;c&#39;</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span>
+                <span class="s1">&#39;d&#39;</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span>
+                <span class="s1">&#39;plane&#39;</span><span class="p">:</span> <span class="s1">&#39;y&#39;</span>
+            <span class="p">},</span>
+            <span class="s1">&#39;xyquad&#39;</span><span class="p">:</span> <span class="p">{</span>
+                <span class="s1">&#39;a&#39;</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span>
+                <span class="s1">&#39;b&#39;</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span>
+                <span class="s1">&#39;c&#39;</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span>
+                <span class="s1">&#39;d&#39;</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span>
+                <span class="s1">&#39;plane&#39;</span><span class="p">:</span> <span class="s1">&#39;x&#39;</span>
+            <span class="p">},</span>
+            <span class="s1">&#39;yxquad&#39;</span><span class="p">:</span> <span class="p">{</span>
+                <span class="s1">&#39;a&#39;</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span>
+                <span class="s1">&#39;b&#39;</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span>
+                <span class="s1">&#39;c&#39;</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span>
+                <span class="s1">&#39;d&#39;</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span>
+                <span class="s1">&#39;plane&#39;</span><span class="p">:</span> <span class="s1">&#39;y&#39;</span>
+            <span class="p">},</span>
+        <span class="p">}</span>
+
+        <span class="k">return</span> <span class="n">pd</span><span class="o">.</span><span class="n">DataFrame</span><span class="p">(</span><span class="n">component_dict</span><span class="p">)</span></div>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">power_x</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+        <span class="n">power_x</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">a</span> <span class="o">/</span> <span class="mi">2</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">c</span> <span class="o">/</span> <span class="mf">2.</span>
+        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">plane</span> <span class="o">==</span> <span class="s1">&#39;x&#39;</span><span class="p">:</span>
+            <span class="n">power_x</span> <span class="o">+=</span> <span class="mf">1.</span> <span class="o">/</span> <span class="mf">2.</span>
+        <span class="k">return</span> <span class="n">power_x</span>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">power_y</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+        <span class="n">power_y</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">b</span> <span class="o">/</span> <span class="mf">2.</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">d</span> <span class="o">/</span> <span class="mf">2.</span>
+        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">plane</span> <span class="o">==</span> <span class="s1">&#39;y&#39;</span><span class="p">:</span>
+            <span class="n">power_y</span> <span class="o">+=</span> <span class="mf">1.</span> <span class="o">/</span> <span class="mf">2.</span>
+        <span class="k">return</span> <span class="n">power_y</span>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">component_type</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_component_type</span>
+
+    <span class="nd">@component_type</span><span class="o">.</span><span class="n">setter</span>
+    <span class="k">def</span> <span class="nf">component_type</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">value</span><span class="p">):</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">_component_type</span> <span class="o">=</span> <span class="n">value</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">initialize_coefficient</span><span class="p">()</span></div>
+
+
+<div class="viewcode-block" id="WakeFunction"><a class="viewcode-back" href="../../../mbtrack2.impedance.html#mbtrack2.impedance.wakefield.WakeFunction">[docs]</a><span class="k">class</span> <span class="nc">WakeFunction</span><span class="p">(</span><span class="n">ComplexData</span><span class="p">):</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    Define a WakeFunction object based on a ComplexData object.</span>
+<span class="sd">    </span>
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">    variable : array-like</span>
+<span class="sd">        Time domain structure of the wake function in [s].</span>
+<span class="sd">    function : array-like</span>
+<span class="sd">        Wake function values in [V/C] for &quot;long&quot; and in [V/C/m] for others.</span>
+<span class="sd">    component_type : str, optinal</span>
+<span class="sd">        Type of the wake function: &quot;long&quot;, &quot;xdip&quot;, &quot;xquad&quot;, ...</span>
+<span class="sd">    </span>
+<span class="sd">    Attributes</span>
+<span class="sd">    ----------</span>
+<span class="sd">    data : DataFrame</span>
+<span class="sd">    wake_type : str</span>
+<span class="sd">    </span>
+<span class="sd">    Methods</span>
+<span class="sd">    -------</span>
+<span class="sd">    to_impedance()</span>
+<span class="sd">        Return an Impedance object from the WakeFunction data.</span>
+<span class="sd">    deconvolution(freq_lim, sigma, mu)</span>
+<span class="sd">        Compute a wake function from wake potential data.</span>
+<span class="sd">    plot()</span>
+<span class="sd">        Plot the wake function data.</span>
+<span class="sd">    loss_factor(sigma)</span>
+<span class="sd">        Compute the loss factor or the kick factor for a Gaussian bunch.</span>
+<span class="sd">    &quot;&quot;&quot;</span>
+
+    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span>
+                 <span class="n">variable</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="o">-</span><span class="mf">1e15</span><span class="p">,</span> <span class="mf">1e15</span><span class="p">]),</span>
+                 <span class="n">function</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">]),</span>
+                 <span class="n">component_type</span><span class="o">=</span><span class="s1">&#39;long&#39;</span><span class="p">):</span>
+        <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__init__</span><span class="p">(</span><span class="n">variable</span><span class="p">,</span> <span class="n">function</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">_component_type</span> <span class="o">=</span> <span class="n">component_type</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">data</span><span class="o">.</span><span class="n">index</span><span class="o">.</span><span class="n">name</span> <span class="o">=</span> <span class="s2">&quot;time [s]&quot;</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">initialize_coefficient</span><span class="p">()</span>
+
+    <span class="k">def</span> <span class="fm">__repr__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Return representation of data&quot;&quot;&quot;</span>
+        <span class="k">return</span> <span class="sa">f</span><span class="s1">&#39;WakeFunction of component_type </span><span class="si">{</span><span class="bp">self</span><span class="o">.</span><span class="n">component_type</span><span class="si">}</span><span class="s1">:</span><span class="se">\n</span><span class="s1"> </span><span class="si">{</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">data</span><span class="p">)</span><span class="si">!r}</span><span class="s1">&#39;</span>
+
+<div class="viewcode-block" id="WakeFunction.add"><a class="viewcode-back" href="../../../mbtrack2.impedance.html#mbtrack2.impedance.wakefield.WakeFunction.add">[docs]</a>    <span class="k">def</span> <span class="nf">add</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">structure_to_add</span><span class="p">,</span> <span class="n">method</span><span class="o">=</span><span class="s1">&#39;zero&#39;</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Method to add two WakeFunction objects. The two structures are</span>
+<span class="sd">        compared so that the addition is self-consistent.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+
+        <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">structure_to_add</span><span class="p">,</span> <span class="p">(</span><span class="nb">int</span><span class="p">,</span> <span class="nb">float</span><span class="p">,</span> <span class="nb">complex</span><span class="p">)):</span>
+            <span class="n">result</span> <span class="o">=</span> <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">structure_to_add</span><span class="p">,</span>
+                                 <span class="n">method</span><span class="o">=</span><span class="n">method</span><span class="p">,</span>
+                                 <span class="n">index_name</span><span class="o">=</span><span class="s2">&quot;time [s]&quot;</span><span class="p">)</span>
+        <span class="k">elif</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">structure_to_add</span><span class="p">,</span> <span class="n">WakeFunction</span><span class="p">):</span>
+            <span class="k">if</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">component_type</span> <span class="o">==</span> <span class="n">structure_to_add</span><span class="o">.</span><span class="n">component_type</span><span class="p">):</span>
+                <span class="n">result</span> <span class="o">=</span> <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">structure_to_add</span><span class="p">,</span>
+                                     <span class="n">method</span><span class="o">=</span><span class="n">method</span><span class="p">,</span>
+                                     <span class="n">index_name</span><span class="o">=</span><span class="s2">&quot;time [s]&quot;</span><span class="p">)</span>
+            <span class="k">else</span><span class="p">:</span>
+                <span class="n">warnings</span><span class="o">.</span><span class="n">warn</span><span class="p">((</span><span class="s1">&#39;The two WakeFunction objects do not have the &#39;</span>
+                               <span class="s1">&#39;same coordinates or plane or type. &#39;</span>
+                               <span class="s1">&#39;Returning initial WakeFunction object.&#39;</span><span class="p">),</span>
+                              <span class="ne">UserWarning</span><span class="p">)</span>
+                <span class="n">result</span> <span class="o">=</span> <span class="bp">self</span>
+
+        <span class="n">wake_to_return</span> <span class="o">=</span> <span class="n">WakeFunction</span><span class="p">(</span><span class="n">result</span><span class="o">.</span><span class="n">data</span><span class="o">.</span><span class="n">index</span><span class="p">,</span>
+                                      <span class="n">result</span><span class="o">.</span><span class="n">data</span><span class="o">.</span><span class="n">real</span><span class="o">.</span><span class="n">values</span><span class="p">,</span>
+                                      <span class="bp">self</span><span class="o">.</span><span class="n">component_type</span><span class="p">)</span>
+        <span class="k">return</span> <span class="n">wake_to_return</span></div>
+
+    <span class="k">def</span> <span class="fm">__radd__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">structure_to_add</span><span class="p">):</span>
+        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">structure_to_add</span><span class="p">)</span>
+
+    <span class="k">def</span> <span class="fm">__add__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">structure_to_add</span><span class="p">):</span>
+        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">structure_to_add</span><span class="p">)</span>
+
+<div class="viewcode-block" id="WakeFunction.multiply"><a class="viewcode-back" href="../../../mbtrack2.impedance.html#mbtrack2.impedance.wakefield.WakeFunction.multiply">[docs]</a>    <span class="k">def</span> <span class="nf">multiply</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">factor</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Multiply a WakeFunction object with a float or an int.</span>
+<span class="sd">        If the multiplication is done with something else, throw a warning.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="n">result</span> <span class="o">=</span> <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="n">multiply</span><span class="p">(</span><span class="n">factor</span><span class="p">)</span>
+        <span class="n">wake_to_return</span> <span class="o">=</span> <span class="n">WakeFunction</span><span class="p">(</span><span class="n">result</span><span class="o">.</span><span class="n">data</span><span class="o">.</span><span class="n">index</span><span class="p">,</span>
+                                      <span class="n">result</span><span class="o">.</span><span class="n">data</span><span class="o">.</span><span class="n">real</span><span class="o">.</span><span class="n">values</span><span class="p">,</span>
+                                      <span class="bp">self</span><span class="o">.</span><span class="n">component_type</span><span class="p">)</span>
+        <span class="k">return</span> <span class="n">wake_to_return</span></div>
+
+    <span class="k">def</span> <span class="fm">__mul__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">factor</span><span class="p">):</span>
+        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">multiply</span><span class="p">(</span><span class="n">factor</span><span class="p">)</span>
+
+    <span class="k">def</span> <span class="fm">__rmul__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">factor</span><span class="p">):</span>
+        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">multiply</span><span class="p">(</span><span class="n">factor</span><span class="p">)</span>
+
+<div class="viewcode-block" id="WakeFunction.to_impedance"><a class="viewcode-back" href="../../../mbtrack2.impedance.html#mbtrack2.impedance.wakefield.WakeFunction.to_impedance">[docs]</a>    <span class="k">def</span> <span class="nf">to_impedance</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">freq_lim</span><span class="p">,</span> <span class="n">nout</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">sigma</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">mu</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Return an Impedance object from the WakeFunction data.</span>
+<span class="sd">        The WakeFunction data is assumed to be sampled equally.</span>
+<span class="sd">        </span>
+<span class="sd">        If both sigma and mu are given, the impedance data is divided by the</span>
+<span class="sd">        Fourier transform of a Gaussian distribution. It then can be used to go </span>
+<span class="sd">        from wake potential data to impedance.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        freq_lim : float</span>
+<span class="sd">            The maximum frequency for calculating the impedance [Hz].</span>
+<span class="sd">        nout : int or float, optional</span>
+<span class="sd">            Length of the transformed axis of the output. If None, it is taken</span>
+<span class="sd">            to be 2*(n-1) where n is the length of the input. If nout &gt; n, the</span>
+<span class="sd">            input is padded with zeros. If nout &lt; n, the input it cropped.</span>
+<span class="sd">            Note that, for any nout value, nout//2+1 input points are required.</span>
+<span class="sd">            The default is None.</span>
+<span class="sd">        sigma : float</span>
+<span class="sd">            RMS of the Gaussian distribution in [s].</span>
+<span class="sd">            The default is None.</span>
+<span class="sd">        mu : float</span>
+<span class="sd">            Offset of the Gaussian distribution in [s].</span>
+<span class="sd">            The default is None.</span>
+
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="n">tau</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">data</span><span class="o">.</span><span class="n">index</span><span class="p">)</span>
+        <span class="n">wp</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">data</span><span class="p">[</span><span class="s2">&quot;real&quot;</span><span class="p">])</span>
+
+        <span class="k">if</span> <span class="n">nout</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="n">nout</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">tau</span><span class="p">)</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="n">nout</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">nout</span><span class="p">)</span>
+
+        <span class="c1"># FT of wake potential</span>
+        <span class="n">sampling</span> <span class="o">=</span> <span class="n">tau</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="n">tau</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
+        <span class="n">freq</span> <span class="o">=</span> <span class="n">sc</span><span class="o">.</span><span class="n">fft</span><span class="o">.</span><span class="n">rfftfreq</span><span class="p">(</span><span class="n">nout</span><span class="p">,</span> <span class="n">sampling</span><span class="p">)</span>
+        <span class="n">dtau</span> <span class="o">=</span> <span class="p">(</span><span class="n">tau</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="n">tau</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span> <span class="o">/</span> <span class="nb">len</span><span class="p">(</span><span class="n">tau</span><span class="p">)</span>
+        <span class="n">dft_wake</span> <span class="o">=</span> <span class="n">sc</span><span class="o">.</span><span class="n">fft</span><span class="o">.</span><span class="n">rfft</span><span class="p">(</span><span class="n">wp</span><span class="p">,</span> <span class="n">n</span><span class="o">=</span><span class="n">nout</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span> <span class="o">*</span> <span class="n">dtau</span>
+
+        <span class="n">i_limit</span> <span class="o">=</span> <span class="n">freq</span> <span class="o">&lt;</span> <span class="n">freq_lim</span>
+        <span class="n">freq_trun</span> <span class="o">=</span> <span class="n">freq</span><span class="p">[</span><span class="n">i_limit</span><span class="p">]</span>
+        <span class="n">dft_wake_trun</span> <span class="o">=</span> <span class="n">dft_wake</span><span class="p">[</span><span class="n">i_limit</span><span class="p">]</span>
+
+        <span class="k">if</span> <span class="p">(</span><span class="n">sigma</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">)</span> <span class="ow">and</span> <span class="p">(</span><span class="n">mu</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">):</span>
+            <span class="n">dft_rho_trun</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="o">-</span><span class="mf">0.5</span><span class="o">*</span><span class="p">(</span><span class="n">sigma</span><span class="o">*</span><span class="mi">2</span><span class="o">*</span><span class="n">np</span><span class="o">.</span><span class="n">pi</span><span class="o">*</span><span class="n">freq_trun</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span> <span class="o">+</span> \
+                                      <span class="mi">1</span><span class="n">j</span><span class="o">*</span><span class="n">mu</span><span class="o">*</span><span class="mi">2</span><span class="o">*</span><span class="n">np</span><span class="o">.</span><span class="n">pi</span><span class="o">*</span><span class="n">freq_trun</span><span class="p">)</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="n">dft_rho_trun</span> <span class="o">=</span> <span class="o">-</span><span class="mi">1</span>
+
+        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">component_type</span> <span class="o">==</span> <span class="s2">&quot;long&quot;</span><span class="p">:</span>
+            <span class="n">imp</span> <span class="o">=</span> <span class="n">dft_wake_trun</span> <span class="o">/</span> <span class="n">dft_rho_trun</span> <span class="o">*</span> <span class="o">-</span><span class="mi">1</span>
+        <span class="k">elif</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">component_type</span> <span class="o">==</span> <span class="s2">&quot;xdip&quot;</span><span class="p">)</span> <span class="ow">or</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">component_type</span>
+                                                 <span class="o">==</span> <span class="s2">&quot;ydip&quot;</span><span class="p">):</span>
+            <span class="n">imp</span> <span class="o">=</span> <span class="n">dft_wake_trun</span> <span class="o">/</span> <span class="n">dft_rho_trun</span> <span class="o">*</span> <span class="o">-</span><span class="mi">1</span><span class="n">j</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="k">raise</span> <span class="ne">NotImplementedError</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">component_type</span> <span class="o">+</span> <span class="s2">&quot; is not correct.&quot;</span><span class="p">)</span>
+
+        <span class="n">imp</span> <span class="o">=</span> <span class="n">Impedance</span><span class="p">(</span><span class="n">variable</span><span class="o">=</span><span class="n">freq_trun</span><span class="p">,</span>
+                        <span class="n">function</span><span class="o">=</span><span class="n">imp</span><span class="p">,</span>
+                        <span class="n">component_type</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">component_type</span><span class="p">)</span>
+
+        <span class="k">return</span> <span class="n">imp</span></div>
+
+<div class="viewcode-block" id="WakeFunction.deconvolution"><a class="viewcode-back" href="../../../mbtrack2.impedance.html#mbtrack2.impedance.wakefield.WakeFunction.deconvolution">[docs]</a>    <span class="k">def</span> <span class="nf">deconvolution</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">freq_lim</span><span class="p">,</span> <span class="n">sigma</span><span class="p">,</span> <span class="n">mu</span><span class="p">,</span> <span class="n">nout</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Compute a wake function from wake potential data.</span>
+<span class="sd">                </span>
+<span class="sd">        The present data loaded into the WakeFunction object is assumed to be </span>
+<span class="sd">        an uniformly sampled wake potential from a Gaussian bunch distribution </span>
+<span class="sd">        with RMS bunch length sigma and offset mu.</span>
+<span class="sd">        </span>
+<span class="sd">        The offset mu depends on the code used to compute the wake potential:</span>
+<span class="sd">            - for CST, it is the first time sample, so self.data.index[0].</span>
+<span class="sd">            - for ABCI, it is &quot;-1 * ISIG * SIG / c&quot;.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        freq_lim : float</span>
+<span class="sd">            The maximum frequency for calculating the impedance [Hz].</span>
+<span class="sd">        sigma : float</span>
+<span class="sd">            RMS of the Gaussian distribution in [s].</span>
+<span class="sd">        mu : float</span>
+<span class="sd">            Offset of the Gaussian distribution in [s].</span>
+<span class="sd">        nout : int or float, optional</span>
+<span class="sd">            Length of the transformed axis of the output. If None, it is taken</span>
+<span class="sd">            to be 2*(n-1) where n is the length of the input. If nout &gt; n, the</span>
+<span class="sd">            input is padded with zeros. If nout &lt; n, the input it cropped.</span>
+<span class="sd">            Note that, for any nout value, nout//2+1 input points are required.</span>
+<span class="sd">            The default is None.</span>
+
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="n">imp</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">to_impedance</span><span class="p">(</span><span class="n">freq_lim</span><span class="p">,</span> <span class="n">sigma</span><span class="o">=</span><span class="n">sigma</span><span class="p">,</span> <span class="n">mu</span><span class="o">=</span><span class="n">mu</span><span class="p">)</span>
+        <span class="n">wf</span> <span class="o">=</span> <span class="n">imp</span><span class="o">.</span><span class="n">to_wakefunction</span><span class="p">(</span><span class="n">nout</span><span class="o">=</span><span class="n">nout</span><span class="p">)</span>
+        <span class="k">return</span> <span class="n">wf</span></div>
+
+<div class="viewcode-block" id="WakeFunction.plot"><a class="viewcode-back" href="../../../mbtrack2.impedance.html#mbtrack2.impedance.wakefield.WakeFunction.plot">[docs]</a>    <span class="k">def</span> <span class="nf">plot</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Plot the wake function data.</span>
+
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        ax : class:`matplotlib.axes.Axes`</span>
+<span class="sd">            Wake function data.</span>
+
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="n">ax</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">data</span><span class="p">[</span><span class="s2">&quot;real&quot;</span><span class="p">]</span><span class="o">.</span><span class="n">plot</span><span class="p">()</span>
+        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">component_type</span> <span class="o">==</span> <span class="s2">&quot;long&quot;</span><span class="p">:</span>
+            <span class="n">unit</span> <span class="o">=</span> <span class="s2">&quot; [V/C]&quot;</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="n">unit</span> <span class="o">=</span> <span class="s2">&quot; [V/C/m]&quot;</span>
+        <span class="n">label</span> <span class="o">=</span> <span class="sa">r</span><span class="s2">&quot;$W_{&quot;</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">component_type</span> <span class="o">+</span> <span class="sa">r</span><span class="s2">&quot;}$&quot;</span> <span class="o">+</span> <span class="n">unit</span>
+        <span class="n">ax</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="n">label</span><span class="p">)</span>
+        <span class="k">return</span> <span class="n">ax</span></div>
+
+<div class="viewcode-block" id="WakeFunction.loss_factor"><a class="viewcode-back" href="../../../mbtrack2.impedance.html#mbtrack2.impedance.wakefield.WakeFunction.loss_factor">[docs]</a>    <span class="k">def</span> <span class="nf">loss_factor</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">sigma</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Compute the loss factor or the kick factor for a Gaussian bunch. </span>
+<span class="sd">        Formulas from Eq. (5.6), Eq. (5.12) and Eq. (5.17) of [1].</span>
+<span class="sd">        </span>
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        sigma : float</span>
+<span class="sd">            RMS bunch length in [s]</span>
+<span class="sd">        </span>
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        kloss: float</span>
+<span class="sd">            Loss factor in [V/C] or kick factor in [V/C/m] depanding on the </span>
+<span class="sd">            impedance type.</span>
+<span class="sd">            </span>
+<span class="sd">        References</span>
+<span class="sd">        ----------</span>
+<span class="sd">        [1] : Zotter, Bruno W., and Semyon A. Kheifets. Impedances and wakes </span>
+<span class="sd">        in high-energy particle accelerators. World Scientific, 1998.</span>
+<span class="sd">        </span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="n">time</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">data</span><span class="o">.</span><span class="n">index</span>
+        <span class="n">S</span> <span class="o">=</span> <span class="mi">1</span> <span class="o">/</span> <span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">pi</span><span class="p">)</span> <span class="o">*</span> <span class="n">sigma</span><span class="p">)</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span> <span class="o">*</span> <span class="n">time</span><span class="o">**</span><span class="mi">2</span> <span class="o">/</span>
+                                                      <span class="p">(</span><span class="mi">4</span> <span class="o">*</span> <span class="n">sigma</span><span class="o">**</span><span class="mi">2</span><span class="p">))</span>
+        <span class="n">kloss</span> <span class="o">=</span> <span class="n">trapz</span><span class="p">(</span><span class="n">x</span><span class="o">=</span><span class="n">time</span><span class="p">,</span> <span class="n">y</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">data</span><span class="p">[</span><span class="s2">&quot;real&quot;</span><span class="p">]</span> <span class="o">*</span> <span class="n">S</span><span class="p">)</span>
+
+        <span class="k">return</span> <span class="n">kloss</span></div></div>
+
+
+<div class="viewcode-block" id="Impedance"><a class="viewcode-back" href="../../../mbtrack2.impedance.html#mbtrack2.impedance.wakefield.Impedance">[docs]</a><span class="k">class</span> <span class="nc">Impedance</span><span class="p">(</span><span class="n">ComplexData</span><span class="p">):</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    Define an Impedance object based on a ComplexData object.</span>
+<span class="sd">    </span>
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">    variable : array-like</span>
+<span class="sd">        Frequency domain structure of the impedance in [Hz].</span>
+<span class="sd">    function : array-like</span>
+<span class="sd">        Impedance values in [Ohm].</span>
+<span class="sd">    component_type : str, optinal</span>
+<span class="sd">        Type of the impedance: &quot;long&quot;, &quot;xdip&quot;, &quot;xquad&quot;, ...</span>
+<span class="sd">    </span>
+<span class="sd">    Attributes</span>
+<span class="sd">    ----------</span>
+<span class="sd">    data : DataFrame</span>
+<span class="sd">    impedance_type : str</span>
+<span class="sd">    </span>
+<span class="sd">    Methods</span>
+<span class="sd">    -------</span>
+<span class="sd">    loss_factor(sigma)</span>
+<span class="sd">        Compute the loss factor or the kick factor for a Gaussian bunch.</span>
+<span class="sd">    to_wakefunction()</span>
+<span class="sd">        Return a WakeFunction object from the impedance data.</span>
+<span class="sd">    plot()</span>
+<span class="sd">        Plot the impedance data.</span>
+<span class="sd">    &quot;&quot;&quot;</span>
+
+    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span>
+                 <span class="n">variable</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="o">-</span><span class="mf">1e15</span><span class="p">,</span> <span class="mf">1e15</span><span class="p">]),</span>
+                 <span class="n">function</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">]),</span>
+                 <span class="n">component_type</span><span class="o">=</span><span class="s1">&#39;long&#39;</span><span class="p">):</span>
+        <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__init__</span><span class="p">(</span><span class="n">variable</span><span class="p">,</span> <span class="n">function</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">_component_type</span> <span class="o">=</span> <span class="n">component_type</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">data</span><span class="o">.</span><span class="n">index</span><span class="o">.</span><span class="n">name</span> <span class="o">=</span> <span class="s1">&#39;frequency [Hz]&#39;</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">initialize_coefficient</span><span class="p">()</span>
+
+    <span class="k">def</span> <span class="fm">__repr__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Return representation of data&quot;&quot;&quot;</span>
+        <span class="k">return</span> <span class="sa">f</span><span class="s1">&#39;Impedance of component_type </span><span class="si">{</span><span class="bp">self</span><span class="o">.</span><span class="n">component_type</span><span class="si">}</span><span class="s1">:</span><span class="se">\n</span><span class="s1"> </span><span class="si">{</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">data</span><span class="p">)</span><span class="si">!r}</span><span class="s1">&#39;</span>
+
+<div class="viewcode-block" id="Impedance.add"><a class="viewcode-back" href="../../../mbtrack2.impedance.html#mbtrack2.impedance.wakefield.Impedance.add">[docs]</a>    <span class="k">def</span> <span class="nf">add</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">structure_to_add</span><span class="p">,</span> <span class="n">beta_x</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">beta_y</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">method</span><span class="o">=</span><span class="s1">&#39;zero&#39;</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Method to add two Impedance objects. The two structures are</span>
+<span class="sd">        compared so that the addition is self-consistent.</span>
+<span class="sd">        Beta functions can be precised as well.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+
+        <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">structure_to_add</span><span class="p">,</span> <span class="p">(</span><span class="nb">int</span><span class="p">,</span> <span class="nb">float</span><span class="p">,</span> <span class="nb">complex</span><span class="p">)):</span>
+            <span class="n">result</span> <span class="o">=</span> <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">structure_to_add</span><span class="p">,</span>
+                                 <span class="n">method</span><span class="o">=</span><span class="n">method</span><span class="p">,</span>
+                                 <span class="n">index_name</span><span class="o">=</span><span class="s2">&quot;frequency [Hz]&quot;</span><span class="p">)</span>
+        <span class="k">elif</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">structure_to_add</span><span class="p">,</span> <span class="n">Impedance</span><span class="p">):</span>
+            <span class="k">if</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">component_type</span> <span class="o">==</span> <span class="n">structure_to_add</span><span class="o">.</span><span class="n">component_type</span><span class="p">):</span>
+                <span class="n">weight</span> <span class="o">=</span> <span class="p">(</span><span class="n">beta_x</span><span class="o">**</span><span class="bp">self</span><span class="o">.</span><span class="n">power_x</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="n">beta_y</span><span class="o">**</span><span class="bp">self</span><span class="o">.</span><span class="n">power_y</span><span class="p">)</span>
+                <span class="n">result</span> <span class="o">=</span> <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">structure_to_add</span> <span class="o">*</span> <span class="n">weight</span><span class="p">,</span>
+                                     <span class="n">method</span><span class="o">=</span><span class="n">method</span><span class="p">,</span>
+                                     <span class="n">index_name</span><span class="o">=</span><span class="s2">&quot;frequency [Hz]&quot;</span><span class="p">)</span>
+            <span class="k">else</span><span class="p">:</span>
+                <span class="n">warnings</span><span class="o">.</span><span class="n">warn</span><span class="p">((</span><span class="s1">&#39;The two Impedance objects do not have the &#39;</span>
+                               <span class="s1">&#39;same coordinates or plane or type. &#39;</span>
+                               <span class="s1">&#39;Returning initial Impedance object.&#39;</span><span class="p">),</span>
+                              <span class="ne">UserWarning</span><span class="p">)</span>
+                <span class="n">result</span> <span class="o">=</span> <span class="bp">self</span>
+
+        <span class="n">impedance_to_return</span> <span class="o">=</span> <span class="n">Impedance</span><span class="p">(</span>
+            <span class="n">result</span><span class="o">.</span><span class="n">data</span><span class="o">.</span><span class="n">index</span><span class="p">,</span>
+            <span class="n">result</span><span class="o">.</span><span class="n">data</span><span class="o">.</span><span class="n">real</span><span class="o">.</span><span class="n">values</span> <span class="o">+</span> <span class="mi">1</span><span class="n">j</span> <span class="o">*</span> <span class="n">result</span><span class="o">.</span><span class="n">data</span><span class="o">.</span><span class="n">imag</span><span class="o">.</span><span class="n">values</span><span class="p">,</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">component_type</span><span class="p">)</span>
+        <span class="k">return</span> <span class="n">impedance_to_return</span></div>
+
+    <span class="k">def</span> <span class="fm">__radd__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">structure_to_add</span><span class="p">):</span>
+        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">structure_to_add</span><span class="p">)</span>
+
+    <span class="k">def</span> <span class="fm">__add__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">structure_to_add</span><span class="p">):</span>
+        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">structure_to_add</span><span class="p">)</span>
+
+<div class="viewcode-block" id="Impedance.multiply"><a class="viewcode-back" href="../../../mbtrack2.impedance.html#mbtrack2.impedance.wakefield.Impedance.multiply">[docs]</a>    <span class="k">def</span> <span class="nf">multiply</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">factor</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Multiply a Impedance object with a float or an int.</span>
+<span class="sd">        If the multiplication is done with something else, throw a warning.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="n">result</span> <span class="o">=</span> <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="n">multiply</span><span class="p">(</span><span class="n">factor</span><span class="p">)</span>
+        <span class="n">impedance_to_return</span> <span class="o">=</span> <span class="n">Impedance</span><span class="p">(</span>
+            <span class="n">result</span><span class="o">.</span><span class="n">data</span><span class="o">.</span><span class="n">index</span><span class="p">,</span>
+            <span class="n">result</span><span class="o">.</span><span class="n">data</span><span class="o">.</span><span class="n">real</span><span class="o">.</span><span class="n">values</span> <span class="o">+</span> <span class="mi">1</span><span class="n">j</span> <span class="o">*</span> <span class="n">result</span><span class="o">.</span><span class="n">data</span><span class="o">.</span><span class="n">imag</span><span class="o">.</span><span class="n">values</span><span class="p">,</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">component_type</span><span class="p">)</span>
+        <span class="k">return</span> <span class="n">impedance_to_return</span></div>
+
+    <span class="k">def</span> <span class="fm">__mul__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">factor</span><span class="p">):</span>
+        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">multiply</span><span class="p">(</span><span class="n">factor</span><span class="p">)</span>
+
+    <span class="k">def</span> <span class="fm">__rmul__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">factor</span><span class="p">):</span>
+        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">multiply</span><span class="p">(</span><span class="n">factor</span><span class="p">)</span>
+
+<div class="viewcode-block" id="Impedance.loss_factor"><a class="viewcode-back" href="../../../mbtrack2.impedance.html#mbtrack2.impedance.wakefield.Impedance.loss_factor">[docs]</a>    <span class="k">def</span> <span class="nf">loss_factor</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">sigma</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Compute the loss factor or the kick factor for a Gaussian bunch. </span>
+<span class="sd">        Formulas from Eq. (2) p239 and Eq.(7) p240 of [1].</span>
+<span class="sd">        </span>
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        sigma : float</span>
+<span class="sd">            RMS bunch length in [s]</span>
+<span class="sd">        </span>
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        kloss: float</span>
+<span class="sd">            Loss factor in [V/C] or kick factor in [V/C/m] depanding on the </span>
+<span class="sd">            impedance type.</span>
+<span class="sd">            </span>
+<span class="sd">        References</span>
+<span class="sd">        ----------</span>
+<span class="sd">        [1] : Handbook of accelerator physics and engineering, 3rd printing.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+
+        <span class="n">positive_index</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">data</span><span class="o">.</span><span class="n">index</span> <span class="o">&gt;</span> <span class="mi">0</span>
+        <span class="n">frequency</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">data</span><span class="o">.</span><span class="n">index</span><span class="p">[</span><span class="n">positive_index</span><span class="p">]</span>
+
+        <span class="c1"># Import here to avoid circular import</span>
+        <span class="kn">from</span> <span class="nn">mbtrack2.utilities</span> <span class="kn">import</span> <span class="n">spectral_density</span>
+        <span class="n">sd</span> <span class="o">=</span> <span class="n">spectral_density</span><span class="p">(</span><span class="n">frequency</span><span class="p">,</span> <span class="n">sigma</span><span class="p">,</span> <span class="n">m</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
+
+        <span class="k">if</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">component_type</span> <span class="o">==</span> <span class="s2">&quot;long&quot;</span><span class="p">):</span>
+            <span class="n">kloss</span> <span class="o">=</span> <span class="n">trapz</span><span class="p">(</span><span class="n">x</span><span class="o">=</span><span class="n">frequency</span><span class="p">,</span>
+                          <span class="n">y</span><span class="o">=</span><span class="mi">2</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">data</span><span class="p">[</span><span class="s2">&quot;real&quot;</span><span class="p">][</span><span class="n">positive_index</span><span class="p">]</span> <span class="o">*</span> <span class="n">sd</span><span class="p">)</span>
+        <span class="k">elif</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">component_type</span> <span class="o">==</span> <span class="s2">&quot;xdip&quot;</span> <span class="ow">or</span> <span class="bp">self</span><span class="o">.</span><span class="n">component_type</span> <span class="o">==</span> <span class="s2">&quot;ydip&quot;</span><span class="p">):</span>
+            <span class="n">kloss</span> <span class="o">=</span> <span class="n">trapz</span><span class="p">(</span><span class="n">x</span><span class="o">=</span><span class="n">frequency</span><span class="p">,</span>
+                          <span class="n">y</span><span class="o">=</span><span class="mi">2</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">data</span><span class="p">[</span><span class="s2">&quot;imag&quot;</span><span class="p">][</span><span class="n">positive_index</span><span class="p">]</span> <span class="o">*</span> <span class="n">sd</span><span class="p">)</span>
+        <span class="k">elif</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">component_type</span> <span class="o">==</span> <span class="s2">&quot;xquad&quot;</span>
+              <span class="ow">or</span> <span class="bp">self</span><span class="o">.</span><span class="n">component_type</span> <span class="o">==</span> <span class="s2">&quot;yquad&quot;</span><span class="p">):</span>
+            <span class="n">kloss</span> <span class="o">=</span> <span class="n">trapz</span><span class="p">(</span><span class="n">x</span><span class="o">=</span><span class="n">frequency</span><span class="p">,</span>
+                          <span class="n">y</span><span class="o">=</span><span class="mi">2</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">data</span><span class="p">[</span><span class="s2">&quot;imag&quot;</span><span class="p">][</span><span class="n">positive_index</span><span class="p">]</span> <span class="o">*</span> <span class="n">sd</span><span class="p">)</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s2">&quot;Impedance type not recognized.&quot;</span><span class="p">)</span>
+
+        <span class="k">return</span> <span class="n">kloss</span></div>
+
+<div class="viewcode-block" id="Impedance.to_wakefunction"><a class="viewcode-back" href="../../../mbtrack2.impedance.html#mbtrack2.impedance.wakefield.Impedance.to_wakefunction">[docs]</a>    <span class="k">def</span> <span class="nf">to_wakefunction</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">nout</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">trim</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Return a WakeFunction object from the impedance data.</span>
+<span class="sd">        The impedance data is assumed to be sampled equally.</span>
+<span class="sd">    </span>
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        nout : int or float, optional</span>
+<span class="sd">            Length of the transformed axis of the output. If None, it is taken</span>
+<span class="sd">            to be 2*(n-1) where n is the length of the input. If nout &gt; n, the</span>
+<span class="sd">            input is padded with zeros. If nout &lt; n, the input it cropped.</span>
+<span class="sd">            Note that, for any nout value, nout//2+1 input points are required.</span>
+<span class="sd">        trim : bool or float, optional</span>
+<span class="sd">            If True, the pseudo wake function is trimmed at time=0 and is forced </span>
+<span class="sd">            to zero where time&lt;0. </span>
+<span class="sd">            If False, the original result is preserved.</span>
+<span class="sd">            If a float is given, the pseudo wake function is trimmed from </span>
+<span class="sd">            time &lt;= trim to 0. </span>
+<span class="sd">        &quot;&quot;&quot;</span>
+
+        <span class="n">Z0</span> <span class="o">=</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">data</span><span class="p">[</span><span class="s1">&#39;real&#39;</span><span class="p">]</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">data</span><span class="p">[</span><span class="s1">&#39;imag&#39;</span><span class="p">]</span> <span class="o">*</span> <span class="mi">1</span><span class="n">j</span><span class="p">)</span>
+        <span class="n">Z</span> <span class="o">=</span> <span class="n">Z0</span><span class="p">[</span><span class="o">~</span><span class="n">np</span><span class="o">.</span><span class="n">isnan</span><span class="p">(</span><span class="n">Z0</span><span class="p">)]</span>
+
+        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">component_type</span> <span class="o">!=</span> <span class="s2">&quot;long&quot;</span><span class="p">:</span>
+            <span class="n">Z</span> <span class="o">=</span> <span class="n">Z</span> <span class="o">/</span> <span class="mi">1</span><span class="n">j</span>
+
+        <span class="n">freq</span> <span class="o">=</span> <span class="n">Z</span><span class="o">.</span><span class="n">index</span>
+        <span class="n">fs</span> <span class="o">=</span> <span class="p">(</span><span class="n">freq</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="n">freq</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span> <span class="o">/</span> <span class="nb">len</span><span class="p">(</span><span class="n">freq</span><span class="p">)</span>
+        <span class="n">sampling</span> <span class="o">=</span> <span class="n">freq</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="n">freq</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
+
+        <span class="k">if</span> <span class="n">nout</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="n">nout</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">Z</span><span class="p">)</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="n">nout</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">nout</span><span class="p">)</span>
+
+        <span class="n">time_array</span> <span class="o">=</span> <span class="n">sc</span><span class="o">.</span><span class="n">fft</span><span class="o">.</span><span class="n">fftfreq</span><span class="p">(</span><span class="n">nout</span><span class="p">,</span> <span class="n">sampling</span><span class="p">)</span>
+        <span class="n">Wlong_raw</span> <span class="o">=</span> <span class="n">sc</span><span class="o">.</span><span class="n">fft</span><span class="o">.</span><span class="n">irfft</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">Z</span><span class="p">),</span> <span class="n">n</span><span class="o">=</span><span class="n">nout</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span> <span class="o">*</span> <span class="n">nout</span> <span class="o">*</span> <span class="n">fs</span>
+
+        <span class="n">time</span> <span class="o">=</span> <span class="n">sc</span><span class="o">.</span><span class="n">fft</span><span class="o">.</span><span class="n">fftshift</span><span class="p">(</span><span class="n">time_array</span><span class="p">)</span>
+        <span class="n">Wlong</span> <span class="o">=</span> <span class="n">sc</span><span class="o">.</span><span class="n">fft</span><span class="o">.</span><span class="n">fftshift</span><span class="p">(</span><span class="n">Wlong_raw</span><span class="p">)</span>
+
+        <span class="k">if</span> <span class="n">trim</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">False</span><span class="p">:</span>
+            <span class="n">i_neg</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">where</span><span class="p">(</span><span class="n">time</span> <span class="o">&lt;</span> <span class="n">trim</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span>
+            <span class="n">Wlong</span><span class="p">[</span><span class="n">i_neg</span><span class="p">]</span> <span class="o">=</span> <span class="mi">0</span>
+
+        <span class="n">wf</span> <span class="o">=</span> <span class="n">WakeFunction</span><span class="p">(</span><span class="n">variable</span><span class="o">=</span><span class="n">time</span><span class="p">,</span>
+                          <span class="n">function</span><span class="o">=</span><span class="n">Wlong</span><span class="p">,</span>
+                          <span class="n">component_type</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">component_type</span><span class="p">)</span>
+        <span class="k">return</span> <span class="n">wf</span></div>
+
+<div class="viewcode-block" id="Impedance.plot"><a class="viewcode-back" href="../../../mbtrack2.impedance.html#mbtrack2.impedance.wakefield.Impedance.plot">[docs]</a>    <span class="k">def</span> <span class="nf">plot</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Plot the impedance data.</span>
+
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        ax : class:`matplotlib.axes.Axes`</span>
+<span class="sd">            Impedance data.</span>
+
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="n">ax</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">data</span><span class="o">.</span><span class="n">plot</span><span class="p">()</span>
+        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">component_type</span> <span class="o">==</span> <span class="s2">&quot;long&quot;</span><span class="p">:</span>
+            <span class="n">unit</span> <span class="o">=</span> <span class="s2">&quot; [ohm]&quot;</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="n">unit</span> <span class="o">=</span> <span class="s2">&quot; [ohm/m]&quot;</span>
+        <span class="n">label</span> <span class="o">=</span> <span class="sa">r</span><span class="s2">&quot;$Z_{&quot;</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">component_type</span> <span class="o">+</span> <span class="sa">r</span><span class="s2">&quot;}$&quot;</span> <span class="o">+</span> <span class="n">unit</span>
+        <span class="n">ax</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="n">label</span><span class="p">)</span>
+        <span class="k">return</span> <span class="n">ax</span></div></div>
+
+
+<div class="viewcode-block" id="WakeField"><a class="viewcode-back" href="../../../mbtrack2.impedance.html#mbtrack2.impedance.wakefield.WakeField">[docs]</a><span class="k">class</span> <span class="nc">WakeField</span><span class="p">:</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    Defines a WakeField which corresponds to a single physical element which </span>
+<span class="sd">    produces different types of wakes, represented by their Impedance or </span>
+<span class="sd">    WakeFunction objects.</span>
+<span class="sd">    </span>
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">    structure_list : list, optional</span>
+<span class="sd">        list of Impedance/WakeFunction objects to add to the WakeField.</span>
+<span class="sd">    name : str, optional</span>
+<span class="sd">    </span>
+<span class="sd">    Attributes</span>
+<span class="sd">    ----------</span>
+<span class="sd">    impedance_components : array of str</span>
+<span class="sd">        Impedance components present for this element.</span>
+<span class="sd">    wake_components : array of str</span>
+<span class="sd">        WakeFunction components present for this element.</span>
+<span class="sd">    components : array of str</span>
+<span class="sd">        Impedance or WakeFunction components present for this element.</span>
+<span class="sd">        </span>
+<span class="sd">    Methods</span>
+<span class="sd">    -------</span>
+<span class="sd">    append_to_model(structure_to_add)</span>
+<span class="sd">        Add Impedance/WakeFunction to WakeField.</span>
+<span class="sd">    list_to_attr(structure_list)</span>
+<span class="sd">        Add list of Impedance/WakeFunction to WakeField.</span>
+<span class="sd">    add_wakefields(wake1, beta1, wake2, beta2)</span>
+<span class="sd">        Add two WakeFields taking into account beta functions.</span>
+<span class="sd">    add_several_wakefields(wakefields, beta)</span>
+<span class="sd">        Add a list of WakeFields taking into account beta functions.</span>
+<span class="sd">    drop(component)</span>
+<span class="sd">        Delete a component or a list of component from the WakeField.</span>
+<span class="sd">    save(file)</span>
+<span class="sd">        Save WakeField element to file.</span>
+<span class="sd">    load(file)</span>
+<span class="sd">        Load WakeField element from file.</span>
+<span class="sd">    &quot;&quot;&quot;</span>
+
+    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">structure_list</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">name</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">list_to_attr</span><span class="p">(</span><span class="n">structure_list</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">name</span> <span class="o">=</span> <span class="n">name</span>
+
+    <span class="k">def</span> <span class="fm">__repr__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Return representation of WakeField components.&quot;&quot;&quot;</span>
+        <span class="k">return</span> <span class="sa">f</span><span class="s1">&#39;WakeField </span><span class="si">{</span><span class="bp">self</span><span class="o">.</span><span class="n">name</span><span class="si">}</span><span class="s1"> with components:</span><span class="se">\n</span><span class="s1"> </span><span class="si">{</span><span class="p">(</span><span class="nb">list</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">components</span><span class="p">))</span><span class="si">!r}</span><span class="s1">&#39;</span>
+
+    <span class="k">def</span> <span class="fm">__radd__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">structure_to_add</span><span class="p">):</span>
+        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_add</span><span class="p">(</span><span class="n">structure_to_add</span><span class="p">)</span>
+
+    <span class="k">def</span> <span class="fm">__add__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">structure_to_add</span><span class="p">):</span>
+        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_add</span><span class="p">(</span><span class="n">structure_to_add</span><span class="p">)</span>
+
+    <span class="k">def</span> <span class="fm">__iter__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Iterate over components&quot;&quot;&quot;</span>
+        <span class="n">comp</span> <span class="o">=</span> <span class="p">[</span><span class="nb">getattr</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">comp</span><span class="p">)</span> <span class="k">for</span> <span class="n">comp</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">components</span><span class="p">]</span>
+        <span class="k">return</span> <span class="n">comp</span><span class="o">.</span><span class="fm">__iter__</span><span class="p">()</span>
+
+    <span class="k">def</span> <span class="nf">_add</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">structure_to_add</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Allow to add two WakeField element with different components.&quot;&quot;&quot;</span>
+        <span class="k">for</span> <span class="n">comp</span> <span class="ow">in</span> <span class="n">structure_to_add</span><span class="o">.</span><span class="n">components</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">append_to_model</span><span class="p">(</span><span class="nb">getattr</span><span class="p">(</span><span class="n">structure_to_add</span><span class="p">,</span> <span class="n">comp</span><span class="p">))</span>
+        <span class="k">return</span> <span class="bp">self</span>
+
+<div class="viewcode-block" id="WakeField.append_to_model"><a class="viewcode-back" href="../../../mbtrack2.impedance.html#mbtrack2.impedance.wakefield.WakeField.append_to_model">[docs]</a>    <span class="k">def</span> <span class="nf">append_to_model</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">structure_to_add</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Add Impedance/WakeFunction component to WakeField.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        structure_to_add : Impedance or WakeFunction object</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="n">list_of_attributes</span> <span class="o">=</span> <span class="nb">dir</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span>
+        <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">structure_to_add</span><span class="p">,</span> <span class="n">Impedance</span><span class="p">):</span>
+            <span class="n">attribute_name</span> <span class="o">=</span> <span class="s2">&quot;Z&quot;</span> <span class="o">+</span> <span class="n">structure_to_add</span><span class="o">.</span><span class="n">component_type</span>
+            <span class="k">if</span> <span class="n">attribute_name</span> <span class="ow">in</span> <span class="n">list_of_attributes</span><span class="p">:</span>
+                <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">&quot;There is already a component of the type &quot;</span>
+                                 <span class="s2">&quot;</span><span class="si">{}</span><span class="s2"> in this element.&quot;</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">attribute_name</span><span class="p">))</span>
+            <span class="k">else</span><span class="p">:</span>
+                <span class="bp">self</span><span class="o">.</span><span class="fm">__setattr__</span><span class="p">(</span><span class="n">attribute_name</span><span class="p">,</span> <span class="n">structure_to_add</span><span class="p">)</span>
+        <span class="k">elif</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">structure_to_add</span><span class="p">,</span> <span class="n">WakeFunction</span><span class="p">):</span>
+            <span class="n">attribute_name</span> <span class="o">=</span> <span class="s2">&quot;W&quot;</span> <span class="o">+</span> <span class="n">structure_to_add</span><span class="o">.</span><span class="n">component_type</span>
+            <span class="k">if</span> <span class="n">attribute_name</span> <span class="ow">in</span> <span class="n">list_of_attributes</span><span class="p">:</span>
+                <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">&quot;There is already a component of the type &quot;</span>
+                                 <span class="s2">&quot;</span><span class="si">{}</span><span class="s2"> in this element.&quot;</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">attribute_name</span><span class="p">))</span>
+            <span class="k">else</span><span class="p">:</span>
+                <span class="bp">self</span><span class="o">.</span><span class="fm">__setattr__</span><span class="p">(</span><span class="n">attribute_name</span><span class="p">,</span> <span class="n">structure_to_add</span><span class="p">)</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span>
+                <span class="s2">&quot;</span><span class="si">{}</span><span class="s2"> is not an Impedance nor a WakeFunction.&quot;</span><span class="o">.</span><span class="n">format</span><span class="p">(</span>
+                    <span class="n">structure_to_add</span><span class="p">))</span></div>
+
+<div class="viewcode-block" id="WakeField.list_to_attr"><a class="viewcode-back" href="../../../mbtrack2.impedance.html#mbtrack2.impedance.wakefield.WakeField.list_to_attr">[docs]</a>    <span class="k">def</span> <span class="nf">list_to_attr</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">structure_list</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Add list of Impedance/WakeFunction components to WakeField.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        structure_list : list of Impedance or WakeFunction objects.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="k">if</span> <span class="n">structure_list</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="k">for</span> <span class="n">component</span> <span class="ow">in</span> <span class="n">structure_list</span><span class="p">:</span>
+                <span class="bp">self</span><span class="o">.</span><span class="n">append_to_model</span><span class="p">(</span><span class="n">component</span><span class="p">)</span></div>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">impedance_components</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Return an array of the impedance component names for the element.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="n">valid</span> <span class="o">=</span> <span class="p">[</span>
+            <span class="s2">&quot;Zlong&quot;</span><span class="p">,</span> <span class="s2">&quot;Zxdip&quot;</span><span class="p">,</span> <span class="s2">&quot;Zydip&quot;</span><span class="p">,</span> <span class="s2">&quot;Zxquad&quot;</span><span class="p">,</span> <span class="s2">&quot;Zyquad&quot;</span><span class="p">,</span> <span class="s2">&quot;Zxcst&quot;</span><span class="p">,</span> <span class="s2">&quot;Zycst&quot;</span>
+        <span class="p">]</span>
+        <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="n">comp</span> <span class="k">for</span> <span class="n">comp</span> <span class="ow">in</span> <span class="nb">dir</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="k">if</span> <span class="n">comp</span> <span class="ow">in</span> <span class="n">valid</span><span class="p">])</span>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">wake_components</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Return an array of the wake function component names for the element.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="n">valid</span> <span class="o">=</span> <span class="p">[</span>
+            <span class="s2">&quot;Wlong&quot;</span><span class="p">,</span> <span class="s2">&quot;Wxdip&quot;</span><span class="p">,</span> <span class="s2">&quot;Wydip&quot;</span><span class="p">,</span> <span class="s2">&quot;Wxquad&quot;</span><span class="p">,</span> <span class="s2">&quot;Wyquad&quot;</span><span class="p">,</span> <span class="s2">&quot;Wxcst&quot;</span><span class="p">,</span> <span class="s2">&quot;Wycst&quot;</span>
+        <span class="p">]</span>
+        <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="n">comp</span> <span class="k">for</span> <span class="n">comp</span> <span class="ow">in</span> <span class="nb">dir</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="k">if</span> <span class="n">comp</span> <span class="ow">in</span> <span class="n">valid</span><span class="p">])</span>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">components</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Return an array of the component names for the element.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="n">valid</span> <span class="o">=</span> <span class="p">[</span>
+            <span class="s2">&quot;Wlong&quot;</span><span class="p">,</span> <span class="s2">&quot;Wxdip&quot;</span><span class="p">,</span> <span class="s2">&quot;Wydip&quot;</span><span class="p">,</span> <span class="s2">&quot;Wxquad&quot;</span><span class="p">,</span> <span class="s2">&quot;Wyquad&quot;</span><span class="p">,</span> <span class="s2">&quot;Wxcst&quot;</span><span class="p">,</span> <span class="s2">&quot;Wycst&quot;</span><span class="p">,</span>
+            <span class="s2">&quot;Zlong&quot;</span><span class="p">,</span> <span class="s2">&quot;Zxdip&quot;</span><span class="p">,</span> <span class="s2">&quot;Zydip&quot;</span><span class="p">,</span> <span class="s2">&quot;Zxquad&quot;</span><span class="p">,</span> <span class="s2">&quot;Zyquad&quot;</span><span class="p">,</span> <span class="s2">&quot;Zxcst&quot;</span><span class="p">,</span> <span class="s2">&quot;Zycst&quot;</span>
+        <span class="p">]</span>
+        <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="n">comp</span> <span class="k">for</span> <span class="n">comp</span> <span class="ow">in</span> <span class="nb">dir</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="k">if</span> <span class="n">comp</span> <span class="ow">in</span> <span class="n">valid</span><span class="p">])</span>
+
+<div class="viewcode-block" id="WakeField.drop"><a class="viewcode-back" href="../../../mbtrack2.impedance.html#mbtrack2.impedance.wakefield.WakeField.drop">[docs]</a>    <span class="k">def</span> <span class="nf">drop</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">component</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Delete a component or a list of component from the WakeField.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        component : str or list of str</span>
+<span class="sd">            Component or list of components to drop.</span>
+<span class="sd">            If &quot;Z&quot;, drop all impedance components.</span>
+<span class="sd">            If &quot;W&quot;&quot;, drop all wake function components.</span>
+
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        None.</span>
+
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="k">if</span> <span class="n">component</span> <span class="o">==</span> <span class="s2">&quot;Z&quot;</span><span class="p">:</span>
+            <span class="n">component</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">impedance_components</span>
+        <span class="k">elif</span> <span class="n">component</span> <span class="o">==</span> <span class="s2">&quot;W&quot;</span><span class="p">:</span>
+            <span class="n">component</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">wake_components</span>
+
+        <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">component</span><span class="p">,</span> <span class="nb">str</span><span class="p">):</span>
+            <span class="nb">delattr</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">component</span><span class="p">)</span>
+        <span class="k">elif</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">component</span><span class="p">,</span> <span class="nb">list</span><span class="p">)</span> <span class="ow">or</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">component</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">):</span>
+            <span class="k">for</span> <span class="n">comp</span> <span class="ow">in</span> <span class="n">component</span><span class="p">:</span>
+                <span class="nb">delattr</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">comp</span><span class="p">)</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s2">&quot;component should be a str or list of str.&quot;</span><span class="p">)</span></div>
+
+<div class="viewcode-block" id="WakeField.save"><a class="viewcode-back" href="../../../mbtrack2.impedance.html#mbtrack2.impedance.wakefield.WakeField.save">[docs]</a>    <span class="k">def</span> <span class="nf">save</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">file</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Save WakeField element to file.</span>
+<span class="sd">        </span>
+<span class="sd">        The same pandas version is needed on both saving and loading computer</span>
+<span class="sd">        for the pickle to work.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        file : str</span>
+<span class="sd">            File where the WakeField element is saved.</span>
+
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        None.</span>
+
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="k">with</span> <span class="nb">open</span><span class="p">(</span><span class="n">file</span><span class="p">,</span> <span class="s2">&quot;wb&quot;</span><span class="p">)</span> <span class="k">as</span> <span class="n">f</span><span class="p">:</span>
+            <span class="n">pickle</span><span class="o">.</span><span class="n">dump</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">f</span><span class="p">)</span></div>
+
+<div class="viewcode-block" id="WakeField.load"><a class="viewcode-back" href="../../../mbtrack2.impedance.html#mbtrack2.impedance.wakefield.WakeField.load">[docs]</a>    <span class="nd">@staticmethod</span>
+    <span class="k">def</span> <span class="nf">load</span><span class="p">(</span><span class="n">file</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Load WakeField element from file.</span>
+<span class="sd">        </span>
+<span class="sd">        The same pandas version is needed on both saving and loading computer</span>
+<span class="sd">        for the pickle to work.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        file : str</span>
+<span class="sd">            File where the WakeField element is saved.</span>
+
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        wakefield : WakeField</span>
+<span class="sd">            Loaded wakefield.</span>
+
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="k">with</span> <span class="nb">open</span><span class="p">(</span><span class="n">file</span><span class="p">,</span> <span class="s1">&#39;rb&#39;</span><span class="p">)</span> <span class="k">as</span> <span class="n">f</span><span class="p">:</span>
+            <span class="n">wakefield</span> <span class="o">=</span> <span class="n">pickle</span><span class="o">.</span><span class="n">load</span><span class="p">(</span><span class="n">f</span><span class="p">)</span>
+
+        <span class="k">return</span> <span class="n">wakefield</span></div>
+
+<div class="viewcode-block" id="WakeField.add_wakefields"><a class="viewcode-back" href="../../../mbtrack2.impedance.html#mbtrack2.impedance.wakefield.WakeField.add_wakefields">[docs]</a>    <span class="nd">@staticmethod</span>
+    <span class="k">def</span> <span class="nf">add_wakefields</span><span class="p">(</span><span class="n">wake1</span><span class="p">,</span> <span class="n">beta1</span><span class="p">,</span> <span class="n">wake2</span><span class="p">,</span> <span class="n">beta2</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Add two WakeFields taking into account beta functions.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        wake1 : WakeField</span>
+<span class="sd">            WakeField to add.</span>
+<span class="sd">        beta1 : array of shape (2,)</span>
+<span class="sd">            Beta functions at wake1 postion.</span>
+<span class="sd">        wake2 : WakeField</span>
+<span class="sd">            WakeField to add.</span>
+<span class="sd">        beta2 : array of shape (2,)</span>
+<span class="sd">            Beta functions at wake2 postion.</span>
+
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        wake_sum : WakeField</span>
+<span class="sd">            WakeField with summed components.</span>
+
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="n">wake_sum</span> <span class="o">=</span> <span class="n">deepcopy</span><span class="p">(</span><span class="n">wake1</span><span class="p">)</span>
+        <span class="k">for</span> <span class="n">component_name1</span> <span class="ow">in</span> <span class="n">wake1</span><span class="o">.</span><span class="n">components</span><span class="p">:</span>
+            <span class="n">comp1</span> <span class="o">=</span> <span class="nb">getattr</span><span class="p">(</span><span class="n">wake_sum</span><span class="p">,</span> <span class="n">component_name1</span><span class="p">)</span>
+            <span class="n">weight1</span> <span class="o">=</span> <span class="p">((</span><span class="n">beta1</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">**</span><span class="n">comp1</span><span class="o">.</span><span class="n">power_x</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="n">beta1</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">**</span><span class="n">comp1</span><span class="o">.</span><span class="n">power_y</span><span class="p">))</span>
+            <span class="nb">setattr</span><span class="p">(</span><span class="n">wake_sum</span><span class="p">,</span> <span class="n">component_name1</span><span class="p">,</span> <span class="n">weight1</span> <span class="o">*</span> <span class="n">comp1</span><span class="p">)</span>
+
+        <span class="k">for</span> <span class="n">component_name2</span> <span class="ow">in</span> <span class="n">wake2</span><span class="o">.</span><span class="n">components</span><span class="p">:</span>
+            <span class="n">comp2</span> <span class="o">=</span> <span class="nb">getattr</span><span class="p">(</span><span class="n">wake2</span><span class="p">,</span> <span class="n">component_name2</span><span class="p">)</span>
+            <span class="n">weight2</span> <span class="o">=</span> <span class="p">((</span><span class="n">beta2</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">**</span><span class="n">comp2</span><span class="o">.</span><span class="n">power_x</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="n">beta2</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">**</span><span class="n">comp2</span><span class="o">.</span><span class="n">power_y</span><span class="p">))</span>
+            <span class="k">try</span><span class="p">:</span>
+                <span class="n">comp1</span> <span class="o">=</span> <span class="nb">getattr</span><span class="p">(</span><span class="n">wake_sum</span><span class="p">,</span> <span class="n">component_name2</span><span class="p">)</span>
+                <span class="nb">setattr</span><span class="p">(</span><span class="n">wake_sum</span><span class="p">,</span> <span class="n">component_name2</span><span class="p">,</span> <span class="n">comp1</span> <span class="o">+</span> <span class="n">weight2</span><span class="o">*</span><span class="n">comp2</span><span class="p">)</span>
+            <span class="k">except</span> <span class="ne">AttributeError</span><span class="p">:</span>
+                <span class="nb">setattr</span><span class="p">(</span><span class="n">wake_sum</span><span class="p">,</span> <span class="n">component_name2</span><span class="p">,</span> <span class="n">weight2</span> <span class="o">*</span> <span class="n">comp2</span><span class="p">)</span>
+
+        <span class="k">return</span> <span class="n">wake_sum</span></div>
+
+<div class="viewcode-block" id="WakeField.add_several_wakefields"><a class="viewcode-back" href="../../../mbtrack2.impedance.html#mbtrack2.impedance.wakefield.WakeField.add_several_wakefields">[docs]</a>    <span class="nd">@staticmethod</span>
+    <span class="k">def</span> <span class="nf">add_several_wakefields</span><span class="p">(</span><span class="n">wakefields</span><span class="p">,</span> <span class="n">beta</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Add a list of WakeFields taking into account beta functions.</span>
+<span class="sd">        </span>
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        wakefields : list of WakeField</span>
+<span class="sd">            WakeFields to add.</span>
+<span class="sd">        beta : array of shape (len(wakefields), 2)</span>
+<span class="sd">            Beta functions at the WakeField postions.</span>
+
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        wake_sum : WakeField</span>
+<span class="sd">            WakeField with summed components.</span>
+
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">wakefields</span><span class="p">)</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
+            <span class="k">return</span> <span class="n">wakefields</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
+        <span class="k">elif</span> <span class="nb">len</span><span class="p">(</span><span class="n">wakefields</span><span class="p">)</span> <span class="o">&gt;</span> <span class="mi">1</span><span class="p">:</span>
+            <span class="n">wake_sum</span> <span class="o">=</span> <span class="n">WakeField</span><span class="o">.</span><span class="n">add_wakefields</span><span class="p">(</span><span class="n">wakefields</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">beta</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">],</span>
+                                                <span class="n">wakefields</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">beta</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">])</span>
+            <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">wakefields</span><span class="p">)</span> <span class="o">-</span> <span class="mi">2</span><span class="p">):</span>
+                <span class="n">wake_sum</span> <span class="o">=</span> <span class="n">WakeField</span><span class="o">.</span><span class="n">add_wakefields</span><span class="p">(</span><span class="n">wake_sum</span><span class="p">,</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span>
+                                                    <span class="n">wakefields</span><span class="p">[</span><span class="n">i</span> <span class="o">+</span> <span class="mi">2</span><span class="p">],</span>
+                                                    <span class="n">beta</span><span class="p">[:,</span> <span class="n">i</span> <span class="o">+</span> <span class="mi">2</span><span class="p">])</span>
+            <span class="k">return</span> <span class="n">wake_sum</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">&quot;Error in input.&quot;</span><span class="p">)</span></div></div>
+</pre></div>
+
+            <div class="clearer"></div>
+          </div>
+        </div>
+      </div>
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+          <li class="nav-item nav-item-1"><a href="../../index.html" >Module code</a> &#187;</li>
+        <li class="nav-item nav-item-this"><a href="">mbtrack2.impedance.wakefield</a></li> 
+      </ul>
+    </div>
+    <div class="footer" role="contentinfo">
+        &#169; Copyright 2024, A. Gamelin et al.
+      Created using <a href="https://www.sphinx-doc.org/">Sphinx</a> 5.0.2.
+    </div>
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+</html>
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diff --git a/docs/build/html/_modules/mbtrack2/instability/instabilities.html b/docs/build/html/_modules/mbtrack2/instability/instabilities.html
new file mode 100644
index 0000000..8a15ff0
--- /dev/null
+++ b/docs/build/html/_modules/mbtrack2/instability/instabilities.html
@@ -0,0 +1,511 @@
+
+<!DOCTYPE html>
+
+<html lang="en">
+  <head>
+    <meta charset="utf-8" />
+    <meta name="viewport" content="width=device-width, initial-scale=1.0" />
+    <title>mbtrack2.instability.instabilities &#8212; mbtrack2 0.6.0 documentation</title>
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+             >modules</a> |</li>
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+          <li class="nav-item nav-item-1"><a href="../../index.html" accesskey="U">Module code</a> &#187;</li>
+        <li class="nav-item nav-item-this"><a href="">mbtrack2.instability.instabilities</a></li> 
+      </ul>
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+
+    <div class="document">
+      <div class="documentwrapper">
+        <div class="bodywrapper">
+          <div class="body" role="main">
+            
+  <h1>Source code for mbtrack2.instability.instabilities</h1><div class="highlight"><pre>
+<span></span><span class="c1"># -*- coding: utf-8 -*-</span>
+<span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">General calculations about instability thresholds.</span>
+<span class="sd">&quot;&quot;&quot;</span>
+
+<span class="kn">import</span> <span class="nn">math</span>
+
+<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
+<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="kn">from</span> <span class="nn">scipy.constants</span> <span class="kn">import</span> <span class="n">c</span><span class="p">,</span> <span class="n">e</span><span class="p">,</span> <span class="n">epsilon_0</span><span class="p">,</span> <span class="n">m_e</span><span class="p">,</span> <span class="n">mu_0</span><span class="p">,</span> <span class="n">pi</span>
+
+
+<div class="viewcode-block" id="mbi_threshold"><a class="viewcode-back" href="../../../mbtrack2.instability.html#mbtrack2.instability.instabilities.mbi_threshold">[docs]</a><span class="k">def</span> <span class="nf">mbi_threshold</span><span class="p">(</span><span class="n">ring</span><span class="p">,</span> <span class="n">sigma</span><span class="p">,</span> <span class="n">R</span><span class="p">,</span> <span class="n">b</span><span class="p">):</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    Compute the microbunching instability (MBI) threshold for a bunched beam</span>
+<span class="sd">    considering the steady-state parallel plate model [1][2].</span>
+<span class="sd">    </span>
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">    ring : Synchrotron object</span>
+<span class="sd">    sigma : float</span>
+<span class="sd">        RMS bunch length in [s]</span>
+<span class="sd">    R : float</span>
+<span class="sd">        dipole bending radius in [m]</span>
+<span class="sd">    b : float</span>
+<span class="sd">        vertical distance between the conducting parallel plates in [m]</span>
+<span class="sd">        </span>
+<span class="sd">    Returns</span>
+<span class="sd">    -------</span>
+<span class="sd">    I : float</span>
+<span class="sd">        MBI current threshold in [A]</span>
+<span class="sd">        </span>
+<span class="sd">    [1] : Y. Cai, &quot;Theory of microwave instability and coherent synchrotron </span>
+<span class="sd">    radiation in electron storage rings&quot;, SLAC-PUB-14561</span>
+<span class="sd">    [2] : D. Zhou, &quot;Coherent synchrotron radiation and microwave instability in </span>
+<span class="sd">    electron storage rings&quot;, PhD thesis, p112</span>
+<span class="sd">    &quot;&quot;&quot;</span>
+
+    <span class="n">sigma</span> <span class="o">=</span> <span class="n">sigma</span> <span class="o">*</span> <span class="n">c</span>
+    <span class="n">Ia</span> <span class="o">=</span> <span class="mi">4</span> <span class="o">*</span> <span class="n">pi</span> <span class="o">*</span> <span class="n">epsilon_0</span> <span class="o">*</span> <span class="n">m_e</span> <span class="o">*</span> <span class="n">c</span><span class="o">**</span><span class="mi">3</span> <span class="o">/</span> <span class="n">e</span>  <span class="c1"># Alfven current</span>
+    <span class="n">chi</span> <span class="o">=</span> <span class="n">sigma</span> <span class="o">*</span> <span class="p">(</span><span class="n">R</span> <span class="o">/</span> <span class="n">b</span><span class="o">**</span><span class="mi">3</span><span class="p">)</span><span class="o">**</span><span class="p">(</span><span class="mi">1</span> <span class="o">/</span> <span class="mi">2</span><span class="p">)</span>  <span class="c1"># Shielding paramter</span>
+    <span class="n">xi</span> <span class="o">=</span> <span class="mf">0.5</span> <span class="o">+</span> <span class="mf">0.34</span><span class="o">*</span><span class="n">chi</span>
+    <span class="n">N</span> <span class="o">=</span> <span class="p">(</span><span class="n">ring</span><span class="o">.</span><span class="n">L</span> <span class="o">*</span> <span class="n">Ia</span> <span class="o">*</span> <span class="n">ring</span><span class="o">.</span><span class="n">ac</span> <span class="o">*</span> <span class="n">ring</span><span class="o">.</span><span class="n">gamma</span> <span class="o">*</span> <span class="n">ring</span><span class="o">.</span><span class="n">sigma_delta</span><span class="o">**</span><span class="mi">2</span> <span class="o">*</span> <span class="n">xi</span> <span class="o">*</span>
+         <span class="n">sigma</span><span class="o">**</span><span class="p">(</span><span class="mi">1</span> <span class="o">/</span> <span class="mi">3</span><span class="p">)</span> <span class="o">/</span> <span class="p">(</span><span class="n">c</span> <span class="o">*</span> <span class="n">e</span> <span class="o">*</span> <span class="n">R</span><span class="o">**</span><span class="p">(</span><span class="mi">1</span> <span class="o">/</span> <span class="mi">3</span><span class="p">)))</span>
+    <span class="n">I</span> <span class="o">=</span> <span class="n">N</span> <span class="o">*</span> <span class="n">e</span> <span class="o">/</span> <span class="n">ring</span><span class="o">.</span><span class="n">T0</span>
+
+    <span class="k">return</span> <span class="n">I</span></div>
+
+
+<div class="viewcode-block" id="cbi_threshold"><a class="viewcode-back" href="../../../mbtrack2.instability.html#mbtrack2.instability.instabilities.cbi_threshold">[docs]</a><span class="k">def</span> <span class="nf">cbi_threshold</span><span class="p">(</span><span class="n">ring</span><span class="p">,</span> <span class="n">I</span><span class="p">,</span> <span class="n">Vrf</span><span class="p">,</span> <span class="n">f</span><span class="p">,</span> <span class="n">beta</span><span class="p">,</span> <span class="n">Ncav</span><span class="o">=</span><span class="mi">1</span><span class="p">):</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    Compute the longitudinal and transverse coupled bunch instability </span>
+<span class="sd">    thresolds driven by HOMs [1].</span>
+<span class="sd">    </span>
+<span class="sd">    Approximate formula, does not take into account variation with Q.</span>
+<span class="sd">    For better estimate use lcbi_growth_rate.</span>
+
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">    ring : Synchrotron object</span>
+<span class="sd">    I : float</span>
+<span class="sd">        Total beam current in [A].</span>
+<span class="sd">    Vrf : float</span>
+<span class="sd">        Total RF voltage in [V].</span>
+<span class="sd">    f : float</span>
+<span class="sd">        Frequency of the HOM in [Hz].</span>
+<span class="sd">    beta : array-like of shape (2,)</span>
+<span class="sd">        Horizontal and vertical beta function at the HOM position in [m].</span>
+<span class="sd">    Ncav : int, optional</span>
+<span class="sd">        Number of RF cavity.</span>
+
+<span class="sd">    Returns</span>
+<span class="sd">    -------</span>
+<span class="sd">    Zlong : float</span>
+<span class="sd">        Maximum longitudinal impedance of the HOM in [ohm].</span>
+<span class="sd">    Zxdip : float</span>
+<span class="sd">        Maximum horizontal dipolar impedance of the HOM in [ohm/m].</span>
+<span class="sd">    Zydip : float</span>
+<span class="sd">        Maximum vertical dipolar impedance of the HOM in [ohm/m].</span>
+<span class="sd">        </span>
+<span class="sd">    References</span>
+<span class="sd">    ----------</span>
+<span class="sd">    [1] : Ruprecht, Martin, et al. &quot;Calculation of Transverse Coupled Bunch </span>
+<span class="sd">    Instabilities in Electron Storage Rings Driven By Quadrupole Higher Order </span>
+<span class="sd">    Modes.&quot; 7th Int. Particle Accelerator Conf.(IPAC&#39;16), Busan, Korea. </span>
+<span class="sd">    &quot;&quot;&quot;</span>
+
+    <span class="n">fs</span> <span class="o">=</span> <span class="n">ring</span><span class="o">.</span><span class="n">synchrotron_tune</span><span class="p">(</span><span class="n">Vrf</span><span class="p">)</span> <span class="o">*</span> <span class="n">ring</span><span class="o">.</span><span class="n">f0</span>
+    <span class="n">Zlong</span> <span class="o">=</span> <span class="n">fs</span> <span class="o">/</span> <span class="p">(</span><span class="n">f</span> <span class="o">*</span> <span class="n">ring</span><span class="o">.</span><span class="n">ac</span> <span class="o">*</span> <span class="n">ring</span><span class="o">.</span><span class="n">tau</span><span class="p">[</span><span class="mi">2</span><span class="p">])</span> <span class="o">*</span> <span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">ring</span><span class="o">.</span><span class="n">E0</span><span class="p">)</span> <span class="o">/</span> <span class="p">(</span><span class="n">ring</span><span class="o">.</span><span class="n">f0</span> <span class="o">*</span> <span class="n">I</span> <span class="o">*</span>
+                                                                <span class="n">Ncav</span><span class="p">)</span>
+    <span class="n">Zxdip</span> <span class="o">=</span> <span class="mi">1</span> <span class="o">/</span> <span class="p">(</span><span class="n">ring</span><span class="o">.</span><span class="n">tau</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">beta</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span> <span class="o">*</span> <span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">ring</span><span class="o">.</span><span class="n">E0</span><span class="p">)</span> <span class="o">/</span> <span class="p">(</span><span class="n">ring</span><span class="o">.</span><span class="n">f0</span> <span class="o">*</span> <span class="n">I</span> <span class="o">*</span> <span class="n">Ncav</span><span class="p">)</span>
+    <span class="n">Zydip</span> <span class="o">=</span> <span class="mi">1</span> <span class="o">/</span> <span class="p">(</span><span class="n">ring</span><span class="o">.</span><span class="n">tau</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="n">beta</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span> <span class="o">*</span> <span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">ring</span><span class="o">.</span><span class="n">E0</span><span class="p">)</span> <span class="o">/</span> <span class="p">(</span><span class="n">ring</span><span class="o">.</span><span class="n">f0</span> <span class="o">*</span> <span class="n">I</span> <span class="o">*</span> <span class="n">Ncav</span><span class="p">)</span>
+
+    <span class="k">return</span> <span class="p">(</span><span class="n">Zlong</span><span class="p">,</span> <span class="n">Zxdip</span><span class="p">,</span> <span class="n">Zydip</span><span class="p">)</span></div>
+
+
+<div class="viewcode-block" id="lcbi_growth_rate_mode"><a class="viewcode-back" href="../../../mbtrack2.instability.html#mbtrack2.instability.instabilities.lcbi_growth_rate_mode">[docs]</a><span class="k">def</span> <span class="nf">lcbi_growth_rate_mode</span><span class="p">(</span><span class="n">ring</span><span class="p">,</span>
+                          <span class="n">I</span><span class="p">,</span>
+                          <span class="n">M</span><span class="p">,</span>
+                          <span class="n">mu</span><span class="p">,</span>
+                          <span class="n">synchrotron_tune</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+                          <span class="n">Vrf</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+                          <span class="n">fr</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+                          <span class="n">RL</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+                          <span class="n">QL</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+                          <span class="n">Z</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    Compute the longitudinal coupled bunch instability growth rate driven by</span>
+<span class="sd">    an impedance for a given coupled bunch mode mu [1].</span>
+<span class="sd">    </span>
+<span class="sd">    Use either a list of resonators (fr, RL, QL) or an Impedance object (Z).</span>
+
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">    ring : Synchrotron object</span>
+<span class="sd">    I : float</span>
+<span class="sd">        Total beam current in [A].</span>
+<span class="sd">    M : int</span>
+<span class="sd">        Nomber of bunches in the beam.</span>
+<span class="sd">    mu : int</span>
+<span class="sd">        Coupled bunch mode number (= 0, ..., M-1).</span>
+<span class="sd">    synchrotron_tune : float, optional</span>
+<span class="sd">        Synchrotron tune.</span>
+<span class="sd">    Vrf : float, optinal</span>
+<span class="sd">        Total RF voltage in [V] used to compute synchrotron tune if not given.</span>
+<span class="sd">    fr : float or list, optional</span>
+<span class="sd">        Frequency of the resonator in [Hz].</span>
+<span class="sd">    RL : float or list, optional</span>
+<span class="sd">        Loaded shunt impedance of the resonator in [Ohm].</span>
+<span class="sd">    QL : float or list, optional</span>
+<span class="sd">        Loaded quality factor of the resonator.</span>
+<span class="sd">    Z : Impedance, optional</span>
+<span class="sd">        Longitunial impedance to consider.</span>
+
+<span class="sd">    Returns</span>
+<span class="sd">    -------</span>
+<span class="sd">    float</span>
+<span class="sd">        Coupled bunch instability growth rate for the mode mu in [s-1].</span>
+<span class="sd">        </span>
+<span class="sd">    References</span>
+<span class="sd">    ----------</span>
+<span class="sd">    [1] : Eq. 51 p139 of Akai, Kazunori. &quot;RF System for Electron Storage </span>
+<span class="sd">    Rings.&quot; Physics And Engineering Of High Performance Electron Storage Rings </span>
+<span class="sd">    And Application Of Superconducting Technology. 2002. 118-149.</span>
+
+<span class="sd">    &quot;&quot;&quot;</span>
+
+    <span class="k">if</span> <span class="n">synchrotron_tune</span> <span class="ow">is</span> <span class="kc">None</span> <span class="ow">and</span> <span class="n">Vrf</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+        <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">&quot;Either synchrotron_tune or Vrf is needed.&quot;</span><span class="p">)</span>
+    <span class="k">if</span> <span class="n">synchrotron_tune</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+        <span class="n">nu_s</span> <span class="o">=</span> <span class="n">ring</span><span class="o">.</span><span class="n">synchrotron_tune</span><span class="p">(</span><span class="n">Vrf</span><span class="p">)</span>
+    <span class="k">else</span><span class="p">:</span>
+        <span class="n">nu_s</span> <span class="o">=</span> <span class="n">synchrotron_tune</span>
+    <span class="n">factor</span> <span class="o">=</span> <span class="n">ring</span><span class="o">.</span><span class="n">eta</span><span class="p">()</span> <span class="o">*</span> <span class="n">I</span> <span class="o">/</span> <span class="p">(</span><span class="mi">4</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="n">ring</span><span class="o">.</span><span class="n">E0</span> <span class="o">*</span> <span class="n">nu_s</span><span class="p">)</span>
+
+    <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">fr</span><span class="p">,</span> <span class="p">(</span><span class="nb">float</span><span class="p">,</span> <span class="nb">int</span><span class="p">)):</span>
+        <span class="n">fr</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="n">fr</span><span class="p">])</span>
+    <span class="k">elif</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">fr</span><span class="p">,</span> <span class="nb">list</span><span class="p">):</span>
+        <span class="n">fr</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">fr</span><span class="p">)</span>
+    <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">RL</span><span class="p">,</span> <span class="p">(</span><span class="nb">float</span><span class="p">,</span> <span class="nb">int</span><span class="p">)):</span>
+        <span class="n">RL</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="n">RL</span><span class="p">])</span>
+    <span class="k">elif</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">RL</span><span class="p">,</span> <span class="nb">list</span><span class="p">):</span>
+        <span class="n">RL</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">RL</span><span class="p">)</span>
+    <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">QL</span><span class="p">,</span> <span class="p">(</span><span class="nb">float</span><span class="p">,</span> <span class="nb">int</span><span class="p">)):</span>
+        <span class="n">QL</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="n">QL</span><span class="p">])</span>
+    <span class="k">elif</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">QL</span><span class="p">,</span> <span class="nb">list</span><span class="p">):</span>
+        <span class="n">QL</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">QL</span><span class="p">)</span>
+
+    <span class="k">if</span> <span class="n">Z</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+        <span class="n">omega_r</span> <span class="o">=</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="n">fr</span>
+        <span class="n">n_max</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="mi">10</span> <span class="o">*</span> <span class="n">omega_r</span><span class="o">.</span><span class="n">max</span><span class="p">()</span> <span class="o">/</span> <span class="p">(</span><span class="n">ring</span><span class="o">.</span><span class="n">omega0</span> <span class="o">*</span> <span class="n">M</span><span class="p">))</span>
+
+        <span class="k">def</span> <span class="nf">Zr</span><span class="p">(</span><span class="n">omega</span><span class="p">):</span>
+            <span class="n">Z</span> <span class="o">=</span> <span class="mi">0</span>
+            <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">fr</span><span class="p">)):</span>
+                <span class="n">Z</span> <span class="o">+=</span> <span class="n">np</span><span class="o">.</span><span class="n">real</span><span class="p">(</span><span class="n">RL</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">/</span>
+                             <span class="p">(</span><span class="mi">1</span> <span class="o">+</span> <span class="mi">1</span><span class="n">j</span> <span class="o">*</span> <span class="n">QL</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">*</span>
+                              <span class="p">(</span><span class="n">omega_r</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">/</span> <span class="n">omega</span> <span class="o">-</span> <span class="n">omega</span> <span class="o">/</span> <span class="n">omega_r</span><span class="p">[</span><span class="n">i</span><span class="p">])))</span>
+            <span class="k">return</span> <span class="n">Z</span>
+    <span class="k">else</span><span class="p">:</span>
+        <span class="n">fmax</span> <span class="o">=</span> <span class="n">Z</span><span class="o">.</span><span class="n">data</span><span class="o">.</span><span class="n">index</span><span class="o">.</span><span class="n">max</span><span class="p">()</span>
+        <span class="n">n_max</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="n">fmax</span> <span class="o">/</span> <span class="p">(</span><span class="n">ring</span><span class="o">.</span><span class="n">omega0</span> <span class="o">*</span> <span class="n">M</span><span class="p">))</span>
+
+        <span class="k">def</span> <span class="nf">Zr</span><span class="p">(</span><span class="n">omega</span><span class="p">):</span>
+            <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">real</span><span class="p">(</span><span class="n">Z</span><span class="p">(</span><span class="n">omega</span> <span class="o">/</span> <span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span><span class="p">)))</span>
+
+    <span class="n">n0</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="n">n_max</span><span class="p">)</span>
+    <span class="n">n1</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">n_max</span><span class="p">)</span>
+    <span class="n">omega_p</span> <span class="o">=</span> <span class="n">ring</span><span class="o">.</span><span class="n">omega0</span> <span class="o">*</span> <span class="p">(</span><span class="n">n0</span><span class="o">*</span><span class="n">M</span> <span class="o">+</span> <span class="n">mu</span> <span class="o">+</span> <span class="n">nu_s</span><span class="p">)</span>
+    <span class="n">omega_m</span> <span class="o">=</span> <span class="n">ring</span><span class="o">.</span><span class="n">omega0</span> <span class="o">*</span> <span class="p">(</span><span class="n">n1</span><span class="o">*</span><span class="n">M</span> <span class="o">-</span> <span class="n">mu</span> <span class="o">-</span> <span class="n">nu_s</span><span class="p">)</span>
+
+    <span class="n">sum_val</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">omega_p</span> <span class="o">*</span> <span class="n">Zr</span><span class="p">(</span><span class="n">omega_p</span><span class="p">))</span> <span class="o">-</span> <span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">omega_m</span> <span class="o">*</span> <span class="n">Zr</span><span class="p">(</span><span class="n">omega_m</span><span class="p">))</span>
+
+    <span class="k">return</span> <span class="n">factor</span> <span class="o">*</span> <span class="n">sum_val</span></div>
+
+
+<div class="viewcode-block" id="lcbi_growth_rate"><a class="viewcode-back" href="../../../mbtrack2.instability.html#mbtrack2.instability.instabilities.lcbi_growth_rate">[docs]</a><span class="k">def</span> <span class="nf">lcbi_growth_rate</span><span class="p">(</span><span class="n">ring</span><span class="p">,</span>
+                     <span class="n">I</span><span class="p">,</span>
+                     <span class="n">M</span><span class="p">,</span>
+                     <span class="n">synchrotron_tune</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+                     <span class="n">Vrf</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+                     <span class="n">fr</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+                     <span class="n">RL</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+                     <span class="n">QL</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+                     <span class="n">Z</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    Compute the maximum growth rate for longitudinal coupled bunch instability </span>
+<span class="sd">    driven an impedance [1].</span>
+<span class="sd">    </span>
+<span class="sd">    Use either a list of resonators (fr, RL, QL) or an Impedance object (Z).</span>
+
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">    ring : Synchrotron object</span>
+<span class="sd">    I : float</span>
+<span class="sd">        Total beam current in [A].</span>
+<span class="sd">    M : int</span>
+<span class="sd">        Nomber of bunches in the beam.</span>
+<span class="sd">    synchrotron_tune : float, optional</span>
+<span class="sd">        Synchrotron tune.</span>
+<span class="sd">    Vrf : float, optinal</span>
+<span class="sd">        Total RF voltage in [V] used to compute synchrotron tune if not given.</span>
+<span class="sd">    fr : float or list, optional</span>
+<span class="sd">        Frequency of the HOM in [Hz].</span>
+<span class="sd">    RL : float or list, optional</span>
+<span class="sd">        Loaded shunt impedance of the HOM in [Ohm].</span>
+<span class="sd">    QL : float or list, optional</span>
+<span class="sd">        Loaded quality factor of the HOM.</span>
+<span class="sd">    Z : Impedance, optional</span>
+<span class="sd">        Longitunial impedance to consider.</span>
+
+<span class="sd">    Returns</span>
+<span class="sd">    -------</span>
+<span class="sd">    growth_rate : float</span>
+<span class="sd">        Maximum coupled bunch instability growth rate in [s-1].</span>
+<span class="sd">    mu : int</span>
+<span class="sd">        Coupled bunch mode number corresponding to the maximum coupled bunch </span>
+<span class="sd">        instability growth rate.</span>
+<span class="sd">    growth_rates : array</span>
+<span class="sd">        Coupled bunch instability growth rates for the different mode numbers </span>
+<span class="sd">        in [s-1].</span>
+<span class="sd">        </span>
+<span class="sd">    References</span>
+<span class="sd">    ----------</span>
+<span class="sd">    [1] : Eq. 51 p139 of Akai, Kazunori. &quot;RF System for Electron Storage </span>
+<span class="sd">    Rings.&quot; Physics And Engineering Of High Performance Electron Storage Rings </span>
+<span class="sd">    And Application Of Superconducting Technology. 2002. 118-149.</span>
+
+<span class="sd">    &quot;&quot;&quot;</span>
+    <span class="n">growth_rates</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">M</span><span class="p">)</span>
+    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">M</span><span class="p">):</span>
+        <span class="n">growth_rates</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="n">lcbi_growth_rate_mode</span><span class="p">(</span>
+            <span class="n">ring</span><span class="p">,</span>
+            <span class="n">I</span><span class="p">,</span>
+            <span class="n">M</span><span class="p">,</span>
+            <span class="n">i</span><span class="p">,</span>
+            <span class="n">synchrotron_tune</span><span class="o">=</span><span class="n">synchrotron_tune</span><span class="p">,</span>
+            <span class="n">Vrf</span><span class="o">=</span><span class="n">Vrf</span><span class="p">,</span>
+            <span class="n">fr</span><span class="o">=</span><span class="n">fr</span><span class="p">,</span>
+            <span class="n">RL</span><span class="o">=</span><span class="n">RL</span><span class="p">,</span>
+            <span class="n">QL</span><span class="o">=</span><span class="n">QL</span><span class="p">,</span>
+            <span class="n">Z</span><span class="o">=</span><span class="n">Z</span><span class="p">)</span>
+
+    <span class="n">growth_rate</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">max</span><span class="p">(</span><span class="n">growth_rates</span><span class="p">)</span>
+    <span class="n">mu</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">argmax</span><span class="p">(</span><span class="n">growth_rates</span><span class="p">)</span>
+
+    <span class="k">return</span> <span class="n">growth_rate</span><span class="p">,</span> <span class="n">mu</span><span class="p">,</span> <span class="n">growth_rates</span></div>
+
+
+<div class="viewcode-block" id="lcbi_stability_diagram"><a class="viewcode-back" href="../../../mbtrack2.instability.html#mbtrack2.instability.instabilities.lcbi_stability_diagram">[docs]</a><span class="k">def</span> <span class="nf">lcbi_stability_diagram</span><span class="p">(</span><span class="n">ring</span><span class="p">,</span>
+                           <span class="n">I</span><span class="p">,</span>
+                           <span class="n">M</span><span class="p">,</span>
+                           <span class="n">modes</span><span class="p">,</span>
+                           <span class="n">cavity_list</span><span class="p">,</span>
+                           <span class="n">detune_range</span><span class="p">,</span>
+                           <span class="n">synchrotron_tune</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+                           <span class="n">Vrf</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    Plot longitudinal coupled bunch instability stability diagram for a </span>
+<span class="sd">    arbitrary list of CavityResonator objects around a detuning range.</span>
+<span class="sd">    </span>
+<span class="sd">    Last object in the cavity_list is assumed to be the one with the variable </span>
+<span class="sd">    detuning.</span>
+
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">    ring : Synchrotron object</span>
+<span class="sd">        Ring parameters.</span>
+<span class="sd">    I : float</span>
+<span class="sd">        Total beam current in [A].</span>
+<span class="sd">    M : int</span>
+<span class="sd">        Nomber of bunches in the beam.</span>
+<span class="sd">    modes : list</span>
+<span class="sd">        Coupled bunch mode numbers to consider.</span>
+<span class="sd">    cavity_list : list</span>
+<span class="sd">        List of CavityResonator objects to consider, which can be:</span>
+<span class="sd">            - active cavities</span>
+<span class="sd">            - passive cavities</span>
+<span class="sd">            - HOMs</span>
+<span class="sd">            - mode dampers</span>
+<span class="sd">    detune_range : array</span>
+<span class="sd">        Detuning range (list of points) of the last CavityResonator object.</span>
+<span class="sd">    synchrotron_tune : float, optional</span>
+<span class="sd">        Synchrotron tune.</span>
+<span class="sd">    Vrf : float, optinal</span>
+<span class="sd">        Total RF voltage in [V] used to compute synchrotron tune if not given.</span>
+
+<span class="sd">    Returns</span>
+<span class="sd">    -------</span>
+<span class="sd">    fig : Figure</span>
+<span class="sd">        Show the shunt impedance threshold for different coupled bunch modes.</span>
+
+<span class="sd">    &quot;&quot;&quot;</span>
+
+    <span class="n">Rth</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros_like</span><span class="p">(</span><span class="n">detune_range</span><span class="p">)</span>
+    <span class="n">fig</span><span class="p">,</span> <span class="n">ax</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">()</span>
+
+    <span class="k">for</span> <span class="n">mu</span> <span class="ow">in</span> <span class="n">modes</span><span class="p">:</span>
+        <span class="n">fixed_gr</span> <span class="o">=</span> <span class="mi">0</span>
+        <span class="k">for</span> <span class="n">cav</span> <span class="ow">in</span> <span class="n">cavity_list</span><span class="p">[:</span><span class="o">-</span><span class="mi">1</span><span class="p">]:</span>
+            <span class="n">fixed_gr</span> <span class="o">+=</span> <span class="n">lcbi_growth_rate_mode</span><span class="p">(</span>
+                <span class="n">ring</span><span class="p">,</span>
+                <span class="n">I</span><span class="o">=</span><span class="n">I</span><span class="p">,</span>
+                <span class="n">mu</span><span class="o">=</span><span class="n">mu</span><span class="p">,</span>
+                <span class="n">fr</span><span class="o">=</span><span class="n">cav</span><span class="o">.</span><span class="n">fr</span><span class="p">,</span>
+                <span class="n">RL</span><span class="o">=</span><span class="n">cav</span><span class="o">.</span><span class="n">RL</span><span class="p">,</span>
+                <span class="n">QL</span><span class="o">=</span><span class="n">cav</span><span class="o">.</span><span class="n">QL</span><span class="p">,</span>
+                <span class="n">M</span><span class="o">=</span><span class="n">M</span><span class="p">,</span>
+                <span class="n">synchrotron_tune</span><span class="o">=</span><span class="n">synchrotron_tune</span><span class="p">,</span>
+                <span class="n">Vrf</span><span class="o">=</span><span class="n">Vrf</span><span class="p">)</span>
+
+        <span class="n">cav</span> <span class="o">=</span> <span class="n">cavity_list</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
+        <span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">det</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">detune_range</span><span class="p">):</span>
+            <span class="n">gr</span> <span class="o">=</span> <span class="n">lcbi_growth_rate_mode</span><span class="p">(</span><span class="n">ring</span><span class="p">,</span>
+                                       <span class="n">I</span><span class="o">=</span><span class="n">I</span><span class="p">,</span>
+                                       <span class="n">mu</span><span class="o">=</span><span class="n">mu</span><span class="p">,</span>
+                                       <span class="n">fr</span><span class="o">=</span><span class="n">cav</span><span class="o">.</span><span class="n">m</span> <span class="o">*</span> <span class="n">ring</span><span class="o">.</span><span class="n">f1</span> <span class="o">+</span> <span class="n">det</span><span class="p">,</span>
+                                       <span class="n">RL</span><span class="o">=</span><span class="n">cav</span><span class="o">.</span><span class="n">RL</span><span class="p">,</span>
+                                       <span class="n">QL</span><span class="o">=</span><span class="n">cav</span><span class="o">.</span><span class="n">QL</span><span class="p">,</span>
+                                       <span class="n">M</span><span class="o">=</span><span class="n">M</span><span class="p">,</span>
+                                       <span class="n">synchrotron_tune</span><span class="o">=</span><span class="n">synchrotron_tune</span><span class="p">,</span>
+                                       <span class="n">Vrf</span><span class="o">=</span><span class="n">Vrf</span><span class="p">)</span>
+            <span class="n">Rth</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="p">(</span><span class="mi">1</span> <span class="o">/</span> <span class="n">ring</span><span class="o">.</span><span class="n">tau</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="o">-</span> <span class="n">fixed_gr</span><span class="p">)</span> <span class="o">*</span> <span class="n">cav</span><span class="o">.</span><span class="n">Rs</span> <span class="o">/</span> <span class="n">gr</span>
+
+        <span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">detune_range</span> <span class="o">*</span> <span class="mf">1e-3</span><span class="p">,</span>
+                <span class="n">Rth</span> <span class="o">*</span> <span class="mf">1e-6</span><span class="p">,</span>
+                <span class="n">label</span><span class="o">=</span><span class="s2">&quot;$\mu$ = &quot;</span> <span class="o">+</span> <span class="nb">str</span><span class="p">(</span><span class="nb">int</span><span class="p">(</span><span class="n">mu</span><span class="p">)))</span>
+
+    <span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="sa">r</span><span class="s2">&quot;$\Delta f$ [kHz]&quot;</span><span class="p">)</span>
+    <span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="sa">r</span><span class="s2">&quot;$R_{s,max}$ $[M\Omega]$&quot;</span><span class="p">)</span>
+    <span class="n">plt</span><span class="o">.</span><span class="n">yscale</span><span class="p">(</span><span class="s2">&quot;log&quot;</span><span class="p">)</span>
+    <span class="n">plt</span><span class="o">.</span><span class="n">legend</span><span class="p">()</span>
+
+    <span class="k">return</span> <span class="n">fig</span></div>
+
+
+<div class="viewcode-block" id="rwmbi_growth_rate"><a class="viewcode-back" href="../../../mbtrack2.instability.html#mbtrack2.instability.instabilities.rwmbi_growth_rate">[docs]</a><span class="k">def</span> <span class="nf">rwmbi_growth_rate</span><span class="p">(</span><span class="n">ring</span><span class="p">,</span> <span class="n">current</span><span class="p">,</span> <span class="n">beff</span><span class="p">,</span> <span class="n">rho_material</span><span class="p">,</span> <span class="n">plane</span><span class="o">=</span><span class="s1">&#39;x&#39;</span><span class="p">):</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    Compute the growth rate of the transverse coupled-bunch instability induced</span>
+<span class="sd">    by resistive wall impedance [1].</span>
+
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">    ring : Synchrotron object</span>
+<span class="sd">    current : float</span>
+<span class="sd">        Total beam current in [A].</span>
+<span class="sd">    beff : float</span>
+<span class="sd">        Effective radius of the vacuum chamber in [m].</span>
+<span class="sd">    rho_material : float</span>
+<span class="sd">        Resistivity of the chamber&#39;s wall material in [Ohm.m].</span>
+<span class="sd">    plane : str, optional</span>
+<span class="sd">        The plane in which the instability will be computed. Use &#39;x&#39; for the </span>
+<span class="sd">        horizontal plane, and &#39;y&#39; for the vertical.</span>
+
+<span class="sd">    Reference</span>
+<span class="sd">    ---------</span>
+<span class="sd">    [1] Eq. (31) in R. Nagaoka and K. L. F. Bane, &quot;Collective effects in a</span>
+<span class="sd">    diffraction-limited storage ring&quot;, J. Synchrotron Rad. Vol 21, 2014. pp.937-960 </span>
+
+<span class="sd">    &quot;&quot;&quot;</span>
+    <span class="n">plane_dict</span> <span class="o">=</span> <span class="p">{</span><span class="s1">&#39;x&#39;</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="s1">&#39;y&#39;</span><span class="p">:</span> <span class="mi">1</span><span class="p">}</span>
+    <span class="n">index</span> <span class="o">=</span> <span class="n">plane_dict</span><span class="p">[</span><span class="n">plane</span><span class="p">]</span>
+    <span class="n">beta0</span> <span class="o">=</span> <span class="n">ring</span><span class="o">.</span><span class="n">optics</span><span class="o">.</span><span class="n">local_beta</span><span class="p">[</span><span class="n">index</span><span class="p">]</span>
+    <span class="n">omega0</span> <span class="o">=</span> <span class="n">ring</span><span class="o">.</span><span class="n">omega0</span>
+    <span class="n">E0</span> <span class="o">=</span> <span class="n">ring</span><span class="o">.</span><span class="n">E0</span>
+    <span class="n">R</span> <span class="o">=</span> <span class="n">ring</span><span class="o">.</span><span class="n">L</span> <span class="o">/</span> <span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span><span class="p">)</span>
+    <span class="n">frac_tune</span><span class="p">,</span> <span class="n">int_tune</span> <span class="o">=</span> <span class="n">math</span><span class="o">.</span><span class="n">modf</span><span class="p">(</span><span class="n">ring</span><span class="o">.</span><span class="n">tune</span><span class="p">[</span><span class="n">index</span><span class="p">])</span>
+    <span class="n">Z0</span> <span class="o">=</span> <span class="n">mu_0</span> <span class="o">*</span> <span class="n">c</span>
+
+    <span class="n">gr</span> <span class="o">=</span> <span class="p">(</span><span class="n">beta0</span><span class="o">*</span><span class="n">omega0</span><span class="o">*</span><span class="n">current</span><span class="o">*</span><span class="n">R</span><span class="p">)</span> <span class="o">/</span> <span class="p">(</span><span class="mi">4</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="n">E0</span> <span class="o">*</span> <span class="n">beff</span><span class="o">**</span><span class="mi">3</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span>
+        <span class="p">(</span><span class="mi">2</span><span class="o">*</span><span class="n">c</span><span class="o">*</span><span class="n">Z0</span><span class="o">*</span><span class="n">rho_material</span><span class="p">)</span> <span class="o">/</span> <span class="p">((</span><span class="mi">1</span><span class="o">-</span><span class="n">frac_tune</span><span class="p">)</span> <span class="o">*</span> <span class="n">omega0</span><span class="p">))</span><span class="o">**</span><span class="mf">0.5</span>
+
+    <span class="k">return</span> <span class="n">gr</span></div>
+
+
+<div class="viewcode-block" id="rwmbi_threshold"><a class="viewcode-back" href="../../../mbtrack2.instability.html#mbtrack2.instability.instabilities.rwmbi_threshold">[docs]</a><span class="k">def</span> <span class="nf">rwmbi_threshold</span><span class="p">(</span><span class="n">ring</span><span class="p">,</span> <span class="n">beff</span><span class="p">,</span> <span class="n">rho_material</span><span class="p">,</span> <span class="n">plane</span><span class="o">=</span><span class="s1">&#39;x&#39;</span><span class="p">):</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    Compute the threshold current of the transverse coupled-bunch instability </span>
+<span class="sd">    induced by resistive wall impedance [1].</span>
+
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">    ring : Synchrotron object</span>
+<span class="sd">    beff : float</span>
+<span class="sd">        Effective radius of the vacuum chamber in [m].</span>
+<span class="sd">    rho_material : float</span>
+<span class="sd">        Resistivity of the chamber&#39;s wall material in [Ohm.m].</span>
+<span class="sd">    plane : str, optional</span>
+<span class="sd">        The plane in which the instability will be computed. Use &#39;x&#39; for the </span>
+<span class="sd">        horizontal plane, and &#39;y&#39; for the vertical.</span>
+
+<span class="sd">    Reference</span>
+<span class="sd">    ---------</span>
+<span class="sd">    [1] Eq. (32) in R. Nagaoka and K. L. F. Bane, &quot;Collective effects in a</span>
+<span class="sd">    diffraction-limited storage ring&quot;, J. Synchrotron Rad. Vol 21, 2014. pp.937-960 </span>
+
+<span class="sd">    &quot;&quot;&quot;</span>
+    <span class="n">plane_dict</span> <span class="o">=</span> <span class="p">{</span><span class="s1">&#39;x&#39;</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="s1">&#39;y&#39;</span><span class="p">:</span> <span class="mi">1</span><span class="p">}</span>
+    <span class="n">index</span> <span class="o">=</span> <span class="n">plane_dict</span><span class="p">[</span><span class="n">plane</span><span class="p">]</span>
+    <span class="n">beta0</span> <span class="o">=</span> <span class="n">ring</span><span class="o">.</span><span class="n">optics</span><span class="o">.</span><span class="n">local_beta</span><span class="p">[</span><span class="n">index</span><span class="p">]</span>
+    <span class="n">omega0</span> <span class="o">=</span> <span class="n">ring</span><span class="o">.</span><span class="n">omega0</span>
+    <span class="n">E0</span> <span class="o">=</span> <span class="n">ring</span><span class="o">.</span><span class="n">E0</span>
+    <span class="n">tau_rad</span> <span class="o">=</span> <span class="n">ring</span><span class="o">.</span><span class="n">tau</span><span class="p">[</span><span class="n">index</span><span class="p">]</span>
+    <span class="n">frac_tune</span><span class="p">,</span> <span class="n">int_tune</span> <span class="o">=</span> <span class="n">math</span><span class="o">.</span><span class="n">modf</span><span class="p">(</span><span class="n">ring</span><span class="o">.</span><span class="n">tune</span><span class="p">[</span><span class="n">index</span><span class="p">])</span>
+    <span class="n">Z0</span> <span class="o">=</span> <span class="n">mu_0</span> <span class="o">*</span> <span class="n">c</span>
+
+    <span class="n">Ith</span> <span class="o">=</span> <span class="p">(</span><span class="mi">4</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="n">E0</span> <span class="o">*</span> <span class="n">beff</span><span class="o">**</span><span class="mi">3</span><span class="p">)</span> <span class="o">/</span> <span class="p">(</span><span class="n">c</span><span class="o">*</span><span class="n">beta0</span><span class="o">*</span><span class="n">tau_rad</span><span class="p">)</span> <span class="o">*</span> <span class="p">((</span>
+        <span class="p">(</span><span class="mi">1</span><span class="o">-</span><span class="n">frac_tune</span><span class="p">)</span> <span class="o">*</span> <span class="n">omega0</span><span class="p">)</span> <span class="o">/</span> <span class="p">(</span><span class="mi">2</span><span class="o">*</span><span class="n">c</span><span class="o">*</span><span class="n">Z0</span><span class="o">*</span><span class="n">rho_material</span><span class="p">))</span><span class="o">**</span><span class="mf">0.5</span>
+
+    <span class="k">return</span> <span class="n">Ith</span></div>
+</pre></div>
+
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+<!DOCTYPE html>
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+            
+  <h1>Source code for mbtrack2.instability.ions</h1><div class="highlight"><pre>
+<span></span><span class="c1"># -*- coding: utf-8 -*-</span>
+<span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">Various calculations about ion trapping and instabilities in electron storage </span>
+<span class="sd">rings.</span>
+<span class="sd">&quot;&quot;&quot;</span>
+
+<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
+<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="kn">from</span> <span class="nn">scipy.constants</span> <span class="kn">import</span> <span class="p">(</span>
+    <span class="n">Boltzmann</span><span class="p">,</span>
+    <span class="n">c</span><span class="p">,</span>
+    <span class="n">e</span><span class="p">,</span>
+    <span class="n">epsilon_0</span><span class="p">,</span>
+    <span class="n">hbar</span><span class="p">,</span>
+    <span class="n">m_e</span><span class="p">,</span>
+    <span class="n">m_p</span><span class="p">,</span>
+    <span class="n">physical_constants</span><span class="p">,</span>
+    <span class="n">pi</span><span class="p">,</span>
+<span class="p">)</span>
+
+<span class="n">rp</span> <span class="o">=</span> <span class="mi">1</span> <span class="o">/</span> <span class="p">(</span><span class="mi">4</span><span class="o">*</span><span class="n">pi</span><span class="o">*</span><span class="n">epsilon_0</span><span class="p">)</span> <span class="o">*</span> <span class="n">e</span><span class="o">**</span><span class="mi">2</span> <span class="o">/</span> <span class="p">(</span><span class="n">m_p</span> <span class="o">*</span> <span class="n">c</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span>
+<span class="n">re</span> <span class="o">=</span> <span class="n">physical_constants</span><span class="p">[</span><span class="s2">&quot;classical electron radius&quot;</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span>
+
+
+<div class="viewcode-block" id="ion_cross_section"><a class="viewcode-back" href="../../../mbtrack2.instability.html#mbtrack2.instability.ions.ion_cross_section">[docs]</a><span class="k">def</span> <span class="nf">ion_cross_section</span><span class="p">(</span><span class="n">ring</span><span class="p">,</span> <span class="n">ion</span><span class="p">):</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    Compute the collisional ionization cross section.</span>
+<span class="sd">    </span>
+<span class="sd">    Compute the inelastic collision cross section between a molecule or an atom</span>
+<span class="sd">    by a relativistic electron using the relativistic Bethe asymptotic formula </span>
+<span class="sd">    [1].</span>
+<span class="sd">    </span>
+<span class="sd">    Values of M02 and C02 from [2].</span>
+
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">    ring : Synchrotron object</span>
+<span class="sd">    ion : str</span>
+<span class="sd">        Ion type.</span>
+
+<span class="sd">    Returns</span>
+<span class="sd">    -------</span>
+<span class="sd">    sigma : float</span>
+<span class="sd">        Cross section in [m**2].</span>
+<span class="sd">        </span>
+<span class="sd">    References</span>
+<span class="sd">    ----------</span>
+<span class="sd">    [1] : M. Inokuti, &quot;Inelastic collisions of fast charged particles with </span>
+<span class="sd">    atoms and molecules-the bethe theory revisited&quot;, Reviews of modern physics </span>
+<span class="sd">    43 (1971).</span>
+<span class="sd">    [2] : P. F. Tavares, &quot;Bremsstrahlung detection of ions trapped in the EPA </span>
+<span class="sd">    electron beam&quot;, Part. Accel. 43 (1993).</span>
+
+<span class="sd">    &quot;&quot;&quot;</span>
+    <span class="k">if</span> <span class="n">ion</span> <span class="o">==</span> <span class="s2">&quot;CO&quot;</span><span class="p">:</span>
+        <span class="n">M02</span> <span class="o">=</span> <span class="mf">3.7</span>
+        <span class="n">C0</span> <span class="o">=</span> <span class="mf">35.1</span>
+    <span class="k">elif</span> <span class="n">ion</span> <span class="o">==</span> <span class="s2">&quot;H2&quot;</span><span class="p">:</span>
+        <span class="n">M02</span> <span class="o">=</span> <span class="mf">0.7</span>
+        <span class="n">C0</span> <span class="o">=</span> <span class="mf">8.1</span>
+    <span class="k">else</span><span class="p">:</span>
+        <span class="k">raise</span> <span class="ne">NotImplementedError</span>
+
+    <span class="n">sigma</span> <span class="o">=</span> <span class="mi">4</span> <span class="o">*</span> <span class="n">pi</span> <span class="o">*</span> <span class="p">(</span><span class="n">hbar</span> <span class="o">/</span> <span class="n">m_e</span> <span class="o">/</span> <span class="n">c</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span> <span class="o">*</span> <span class="p">(</span>
+        <span class="n">M02</span> <span class="o">*</span> <span class="p">(</span><span class="mi">1</span> <span class="o">/</span> <span class="n">ring</span><span class="o">.</span><span class="n">beta</span><span class="o">**</span><span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">log</span><span class="p">(</span><span class="n">ring</span><span class="o">.</span><span class="n">beta</span><span class="o">**</span><span class="mi">2</span> <span class="o">/</span>
+                                         <span class="p">(</span><span class="mi">1</span> <span class="o">-</span> <span class="n">ring</span><span class="o">.</span><span class="n">beta</span><span class="o">**</span><span class="mi">2</span><span class="p">))</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span> <span class="o">+</span>
+        <span class="n">C0</span> <span class="o">/</span> <span class="n">ring</span><span class="o">.</span><span class="n">beta</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span>
+
+    <span class="k">return</span> <span class="n">sigma</span></div>
+
+
+<div class="viewcode-block" id="ion_frequency"><a class="viewcode-back" href="../../../mbtrack2.instability.html#mbtrack2.instability.ions.ion_frequency">[docs]</a><span class="k">def</span> <span class="nf">ion_frequency</span><span class="p">(</span><span class="n">N</span><span class="p">,</span>
+                  <span class="n">Lsep</span><span class="p">,</span>
+                  <span class="n">sigmax</span><span class="p">,</span>
+                  <span class="n">sigmay</span><span class="p">,</span>
+                  <span class="n">ion</span><span class="o">=</span><span class="s2">&quot;CO&quot;</span><span class="p">,</span>
+                  <span class="n">dim</span><span class="o">=</span><span class="s2">&quot;y&quot;</span><span class="p">,</span>
+                  <span class="n">express</span><span class="o">=</span><span class="s2">&quot;coupling&quot;</span><span class="p">):</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    Compute the ion oscillation frequnecy.</span>
+
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">    N : float</span>
+<span class="sd">        Number of electrons per bunch.</span>
+<span class="sd">    Lsep : float</span>
+<span class="sd">        Bunch spacing in [m].</span>
+<span class="sd">    sigmax : float or array</span>
+<span class="sd">        Horizontal beam size in [m].</span>
+<span class="sd">    sigmay : float or array</span>
+<span class="sd">        Vertical beam size in [m].</span>
+<span class="sd">    ion : str, optional</span>
+<span class="sd">        Ion type. The default is &quot;CO&quot;.</span>
+<span class="sd">    dim : &quot;y&quot; o &quot;x&quot;, optional</span>
+<span class="sd">        Dimension to consider. The default is &quot;y&quot;.</span>
+<span class="sd">    express : str, optional</span>
+<span class="sd">        Expression to use to compute the ion oscillation frequency. </span>
+<span class="sd">        The default is &quot;coupling&quot; corresponding to Gaussian electron and ion </span>
+<span class="sd">        distributions with coupling [1].</span>
+<span class="sd">        Also possible is &quot;no_coupling&quot; corresponding to Gaussian electron and </span>
+<span class="sd">        ion distributions without coupling [2].</span>
+
+<span class="sd">    Returns</span>
+<span class="sd">    -------</span>
+<span class="sd">    f : float or array</span>
+<span class="sd">        Ion oscillation frequencies in [Hz].</span>
+<span class="sd">        </span>
+<span class="sd">    References</span>
+<span class="sd">    ----------</span>
+<span class="sd">    [1] : T. O. Raubenheimer and F. Zimmermann, &quot;Fast beam-ion instability. I. </span>
+<span class="sd">    linear theory and simulations&quot;, Physical Review E 52 (1995).</span>
+<span class="sd">    [2] : G. V. Stupakov, T. O. Raubenheimer, and F. Zimmermann, &quot;Fast beam-ion </span>
+<span class="sd">    instability. II. effect of ion decoherence&quot;, Physical Review E 52 (1995).</span>
+
+<span class="sd">    &quot;&quot;&quot;</span>
+
+    <span class="k">if</span> <span class="n">ion</span> <span class="o">==</span> <span class="s2">&quot;CO&quot;</span><span class="p">:</span>
+        <span class="n">A</span> <span class="o">=</span> <span class="mi">28</span>
+    <span class="k">elif</span> <span class="n">ion</span> <span class="o">==</span> <span class="s2">&quot;H2&quot;</span><span class="p">:</span>
+        <span class="n">A</span> <span class="o">=</span> <span class="mi">2</span>
+    <span class="k">elif</span> <span class="n">ion</span> <span class="o">==</span> <span class="s2">&quot;CH4&quot;</span><span class="p">:</span>
+        <span class="n">A</span> <span class="o">=</span> <span class="mi">18</span>
+    <span class="k">elif</span> <span class="n">ion</span> <span class="o">==</span> <span class="s2">&quot;H2O&quot;</span><span class="p">:</span>
+        <span class="n">A</span> <span class="o">=</span> <span class="mi">16</span>
+    <span class="k">elif</span> <span class="n">ion</span> <span class="o">==</span> <span class="s2">&quot;CO2&quot;</span><span class="p">:</span>
+        <span class="n">A</span> <span class="o">=</span> <span class="mi">44</span>
+
+    <span class="k">if</span> <span class="n">dim</span> <span class="o">==</span> <span class="s2">&quot;y&quot;</span><span class="p">:</span>
+        <span class="k">pass</span>
+    <span class="k">elif</span> <span class="n">dim</span> <span class="o">==</span> <span class="s2">&quot;x&quot;</span><span class="p">:</span>
+        <span class="n">sigmay</span><span class="p">,</span> <span class="n">sigmax</span> <span class="o">=</span> <span class="n">sigmax</span><span class="p">,</span> <span class="n">sigmay</span>
+    <span class="k">else</span><span class="p">:</span>
+        <span class="k">raise</span> <span class="ne">ValueError</span>
+
+    <span class="k">if</span> <span class="n">express</span> <span class="o">==</span> <span class="s2">&quot;coupling&quot;</span><span class="p">:</span>
+        <span class="n">k</span> <span class="o">=</span> <span class="mi">3</span> <span class="o">/</span> <span class="mi">2</span>
+    <span class="k">elif</span> <span class="n">express</span> <span class="o">==</span> <span class="s2">&quot;no_coupling&quot;</span><span class="p">:</span>
+        <span class="n">k</span> <span class="o">=</span> <span class="mi">1</span>
+
+    <span class="n">f</span> <span class="o">=</span> <span class="n">c</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">rp</span> <span class="o">*</span> <span class="n">N</span> <span class="o">/</span> <span class="p">(</span><span class="n">A</span> <span class="o">*</span> <span class="n">k</span> <span class="o">*</span> <span class="n">Lsep</span> <span class="o">*</span> <span class="n">sigmay</span> <span class="o">*</span>
+                                  <span class="p">(</span><span class="n">sigmax</span><span class="o">+</span><span class="n">sigmay</span><span class="p">)))</span> <span class="o">/</span> <span class="p">(</span><span class="mi">2</span><span class="o">*</span><span class="n">pi</span><span class="p">)</span>
+
+    <span class="k">return</span> <span class="n">f</span></div>
+
+
+<div class="viewcode-block" id="fast_beam_ion"><a class="viewcode-back" href="../../../mbtrack2.instability.html#mbtrack2.instability.ions.fast_beam_ion">[docs]</a><span class="k">def</span> <span class="nf">fast_beam_ion</span><span class="p">(</span><span class="n">ring</span><span class="p">,</span>
+                  <span class="n">Nb</span><span class="p">,</span>
+                  <span class="n">nb</span><span class="p">,</span>
+                  <span class="n">Lsep</span><span class="p">,</span>
+                  <span class="n">sigmax</span><span class="p">,</span>
+                  <span class="n">sigmay</span><span class="p">,</span>
+                  <span class="n">P</span><span class="p">,</span>
+                  <span class="n">T</span><span class="p">,</span>
+                  <span class="n">beta</span><span class="p">,</span>
+                  <span class="n">model</span><span class="o">=</span><span class="s2">&quot;linear&quot;</span><span class="p">,</span>
+                  <span class="n">delta_omega</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span>
+                  <span class="n">ion</span><span class="o">=</span><span class="s2">&quot;CO&quot;</span><span class="p">,</span>
+                  <span class="n">dim</span><span class="o">=</span><span class="s2">&quot;y&quot;</span><span class="p">):</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    Compute fast beam ion instability rise time [1].</span>
+<span class="sd">    </span>
+<span class="sd">    Warning ! </span>
+<span class="sd">    If model=&quot;linear&quot;, the rise time is an assymptotic grow time </span>
+<span class="sd">    (i.e. y ~ exp(sqrt(t/tau))) [1].</span>
+<span class="sd">    If model=&quot;decoherence&quot;, the rise time is an e-folding time </span>
+<span class="sd">    (i.e. y ~ exp(t/tau)) [2].</span>
+<span class="sd">    If model=&quot;non-linear&quot;, the rise time is a linear growth time</span>
+<span class="sd">    (i.e. y ~ t/tau) [3].</span>
+<span class="sd">    </span>
+<span class="sd">    The linear model assumes that [1]:</span>
+<span class="sd">        x,y &lt;&lt; sigmax,sigmay</span>
+<span class="sd">    </span>
+<span class="sd">    The decoherence model assumes that [2]:</span>
+<span class="sd">        Lsep &lt;&lt; c / (2 * pi * ion_frequency) </span>
+<span class="sd">        Lsep &lt;&lt; c / (2 * pi * betatron_frequency)</span>
+<span class="sd">        </span>
+<span class="sd">    The non-linear model assumes that [3]:</span>
+<span class="sd">        x,y &gt;&gt; sigmax,sigmay</span>
+
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">    ring : Synchrotron object</span>
+<span class="sd">    Nb : float</span>
+<span class="sd">        Number of electron per bunch.</span>
+<span class="sd">    nb : float</span>
+<span class="sd">        Number of bunches.</span>
+<span class="sd">    Lsep : float</span>
+<span class="sd">        Bunch spacing in [m].</span>
+<span class="sd">    sigmax : float</span>
+<span class="sd">        Horizontal beam size in [m].</span>
+<span class="sd">    sigmay : float</span>
+<span class="sd">        Vertical beam size in [m].</span>
+<span class="sd">    P : float</span>
+<span class="sd">        Partial pressure of the molecular ion in [Pa].</span>
+<span class="sd">    T : float</span>
+<span class="sd">        Tempertature in [K].</span>
+<span class="sd">    beta : float</span>
+<span class="sd">        Average betatron function around the ring in [m].</span>
+<span class="sd">    model : str, optional</span>
+<span class="sd">        If &quot;linear&quot;, use [1].</span>
+<span class="sd">        If &quot;decoherence&quot;, use [2].</span>
+<span class="sd">        If &quot;non-linear&quot;, use [3].</span>
+<span class="sd">    delta_omega : float, optional</span>
+<span class="sd">        RMS variation of the ion oscillation angular frequnecy around the ring</span>
+<span class="sd">        in [Hz].</span>
+<span class="sd">    ion : str, optional</span>
+<span class="sd">        Ion type. The default is &quot;CO&quot;.</span>
+<span class="sd">    dim : &quot;y&quot; o &quot;x&quot;, optional</span>
+<span class="sd">        Dimension to consider. The default is &quot;y&quot;.</span>
+
+<span class="sd">    Returns</span>
+<span class="sd">    -------</span>
+<span class="sd">    tau : float</span>
+<span class="sd">        Instability rise time in [s].</span>
+<span class="sd">        </span>
+<span class="sd">    References</span>
+<span class="sd">    ----------</span>
+<span class="sd">    [1] : T. O. Raubenheimer and F. Zimmermann, &quot;Fast beam-ion instability. I. </span>
+<span class="sd">    linear theory and simulations&quot;, Physical Review E 52 (1995).</span>
+<span class="sd">    [2] : G. V. Stupakov, T. O. Raubenheimer, and F. Zimmermann, &quot;Fast beam-ion </span>
+<span class="sd">    instability. II. effect of ion decoherence&quot;, Physical Review E 52 (1995).</span>
+<span class="sd">    [3] : Chao, A. W., &amp; Mess, K. H. (Eds.). (2013). Handbook of accelerator </span>
+<span class="sd">    physics and engineering. World scientific. 3rd Printing. p417.</span>
+<span class="sd">    </span>
+<span class="sd">    &quot;&quot;&quot;</span>
+    <span class="k">if</span> <span class="n">dim</span> <span class="o">==</span> <span class="s2">&quot;y&quot;</span><span class="p">:</span>
+        <span class="k">pass</span>
+    <span class="k">elif</span> <span class="n">dim</span> <span class="o">==</span> <span class="s2">&quot;x&quot;</span><span class="p">:</span>
+        <span class="n">sigmay</span><span class="p">,</span> <span class="n">sigmax</span> <span class="o">=</span> <span class="n">sigmax</span><span class="p">,</span> <span class="n">sigmay</span>
+    <span class="k">else</span><span class="p">:</span>
+        <span class="k">raise</span> <span class="ne">ValueError</span>
+
+    <span class="k">if</span> <span class="n">ion</span> <span class="o">==</span> <span class="s2">&quot;CO&quot;</span><span class="p">:</span>
+        <span class="n">A</span> <span class="o">=</span> <span class="mi">28</span>
+    <span class="k">elif</span> <span class="n">ion</span> <span class="o">==</span> <span class="s2">&quot;H2&quot;</span><span class="p">:</span>
+        <span class="n">A</span> <span class="o">=</span> <span class="mi">2</span>
+
+    <span class="n">sigma_i</span> <span class="o">=</span> <span class="n">ion_cross_section</span><span class="p">(</span><span class="n">ring</span><span class="p">,</span> <span class="n">ion</span><span class="p">)</span>
+
+    <span class="n">d_gas</span> <span class="o">=</span> <span class="n">P</span> <span class="o">/</span> <span class="p">(</span><span class="n">Boltzmann</span><span class="o">*</span><span class="n">T</span><span class="p">)</span>
+
+    <span class="n">num</span> <span class="o">=</span> <span class="mi">4</span> <span class="o">*</span> <span class="n">d_gas</span> <span class="o">*</span> <span class="n">sigma_i</span> <span class="o">*</span> <span class="n">beta</span> <span class="o">*</span> <span class="n">Nb</span><span class="o">**</span><span class="p">(</span><span class="mi">3</span> <span class="o">/</span> <span class="mi">2</span><span class="p">)</span> <span class="o">*</span> <span class="n">nb</span><span class="o">**</span><span class="mi">2</span> <span class="o">*</span> <span class="n">re</span> <span class="o">*</span> <span class="n">rp</span><span class="o">**</span><span class="p">(</span>
+        <span class="mi">1</span> <span class="o">/</span> <span class="mi">2</span><span class="p">)</span> <span class="o">*</span> <span class="n">Lsep</span><span class="o">**</span><span class="p">(</span><span class="mi">1</span> <span class="o">/</span> <span class="mi">2</span><span class="p">)</span> <span class="o">*</span> <span class="n">c</span>
+    <span class="n">den</span> <span class="o">=</span> <span class="mi">3</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="mi">3</span><span class="p">)</span> <span class="o">*</span> <span class="n">ring</span><span class="o">.</span><span class="n">gamma</span> <span class="o">*</span> <span class="n">sigmay</span><span class="o">**</span><span class="p">(</span><span class="mi">3</span> <span class="o">/</span> <span class="mi">2</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="n">sigmay</span> <span class="o">+</span> <span class="n">sigmax</span><span class="p">)</span><span class="o">**</span><span class="p">(</span>
+        <span class="mi">3</span> <span class="o">/</span> <span class="mi">2</span><span class="p">)</span> <span class="o">*</span> <span class="n">A</span><span class="o">**</span><span class="p">(</span><span class="mi">1</span> <span class="o">/</span> <span class="mi">2</span><span class="p">)</span>
+
+    <span class="n">tau</span> <span class="o">=</span> <span class="n">den</span> <span class="o">/</span> <span class="n">num</span>
+
+    <span class="k">if</span> <span class="n">model</span> <span class="o">==</span> <span class="s2">&quot;decoherence&quot;</span><span class="p">:</span>
+        <span class="n">tau</span> <span class="o">=</span> <span class="n">tau</span> <span class="o">*</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span> <span class="o">*</span> <span class="n">nb</span> <span class="o">*</span> <span class="n">Lsep</span> <span class="o">*</span> <span class="n">delta_omega</span> <span class="o">/</span> <span class="n">c</span>
+    <span class="k">elif</span> <span class="n">model</span> <span class="o">==</span> <span class="s2">&quot;non-linear&quot;</span><span class="p">:</span>
+        <span class="n">fi</span> <span class="o">=</span> <span class="n">ion_frequency</span><span class="p">(</span><span class="n">Nb</span><span class="p">,</span> <span class="n">Lsep</span><span class="p">,</span> <span class="n">sigmax</span><span class="p">,</span> <span class="n">sigmay</span><span class="p">,</span> <span class="n">ion</span><span class="p">,</span> <span class="n">dim</span><span class="p">)</span>
+        <span class="n">tau</span> <span class="o">=</span> <span class="n">tau</span> <span class="o">*</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">pi</span> <span class="o">*</span> <span class="n">fi</span> <span class="o">*</span> <span class="n">ring</span><span class="o">.</span><span class="n">T1</span> <span class="o">*</span> <span class="n">nb</span><span class="o">**</span><span class="p">(</span><span class="mi">3</span> <span class="o">/</span> <span class="mi">2</span><span class="p">)</span>
+    <span class="k">elif</span> <span class="n">model</span> <span class="o">==</span> <span class="s2">&quot;linear&quot;</span><span class="p">:</span>
+        <span class="k">pass</span>
+    <span class="k">else</span><span class="p">:</span>
+        <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">&quot;model unknown&quot;</span><span class="p">)</span>
+
+    <span class="k">return</span> <span class="n">tau</span></div>
+
+
+<div class="viewcode-block" id="plot_critical_mass"><a class="viewcode-back" href="../../../mbtrack2.instability.html#mbtrack2.instability.ions.plot_critical_mass">[docs]</a><span class="k">def</span> <span class="nf">plot_critical_mass</span><span class="p">(</span><span class="n">ring</span><span class="p">,</span> <span class="n">bunch_charge</span><span class="p">,</span> <span class="n">bunch_spacing</span><span class="p">,</span> <span class="n">n_points</span><span class="o">=</span><span class="mf">1e4</span><span class="p">):</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    Plot ion critical mass, using Eq. (7.70) p147 of [1]</span>
+
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">    ring : Synchrotron object</span>
+<span class="sd">    bunch_charge : float</span>
+<span class="sd">        Bunch charge in [C].</span>
+<span class="sd">    bunch_spacing : float</span>
+<span class="sd">        Time in between two adjacent bunches in [s].</span>
+<span class="sd">    n_points : float or int, optional</span>
+<span class="sd">        Number of point used in the plot. The default is 1e4.</span>
+
+<span class="sd">    Returns</span>
+<span class="sd">    -------</span>
+<span class="sd">    fig : figure</span>
+<span class="sd">        </span>
+<span class="sd">    References</span>
+<span class="sd">    ----------</span>
+<span class="sd">    [1] : Gamelin, A. (2018). Collective effects in a transient microbunching </span>
+<span class="sd">    regime and ion cloud mitigation in ThomX (Doctoral dissertation, </span>
+<span class="sd">    Université Paris-Saclay).</span>
+
+<span class="sd">    &quot;&quot;&quot;</span>
+
+    <span class="n">n_points</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">n_points</span><span class="p">)</span>
+    <span class="n">s</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">ring</span><span class="o">.</span><span class="n">L</span><span class="p">,</span> <span class="n">n_points</span><span class="p">)</span>
+    <span class="n">sigma</span> <span class="o">=</span> <span class="n">ring</span><span class="o">.</span><span class="n">sigma</span><span class="p">(</span><span class="n">s</span><span class="p">)</span>
+    <span class="n">N</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">bunch_charge</span> <span class="o">/</span> <span class="n">e</span><span class="p">)</span>
+
+    <span class="n">Ay</span> <span class="o">=</span> <span class="n">N</span> <span class="o">*</span> <span class="n">rp</span> <span class="o">*</span> <span class="n">bunch_spacing</span> <span class="o">*</span> <span class="n">c</span> <span class="o">/</span> <span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">sigma</span><span class="p">[</span><span class="mi">2</span><span class="p">,</span> <span class="p">:]</span> <span class="o">*</span>
+                                       <span class="p">(</span><span class="n">sigma</span><span class="p">[</span><span class="mi">2</span><span class="p">,</span> <span class="p">:]</span> <span class="o">+</span> <span class="n">sigma</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="p">:]))</span>
+    <span class="n">Ax</span> <span class="o">=</span> <span class="n">N</span> <span class="o">*</span> <span class="n">rp</span> <span class="o">*</span> <span class="n">bunch_spacing</span> <span class="o">*</span> <span class="n">c</span> <span class="o">/</span> <span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">sigma</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="p">:]</span> <span class="o">*</span>
+                                       <span class="p">(</span><span class="n">sigma</span><span class="p">[</span><span class="mi">2</span><span class="p">,</span> <span class="p">:]</span> <span class="o">+</span> <span class="n">sigma</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="p">:]))</span>
+
+    <span class="n">fig</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">()</span>
+    <span class="n">ax</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">gca</span><span class="p">()</span>
+    <span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">s</span><span class="p">,</span> <span class="n">Ax</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="sa">r</span><span class="s2">&quot;$A_x^c$&quot;</span><span class="p">)</span>
+    <span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">s</span><span class="p">,</span> <span class="n">Ay</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="sa">r</span><span class="s2">&quot;$A_y^c$&quot;</span><span class="p">)</span>
+    <span class="n">ax</span><span class="o">.</span><span class="n">set_yscale</span><span class="p">(</span><span class="s2">&quot;log&quot;</span><span class="p">)</span>
+    <span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">s</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">ones_like</span><span class="p">(</span><span class="n">s</span><span class="p">)</span> <span class="o">*</span> <span class="mi">2</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="sa">r</span><span class="s2">&quot;$H_2^+$&quot;</span><span class="p">)</span>
+    <span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">s</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">ones_like</span><span class="p">(</span><span class="n">s</span><span class="p">)</span> <span class="o">*</span> <span class="mi">16</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="sa">r</span><span class="s2">&quot;$H_2O^+$&quot;</span><span class="p">)</span>
+    <span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">s</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">ones_like</span><span class="p">(</span><span class="n">s</span><span class="p">)</span> <span class="o">*</span> <span class="mi">18</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="sa">r</span><span class="s2">&quot;$CH_4^+$&quot;</span><span class="p">)</span>
+    <span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">s</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">ones_like</span><span class="p">(</span><span class="n">s</span><span class="p">)</span> <span class="o">*</span> <span class="mi">28</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="sa">r</span><span class="s2">&quot;$CO^+$&quot;</span><span class="p">)</span>
+    <span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">s</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">ones_like</span><span class="p">(</span><span class="n">s</span><span class="p">)</span> <span class="o">*</span> <span class="mi">44</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="sa">r</span><span class="s2">&quot;$CO_2^+$&quot;</span><span class="p">)</span>
+    <span class="n">ax</span><span class="o">.</span><span class="n">legend</span><span class="p">()</span>
+    <span class="n">ax</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="s2">&quot;Critical mass&quot;</span><span class="p">)</span>
+    <span class="n">ax</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="s2">&quot;Longitudinal position [m]&quot;</span><span class="p">)</span>
+
+    <span class="k">return</span> <span class="n">fig</span></div>
+</pre></div>
+
+            <div class="clearer"></div>
+          </div>
+        </div>
+      </div>
+      <div class="sphinxsidebar" role="navigation" aria-label="main navigation">
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+      <h3>Navigation</h3>
+      <ul>
+        <li class="right" style="margin-right: 10px">
+          <a href="../../../genindex.html" title="General Index"
+             >index</a></li>
+        <li class="right" >
+          <a href="../../../py-modindex.html" title="Python Module Index"
+             >modules</a> |</li>
+        <li class="nav-item nav-item-0"><a href="../../../index.html">mbtrack2 0.6.0 documentation</a> &#187;</li>
+          <li class="nav-item nav-item-1"><a href="../../index.html" >Module code</a> &#187;</li>
+        <li class="nav-item nav-item-this"><a href="">mbtrack2.instability.ions</a></li> 
+      </ul>
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+    <div class="footer" role="contentinfo">
+        &#169; Copyright 2024, A. Gamelin et al.
+      Created using <a href="https://www.sphinx-doc.org/">Sphinx</a> 5.0.2.
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diff --git a/docs/build/html/_modules/mbtrack2/tracking/aperture.html b/docs/build/html/_modules/mbtrack2/tracking/aperture.html
new file mode 100644
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--- /dev/null
+++ b/docs/build/html/_modules/mbtrack2/tracking/aperture.html
@@ -0,0 +1,245 @@
+
+<!DOCTYPE html>
+
+<html lang="en">
+  <head>
+    <meta charset="utf-8" />
+    <meta name="viewport" content="width=device-width, initial-scale=1.0" />
+    <title>mbtrack2.tracking.aperture &#8212; mbtrack2 0.6.0 documentation</title>
+    <link rel="stylesheet" type="text/css" href="../../../_static/pygments.css" />
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+             >modules</a> |</li>
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+        <li class="nav-item nav-item-this"><a href="">mbtrack2.tracking.aperture</a></li> 
+      </ul>
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+
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+      <div class="documentwrapper">
+        <div class="bodywrapper">
+          <div class="body" role="main">
+            
+  <h1>Source code for mbtrack2.tracking.aperture</h1><div class="highlight"><pre>
+<span></span><span class="c1"># -*- coding: utf-8 -*-</span>
+<span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">This module defines aperture elements for tracking.</span>
+<span class="sd">&quot;&quot;&quot;</span>
+
+<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
+
+<span class="kn">from</span> <span class="nn">mbtrack2.tracking.element</span> <span class="kn">import</span> <span class="n">Element</span>
+
+
+<div class="viewcode-block" id="CircularAperture"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.aperture.CircularAperture">[docs]</a><span class="k">class</span> <span class="nc">CircularAperture</span><span class="p">(</span><span class="n">Element</span><span class="p">):</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    Circular aperture element. The particles which are outside of the circle </span>
+<span class="sd">    are &#39;lost&#39; and not used in the tracking any more.</span>
+<span class="sd">    </span>
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">    radius : float</span>
+<span class="sd">        radius of the circle in [m]</span>
+<span class="sd">    &quot;&quot;&quot;</span>
+
+    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">radius</span><span class="p">):</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">radius</span> <span class="o">=</span> <span class="n">radius</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">radius_squared</span> <span class="o">=</span> <span class="n">radius</span><span class="o">**</span><span class="mi">2</span>
+
+<div class="viewcode-block" id="CircularAperture.track"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.aperture.CircularAperture.track">[docs]</a>    <span class="nd">@Element</span><span class="o">.</span><span class="n">parallel</span>
+    <span class="k">def</span> <span class="nf">track</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">bunch</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Tracking method for the element.</span>
+<span class="sd">        No bunch to bunch interaction, so written for Bunch objects and</span>
+<span class="sd">        @Element.parallel is used to handle Beam objects.</span>
+<span class="sd">        </span>
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        bunch : Bunch or Beam object</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="n">alive</span> <span class="o">=</span> <span class="n">bunch</span><span class="o">.</span><span class="n">particles</span><span class="p">[</span><span class="s2">&quot;x&quot;</span><span class="p">]</span><span class="o">**</span><span class="mi">2</span> <span class="o">+</span> <span class="n">bunch</span><span class="o">.</span><span class="n">particles</span><span class="p">[</span>
+            <span class="s2">&quot;y&quot;</span><span class="p">]</span><span class="o">**</span><span class="mi">2</span> <span class="o">&lt;</span> <span class="bp">self</span><span class="o">.</span><span class="n">radius_squared</span>
+        <span class="n">bunch</span><span class="o">.</span><span class="n">alive</span><span class="p">[</span><span class="o">~</span><span class="n">alive</span><span class="p">]</span> <span class="o">=</span> <span class="kc">False</span></div></div>
+
+
+<div class="viewcode-block" id="ElipticalAperture"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.aperture.ElipticalAperture">[docs]</a><span class="k">class</span> <span class="nc">ElipticalAperture</span><span class="p">(</span><span class="n">Element</span><span class="p">):</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    Eliptical aperture element. The particles which are outside of the elipse </span>
+<span class="sd">    are &#39;lost&#39; and not used in the tracking any more.</span>
+<span class="sd">    </span>
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">    X_radius : float</span>
+<span class="sd">        horizontal radius of the elipse in [m]</span>
+<span class="sd">    Y_radius : float</span>
+<span class="sd">        vertical radius of the elipse in [m]</span>
+<span class="sd">    &quot;&quot;&quot;</span>
+
+    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">X_radius</span><span class="p">,</span> <span class="n">Y_radius</span><span class="p">):</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">X_radius</span> <span class="o">=</span> <span class="n">X_radius</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">X_radius_squared</span> <span class="o">=</span> <span class="n">X_radius</span><span class="o">**</span><span class="mi">2</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">Y_radius</span> <span class="o">=</span> <span class="n">Y_radius</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">Y_radius_squared</span> <span class="o">=</span> <span class="n">Y_radius</span><span class="o">**</span><span class="mi">2</span>
+
+<div class="viewcode-block" id="ElipticalAperture.track"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.aperture.ElipticalAperture.track">[docs]</a>    <span class="nd">@Element</span><span class="o">.</span><span class="n">parallel</span>
+    <span class="k">def</span> <span class="nf">track</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">bunch</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Tracking method for the element.</span>
+<span class="sd">        No bunch to bunch interaction, so written for Bunch objects and</span>
+<span class="sd">        @Element.parallel is used to handle Beam objects.</span>
+<span class="sd">        </span>
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        bunch : Bunch or Beam object</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="n">alive</span> <span class="o">=</span> <span class="p">(</span><span class="n">bunch</span><span class="o">.</span><span class="n">particles</span><span class="p">[</span><span class="s2">&quot;x&quot;</span><span class="p">]</span><span class="o">**</span><span class="mi">2</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">X_radius_squared</span> <span class="o">+</span>
+                 <span class="n">bunch</span><span class="o">.</span><span class="n">particles</span><span class="p">[</span><span class="s2">&quot;y&quot;</span><span class="p">]</span><span class="o">**</span><span class="mi">2</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">Y_radius_squared</span> <span class="o">&lt;</span> <span class="mi">1</span><span class="p">)</span>
+        <span class="n">bunch</span><span class="o">.</span><span class="n">alive</span><span class="p">[</span><span class="o">~</span><span class="n">alive</span><span class="p">]</span> <span class="o">=</span> <span class="kc">False</span></div></div>
+
+
+<div class="viewcode-block" id="RectangularAperture"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.aperture.RectangularAperture">[docs]</a><span class="k">class</span> <span class="nc">RectangularAperture</span><span class="p">(</span><span class="n">Element</span><span class="p">):</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    Rectangular aperture element. The particles which are outside of the </span>
+<span class="sd">    rectangle are &#39;lost&#39; and not used in the tracking any more.</span>
+<span class="sd">    </span>
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">    X_right : float</span>
+<span class="sd">        right horizontal aperture of the rectangle in [m]</span>
+<span class="sd">    Y_top : float</span>
+<span class="sd">        top vertical aperture of the rectangle in [m]</span>
+<span class="sd">    X_left : float, optional</span>
+<span class="sd">        left horizontal aperture of the rectangle in [m]</span>
+<span class="sd">    Y_bottom : float, optional</span>
+<span class="sd">        bottom vertical aperture of the rectangle in [m]</span>
+<span class="sd">    &quot;&quot;&quot;</span>
+
+    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">X_right</span><span class="p">,</span> <span class="n">Y_top</span><span class="p">,</span> <span class="n">X_left</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">Y_bottom</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">X_right</span> <span class="o">=</span> <span class="n">X_right</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">X_left</span> <span class="o">=</span> <span class="n">X_left</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">Y_top</span> <span class="o">=</span> <span class="n">Y_top</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">Y_bottom</span> <span class="o">=</span> <span class="n">Y_bottom</span>
+
+<div class="viewcode-block" id="RectangularAperture.track"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.aperture.RectangularAperture.track">[docs]</a>    <span class="nd">@Element</span><span class="o">.</span><span class="n">parallel</span>
+    <span class="k">def</span> <span class="nf">track</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">bunch</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Tracking method for the element.</span>
+<span class="sd">        No bunch to bunch interaction, so written for Bunch objects and</span>
+<span class="sd">        @Element.parallel is used to handle Beam objects.</span>
+<span class="sd">        </span>
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        bunch : Bunch or Beam object</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+
+        <span class="k">if</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">X_left</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">):</span>
+            <span class="n">alive_X</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">bunch</span><span class="o">.</span><span class="n">particles</span><span class="p">[</span><span class="s2">&quot;x&quot;</span><span class="p">])</span> <span class="o">&lt;</span> <span class="bp">self</span><span class="o">.</span><span class="n">X_right</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="n">alive_X</span> <span class="o">=</span> <span class="p">((</span><span class="n">bunch</span><span class="o">.</span><span class="n">particles</span><span class="p">[</span><span class="s2">&quot;x&quot;</span><span class="p">]</span> <span class="o">&lt;</span> <span class="bp">self</span><span class="o">.</span><span class="n">X_right</span><span class="p">)</span> <span class="o">&amp;</span>
+                       <span class="p">(</span><span class="n">bunch</span><span class="o">.</span><span class="n">particles</span><span class="p">[</span><span class="s2">&quot;x&quot;</span><span class="p">]</span> <span class="o">&gt;</span> <span class="bp">self</span><span class="o">.</span><span class="n">X_left</span><span class="p">))</span>
+
+        <span class="k">if</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">Y_bottom</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">):</span>
+            <span class="n">alive_Y</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">bunch</span><span class="o">.</span><span class="n">particles</span><span class="p">[</span><span class="s2">&quot;y&quot;</span><span class="p">])</span> <span class="o">&lt;</span> <span class="bp">self</span><span class="o">.</span><span class="n">Y_top</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="n">alive_Y</span> <span class="o">=</span> <span class="p">((</span><span class="n">bunch</span><span class="o">.</span><span class="n">particles</span><span class="p">[</span><span class="s2">&quot;y&quot;</span><span class="p">]</span> <span class="o">&lt;</span> <span class="bp">self</span><span class="o">.</span><span class="n">Y_top</span><span class="p">)</span> <span class="o">&amp;</span>
+                       <span class="p">(</span><span class="n">bunch</span><span class="o">.</span><span class="n">particles</span><span class="p">[</span><span class="s2">&quot;y&quot;</span><span class="p">]</span> <span class="o">&gt;</span> <span class="bp">self</span><span class="o">.</span><span class="n">Y_bottom</span><span class="p">))</span>
+
+        <span class="n">alive</span> <span class="o">=</span> <span class="n">alive_X</span> <span class="o">&amp;</span> <span class="n">alive_Y</span>
+        <span class="n">bunch</span><span class="o">.</span><span class="n">alive</span><span class="p">[</span><span class="o">~</span><span class="n">alive</span><span class="p">]</span> <span class="o">=</span> <span class="kc">False</span></div></div>
+
+
+<div class="viewcode-block" id="LongitudinalAperture"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.aperture.LongitudinalAperture">[docs]</a><span class="k">class</span> <span class="nc">LongitudinalAperture</span><span class="p">(</span><span class="n">Element</span><span class="p">):</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    Longitudinal aperture element. The particles which are outside of the </span>
+<span class="sd">    longitudinal bounds are &#39;lost&#39; and not used in the tracking any more.</span>
+<span class="sd">    </span>
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">    ring : Synchrotron object</span>
+<span class="sd">    tau_up : float</span>
+<span class="sd">        Upper longitudinal bound in [s].</span>
+<span class="sd">    tau_low : float, optional</span>
+<span class="sd">        Lower longitudinal bound in [s].</span>
+<span class="sd">    &quot;&quot;&quot;</span>
+
+    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">tau_up</span><span class="p">,</span> <span class="n">tau_low</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">tau_up</span> <span class="o">=</span> <span class="n">tau_up</span>
+        <span class="k">if</span> <span class="n">tau_low</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">tau_low</span> <span class="o">=</span> <span class="n">tau_up</span> <span class="o">*</span> <span class="o">-</span><span class="mi">1</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">tau_low</span> <span class="o">=</span> <span class="n">tau_low</span>
+
+<div class="viewcode-block" id="LongitudinalAperture.track"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.aperture.LongitudinalAperture.track">[docs]</a>    <span class="nd">@Element</span><span class="o">.</span><span class="n">parallel</span>
+    <span class="k">def</span> <span class="nf">track</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">bunch</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Tracking method for the element.</span>
+<span class="sd">        No bunch to bunch interaction, so written for Bunch objects and</span>
+<span class="sd">        @Element.parallel is used to handle Beam objects.</span>
+<span class="sd">        </span>
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        bunch : Bunch or Beam object</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+
+        <span class="n">alive</span> <span class="o">=</span> <span class="p">((</span><span class="n">bunch</span><span class="o">.</span><span class="n">particles</span><span class="p">[</span><span class="s2">&quot;tau&quot;</span><span class="p">]</span> <span class="o">&lt;</span> <span class="bp">self</span><span class="o">.</span><span class="n">tau_up</span><span class="p">)</span> <span class="o">&amp;</span>
+                 <span class="p">(</span><span class="n">bunch</span><span class="o">.</span><span class="n">particles</span><span class="p">[</span><span class="s2">&quot;tau&quot;</span><span class="p">]</span> <span class="o">&gt;</span> <span class="bp">self</span><span class="o">.</span><span class="n">tau_low</span><span class="p">))</span>
+
+        <span class="n">bunch</span><span class="o">.</span><span class="n">alive</span><span class="p">[</span><span class="o">~</span><span class="n">alive</span><span class="p">]</span> <span class="o">=</span> <span class="kc">False</span></div></div>
+</pre></div>
+
+            <div class="clearer"></div>
+          </div>
+        </div>
+      </div>
+      <div class="sphinxsidebar" role="navigation" aria-label="main navigation">
+        <div class="sphinxsidebarwrapper">
+<div id="searchbox" style="display: none" role="search">
+  <h3 id="searchlabel">Quick search</h3>
+    <div class="searchformwrapper">
+    <form class="search" action="../../../search.html" method="get">
+      <input type="text" name="q" aria-labelledby="searchlabel" autocomplete="off" autocorrect="off" autocapitalize="off" spellcheck="false"/>
+      <input type="submit" value="Go" />
+    </form>
+    </div>
+</div>
+<script>document.getElementById('searchbox').style.display = "block"</script>
+        </div>
+      </div>
+      <div class="clearer"></div>
+    </div>
+    <div class="related" role="navigation" aria-label="related navigation">
+      <h3>Navigation</h3>
+      <ul>
+        <li class="right" style="margin-right: 10px">
+          <a href="../../../genindex.html" title="General Index"
+             >index</a></li>
+        <li class="right" >
+          <a href="../../../py-modindex.html" title="Python Module Index"
+             >modules</a> |</li>
+        <li class="nav-item nav-item-0"><a href="../../../index.html">mbtrack2 0.6.0 documentation</a> &#187;</li>
+          <li class="nav-item nav-item-1"><a href="../../index.html" >Module code</a> &#187;</li>
+        <li class="nav-item nav-item-this"><a href="">mbtrack2.tracking.aperture</a></li> 
+      </ul>
+    </div>
+    <div class="footer" role="contentinfo">
+        &#169; Copyright 2024, A. Gamelin et al.
+      Created using <a href="https://www.sphinx-doc.org/">Sphinx</a> 5.0.2.
+    </div>
+  </body>
+</html>
\ No newline at end of file
diff --git a/docs/build/html/_modules/mbtrack2/tracking/element.html b/docs/build/html/_modules/mbtrack2/tracking/element.html
new file mode 100644
index 0000000..9c89459
--- /dev/null
+++ b/docs/build/html/_modules/mbtrack2/tracking/element.html
@@ -0,0 +1,591 @@
+
+<!DOCTYPE html>
+
+<html lang="en">
+  <head>
+    <meta charset="utf-8" />
+    <meta name="viewport" content="width=device-width, initial-scale=1.0" />
+    <title>mbtrack2.tracking.element &#8212; mbtrack2 0.6.0 documentation</title>
+    <link rel="stylesheet" type="text/css" href="../../../_static/pygments.css" />
+    <link rel="stylesheet" type="text/css" href="../../../_static/nature.css" />
+    <script data-url_root="../../../" id="documentation_options" src="../../../_static/documentation_options.js"></script>
+    <script src="../../../_static/jquery.js"></script>
+    <script src="../../../_static/underscore.js"></script>
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+    <script src="../../../_static/doctools.js"></script>
+    <link rel="index" title="Index" href="../../../genindex.html" />
+    <link rel="search" title="Search" href="../../../search.html" /> 
+  </head><body>
+    <div class="related" role="navigation" aria-label="related navigation">
+      <h3>Navigation</h3>
+      <ul>
+        <li class="right" style="margin-right: 10px">
+          <a href="../../../genindex.html" title="General Index"
+             accesskey="I">index</a></li>
+        <li class="right" >
+          <a href="../../../py-modindex.html" title="Python Module Index"
+             >modules</a> |</li>
+        <li class="nav-item nav-item-0"><a href="../../../index.html">mbtrack2 0.6.0 documentation</a> &#187;</li>
+          <li class="nav-item nav-item-1"><a href="../../index.html" accesskey="U">Module code</a> &#187;</li>
+        <li class="nav-item nav-item-this"><a href="">mbtrack2.tracking.element</a></li> 
+      </ul>
+    </div>  
+
+    <div class="document">
+      <div class="documentwrapper">
+        <div class="bodywrapper">
+          <div class="body" role="main">
+            
+  <h1>Source code for mbtrack2.tracking.element</h1><div class="highlight"><pre>
+<span></span><span class="c1"># -*- coding: utf-8 -*-</span>
+<span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">This module defines the most basic elements for tracking, including Element,</span>
+<span class="sd">an abstract base class which is to be used as mother class to every elements</span>
+<span class="sd">included in the tracking.</span>
+<span class="sd">&quot;&quot;&quot;</span>
+
+<span class="kn">from</span> <span class="nn">abc</span> <span class="kn">import</span> <span class="n">ABCMeta</span><span class="p">,</span> <span class="n">abstractmethod</span>
+<span class="kn">from</span> <span class="nn">copy</span> <span class="kn">import</span> <span class="n">deepcopy</span>
+<span class="kn">from</span> <span class="nn">functools</span> <span class="kn">import</span> <span class="n">wraps</span>
+
+<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
+
+<span class="kn">from</span> <span class="nn">mbtrack2.tracking.particles</span> <span class="kn">import</span> <span class="n">Beam</span>
+
+
+<div class="viewcode-block" id="Element"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.element.Element">[docs]</a><span class="k">class</span> <span class="nc">Element</span><span class="p">(</span><span class="n">metaclass</span><span class="o">=</span><span class="n">ABCMeta</span><span class="p">):</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    Abstract Element class used for subclass inheritance to define all kinds </span>
+<span class="sd">    of objects which intervene in the tracking.</span>
+<span class="sd">    &quot;&quot;&quot;</span>
+
+<div class="viewcode-block" id="Element.track"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.element.Element.track">[docs]</a>    <span class="nd">@abstractmethod</span>
+    <span class="k">def</span> <span class="nf">track</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">beam</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Track a beam object through this Element.</span>
+<span class="sd">        This method needs to be overloaded in each Element subclass.</span>
+<span class="sd">        </span>
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        beam : Beam object</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="k">raise</span> <span class="ne">NotImplementedError</span></div>
+
+<div class="viewcode-block" id="Element.parallel"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.element.Element.parallel">[docs]</a>    <span class="nd">@staticmethod</span>
+    <span class="k">def</span> <span class="nf">parallel</span><span class="p">(</span><span class="n">track</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Defines the decorator @parallel which handle the embarrassingly </span>
+<span class="sd">        parallel case which happens when there is no bunch to bunch </span>
+<span class="sd">        interaction in the tracking routine.</span>
+<span class="sd">        </span>
+<span class="sd">        Adding @Element.parallel allows to write the track method of the </span>
+<span class="sd">        Element subclass for a Bunch object instead of a Beam object.</span>
+<span class="sd">        </span>
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        track : function, method of an Element subclass</span>
+<span class="sd">            track method of an Element subclass which takes a Bunch object as</span>
+<span class="sd">            input</span>
+<span class="sd">            </span>
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        track_wrapper: function, method of an Element subclass</span>
+<span class="sd">            track method of an Element subclass which takes a Beam object or a</span>
+<span class="sd">            Bunch object as input</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+
+        <span class="nd">@wraps</span><span class="p">(</span><span class="n">track</span><span class="p">)</span>
+        <span class="k">def</span> <span class="nf">track_wrapper</span><span class="p">(</span><span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
+            <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">args</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">Beam</span><span class="p">):</span>
+                <span class="bp">self</span> <span class="o">=</span> <span class="n">args</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
+                <span class="n">beam</span> <span class="o">=</span> <span class="n">args</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span>
+                <span class="k">if</span> <span class="p">(</span><span class="n">beam</span><span class="o">.</span><span class="n">mpi_switch</span> <span class="o">==</span> <span class="kc">True</span><span class="p">):</span>
+                    <span class="n">track</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">beam</span><span class="p">[</span><span class="n">beam</span><span class="o">.</span><span class="n">mpi</span><span class="o">.</span><span class="n">bunch_num</span><span class="p">],</span> <span class="o">*</span><span class="n">args</span><span class="p">[</span><span class="mi">2</span><span class="p">:],</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
+                <span class="k">else</span><span class="p">:</span>
+                    <span class="k">for</span> <span class="n">bunch</span> <span class="ow">in</span> <span class="n">beam</span><span class="o">.</span><span class="n">not_empty</span><span class="p">:</span>
+                        <span class="n">track</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">bunch</span><span class="p">,</span> <span class="o">*</span><span class="n">args</span><span class="p">[</span><span class="mi">2</span><span class="p">:],</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
+            <span class="k">else</span><span class="p">:</span>
+                <span class="bp">self</span> <span class="o">=</span> <span class="n">args</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
+                <span class="n">bunch</span> <span class="o">=</span> <span class="n">args</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span>
+                <span class="n">track</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">bunch</span><span class="p">,</span> <span class="o">*</span><span class="n">args</span><span class="p">[</span><span class="mi">2</span><span class="p">:],</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
+
+        <span class="k">return</span> <span class="n">track_wrapper</span></div></div>
+
+
+<div class="viewcode-block" id="LongitudinalMap"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.element.LongitudinalMap">[docs]</a><span class="k">class</span> <span class="nc">LongitudinalMap</span><span class="p">(</span><span class="n">Element</span><span class="p">):</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    Longitudinal map for a single turn in the synchrotron.</span>
+<span class="sd">    </span>
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">    ring : Synchrotron object</span>
+<span class="sd">    &quot;&quot;&quot;</span>
+
+    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">ring</span><span class="p">):</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">ring</span> <span class="o">=</span> <span class="n">ring</span>
+
+<div class="viewcode-block" id="LongitudinalMap.track"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.element.LongitudinalMap.track">[docs]</a>    <span class="nd">@Element</span><span class="o">.</span><span class="n">parallel</span>
+    <span class="k">def</span> <span class="nf">track</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">bunch</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Tracking method for the element.</span>
+<span class="sd">        No bunch to bunch interaction, so written for Bunch objects and</span>
+<span class="sd">        @Element.parallel is used to handle Beam objects.</span>
+<span class="sd">        </span>
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        bunch : Bunch or Beam object</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="n">bunch</span><span class="p">[</span><span class="s2">&quot;delta&quot;</span><span class="p">]</span> <span class="o">-=</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">U0</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">E0</span>
+        <span class="n">bunch</span><span class="p">[</span><span class="s2">&quot;tau&quot;</span><span class="p">]</span> <span class="o">+=</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">eta</span><span class="p">(</span>
+            <span class="n">bunch</span><span class="p">[</span><span class="s2">&quot;delta&quot;</span><span class="p">])</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">T0</span> <span class="o">*</span> <span class="n">bunch</span><span class="p">[</span><span class="s2">&quot;delta&quot;</span><span class="p">]</span></div></div>
+
+
+<div class="viewcode-block" id="SynchrotronRadiation"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.element.SynchrotronRadiation">[docs]</a><span class="k">class</span> <span class="nc">SynchrotronRadiation</span><span class="p">(</span><span class="n">Element</span><span class="p">):</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    Element to handle synchrotron radiation, radiation damping and quantum </span>
+<span class="sd">    excitation, for a single turn in the synchrotron.</span>
+<span class="sd">    </span>
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">    ring : Synchrotron object</span>
+<span class="sd">    switch : bool array of shape (3,), optional</span>
+<span class="sd">        allow to choose on which plane the synchrotron radiation is active</span>
+<span class="sd">    &quot;&quot;&quot;</span>
+
+    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">ring</span><span class="p">,</span> <span class="n">switch</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">((</span><span class="mi">3</span><span class="p">,</span> <span class="p">),</span> <span class="n">dtype</span><span class="o">=</span><span class="nb">bool</span><span class="p">)):</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">ring</span> <span class="o">=</span> <span class="n">ring</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">switch</span> <span class="o">=</span> <span class="n">switch</span>
+
+<div class="viewcode-block" id="SynchrotronRadiation.track"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.element.SynchrotronRadiation.track">[docs]</a>    <span class="nd">@Element</span><span class="o">.</span><span class="n">parallel</span>
+    <span class="k">def</span> <span class="nf">track</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">bunch</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Tracking method for the element.</span>
+<span class="sd">        No bunch to bunch interaction, so written for Bunch objects and</span>
+<span class="sd">        @Element.parallel is used to handle Beam objects.</span>
+<span class="sd">        </span>
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        bunch : Bunch or Beam object</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="k">if</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">switch</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">==</span> <span class="kc">True</span><span class="p">):</span>
+            <span class="n">rand</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">normal</span><span class="p">(</span><span class="n">size</span><span class="o">=</span><span class="nb">len</span><span class="p">(</span><span class="n">bunch</span><span class="p">))</span>
+            <span class="n">bunch</span><span class="p">[</span><span class="s2">&quot;delta&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="p">(</span>
+                <span class="p">(</span><span class="mi">1</span> <span class="o">-</span> <span class="mi">2</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">T0</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">tau</span><span class="p">[</span><span class="mi">2</span><span class="p">])</span> <span class="o">*</span> <span class="n">bunch</span><span class="p">[</span><span class="s2">&quot;delta&quot;</span><span class="p">]</span> <span class="o">+</span>
+                <span class="mi">2</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">sigma_delta</span> <span class="o">*</span>
+                <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">T0</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">tau</span><span class="p">[</span><span class="mi">2</span><span class="p">])</span><span class="o">**</span><span class="mf">0.5</span> <span class="o">*</span> <span class="n">rand</span><span class="p">)</span>
+
+        <span class="k">if</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">switch</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">==</span> <span class="kc">True</span><span class="p">):</span>
+            <span class="n">rand</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">normal</span><span class="p">(</span><span class="n">size</span><span class="o">=</span><span class="nb">len</span><span class="p">(</span><span class="n">bunch</span><span class="p">))</span>
+            <span class="n">bunch</span><span class="p">[</span><span class="s2">&quot;xp&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="p">(</span>
+                <span class="p">(</span><span class="mi">1</span> <span class="o">-</span> <span class="mi">2</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">T0</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">tau</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span> <span class="o">*</span> <span class="n">bunch</span><span class="p">[</span><span class="s2">&quot;xp&quot;</span><span class="p">]</span> <span class="o">+</span>
+                <span class="mi">2</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">sigma</span><span class="p">()[</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span>
+                <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">T0</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">tau</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span><span class="o">**</span><span class="mf">0.5</span> <span class="o">*</span> <span class="n">rand</span><span class="p">)</span>
+
+        <span class="k">if</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">switch</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="o">==</span> <span class="kc">True</span><span class="p">):</span>
+            <span class="n">rand</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">normal</span><span class="p">(</span><span class="n">size</span><span class="o">=</span><span class="nb">len</span><span class="p">(</span><span class="n">bunch</span><span class="p">))</span>
+            <span class="n">bunch</span><span class="p">[</span><span class="s2">&quot;yp&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="p">(</span>
+                <span class="p">(</span><span class="mi">1</span> <span class="o">-</span> <span class="mi">2</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">T0</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">tau</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span> <span class="o">*</span> <span class="n">bunch</span><span class="p">[</span><span class="s2">&quot;yp&quot;</span><span class="p">]</span> <span class="o">+</span>
+                <span class="mi">2</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">sigma</span><span class="p">()[</span><span class="mi">3</span><span class="p">]</span> <span class="o">*</span>
+                <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">T0</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">tau</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span><span class="o">**</span><span class="mf">0.5</span> <span class="o">*</span> <span class="n">rand</span><span class="p">)</span></div></div>
+
+
+<div class="viewcode-block" id="TransverseMap"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.element.TransverseMap">[docs]</a><span class="k">class</span> <span class="nc">TransverseMap</span><span class="p">(</span><span class="n">Element</span><span class="p">):</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    Transverse map for a single turn in the synchrotron.</span>
+<span class="sd">    </span>
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">    ring : Synchrotron object</span>
+<span class="sd">    &quot;&quot;&quot;</span>
+
+    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">ring</span><span class="p">):</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">ring</span> <span class="o">=</span> <span class="n">ring</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">alpha</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">optics</span><span class="o">.</span><span class="n">local_alpha</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">beta</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">optics</span><span class="o">.</span><span class="n">local_beta</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">gamma</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">optics</span><span class="o">.</span><span class="n">local_gamma</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">dispersion</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">optics</span><span class="o">.</span><span class="n">local_dispersion</span>
+        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">adts</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">adts_poly</span> <span class="o">=</span> <span class="p">[</span>
+                <span class="n">np</span><span class="o">.</span><span class="n">poly1d</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">adts</span><span class="p">[</span><span class="mi">0</span><span class="p">]),</span>
+                <span class="n">np</span><span class="o">.</span><span class="n">poly1d</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">adts</span><span class="p">[</span><span class="mi">1</span><span class="p">]),</span>
+                <span class="n">np</span><span class="o">.</span><span class="n">poly1d</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">adts</span><span class="p">[</span><span class="mi">2</span><span class="p">]),</span>
+                <span class="n">np</span><span class="o">.</span><span class="n">poly1d</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">adts</span><span class="p">[</span><span class="mi">3</span><span class="p">])</span>
+            <span class="p">]</span>
+
+<div class="viewcode-block" id="TransverseMap.track"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.element.TransverseMap.track">[docs]</a>    <span class="nd">@Element</span><span class="o">.</span><span class="n">parallel</span>
+    <span class="k">def</span> <span class="nf">track</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">bunch</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Tracking method for the element.</span>
+<span class="sd">        No bunch to bunch interaction, so written for Bunch objects and</span>
+<span class="sd">        @Element.parallel is used to handle Beam objects.</span>
+<span class="sd">        </span>
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        bunch : Bunch or Beam object</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+
+        <span class="c1"># Compute phase advance which depends on energy via chromaticity and ADTS</span>
+        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">adts</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="n">phase_advance_x</span> <span class="o">=</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">tune</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">+</span>
+                                           <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">chro</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">bunch</span><span class="p">[</span><span class="s2">&quot;delta&quot;</span><span class="p">])</span>
+            <span class="n">phase_advance_y</span> <span class="o">=</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">tune</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">+</span>
+                                           <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">chro</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="n">bunch</span><span class="p">[</span><span class="s2">&quot;delta&quot;</span><span class="p">])</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="n">Jx</span> <span class="o">=</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">optics</span><span class="o">.</span><span class="n">local_gamma</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">bunch</span><span class="p">[</span><span class="s1">&#39;x&#39;</span><span class="p">]</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span> <span class="o">+</span> \
+                  <span class="p">(</span><span class="mi">2</span><span class="o">*</span><span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">optics</span><span class="o">.</span><span class="n">local_alpha</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">bunch</span><span class="p">[</span><span class="s1">&#39;x&#39;</span><span class="p">]</span><span class="o">*</span><span class="n">bunch</span><span class="p">[</span><span class="s1">&#39;xp&#39;</span><span class="p">])</span> <span class="o">+</span> \
+                  <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">optics</span><span class="o">.</span><span class="n">local_beta</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">bunch</span><span class="p">[</span><span class="s1">&#39;xp&#39;</span><span class="p">]</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span>
+            <span class="n">Jy</span> <span class="o">=</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">optics</span><span class="o">.</span><span class="n">local_gamma</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="n">bunch</span><span class="p">[</span><span class="s1">&#39;y&#39;</span><span class="p">]</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span> <span class="o">+</span> \
+                  <span class="p">(</span><span class="mi">2</span><span class="o">*</span><span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">optics</span><span class="o">.</span><span class="n">local_alpha</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="n">bunch</span><span class="p">[</span><span class="s1">&#39;y&#39;</span><span class="p">]</span><span class="o">*</span><span class="n">bunch</span><span class="p">[</span><span class="s1">&#39;yp&#39;</span><span class="p">])</span> <span class="o">+</span> \
+                  <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">optics</span><span class="o">.</span><span class="n">local_beta</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="n">bunch</span><span class="p">[</span><span class="s1">&#39;yp&#39;</span><span class="p">]</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span>
+            <span class="n">phase_advance_x</span> <span class="o">=</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="p">(</span>
+                <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">tune</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">chro</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">bunch</span><span class="p">[</span><span class="s2">&quot;delta&quot;</span><span class="p">]</span> <span class="o">+</span>
+                <span class="bp">self</span><span class="o">.</span><span class="n">adts_poly</span><span class="p">[</span><span class="mi">0</span><span class="p">](</span><span class="n">Jx</span><span class="p">)</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">adts_poly</span><span class="p">[</span><span class="mi">2</span><span class="p">](</span><span class="n">Jy</span><span class="p">))</span>
+            <span class="n">phase_advance_y</span> <span class="o">=</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="p">(</span>
+                <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">tune</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">chro</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="n">bunch</span><span class="p">[</span><span class="s2">&quot;delta&quot;</span><span class="p">]</span> <span class="o">+</span>
+                <span class="bp">self</span><span class="o">.</span><span class="n">adts_poly</span><span class="p">[</span><span class="mi">1</span><span class="p">](</span><span class="n">Jx</span><span class="p">)</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">adts_poly</span><span class="p">[</span><span class="mi">3</span><span class="p">](</span><span class="n">Jy</span><span class="p">))</span>
+
+        <span class="c1"># 6x6 matrix corresponding to (x, xp, delta, y, yp, delta)</span>
+        <span class="n">matrix</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="mi">6</span><span class="p">,</span> <span class="mi">6</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">bunch</span><span class="p">)),</span> <span class="n">dtype</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">float64</span><span class="p">)</span>
+
+        <span class="c1"># Horizontal</span>
+        <span class="n">c_x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">phase_advance_x</span><span class="p">)</span>
+        <span class="n">s_x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">phase_advance_x</span><span class="p">)</span>
+
+        <span class="n">matrix</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="p">:]</span> <span class="o">=</span> <span class="n">c_x</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">alpha</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">s_x</span>
+        <span class="n">matrix</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="p">:]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">beta</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">s_x</span>
+        <span class="n">matrix</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="p">:]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">dispersion</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
+        <span class="n">matrix</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="p">:]</span> <span class="o">=</span> <span class="o">-</span><span class="mi">1</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">gamma</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">s_x</span>
+        <span class="n">matrix</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="p">:]</span> <span class="o">=</span> <span class="n">c_x</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">alpha</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">s_x</span>
+        <span class="n">matrix</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="p">:]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">dispersion</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span>
+        <span class="n">matrix</span><span class="p">[</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="p">:]</span> <span class="o">=</span> <span class="mi">1</span>
+
+        <span class="c1"># Vertical</span>
+        <span class="n">c_y</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">phase_advance_y</span><span class="p">)</span>
+        <span class="n">s_y</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">phase_advance_y</span><span class="p">)</span>
+
+        <span class="n">matrix</span><span class="p">[</span><span class="mi">3</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="p">:]</span> <span class="o">=</span> <span class="n">c_y</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">alpha</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="n">s_y</span>
+        <span class="n">matrix</span><span class="p">[</span><span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="p">:]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">beta</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="n">s_y</span>
+        <span class="n">matrix</span><span class="p">[</span><span class="mi">3</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="p">:]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">dispersion</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span>
+        <span class="n">matrix</span><span class="p">[</span><span class="mi">4</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="p">:]</span> <span class="o">=</span> <span class="o">-</span><span class="mi">1</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">gamma</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="n">s_y</span>
+        <span class="n">matrix</span><span class="p">[</span><span class="mi">4</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="p">:]</span> <span class="o">=</span> <span class="n">c_y</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">alpha</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="n">s_y</span>
+        <span class="n">matrix</span><span class="p">[</span><span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="p">:]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">dispersion</span><span class="p">[</span><span class="mi">3</span><span class="p">]</span>
+        <span class="n">matrix</span><span class="p">[</span><span class="mi">5</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="p">:]</span> <span class="o">=</span> <span class="mi">1</span>
+
+        <span class="n">x</span> <span class="o">=</span> <span class="n">matrix</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="p">:]</span> <span class="o">*</span> <span class="n">bunch</span><span class="p">[</span><span class="s2">&quot;x&quot;</span><span class="p">]</span> <span class="o">+</span> <span class="n">matrix</span><span class="p">[</span>
+            <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="p">:]</span> <span class="o">*</span> <span class="n">bunch</span><span class="p">[</span><span class="s2">&quot;xp&quot;</span><span class="p">]</span> <span class="o">+</span> <span class="n">matrix</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="p">:]</span> <span class="o">*</span> <span class="n">bunch</span><span class="p">[</span><span class="s2">&quot;delta&quot;</span><span class="p">]</span>
+        <span class="n">xp</span> <span class="o">=</span> <span class="n">matrix</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="p">:]</span> <span class="o">*</span> <span class="n">bunch</span><span class="p">[</span><span class="s2">&quot;x&quot;</span><span class="p">]</span> <span class="o">+</span> <span class="n">matrix</span><span class="p">[</span>
+            <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="p">:]</span> <span class="o">*</span> <span class="n">bunch</span><span class="p">[</span><span class="s2">&quot;xp&quot;</span><span class="p">]</span> <span class="o">+</span> <span class="n">matrix</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="p">:]</span> <span class="o">*</span> <span class="n">bunch</span><span class="p">[</span><span class="s2">&quot;delta&quot;</span><span class="p">]</span>
+        <span class="n">y</span> <span class="o">=</span> <span class="n">matrix</span><span class="p">[</span><span class="mi">3</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="p">:]</span> <span class="o">*</span> <span class="n">bunch</span><span class="p">[</span><span class="s2">&quot;y&quot;</span><span class="p">]</span> <span class="o">+</span> <span class="n">matrix</span><span class="p">[</span>
+            <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="p">:]</span> <span class="o">*</span> <span class="n">bunch</span><span class="p">[</span><span class="s2">&quot;yp&quot;</span><span class="p">]</span> <span class="o">+</span> <span class="n">matrix</span><span class="p">[</span><span class="mi">3</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="p">:]</span> <span class="o">*</span> <span class="n">bunch</span><span class="p">[</span><span class="s2">&quot;delta&quot;</span><span class="p">]</span>
+        <span class="n">yp</span> <span class="o">=</span> <span class="n">matrix</span><span class="p">[</span><span class="mi">4</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="p">:]</span> <span class="o">*</span> <span class="n">bunch</span><span class="p">[</span><span class="s2">&quot;y&quot;</span><span class="p">]</span> <span class="o">+</span> <span class="n">matrix</span><span class="p">[</span>
+            <span class="mi">4</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="p">:]</span> <span class="o">*</span> <span class="n">bunch</span><span class="p">[</span><span class="s2">&quot;yp&quot;</span><span class="p">]</span> <span class="o">+</span> <span class="n">matrix</span><span class="p">[</span><span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="p">:]</span> <span class="o">*</span> <span class="n">bunch</span><span class="p">[</span><span class="s2">&quot;delta&quot;</span><span class="p">]</span>
+
+        <span class="n">bunch</span><span class="p">[</span><span class="s2">&quot;x&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="n">x</span>
+        <span class="n">bunch</span><span class="p">[</span><span class="s2">&quot;xp&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="n">xp</span>
+        <span class="n">bunch</span><span class="p">[</span><span class="s2">&quot;y&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="n">y</span>
+        <span class="n">bunch</span><span class="p">[</span><span class="s2">&quot;yp&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="n">yp</span></div></div>
+
+
+<div class="viewcode-block" id="SkewQuadrupole"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.element.SkewQuadrupole">[docs]</a><span class="k">class</span> <span class="nc">SkewQuadrupole</span><span class="p">:</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    Thin skew quadrupole element used to introduce betatron coupling (the </span>
+<span class="sd">    length of the quadrupole is neglected).</span>
+<span class="sd">    </span>
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">    strength : float</span>
+<span class="sd">        Integrated strength of the skew quadrupole [m].</span>
+<span class="sd">        </span>
+<span class="sd">    &quot;&quot;&quot;</span>
+
+    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">strength</span><span class="p">):</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">strength</span> <span class="o">=</span> <span class="n">strength</span>
+
+<div class="viewcode-block" id="SkewQuadrupole.track"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.element.SkewQuadrupole.track">[docs]</a>    <span class="nd">@Element</span><span class="o">.</span><span class="n">parallel</span>
+    <span class="k">def</span> <span class="nf">track</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">bunch</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Tracking method for the element.</span>
+<span class="sd">        No bunch to bunch interaction, so written for Bunch objects and</span>
+<span class="sd">        @Element.parallel is used to handle Beam objects.</span>
+<span class="sd">        </span>
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        bunch : Bunch or Beam object</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+
+        <span class="n">bunch</span><span class="p">[</span><span class="s1">&#39;xp&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="n">bunch</span><span class="p">[</span><span class="s1">&#39;xp&#39;</span><span class="p">]</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">strength</span> <span class="o">*</span> <span class="n">bunch</span><span class="p">[</span><span class="s1">&#39;y&#39;</span><span class="p">]</span>
+        <span class="n">bunch</span><span class="p">[</span><span class="s1">&#39;yp&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="n">bunch</span><span class="p">[</span><span class="s1">&#39;yp&#39;</span><span class="p">]</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">strength</span> <span class="o">*</span> <span class="n">bunch</span><span class="p">[</span><span class="s1">&#39;x&#39;</span><span class="p">]</span></div></div>
+
+
+<div class="viewcode-block" id="TransverseMapSector"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.element.TransverseMapSector">[docs]</a><span class="k">class</span> <span class="nc">TransverseMapSector</span><span class="p">(</span><span class="n">Element</span><span class="p">):</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    Transverse map for a sector of the synchrotron, from an initial </span>
+<span class="sd">    position s0 to a final position s1.</span>
+
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">    ring : Synchrotron object</span>
+<span class="sd">        Ring parameters.</span>
+<span class="sd">    alpha0 : array of shape (2,)</span>
+<span class="sd">        Alpha Twiss function at the initial location of the sector.</span>
+<span class="sd">    beta0 : array of shape (2,)</span>
+<span class="sd">        Beta Twiss function at the initial location of the sector.</span>
+<span class="sd">    dispersion0 : array of shape (4,)</span>
+<span class="sd">        Dispersion function at the initial location of the sector.</span>
+<span class="sd">    alpha1 : array of shape (2,)</span>
+<span class="sd">        Alpha Twiss function at the final location of the sector.</span>
+<span class="sd">    beta1 : array of shape (2,)</span>
+<span class="sd">        Beta Twiss function at the final location of the sector.</span>
+<span class="sd">    dispersion1 : array of shape (4,)</span>
+<span class="sd">        Dispersion function at the final location of the sector.</span>
+<span class="sd">    phase_diff : array of shape (2,)</span>
+<span class="sd">        Phase difference between the initial and final location of the </span>
+<span class="sd">        sector.</span>
+<span class="sd">    chro_diff : array of shape (2,)</span>
+<span class="sd">        Chromaticity difference between the initial and final location of </span>
+<span class="sd">        the sector.</span>
+<span class="sd">    adts : array of shape (4,), optional</span>
+<span class="sd">        Amplitude-dependent tune shift of the sector, see Synchrotron class </span>
+<span class="sd">        for details. The default is None.</span>
+
+<span class="sd">    &quot;&quot;&quot;</span>
+
+    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span>
+                 <span class="n">ring</span><span class="p">,</span>
+                 <span class="n">alpha0</span><span class="p">,</span>
+                 <span class="n">beta0</span><span class="p">,</span>
+                 <span class="n">dispersion0</span><span class="p">,</span>
+                 <span class="n">alpha1</span><span class="p">,</span>
+                 <span class="n">beta1</span><span class="p">,</span>
+                 <span class="n">dispersion1</span><span class="p">,</span>
+                 <span class="n">phase_diff</span><span class="p">,</span>
+                 <span class="n">chro_diff</span><span class="p">,</span>
+                 <span class="n">adts</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">ring</span> <span class="o">=</span> <span class="n">ring</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">alpha0</span> <span class="o">=</span> <span class="n">alpha0</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">beta0</span> <span class="o">=</span> <span class="n">beta0</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">gamma0</span> <span class="o">=</span> <span class="p">(</span><span class="mi">1</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">alpha0</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">beta0</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">dispersion0</span> <span class="o">=</span> <span class="n">dispersion0</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">alpha1</span> <span class="o">=</span> <span class="n">alpha1</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">beta1</span> <span class="o">=</span> <span class="n">beta1</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">gamma1</span> <span class="o">=</span> <span class="p">(</span><span class="mi">1</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">alpha1</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">beta1</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">dispersion1</span> <span class="o">=</span> <span class="n">dispersion1</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">tune_diff</span> <span class="o">=</span> <span class="n">phase_diff</span> <span class="o">/</span> <span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">chro_diff</span> <span class="o">=</span> <span class="n">chro_diff</span>
+        <span class="k">if</span> <span class="n">adts</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">adts_poly</span> <span class="o">=</span> <span class="p">[</span>
+                <span class="n">np</span><span class="o">.</span><span class="n">poly1d</span><span class="p">(</span><span class="n">adts</span><span class="p">[</span><span class="mi">0</span><span class="p">]),</span>
+                <span class="n">np</span><span class="o">.</span><span class="n">poly1d</span><span class="p">(</span><span class="n">adts</span><span class="p">[</span><span class="mi">1</span><span class="p">]),</span>
+                <span class="n">np</span><span class="o">.</span><span class="n">poly1d</span><span class="p">(</span><span class="n">adts</span><span class="p">[</span><span class="mi">2</span><span class="p">]),</span>
+                <span class="n">np</span><span class="o">.</span><span class="n">poly1d</span><span class="p">(</span><span class="n">adts</span><span class="p">[</span><span class="mi">3</span><span class="p">])</span>
+            <span class="p">]</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">adts_poly</span> <span class="o">=</span> <span class="kc">None</span>
+
+<div class="viewcode-block" id="TransverseMapSector.track"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.element.TransverseMapSector.track">[docs]</a>    <span class="nd">@Element</span><span class="o">.</span><span class="n">parallel</span>
+    <span class="k">def</span> <span class="nf">track</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">bunch</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Tracking method for the element.</span>
+<span class="sd">        No bunch to bunch interaction, so written for Bunch objects and</span>
+<span class="sd">        @Element.parallel is used to handle Beam objects.</span>
+<span class="sd">        </span>
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        bunch : Bunch or Beam object</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+
+        <span class="c1"># Compute phase advance which depends on energy via chromaticity and ADTS</span>
+        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">adts_poly</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="n">phase_advance_x</span> <span class="o">=</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">tune_diff</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">+</span>
+                                           <span class="bp">self</span><span class="o">.</span><span class="n">chro_diff</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">bunch</span><span class="p">[</span><span class="s2">&quot;delta&quot;</span><span class="p">])</span>
+            <span class="n">phase_advance_y</span> <span class="o">=</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">tune_diff</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">+</span>
+                                           <span class="bp">self</span><span class="o">.</span><span class="n">chro_diff</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="n">bunch</span><span class="p">[</span><span class="s2">&quot;delta&quot;</span><span class="p">])</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="n">Jx</span> <span class="o">=</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">gamma0</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">bunch</span><span class="p">[</span><span class="s1">&#39;x&#39;</span><span class="p">]</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span> <span class="o">+</span> \
+                  <span class="p">(</span><span class="mi">2</span><span class="o">*</span><span class="bp">self</span><span class="o">.</span><span class="n">alpha0</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">bunch</span><span class="p">[</span><span class="s1">&#39;x&#39;</span><span class="p">]</span><span class="o">*</span><span class="bp">self</span><span class="p">[</span><span class="s1">&#39;xp&#39;</span><span class="p">])</span> <span class="o">+</span> \
+                  <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">beta0</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">bunch</span><span class="p">[</span><span class="s1">&#39;xp&#39;</span><span class="p">]</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span>
+            <span class="n">Jy</span> <span class="o">=</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">gamma0</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="n">bunch</span><span class="p">[</span><span class="s1">&#39;y&#39;</span><span class="p">]</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span> <span class="o">+</span> \
+                  <span class="p">(</span><span class="mi">2</span><span class="o">*</span><span class="bp">self</span><span class="o">.</span><span class="n">alpha0</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="n">bunch</span><span class="p">[</span><span class="s1">&#39;y&#39;</span><span class="p">]</span><span class="o">*</span><span class="n">bunch</span><span class="p">[</span><span class="s1">&#39;yp&#39;</span><span class="p">])</span> <span class="o">+</span> \
+                  <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">beta0</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="n">bunch</span><span class="p">[</span><span class="s1">&#39;yp&#39;</span><span class="p">]</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span>
+            <span class="n">phase_advance_x</span> <span class="o">=</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="p">(</span>
+                <span class="bp">self</span><span class="o">.</span><span class="n">tune_diff</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">chro_diff</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">bunch</span><span class="p">[</span><span class="s2">&quot;delta&quot;</span><span class="p">]</span> <span class="o">+</span>
+                <span class="bp">self</span><span class="o">.</span><span class="n">adts_poly</span><span class="p">[</span><span class="mi">0</span><span class="p">](</span><span class="n">Jx</span><span class="p">)</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">adts_poly</span><span class="p">[</span><span class="mi">2</span><span class="p">](</span><span class="n">Jy</span><span class="p">))</span>
+            <span class="n">phase_advance_y</span> <span class="o">=</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="p">(</span>
+                <span class="bp">self</span><span class="o">.</span><span class="n">tune_diff</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">chro_diff</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="n">bunch</span><span class="p">[</span><span class="s2">&quot;delta&quot;</span><span class="p">]</span> <span class="o">+</span>
+                <span class="bp">self</span><span class="o">.</span><span class="n">adts_poly</span><span class="p">[</span><span class="mi">1</span><span class="p">](</span><span class="n">Jx</span><span class="p">)</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">adts_poly</span><span class="p">[</span><span class="mi">3</span><span class="p">](</span><span class="n">Jy</span><span class="p">))</span>
+
+        <span class="c1"># 6x6 matrix corresponding to (x, xp, delta, y, yp, delta)</span>
+        <span class="n">matrix</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="mi">6</span><span class="p">,</span> <span class="mi">6</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">bunch</span><span class="p">)))</span>
+
+        <span class="c1"># Horizontal</span>
+        <span class="n">matrix</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="p">:]</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">beta1</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">beta0</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span> <span class="o">*</span> <span class="p">(</span>
+            <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">phase_advance_x</span><span class="p">)</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">alpha0</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">phase_advance_x</span><span class="p">))</span>
+        <span class="n">matrix</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="p">:]</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">beta0</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">beta1</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">phase_advance_x</span><span class="p">)</span>
+        <span class="n">matrix</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="p">:]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">dispersion1</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">-</span> <span class="n">matrix</span><span class="p">[</span>
+            <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="p">:]</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">dispersion0</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">-</span> <span class="n">matrix</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span>
+                                                    <span class="mi">1</span><span class="p">,</span> <span class="p">:]</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">dispersion0</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span>
+        <span class="n">matrix</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="p">:]</span> <span class="o">=</span> <span class="p">(</span>
+            <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">alpha0</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">alpha1</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">phase_advance_x</span><span class="p">)</span> <span class="o">-</span>
+            <span class="p">(</span><span class="mi">1</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">alpha0</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">alpha1</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span> <span class="o">*</span>
+            <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">phase_advance_x</span><span class="p">))</span> <span class="o">/</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">beta0</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">beta1</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
+        <span class="n">matrix</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="p">:]</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">beta0</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">beta1</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span> <span class="o">*</span> <span class="p">(</span>
+            <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">phase_advance_x</span><span class="p">)</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">alpha1</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">phase_advance_x</span><span class="p">))</span>
+        <span class="n">matrix</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="p">:]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">dispersion1</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="n">matrix</span><span class="p">[</span>
+            <span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="p">:]</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">dispersion0</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">-</span> <span class="n">matrix</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span>
+                                                    <span class="mi">1</span><span class="p">,</span> <span class="p">:]</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">dispersion0</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span>
+        <span class="n">matrix</span><span class="p">[</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="p">:]</span> <span class="o">=</span> <span class="mi">1</span>
+
+        <span class="c1"># Vertical</span>
+        <span class="n">matrix</span><span class="p">[</span><span class="mi">3</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="p">:]</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">beta1</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">beta0</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span> <span class="o">*</span> <span class="p">(</span>
+            <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">phase_advance_y</span><span class="p">)</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">alpha0</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">phase_advance_y</span><span class="p">))</span>
+        <span class="n">matrix</span><span class="p">[</span><span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="p">:]</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">beta0</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">beta1</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">phase_advance_y</span><span class="p">)</span>
+        <span class="n">matrix</span><span class="p">[</span><span class="mi">3</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="p">:]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">dispersion1</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="o">-</span> <span class="n">matrix</span><span class="p">[</span>
+            <span class="mi">3</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="p">:]</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">dispersion0</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="o">-</span> <span class="n">matrix</span><span class="p">[</span><span class="mi">3</span><span class="p">,</span>
+                                                    <span class="mi">4</span><span class="p">,</span> <span class="p">:]</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">dispersion0</span><span class="p">[</span><span class="mi">3</span><span class="p">]</span>
+        <span class="n">matrix</span><span class="p">[</span><span class="mi">4</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="p">:]</span> <span class="o">=</span> <span class="p">(</span>
+            <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">alpha0</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">alpha1</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">phase_advance_y</span><span class="p">)</span> <span class="o">-</span>
+            <span class="p">(</span><span class="mi">1</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">alpha0</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">alpha1</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span> <span class="o">*</span>
+            <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">phase_advance_y</span><span class="p">))</span> <span class="o">/</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">beta0</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">beta1</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
+        <span class="n">matrix</span><span class="p">[</span><span class="mi">4</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="p">:]</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">beta0</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">beta1</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span> <span class="o">*</span> <span class="p">(</span>
+            <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">phase_advance_y</span><span class="p">)</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">alpha1</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">phase_advance_y</span><span class="p">))</span>
+        <span class="n">matrix</span><span class="p">[</span><span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="p">:]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">dispersion1</span><span class="p">[</span><span class="mi">3</span><span class="p">]</span> <span class="o">-</span> <span class="n">matrix</span><span class="p">[</span>
+            <span class="mi">4</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="p">:]</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">dispersion0</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="o">-</span> <span class="n">matrix</span><span class="p">[</span><span class="mi">4</span><span class="p">,</span>
+                                                    <span class="mi">4</span><span class="p">,</span> <span class="p">:]</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">dispersion0</span><span class="p">[</span><span class="mi">3</span><span class="p">]</span>
+        <span class="n">matrix</span><span class="p">[</span><span class="mi">5</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="p">:]</span> <span class="o">=</span> <span class="mi">1</span>
+
+        <span class="n">x</span> <span class="o">=</span> <span class="n">matrix</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="p">:]</span> <span class="o">*</span> <span class="n">bunch</span><span class="p">[</span><span class="s2">&quot;x&quot;</span><span class="p">]</span> <span class="o">+</span> <span class="n">matrix</span><span class="p">[</span>
+            <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="p">:]</span> <span class="o">*</span> <span class="n">bunch</span><span class="p">[</span><span class="s2">&quot;xp&quot;</span><span class="p">]</span> <span class="o">+</span> <span class="n">matrix</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="p">:]</span> <span class="o">*</span> <span class="n">bunch</span><span class="p">[</span><span class="s2">&quot;delta&quot;</span><span class="p">]</span>
+        <span class="n">xp</span> <span class="o">=</span> <span class="n">matrix</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="p">:]</span> <span class="o">*</span> <span class="n">bunch</span><span class="p">[</span><span class="s2">&quot;x&quot;</span><span class="p">]</span> <span class="o">+</span> <span class="n">matrix</span><span class="p">[</span>
+            <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="p">:]</span> <span class="o">*</span> <span class="n">bunch</span><span class="p">[</span><span class="s2">&quot;xp&quot;</span><span class="p">]</span> <span class="o">+</span> <span class="n">matrix</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="p">:]</span> <span class="o">*</span> <span class="n">bunch</span><span class="p">[</span><span class="s2">&quot;delta&quot;</span><span class="p">]</span>
+        <span class="n">y</span> <span class="o">=</span> <span class="n">matrix</span><span class="p">[</span><span class="mi">3</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="p">:]</span> <span class="o">*</span> <span class="n">bunch</span><span class="p">[</span><span class="s2">&quot;y&quot;</span><span class="p">]</span> <span class="o">+</span> <span class="n">matrix</span><span class="p">[</span>
+            <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="p">:]</span> <span class="o">*</span> <span class="n">bunch</span><span class="p">[</span><span class="s2">&quot;yp&quot;</span><span class="p">]</span> <span class="o">+</span> <span class="n">matrix</span><span class="p">[</span><span class="mi">3</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="p">:]</span> <span class="o">*</span> <span class="n">bunch</span><span class="p">[</span><span class="s2">&quot;delta&quot;</span><span class="p">]</span>
+        <span class="n">yp</span> <span class="o">=</span> <span class="n">matrix</span><span class="p">[</span><span class="mi">4</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="p">:]</span> <span class="o">*</span> <span class="n">bunch</span><span class="p">[</span><span class="s2">&quot;y&quot;</span><span class="p">]</span> <span class="o">+</span> <span class="n">matrix</span><span class="p">[</span>
+            <span class="mi">4</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="p">:]</span> <span class="o">*</span> <span class="n">bunch</span><span class="p">[</span><span class="s2">&quot;yp&quot;</span><span class="p">]</span> <span class="o">+</span> <span class="n">matrix</span><span class="p">[</span><span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="p">:]</span> <span class="o">*</span> <span class="n">bunch</span><span class="p">[</span><span class="s2">&quot;delta&quot;</span><span class="p">]</span>
+
+        <span class="n">bunch</span><span class="p">[</span><span class="s2">&quot;x&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="n">x</span>
+        <span class="n">bunch</span><span class="p">[</span><span class="s2">&quot;xp&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="n">xp</span>
+        <span class="n">bunch</span><span class="p">[</span><span class="s2">&quot;y&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="n">y</span>
+        <span class="n">bunch</span><span class="p">[</span><span class="s2">&quot;yp&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="n">yp</span></div></div>
+
+
+<div class="viewcode-block" id="transverse_map_sector_generator"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.element.transverse_map_sector_generator">[docs]</a><span class="k">def</span> <span class="nf">transverse_map_sector_generator</span><span class="p">(</span><span class="n">ring</span><span class="p">,</span> <span class="n">positions</span><span class="p">):</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    Convenience function which generate a list of TransverseMapSector elements</span>
+<span class="sd">    from a ring with an AT lattice.</span>
+<span class="sd">    </span>
+<span class="sd">    Tracking through all the sectors is equivalent to a full turn (and thus to </span>
+<span class="sd">    the TransverseMap object).</span>
+
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">    ring : Synchrotron object</span>
+<span class="sd">        Ring parameters, must .</span>
+<span class="sd">    positions : array</span>
+<span class="sd">        List of longitudinal positions in [m] to use as starting and end points</span>
+<span class="sd">        of the TransverseMapSector elements.</span>
+<span class="sd">        The array should contain the initial position (s=0) but not the end </span>
+<span class="sd">        position (s=ring.L), so like position = np.array([0, pos1, pos2, ...]).</span>
+
+<span class="sd">    Returns</span>
+<span class="sd">    -------</span>
+<span class="sd">    sectors : list</span>
+<span class="sd">        List of TransverseMapSector elements.</span>
+
+<span class="sd">    &quot;&quot;&quot;</span>
+    <span class="kn">import</span> <span class="nn">at</span>
+
+    <span class="k">def</span> <span class="nf">_compute_chro</span><span class="p">(</span><span class="n">ring</span><span class="p">,</span> <span class="n">pos</span><span class="p">,</span> <span class="n">dp</span><span class="o">=</span><span class="mf">1e-4</span><span class="p">):</span>
+        <span class="n">lat</span> <span class="o">=</span> <span class="n">deepcopy</span><span class="p">(</span><span class="n">ring</span><span class="o">.</span><span class="n">optics</span><span class="o">.</span><span class="n">lattice</span><span class="p">)</span>
+        <span class="n">lat</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">at</span><span class="o">.</span><span class="n">Marker</span><span class="p">(</span><span class="s2">&quot;END&quot;</span><span class="p">))</span>
+        <span class="n">N</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">lat</span><span class="p">)</span>
+        <span class="n">refpts</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="n">N</span><span class="p">)</span>
+        <span class="o">*</span><span class="n">elem_neg_dp</span><span class="p">,</span> <span class="o">=</span> <span class="n">at</span><span class="o">.</span><span class="n">linopt2</span><span class="p">(</span><span class="n">lat</span><span class="p">,</span> <span class="n">refpts</span><span class="o">=</span><span class="n">refpts</span><span class="p">,</span> <span class="n">dp</span><span class="o">=-</span><span class="n">dp</span><span class="p">)</span>
+        <span class="o">*</span><span class="n">elem_pos_dp</span><span class="p">,</span> <span class="o">=</span> <span class="n">at</span><span class="o">.</span><span class="n">linopt2</span><span class="p">(</span><span class="n">lat</span><span class="p">,</span> <span class="n">refpts</span><span class="o">=</span><span class="n">refpts</span><span class="p">,</span> <span class="n">dp</span><span class="o">=</span><span class="n">dp</span><span class="p">)</span>
+
+        <span class="n">s</span> <span class="o">=</span> <span class="n">elem_neg_dp</span><span class="p">[</span><span class="mi">2</span><span class="p">][</span><span class="s2">&quot;s_pos&quot;</span><span class="p">]</span>
+        <span class="n">mux0</span> <span class="o">=</span> <span class="n">elem_neg_dp</span><span class="p">[</span><span class="mi">2</span><span class="p">][</span><span class="s1">&#39;mu&#39;</span><span class="p">][:,</span> <span class="mi">0</span><span class="p">]</span>
+        <span class="n">mux1</span> <span class="o">=</span> <span class="n">elem_pos_dp</span><span class="p">[</span><span class="mi">2</span><span class="p">][</span><span class="s1">&#39;mu&#39;</span><span class="p">][:,</span> <span class="mi">0</span><span class="p">]</span>
+        <span class="n">muy0</span> <span class="o">=</span> <span class="n">elem_neg_dp</span><span class="p">[</span><span class="mi">2</span><span class="p">][</span><span class="s1">&#39;mu&#39;</span><span class="p">][:,</span> <span class="mi">1</span><span class="p">]</span>
+        <span class="n">muy1</span> <span class="o">=</span> <span class="n">elem_pos_dp</span><span class="p">[</span><span class="mi">2</span><span class="p">][</span><span class="s1">&#39;mu&#39;</span><span class="p">][:,</span> <span class="mi">1</span><span class="p">]</span>
+
+        <span class="n">Chrox</span> <span class="o">=</span> <span class="p">(</span><span class="n">mux1</span><span class="o">-</span><span class="n">mux0</span><span class="p">)</span> <span class="o">/</span> <span class="p">(</span><span class="mi">2</span><span class="o">*</span><span class="n">dp</span><span class="p">)</span> <span class="o">/</span> <span class="mi">2</span> <span class="o">/</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span>
+        <span class="n">Chroy</span> <span class="o">=</span> <span class="p">(</span><span class="n">muy1</span><span class="o">-</span><span class="n">muy0</span><span class="p">)</span> <span class="o">/</span> <span class="p">(</span><span class="mi">2</span><span class="o">*</span><span class="n">dp</span><span class="p">)</span> <span class="o">/</span> <span class="mi">2</span> <span class="o">/</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span>
+        <span class="n">chrox</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">interp</span><span class="p">(</span><span class="n">pos</span><span class="p">,</span> <span class="n">s</span><span class="p">,</span> <span class="n">Chrox</span><span class="p">)</span>
+        <span class="n">chroy</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">interp</span><span class="p">(</span><span class="n">pos</span><span class="p">,</span> <span class="n">s</span><span class="p">,</span> <span class="n">Chroy</span><span class="p">)</span>
+
+        <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="n">chrox</span><span class="p">,</span> <span class="n">chroy</span><span class="p">])</span>
+
+    <span class="k">if</span> <span class="n">ring</span><span class="o">.</span><span class="n">optics</span><span class="o">.</span><span class="n">use_local_values</span><span class="p">:</span>
+        <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span>
+            <span class="s2">&quot;The Synchrotron object must be loaded from an AT lattice&quot;</span><span class="p">)</span>
+
+    <span class="n">N_sec</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">positions</span><span class="p">)</span>
+    <span class="n">sectors</span> <span class="o">=</span> <span class="p">[]</span>
+    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">N_sec</span><span class="p">):</span>
+        <span class="n">alpha0</span> <span class="o">=</span> <span class="n">ring</span><span class="o">.</span><span class="n">optics</span><span class="o">.</span><span class="n">alpha</span><span class="p">(</span><span class="n">positions</span><span class="p">[</span><span class="n">i</span><span class="p">])</span>
+        <span class="n">beta0</span> <span class="o">=</span> <span class="n">ring</span><span class="o">.</span><span class="n">optics</span><span class="o">.</span><span class="n">beta</span><span class="p">(</span><span class="n">positions</span><span class="p">[</span><span class="n">i</span><span class="p">])</span>
+        <span class="n">dispersion0</span> <span class="o">=</span> <span class="n">ring</span><span class="o">.</span><span class="n">optics</span><span class="o">.</span><span class="n">dispersion</span><span class="p">(</span><span class="n">positions</span><span class="p">[</span><span class="n">i</span><span class="p">])</span>
+        <span class="n">mu0</span> <span class="o">=</span> <span class="n">ring</span><span class="o">.</span><span class="n">optics</span><span class="o">.</span><span class="n">mu</span><span class="p">(</span><span class="n">positions</span><span class="p">[</span><span class="n">i</span><span class="p">])</span>
+        <span class="n">chro0</span> <span class="o">=</span> <span class="n">_compute_chro</span><span class="p">(</span><span class="n">ring</span><span class="p">,</span> <span class="n">positions</span><span class="p">[</span><span class="n">i</span><span class="p">])</span>
+        <span class="k">if</span> <span class="n">i</span> <span class="o">!=</span> <span class="p">(</span><span class="n">N_sec</span> <span class="o">-</span> <span class="mi">1</span><span class="p">):</span>
+            <span class="n">alpha1</span> <span class="o">=</span> <span class="n">ring</span><span class="o">.</span><span class="n">optics</span><span class="o">.</span><span class="n">alpha</span><span class="p">(</span><span class="n">positions</span><span class="p">[</span><span class="n">i</span> <span class="o">+</span> <span class="mi">1</span><span class="p">])</span>
+            <span class="n">beta1</span> <span class="o">=</span> <span class="n">ring</span><span class="o">.</span><span class="n">optics</span><span class="o">.</span><span class="n">beta</span><span class="p">(</span><span class="n">positions</span><span class="p">[</span><span class="n">i</span> <span class="o">+</span> <span class="mi">1</span><span class="p">])</span>
+            <span class="n">dispersion1</span> <span class="o">=</span> <span class="n">ring</span><span class="o">.</span><span class="n">optics</span><span class="o">.</span><span class="n">dispersion</span><span class="p">(</span><span class="n">positions</span><span class="p">[</span><span class="n">i</span> <span class="o">+</span> <span class="mi">1</span><span class="p">])</span>
+            <span class="n">mu1</span> <span class="o">=</span> <span class="n">ring</span><span class="o">.</span><span class="n">optics</span><span class="o">.</span><span class="n">mu</span><span class="p">(</span><span class="n">positions</span><span class="p">[</span><span class="n">i</span> <span class="o">+</span> <span class="mi">1</span><span class="p">])</span>
+            <span class="n">chro1</span> <span class="o">=</span> <span class="n">_compute_chro</span><span class="p">(</span><span class="n">ring</span><span class="p">,</span> <span class="n">positions</span><span class="p">[</span><span class="n">i</span> <span class="o">+</span> <span class="mi">1</span><span class="p">])</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="n">alpha1</span> <span class="o">=</span> <span class="n">ring</span><span class="o">.</span><span class="n">optics</span><span class="o">.</span><span class="n">alpha</span><span class="p">(</span><span class="n">positions</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
+            <span class="n">beta1</span> <span class="o">=</span> <span class="n">ring</span><span class="o">.</span><span class="n">optics</span><span class="o">.</span><span class="n">beta</span><span class="p">(</span><span class="n">positions</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
+            <span class="n">dispersion1</span> <span class="o">=</span> <span class="n">ring</span><span class="o">.</span><span class="n">optics</span><span class="o">.</span><span class="n">dispersion</span><span class="p">(</span><span class="n">positions</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
+            <span class="n">mu1</span> <span class="o">=</span> <span class="n">ring</span><span class="o">.</span><span class="n">optics</span><span class="o">.</span><span class="n">mu</span><span class="p">(</span><span class="n">ring</span><span class="o">.</span><span class="n">L</span><span class="p">)</span>
+            <span class="n">chro1</span> <span class="o">=</span> <span class="n">_compute_chro</span><span class="p">(</span><span class="n">ring</span><span class="p">,</span> <span class="n">ring</span><span class="o">.</span><span class="n">L</span><span class="p">)</span>
+        <span class="n">phase_diff</span> <span class="o">=</span> <span class="n">mu1</span> <span class="o">-</span> <span class="n">mu0</span>
+        <span class="n">chro_diff</span> <span class="o">=</span> <span class="n">chro1</span> <span class="o">-</span> <span class="n">chro0</span>
+        <span class="n">sectors</span><span class="o">.</span><span class="n">append</span><span class="p">(</span>
+            <span class="n">TransverseMapSector</span><span class="p">(</span><span class="n">ring</span><span class="p">,</span> <span class="n">alpha0</span><span class="p">,</span> <span class="n">beta0</span><span class="p">,</span> <span class="n">dispersion0</span><span class="p">,</span> <span class="n">alpha1</span><span class="p">,</span>
+                                <span class="n">beta1</span><span class="p">,</span> <span class="n">dispersion1</span><span class="p">,</span> <span class="n">phase_diff</span><span class="p">,</span> <span class="n">chro_diff</span><span class="p">))</span>
+    <span class="k">return</span> <span class="n">sectors</span></div>
+</pre></div>
+
+            <div class="clearer"></div>
+          </div>
+        </div>
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+        &#169; Copyright 2024, A. Gamelin et al.
+      Created using <a href="https://www.sphinx-doc.org/">Sphinx</a> 5.0.2.
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diff --git a/docs/build/html/_modules/mbtrack2/tracking/feedback.html b/docs/build/html/_modules/mbtrack2/tracking/feedback.html
new file mode 100644
index 0000000..3db407b
--- /dev/null
+++ b/docs/build/html/_modules/mbtrack2/tracking/feedback.html
@@ -0,0 +1,382 @@
+
+<!DOCTYPE html>
+
+<html lang="en">
+  <head>
+    <meta charset="utf-8" />
+    <meta name="viewport" content="width=device-width, initial-scale=1.0" />
+    <title>mbtrack2.tracking.feedback &#8212; mbtrack2 0.6.0 documentation</title>
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+             >modules</a> |</li>
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+
+    <div class="document">
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+        <div class="bodywrapper">
+          <div class="body" role="main">
+            
+  <h1>Source code for mbtrack2.tracking.feedback</h1><div class="highlight"><pre>
+<span></span><span class="c1"># -*- coding: utf-8 -*-</span>
+<span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">This module defines both exponential and FIR based bunch by bunch damper </span>
+<span class="sd">feedback for tracking.</span>
+<span class="sd">&quot;&quot;&quot;</span>
+<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
+<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
+
+<span class="kn">from</span> <span class="nn">mbtrack2.tracking.element</span> <span class="kn">import</span> <span class="n">Element</span>
+<span class="kn">from</span> <span class="nn">mbtrack2.tracking.particles</span> <span class="kn">import</span> <span class="n">Beam</span><span class="p">,</span> <span class="n">Bunch</span>
+
+
+<div class="viewcode-block" id="ExponentialDamper"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.feedback.ExponentialDamper">[docs]</a><span class="k">class</span> <span class="nc">ExponentialDamper</span><span class="p">(</span><span class="n">Element</span><span class="p">):</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot; </span>
+<span class="sd">    Simple bunch by bunch damper feedback system based on exponential damping.</span>
+<span class="sd">    </span>
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">    ring : Synchrotron object</span>
+<span class="sd">        Synchrotron to use.</span>
+<span class="sd">    plane : {&quot;x&quot;,&quot;y&quot;,&quot;s&quot;}</span>
+<span class="sd">        Allow to choose on which plane the damper is active.</span>
+<span class="sd">    damping_time : float</span>
+<span class="sd">        Damping time in [s].</span>
+<span class="sd">    phase_diff : array of shape (3,)</span>
+<span class="sd">        Phase difference between the damper and the position monitor in [rad].</span>
+<span class="sd">        </span>
+<span class="sd">    &quot;&quot;&quot;</span>
+
+    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">ring</span><span class="p">,</span> <span class="n">plane</span><span class="p">,</span> <span class="n">damping_time</span><span class="p">,</span> <span class="n">phase_diff</span><span class="p">):</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">ring</span> <span class="o">=</span> <span class="n">ring</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">damping_time</span> <span class="o">=</span> <span class="n">damping_time</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">phase_diff</span> <span class="o">=</span> <span class="n">phase_diff</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">plane</span> <span class="o">=</span> <span class="n">plane</span>
+        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">plane</span> <span class="o">==</span> <span class="s2">&quot;x&quot;</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">action</span> <span class="o">=</span> <span class="s2">&quot;xp&quot;</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">mean_idx</span> <span class="o">=</span> <span class="mi">1</span>
+        <span class="k">elif</span> <span class="bp">self</span><span class="o">.</span><span class="n">plane</span> <span class="o">==</span> <span class="s2">&quot;y&quot;</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">action</span> <span class="o">=</span> <span class="s2">&quot;yp&quot;</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">mean_idx</span> <span class="o">=</span> <span class="mi">3</span>
+        <span class="k">elif</span> <span class="bp">self</span><span class="o">.</span><span class="n">plane</span> <span class="o">==</span> <span class="s2">&quot;s&quot;</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">action</span> <span class="o">=</span> <span class="s2">&quot;delta&quot;</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">mean_idx</span> <span class="o">=</span> <span class="mi">5</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;plane should be x, y or s, not </span><span class="si">{</span><span class="bp">self</span><span class="o">.</span><span class="n">plane</span><span class="si">}</span><span class="s2">&quot;</span><span class="p">)</span>
+
+<div class="viewcode-block" id="ExponentialDamper.track"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.feedback.ExponentialDamper.track">[docs]</a>    <span class="nd">@Element</span><span class="o">.</span><span class="n">parallel</span>
+    <span class="k">def</span> <span class="nf">track</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">bunch</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Tracking method for the feedback system</span>
+<span class="sd">        No bunch to bunch interaction, so written for Bunch object and</span>
+<span class="sd">        @Element.parallel is used to handle Beam object.</span>
+<span class="sd">        </span>
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        bunch : Bunch or Beam object</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="n">bunch</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">action</span><span class="p">]</span> <span class="o">-=</span> <span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">T0</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">damping_time</span> <span class="o">*</span>
+                               <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">phase_diff</span><span class="p">)</span> <span class="o">*</span>
+                               <span class="n">bunch</span><span class="o">.</span><span class="n">mean</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">mean_idx</span><span class="p">])</span></div></div>
+
+
+<div class="viewcode-block" id="FIRDamper"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.feedback.FIRDamper">[docs]</a><span class="k">class</span> <span class="nc">FIRDamper</span><span class="p">(</span><span class="n">Element</span><span class="p">):</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot; </span>
+<span class="sd">    Bunch by bunch damper feedback system based on FIR filters.</span>
+<span class="sd">    </span>
+<span class="sd">    FIR computation is based on [1].</span>
+<span class="sd">    </span>
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">    ring : Synchrotron object</span>
+<span class="sd">        Synchrotron to use.</span>
+<span class="sd">    plane : {&quot;x&quot;,&quot;y&quot;,&quot;s&quot;}</span>
+<span class="sd">        Allow to choose on which plane the damper is active.</span>
+<span class="sd">    tune : float</span>
+<span class="sd">        Reference (betatron or synchrotron) tune for which the damper system </span>
+<span class="sd">        is set.</span>
+<span class="sd">    turn_delay : int</span>
+<span class="sd">        Number of turn delay before the kick is applied.</span>
+<span class="sd">    tap_number : int</span>
+<span class="sd">        Number of tap for the FIR filter.</span>
+<span class="sd">    gain : float</span>
+<span class="sd">        Gain of the FIR filter.</span>
+<span class="sd">    phase : float</span>
+<span class="sd">        Phase of the FIR filter in [degree].</span>
+<span class="sd">    bpm_error : float, optional</span>
+<span class="sd">        RMS measurement error applied to the computed mean position.</span>
+<span class="sd">        Unit is [m] if the plane is &quot;x&quot; or &quot;y&quot; and [s] if the plane is &quot;s&quot;.</span>
+<span class="sd">        The default is None.</span>
+<span class="sd">    max_kick : float, optional</span>
+<span class="sd">        Maximum kick strength limitation.</span>
+<span class="sd">        Unit is [rad] if the plane is &quot;x&quot; or &quot;y&quot; and no unit (delta) if the </span>
+<span class="sd">        plane is &quot;s&quot;.</span>
+<span class="sd">        The default is None.</span>
+
+<span class="sd">    Attributes</span>
+<span class="sd">    ----------</span>
+<span class="sd">    pos : array</span>
+<span class="sd">        Stored beam postions.</span>
+<span class="sd">    kick : array</span>
+<span class="sd">        Stored damper kicks.</span>
+<span class="sd">    coef : array</span>
+<span class="sd">        Coefficients of the FIR filter.</span>
+<span class="sd">         </span>
+<span class="sd">    Methods</span>
+<span class="sd">    -------</span>
+<span class="sd">    get_fir(tap_number, tune, phase, turn_delay, gain)</span>
+<span class="sd">        Initialize the FIR filter and return an array containing the FIR </span>
+<span class="sd">        coefficients.</span>
+<span class="sd">    plot_fir()</span>
+<span class="sd">        Plot the gain and the phase of the FIR filter.</span>
+<span class="sd">    track(beam_or_bunch)</span>
+<span class="sd">        Tracking method.</span>
+<span class="sd">      </span>
+<span class="sd">    References</span>
+<span class="sd">    ----------</span>
+<span class="sd">    [1] T.Nakamura, S.Daté, K. Kobayashi, T. Ohshima. Proceedings of EPAC </span>
+<span class="sd">    2004. Transverse bunch by bunch feedback system for the Spring-8 </span>
+<span class="sd">    storage ring.</span>
+<span class="sd">    &quot;&quot;&quot;</span>
+
+    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span>
+                 <span class="n">ring</span><span class="p">,</span>
+                 <span class="n">plane</span><span class="p">,</span>
+                 <span class="n">tune</span><span class="p">,</span>
+                 <span class="n">turn_delay</span><span class="p">,</span>
+                 <span class="n">tap_number</span><span class="p">,</span>
+                 <span class="n">gain</span><span class="p">,</span>
+                 <span class="n">phase</span><span class="p">,</span>
+                 <span class="n">bpm_error</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+                 <span class="n">max_kick</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">ring</span> <span class="o">=</span> <span class="n">ring</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">tune</span> <span class="o">=</span> <span class="n">tune</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">turn_delay</span> <span class="o">=</span> <span class="n">turn_delay</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">tap_number</span> <span class="o">=</span> <span class="n">tap_number</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">gain</span> <span class="o">=</span> <span class="n">gain</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">phase</span> <span class="o">=</span> <span class="n">phase</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">bpm_error</span> <span class="o">=</span> <span class="n">bpm_error</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">max_kick</span> <span class="o">=</span> <span class="n">max_kick</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">plane</span> <span class="o">=</span> <span class="n">plane</span>
+
+        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">plane</span> <span class="o">==</span> <span class="s2">&quot;x&quot;</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">action</span> <span class="o">=</span> <span class="s2">&quot;xp&quot;</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">damp_idx</span> <span class="o">=</span> <span class="mi">0</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">mean_idx</span> <span class="o">=</span> <span class="mi">0</span>
+        <span class="k">elif</span> <span class="bp">self</span><span class="o">.</span><span class="n">plane</span> <span class="o">==</span> <span class="s2">&quot;y&quot;</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">action</span> <span class="o">=</span> <span class="s2">&quot;yp&quot;</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">damp_idx</span> <span class="o">=</span> <span class="mi">1</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">mean_idx</span> <span class="o">=</span> <span class="mi">2</span>
+        <span class="k">elif</span> <span class="bp">self</span><span class="o">.</span><span class="n">plane</span> <span class="o">==</span> <span class="s2">&quot;s&quot;</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">action</span> <span class="o">=</span> <span class="s2">&quot;delta&quot;</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">damp_idx</span> <span class="o">=</span> <span class="mi">2</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">mean_idx</span> <span class="o">=</span> <span class="mi">4</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">beam_no_mpi</span> <span class="o">=</span> <span class="kc">False</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">pos</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="bp">self</span><span class="o">.</span><span class="n">tap_number</span><span class="p">,</span> <span class="mi">1</span><span class="p">))</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">kick</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="bp">self</span><span class="o">.</span><span class="n">turn_delay</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">))</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">coef</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">get_fir</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">tap_number</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">tune</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">phase</span><span class="p">,</span>
+                                 <span class="bp">self</span><span class="o">.</span><span class="n">turn_delay</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">gain</span><span class="p">)</span>
+
+<div class="viewcode-block" id="FIRDamper.get_fir"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.feedback.FIRDamper.get_fir">[docs]</a>    <span class="k">def</span> <span class="nf">get_fir</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">tap_number</span><span class="p">,</span> <span class="n">tune</span><span class="p">,</span> <span class="n">phase</span><span class="p">,</span> <span class="n">turn_delay</span><span class="p">,</span> <span class="n">gain</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Compute the FIR coefficients.</span>
+<span class="sd">        </span>
+<span class="sd">        FIR computation is based on [1].</span>
+<span class="sd">        </span>
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        FIR_coef : array</span>
+<span class="sd">            Array containing the FIR coefficients.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="n">it</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="n">tap_number</span><span class="p">,</span> <span class="p">))</span>
+        <span class="n">CC</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span>
+            <span class="mi">5</span><span class="p">,</span>
+            <span class="n">tap_number</span><span class="p">,</span>
+        <span class="p">))</span>
+        <span class="n">zeta</span> <span class="o">=</span> <span class="p">(</span><span class="n">phase</span> <span class="o">*</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span><span class="p">)</span> <span class="o">/</span> <span class="mi">360</span>
+        <span class="k">for</span> <span class="n">k</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">tap_number</span><span class="p">):</span>
+            <span class="n">it</span><span class="p">[</span><span class="n">k</span><span class="p">]</span> <span class="o">=</span> <span class="p">(</span><span class="o">-</span><span class="n">k</span> <span class="o">-</span> <span class="n">turn_delay</span><span class="p">)</span>
+
+        <span class="n">phi</span> <span class="o">=</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="n">tune</span>
+        <span class="n">cs</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">phi</span> <span class="o">*</span> <span class="n">it</span><span class="p">)</span>
+        <span class="n">sn</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">phi</span> <span class="o">*</span> <span class="n">it</span><span class="p">)</span>
+
+        <span class="n">CC</span><span class="p">[</span><span class="mi">0</span><span class="p">][:]</span> <span class="o">=</span> <span class="mi">1</span>
+        <span class="n">CC</span><span class="p">[</span><span class="mi">1</span><span class="p">][:]</span> <span class="o">=</span> <span class="n">cs</span>
+        <span class="n">CC</span><span class="p">[</span><span class="mi">2</span><span class="p">][:]</span> <span class="o">=</span> <span class="n">sn</span>
+        <span class="n">CC</span><span class="p">[</span><span class="mi">3</span><span class="p">][:]</span> <span class="o">=</span> <span class="n">it</span> <span class="o">*</span> <span class="n">sn</span>
+        <span class="n">CC</span><span class="p">[</span><span class="mi">4</span><span class="p">][:]</span> <span class="o">=</span> <span class="n">it</span> <span class="o">*</span> <span class="n">cs</span>
+
+        <span class="n">TCC</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">transpose</span><span class="p">(</span><span class="n">CC</span><span class="p">)</span>
+        <span class="n">W</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">inv</span><span class="p">(</span><span class="n">CC</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">TCC</span><span class="p">))</span>
+        <span class="n">D</span> <span class="o">=</span> <span class="n">W</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">CC</span><span class="p">)</span>
+
+        <span class="n">FIR_coef</span> <span class="o">=</span> <span class="n">gain</span> <span class="o">*</span> <span class="p">(</span><span class="n">D</span><span class="p">[</span><span class="mi">1</span><span class="p">][:]</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">zeta</span><span class="p">)</span> <span class="o">+</span> <span class="n">D</span><span class="p">[</span><span class="mi">2</span><span class="p">][:]</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">zeta</span><span class="p">))</span>
+        <span class="k">return</span> <span class="n">FIR_coef</span></div>
+
+<div class="viewcode-block" id="FIRDamper.plot_fir"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.feedback.FIRDamper.plot_fir">[docs]</a>    <span class="k">def</span> <span class="nf">plot_fir</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Plot the gain and the phase of the FIR filter.</span>
+<span class="sd">        </span>
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        fig : Figure</span>
+<span class="sd">            Plot of the gain and phase.</span>
+<span class="sd">            </span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="n">tune</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mf">0.0001</span><span class="p">)</span>
+
+        <span class="n">H_FIR</span> <span class="o">=</span> <span class="mi">0</span>
+        <span class="k">for</span> <span class="n">k</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">coef</span><span class="p">)):</span>
+            <span class="n">H_FIR</span> <span class="o">+=</span> <span class="bp">self</span><span class="o">.</span><span class="n">coef</span><span class="p">[</span><span class="n">k</span><span class="p">]</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="n">j</span> <span class="o">*</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="p">(</span><span class="n">k</span><span class="p">)</span> <span class="o">*</span> <span class="n">tune</span><span class="p">)</span>
+        <span class="n">latency</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="n">j</span> <span class="o">*</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="n">tune</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">turn_delay</span><span class="p">)</span>
+        <span class="n">H_tot</span> <span class="o">=</span> <span class="n">H_FIR</span> <span class="o">*</span> <span class="n">latency</span>
+
+        <span class="n">gain</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">H_tot</span><span class="p">)</span>
+        <span class="n">phase</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">angle</span><span class="p">(</span><span class="n">H_tot</span><span class="p">,</span> <span class="n">deg</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
+
+        <span class="n">fig</span><span class="p">,</span> <span class="p">[</span><span class="n">ax1</span><span class="p">,</span> <span class="n">ax2</span><span class="p">]</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
+        <span class="n">ax1</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">tune</span><span class="p">,</span> <span class="n">gain</span><span class="p">)</span>
+        <span class="n">ax1</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="s2">&quot;Gain&quot;</span><span class="p">)</span>
+
+        <span class="n">ax2</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">tune</span><span class="p">,</span> <span class="n">phase</span><span class="p">)</span>
+        <span class="n">ax2</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="s2">&quot;Tune&quot;</span><span class="p">)</span>
+        <span class="n">ax2</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="s2">&quot;Phase in degree&quot;</span><span class="p">)</span>
+
+        <span class="k">return</span> <span class="n">fig</span></div>
+
+<div class="viewcode-block" id="FIRDamper.track"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.feedback.FIRDamper.track">[docs]</a>    <span class="k">def</span> <span class="nf">track</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">beam_or_bunch</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Tracking method.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        beam_or_bunch : Beam or Bunch</span>
+<span class="sd">            Data to track.</span>
+<span class="sd">            </span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">beam_or_bunch</span><span class="p">,</span> <span class="n">Bunch</span><span class="p">):</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">track_sb</span><span class="p">(</span><span class="n">beam_or_bunch</span><span class="p">)</span>
+        <span class="k">elif</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">beam_or_bunch</span><span class="p">,</span> <span class="n">Beam</span><span class="p">):</span>
+            <span class="n">beam</span> <span class="o">=</span> <span class="n">beam_or_bunch</span>
+            <span class="k">if</span> <span class="p">(</span><span class="n">beam</span><span class="o">.</span><span class="n">mpi_switch</span> <span class="o">==</span> <span class="kc">True</span><span class="p">):</span>
+                <span class="bp">self</span><span class="o">.</span><span class="n">track_sb</span><span class="p">(</span><span class="n">beam</span><span class="p">[</span><span class="n">beam</span><span class="o">.</span><span class="n">mpi</span><span class="o">.</span><span class="n">bunch_num</span><span class="p">])</span>
+            <span class="k">else</span><span class="p">:</span>
+                <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">beam_no_mpi</span> <span class="ow">is</span> <span class="kc">False</span><span class="p">:</span>
+                    <span class="bp">self</span><span class="o">.</span><span class="n">init_beam_no_mpi</span><span class="p">(</span><span class="n">beam</span><span class="p">)</span>
+                <span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">bunch</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">beam</span><span class="o">.</span><span class="n">not_empty</span><span class="p">):</span>
+                    <span class="bp">self</span><span class="o">.</span><span class="n">track_sb</span><span class="p">(</span><span class="n">bunch</span><span class="p">,</span> <span class="n">i</span><span class="p">)</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="ne">TypeError</span><span class="p">(</span><span class="s2">&quot;beam_or_bunch must be a Beam or Bunch&quot;</span><span class="p">)</span></div>
+
+<div class="viewcode-block" id="FIRDamper.init_beam_no_mpi"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.feedback.FIRDamper.init_beam_no_mpi">[docs]</a>    <span class="k">def</span> <span class="nf">init_beam_no_mpi</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">beam</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Change array sizes if Beam is used without mpi.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        beam : Beam</span>
+<span class="sd">            Beam to track.</span>
+
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="n">n_bunch</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">beam</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">pos</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="bp">self</span><span class="o">.</span><span class="n">tap_number</span><span class="p">,</span> <span class="n">n_bunch</span><span class="p">))</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">kick</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="bp">self</span><span class="o">.</span><span class="n">turn_delay</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span> <span class="n">n_bunch</span><span class="p">))</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">beam_no_mpi</span> <span class="o">=</span> <span class="kc">True</span></div>
+
+<div class="viewcode-block" id="FIRDamper.track_sb"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.feedback.FIRDamper.track_sb">[docs]</a>    <span class="k">def</span> <span class="nf">track_sb</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">bunch</span><span class="p">,</span> <span class="n">bunch_number</span><span class="o">=</span><span class="mi">0</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Core of the tracking method.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        bunch : Bunch</span>
+<span class="sd">            Bunch to track.</span>
+<span class="sd">        bunch_number : int, optional</span>
+<span class="sd">            Number of bunch in beam.not_empty. </span>
+<span class="sd">            The default is 0.</span>
+<span class="sd">            </span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">pos</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="n">bunch_number</span><span class="p">]</span> <span class="o">=</span> <span class="n">bunch</span><span class="o">.</span><span class="n">mean</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">mean_idx</span><span class="p">]</span>
+        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">bpm_error</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">pos</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="n">bunch_number</span><span class="p">]</span> <span class="o">+=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">normal</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">bpm_error</span><span class="p">)</span>
+
+        <span class="n">kick</span> <span class="o">=</span> <span class="mi">0</span>
+        <span class="k">for</span> <span class="n">k</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">tap_number</span><span class="p">):</span>
+            <span class="n">kick</span> <span class="o">+=</span> <span class="bp">self</span><span class="o">.</span><span class="n">coef</span><span class="p">[</span><span class="n">k</span><span class="p">]</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">pos</span><span class="p">[</span><span class="n">k</span><span class="p">,</span> <span class="n">bunch_number</span><span class="p">]</span>
+
+        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">max_kick</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="k">if</span> <span class="n">kick</span> <span class="o">&gt;</span> <span class="bp">self</span><span class="o">.</span><span class="n">max_kick</span><span class="p">:</span>
+                <span class="n">kick</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">max_kick</span>
+            <span class="k">elif</span> <span class="n">kick</span> <span class="o">&lt;</span> <span class="o">-</span><span class="mi">1</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">max_kick</span><span class="p">:</span>
+                <span class="n">kick</span> <span class="o">=</span> <span class="o">-</span><span class="mi">1</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">max_kick</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">kick</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="n">bunch_number</span><span class="p">]</span> <span class="o">=</span> <span class="n">kick</span>
+        <span class="n">bunch</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">action</span><span class="p">]</span> <span class="o">+=</span> <span class="bp">self</span><span class="o">.</span><span class="n">kick</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="n">bunch_number</span><span class="p">]</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">pos</span><span class="p">[:,</span> <span class="n">bunch_number</span><span class="p">]</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">roll</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">pos</span><span class="p">[:,</span> <span class="n">bunch_number</span><span class="p">],</span> <span class="mi">1</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">kick</span><span class="p">[:,</span> <span class="n">bunch_number</span><span class="p">]</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">roll</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">kick</span><span class="p">[:,</span> <span class="n">bunch_number</span><span class="p">],</span> <span class="o">-</span><span class="mi">1</span><span class="p">)</span></div></div>
+</pre></div>
+
+            <div class="clearer"></div>
+          </div>
+        </div>
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+      <div class="sphinxsidebar" role="navigation" aria-label="main navigation">
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+      <h3>Navigation</h3>
+      <ul>
+        <li class="right" style="margin-right: 10px">
+          <a href="../../../genindex.html" title="General Index"
+             >index</a></li>
+        <li class="right" >
+          <a href="../../../py-modindex.html" title="Python Module Index"
+             >modules</a> |</li>
+        <li class="nav-item nav-item-0"><a href="../../../index.html">mbtrack2 0.6.0 documentation</a> &#187;</li>
+          <li class="nav-item nav-item-1"><a href="../../index.html" >Module code</a> &#187;</li>
+        <li class="nav-item nav-item-this"><a href="">mbtrack2.tracking.feedback</a></li> 
+      </ul>
+    </div>
+    <div class="footer" role="contentinfo">
+        &#169; Copyright 2024, A. Gamelin et al.
+      Created using <a href="https://www.sphinx-doc.org/">Sphinx</a> 5.0.2.
+    </div>
+  </body>
+</html>
\ No newline at end of file
diff --git a/docs/build/html/_modules/mbtrack2/tracking/monitors/monitors.html b/docs/build/html/_modules/mbtrack2/tracking/monitors/monitors.html
new file mode 100644
index 0000000..713b2e2
--- /dev/null
+++ b/docs/build/html/_modules/mbtrack2/tracking/monitors/monitors.html
@@ -0,0 +1,1750 @@
+
+<!DOCTYPE html>
+
+<html lang="en">
+  <head>
+    <meta charset="utf-8" />
+    <meta name="viewport" content="width=device-width, initial-scale=1.0" />
+    <title>mbtrack2.tracking.monitors.monitors &#8212; mbtrack2 0.6.0 documentation</title>
+    <link rel="stylesheet" type="text/css" href="../../../../_static/pygments.css" />
+    <link rel="stylesheet" type="text/css" href="../../../../_static/nature.css" />
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+    <link rel="index" title="Index" href="../../../../genindex.html" />
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+    <div class="related" role="navigation" aria-label="related navigation">
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+          <a href="../../../../genindex.html" title="General Index"
+             accesskey="I">index</a></li>
+        <li class="right" >
+          <a href="../../../../py-modindex.html" title="Python Module Index"
+             >modules</a> |</li>
+        <li class="nav-item nav-item-0"><a href="../../../../index.html">mbtrack2 0.6.0 documentation</a> &#187;</li>
+          <li class="nav-item nav-item-1"><a href="../../../index.html" accesskey="U">Module code</a> &#187;</li>
+        <li class="nav-item nav-item-this"><a href="">mbtrack2.tracking.monitors.monitors</a></li> 
+      </ul>
+    </div>  
+
+    <div class="document">
+      <div class="documentwrapper">
+        <div class="bodywrapper">
+          <div class="body" role="main">
+            
+  <h1>Source code for mbtrack2.tracking.monitors.monitors</h1><div class="highlight"><pre>
+<span></span><span class="c1"># -*- coding: utf-8 -*-</span>
+<span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">This module defines the different monitor class which are used to save data</span>
+<span class="sd">during tracking.</span>
+<span class="sd">&quot;&quot;&quot;</span>
+
+<span class="kn">import</span> <span class="nn">random</span>
+<span class="kn">from</span> <span class="nn">abc</span> <span class="kn">import</span> <span class="n">ABCMeta</span>
+
+<span class="kn">import</span> <span class="nn">h5py</span> <span class="k">as</span> <span class="nn">hp</span>
+<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="kn">from</span> <span class="nn">scipy.fft</span> <span class="kn">import</span> <span class="n">rfft</span><span class="p">,</span> <span class="n">rfftfreq</span>
+<span class="kn">from</span> <span class="nn">scipy.interpolate</span> <span class="kn">import</span> <span class="n">interp1d</span>
+
+<span class="kn">from</span> <span class="nn">mbtrack2.tracking.element</span> <span class="kn">import</span> <span class="n">Element</span>
+<span class="kn">from</span> <span class="nn">mbtrack2.tracking.particles</span> <span class="kn">import</span> <span class="n">Beam</span><span class="p">,</span> <span class="n">Bunch</span>
+<span class="kn">from</span> <span class="nn">mbtrack2.tracking.rf</span> <span class="kn">import</span> <span class="n">CavityResonator</span>
+
+
+<div class="viewcode-block" id="Monitor"><a class="viewcode-back" href="../../../../mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.monitors.Monitor">[docs]</a><span class="k">class</span> <span class="nc">Monitor</span><span class="p">(</span><span class="n">Element</span><span class="p">,</span> <span class="n">metaclass</span><span class="o">=</span><span class="n">ABCMeta</span><span class="p">):</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    Abstract Monitor class used for subclass inheritance to define all the</span>
+<span class="sd">    different kind of monitors objects. </span>
+<span class="sd">    </span>
+<span class="sd">    The Monitor class is based on h5py module to be able to write data on </span>
+<span class="sd">    structured binary files. The class provides a common file where the </span>
+<span class="sd">    different Monitor subclass can write.</span>
+<span class="sd">    </span>
+<span class="sd">    Attributes</span>
+<span class="sd">    ----------</span>
+<span class="sd">    file : HDF5 file</span>
+<span class="sd">        Common file where all monitors, Monitor subclass elements, write the</span>
+<span class="sd">        saved data. Based on class attribute _file_storage.</span>
+<span class="sd">    file_name : string</span>
+<span class="sd">        Name of the HDF5 file where the data is stored. Based on class </span>
+<span class="sd">        attribute _file_name_storage.</span>
+<span class="sd">        </span>
+<span class="sd">    Methods</span>
+<span class="sd">    -------</span>
+<span class="sd">    monitor_init(group_name, save_every, buffer_size, total_size,</span>
+<span class="sd">                     dict_buffer, dict_file, file_name=None, mpi_mode=True)</span>
+<span class="sd">        Method called to initialize Monitor subclass.</span>
+<span class="sd">    write()</span>
+<span class="sd">        Write data from buffer to the HDF5 file.</span>
+<span class="sd">    to_buffer(object_to_save)</span>
+<span class="sd">        Save data to buffer.</span>
+<span class="sd">    close()</span>
+<span class="sd">        Close the HDF5 file shared by all Monitor subclass, must be called </span>
+<span class="sd">        by at least an instance of a Montior subclass at the end of the </span>
+<span class="sd">        tracking.</span>
+<span class="sd">    track_bunch_data(object_to_save)</span>
+<span class="sd">        Track method to use when saving bunch data.</span>
+<span class="sd">    &quot;&quot;&quot;</span>
+
+    <span class="n">_file_name_storage</span> <span class="o">=</span> <span class="p">[]</span>
+    <span class="n">_file_storage</span> <span class="o">=</span> <span class="p">[]</span>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">file_name</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Common file where all monitors, Monitor subclass elements, write the</span>
+<span class="sd">        saved data.&quot;&quot;&quot;</span>
+        <span class="k">try</span><span class="p">:</span>
+            <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_file_name_storage</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
+        <span class="k">except</span> <span class="ne">IndexError</span><span class="p">:</span>
+            <span class="nb">print</span><span class="p">(</span><span class="s2">&quot;The HDF5 file name for monitors is not set.&quot;</span><span class="p">)</span>
+            <span class="k">raise</span> <span class="ne">ValueError</span>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">file</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Name of the HDF5 file where the data is stored.&quot;&quot;&quot;</span>
+        <span class="k">try</span><span class="p">:</span>
+            <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_file_storage</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
+        <span class="k">except</span> <span class="ne">IndexError</span><span class="p">:</span>
+            <span class="nb">print</span><span class="p">(</span><span class="s2">&quot;The HDF5 file to store data is not set.&quot;</span><span class="p">)</span>
+            <span class="k">raise</span> <span class="ne">ValueError</span>
+
+<div class="viewcode-block" id="Monitor.monitor_init"><a class="viewcode-back" href="../../../../mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.monitors.Monitor.monitor_init">[docs]</a>    <span class="k">def</span> <span class="nf">monitor_init</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span>
+                     <span class="n">group_name</span><span class="p">,</span>
+                     <span class="n">save_every</span><span class="p">,</span>
+                     <span class="n">buffer_size</span><span class="p">,</span>
+                     <span class="n">total_size</span><span class="p">,</span>
+                     <span class="n">dict_buffer</span><span class="p">,</span>
+                     <span class="n">dict_file</span><span class="p">,</span>
+                     <span class="n">file_name</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+                     <span class="n">mpi_mode</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span>
+                     <span class="n">dict_dtype</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Method called to initialize Monitor subclass. </span>
+<span class="sd">        </span>
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        group_name : string</span>
+<span class="sd">            Name of the HDF5 group in which the data for the current monitor </span>
+<span class="sd">            will be saved.</span>
+<span class="sd">        save_every : int or float</span>
+<span class="sd">            Set the frequency of the save. The data is saved every save_every </span>
+<span class="sd">            call of the montior.</span>
+<span class="sd">        buffer_size : int or float</span>
+<span class="sd">            Size of the save buffer.</span>
+<span class="sd">        total_size : int or float</span>
+<span class="sd">            Total size of the save. The following relationships between the </span>
+<span class="sd">            parameters must exist: </span>
+<span class="sd">                total_size % buffer_size == 0</span>
+<span class="sd">                number of call to track / save_every == total_size</span>
+<span class="sd">        dict_buffer : dict</span>
+<span class="sd">            Dictionary with keys as the attribute name to save and values as</span>
+<span class="sd">            the shape of the buffer to create to hold the attribute, like </span>
+<span class="sd">            (key.shape, buffer_size)</span>
+<span class="sd">        dict_file : dict</span>
+<span class="sd">            Dictionary with keys as the attribute name to save and values as</span>
+<span class="sd">            the shape of the dataset to create to hold the attribute, like </span>
+<span class="sd">            (key.shape, total_size)</span>
+<span class="sd">        file_name : string, optional</span>
+<span class="sd">            Name of the HDF5 where the data will be stored. Must be specified</span>
+<span class="sd">            the first time a subclass of Monitor is instancied and must be None</span>
+<span class="sd">            the following times.</span>
+<span class="sd">        mpi_mode : bool, optional</span>
+<span class="sd">            If True, open the HDF5 file in parallel mode, which is needed to</span>
+<span class="sd">            allow several cores to write in the same file at the same time.</span>
+<span class="sd">            If False, open the HDF5 file in standard mode.</span>
+<span class="sd">        dict_dtype : dict, optional</span>
+<span class="sd">            Dictionary with keys as the attribute name to save and values as</span>
+<span class="sd">            the dtype to use to save the values.</span>
+<span class="sd">            If None, float is used for all attributes.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+
+        <span class="c1"># setup and open common file for all monitors</span>
+        <span class="k">if</span> <span class="n">file_name</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_file_name_storage</span><span class="p">)</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
+                <span class="bp">self</span><span class="o">.</span><span class="n">_file_name_storage</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">file_name</span> <span class="o">+</span> <span class="s2">&quot;.hdf5&quot;</span><span class="p">)</span>
+                <span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_file_storage</span><span class="p">)</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
+                    <span class="k">if</span> <span class="n">mpi_mode</span> <span class="o">==</span> <span class="kc">True</span><span class="p">:</span>
+                        <span class="kn">from</span> <span class="nn">mpi4py</span> <span class="kn">import</span> <span class="n">MPI</span>
+                        <span class="n">f</span> <span class="o">=</span> <span class="n">hp</span><span class="o">.</span><span class="n">File</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">file_name</span><span class="p">,</span>
+                                    <span class="s2">&quot;a&quot;</span><span class="p">,</span>
+                                    <span class="n">libver</span><span class="o">=</span><span class="s1">&#39;earliest&#39;</span><span class="p">,</span>
+                                    <span class="n">driver</span><span class="o">=</span><span class="s1">&#39;mpio&#39;</span><span class="p">,</span>
+                                    <span class="n">comm</span><span class="o">=</span><span class="n">MPI</span><span class="o">.</span><span class="n">COMM_WORLD</span><span class="p">)</span>
+                    <span class="k">else</span><span class="p">:</span>
+                        <span class="n">f</span> <span class="o">=</span> <span class="n">hp</span><span class="o">.</span><span class="n">File</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">file_name</span><span class="p">,</span> <span class="s2">&quot;a&quot;</span><span class="p">,</span> <span class="n">libver</span><span class="o">=</span><span class="s1">&#39;earliest&#39;</span><span class="p">)</span>
+                    <span class="bp">self</span><span class="o">.</span><span class="n">_file_storage</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">f</span><span class="p">)</span>
+                <span class="k">else</span><span class="p">:</span>
+                    <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">&quot;File is already open.&quot;</span><span class="p">)</span>
+            <span class="k">else</span><span class="p">:</span>
+                <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span>
+                    <span class="s2">&quot;File name for monitors is already attributed.&quot;</span><span class="p">)</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">group_name</span> <span class="o">=</span> <span class="n">group_name</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">save_every</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">save_every</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">total_size</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">total_size</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">buffer_size</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">buffer_size</span><span class="p">)</span>
+        <span class="k">if</span> <span class="n">total_size</span> <span class="o">%</span> <span class="n">buffer_size</span> <span class="o">!=</span> <span class="mi">0</span><span class="p">:</span>
+            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">&quot;total_size must be divisible by buffer_size.&quot;</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">buffer_count</span> <span class="o">=</span> <span class="mi">0</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">write_count</span> <span class="o">=</span> <span class="mi">0</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">track_count</span> <span class="o">=</span> <span class="mi">0</span>
+
+        <span class="c1"># setup attribute buffers from values given in dict_buffer</span>
+        <span class="k">for</span> <span class="n">key</span><span class="p">,</span> <span class="n">value</span> <span class="ow">in</span> <span class="n">dict_buffer</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
+            <span class="k">if</span> <span class="n">dict_dtype</span> <span class="o">==</span> <span class="kc">None</span><span class="p">:</span>
+                <span class="bp">self</span><span class="o">.</span><span class="fm">__setattr__</span><span class="p">(</span><span class="n">key</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">value</span><span class="p">))</span>
+            <span class="k">else</span><span class="p">:</span>
+                <span class="bp">self</span><span class="o">.</span><span class="fm">__setattr__</span><span class="p">(</span><span class="n">key</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">value</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">dict_dtype</span><span class="p">[</span><span class="n">key</span><span class="p">]))</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">time</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="bp">self</span><span class="o">.</span><span class="n">buffer_size</span><span class="p">,</span> <span class="p">),</span> <span class="n">dtype</span><span class="o">=</span><span class="nb">int</span><span class="p">)</span>
+
+        <span class="c1"># create HDF5 groups and datasets to save data from group_name and</span>
+        <span class="c1"># dict_file</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">g</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">file</span><span class="o">.</span><span class="n">require_group</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">group_name</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">g</span><span class="o">.</span><span class="n">require_dataset</span><span class="p">(</span><span class="s2">&quot;time&quot;</span><span class="p">,</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">total_size</span><span class="p">,</span> <span class="p">),</span> <span class="n">dtype</span><span class="o">=</span><span class="nb">int</span><span class="p">)</span>
+        <span class="k">for</span> <span class="n">key</span><span class="p">,</span> <span class="n">value</span> <span class="ow">in</span> <span class="n">dict_file</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
+            <span class="k">if</span> <span class="n">dict_dtype</span> <span class="o">==</span> <span class="kc">None</span><span class="p">:</span>
+                <span class="bp">self</span><span class="o">.</span><span class="n">g</span><span class="o">.</span><span class="n">require_dataset</span><span class="p">(</span><span class="n">key</span><span class="p">,</span> <span class="n">value</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="nb">float</span><span class="p">)</span>
+            <span class="k">else</span><span class="p">:</span>
+                <span class="bp">self</span><span class="o">.</span><span class="n">g</span><span class="o">.</span><span class="n">require_dataset</span><span class="p">(</span><span class="n">key</span><span class="p">,</span> <span class="n">value</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">dict_dtype</span><span class="p">[</span><span class="n">key</span><span class="p">])</span>
+
+        <span class="c1"># create a dictionary which handle slices</span>
+        <span class="n">slice_dict</span> <span class="o">=</span> <span class="p">{}</span>
+        <span class="k">for</span> <span class="n">key</span><span class="p">,</span> <span class="n">value</span> <span class="ow">in</span> <span class="n">dict_file</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
+            <span class="n">slice_dict</span><span class="p">[</span><span class="n">key</span><span class="p">]</span> <span class="o">=</span> <span class="p">[]</span>
+            <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">value</span><span class="p">)</span> <span class="o">-</span> <span class="mi">1</span><span class="p">):</span>
+                <span class="n">slice_dict</span><span class="p">[</span><span class="n">key</span><span class="p">]</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="nb">slice</span><span class="p">(</span><span class="kc">None</span><span class="p">))</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">slice_dict</span> <span class="o">=</span> <span class="n">slice_dict</span></div>
+
+<div class="viewcode-block" id="Monitor.write"><a class="viewcode-back" href="../../../../mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.monitors.Monitor.write">[docs]</a>    <span class="k">def</span> <span class="nf">write</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Write data from buffer to the HDF5 file.&quot;&quot;&quot;</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">file</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">group_name</span><span class="p">][</span><span class="s2">&quot;time&quot;</span><span class="p">][</span><span class="bp">self</span><span class="o">.</span><span class="n">write_count</span> <span class="o">*</span>
+                                           <span class="bp">self</span><span class="o">.</span><span class="n">buffer_size</span><span class="p">:(</span><span class="bp">self</span><span class="o">.</span><span class="n">write_count</span> <span class="o">+</span>
+                                                             <span class="mi">1</span><span class="p">)</span> <span class="o">*</span>
+                                           <span class="bp">self</span><span class="o">.</span><span class="n">buffer_size</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">time</span>
+        <span class="k">for</span> <span class="n">key</span><span class="p">,</span> <span class="n">value</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">dict_buffer</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
+            <span class="n">slice_list</span> <span class="o">=</span> <span class="nb">list</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">slice_dict</span><span class="p">[</span><span class="n">key</span><span class="p">])</span>
+            <span class="n">slice_list</span><span class="o">.</span><span class="n">append</span><span class="p">(</span>
+                <span class="nb">slice</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">write_count</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">buffer_size</span><span class="p">,</span>
+                      <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">write_count</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">buffer_size</span><span class="p">))</span>
+            <span class="n">slice_tuple</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">slice_list</span><span class="p">)</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">file</span><span class="p">[</span>
+                <span class="bp">self</span><span class="o">.</span><span class="n">group_name</span><span class="p">][</span><span class="n">key</span><span class="p">][</span><span class="n">slice_tuple</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="fm">__getattribute__</span><span class="p">(</span><span class="n">key</span><span class="p">)</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">file</span><span class="o">.</span><span class="n">flush</span><span class="p">()</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">write_count</span> <span class="o">+=</span> <span class="mi">1</span></div>
+
+<div class="viewcode-block" id="Monitor.to_buffer"><a class="viewcode-back" href="../../../../mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.monitors.Monitor.to_buffer">[docs]</a>    <span class="k">def</span> <span class="nf">to_buffer</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">object_to_save</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Save data to buffer.</span>
+<span class="sd">        </span>
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        object_to_save : python object</span>
+<span class="sd">            Depends on the Monitor subclass, typically a Beam or Bunch object.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">time</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">buffer_count</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">track_count</span>
+        <span class="k">for</span> <span class="n">key</span><span class="p">,</span> <span class="n">value</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">dict_buffer</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
+            <span class="n">slice_list</span> <span class="o">=</span> <span class="nb">list</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">slice_dict</span><span class="p">[</span><span class="n">key</span><span class="p">])</span>
+            <span class="n">slice_list</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">buffer_count</span><span class="p">)</span>
+            <span class="n">slice_tuple</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">slice_list</span><span class="p">)</span>
+            <span class="bp">self</span><span class="o">.</span><span class="fm">__getattribute__</span><span class="p">(</span>
+                <span class="n">key</span><span class="p">)[</span><span class="n">slice_tuple</span><span class="p">]</span> <span class="o">=</span> <span class="n">object_to_save</span><span class="o">.</span><span class="fm">__getattribute__</span><span class="p">(</span><span class="n">key</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">buffer_count</span> <span class="o">+=</span> <span class="mi">1</span>
+
+        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">buffer_count</span> <span class="o">==</span> <span class="bp">self</span><span class="o">.</span><span class="n">buffer_size</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">write</span><span class="p">()</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">buffer_count</span> <span class="o">=</span> <span class="mi">0</span></div>
+
+<div class="viewcode-block" id="Monitor.close"><a class="viewcode-back" href="../../../../mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.monitors.Monitor.close">[docs]</a>    <span class="k">def</span> <span class="nf">close</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Close the HDF5 file shared by all Monitor subclass, must be called </span>
+<span class="sd">        by at least an instance of a Montior subclass at the end of the </span>
+<span class="sd">        tracking.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="k">try</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">file</span><span class="o">.</span><span class="n">close</span><span class="p">()</span>
+            <span class="n">Monitor</span><span class="o">.</span><span class="n">_file_name_storage</span> <span class="o">=</span> <span class="p">[]</span>
+            <span class="n">Monitor</span><span class="o">.</span><span class="n">_file_storage</span> <span class="o">=</span> <span class="p">[]</span>
+        <span class="k">except</span> <span class="ne">ValueError</span><span class="p">:</span>
+            <span class="k">pass</span></div>
+
+<div class="viewcode-block" id="Monitor.track_bunch_data"><a class="viewcode-back" href="../../../../mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.monitors.Monitor.track_bunch_data">[docs]</a>    <span class="k">def</span> <span class="nf">track_bunch_data</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">object_to_save</span><span class="p">,</span> <span class="n">check_empty</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Track method to use when saving bunch data.</span>
+<span class="sd">        </span>
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        object_to_save : Beam or Bunch</span>
+<span class="sd">        check_emptiness: bool</span>
+<span class="sd">            If True, check if the bunch is empty. If it is, then do nothing.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="n">save</span> <span class="o">=</span> <span class="kc">True</span>
+        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">track_count</span> <span class="o">%</span> <span class="bp">self</span><span class="o">.</span><span class="n">save_every</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
+
+            <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">object_to_save</span><span class="p">,</span> <span class="n">Beam</span><span class="p">):</span>
+                <span class="k">if</span> <span class="p">(</span><span class="n">object_to_save</span><span class="o">.</span><span class="n">mpi_switch</span> <span class="o">==</span> <span class="kc">True</span><span class="p">):</span>
+                    <span class="k">if</span> <span class="n">object_to_save</span><span class="o">.</span><span class="n">mpi</span><span class="o">.</span><span class="n">bunch_num</span> <span class="o">==</span> <span class="bp">self</span><span class="o">.</span><span class="n">bunch_number</span><span class="p">:</span>
+                        <span class="n">bunch</span> <span class="o">=</span> <span class="n">object_to_save</span><span class="p">[</span><span class="n">object_to_save</span><span class="o">.</span><span class="n">mpi</span><span class="o">.</span><span class="n">bunch_num</span><span class="p">]</span>
+                    <span class="k">else</span><span class="p">:</span>
+                        <span class="n">save</span> <span class="o">=</span> <span class="kc">False</span>
+                <span class="k">else</span><span class="p">:</span>
+                    <span class="n">bunch</span> <span class="o">=</span> <span class="n">object_to_save</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">bunch_number</span><span class="p">]</span>
+            <span class="k">elif</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">object_to_save</span><span class="p">,</span> <span class="n">Bunch</span><span class="p">):</span>
+                <span class="n">bunch</span> <span class="o">=</span> <span class="n">object_to_save</span>
+            <span class="k">else</span><span class="p">:</span>
+                <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span>
+                    <span class="s2">&quot;object_to_save should be a Beam or Bunch object.&quot;</span><span class="p">)</span>
+
+            <span class="k">if</span> <span class="n">save</span><span class="p">:</span>
+                <span class="k">if</span> <span class="p">(</span><span class="n">check_empty</span> <span class="o">==</span> <span class="kc">False</span><span class="p">)</span> <span class="ow">or</span> <span class="p">(</span><span class="n">bunch</span><span class="o">.</span><span class="n">is_empty</span> <span class="o">==</span> <span class="kc">False</span><span class="p">):</span>
+                    <span class="bp">self</span><span class="o">.</span><span class="n">to_buffer</span><span class="p">(</span><span class="n">bunch</span><span class="p">)</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">track_count</span> <span class="o">+=</span> <span class="mi">1</span></div></div>
+
+
+<div class="viewcode-block" id="BunchMonitor"><a class="viewcode-back" href="../../../../mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.monitors.BunchMonitor">[docs]</a><span class="k">class</span> <span class="nc">BunchMonitor</span><span class="p">(</span><span class="n">Monitor</span><span class="p">):</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    Monitor a single bunch and save attributes </span>
+<span class="sd">    (mean, std, emit, current, and cs_invariant).</span>
+<span class="sd">    </span>
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">    bunch_number : int</span>
+<span class="sd">        Bunch to monitor</span>
+<span class="sd">    save_every : int or float</span>
+<span class="sd">        Set the frequency of the save. The data is saved every save_every </span>
+<span class="sd">        call of the montior.</span>
+<span class="sd">    buffer_size : int or float</span>
+<span class="sd">        Size of the save buffer.</span>
+<span class="sd">    total_size : int or float</span>
+<span class="sd">        Total size of the save. The following relationships between the </span>
+<span class="sd">        parameters must exist: </span>
+<span class="sd">            total_size % buffer_size == 0</span>
+<span class="sd">            number of call to track / save_every == total_size</span>
+<span class="sd">    file_name : string, optional</span>
+<span class="sd">        Name of the HDF5 where the data will be stored. Must be specified</span>
+<span class="sd">        the first time a subclass of Monitor is instancied and must be None</span>
+<span class="sd">        the following times.</span>
+<span class="sd">    mpi_mode : bool, optional</span>
+<span class="sd">        If True, open the HDF5 file in parallel mode, which is needed to</span>
+<span class="sd">        allow several cores to write in the same file at the same time.</span>
+<span class="sd">        If False, open the HDF5 file in standard mode.</span>
+
+<span class="sd">    Methods</span>
+<span class="sd">    -------</span>
+<span class="sd">    track(object_to_save)</span>
+<span class="sd">        Save data</span>
+<span class="sd">    &quot;&quot;&quot;</span>
+
+    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span>
+                 <span class="n">bunch_number</span><span class="p">,</span>
+                 <span class="n">save_every</span><span class="p">,</span>
+                 <span class="n">buffer_size</span><span class="p">,</span>
+                 <span class="n">total_size</span><span class="p">,</span>
+                 <span class="n">file_name</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+                 <span class="n">mpi_mode</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">bunch_number</span> <span class="o">=</span> <span class="n">bunch_number</span>
+        <span class="n">group_name</span> <span class="o">=</span> <span class="s2">&quot;BunchData_&quot;</span> <span class="o">+</span> <span class="nb">str</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">bunch_number</span><span class="p">)</span>
+        <span class="n">dict_buffer</span> <span class="o">=</span> <span class="p">{</span>
+            <span class="s2">&quot;mean&quot;</span><span class="p">:</span> <span class="p">(</span><span class="mi">6</span><span class="p">,</span> <span class="n">buffer_size</span><span class="p">),</span>
+            <span class="s2">&quot;std&quot;</span><span class="p">:</span> <span class="p">(</span><span class="mi">6</span><span class="p">,</span> <span class="n">buffer_size</span><span class="p">),</span>
+            <span class="s2">&quot;emit&quot;</span><span class="p">:</span> <span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="n">buffer_size</span><span class="p">),</span>
+            <span class="s2">&quot;current&quot;</span><span class="p">:</span> <span class="p">(</span><span class="n">buffer_size</span><span class="p">,</span> <span class="p">),</span>
+            <span class="s2">&quot;cs_invariant&quot;</span><span class="p">:</span> <span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="n">buffer_size</span><span class="p">)</span>
+        <span class="p">}</span>
+        <span class="n">dict_file</span> <span class="o">=</span> <span class="p">{</span>
+            <span class="s2">&quot;mean&quot;</span><span class="p">:</span> <span class="p">(</span><span class="mi">6</span><span class="p">,</span> <span class="n">total_size</span><span class="p">),</span>
+            <span class="s2">&quot;std&quot;</span><span class="p">:</span> <span class="p">(</span><span class="mi">6</span><span class="p">,</span> <span class="n">total_size</span><span class="p">),</span>
+            <span class="s2">&quot;emit&quot;</span><span class="p">:</span> <span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="n">total_size</span><span class="p">),</span>
+            <span class="s2">&quot;current&quot;</span><span class="p">:</span> <span class="p">(</span><span class="n">total_size</span><span class="p">,</span> <span class="p">),</span>
+            <span class="s2">&quot;cs_invariant&quot;</span><span class="p">:</span> <span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="n">total_size</span><span class="p">)</span>
+        <span class="p">}</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">monitor_init</span><span class="p">(</span><span class="n">group_name</span><span class="p">,</span> <span class="n">save_every</span><span class="p">,</span> <span class="n">buffer_size</span><span class="p">,</span> <span class="n">total_size</span><span class="p">,</span>
+                          <span class="n">dict_buffer</span><span class="p">,</span> <span class="n">dict_file</span><span class="p">,</span> <span class="n">file_name</span><span class="p">,</span> <span class="n">mpi_mode</span><span class="p">)</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">dict_buffer</span> <span class="o">=</span> <span class="n">dict_buffer</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">dict_file</span> <span class="o">=</span> <span class="n">dict_file</span>
+
+<div class="viewcode-block" id="BunchMonitor.track"><a class="viewcode-back" href="../../../../mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.monitors.BunchMonitor.track">[docs]</a>    <span class="k">def</span> <span class="nf">track</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">object_to_save</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Save data</span>
+<span class="sd">        </span>
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        object_to_save : Bunch or Beam object</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">track_bunch_data</span><span class="p">(</span><span class="n">object_to_save</span><span class="p">)</span></div></div>
+
+
+<div class="viewcode-block" id="PhaseSpaceMonitor"><a class="viewcode-back" href="../../../../mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.monitors.PhaseSpaceMonitor">[docs]</a><span class="k">class</span> <span class="nc">PhaseSpaceMonitor</span><span class="p">(</span><span class="n">Monitor</span><span class="p">):</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    Monitor a single bunch and save the full phase space.</span>
+<span class="sd">    </span>
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">    bunch_number : int</span>
+<span class="sd">        Bunch to monitor</span>
+<span class="sd">    mp_number : int or float</span>
+<span class="sd">        Number of macroparticle in the phase space to save. If less than the </span>
+<span class="sd">        total number of macroparticles, a random fraction of the bunch is saved.</span>
+<span class="sd">    save_every : int or float</span>
+<span class="sd">        Set the frequency of the save. The data is saved every save_every </span>
+<span class="sd">        call of the montior.</span>
+<span class="sd">    buffer_size : int or float</span>
+<span class="sd">        Size of the save buffer.</span>
+<span class="sd">    total_size : int or float</span>
+<span class="sd">        Total size of the save. The following relationships between the </span>
+<span class="sd">        parameters must exist: </span>
+<span class="sd">            total_size % buffer_size == 0</span>
+<span class="sd">            number of call to track / save_every == total_size</span>
+<span class="sd">    file_name : string, optional</span>
+<span class="sd">        Name of the HDF5 where the data will be stored. Must be specified</span>
+<span class="sd">        the first time a subclass of Monitor is instancied and must be None</span>
+<span class="sd">        the following times.</span>
+<span class="sd">    mpi_mode : bool, optional</span>
+<span class="sd">        If True, open the HDF5 file in parallel mode, which is needed to</span>
+<span class="sd">        allow several cores to write in the same file at the same time.</span>
+<span class="sd">        If False, open the HDF5 file in standard mode.</span>
+
+<span class="sd">    Methods</span>
+<span class="sd">    -------</span>
+<span class="sd">    track(object_to_save)</span>
+<span class="sd">        Save data</span>
+<span class="sd">    &quot;&quot;&quot;</span>
+
+    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span>
+                 <span class="n">bunch_number</span><span class="p">,</span>
+                 <span class="n">mp_number</span><span class="p">,</span>
+                 <span class="n">save_every</span><span class="p">,</span>
+                 <span class="n">buffer_size</span><span class="p">,</span>
+                 <span class="n">total_size</span><span class="p">,</span>
+                 <span class="n">file_name</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+                 <span class="n">mpi_mode</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">bunch_number</span> <span class="o">=</span> <span class="n">bunch_number</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">mp_number</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">mp_number</span><span class="p">)</span>
+        <span class="n">group_name</span> <span class="o">=</span> <span class="s2">&quot;PhaseSpaceData_&quot;</span> <span class="o">+</span> <span class="nb">str</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">bunch_number</span><span class="p">)</span>
+        <span class="n">dict_buffer</span> <span class="o">=</span> <span class="p">{</span>
+            <span class="s2">&quot;particles&quot;</span><span class="p">:</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">mp_number</span><span class="p">,</span> <span class="mi">6</span><span class="p">,</span> <span class="n">buffer_size</span><span class="p">),</span>
+            <span class="s2">&quot;alive&quot;</span><span class="p">:</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">mp_number</span><span class="p">,</span> <span class="n">buffer_size</span><span class="p">)</span>
+        <span class="p">}</span>
+        <span class="n">dict_file</span> <span class="o">=</span> <span class="p">{</span>
+            <span class="s2">&quot;particles&quot;</span><span class="p">:</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">mp_number</span><span class="p">,</span> <span class="mi">6</span><span class="p">,</span> <span class="n">total_size</span><span class="p">),</span>
+            <span class="s2">&quot;alive&quot;</span><span class="p">:</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">mp_number</span><span class="p">,</span> <span class="n">total_size</span><span class="p">)</span>
+        <span class="p">}</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">monitor_init</span><span class="p">(</span><span class="n">group_name</span><span class="p">,</span> <span class="n">save_every</span><span class="p">,</span> <span class="n">buffer_size</span><span class="p">,</span> <span class="n">total_size</span><span class="p">,</span>
+                          <span class="n">dict_buffer</span><span class="p">,</span> <span class="n">dict_file</span><span class="p">,</span> <span class="n">file_name</span><span class="p">,</span> <span class="n">mpi_mode</span><span class="p">)</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">dict_buffer</span> <span class="o">=</span> <span class="n">dict_buffer</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">dict_file</span> <span class="o">=</span> <span class="n">dict_file</span>
+
+<div class="viewcode-block" id="PhaseSpaceMonitor.track"><a class="viewcode-back" href="../../../../mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.monitors.PhaseSpaceMonitor.track">[docs]</a>    <span class="k">def</span> <span class="nf">track</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">object_to_save</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Save data</span>
+<span class="sd">        </span>
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        object_to_save : Bunch or Beam object</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">track_bunch_data</span><span class="p">(</span><span class="n">object_to_save</span><span class="p">)</span></div>
+
+<div class="viewcode-block" id="PhaseSpaceMonitor.to_buffer"><a class="viewcode-back" href="../../../../mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.monitors.PhaseSpaceMonitor.to_buffer">[docs]</a>    <span class="k">def</span> <span class="nf">to_buffer</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">bunch</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Save data to buffer.</span>
+<span class="sd">        </span>
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        bunch : Bunch object</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">time</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">buffer_count</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">track_count</span>
+
+        <span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">bunch</span><span class="o">.</span><span class="n">alive</span><span class="p">)</span> <span class="o">!=</span> <span class="bp">self</span><span class="o">.</span><span class="n">mp_number</span><span class="p">:</span>
+            <span class="n">index</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">bunch</span><span class="o">.</span><span class="n">alive</span><span class="p">))</span>
+            <span class="n">samples_meta</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">sample</span><span class="p">(</span><span class="nb">list</span><span class="p">(</span><span class="n">index</span><span class="p">),</span> <span class="bp">self</span><span class="o">.</span><span class="n">mp_number</span><span class="p">)</span>
+            <span class="n">samples</span> <span class="o">=</span> <span class="nb">sorted</span><span class="p">(</span><span class="n">samples_meta</span><span class="p">)</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="n">samples</span> <span class="o">=</span> <span class="nb">slice</span><span class="p">(</span><span class="kc">None</span><span class="p">)</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">alive</span><span class="p">[:,</span> <span class="bp">self</span><span class="o">.</span><span class="n">buffer_count</span><span class="p">]</span> <span class="o">=</span> <span class="n">bunch</span><span class="o">.</span><span class="n">alive</span><span class="p">[</span><span class="n">samples</span><span class="p">]</span>
+        <span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">dim</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">bunch</span><span class="p">):</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">particles</span><span class="p">[:,</span> <span class="n">i</span><span class="p">,</span>
+                           <span class="bp">self</span><span class="o">.</span><span class="n">buffer_count</span><span class="p">]</span> <span class="o">=</span> <span class="n">bunch</span><span class="o">.</span><span class="n">particles</span><span class="p">[</span><span class="n">dim</span><span class="p">][</span><span class="n">samples</span><span class="p">]</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">buffer_count</span> <span class="o">+=</span> <span class="mi">1</span>
+
+        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">buffer_count</span> <span class="o">==</span> <span class="bp">self</span><span class="o">.</span><span class="n">buffer_size</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">write</span><span class="p">()</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">buffer_count</span> <span class="o">=</span> <span class="mi">0</span></div></div>
+
+
+<div class="viewcode-block" id="BeamMonitor"><a class="viewcode-back" href="../../../../mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.monitors.BeamMonitor">[docs]</a><span class="k">class</span> <span class="nc">BeamMonitor</span><span class="p">(</span><span class="n">Monitor</span><span class="p">):</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    Monitor the full beam and save each bunch attributes (mean, std, emit and </span>
+<span class="sd">    current).</span>
+<span class="sd">    </span>
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">    h : int</span>
+<span class="sd">        Harmonic number of the ring.</span>
+<span class="sd">    save_every : int or float</span>
+<span class="sd">        Set the frequency of the save. The data is saved every save_every </span>
+<span class="sd">        call of the montior.</span>
+<span class="sd">    buffer_size : int or float</span>
+<span class="sd">        Size of the save buffer.</span>
+<span class="sd">    total_size : int or float</span>
+<span class="sd">        Total size of the save. The following relationships between the </span>
+<span class="sd">        parameters must exist: </span>
+<span class="sd">            total_size % buffer_size == 0</span>
+<span class="sd">            number of call to track / save_every == total_size</span>
+<span class="sd">    file_name : string, optional</span>
+<span class="sd">        Name of the HDF5 where the data will be stored. Must be specified</span>
+<span class="sd">        the first time a subclass of Monitor is instancied and must be None</span>
+<span class="sd">        the following times.</span>
+<span class="sd">    mpi_mode : bool, optional</span>
+<span class="sd">        If True, open the HDF5 file in parallel mode, which is needed to</span>
+<span class="sd">        allow several cores to write in the same file at the same time.</span>
+<span class="sd">        If False, open the HDF5 file in standard mode.</span>
+
+<span class="sd">    Methods</span>
+<span class="sd">    -------</span>
+<span class="sd">    track(beam)</span>
+<span class="sd">        Save data    </span>
+<span class="sd">    &quot;&quot;&quot;</span>
+
+    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span>
+                 <span class="n">h</span><span class="p">,</span>
+                 <span class="n">save_every</span><span class="p">,</span>
+                 <span class="n">buffer_size</span><span class="p">,</span>
+                 <span class="n">total_size</span><span class="p">,</span>
+                 <span class="n">file_name</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+                 <span class="n">mpi_mode</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
+
+        <span class="n">group_name</span> <span class="o">=</span> <span class="s2">&quot;Beam&quot;</span>
+        <span class="n">dict_buffer</span> <span class="o">=</span> <span class="p">{</span>
+            <span class="s2">&quot;mean&quot;</span><span class="p">:</span> <span class="p">(</span><span class="mi">6</span><span class="p">,</span> <span class="n">h</span><span class="p">,</span> <span class="n">buffer_size</span><span class="p">),</span>
+            <span class="s2">&quot;std&quot;</span><span class="p">:</span> <span class="p">(</span><span class="mi">6</span><span class="p">,</span> <span class="n">h</span><span class="p">,</span> <span class="n">buffer_size</span><span class="p">),</span>
+            <span class="s2">&quot;emit&quot;</span><span class="p">:</span> <span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="n">h</span><span class="p">,</span> <span class="n">buffer_size</span><span class="p">),</span>
+            <span class="s2">&quot;current&quot;</span><span class="p">:</span> <span class="p">(</span><span class="n">h</span><span class="p">,</span> <span class="n">buffer_size</span><span class="p">),</span>
+            <span class="s2">&quot;cs_invariant&quot;</span><span class="p">:</span> <span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="n">h</span><span class="p">,</span> <span class="n">buffer_size</span><span class="p">)</span>
+        <span class="p">}</span>
+        <span class="n">dict_file</span> <span class="o">=</span> <span class="p">{</span>
+            <span class="s2">&quot;mean&quot;</span><span class="p">:</span> <span class="p">(</span><span class="mi">6</span><span class="p">,</span> <span class="n">h</span><span class="p">,</span> <span class="n">total_size</span><span class="p">),</span>
+            <span class="s2">&quot;std&quot;</span><span class="p">:</span> <span class="p">(</span><span class="mi">6</span><span class="p">,</span> <span class="n">h</span><span class="p">,</span> <span class="n">total_size</span><span class="p">),</span>
+            <span class="s2">&quot;emit&quot;</span><span class="p">:</span> <span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="n">h</span><span class="p">,</span> <span class="n">total_size</span><span class="p">),</span>
+            <span class="s2">&quot;current&quot;</span><span class="p">:</span> <span class="p">(</span><span class="n">h</span><span class="p">,</span> <span class="n">total_size</span><span class="p">),</span>
+            <span class="s2">&quot;cs_invariant&quot;</span><span class="p">:</span> <span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="n">h</span><span class="p">,</span> <span class="n">total_size</span><span class="p">)</span>
+        <span class="p">}</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">monitor_init</span><span class="p">(</span><span class="n">group_name</span><span class="p">,</span> <span class="n">save_every</span><span class="p">,</span> <span class="n">buffer_size</span><span class="p">,</span> <span class="n">total_size</span><span class="p">,</span>
+                          <span class="n">dict_buffer</span><span class="p">,</span> <span class="n">dict_file</span><span class="p">,</span> <span class="n">file_name</span><span class="p">,</span> <span class="n">mpi_mode</span><span class="p">)</span>
+
+<div class="viewcode-block" id="BeamMonitor.track"><a class="viewcode-back" href="../../../../mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.monitors.BeamMonitor.track">[docs]</a>    <span class="k">def</span> <span class="nf">track</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">beam</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Save data</span>
+<span class="sd">        </span>
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        beam : Beam object</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">track_count</span> <span class="o">%</span> <span class="bp">self</span><span class="o">.</span><span class="n">save_every</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
+            <span class="k">if</span> <span class="p">(</span><span class="n">beam</span><span class="o">.</span><span class="n">mpi_switch</span> <span class="o">==</span> <span class="kc">True</span><span class="p">):</span>
+                <span class="bp">self</span><span class="o">.</span><span class="n">to_buffer</span><span class="p">(</span><span class="n">beam</span><span class="p">[</span><span class="n">beam</span><span class="o">.</span><span class="n">mpi</span><span class="o">.</span><span class="n">bunch_num</span><span class="p">],</span> <span class="n">beam</span><span class="o">.</span><span class="n">mpi</span><span class="o">.</span><span class="n">bunch_num</span><span class="p">)</span>
+            <span class="k">else</span><span class="p">:</span>
+                <span class="bp">self</span><span class="o">.</span><span class="n">to_buffer_no_mpi</span><span class="p">(</span><span class="n">beam</span><span class="p">)</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">track_count</span> <span class="o">+=</span> <span class="mi">1</span></div>
+
+<div class="viewcode-block" id="BeamMonitor.to_buffer"><a class="viewcode-back" href="../../../../mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.monitors.BeamMonitor.to_buffer">[docs]</a>    <span class="k">def</span> <span class="nf">to_buffer</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">bunch</span><span class="p">,</span> <span class="n">bunch_num</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Save data to buffer, if mpi is being used.</span>
+<span class="sd">        </span>
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        bunch : Bunch object</span>
+<span class="sd">        bunch_num : int</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">time</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">buffer_count</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">track_count</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">mean</span><span class="p">[:,</span> <span class="n">bunch_num</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">buffer_count</span><span class="p">]</span> <span class="o">=</span> <span class="n">bunch</span><span class="o">.</span><span class="n">mean</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">std</span><span class="p">[:,</span> <span class="n">bunch_num</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">buffer_count</span><span class="p">]</span> <span class="o">=</span> <span class="n">bunch</span><span class="o">.</span><span class="n">std</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">emit</span><span class="p">[:,</span> <span class="n">bunch_num</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">buffer_count</span><span class="p">]</span> <span class="o">=</span> <span class="n">bunch</span><span class="o">.</span><span class="n">emit</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">current</span><span class="p">[</span><span class="n">bunch_num</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">buffer_count</span><span class="p">]</span> <span class="o">=</span> <span class="n">bunch</span><span class="o">.</span><span class="n">current</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">cs_invariant</span><span class="p">[:,</span> <span class="n">bunch_num</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">buffer_count</span><span class="p">]</span> <span class="o">=</span> <span class="n">bunch</span><span class="o">.</span><span class="n">cs_invariant</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">buffer_count</span> <span class="o">+=</span> <span class="mi">1</span>
+
+        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">buffer_count</span> <span class="o">==</span> <span class="bp">self</span><span class="o">.</span><span class="n">buffer_size</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">write</span><span class="p">(</span><span class="n">bunch_num</span><span class="p">)</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">buffer_count</span> <span class="o">=</span> <span class="mi">0</span></div>
+
+<div class="viewcode-block" id="BeamMonitor.to_buffer_no_mpi"><a class="viewcode-back" href="../../../../mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.monitors.BeamMonitor.to_buffer_no_mpi">[docs]</a>    <span class="k">def</span> <span class="nf">to_buffer_no_mpi</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">beam</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Save data to buffer, if mpi is not being used.</span>
+<span class="sd">        </span>
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        beam : Beam object</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">time</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">buffer_count</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">track_count</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">mean</span><span class="p">[:,</span> <span class="p">:,</span> <span class="bp">self</span><span class="o">.</span><span class="n">buffer_count</span><span class="p">]</span> <span class="o">=</span> <span class="n">beam</span><span class="o">.</span><span class="n">bunch_mean</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">std</span><span class="p">[:,</span> <span class="p">:,</span> <span class="bp">self</span><span class="o">.</span><span class="n">buffer_count</span><span class="p">]</span> <span class="o">=</span> <span class="n">beam</span><span class="o">.</span><span class="n">bunch_std</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">emit</span><span class="p">[:,</span> <span class="p">:,</span> <span class="bp">self</span><span class="o">.</span><span class="n">buffer_count</span><span class="p">]</span> <span class="o">=</span> <span class="n">beam</span><span class="o">.</span><span class="n">bunch_emit</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">current</span><span class="p">[:,</span> <span class="bp">self</span><span class="o">.</span><span class="n">buffer_count</span><span class="p">]</span> <span class="o">=</span> <span class="n">beam</span><span class="o">.</span><span class="n">bunch_current</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">cs_invariant</span><span class="p">[:,</span> <span class="p">:,</span> <span class="bp">self</span><span class="o">.</span><span class="n">buffer_count</span><span class="p">]</span> <span class="o">=</span> <span class="n">beam</span><span class="o">.</span><span class="n">bunch_cs</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">buffer_count</span> <span class="o">+=</span> <span class="mi">1</span>
+
+        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">buffer_count</span> <span class="o">==</span> <span class="bp">self</span><span class="o">.</span><span class="n">buffer_size</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">write_no_mpi</span><span class="p">()</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">buffer_count</span> <span class="o">=</span> <span class="mi">0</span></div>
+
+<div class="viewcode-block" id="BeamMonitor.write"><a class="viewcode-back" href="../../../../mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.monitors.BeamMonitor.write">[docs]</a>    <span class="k">def</span> <span class="nf">write</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">bunch_num</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Write data from buffer to the HDF5 file, if mpi is being used.</span>
+<span class="sd">        </span>
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        bunch_num : int</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">file</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">group_name</span><span class="p">][</span><span class="s2">&quot;time&quot;</span><span class="p">][</span><span class="bp">self</span><span class="o">.</span><span class="n">write_count</span> <span class="o">*</span>
+                                           <span class="bp">self</span><span class="o">.</span><span class="n">buffer_size</span><span class="p">:(</span><span class="bp">self</span><span class="o">.</span><span class="n">write_count</span> <span class="o">+</span>
+                                                             <span class="mi">1</span><span class="p">)</span> <span class="o">*</span>
+                                           <span class="bp">self</span><span class="o">.</span><span class="n">buffer_size</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">time</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">file</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">group_name</span><span class="p">][</span>
+            <span class="s2">&quot;mean&quot;</span><span class="p">][:,</span> <span class="n">bunch_num</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">write_count</span> <span class="o">*</span>
+                    <span class="bp">self</span><span class="o">.</span><span class="n">buffer_size</span><span class="p">:(</span><span class="bp">self</span><span class="o">.</span><span class="n">write_count</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span> <span class="o">*</span>
+                    <span class="bp">self</span><span class="o">.</span><span class="n">buffer_size</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">mean</span><span class="p">[:,</span> <span class="n">bunch_num</span><span class="p">,</span> <span class="p">:]</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">file</span><span class="p">[</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">group_name</span><span class="p">][</span><span class="s2">&quot;std&quot;</span><span class="p">][:,</span> <span class="n">bunch_num</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">write_count</span> <span class="o">*</span>
+                                    <span class="bp">self</span><span class="o">.</span><span class="n">buffer_size</span><span class="p">:(</span><span class="bp">self</span><span class="o">.</span><span class="n">write_count</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span> <span class="o">*</span>
+                                    <span class="bp">self</span><span class="o">.</span><span class="n">buffer_size</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">std</span><span class="p">[:,</span>
+                                                                 <span class="n">bunch_num</span><span class="p">,</span> <span class="p">:]</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">file</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">group_name</span><span class="p">][</span>
+            <span class="s2">&quot;emit&quot;</span><span class="p">][:,</span> <span class="n">bunch_num</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">write_count</span> <span class="o">*</span>
+                    <span class="bp">self</span><span class="o">.</span><span class="n">buffer_size</span><span class="p">:(</span><span class="bp">self</span><span class="o">.</span><span class="n">write_count</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span> <span class="o">*</span>
+                    <span class="bp">self</span><span class="o">.</span><span class="n">buffer_size</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">emit</span><span class="p">[:,</span> <span class="n">bunch_num</span><span class="p">,</span> <span class="p">:]</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">file</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">group_name</span><span class="p">][</span><span class="s2">&quot;current&quot;</span><span class="p">][</span>
+            <span class="n">bunch_num</span><span class="p">,</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">write_count</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">buffer_size</span><span class="p">:(</span><span class="bp">self</span><span class="o">.</span><span class="n">write_count</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span> <span class="o">*</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">buffer_size</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">current</span><span class="p">[</span><span class="n">bunch_num</span><span class="p">,</span> <span class="p">:]</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">file</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">group_name</span><span class="p">][</span>
+            <span class="s2">&quot;cs_invariant&quot;</span><span class="p">][:,</span> <span class="n">bunch_num</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">write_count</span> <span class="o">*</span>
+                            <span class="bp">self</span><span class="o">.</span><span class="n">buffer_size</span><span class="p">:(</span><span class="bp">self</span><span class="o">.</span><span class="n">write_count</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span> <span class="o">*</span>
+                            <span class="bp">self</span><span class="o">.</span><span class="n">buffer_size</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">cs_invariant</span><span class="p">[:,</span>
+                                                                  <span class="n">bunch_num</span><span class="p">,</span> <span class="p">:]</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">file</span><span class="o">.</span><span class="n">flush</span><span class="p">()</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">write_count</span> <span class="o">+=</span> <span class="mi">1</span></div>
+
+<div class="viewcode-block" id="BeamMonitor.write_no_mpi"><a class="viewcode-back" href="../../../../mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.monitors.BeamMonitor.write_no_mpi">[docs]</a>    <span class="k">def</span> <span class="nf">write_no_mpi</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Write data from buffer to the HDF5 file, if mpi is not being used.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">file</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">group_name</span><span class="p">][</span><span class="s2">&quot;time&quot;</span><span class="p">][</span><span class="bp">self</span><span class="o">.</span><span class="n">write_count</span> <span class="o">*</span>
+                                           <span class="bp">self</span><span class="o">.</span><span class="n">buffer_size</span><span class="p">:(</span><span class="bp">self</span><span class="o">.</span><span class="n">write_count</span> <span class="o">+</span>
+                                                             <span class="mi">1</span><span class="p">)</span> <span class="o">*</span>
+                                           <span class="bp">self</span><span class="o">.</span><span class="n">buffer_size</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">time</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">file</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">group_name</span><span class="p">][</span><span class="s2">&quot;mean&quot;</span><span class="p">][:,</span> <span class="p">:,</span> <span class="bp">self</span><span class="o">.</span><span class="n">write_count</span> <span class="o">*</span>
+                                           <span class="bp">self</span><span class="o">.</span><span class="n">buffer_size</span><span class="p">:(</span><span class="bp">self</span><span class="o">.</span><span class="n">write_count</span> <span class="o">+</span>
+                                                             <span class="mi">1</span><span class="p">)</span> <span class="o">*</span>
+                                           <span class="bp">self</span><span class="o">.</span><span class="n">buffer_size</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">mean</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">file</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">group_name</span><span class="p">][</span><span class="s2">&quot;std&quot;</span><span class="p">][:,</span> <span class="p">:,</span> <span class="bp">self</span><span class="o">.</span><span class="n">write_count</span> <span class="o">*</span>
+                                          <span class="bp">self</span><span class="o">.</span><span class="n">buffer_size</span><span class="p">:(</span><span class="bp">self</span><span class="o">.</span><span class="n">write_count</span> <span class="o">+</span>
+                                                            <span class="mi">1</span><span class="p">)</span> <span class="o">*</span>
+                                          <span class="bp">self</span><span class="o">.</span><span class="n">buffer_size</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">std</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">file</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">group_name</span><span class="p">][</span><span class="s2">&quot;emit&quot;</span><span class="p">][:,</span> <span class="p">:,</span> <span class="bp">self</span><span class="o">.</span><span class="n">write_count</span> <span class="o">*</span>
+                                           <span class="bp">self</span><span class="o">.</span><span class="n">buffer_size</span><span class="p">:(</span><span class="bp">self</span><span class="o">.</span><span class="n">write_count</span> <span class="o">+</span>
+                                                             <span class="mi">1</span><span class="p">)</span> <span class="o">*</span>
+                                           <span class="bp">self</span><span class="o">.</span><span class="n">buffer_size</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">emit</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">file</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">group_name</span><span class="p">][</span><span class="s2">&quot;current&quot;</span><span class="p">][:,</span> <span class="bp">self</span><span class="o">.</span><span class="n">write_count</span> <span class="o">*</span>
+                                              <span class="bp">self</span><span class="o">.</span><span class="n">buffer_size</span><span class="p">:</span>
+                                              <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">write_count</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span> <span class="o">*</span>
+                                              <span class="bp">self</span><span class="o">.</span><span class="n">buffer_size</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">current</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">file</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">group_name</span><span class="p">][</span>
+            <span class="s2">&quot;cs_invariant&quot;</span><span class="p">][:,</span> <span class="p">:,</span> <span class="bp">self</span><span class="o">.</span><span class="n">write_count</span> <span class="o">*</span>
+                            <span class="bp">self</span><span class="o">.</span><span class="n">buffer_size</span><span class="p">:(</span><span class="bp">self</span><span class="o">.</span><span class="n">write_count</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span> <span class="o">*</span>
+                            <span class="bp">self</span><span class="o">.</span><span class="n">buffer_size</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">cs_invariant</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">file</span><span class="o">.</span><span class="n">flush</span><span class="p">()</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">write_count</span> <span class="o">+=</span> <span class="mi">1</span></div></div>
+
+
+<div class="viewcode-block" id="ProfileMonitor"><a class="viewcode-back" href="../../../../mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.monitors.ProfileMonitor">[docs]</a><span class="k">class</span> <span class="nc">ProfileMonitor</span><span class="p">(</span><span class="n">Monitor</span><span class="p">):</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    Monitor a single bunch and save bunch profiles.</span>
+<span class="sd">    </span>
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">    bunch_number : int</span>
+<span class="sd">        Bunch to monitor.</span>
+<span class="sd">    save_every : int or float</span>
+<span class="sd">        Set the frequency of the save. The data is saved every save_every </span>
+<span class="sd">        call of the montior.</span>
+<span class="sd">    buffer_size : int or float</span>
+<span class="sd">        Size of the save buffer.</span>
+<span class="sd">    total_size : int or float</span>
+<span class="sd">        Total size of the save. The following relationships between the </span>
+<span class="sd">        parameters must exist: </span>
+<span class="sd">            total_size % buffer_size == 0</span>
+<span class="sd">            number of call to track / save_every == total_size</span>
+<span class="sd">    dimensions : str or list of str, optional</span>
+<span class="sd">        Dimensions to save.</span>
+<span class="sd">    n_bin : int or list of int, optional</span>
+<span class="sd">        Number of bin to use in each dimension.</span>
+<span class="sd">    file_name : string, optional</span>
+<span class="sd">        Name of the HDF5 where the data will be stored. Must be specified</span>
+<span class="sd">        the first time a subclass of Monitor is instancied and must be None</span>
+<span class="sd">        the following times.</span>
+<span class="sd">    mpi_mode : bool, optional</span>
+<span class="sd">        If True, open the HDF5 file in parallel mode, which is needed to</span>
+<span class="sd">        allow several cores to write in the same file at the same time.</span>
+<span class="sd">        If False, open the HDF5 file in standard mode.</span>
+
+<span class="sd">    Methods</span>
+<span class="sd">    -------</span>
+<span class="sd">    track(object_to_save)</span>
+<span class="sd">        Save data.</span>
+<span class="sd">    &quot;&quot;&quot;</span>
+
+    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span>
+                 <span class="n">bunch_number</span><span class="p">,</span>
+                 <span class="n">save_every</span><span class="p">,</span>
+                 <span class="n">buffer_size</span><span class="p">,</span>
+                 <span class="n">total_size</span><span class="p">,</span>
+                 <span class="n">dimensions</span><span class="o">=</span><span class="s2">&quot;tau&quot;</span><span class="p">,</span>
+                 <span class="n">n_bin</span><span class="o">=</span><span class="mi">75</span><span class="p">,</span>
+                 <span class="n">file_name</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+                 <span class="n">mpi_mode</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">bunch_number</span> <span class="o">=</span> <span class="n">bunch_number</span>
+        <span class="n">group_name</span> <span class="o">=</span> <span class="s2">&quot;ProfileData_&quot;</span> <span class="o">+</span> <span class="nb">str</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">bunch_number</span><span class="p">)</span>
+
+        <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">dimensions</span><span class="p">,</span> <span class="nb">str</span><span class="p">):</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">dimensions</span> <span class="o">=</span> <span class="p">[</span><span class="n">dimensions</span><span class="p">]</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">dimensions</span> <span class="o">=</span> <span class="n">dimensions</span>
+
+        <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">n_bin</span><span class="p">,</span> <span class="nb">int</span><span class="p">):</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">n_bin</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">((</span><span class="nb">len</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">dimensions</span><span class="p">),</span> <span class="p">),</span> <span class="n">dtype</span><span class="o">=</span><span class="nb">int</span><span class="p">)</span> <span class="o">*</span> <span class="n">n_bin</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">n_bin</span> <span class="o">=</span> <span class="n">n_bin</span>
+
+        <span class="n">dict_buffer</span> <span class="o">=</span> <span class="p">{}</span>
+        <span class="n">dict_file</span> <span class="o">=</span> <span class="p">{}</span>
+        <span class="k">for</span> <span class="n">index</span><span class="p">,</span> <span class="n">dim</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">dimensions</span><span class="p">):</span>
+            <span class="n">dict_buffer</span><span class="o">.</span><span class="n">update</span><span class="p">({</span><span class="n">dim</span><span class="p">:</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">n_bin</span><span class="p">[</span><span class="n">index</span><span class="p">]</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="n">buffer_size</span><span class="p">)})</span>
+            <span class="n">dict_buffer</span><span class="o">.</span><span class="n">update</span><span class="p">(</span>
+                <span class="p">{</span><span class="n">dim</span> <span class="o">+</span> <span class="s2">&quot;_bin&quot;</span><span class="p">:</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">n_bin</span><span class="p">[</span><span class="n">index</span><span class="p">]</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="n">buffer_size</span><span class="p">)})</span>
+            <span class="n">dict_file</span><span class="o">.</span><span class="n">update</span><span class="p">({</span><span class="n">dim</span><span class="p">:</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">n_bin</span><span class="p">[</span><span class="n">index</span><span class="p">]</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="n">total_size</span><span class="p">)})</span>
+            <span class="n">dict_file</span><span class="o">.</span><span class="n">update</span><span class="p">(</span>
+                <span class="p">{</span><span class="n">dim</span> <span class="o">+</span> <span class="s2">&quot;_bin&quot;</span><span class="p">:</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">n_bin</span><span class="p">[</span><span class="n">index</span><span class="p">]</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="n">total_size</span><span class="p">)})</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">monitor_init</span><span class="p">(</span><span class="n">group_name</span><span class="p">,</span> <span class="n">save_every</span><span class="p">,</span> <span class="n">buffer_size</span><span class="p">,</span> <span class="n">total_size</span><span class="p">,</span>
+                          <span class="n">dict_buffer</span><span class="p">,</span> <span class="n">dict_file</span><span class="p">,</span> <span class="n">file_name</span><span class="p">,</span> <span class="n">mpi_mode</span><span class="p">)</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">dict_buffer</span> <span class="o">=</span> <span class="n">dict_buffer</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">dict_file</span> <span class="o">=</span> <span class="n">dict_file</span>
+
+<div class="viewcode-block" id="ProfileMonitor.to_buffer"><a class="viewcode-back" href="../../../../mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.monitors.ProfileMonitor.to_buffer">[docs]</a>    <span class="k">def</span> <span class="nf">to_buffer</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">bunch</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Save data to buffer.</span>
+<span class="sd">        </span>
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        bunch : Bunch object</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">time</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">buffer_count</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">track_count</span>
+        <span class="k">for</span> <span class="n">index</span><span class="p">,</span> <span class="n">dim</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">dimensions</span><span class="p">):</span>
+            <span class="n">bins</span><span class="p">,</span> <span class="n">sorted_index</span><span class="p">,</span> <span class="n">profile</span><span class="p">,</span> <span class="n">center</span> <span class="o">=</span> <span class="n">bunch</span><span class="o">.</span><span class="n">binning</span><span class="p">(</span>
+                <span class="n">dim</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">n_bin</span><span class="p">[</span><span class="n">index</span><span class="p">])</span>
+            <span class="bp">self</span><span class="o">.</span><span class="fm">__getattribute__</span><span class="p">(</span><span class="n">dim</span> <span class="o">+</span> <span class="s2">&quot;_bin&quot;</span><span class="p">)[:,</span> <span class="bp">self</span><span class="o">.</span><span class="n">buffer_count</span><span class="p">]</span> <span class="o">=</span> <span class="n">center</span>
+            <span class="bp">self</span><span class="o">.</span><span class="fm">__getattribute__</span><span class="p">(</span><span class="n">dim</span><span class="p">)[:,</span> <span class="bp">self</span><span class="o">.</span><span class="n">buffer_count</span><span class="p">]</span> <span class="o">=</span> <span class="n">profile</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">buffer_count</span> <span class="o">+=</span> <span class="mi">1</span>
+
+        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">buffer_count</span> <span class="o">==</span> <span class="bp">self</span><span class="o">.</span><span class="n">buffer_size</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">write</span><span class="p">()</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">buffer_count</span> <span class="o">=</span> <span class="mi">0</span></div>
+
+<div class="viewcode-block" id="ProfileMonitor.write"><a class="viewcode-back" href="../../../../mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.monitors.ProfileMonitor.write">[docs]</a>    <span class="k">def</span> <span class="nf">write</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Write data from buffer to the HDF5 file.&quot;&quot;&quot;</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">file</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">group_name</span><span class="p">][</span><span class="s2">&quot;time&quot;</span><span class="p">][</span><span class="bp">self</span><span class="o">.</span><span class="n">write_count</span> <span class="o">*</span>
+                                           <span class="bp">self</span><span class="o">.</span><span class="n">buffer_size</span><span class="p">:(</span><span class="bp">self</span><span class="o">.</span><span class="n">write_count</span> <span class="o">+</span>
+                                                             <span class="mi">1</span><span class="p">)</span> <span class="o">*</span>
+                                           <span class="bp">self</span><span class="o">.</span><span class="n">buffer_size</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">time</span>
+
+        <span class="k">for</span> <span class="n">dim</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">dimensions</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">file</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">group_name</span><span class="p">][</span>
+                <span class="n">dim</span><span class="p">][:,</span> <span class="bp">self</span><span class="o">.</span><span class="n">write_count</span> <span class="o">*</span>
+                     <span class="bp">self</span><span class="o">.</span><span class="n">buffer_size</span><span class="p">:(</span><span class="bp">self</span><span class="o">.</span><span class="n">write_count</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span> <span class="o">*</span>
+                     <span class="bp">self</span><span class="o">.</span><span class="n">buffer_size</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="fm">__getattribute__</span><span class="p">(</span><span class="n">dim</span><span class="p">)</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">file</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">group_name</span><span class="p">][</span>
+                <span class="n">dim</span> <span class="o">+</span> <span class="s2">&quot;_bin&quot;</span><span class="p">][:,</span> <span class="bp">self</span><span class="o">.</span><span class="n">write_count</span> <span class="o">*</span>
+                              <span class="bp">self</span><span class="o">.</span><span class="n">buffer_size</span><span class="p">:(</span><span class="bp">self</span><span class="o">.</span><span class="n">write_count</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span> <span class="o">*</span>
+                              <span class="bp">self</span><span class="o">.</span><span class="n">buffer_size</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="fm">__getattribute__</span><span class="p">(</span><span class="n">dim</span> <span class="o">+</span>
+                                                                        <span class="s2">&quot;_bin&quot;</span><span class="p">)</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">write_count</span> <span class="o">+=</span> <span class="mi">1</span></div>
+
+<div class="viewcode-block" id="ProfileMonitor.track"><a class="viewcode-back" href="../../../../mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.monitors.ProfileMonitor.track">[docs]</a>    <span class="k">def</span> <span class="nf">track</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">object_to_save</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Save data.</span>
+<span class="sd">        </span>
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        object_to_save : Bunch or Beam object</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">track_bunch_data</span><span class="p">(</span><span class="n">object_to_save</span><span class="p">,</span> <span class="n">check_empty</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span></div></div>
+
+
+<div class="viewcode-block" id="WakePotentialMonitor"><a class="viewcode-back" href="../../../../mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.monitors.WakePotentialMonitor">[docs]</a><span class="k">class</span> <span class="nc">WakePotentialMonitor</span><span class="p">(</span><span class="n">Monitor</span><span class="p">):</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    Monitor the wake potential from a single bunch and save attributes (tau, </span>
+<span class="sd">    ...).</span>
+<span class="sd">    </span>
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">    bunch_number : int</span>
+<span class="sd">        Bunch to monitor.</span>
+<span class="sd">    wake_types : str or list of str</span>
+<span class="sd">        Wake types to save: &quot;Wlong, &quot;Wxdip&quot;, ...</span>
+<span class="sd">    n_bin : int</span>
+<span class="sd">        Number of bin to be used to interpolate the wake potential on a fixed</span>
+<span class="sd">        grid.</span>
+<span class="sd">    save_every : int or float</span>
+<span class="sd">        Set the frequency of the save. The data is saved every save_every </span>
+<span class="sd">        call of the montior.</span>
+<span class="sd">    buffer_size : int or float</span>
+<span class="sd">        Size of the save buffer.</span>
+<span class="sd">    total_size : int or float</span>
+<span class="sd">        Total size of the save. The following relationships between the </span>
+<span class="sd">        parameters must exist: </span>
+<span class="sd">            total_size % buffer_size == 0</span>
+<span class="sd">            number of call to track / save_every == total_size</span>
+<span class="sd">    file_name : string, optional</span>
+<span class="sd">        Name of the HDF5 where the data will be stored. Must be specified</span>
+<span class="sd">        the first time a subclass of Monitor is instancied and must be None</span>
+<span class="sd">        the following times.</span>
+<span class="sd">    mpi_mode : bool, optional</span>
+<span class="sd">        If True, open the HDF5 file in parallel mode, which is needed to</span>
+<span class="sd">        allow several cores to write in the same file at the same time.</span>
+<span class="sd">        If False, open the HDF5 file in standard mode.</span>
+
+<span class="sd">    Methods</span>
+<span class="sd">    -------</span>
+<span class="sd">    track(object_to_save, wake_potential_to_save)</span>
+<span class="sd">        Save data.</span>
+<span class="sd">    &quot;&quot;&quot;</span>
+
+    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span>
+                 <span class="n">bunch_number</span><span class="p">,</span>
+                 <span class="n">wake_types</span><span class="p">,</span>
+                 <span class="n">n_bin</span><span class="p">,</span>
+                 <span class="n">save_every</span><span class="p">,</span>
+                 <span class="n">buffer_size</span><span class="p">,</span>
+                 <span class="n">total_size</span><span class="p">,</span>
+                 <span class="n">file_name</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+                 <span class="n">mpi_mode</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">bunch_number</span> <span class="o">=</span> <span class="n">bunch_number</span>
+        <span class="n">group_name</span> <span class="o">=</span> <span class="s2">&quot;WakePotentialData_&quot;</span> <span class="o">+</span> <span class="nb">str</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">bunch_number</span><span class="p">)</span>
+
+        <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">wake_types</span><span class="p">,</span> <span class="nb">str</span><span class="p">):</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">wake_types</span> <span class="o">=</span> <span class="p">[</span><span class="n">wake_types</span><span class="p">]</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">wake_types</span> <span class="o">=</span> <span class="n">wake_types</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">n_bin</span> <span class="o">=</span> <span class="n">n_bin</span> <span class="o">*</span> <span class="mi">2</span>
+
+        <span class="n">dict_buffer</span> <span class="o">=</span> <span class="p">{}</span>
+        <span class="n">dict_file</span> <span class="o">=</span> <span class="p">{}</span>
+        <span class="k">for</span> <span class="n">index</span><span class="p">,</span> <span class="n">dim</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">wake_types</span><span class="p">):</span>
+            <span class="n">dict_buffer</span><span class="o">.</span><span class="n">update</span><span class="p">({</span><span class="s2">&quot;tau_&quot;</span> <span class="o">+</span> <span class="n">dim</span><span class="p">:</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">n_bin</span><span class="p">,</span> <span class="n">buffer_size</span><span class="p">)})</span>
+            <span class="n">dict_file</span><span class="o">.</span><span class="n">update</span><span class="p">({</span><span class="s2">&quot;tau_&quot;</span> <span class="o">+</span> <span class="n">dim</span><span class="p">:</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">n_bin</span><span class="p">,</span> <span class="n">total_size</span><span class="p">)})</span>
+            <span class="n">dict_buffer</span><span class="o">.</span><span class="n">update</span><span class="p">({</span><span class="s2">&quot;profile_&quot;</span> <span class="o">+</span> <span class="n">dim</span><span class="p">:</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">n_bin</span><span class="p">,</span> <span class="n">buffer_size</span><span class="p">)})</span>
+            <span class="n">dict_file</span><span class="o">.</span><span class="n">update</span><span class="p">({</span><span class="s2">&quot;profile_&quot;</span> <span class="o">+</span> <span class="n">dim</span><span class="p">:</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">n_bin</span><span class="p">,</span> <span class="n">total_size</span><span class="p">)})</span>
+            <span class="n">dict_buffer</span><span class="o">.</span><span class="n">update</span><span class="p">({</span><span class="n">dim</span><span class="p">:</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">n_bin</span><span class="p">,</span> <span class="n">buffer_size</span><span class="p">)})</span>
+            <span class="n">dict_file</span><span class="o">.</span><span class="n">update</span><span class="p">({</span><span class="n">dim</span><span class="p">:</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">n_bin</span><span class="p">,</span> <span class="n">total_size</span><span class="p">)})</span>
+            <span class="k">if</span> <span class="n">dim</span> <span class="o">==</span> <span class="s2">&quot;Wxdip&quot;</span> <span class="ow">or</span> <span class="n">dim</span> <span class="o">==</span> <span class="s2">&quot;Wydip&quot;</span><span class="p">:</span>
+                <span class="n">dict_buffer</span><span class="o">.</span><span class="n">update</span><span class="p">(</span>
+                    <span class="p">{</span><span class="s2">&quot;dipole_&quot;</span> <span class="o">+</span> <span class="n">dim</span><span class="p">:</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">n_bin</span><span class="p">,</span> <span class="n">buffer_size</span><span class="p">)})</span>
+                <span class="n">dict_file</span><span class="o">.</span><span class="n">update</span><span class="p">({</span><span class="s2">&quot;dipole_&quot;</span> <span class="o">+</span> <span class="n">dim</span><span class="p">:</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">n_bin</span><span class="p">,</span> <span class="n">total_size</span><span class="p">)})</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">monitor_init</span><span class="p">(</span><span class="n">group_name</span><span class="p">,</span> <span class="n">save_every</span><span class="p">,</span> <span class="n">buffer_size</span><span class="p">,</span> <span class="n">total_size</span><span class="p">,</span>
+                          <span class="n">dict_buffer</span><span class="p">,</span> <span class="n">dict_file</span><span class="p">,</span> <span class="n">file_name</span><span class="p">,</span> <span class="n">mpi_mode</span><span class="p">)</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">dict_buffer</span> <span class="o">=</span> <span class="n">dict_buffer</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">dict_file</span> <span class="o">=</span> <span class="n">dict_file</span>
+
+<div class="viewcode-block" id="WakePotentialMonitor.to_buffer"><a class="viewcode-back" href="../../../../mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.monitors.WakePotentialMonitor.to_buffer">[docs]</a>    <span class="k">def</span> <span class="nf">to_buffer</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">wp</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Save data to buffer.</span>
+<span class="sd">        </span>
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        wp : WakePotential object</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">time</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">buffer_count</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">track_count</span>
+        <span class="k">for</span> <span class="n">index</span><span class="p">,</span> <span class="n">dim</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">wake_types</span><span class="p">):</span>
+            <span class="n">tau0</span> <span class="o">=</span> <span class="n">wp</span><span class="o">.</span><span class="fm">__getattribute__</span><span class="p">(</span><span class="s2">&quot;tau0_&quot;</span> <span class="o">+</span> <span class="n">dim</span><span class="p">)</span>
+            <span class="n">profile0</span> <span class="o">=</span> <span class="n">wp</span><span class="o">.</span><span class="fm">__getattribute__</span><span class="p">(</span><span class="s2">&quot;profile0_&quot;</span> <span class="o">+</span> <span class="n">dim</span><span class="p">)</span>
+            <span class="n">WP0</span> <span class="o">=</span> <span class="n">wp</span><span class="o">.</span><span class="fm">__getattribute__</span><span class="p">(</span><span class="n">dim</span><span class="p">)</span>
+            <span class="k">if</span> <span class="n">dim</span> <span class="o">==</span> <span class="s2">&quot;Wxdip&quot;</span><span class="p">:</span>
+                <span class="n">dipole0</span> <span class="o">=</span> <span class="n">wp</span><span class="o">.</span><span class="fm">__getattribute__</span><span class="p">(</span><span class="s2">&quot;dipole_x&quot;</span><span class="p">)</span>
+            <span class="k">if</span> <span class="n">dim</span> <span class="o">==</span> <span class="s2">&quot;Wydip&quot;</span><span class="p">:</span>
+                <span class="n">dipole0</span> <span class="o">=</span> <span class="n">wp</span><span class="o">.</span><span class="fm">__getattribute__</span><span class="p">(</span><span class="s2">&quot;dipole_y&quot;</span><span class="p">)</span>
+
+            <span class="n">tau</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="n">tau0</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">tau0</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">],</span> <span class="bp">self</span><span class="o">.</span><span class="n">n_bin</span><span class="p">)</span>
+            <span class="n">f</span> <span class="o">=</span> <span class="n">interp1d</span><span class="p">(</span><span class="n">tau0</span><span class="p">,</span> <span class="n">WP0</span><span class="p">,</span> <span class="n">fill_value</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">bounds_error</span><span class="o">=</span><span class="kc">False</span><span class="p">)</span>
+            <span class="n">WP</span> <span class="o">=</span> <span class="n">f</span><span class="p">(</span><span class="n">tau</span><span class="p">)</span>
+            <span class="n">g</span> <span class="o">=</span> <span class="n">interp1d</span><span class="p">(</span><span class="n">tau0</span><span class="p">,</span> <span class="n">profile0</span><span class="p">,</span> <span class="n">fill_value</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">bounds_error</span><span class="o">=</span><span class="kc">False</span><span class="p">)</span>
+            <span class="n">profile</span> <span class="o">=</span> <span class="n">g</span><span class="p">(</span><span class="n">tau</span><span class="p">)</span>
+            <span class="k">if</span> <span class="n">dim</span> <span class="o">==</span> <span class="s2">&quot;Wxdip&quot;</span> <span class="ow">or</span> <span class="n">dim</span> <span class="o">==</span> <span class="s2">&quot;Wydip&quot;</span><span class="p">:</span>
+                <span class="n">h</span> <span class="o">=</span> <span class="n">interp1d</span><span class="p">(</span><span class="n">tau0</span><span class="p">,</span> <span class="n">dipole0</span><span class="p">,</span> <span class="n">fill_value</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">bounds_error</span><span class="o">=</span><span class="kc">False</span><span class="p">)</span>
+                <span class="n">dipole</span> <span class="o">=</span> <span class="n">h</span><span class="p">(</span><span class="n">tau</span><span class="p">)</span>
+
+            <span class="bp">self</span><span class="o">.</span><span class="fm">__getattribute__</span><span class="p">(</span><span class="s2">&quot;tau_&quot;</span> <span class="o">+</span>
+                                  <span class="n">dim</span><span class="p">)[:,</span>
+                                       <span class="bp">self</span><span class="o">.</span><span class="n">buffer_count</span><span class="p">]</span> <span class="o">=</span> <span class="n">tau</span> <span class="o">+</span> <span class="n">wp</span><span class="o">.</span><span class="n">tau_mean</span>
+            <span class="bp">self</span><span class="o">.</span><span class="fm">__getattribute__</span><span class="p">(</span><span class="s2">&quot;profile_&quot;</span> <span class="o">+</span>
+                                  <span class="n">dim</span><span class="p">)[:,</span> <span class="bp">self</span><span class="o">.</span><span class="n">buffer_count</span><span class="p">]</span> <span class="o">=</span> <span class="n">profile</span>
+            <span class="bp">self</span><span class="o">.</span><span class="fm">__getattribute__</span><span class="p">(</span><span class="n">dim</span><span class="p">)[:,</span> <span class="bp">self</span><span class="o">.</span><span class="n">buffer_count</span><span class="p">]</span> <span class="o">=</span> <span class="n">WP</span>
+            <span class="k">if</span> <span class="n">dim</span> <span class="o">==</span> <span class="s2">&quot;Wxdip&quot;</span> <span class="ow">or</span> <span class="n">dim</span> <span class="o">==</span> <span class="s2">&quot;Wydip&quot;</span><span class="p">:</span>
+                <span class="bp">self</span><span class="o">.</span><span class="fm">__getattribute__</span><span class="p">(</span><span class="s2">&quot;dipole_&quot;</span> <span class="o">+</span>
+                                      <span class="n">dim</span><span class="p">)[:,</span> <span class="bp">self</span><span class="o">.</span><span class="n">buffer_count</span><span class="p">]</span> <span class="o">=</span> <span class="n">dipole</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">buffer_count</span> <span class="o">+=</span> <span class="mi">1</span>
+
+        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">buffer_count</span> <span class="o">==</span> <span class="bp">self</span><span class="o">.</span><span class="n">buffer_size</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">write</span><span class="p">()</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">buffer_count</span> <span class="o">=</span> <span class="mi">0</span></div>
+
+<div class="viewcode-block" id="WakePotentialMonitor.write"><a class="viewcode-back" href="../../../../mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.monitors.WakePotentialMonitor.write">[docs]</a>    <span class="k">def</span> <span class="nf">write</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Write data from buffer to the HDF5 file.&quot;&quot;&quot;</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">file</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">group_name</span><span class="p">][</span><span class="s2">&quot;time&quot;</span><span class="p">][</span><span class="bp">self</span><span class="o">.</span><span class="n">write_count</span> <span class="o">*</span>
+                                           <span class="bp">self</span><span class="o">.</span><span class="n">buffer_size</span><span class="p">:(</span><span class="bp">self</span><span class="o">.</span><span class="n">write_count</span> <span class="o">+</span>
+                                                             <span class="mi">1</span><span class="p">)</span> <span class="o">*</span>
+                                           <span class="bp">self</span><span class="o">.</span><span class="n">buffer_size</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">time</span>
+
+        <span class="k">for</span> <span class="n">dim</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">wake_types</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">file</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">group_name</span><span class="p">][</span>
+                <span class="s2">&quot;tau_&quot;</span> <span class="o">+</span>
+                <span class="n">dim</span><span class="p">][:,</span> <span class="bp">self</span><span class="o">.</span><span class="n">write_count</span> <span class="o">*</span>
+                     <span class="bp">self</span><span class="o">.</span><span class="n">buffer_size</span><span class="p">:(</span><span class="bp">self</span><span class="o">.</span><span class="n">write_count</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span> <span class="o">*</span>
+                     <span class="bp">self</span><span class="o">.</span><span class="n">buffer_size</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="fm">__getattribute__</span><span class="p">(</span><span class="s2">&quot;tau_&quot;</span> <span class="o">+</span> <span class="n">dim</span><span class="p">)</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">file</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">group_name</span><span class="p">][</span>
+                <span class="s2">&quot;profile_&quot;</span> <span class="o">+</span>
+                <span class="n">dim</span><span class="p">][:,</span> <span class="bp">self</span><span class="o">.</span><span class="n">write_count</span> <span class="o">*</span>
+                     <span class="bp">self</span><span class="o">.</span><span class="n">buffer_size</span><span class="p">:(</span><span class="bp">self</span><span class="o">.</span><span class="n">write_count</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span> <span class="o">*</span>
+                     <span class="bp">self</span><span class="o">.</span><span class="n">buffer_size</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="fm">__getattribute__</span><span class="p">(</span><span class="s2">&quot;profile_&quot;</span> <span class="o">+</span>
+                                                               <span class="n">dim</span><span class="p">)</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">file</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">group_name</span><span class="p">][</span>
+                <span class="n">dim</span><span class="p">][:,</span> <span class="bp">self</span><span class="o">.</span><span class="n">write_count</span> <span class="o">*</span>
+                     <span class="bp">self</span><span class="o">.</span><span class="n">buffer_size</span><span class="p">:(</span><span class="bp">self</span><span class="o">.</span><span class="n">write_count</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span> <span class="o">*</span>
+                     <span class="bp">self</span><span class="o">.</span><span class="n">buffer_size</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="fm">__getattribute__</span><span class="p">(</span><span class="n">dim</span><span class="p">)</span>
+            <span class="k">if</span> <span class="n">dim</span> <span class="o">==</span> <span class="s2">&quot;Wxdip&quot;</span> <span class="ow">or</span> <span class="n">dim</span> <span class="o">==</span> <span class="s2">&quot;Wydip&quot;</span><span class="p">:</span>
+                <span class="bp">self</span><span class="o">.</span><span class="n">file</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">group_name</span><span class="p">][</span>
+                    <span class="s2">&quot;dipole_&quot;</span> <span class="o">+</span>
+                    <span class="n">dim</span><span class="p">][:,</span> <span class="bp">self</span><span class="o">.</span><span class="n">write_count</span> <span class="o">*</span>
+                         <span class="bp">self</span><span class="o">.</span><span class="n">buffer_size</span><span class="p">:(</span><span class="bp">self</span><span class="o">.</span><span class="n">write_count</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span> <span class="o">*</span>
+                         <span class="bp">self</span><span class="o">.</span><span class="n">buffer_size</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="fm">__getattribute__</span><span class="p">(</span><span class="s2">&quot;dipole_&quot;</span> <span class="o">+</span>
+                                                                   <span class="n">dim</span><span class="p">)</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">file</span><span class="o">.</span><span class="n">flush</span><span class="p">()</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">write_count</span> <span class="o">+=</span> <span class="mi">1</span></div>
+
+<div class="viewcode-block" id="WakePotentialMonitor.track"><a class="viewcode-back" href="../../../../mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.monitors.WakePotentialMonitor.track">[docs]</a>    <span class="k">def</span> <span class="nf">track</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">object_to_save</span><span class="p">,</span> <span class="n">wake_potential_to_save</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Save data.</span>
+<span class="sd">        </span>
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        object_to_save : Bunch or Beam object</span>
+<span class="sd">        wake_potential_to_save : WakePotential object</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">object_to_save</span><span class="p">,</span> <span class="n">Beam</span><span class="p">):</span>
+            <span class="k">if</span> <span class="p">(</span><span class="n">object_to_save</span><span class="o">.</span><span class="n">mpi_switch</span> <span class="o">==</span> <span class="kc">True</span><span class="p">):</span>
+                <span class="k">if</span> <span class="n">object_to_save</span><span class="o">.</span><span class="n">mpi</span><span class="o">.</span><span class="n">bunch_num</span> <span class="o">==</span> <span class="bp">self</span><span class="o">.</span><span class="n">bunch_number</span><span class="p">:</span>
+                    <span class="n">save</span> <span class="o">=</span> <span class="kc">True</span>
+                <span class="k">else</span><span class="p">:</span>
+                    <span class="n">save</span> <span class="o">=</span> <span class="kc">False</span>
+            <span class="k">else</span><span class="p">:</span>
+                <span class="k">raise</span> <span class="ne">NotImplementedError</span><span class="p">(</span><span class="s2">&quot;WakePotentialMonitor for Beam &quot;</span> <span class="o">+</span>
+                                          <span class="s2">&quot;objects is only available &quot;</span> <span class="o">+</span>
+                                          <span class="s2">&quot;with MPI mode.&quot;</span><span class="p">)</span>
+        <span class="k">elif</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">object_to_save</span><span class="p">,</span> <span class="n">Bunch</span><span class="p">):</span>
+            <span class="n">save</span> <span class="o">=</span> <span class="kc">True</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s2">&quot;object_to_save should be a Beam or Bunch object.&quot;</span><span class="p">)</span>
+
+        <span class="k">if</span> <span class="n">save</span> <span class="ow">and</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">track_count</span> <span class="o">%</span> <span class="bp">self</span><span class="o">.</span><span class="n">save_every</span> <span class="o">==</span> <span class="mi">0</span><span class="p">):</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">to_buffer</span><span class="p">(</span><span class="n">wake_potential_to_save</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">track_count</span> <span class="o">+=</span> <span class="mi">1</span></div></div>
+
+
+<div class="viewcode-block" id="BunchSpectrumMonitor"><a class="viewcode-back" href="../../../../mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.monitors.BunchSpectrumMonitor">[docs]</a><span class="k">class</span> <span class="nc">BunchSpectrumMonitor</span><span class="p">(</span><span class="n">Monitor</span><span class="p">):</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    Monitor the coherent and incoherent bunch spectrums. </span>
+<span class="sd">    </span>
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">    ring : Synchrotron object</span>
+<span class="sd">    bunch_number : int</span>
+<span class="sd">        Bunch to monitor</span>
+<span class="sd">    mp_number : int or float</span>
+<span class="sd">        Total number of macro-particles in the bunch.</span>
+<span class="sd">    sample_size : int or float</span>
+<span class="sd">        Number of macro-particles to be used for tune and FFT computation.</span>
+<span class="sd">        This number cannot exceed mp_number.  </span>
+<span class="sd">    save_every : int or float</span>
+<span class="sd">        Set the frequency of the save. The spectrums are computed every </span>
+<span class="sd">        save_every call of the montior.</span>
+<span class="sd">    buffer_size : int or float</span>
+<span class="sd">        Size of the save buffer.</span>
+<span class="sd">    total_size : int or float</span>
+<span class="sd">        Total size of the save. The following relationships between the </span>
+<span class="sd">        parameters must exist: </span>
+<span class="sd">            total_size % buffer_size == 0</span>
+<span class="sd">            number of call to track / save_every == total_size - 1 </span>
+<span class="sd">    dim : str, optional</span>
+<span class="sd">        Dimensions in which the spectrums have to be computed.</span>
+<span class="sd">        Can be:</span>
+<span class="sd">                - &quot;all&quot;</span>
+<span class="sd">                - &quot;tau&quot;</span>
+<span class="sd">                - &quot;x&quot;</span>
+<span class="sd">                - &quot;y&quot;</span>
+<span class="sd">                - &quot;xy&quot; or &quot;yx&quot;</span>
+<span class="sd">                - &quot;xtau&quot; or &quot;taux&quot;</span>
+<span class="sd">                - &quot;ytau&quot; or &quot;tauy&quot;</span>
+<span class="sd">    n_fft : int or float, optional</span>
+<span class="sd">        The number of points used for FFT computation, if n_fft is bigger than</span>
+<span class="sd">        save_every zero-padding is applied.</span>
+<span class="sd">        If None, save_every is used.</span>
+<span class="sd">    file_name : string, optional</span>
+<span class="sd">        Name of the HDF5 where the data will be stored. Must be specified</span>
+<span class="sd">        the first time a subclass of Monitor is instancied and must be None</span>
+<span class="sd">        the following times.</span>
+<span class="sd">    mpi_mode : bool, optional</span>
+<span class="sd">        If True, open the HDF5 file in parallel mode, which is needed to</span>
+<span class="sd">        allow several cores to write in the same file at the same time.</span>
+<span class="sd">        If False, open the HDF5 file in standard mode.</span>
+<span class="sd">        </span>
+<span class="sd">    Attributes</span>
+<span class="sd">    ----------</span>
+<span class="sd">    fft_resolution : float</span>
+<span class="sd">        Return the fft resolution in [Hz].</span>
+<span class="sd">    signal_resolution : float</span>
+<span class="sd">        Return the signal resolution in [Hz].</span>
+<span class="sd">    frequency_samples : array of float</span>
+<span class="sd">        Return the fft frequency samples in [Hz].        </span>
+<span class="sd">        </span>
+<span class="sd">    Methods</span>
+<span class="sd">    -------</span>
+<span class="sd">    track(bunch):</span>
+<span class="sd">        Save spectrum data.</span>
+<span class="sd">    </span>
+<span class="sd">    &quot;&quot;&quot;</span>
+
+    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span>
+                 <span class="n">ring</span><span class="p">,</span>
+                 <span class="n">bunch_number</span><span class="p">,</span>
+                 <span class="n">mp_number</span><span class="p">,</span>
+                 <span class="n">sample_size</span><span class="p">,</span>
+                 <span class="n">save_every</span><span class="p">,</span>
+                 <span class="n">buffer_size</span><span class="p">,</span>
+                 <span class="n">total_size</span><span class="p">,</span>
+                 <span class="n">dim</span><span class="o">=</span><span class="s2">&quot;all&quot;</span><span class="p">,</span>
+                 <span class="n">n_fft</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+                 <span class="n">file_name</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+                 <span class="n">mpi_mode</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
+
+        <span class="k">if</span> <span class="n">n_fft</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">n_fft</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">save_every</span><span class="p">)</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">n_fft</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">n_fft</span><span class="p">)</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">sample_size</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">sample_size</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">store_dict</span> <span class="o">=</span> <span class="p">{</span><span class="s2">&quot;x&quot;</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="s2">&quot;y&quot;</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span> <span class="s2">&quot;tau&quot;</span><span class="p">:</span> <span class="mi">2</span><span class="p">}</span>
+
+        <span class="k">if</span> <span class="n">dim</span> <span class="o">==</span> <span class="s2">&quot;all&quot;</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">track_dict</span> <span class="o">=</span> <span class="p">{</span><span class="s2">&quot;x&quot;</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="s2">&quot;y&quot;</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span> <span class="s2">&quot;tau&quot;</span><span class="p">:</span> <span class="mi">2</span><span class="p">}</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">mean_index</span> <span class="o">=</span> <span class="p">[</span><span class="kc">True</span><span class="p">,</span> <span class="kc">False</span><span class="p">,</span> <span class="kc">True</span><span class="p">,</span> <span class="kc">False</span><span class="p">,</span> <span class="kc">True</span><span class="p">,</span> <span class="kc">False</span><span class="p">]</span>
+        <span class="k">elif</span> <span class="n">dim</span> <span class="o">==</span> <span class="s2">&quot;tau&quot;</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">track_dict</span> <span class="o">=</span> <span class="p">{</span><span class="s2">&quot;tau&quot;</span><span class="p">:</span> <span class="mi">0</span><span class="p">}</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">mean_index</span> <span class="o">=</span> <span class="p">[</span><span class="kc">False</span><span class="p">,</span> <span class="kc">False</span><span class="p">,</span> <span class="kc">False</span><span class="p">,</span> <span class="kc">False</span><span class="p">,</span> <span class="kc">True</span><span class="p">,</span> <span class="kc">False</span><span class="p">]</span>
+        <span class="k">elif</span> <span class="n">dim</span> <span class="o">==</span> <span class="s2">&quot;x&quot;</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">track_dict</span> <span class="o">=</span> <span class="p">{</span><span class="s2">&quot;x&quot;</span><span class="p">:</span> <span class="mi">0</span><span class="p">}</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">mean_index</span> <span class="o">=</span> <span class="p">[</span><span class="kc">True</span><span class="p">,</span> <span class="kc">False</span><span class="p">,</span> <span class="kc">False</span><span class="p">,</span> <span class="kc">False</span><span class="p">,</span> <span class="kc">False</span><span class="p">,</span> <span class="kc">False</span><span class="p">]</span>
+        <span class="k">elif</span> <span class="n">dim</span> <span class="o">==</span> <span class="s2">&quot;y&quot;</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">track_dict</span> <span class="o">=</span> <span class="p">{</span><span class="s2">&quot;y&quot;</span><span class="p">:</span> <span class="mi">0</span><span class="p">}</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">mean_index</span> <span class="o">=</span> <span class="p">[</span><span class="kc">False</span><span class="p">,</span> <span class="kc">False</span><span class="p">,</span> <span class="kc">True</span><span class="p">,</span> <span class="kc">False</span><span class="p">,</span> <span class="kc">False</span><span class="p">,</span> <span class="kc">False</span><span class="p">]</span>
+        <span class="k">elif</span> <span class="n">dim</span> <span class="o">==</span> <span class="s2">&quot;xy&quot;</span> <span class="ow">or</span> <span class="n">dim</span> <span class="o">==</span> <span class="s2">&quot;yx&quot;</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">track_dict</span> <span class="o">=</span> <span class="p">{</span><span class="s2">&quot;x&quot;</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="s2">&quot;y&quot;</span><span class="p">:</span> <span class="mi">1</span><span class="p">}</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">mean_index</span> <span class="o">=</span> <span class="p">[</span><span class="kc">True</span><span class="p">,</span> <span class="kc">False</span><span class="p">,</span> <span class="kc">True</span><span class="p">,</span> <span class="kc">False</span><span class="p">,</span> <span class="kc">False</span><span class="p">,</span> <span class="kc">False</span><span class="p">]</span>
+        <span class="k">elif</span> <span class="n">dim</span> <span class="o">==</span> <span class="s2">&quot;xtau&quot;</span> <span class="ow">or</span> <span class="n">dim</span> <span class="o">==</span> <span class="s2">&quot;taux&quot;</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">track_dict</span> <span class="o">=</span> <span class="p">{</span><span class="s2">&quot;x&quot;</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="s2">&quot;tau&quot;</span><span class="p">:</span> <span class="mi">1</span><span class="p">}</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">mean_index</span> <span class="o">=</span> <span class="p">[</span><span class="kc">True</span><span class="p">,</span> <span class="kc">False</span><span class="p">,</span> <span class="kc">False</span><span class="p">,</span> <span class="kc">False</span><span class="p">,</span> <span class="kc">True</span><span class="p">,</span> <span class="kc">False</span><span class="p">]</span>
+        <span class="k">elif</span> <span class="n">dim</span> <span class="o">==</span> <span class="s2">&quot;ytau&quot;</span> <span class="ow">or</span> <span class="n">dim</span> <span class="o">==</span> <span class="s2">&quot;tauy&quot;</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">track_dict</span> <span class="o">=</span> <span class="p">{</span><span class="s2">&quot;y&quot;</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="s2">&quot;tau&quot;</span><span class="p">:</span> <span class="mi">1</span><span class="p">}</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">mean_index</span> <span class="o">=</span> <span class="p">[</span><span class="kc">False</span><span class="p">,</span> <span class="kc">False</span><span class="p">,</span> <span class="kc">True</span><span class="p">,</span> <span class="kc">False</span><span class="p">,</span> <span class="kc">True</span><span class="p">,</span> <span class="kc">False</span><span class="p">]</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">&quot;dim is not correct.&quot;</span><span class="p">)</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">size_list</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">track_dict</span><span class="p">)</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">ring</span> <span class="o">=</span> <span class="n">ring</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">bunch_number</span> <span class="o">=</span> <span class="n">bunch_number</span>
+        <span class="n">group_name</span> <span class="o">=</span> <span class="s2">&quot;BunchSpectrum_&quot;</span> <span class="o">+</span> <span class="nb">str</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">bunch_number</span><span class="p">)</span>
+
+        <span class="n">dict_buffer</span> <span class="o">=</span> <span class="p">{</span>
+            <span class="s2">&quot;incoherent&quot;</span><span class="p">:</span> <span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">n_fft</span> <span class="o">//</span> <span class="mi">2</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span> <span class="n">buffer_size</span><span class="p">),</span>
+            <span class="s2">&quot;coherent&quot;</span><span class="p">:</span> <span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">n_fft</span> <span class="o">//</span> <span class="mi">2</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span> <span class="n">buffer_size</span><span class="p">),</span>
+            <span class="s2">&quot;mean_incoherent&quot;</span><span class="p">:</span> <span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="n">buffer_size</span><span class="p">),</span>
+            <span class="s2">&quot;std_incoherent&quot;</span><span class="p">:</span> <span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="n">buffer_size</span><span class="p">)</span>
+        <span class="p">}</span>
+        <span class="n">dict_file</span> <span class="o">=</span> <span class="p">{</span>
+            <span class="s2">&quot;incoherent&quot;</span><span class="p">:</span> <span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">n_fft</span> <span class="o">//</span> <span class="mi">2</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span> <span class="n">total_size</span><span class="p">),</span>
+            <span class="s2">&quot;coherent&quot;</span><span class="p">:</span> <span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">n_fft</span> <span class="o">//</span> <span class="mi">2</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span> <span class="n">total_size</span><span class="p">),</span>
+            <span class="s2">&quot;mean_incoherent&quot;</span><span class="p">:</span> <span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="n">total_size</span><span class="p">),</span>
+            <span class="s2">&quot;std_incoherent&quot;</span><span class="p">:</span> <span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="n">total_size</span><span class="p">)</span>
+        <span class="p">}</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">monitor_init</span><span class="p">(</span><span class="n">group_name</span><span class="p">,</span> <span class="n">save_every</span><span class="p">,</span> <span class="n">buffer_size</span><span class="p">,</span> <span class="n">total_size</span><span class="p">,</span>
+                          <span class="n">dict_buffer</span><span class="p">,</span> <span class="n">dict_file</span><span class="p">,</span> <span class="n">file_name</span><span class="p">,</span> <span class="n">mpi_mode</span><span class="p">)</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">dict_buffer</span> <span class="o">=</span> <span class="n">dict_buffer</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">dict_file</span> <span class="o">=</span> <span class="n">dict_file</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">save_count</span> <span class="o">=</span> <span class="mi">0</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">positions</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span>
+            <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">size_list</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">sample_size</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">save_every</span> <span class="o">+</span> <span class="mi">1</span><span class="p">))</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">mean</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="bp">self</span><span class="o">.</span><span class="n">size_list</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">save_every</span> <span class="o">+</span> <span class="mi">1</span><span class="p">))</span>
+
+        <span class="n">index</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="nb">int</span><span class="p">(</span><span class="n">mp_number</span><span class="p">))</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">index_sample</span> <span class="o">=</span> <span class="nb">sorted</span><span class="p">(</span><span class="n">random</span><span class="o">.</span><span class="n">sample</span><span class="p">(</span><span class="nb">list</span><span class="p">(</span><span class="n">index</span><span class="p">),</span>
+                                                 <span class="bp">self</span><span class="o">.</span><span class="n">sample_size</span><span class="p">))</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">incoherent</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="mi">3</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">n_fft</span> <span class="o">//</span> <span class="mi">2</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">buffer_size</span><span class="p">))</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">coherent</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="mi">3</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">n_fft</span> <span class="o">//</span> <span class="mi">2</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">buffer_size</span><span class="p">))</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">file</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">group_name</span><span class="p">]</span><span class="o">.</span><span class="n">create_dataset</span><span class="p">(</span><span class="s2">&quot;freq&quot;</span><span class="p">,</span>
+                                                  <span class="n">data</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">frequency_samples</span><span class="p">)</span>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">fft_resolution</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Return the fft resolution in [Hz].</span>
+<span class="sd">        </span>
+<span class="sd">        It is defined as the sampling frequency over the number of samples.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">f0</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">n_fft</span>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">signal_resolution</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Return the signal resolution in [Hz].</span>
+<span class="sd">        </span>
+<span class="sd">        It is defined as the inverse of the signal length.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="k">return</span> <span class="mi">1</span> <span class="o">/</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">T0</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">save_every</span><span class="p">)</span>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">frequency_samples</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Return the fft frequency samples in [Hz].</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="k">return</span> <span class="n">rfftfreq</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">n_fft</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">T0</span><span class="p">)</span>
+
+<div class="viewcode-block" id="BunchSpectrumMonitor.track"><a class="viewcode-back" href="../../../../mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.monitors.BunchSpectrumMonitor.track">[docs]</a>    <span class="k">def</span> <span class="nf">track</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">object_to_save</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Save spectrum data.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        object_to_save : Beam or Bunch object</span>
+
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="n">save</span> <span class="o">=</span> <span class="kc">True</span>
+        <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">object_to_save</span><span class="p">,</span> <span class="n">Beam</span><span class="p">):</span>
+            <span class="k">if</span> <span class="p">(</span><span class="n">object_to_save</span><span class="o">.</span><span class="n">mpi_switch</span> <span class="o">==</span> <span class="kc">True</span><span class="p">):</span>
+                <span class="k">if</span> <span class="n">object_to_save</span><span class="o">.</span><span class="n">mpi</span><span class="o">.</span><span class="n">bunch_num</span> <span class="o">==</span> <span class="bp">self</span><span class="o">.</span><span class="n">bunch_number</span><span class="p">:</span>
+                    <span class="n">bunch</span> <span class="o">=</span> <span class="n">object_to_save</span><span class="p">[</span><span class="n">object_to_save</span><span class="o">.</span><span class="n">mpi</span><span class="o">.</span><span class="n">bunch_num</span><span class="p">]</span>
+                <span class="k">else</span><span class="p">:</span>
+                    <span class="n">save</span> <span class="o">=</span> <span class="kc">False</span>
+            <span class="k">else</span><span class="p">:</span>
+                <span class="n">bunch</span> <span class="o">=</span> <span class="n">object_to_save</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">bunch_number</span><span class="p">]</span>
+        <span class="k">elif</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">object_to_save</span><span class="p">,</span> <span class="n">Bunch</span><span class="p">):</span>
+            <span class="n">bunch</span> <span class="o">=</span> <span class="n">object_to_save</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s2">&quot;object_to_save should be a Beam or Bunch object.&quot;</span><span class="p">)</span>
+
+        <span class="k">if</span> <span class="n">save</span><span class="p">:</span>
+            <span class="k">try</span><span class="p">:</span>
+                <span class="k">for</span> <span class="n">key</span><span class="p">,</span> <span class="n">value</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">track_dict</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
+                    <span class="bp">self</span><span class="o">.</span><span class="n">positions</span><span class="p">[</span><span class="n">value</span><span class="p">,</span> <span class="p">:,</span> <span class="bp">self</span><span class="o">.</span><span class="n">save_count</span><span class="p">]</span> <span class="o">=</span> <span class="n">bunch</span><span class="p">[</span><span class="n">key</span><span class="p">][</span>
+                        <span class="bp">self</span><span class="o">.</span><span class="n">index_sample</span><span class="p">]</span>
+            <span class="k">except</span> <span class="ne">IndexError</span><span class="p">:</span>
+                <span class="bp">self</span><span class="o">.</span><span class="n">positions</span><span class="p">[</span><span class="n">value</span><span class="p">,</span> <span class="p">:,</span> <span class="bp">self</span><span class="o">.</span><span class="n">save_count</span><span class="p">]</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">nan</span>
+
+            <span class="bp">self</span><span class="o">.</span><span class="n">mean</span><span class="p">[:,</span> <span class="bp">self</span><span class="o">.</span><span class="n">save_count</span><span class="p">]</span> <span class="o">=</span> <span class="n">bunch</span><span class="o">.</span><span class="n">mean</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">mean_index</span><span class="p">]</span>
+
+            <span class="bp">self</span><span class="o">.</span><span class="n">save_count</span> <span class="o">+=</span> <span class="mi">1</span>
+
+            <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">track_count</span> <span class="o">&gt;</span> <span class="mi">0</span> <span class="ow">and</span> <span class="bp">self</span><span class="o">.</span><span class="n">track_count</span> <span class="o">%</span> <span class="bp">self</span><span class="o">.</span><span class="n">save_every</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
+                <span class="bp">self</span><span class="o">.</span><span class="n">to_buffer</span><span class="p">(</span><span class="n">bunch</span><span class="p">)</span>
+                <span class="bp">self</span><span class="o">.</span><span class="n">save_count</span> <span class="o">=</span> <span class="mi">0</span>
+
+            <span class="bp">self</span><span class="o">.</span><span class="n">track_count</span> <span class="o">+=</span> <span class="mi">1</span></div>
+
+<div class="viewcode-block" id="BunchSpectrumMonitor.to_buffer"><a class="viewcode-back" href="../../../../mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.monitors.BunchSpectrumMonitor.to_buffer">[docs]</a>    <span class="k">def</span> <span class="nf">to_buffer</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">bunch</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        A method to hold saved data before writing it to the output file.</span>
+
+<span class="sd">        &quot;&quot;&quot;</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">time</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">buffer_count</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">track_count</span>
+
+        <span class="k">for</span> <span class="n">key</span><span class="p">,</span> <span class="n">value</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">track_dict</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
+            <span class="n">incoherent</span><span class="p">,</span> <span class="n">mean_incoherent</span><span class="p">,</span> <span class="n">std_incoherent</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">get_incoherent_spectrum</span><span class="p">(</span>
+                <span class="bp">self</span><span class="o">.</span><span class="n">positions</span><span class="p">[</span><span class="n">value</span><span class="p">,</span> <span class="p">:,</span> <span class="p">:])</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">incoherent</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">store_dict</span><span class="p">[</span><span class="n">key</span><span class="p">],</span> <span class="p">:,</span>
+                            <span class="bp">self</span><span class="o">.</span><span class="n">buffer_count</span><span class="p">]</span> <span class="o">=</span> <span class="n">incoherent</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">mean_incoherent</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">store_dict</span><span class="p">[</span><span class="n">key</span><span class="p">],</span>
+                                 <span class="bp">self</span><span class="o">.</span><span class="n">buffer_count</span><span class="p">]</span> <span class="o">=</span> <span class="n">mean_incoherent</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">std_incoherent</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">store_dict</span><span class="p">[</span><span class="n">key</span><span class="p">],</span>
+                                <span class="bp">self</span><span class="o">.</span><span class="n">buffer_count</span><span class="p">]</span> <span class="o">=</span> <span class="n">std_incoherent</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">coherent</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">store_dict</span><span class="p">[</span><span class="n">key</span><span class="p">],</span> <span class="p">:,</span>
+                          <span class="bp">self</span><span class="o">.</span><span class="n">buffer_count</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">get_coherent_spectrum</span><span class="p">(</span>
+                              <span class="bp">self</span><span class="o">.</span><span class="n">mean</span><span class="p">[</span><span class="n">value</span><span class="p">])</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">buffer_count</span> <span class="o">+=</span> <span class="mi">1</span>
+
+        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">buffer_count</span> <span class="o">==</span> <span class="bp">self</span><span class="o">.</span><span class="n">buffer_size</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">write</span><span class="p">()</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">buffer_count</span> <span class="o">=</span> <span class="mi">0</span></div>
+
+<div class="viewcode-block" id="BunchSpectrumMonitor.write"><a class="viewcode-back" href="../../../../mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.monitors.BunchSpectrumMonitor.write">[docs]</a>    <span class="k">def</span> <span class="nf">write</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Write data from buffer to output file.</span>
+
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">file</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">group_name</span><span class="p">][</span><span class="s2">&quot;time&quot;</span><span class="p">][</span><span class="bp">self</span><span class="o">.</span><span class="n">write_count</span> <span class="o">*</span>
+                                           <span class="bp">self</span><span class="o">.</span><span class="n">buffer_size</span><span class="p">:(</span><span class="bp">self</span><span class="o">.</span><span class="n">write_count</span> <span class="o">+</span>
+                                                             <span class="mi">1</span><span class="p">)</span> <span class="o">*</span>
+                                           <span class="bp">self</span><span class="o">.</span><span class="n">buffer_size</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">time</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">file</span><span class="p">[</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">group_name</span><span class="p">][</span><span class="s2">&quot;incoherent&quot;</span><span class="p">][:,</span> <span class="p">:,</span> <span class="bp">self</span><span class="o">.</span><span class="n">write_count</span> <span class="o">*</span>
+                                           <span class="bp">self</span><span class="o">.</span><span class="n">buffer_size</span><span class="p">:(</span><span class="bp">self</span><span class="o">.</span><span class="n">write_count</span> <span class="o">+</span>
+                                                             <span class="mi">1</span><span class="p">)</span> <span class="o">*</span>
+                                           <span class="bp">self</span><span class="o">.</span><span class="n">buffer_size</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">incoherent</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">file</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">group_name</span><span class="p">][</span>
+            <span class="s2">&quot;mean_incoherent&quot;</span><span class="p">][:,</span> <span class="bp">self</span><span class="o">.</span><span class="n">write_count</span> <span class="o">*</span>
+                               <span class="bp">self</span><span class="o">.</span><span class="n">buffer_size</span><span class="p">:(</span><span class="bp">self</span><span class="o">.</span><span class="n">write_count</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span> <span class="o">*</span>
+                               <span class="bp">self</span><span class="o">.</span><span class="n">buffer_size</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">mean_incoherent</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">file</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">group_name</span><span class="p">][</span>
+            <span class="s2">&quot;std_incoherent&quot;</span><span class="p">][:,</span> <span class="bp">self</span><span class="o">.</span><span class="n">write_count</span> <span class="o">*</span>
+                              <span class="bp">self</span><span class="o">.</span><span class="n">buffer_size</span><span class="p">:(</span><span class="bp">self</span><span class="o">.</span><span class="n">write_count</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span> <span class="o">*</span>
+                              <span class="bp">self</span><span class="o">.</span><span class="n">buffer_size</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">std_incoherent</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">file</span><span class="p">[</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">group_name</span><span class="p">][</span><span class="s2">&quot;coherent&quot;</span><span class="p">][:,</span> <span class="p">:,</span> <span class="bp">self</span><span class="o">.</span><span class="n">write_count</span> <span class="o">*</span>
+                                         <span class="bp">self</span><span class="o">.</span><span class="n">buffer_size</span><span class="p">:(</span><span class="bp">self</span><span class="o">.</span><span class="n">write_count</span> <span class="o">+</span>
+                                                           <span class="mi">1</span><span class="p">)</span> <span class="o">*</span>
+                                         <span class="bp">self</span><span class="o">.</span><span class="n">buffer_size</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">coherent</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">file</span><span class="o">.</span><span class="n">flush</span><span class="p">()</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">write_count</span> <span class="o">+=</span> <span class="mi">1</span></div>
+
+<div class="viewcode-block" id="BunchSpectrumMonitor.get_incoherent_spectrum"><a class="viewcode-back" href="../../../../mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.monitors.BunchSpectrumMonitor.get_incoherent_spectrum">[docs]</a>    <span class="k">def</span> <span class="nf">get_incoherent_spectrum</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">positions</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Compute the incoherent spectrum i.e. the average of the absolute value </span>
+<span class="sd">        of the FT of the position of every particule of the bunch. </span>
+
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        incoherent : array</span>
+<span class="sd">            Bunch incoherent spectrum.</span>
+<span class="sd">        mean_incoherent : float</span>
+<span class="sd">            Mean frequency of the maximum of each individual particle spectrum</span>
+<span class="sd">            in [Hz].</span>
+<span class="sd">        std_incoherent : float</span>
+<span class="sd">            Standard deviation of the frequency of the maximum of each </span>
+<span class="sd">            individual particle spectrum in [Hz].</span>
+
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="n">fourier</span> <span class="o">=</span> <span class="n">rfft</span><span class="p">(</span><span class="n">positions</span><span class="p">,</span> <span class="n">n</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">n_fft</span><span class="p">)</span>
+        <span class="n">fourier_abs</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">fourier</span><span class="p">)</span>
+        <span class="n">max_array</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">argmax</span><span class="p">(</span><span class="n">fourier_abs</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
+        <span class="n">freq_array</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">frequency_samples</span><span class="p">[</span><span class="n">max_array</span><span class="p">]</span>
+        <span class="n">mean_incoherent</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">freq_array</span><span class="p">)</span>
+        <span class="n">std_incoherent</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">std</span><span class="p">(</span><span class="n">freq_array</span><span class="p">)</span>
+        <span class="n">incoherent</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">fourier_abs</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
+
+        <span class="k">return</span> <span class="n">incoherent</span><span class="p">,</span> <span class="n">mean_incoherent</span><span class="p">,</span> <span class="n">std_incoherent</span></div>
+
+<div class="viewcode-block" id="BunchSpectrumMonitor.get_coherent_spectrum"><a class="viewcode-back" href="../../../../mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.monitors.BunchSpectrumMonitor.get_coherent_spectrum">[docs]</a>    <span class="k">def</span> <span class="nf">get_coherent_spectrum</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">mean</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Compute the coherent spectrum i.e. the absolute value of the FT of the</span>
+<span class="sd">        mean position of the bunch.</span>
+
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        coherent : array</span>
+<span class="sd">            Bunch coherent spectrum.</span>
+
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="n">coherent</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">rfft</span><span class="p">(</span><span class="n">mean</span><span class="p">,</span> <span class="n">n</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">n_fft</span><span class="p">))</span>
+
+        <span class="k">return</span> <span class="n">coherent</span></div></div>
+
+
+<div class="viewcode-block" id="BeamSpectrumMonitor"><a class="viewcode-back" href="../../../../mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.monitors.BeamSpectrumMonitor">[docs]</a><span class="k">class</span> <span class="nc">BeamSpectrumMonitor</span><span class="p">(</span><span class="n">Monitor</span><span class="p">):</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    Monitor coherent beam spectrum. </span>
+<span class="sd">    </span>
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">    ring : Synchrotron object</span>
+<span class="sd">    save_every : int or float</span>
+<span class="sd">        Set the frequency of the save. The spectrums are computed every </span>
+<span class="sd">        save_every call of the montior.</span>
+<span class="sd">    buffer_size : int or float</span>
+<span class="sd">        Size of the save buffer.</span>
+<span class="sd">    total_size : int or float</span>
+<span class="sd">        Total size of the save. The following relationships between the </span>
+<span class="sd">        parameters must exist: </span>
+<span class="sd">            total_size % buffer_size == 0</span>
+<span class="sd">            number of call to track / save_every == total_size - 1 </span>
+<span class="sd">    dim : str, optional</span>
+<span class="sd">        Dimensions in which the spectrums have to be computed.</span>
+<span class="sd">        Can be:</span>
+<span class="sd">                - &quot;all&quot;</span>
+<span class="sd">                - &quot;tau&quot;</span>
+<span class="sd">                - &quot;x&quot;</span>
+<span class="sd">                - &quot;y&quot;</span>
+<span class="sd">                - &quot;xy&quot; or &quot;yx&quot;</span>
+<span class="sd">                - &quot;xtau&quot; or &quot;taux&quot;</span>
+<span class="sd">                - &quot;ytau&quot; or &quot;tauy&quot;</span>
+<span class="sd">    n_fft : int or float, optional</span>
+<span class="sd">        The number of points used for FFT computation, if n_fft is bigger than</span>
+<span class="sd">        save_every zero-padding is applied.</span>
+<span class="sd">        If None, save_every is used.</span>
+<span class="sd">    file_name : string, optional</span>
+<span class="sd">        Name of the HDF5 where the data will be stored. Must be specified</span>
+<span class="sd">        the first time a subclass of Monitor is instancied and must be None</span>
+<span class="sd">        the following times.</span>
+<span class="sd">    mpi_mode : bool, optional</span>
+<span class="sd">        If True, open the HDF5 file in parallel mode, which is needed to</span>
+<span class="sd">        allow several cores to write in the same file at the same time.</span>
+<span class="sd">        If False, open the HDF5 file in standard mode.</span>
+<span class="sd">        </span>
+<span class="sd">    Attributes</span>
+<span class="sd">    ----------</span>
+<span class="sd">    fft_resolution : float</span>
+<span class="sd">        Return the fft resolution in [Hz].</span>
+<span class="sd">    signal_resolution : float</span>
+<span class="sd">        Return the signal resolution in [Hz].</span>
+<span class="sd">    frequency_samples : array of float</span>
+<span class="sd">        Return the fft frequency samples in [Hz].        </span>
+<span class="sd">        </span>
+<span class="sd">    Methods</span>
+<span class="sd">    -------</span>
+<span class="sd">    track(bunch):</span>
+<span class="sd">        Save spectrum data.</span>
+<span class="sd">    </span>
+<span class="sd">    &quot;&quot;&quot;</span>
+
+    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span>
+                 <span class="n">ring</span><span class="p">,</span>
+                 <span class="n">save_every</span><span class="p">,</span>
+                 <span class="n">buffer_size</span><span class="p">,</span>
+                 <span class="n">total_size</span><span class="p">,</span>
+                 <span class="n">dim</span><span class="o">=</span><span class="s2">&quot;all&quot;</span><span class="p">,</span>
+                 <span class="n">n_fft</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+                 <span class="n">file_name</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+                 <span class="n">mpi_mode</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
+
+        <span class="k">if</span> <span class="n">n_fft</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">n_fft</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">save_every</span><span class="p">)</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">n_fft</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">n_fft</span><span class="p">)</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">store_dict</span> <span class="o">=</span> <span class="p">{</span><span class="s2">&quot;x&quot;</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="s2">&quot;y&quot;</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span> <span class="s2">&quot;tau&quot;</span><span class="p">:</span> <span class="mi">2</span><span class="p">}</span>
+
+        <span class="k">if</span> <span class="n">dim</span> <span class="o">==</span> <span class="s2">&quot;all&quot;</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">track_dict</span> <span class="o">=</span> <span class="p">{</span><span class="s2">&quot;x&quot;</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="s2">&quot;y&quot;</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span> <span class="s2">&quot;tau&quot;</span><span class="p">:</span> <span class="mi">2</span><span class="p">}</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">mean_index</span> <span class="o">=</span> <span class="p">[</span><span class="kc">True</span><span class="p">,</span> <span class="kc">False</span><span class="p">,</span> <span class="kc">True</span><span class="p">,</span> <span class="kc">False</span><span class="p">,</span> <span class="kc">True</span><span class="p">,</span> <span class="kc">False</span><span class="p">]</span>
+        <span class="k">elif</span> <span class="n">dim</span> <span class="o">==</span> <span class="s2">&quot;tau&quot;</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">track_dict</span> <span class="o">=</span> <span class="p">{</span><span class="s2">&quot;tau&quot;</span><span class="p">:</span> <span class="mi">0</span><span class="p">}</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">mean_index</span> <span class="o">=</span> <span class="p">[</span><span class="kc">False</span><span class="p">,</span> <span class="kc">False</span><span class="p">,</span> <span class="kc">False</span><span class="p">,</span> <span class="kc">False</span><span class="p">,</span> <span class="kc">True</span><span class="p">,</span> <span class="kc">False</span><span class="p">]</span>
+        <span class="k">elif</span> <span class="n">dim</span> <span class="o">==</span> <span class="s2">&quot;x&quot;</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">track_dict</span> <span class="o">=</span> <span class="p">{</span><span class="s2">&quot;x&quot;</span><span class="p">:</span> <span class="mi">0</span><span class="p">}</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">mean_index</span> <span class="o">=</span> <span class="p">[</span><span class="kc">True</span><span class="p">,</span> <span class="kc">False</span><span class="p">,</span> <span class="kc">False</span><span class="p">,</span> <span class="kc">False</span><span class="p">,</span> <span class="kc">False</span><span class="p">,</span> <span class="kc">False</span><span class="p">]</span>
+        <span class="k">elif</span> <span class="n">dim</span> <span class="o">==</span> <span class="s2">&quot;y&quot;</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">track_dict</span> <span class="o">=</span> <span class="p">{</span><span class="s2">&quot;y&quot;</span><span class="p">:</span> <span class="mi">0</span><span class="p">}</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">mean_index</span> <span class="o">=</span> <span class="p">[</span><span class="kc">False</span><span class="p">,</span> <span class="kc">False</span><span class="p">,</span> <span class="kc">True</span><span class="p">,</span> <span class="kc">False</span><span class="p">,</span> <span class="kc">False</span><span class="p">,</span> <span class="kc">False</span><span class="p">]</span>
+        <span class="k">elif</span> <span class="n">dim</span> <span class="o">==</span> <span class="s2">&quot;xy&quot;</span> <span class="ow">or</span> <span class="n">dim</span> <span class="o">==</span> <span class="s2">&quot;yx&quot;</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">track_dict</span> <span class="o">=</span> <span class="p">{</span><span class="s2">&quot;x&quot;</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="s2">&quot;y&quot;</span><span class="p">:</span> <span class="mi">1</span><span class="p">}</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">mean_index</span> <span class="o">=</span> <span class="p">[</span><span class="kc">True</span><span class="p">,</span> <span class="kc">False</span><span class="p">,</span> <span class="kc">True</span><span class="p">,</span> <span class="kc">False</span><span class="p">,</span> <span class="kc">False</span><span class="p">,</span> <span class="kc">False</span><span class="p">]</span>
+        <span class="k">elif</span> <span class="n">dim</span> <span class="o">==</span> <span class="s2">&quot;xtau&quot;</span> <span class="ow">or</span> <span class="n">dim</span> <span class="o">==</span> <span class="s2">&quot;taux&quot;</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">track_dict</span> <span class="o">=</span> <span class="p">{</span><span class="s2">&quot;x&quot;</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="s2">&quot;tau&quot;</span><span class="p">:</span> <span class="mi">1</span><span class="p">}</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">mean_index</span> <span class="o">=</span> <span class="p">[</span><span class="kc">True</span><span class="p">,</span> <span class="kc">False</span><span class="p">,</span> <span class="kc">False</span><span class="p">,</span> <span class="kc">False</span><span class="p">,</span> <span class="kc">True</span><span class="p">,</span> <span class="kc">False</span><span class="p">]</span>
+        <span class="k">elif</span> <span class="n">dim</span> <span class="o">==</span> <span class="s2">&quot;ytau&quot;</span> <span class="ow">or</span> <span class="n">dim</span> <span class="o">==</span> <span class="s2">&quot;tauy&quot;</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">track_dict</span> <span class="o">=</span> <span class="p">{</span><span class="s2">&quot;y&quot;</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="s2">&quot;tau&quot;</span><span class="p">:</span> <span class="mi">1</span><span class="p">}</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">mean_index</span> <span class="o">=</span> <span class="p">[</span><span class="kc">False</span><span class="p">,</span> <span class="kc">False</span><span class="p">,</span> <span class="kc">True</span><span class="p">,</span> <span class="kc">False</span><span class="p">,</span> <span class="kc">True</span><span class="p">,</span> <span class="kc">False</span><span class="p">]</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">&quot;dim is not correct.&quot;</span><span class="p">)</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">size_list</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">track_dict</span><span class="p">)</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">ring</span> <span class="o">=</span> <span class="n">ring</span>
+        <span class="n">group_name</span> <span class="o">=</span> <span class="s2">&quot;BeamSpectrum&quot;</span>
+
+        <span class="n">dict_buffer</span> <span class="o">=</span> <span class="p">{</span><span class="s2">&quot;coherent&quot;</span><span class="p">:</span> <span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">n_fft</span> <span class="o">//</span> <span class="mi">2</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span> <span class="n">buffer_size</span><span class="p">)}</span>
+        <span class="n">dict_file</span> <span class="o">=</span> <span class="p">{</span><span class="s2">&quot;coherent&quot;</span><span class="p">:</span> <span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">n_fft</span> <span class="o">//</span> <span class="mi">2</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span> <span class="n">total_size</span><span class="p">)}</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">monitor_init</span><span class="p">(</span><span class="n">group_name</span><span class="p">,</span> <span class="n">save_every</span><span class="p">,</span> <span class="n">buffer_size</span><span class="p">,</span> <span class="n">total_size</span><span class="p">,</span>
+                          <span class="n">dict_buffer</span><span class="p">,</span> <span class="n">dict_file</span><span class="p">,</span> <span class="n">file_name</span><span class="p">,</span> <span class="n">mpi_mode</span><span class="p">)</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">dict_buffer</span> <span class="o">=</span> <span class="n">dict_buffer</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">dict_file</span> <span class="o">=</span> <span class="n">dict_file</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">save_count</span> <span class="o">=</span> <span class="mi">0</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">mean</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="bp">self</span><span class="o">.</span><span class="n">size_list</span><span class="p">,</span> <span class="n">ring</span><span class="o">.</span><span class="n">h</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">save_every</span><span class="p">))</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">coherent</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="mi">3</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">n_fft</span> <span class="o">//</span> <span class="mi">2</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">buffer_size</span><span class="p">))</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">file</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">group_name</span><span class="p">]</span><span class="o">.</span><span class="n">create_dataset</span><span class="p">(</span><span class="s2">&quot;freq&quot;</span><span class="p">,</span>
+                                                  <span class="n">data</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">frequency_samples</span><span class="p">)</span>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">fft_resolution</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Return the fft resolution in [Hz].</span>
+<span class="sd">        </span>
+<span class="sd">        It is defined as the sampling frequency over the number of samples.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">f1</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">n_fft</span>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">signal_resolution</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Return the signal resolution in [Hz].</span>
+<span class="sd">        </span>
+<span class="sd">        It is defined as the inverse of the signal length.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="k">return</span> <span class="mi">1</span> <span class="o">/</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">T0</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">save_every</span><span class="p">)</span>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">frequency_samples</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Return the fft frequency samples in [Hz].</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="k">return</span> <span class="n">rfftfreq</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">n_fft</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">T1</span><span class="p">)</span>
+
+<div class="viewcode-block" id="BeamSpectrumMonitor.track"><a class="viewcode-back" href="../../../../mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.monitors.BeamSpectrumMonitor.track">[docs]</a>    <span class="k">def</span> <span class="nf">track</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">beam</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Save mean data.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        beam : Beam object</span>
+
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="k">if</span> <span class="p">(</span><span class="n">beam</span><span class="o">.</span><span class="n">mpi_switch</span> <span class="o">==</span> <span class="kc">True</span><span class="p">):</span>
+            <span class="n">bunch_num</span> <span class="o">=</span> <span class="n">beam</span><span class="o">.</span><span class="n">mpi</span><span class="o">.</span><span class="n">bunch_num</span>
+            <span class="n">bunch</span> <span class="o">=</span> <span class="n">beam</span><span class="p">[</span><span class="n">bunch_num</span><span class="p">]</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">mean</span><span class="p">[:,</span> <span class="n">bunch_num</span><span class="p">,</span>
+                      <span class="bp">self</span><span class="o">.</span><span class="n">save_count</span><span class="p">]</span> <span class="o">=</span> <span class="n">bunch</span><span class="o">.</span><span class="n">mean</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">mean_index</span><span class="p">]</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">mean</span><span class="p">[:,</span> <span class="p">:,</span>
+                      <span class="bp">self</span><span class="o">.</span><span class="n">save_count</span><span class="p">]</span> <span class="o">=</span> <span class="n">beam</span><span class="o">.</span><span class="n">bunch_mean</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">mean_index</span><span class="p">,</span> <span class="p">:]</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">save_count</span> <span class="o">+=</span> <span class="mi">1</span>
+
+        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">save_count</span> <span class="o">==</span> <span class="bp">self</span><span class="o">.</span><span class="n">save_every</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">to_buffer</span><span class="p">(</span><span class="n">beam</span><span class="p">)</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">save_count</span> <span class="o">=</span> <span class="mi">0</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">track_count</span> <span class="o">+=</span> <span class="mi">1</span></div>
+
+<div class="viewcode-block" id="BeamSpectrumMonitor.to_buffer"><a class="viewcode-back" href="../../../../mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.monitors.BeamSpectrumMonitor.to_buffer">[docs]</a>    <span class="k">def</span> <span class="nf">to_buffer</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">beam</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        A method to hold saved data before writing it to the output file.</span>
+
+<span class="sd">        &quot;&quot;&quot;</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">time</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">buffer_count</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">track_count</span>
+
+        <span class="k">for</span> <span class="n">key</span><span class="p">,</span> <span class="n">value</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">track_dict</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
+            <span class="k">if</span> <span class="p">(</span><span class="n">beam</span><span class="o">.</span><span class="n">mpi_switch</span> <span class="o">==</span> <span class="kc">True</span><span class="p">):</span>
+                <span class="n">data_core</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">mean</span><span class="p">[</span><span class="n">value</span><span class="p">,</span> <span class="n">beam</span><span class="o">.</span><span class="n">mpi</span><span class="o">.</span><span class="n">bunch_num</span><span class="p">,</span> <span class="p">:]</span>
+                <span class="n">full_data</span> <span class="o">=</span> <span class="n">beam</span><span class="o">.</span><span class="n">mpi</span><span class="o">.</span><span class="n">comm</span><span class="o">.</span><span class="n">allgather</span><span class="p">(</span><span class="n">data_core</span><span class="p">)</span>
+                <span class="n">data</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">full_data</span><span class="p">,</span> <span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">),</span> <span class="s1">&#39;F&#39;</span><span class="p">)</span>
+            <span class="k">else</span><span class="p">:</span>
+                <span class="n">data</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">mean</span><span class="p">[</span><span class="n">value</span><span class="p">,</span> <span class="p">:,</span> <span class="p">:],</span> <span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">),</span> <span class="s1">&#39;F&#39;</span><span class="p">)</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">coherent</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">store_dict</span><span class="p">[</span><span class="n">key</span><span class="p">],</span> <span class="p">:,</span>
+                          <span class="bp">self</span><span class="o">.</span><span class="n">buffer_count</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">get_beam_spectrum</span><span class="p">(</span><span class="n">data</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">buffer_count</span> <span class="o">+=</span> <span class="mi">1</span>
+
+        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">buffer_count</span> <span class="o">==</span> <span class="bp">self</span><span class="o">.</span><span class="n">buffer_size</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">write</span><span class="p">()</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">buffer_count</span> <span class="o">=</span> <span class="mi">0</span></div>
+
+<div class="viewcode-block" id="BeamSpectrumMonitor.write"><a class="viewcode-back" href="../../../../mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.monitors.BeamSpectrumMonitor.write">[docs]</a>    <span class="k">def</span> <span class="nf">write</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Write data from buffer to output file.</span>
+
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">file</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">group_name</span><span class="p">][</span><span class="s2">&quot;time&quot;</span><span class="p">][</span><span class="bp">self</span><span class="o">.</span><span class="n">write_count</span> <span class="o">*</span>
+                                           <span class="bp">self</span><span class="o">.</span><span class="n">buffer_size</span><span class="p">:(</span><span class="bp">self</span><span class="o">.</span><span class="n">write_count</span> <span class="o">+</span>
+                                                             <span class="mi">1</span><span class="p">)</span> <span class="o">*</span>
+                                           <span class="bp">self</span><span class="o">.</span><span class="n">buffer_size</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">time</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">file</span><span class="p">[</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">group_name</span><span class="p">][</span><span class="s2">&quot;coherent&quot;</span><span class="p">][:,</span> <span class="p">:,</span> <span class="bp">self</span><span class="o">.</span><span class="n">write_count</span> <span class="o">*</span>
+                                         <span class="bp">self</span><span class="o">.</span><span class="n">buffer_size</span><span class="p">:(</span><span class="bp">self</span><span class="o">.</span><span class="n">write_count</span> <span class="o">+</span>
+                                                           <span class="mi">1</span><span class="p">)</span> <span class="o">*</span>
+                                         <span class="bp">self</span><span class="o">.</span><span class="n">buffer_size</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">coherent</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">file</span><span class="o">.</span><span class="n">flush</span><span class="p">()</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">write_count</span> <span class="o">+=</span> <span class="mi">1</span></div>
+
+<div class="viewcode-block" id="BeamSpectrumMonitor.get_beam_spectrum"><a class="viewcode-back" href="../../../../mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.monitors.BeamSpectrumMonitor.get_beam_spectrum">[docs]</a>    <span class="k">def</span> <span class="nf">get_beam_spectrum</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">mean</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Compute the beam coherent spectrum i.e. the absolute value of the FT </span>
+<span class="sd">        of the mean position of every bunch.</span>
+
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        coherent : array</span>
+<span class="sd">            The beam coherent spectrum.</span>
+
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="n">coherent</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">rfft</span><span class="p">(</span><span class="n">mean</span><span class="p">,</span> <span class="n">n</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">n_fft</span><span class="p">))</span>
+
+        <span class="k">return</span> <span class="n">coherent</span></div></div>
+
+
+<div class="viewcode-block" id="CavityMonitor"><a class="viewcode-back" href="../../../../mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.monitors.CavityMonitor">[docs]</a><span class="k">class</span> <span class="nc">CavityMonitor</span><span class="p">(</span><span class="n">Monitor</span><span class="p">):</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    Monitor a CavityResonator object and save attributes.</span>
+<span class="sd">    </span>
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">    cavity_name : str</span>
+<span class="sd">        Name of the CavityResonator object to monitor.</span>
+<span class="sd">    ring : Synchrotron object</span>
+<span class="sd">    save_every : int or float</span>
+<span class="sd">        Set the frequency of the save. The data is saved every save_every </span>
+<span class="sd">        call of the montior.</span>
+<span class="sd">    buffer_size : int or float</span>
+<span class="sd">        Size of the save buffer.</span>
+<span class="sd">    total_size : int or float</span>
+<span class="sd">        Total size of the save. The following relationships between the </span>
+<span class="sd">        parameters must exist: </span>
+<span class="sd">            total_size % buffer_size == 0</span>
+<span class="sd">            number of call to track / save_every == total_size</span>
+<span class="sd">    file_name : string, optional</span>
+<span class="sd">        Name of the HDF5 where the data will be stored. Must be specified</span>
+<span class="sd">        the first time a subclass of Monitor is instancied and must be None</span>
+<span class="sd">        the following times.</span>
+<span class="sd">    mpi_mode : bool, optional</span>
+<span class="sd">        If True, open the HDF5 file in parallel mode, which is needed to</span>
+<span class="sd">        allow several cores to write in the same file at the same time.</span>
+<span class="sd">        If False, open the HDF5 file in standard mode.</span>
+
+<span class="sd">    Methods</span>
+<span class="sd">    -------</span>
+<span class="sd">    track(beam, cavity)</span>
+<span class="sd">        Save data</span>
+<span class="sd">    &quot;&quot;&quot;</span>
+
+    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span>
+                 <span class="n">cavity_name</span><span class="p">,</span>
+                 <span class="n">ring</span><span class="p">,</span>
+                 <span class="n">save_every</span><span class="p">,</span>
+                 <span class="n">buffer_size</span><span class="p">,</span>
+                 <span class="n">total_size</span><span class="p">,</span>
+                 <span class="n">file_name</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+                 <span class="n">mpi_mode</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">cavity_name</span> <span class="o">=</span> <span class="n">cavity_name</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">ring</span> <span class="o">=</span> <span class="n">ring</span>
+
+        <span class="n">group_name</span> <span class="o">=</span> <span class="n">cavity_name</span>
+        <span class="n">dict_buffer</span> <span class="o">=</span> <span class="p">{</span>
+            <span class="s2">&quot;cavity_phasor_record&quot;</span><span class="p">:</span> <span class="p">(</span>
+                <span class="n">ring</span><span class="o">.</span><span class="n">h</span><span class="p">,</span>
+                <span class="n">buffer_size</span><span class="p">,</span>
+            <span class="p">),</span>
+            <span class="s2">&quot;beam_phasor_record&quot;</span><span class="p">:</span> <span class="p">(</span>
+                <span class="n">ring</span><span class="o">.</span><span class="n">h</span><span class="p">,</span>
+                <span class="n">buffer_size</span><span class="p">,</span>
+            <span class="p">),</span>
+            <span class="s2">&quot;generator_phasor_record&quot;</span><span class="p">:</span> <span class="p">(</span>
+                <span class="n">ring</span><span class="o">.</span><span class="n">h</span><span class="p">,</span>
+                <span class="n">buffer_size</span><span class="p">,</span>
+            <span class="p">),</span>
+            <span class="s2">&quot;ig_phasor_record&quot;</span><span class="p">:</span> <span class="p">(</span>
+                <span class="n">ring</span><span class="o">.</span><span class="n">h</span><span class="p">,</span>
+                <span class="n">buffer_size</span><span class="p">,</span>
+            <span class="p">),</span>
+            <span class="s2">&quot;DFB_ig_phasor&quot;</span><span class="p">:</span> <span class="p">(</span>
+                <span class="n">ring</span><span class="o">.</span><span class="n">h</span><span class="p">,</span>
+                <span class="n">buffer_size</span><span class="p">,</span>
+            <span class="p">),</span>
+            <span class="s2">&quot;detune&quot;</span><span class="p">:</span> <span class="p">(</span><span class="n">buffer_size</span><span class="p">,</span> <span class="p">),</span>
+            <span class="s2">&quot;psi&quot;</span><span class="p">:</span> <span class="p">(</span><span class="n">buffer_size</span><span class="p">,</span> <span class="p">),</span>
+            <span class="s2">&quot;Vg&quot;</span><span class="p">:</span> <span class="p">(</span><span class="n">buffer_size</span><span class="p">,</span> <span class="p">),</span>
+            <span class="s2">&quot;theta_g&quot;</span><span class="p">:</span> <span class="p">(</span><span class="n">buffer_size</span><span class="p">,</span> <span class="p">),</span>
+            <span class="s2">&quot;Pg&quot;</span><span class="p">:</span> <span class="p">(</span><span class="n">buffer_size</span><span class="p">,</span> <span class="p">),</span>
+            <span class="s2">&quot;Rs&quot;</span><span class="p">:</span> <span class="p">(</span><span class="n">buffer_size</span><span class="p">,</span> <span class="p">),</span>
+            <span class="s2">&quot;Q&quot;</span><span class="p">:</span> <span class="p">(</span><span class="n">buffer_size</span><span class="p">,</span> <span class="p">),</span>
+            <span class="s2">&quot;QL&quot;</span><span class="p">:</span> <span class="p">(</span><span class="n">buffer_size</span><span class="p">,</span> <span class="p">),</span>
+            <span class="s2">&quot;Vc&quot;</span><span class="p">:</span> <span class="p">(</span><span class="n">buffer_size</span><span class="p">,</span> <span class="p">),</span>
+            <span class="s2">&quot;theta&quot;</span><span class="p">:</span> <span class="p">(</span><span class="n">buffer_size</span><span class="p">,</span> <span class="p">),</span>
+        <span class="p">}</span>
+        <span class="n">dict_file</span> <span class="o">=</span> <span class="p">{</span>
+            <span class="s2">&quot;cavity_phasor_record&quot;</span><span class="p">:</span> <span class="p">(</span>
+                <span class="n">ring</span><span class="o">.</span><span class="n">h</span><span class="p">,</span>
+                <span class="n">total_size</span><span class="p">,</span>
+            <span class="p">),</span>
+            <span class="s2">&quot;beam_phasor_record&quot;</span><span class="p">:</span> <span class="p">(</span>
+                <span class="n">ring</span><span class="o">.</span><span class="n">h</span><span class="p">,</span>
+                <span class="n">total_size</span><span class="p">,</span>
+            <span class="p">),</span>
+            <span class="s2">&quot;generator_phasor_record&quot;</span><span class="p">:</span> <span class="p">(</span>
+                <span class="n">ring</span><span class="o">.</span><span class="n">h</span><span class="p">,</span>
+                <span class="n">total_size</span><span class="p">,</span>
+            <span class="p">),</span>
+            <span class="s2">&quot;ig_phasor_record&quot;</span><span class="p">:</span> <span class="p">(</span>
+                <span class="n">ring</span><span class="o">.</span><span class="n">h</span><span class="p">,</span>
+                <span class="n">total_size</span><span class="p">,</span>
+            <span class="p">),</span>
+            <span class="s2">&quot;DFB_ig_phasor&quot;</span><span class="p">:</span> <span class="p">(</span>
+                <span class="n">ring</span><span class="o">.</span><span class="n">h</span><span class="p">,</span>
+                <span class="n">total_size</span><span class="p">,</span>
+            <span class="p">),</span>
+            <span class="s2">&quot;detune&quot;</span><span class="p">:</span> <span class="p">(</span><span class="n">total_size</span><span class="p">,</span> <span class="p">),</span>
+            <span class="s2">&quot;psi&quot;</span><span class="p">:</span> <span class="p">(</span><span class="n">total_size</span><span class="p">,</span> <span class="p">),</span>
+            <span class="s2">&quot;Vg&quot;</span><span class="p">:</span> <span class="p">(</span><span class="n">total_size</span><span class="p">,</span> <span class="p">),</span>
+            <span class="s2">&quot;theta_g&quot;</span><span class="p">:</span> <span class="p">(</span><span class="n">total_size</span><span class="p">,</span> <span class="p">),</span>
+            <span class="s2">&quot;Pg&quot;</span><span class="p">:</span> <span class="p">(</span><span class="n">total_size</span><span class="p">,</span> <span class="p">),</span>
+            <span class="s2">&quot;Rs&quot;</span><span class="p">:</span> <span class="p">(</span><span class="n">total_size</span><span class="p">,</span> <span class="p">),</span>
+            <span class="s2">&quot;Q&quot;</span><span class="p">:</span> <span class="p">(</span><span class="n">total_size</span><span class="p">,</span> <span class="p">),</span>
+            <span class="s2">&quot;QL&quot;</span><span class="p">:</span> <span class="p">(</span><span class="n">total_size</span><span class="p">,</span> <span class="p">),</span>
+            <span class="s2">&quot;Vc&quot;</span><span class="p">:</span> <span class="p">(</span><span class="n">total_size</span><span class="p">,</span> <span class="p">),</span>
+            <span class="s2">&quot;theta&quot;</span><span class="p">:</span> <span class="p">(</span><span class="n">total_size</span><span class="p">,</span> <span class="p">)</span>
+        <span class="p">}</span>
+        <span class="n">dict_dtype</span> <span class="o">=</span> <span class="p">{</span>
+            <span class="s2">&quot;cavity_phasor_record&quot;</span><span class="p">:</span> <span class="nb">complex</span><span class="p">,</span>
+            <span class="s2">&quot;beam_phasor_record&quot;</span><span class="p">:</span> <span class="nb">complex</span><span class="p">,</span>
+            <span class="s2">&quot;generator_phasor_record&quot;</span><span class="p">:</span> <span class="nb">complex</span><span class="p">,</span>
+            <span class="s2">&quot;ig_phasor_record&quot;</span><span class="p">:</span> <span class="nb">complex</span><span class="p">,</span>
+            <span class="s2">&quot;DFB_ig_phasor&quot;</span><span class="p">:</span> <span class="nb">complex</span><span class="p">,</span>
+            <span class="s2">&quot;detune&quot;</span><span class="p">:</span> <span class="nb">float</span><span class="p">,</span>
+            <span class="s2">&quot;psi&quot;</span><span class="p">:</span> <span class="nb">float</span><span class="p">,</span>
+            <span class="s2">&quot;Vg&quot;</span><span class="p">:</span> <span class="nb">float</span><span class="p">,</span>
+            <span class="s2">&quot;theta_g&quot;</span><span class="p">:</span> <span class="nb">float</span><span class="p">,</span>
+            <span class="s2">&quot;Pg&quot;</span><span class="p">:</span> <span class="nb">float</span><span class="p">,</span>
+            <span class="s2">&quot;Rs&quot;</span><span class="p">:</span> <span class="nb">float</span><span class="p">,</span>
+            <span class="s2">&quot;Q&quot;</span><span class="p">:</span> <span class="nb">float</span><span class="p">,</span>
+            <span class="s2">&quot;QL&quot;</span><span class="p">:</span> <span class="nb">float</span><span class="p">,</span>
+            <span class="s2">&quot;Vc&quot;</span><span class="p">:</span> <span class="nb">float</span><span class="p">,</span>
+            <span class="s2">&quot;theta&quot;</span><span class="p">:</span> <span class="nb">float</span>
+        <span class="p">}</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">monitor_init</span><span class="p">(</span><span class="n">group_name</span><span class="p">,</span> <span class="n">save_every</span><span class="p">,</span> <span class="n">buffer_size</span><span class="p">,</span> <span class="n">total_size</span><span class="p">,</span>
+                          <span class="n">dict_buffer</span><span class="p">,</span> <span class="n">dict_file</span><span class="p">,</span> <span class="n">file_name</span><span class="p">,</span> <span class="n">mpi_mode</span><span class="p">,</span>
+                          <span class="n">dict_dtype</span><span class="p">)</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">dict_buffer</span> <span class="o">=</span> <span class="n">dict_buffer</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">dict_file</span> <span class="o">=</span> <span class="n">dict_file</span>
+
+<div class="viewcode-block" id="CavityMonitor.track"><a class="viewcode-back" href="../../../../mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.monitors.CavityMonitor.track">[docs]</a>    <span class="k">def</span> <span class="nf">track</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">beam</span><span class="p">,</span> <span class="n">cavity</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Save data</span>
+<span class="sd">        </span>
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        beam : Beam object</span>
+<span class="sd">        cavity : CavityResonator object</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">track_count</span> <span class="o">%</span> <span class="bp">self</span><span class="o">.</span><span class="n">save_every</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
+            <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">cavity</span><span class="p">,</span> <span class="n">CavityResonator</span><span class="p">):</span>
+                <span class="k">if</span> <span class="n">beam</span><span class="o">.</span><span class="n">mpi_switch</span> <span class="o">==</span> <span class="kc">False</span><span class="p">:</span>
+                    <span class="bp">self</span><span class="o">.</span><span class="n">to_buffer</span><span class="p">(</span><span class="n">cavity</span><span class="p">)</span>
+                <span class="k">elif</span> <span class="n">beam</span><span class="o">.</span><span class="n">mpi</span><span class="o">.</span><span class="n">rank</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
+                    <span class="bp">self</span><span class="o">.</span><span class="n">to_buffer</span><span class="p">(</span><span class="n">cavity</span><span class="p">)</span>
+                <span class="k">else</span><span class="p">:</span>
+                    <span class="k">pass</span>
+            <span class="k">else</span><span class="p">:</span>
+                <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s2">&quot;cavity should be a CavityResonator object.&quot;</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">track_count</span> <span class="o">+=</span> <span class="mi">1</span></div></div>
+</pre></div>
+
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+             >modules</a> |</li>
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+      Created using <a href="https://www.sphinx-doc.org/">Sphinx</a> 5.0.2.
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diff --git a/docs/build/html/_modules/mbtrack2/tracking/monitors/plotting.html b/docs/build/html/_modules/mbtrack2/tracking/monitors/plotting.html
new file mode 100644
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@@ -0,0 +1,1545 @@
+
+<!DOCTYPE html>
+
+<html lang="en">
+  <head>
+    <meta charset="utf-8" />
+    <meta name="viewport" content="width=device-width, initial-scale=1.0" />
+    <title>mbtrack2.tracking.monitors.plotting &#8212; mbtrack2 0.6.0 documentation</title>
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+             >modules</a> |</li>
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+        <li class="nav-item nav-item-this"><a href="">mbtrack2.tracking.monitors.plotting</a></li> 
+      </ul>
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+
+    <div class="document">
+      <div class="documentwrapper">
+        <div class="bodywrapper">
+          <div class="body" role="main">
+            
+  <h1>Source code for mbtrack2.tracking.monitors.plotting</h1><div class="highlight"><pre>
+<span></span><span class="c1"># -*- coding: utf-8 -*-</span>
+<span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">Module for plotting the data recorded by the monitor module during the </span>
+<span class="sd">tracking.</span>
+<span class="sd">&quot;&quot;&quot;</span>
+
+<span class="kn">import</span> <span class="nn">random</span>
+
+<span class="kn">import</span> <span class="nn">h5py</span> <span class="k">as</span> <span class="nn">hp</span>
+<span class="kn">import</span> <span class="nn">matplotlib</span> <span class="k">as</span> <span class="nn">mpl</span>
+<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
+<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="kn">import</span> <span class="nn">seaborn</span> <span class="k">as</span> <span class="nn">sns</span>
+<span class="kn">from</span> <span class="nn">scipy.stats</span> <span class="kn">import</span> <span class="n">gmean</span>
+
+
+<div class="viewcode-block" id="plot_beamdata"><a class="viewcode-back" href="../../../../mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.plotting.plot_beamdata">[docs]</a><span class="k">def</span> <span class="nf">plot_beamdata</span><span class="p">(</span><span class="n">filenames</span><span class="p">,</span>
+                  <span class="n">dataset</span><span class="o">=</span><span class="s2">&quot;mean&quot;</span><span class="p">,</span>
+                  <span class="n">dimension</span><span class="o">=</span><span class="s2">&quot;tau&quot;</span><span class="p">,</span>
+                  <span class="n">stat_var</span><span class="o">=</span><span class="s2">&quot;mean&quot;</span><span class="p">,</span>
+                  <span class="n">x_var</span><span class="o">=</span><span class="s2">&quot;time&quot;</span><span class="p">,</span>
+                  <span class="n">turn</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+                  <span class="n">legend</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    Plot 2D data recorded by BeamMonitor.</span>
+
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">    filenames : str or list of str</span>
+<span class="sd">        Names of the HDF5 files to be plotted.</span>
+<span class="sd">    dataset : {&quot;current&quot;,&quot;emit&quot;,&quot;mean&quot;,&quot;std&quot;,&quot;cs_invariant&quot;}</span>
+<span class="sd">        HDF5 file&#39;s dataset to be plotted. The default is &quot;mean&quot;.</span>
+<span class="sd">    dimension : str</span>
+<span class="sd">         The dimension of the dataset to plot:</span>
+<span class="sd">            for &quot;emit&quot;, dimension = {&quot;x&quot;,&quot;y&quot;,&quot;s&quot;},</span>
+<span class="sd">            for &quot;cs_invariant&quot;, dimension = {&quot;x&quot;,&quot;y&quot;,&quot;s&quot;},</span>
+<span class="sd">            for &quot;mean&quot; and &quot;std&quot;, dimension = {&quot;x&quot;,&quot;xp&quot;,&quot;y&quot;,&quot;yp&quot;,&quot;tau&quot;,&quot;delta&quot;}.</span>
+<span class="sd">            not used if &quot;current&quot;.</span>
+<span class="sd">        The default is &quot;tau&quot;.</span>
+<span class="sd">    stat_var : {&quot;mean&quot;, &quot;std&quot;}</span>
+<span class="sd">        Statistical value of the dimension.</span>
+<span class="sd">    x_var : {&quot;time&quot;, &quot;index&quot;}</span>
+<span class="sd">        Choice of the horizontal axis:</span>
+<span class="sd">            &quot;time&quot; corresponds to turn number.</span>
+<span class="sd">            &quot;index&quot; corresponds to bunch index.</span>
+<span class="sd">    turn : int or float, optional</span>
+<span class="sd">        Choice of the turn to plot when x_var = &quot;index&quot;.</span>
+<span class="sd">        If None, the last turn is plotted.</span>
+<span class="sd">    legend : list of str, optional</span>
+<span class="sd">        Legend to add for each file.</span>
+
+<span class="sd">    Return</span>
+<span class="sd">    ------</span>
+<span class="sd">    fig : Figure</span>
+<span class="sd">        Figure object with the plot on it.</span>
+
+<span class="sd">    &quot;&quot;&quot;</span>
+
+    <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">filenames</span><span class="p">,</span> <span class="nb">str</span><span class="p">):</span>
+        <span class="n">filenames</span> <span class="o">=</span> <span class="p">[</span><span class="n">filenames</span><span class="p">]</span>
+
+    <span class="n">fig</span><span class="p">,</span> <span class="n">ax</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">()</span>
+
+    <span class="k">for</span> <span class="n">filename</span> <span class="ow">in</span> <span class="n">filenames</span><span class="p">:</span>
+        <span class="n">file</span> <span class="o">=</span> <span class="n">hp</span><span class="o">.</span><span class="n">File</span><span class="p">(</span><span class="n">filename</span><span class="p">,</span> <span class="s2">&quot;r&quot;</span><span class="p">)</span>
+        <span class="n">time</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">file</span><span class="p">[</span><span class="s2">&quot;Beam&quot;</span><span class="p">][</span><span class="s2">&quot;time&quot;</span><span class="p">])</span>
+        <span class="n">data</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">file</span><span class="p">[</span><span class="s2">&quot;Beam&quot;</span><span class="p">][</span><span class="n">dataset</span><span class="p">])</span>
+
+        <span class="k">if</span> <span class="n">x_var</span> <span class="o">==</span> <span class="s2">&quot;time&quot;</span><span class="p">:</span>
+            <span class="n">x</span> <span class="o">=</span> <span class="n">time</span>
+            <span class="n">x_label</span> <span class="o">=</span> <span class="s2">&quot;Number of turns&quot;</span>
+            <span class="n">bunch_index</span> <span class="o">=</span> <span class="p">(</span><span class="n">file</span><span class="p">[</span><span class="s2">&quot;Beam&quot;</span><span class="p">][</span><span class="s2">&quot;current&quot;</span><span class="p">][:,</span> <span class="mi">0</span><span class="p">]</span> <span class="o">!=</span> <span class="mi">0</span><span class="p">)</span><span class="o">.</span><span class="n">nonzero</span><span class="p">()[</span><span class="mi">0</span><span class="p">]</span>
+            <span class="k">if</span> <span class="n">dataset</span> <span class="o">==</span> <span class="s2">&quot;current&quot;</span><span class="p">:</span>
+                <span class="n">y</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">nansum</span><span class="p">(</span><span class="n">data</span><span class="p">[</span><span class="n">bunch_index</span><span class="p">,</span> <span class="p">:],</span> <span class="mi">0</span><span class="p">)</span> <span class="o">*</span> <span class="mf">1e3</span>
+                <span class="n">y_label</span> <span class="o">=</span> <span class="s2">&quot;Total current (mA)&quot;</span>
+            <span class="k">elif</span> <span class="n">dataset</span> <span class="o">==</span> <span class="s2">&quot;emit&quot;</span><span class="p">:</span>
+                <span class="n">dimension_dict</span> <span class="o">=</span> <span class="p">{</span><span class="s2">&quot;x&quot;</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="s2">&quot;y&quot;</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span> <span class="s2">&quot;s&quot;</span><span class="p">:</span> <span class="mi">2</span><span class="p">}</span>
+                <span class="n">axis</span> <span class="o">=</span> <span class="n">dimension_dict</span><span class="p">[</span><span class="n">dimension</span><span class="p">]</span>
+                <span class="n">label</span> <span class="o">=</span> <span class="p">[</span>
+                    <span class="s2">&quot;$</span><span class="se">\\</span><span class="s2">epsilon_</span><span class="si">{x}</span><span class="s2">$ (m.rad)&quot;</span><span class="p">,</span> <span class="s2">&quot;$</span><span class="se">\\</span><span class="s2">epsilon_</span><span class="si">{y}</span><span class="s2">$ (m.rad)&quot;</span><span class="p">,</span>
+                    <span class="s2">&quot;$</span><span class="se">\\</span><span class="s2">epsilon_</span><span class="si">{s}</span><span class="s2">$ (s)&quot;</span>
+                <span class="p">]</span>
+                <span class="k">if</span> <span class="n">stat_var</span> <span class="o">==</span> <span class="s2">&quot;mean&quot;</span><span class="p">:</span>
+                    <span class="n">y</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">nanmean</span><span class="p">(</span><span class="n">data</span><span class="p">[</span><span class="n">axis</span><span class="p">,</span> <span class="n">bunch_index</span><span class="p">,</span> <span class="p">:],</span> <span class="mi">0</span><span class="p">)</span>
+                <span class="k">elif</span> <span class="n">stat_var</span> <span class="o">==</span> <span class="s2">&quot;std&quot;</span><span class="p">:</span>
+                    <span class="n">y</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">nanstd</span><span class="p">(</span><span class="n">data</span><span class="p">[</span><span class="n">axis</span><span class="p">,</span> <span class="n">bunch_index</span><span class="p">,</span> <span class="p">:],</span> <span class="mi">0</span><span class="p">)</span>
+                <span class="n">y_label</span> <span class="o">=</span> <span class="n">stat_var</span> <span class="o">+</span> <span class="s2">&quot; &quot;</span> <span class="o">+</span> <span class="n">label</span><span class="p">[</span><span class="n">axis</span><span class="p">]</span>
+            <span class="k">elif</span> <span class="n">dataset</span> <span class="o">==</span> <span class="s2">&quot;cs_invariant&quot;</span><span class="p">:</span>
+                <span class="n">dimension_dict</span> <span class="o">=</span> <span class="p">{</span><span class="s2">&quot;x&quot;</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="s2">&quot;y&quot;</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span> <span class="s2">&quot;s&quot;</span><span class="p">:</span> <span class="mi">2</span><span class="p">}</span>
+                <span class="n">axis</span> <span class="o">=</span> <span class="n">dimension_dict</span><span class="p">[</span><span class="n">dimension</span><span class="p">]</span>
+                <span class="n">label</span> <span class="o">=</span> <span class="p">[</span><span class="s1">&#39;$J_x$ (m)&#39;</span><span class="p">,</span> <span class="s1">&#39;$J_y$ (m)&#39;</span><span class="p">,</span> <span class="s1">&#39;$J_s$ (s)&#39;</span><span class="p">]</span>
+                <span class="k">if</span> <span class="n">stat_var</span> <span class="o">==</span> <span class="s2">&quot;mean&quot;</span><span class="p">:</span>
+                    <span class="n">y</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">nanmean</span><span class="p">(</span><span class="n">data</span><span class="p">[</span><span class="n">axis</span><span class="p">,</span> <span class="n">bunch_index</span><span class="p">,</span> <span class="p">:],</span> <span class="mi">0</span><span class="p">)</span>
+                <span class="k">elif</span> <span class="n">stat_var</span> <span class="o">==</span> <span class="s2">&quot;std&quot;</span><span class="p">:</span>
+                    <span class="n">y</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">nanstd</span><span class="p">(</span><span class="n">data</span><span class="p">[</span><span class="n">axis</span><span class="p">,</span> <span class="n">bunch_index</span><span class="p">,</span> <span class="p">:],</span> <span class="mi">0</span><span class="p">)</span>
+                <span class="n">y_label</span> <span class="o">=</span> <span class="n">stat_var</span> <span class="o">+</span> <span class="s2">&quot; &quot;</span> <span class="o">+</span> <span class="n">label</span><span class="p">[</span><span class="n">axis</span><span class="p">]</span>
+            <span class="k">elif</span> <span class="n">dataset</span> <span class="o">==</span> <span class="s2">&quot;mean&quot;</span> <span class="ow">or</span> <span class="n">dataset</span> <span class="o">==</span> <span class="s2">&quot;std&quot;</span><span class="p">:</span>
+                <span class="n">dimension_dict</span> <span class="o">=</span> <span class="p">{</span>
+                    <span class="s2">&quot;x&quot;</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span>
+                    <span class="s2">&quot;xp&quot;</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span>
+                    <span class="s2">&quot;y&quot;</span><span class="p">:</span> <span class="mi">2</span><span class="p">,</span>
+                    <span class="s2">&quot;yp&quot;</span><span class="p">:</span> <span class="mi">3</span><span class="p">,</span>
+                    <span class="s2">&quot;tau&quot;</span><span class="p">:</span> <span class="mi">4</span><span class="p">,</span>
+                    <span class="s2">&quot;delta&quot;</span><span class="p">:</span> <span class="mi">5</span>
+                <span class="p">}</span>
+                <span class="n">axis</span> <span class="o">=</span> <span class="n">dimension_dict</span><span class="p">[</span><span class="n">dimension</span><span class="p">]</span>
+                <span class="n">scale</span> <span class="o">=</span> <span class="p">[</span><span class="mf">1e6</span><span class="p">,</span> <span class="mf">1e6</span><span class="p">,</span> <span class="mf">1e6</span><span class="p">,</span> <span class="mf">1e6</span><span class="p">,</span> <span class="mf">1e12</span><span class="p">,</span> <span class="mi">1</span><span class="p">]</span>
+                <span class="n">label</span> <span class="o">=</span> <span class="p">[</span>
+                    <span class="s2">&quot;x (um)&quot;</span><span class="p">,</span> <span class="s2">&quot;x&#39; ($</span><span class="se">\\</span><span class="s2">mu$rad)&quot;</span><span class="p">,</span> <span class="s2">&quot;y (um)&quot;</span><span class="p">,</span> <span class="s2">&quot;y&#39; ($</span><span class="se">\\</span><span class="s2">mu$rad)&quot;</span><span class="p">,</span>
+                    <span class="s2">&quot;$</span><span class="se">\\</span><span class="s2">tau$ (ps)&quot;</span><span class="p">,</span> <span class="s2">&quot;$</span><span class="se">\\</span><span class="s2">delta$&quot;</span>
+                <span class="p">]</span>
+                <span class="k">if</span> <span class="n">stat_var</span> <span class="o">==</span> <span class="s2">&quot;mean&quot;</span><span class="p">:</span>
+                    <span class="n">y</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">nanmean</span><span class="p">(</span><span class="n">data</span><span class="p">[</span><span class="n">axis</span><span class="p">,</span> <span class="n">bunch_index</span><span class="p">,</span> <span class="p">:],</span> <span class="mi">0</span><span class="p">)</span> <span class="o">*</span> <span class="n">scale</span><span class="p">[</span><span class="n">axis</span><span class="p">]</span>
+                <span class="k">elif</span> <span class="n">stat_var</span> <span class="o">==</span> <span class="s2">&quot;std&quot;</span><span class="p">:</span>
+                    <span class="n">y</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">nanstd</span><span class="p">(</span><span class="n">data</span><span class="p">[</span><span class="n">axis</span><span class="p">,</span> <span class="n">bunch_index</span><span class="p">,</span> <span class="p">:],</span> <span class="mi">0</span><span class="p">)</span> <span class="o">*</span> <span class="n">scale</span><span class="p">[</span><span class="n">axis</span><span class="p">]</span>
+                <span class="n">label_sup</span> <span class="o">=</span> <span class="p">{</span><span class="s2">&quot;mean&quot;</span><span class="p">:</span> <span class="s2">&quot;mean of &quot;</span><span class="p">,</span> <span class="s2">&quot;std&quot;</span><span class="p">:</span> <span class="s2">&quot;std of &quot;</span><span class="p">}</span>
+                <span class="n">y_label</span> <span class="o">=</span> <span class="n">label_sup</span><span class="p">[</span><span class="n">stat_var</span><span class="p">]</span> <span class="o">+</span> <span class="n">dataset</span> <span class="o">+</span> <span class="s2">&quot; &quot;</span> <span class="o">+</span> <span class="n">label</span><span class="p">[</span><span class="n">axis</span><span class="p">]</span>
+
+        <span class="k">elif</span> <span class="n">x_var</span> <span class="o">==</span> <span class="s2">&quot;index&quot;</span><span class="p">:</span>
+            <span class="n">h</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">file</span><span class="p">[</span><span class="s2">&quot;Beam&quot;</span><span class="p">][</span><span class="s2">&quot;mean&quot;</span><span class="p">][</span><span class="mi">0</span><span class="p">,</span> <span class="p">:,</span> <span class="mi">0</span><span class="p">])</span>
+            <span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="n">h</span><span class="p">)</span>
+            <span class="n">x_label</span> <span class="o">=</span> <span class="s2">&quot;Bunch index&quot;</span>
+            <span class="k">if</span> <span class="n">turn</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+                <span class="n">idx</span> <span class="o">=</span> <span class="o">-</span><span class="mi">1</span>
+            <span class="k">else</span><span class="p">:</span>
+                <span class="n">idx</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">where</span><span class="p">(</span><span class="n">time</span> <span class="o">==</span> <span class="nb">int</span><span class="p">(</span><span class="n">turn</span><span class="p">))[</span><span class="mi">0</span><span class="p">]</span>
+                <span class="k">if</span> <span class="p">(</span><span class="n">idx</span><span class="o">.</span><span class="n">size</span> <span class="o">==</span> <span class="mi">0</span><span class="p">):</span>
+                    <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">&quot;Turn is not valid.&quot;</span><span class="p">)</span>
+
+            <span class="k">if</span> <span class="n">dataset</span> <span class="o">==</span> <span class="s2">&quot;current&quot;</span><span class="p">:</span>
+                <span class="n">y</span> <span class="o">=</span> <span class="n">data</span><span class="p">[:,</span> <span class="n">idx</span><span class="p">]</span> <span class="o">*</span> <span class="mf">1e3</span>
+                <span class="n">y_label</span> <span class="o">=</span> <span class="s2">&quot;Bunch current (mA)&quot;</span>
+            <span class="k">elif</span> <span class="n">dataset</span> <span class="o">==</span> <span class="s2">&quot;emit&quot;</span><span class="p">:</span>
+                <span class="n">dimension_dict</span> <span class="o">=</span> <span class="p">{</span><span class="s2">&quot;x&quot;</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="s2">&quot;y&quot;</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span> <span class="s2">&quot;s&quot;</span><span class="p">:</span> <span class="mi">2</span><span class="p">}</span>
+                <span class="n">axis</span> <span class="o">=</span> <span class="n">dimension_dict</span><span class="p">[</span><span class="n">dimension</span><span class="p">]</span>
+                <span class="n">label</span> <span class="o">=</span> <span class="p">[</span>
+                    <span class="s2">&quot;$</span><span class="se">\\</span><span class="s2">epsilon_</span><span class="si">{x}</span><span class="s2">$ (m.rad)&quot;</span><span class="p">,</span> <span class="s2">&quot;$</span><span class="se">\\</span><span class="s2">epsilon_</span><span class="si">{y}</span><span class="s2">$ (m.rad)&quot;</span><span class="p">,</span>
+                    <span class="s2">&quot;$</span><span class="se">\\</span><span class="s2">epsilon_</span><span class="si">{s}</span><span class="s2">$ (s)&quot;</span>
+                <span class="p">]</span>
+                <span class="n">y</span> <span class="o">=</span> <span class="n">data</span><span class="p">[</span><span class="n">axis</span><span class="p">,</span> <span class="p">:,</span> <span class="n">idx</span><span class="p">]</span>
+                <span class="n">y_label</span> <span class="o">=</span> <span class="n">label</span><span class="p">[</span><span class="n">axis</span><span class="p">]</span>
+            <span class="k">elif</span> <span class="n">dataset</span> <span class="o">==</span> <span class="s2">&quot;cs_invariant&quot;</span><span class="p">:</span>
+                <span class="n">dimension_dict</span> <span class="o">=</span> <span class="p">{</span><span class="s2">&quot;x&quot;</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="s2">&quot;y&quot;</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span> <span class="s2">&quot;s&quot;</span><span class="p">:</span> <span class="mi">2</span><span class="p">}</span>
+                <span class="n">axis</span> <span class="o">=</span> <span class="n">dimension_dict</span><span class="p">[</span><span class="n">dimension</span><span class="p">]</span>
+                <span class="n">label</span> <span class="o">=</span> <span class="p">[</span><span class="s1">&#39;$J_x$ (m)&#39;</span><span class="p">,</span> <span class="s1">&#39;$J_y$ (m)&#39;</span><span class="p">,</span> <span class="s1">&#39;$J_s$ (s)&#39;</span><span class="p">]</span>
+                <span class="n">y</span> <span class="o">=</span> <span class="n">data</span><span class="p">[</span><span class="n">axis</span><span class="p">,</span> <span class="p">:,</span> <span class="n">idx</span><span class="p">]</span>
+                <span class="n">y_label</span> <span class="o">=</span> <span class="n">label</span><span class="p">[</span><span class="n">axis</span><span class="p">]</span>
+            <span class="k">elif</span> <span class="n">dataset</span> <span class="o">==</span> <span class="s2">&quot;mean&quot;</span> <span class="ow">or</span> <span class="n">dataset</span> <span class="o">==</span> <span class="s2">&quot;std&quot;</span><span class="p">:</span>
+                <span class="n">dimension_dict</span> <span class="o">=</span> <span class="p">{</span>
+                    <span class="s2">&quot;x&quot;</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span>
+                    <span class="s2">&quot;xp&quot;</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span>
+                    <span class="s2">&quot;y&quot;</span><span class="p">:</span> <span class="mi">2</span><span class="p">,</span>
+                    <span class="s2">&quot;yp&quot;</span><span class="p">:</span> <span class="mi">3</span><span class="p">,</span>
+                    <span class="s2">&quot;tau&quot;</span><span class="p">:</span> <span class="mi">4</span><span class="p">,</span>
+                    <span class="s2">&quot;delta&quot;</span><span class="p">:</span> <span class="mi">5</span>
+                <span class="p">}</span>
+                <span class="n">axis</span> <span class="o">=</span> <span class="n">dimension_dict</span><span class="p">[</span><span class="n">dimension</span><span class="p">]</span>
+                <span class="n">scale</span> <span class="o">=</span> <span class="p">[</span><span class="mf">1e6</span><span class="p">,</span> <span class="mf">1e6</span><span class="p">,</span> <span class="mf">1e6</span><span class="p">,</span> <span class="mf">1e6</span><span class="p">,</span> <span class="mf">1e12</span><span class="p">,</span> <span class="mi">1</span><span class="p">]</span>
+                <span class="n">label</span> <span class="o">=</span> <span class="p">[</span>
+                    <span class="s2">&quot;x (um)&quot;</span><span class="p">,</span> <span class="s2">&quot;x&#39; ($</span><span class="se">\\</span><span class="s2">mu$rad)&quot;</span><span class="p">,</span> <span class="s2">&quot;y (um)&quot;</span><span class="p">,</span> <span class="s2">&quot;y&#39; ($</span><span class="se">\\</span><span class="s2">mu$rad)&quot;</span><span class="p">,</span>
+                    <span class="s2">&quot;$</span><span class="se">\\</span><span class="s2">tau$ (ps)&quot;</span><span class="p">,</span> <span class="s2">&quot;$</span><span class="se">\\</span><span class="s2">delta$&quot;</span>
+                <span class="p">]</span>
+                <span class="n">y</span> <span class="o">=</span> <span class="n">data</span><span class="p">[</span><span class="n">axis</span><span class="p">,</span> <span class="p">:,</span> <span class="n">idx</span><span class="p">]</span> <span class="o">*</span> <span class="n">scale</span><span class="p">[</span><span class="n">axis</span><span class="p">]</span>
+                <span class="n">y_label</span> <span class="o">=</span> <span class="n">dataset</span> <span class="o">+</span> <span class="s2">&quot; &quot;</span> <span class="o">+</span> <span class="n">label</span><span class="p">[</span><span class="n">axis</span><span class="p">]</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">&quot;x_var should be time or index&quot;</span><span class="p">)</span>
+
+        <span class="n">y</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">squeeze</span><span class="p">(</span><span class="n">y</span><span class="p">)</span>
+
+        <span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span>
+        <span class="n">ax</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="n">x_label</span><span class="p">)</span>
+        <span class="n">ax</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="n">y_label</span><span class="p">)</span>
+        <span class="k">if</span> <span class="n">legend</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="n">plt</span><span class="o">.</span><span class="n">legend</span><span class="p">(</span><span class="n">legend</span><span class="p">)</span>
+
+        <span class="n">file</span><span class="o">.</span><span class="n">close</span><span class="p">()</span>
+
+    <span class="k">return</span> <span class="n">fig</span></div>
+
+
+<div class="viewcode-block" id="streak_beamdata"><a class="viewcode-back" href="../../../../mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.plotting.streak_beamdata">[docs]</a><span class="k">def</span> <span class="nf">streak_beamdata</span><span class="p">(</span><span class="n">filename</span><span class="p">,</span> <span class="n">dataset</span><span class="o">=</span><span class="s2">&quot;mean&quot;</span><span class="p">,</span> <span class="n">dimension</span><span class="o">=</span><span class="s2">&quot;tau&quot;</span><span class="p">,</span> <span class="n">cm_lim</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    Plot 3D data recorded by BeamMonitor.</span>
+
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">    filename : str</span>
+<span class="sd">        Name of the HDF5 file that contains the data.</span>
+<span class="sd">    dataset : {&quot;current&quot;,&quot;emit&quot;,&quot;mean&quot;,&quot;std&quot;,&quot;cs_invariant&quot;}</span>
+<span class="sd">        HDF5 file&#39;s dataset to be plotted. The default is &quot;mean&quot;.</span>
+<span class="sd">    dimension : str</span>
+<span class="sd">         The dimension of the dataset to plot:</span>
+<span class="sd">            for &quot;emit&quot;, dimension = {&quot;x&quot;,&quot;y&quot;,&quot;s&quot;},</span>
+<span class="sd">            for &quot;cs_invariant&quot;, dimension = {&quot;x&quot;,&quot;y&quot;,&quot;s&quot;},</span>
+<span class="sd">            for &quot;mean&quot; and &quot;std&quot;, dimension = {&quot;x&quot;,&quot;xp&quot;,&quot;y&quot;,&quot;yp&quot;,&quot;tau&quot;,&quot;delta&quot;}.</span>
+<span class="sd">            not used if &quot;current&quot;.</span>
+<span class="sd">        The default is &quot;tau&quot;.</span>
+<span class="sd">    cm_lim : list [vmin, vmax], optional</span>
+<span class="sd">        Colormap scale for the &quot;streak&quot; plot.</span>
+
+<span class="sd">    Return</span>
+<span class="sd">    ------</span>
+<span class="sd">    fig : Figure</span>
+<span class="sd">        Figure object with the plot on it.</span>
+
+<span class="sd">    &quot;&quot;&quot;</span>
+
+    <span class="n">file</span> <span class="o">=</span> <span class="n">hp</span><span class="o">.</span><span class="n">File</span><span class="p">(</span><span class="n">filename</span><span class="p">,</span> <span class="s2">&quot;r&quot;</span><span class="p">)</span>
+    <span class="n">data</span> <span class="o">=</span> <span class="n">file</span><span class="p">[</span><span class="s2">&quot;Beam&quot;</span><span class="p">]</span>
+    <span class="n">time</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">data</span><span class="p">[</span><span class="s2">&quot;time&quot;</span><span class="p">])</span>
+
+    <span class="n">h</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">data</span><span class="p">[</span><span class="s2">&quot;mean&quot;</span><span class="p">][</span><span class="mi">0</span><span class="p">,</span> <span class="p">:,</span> <span class="mi">0</span><span class="p">])</span>
+    <span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="n">h</span><span class="p">)</span>
+    <span class="n">x_label</span> <span class="o">=</span> <span class="s2">&quot;Bunch index&quot;</span>
+    <span class="n">y</span> <span class="o">=</span> <span class="n">time</span>
+    <span class="n">y_label</span> <span class="o">=</span> <span class="s2">&quot;Number of turns&quot;</span>
+    <span class="k">if</span> <span class="n">dataset</span> <span class="o">==</span> <span class="s2">&quot;current&quot;</span><span class="p">:</span>
+        <span class="n">z</span> <span class="o">=</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">data</span><span class="p">[</span><span class="s2">&quot;current&quot;</span><span class="p">])</span> <span class="o">*</span> <span class="mf">1e3</span><span class="p">)</span><span class="o">.</span><span class="n">T</span>
+        <span class="n">z_label</span> <span class="o">=</span> <span class="s2">&quot;Bunch current (mA)&quot;</span>
+        <span class="n">title</span> <span class="o">=</span> <span class="n">z_label</span>
+    <span class="k">elif</span> <span class="n">dataset</span> <span class="o">==</span> <span class="s2">&quot;emit&quot;</span><span class="p">:</span>
+        <span class="n">dimension_dict</span> <span class="o">=</span> <span class="p">{</span><span class="s2">&quot;x&quot;</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="s2">&quot;y&quot;</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span> <span class="s2">&quot;s&quot;</span><span class="p">:</span> <span class="mi">2</span><span class="p">}</span>
+        <span class="n">axis</span> <span class="o">=</span> <span class="n">dimension_dict</span><span class="p">[</span><span class="n">dimension</span><span class="p">]</span>
+        <span class="n">label</span> <span class="o">=</span> <span class="p">[</span>
+            <span class="s2">&quot;$</span><span class="se">\\</span><span class="s2">epsilon_</span><span class="si">{x}</span><span class="s2">$ (m.rad)&quot;</span><span class="p">,</span> <span class="s2">&quot;$</span><span class="se">\\</span><span class="s2">epsilon_</span><span class="si">{y}</span><span class="s2">$ (m.rad)&quot;</span><span class="p">,</span>
+            <span class="s2">&quot;$</span><span class="se">\\</span><span class="s2">epsilon_</span><span class="si">{s}</span><span class="s2">$ (s)&quot;</span>
+        <span class="p">]</span>
+        <span class="n">z</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">data</span><span class="p">[</span><span class="s2">&quot;emit&quot;</span><span class="p">][</span><span class="n">axis</span><span class="p">,</span> <span class="p">:,</span> <span class="p">:])</span><span class="o">.</span><span class="n">T</span>
+        <span class="n">z_label</span> <span class="o">=</span> <span class="n">label</span><span class="p">[</span><span class="n">axis</span><span class="p">]</span>
+        <span class="n">title</span> <span class="o">=</span> <span class="n">z_label</span>
+    <span class="k">elif</span> <span class="n">dataset</span> <span class="o">==</span> <span class="s2">&quot;cs_invariant&quot;</span><span class="p">:</span>
+        <span class="n">dimension_dict</span> <span class="o">=</span> <span class="p">{</span><span class="s2">&quot;x&quot;</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="s2">&quot;y&quot;</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span> <span class="s2">&quot;s&quot;</span><span class="p">:</span> <span class="mi">2</span><span class="p">}</span>
+        <span class="n">axis</span> <span class="o">=</span> <span class="n">dimension_dict</span><span class="p">[</span><span class="n">dimension</span><span class="p">]</span>
+        <span class="n">label</span> <span class="o">=</span> <span class="p">[</span><span class="s1">&#39;$J_x$ (m)&#39;</span><span class="p">,</span> <span class="s1">&#39;$J_y$ (m)&#39;</span><span class="p">,</span> <span class="s1">&#39;$J_s$ (s)&#39;</span><span class="p">]</span>
+        <span class="n">z</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">data</span><span class="p">[</span><span class="s2">&quot;cs_invariant&quot;</span><span class="p">][</span><span class="n">axis</span><span class="p">,</span> <span class="p">:,</span> <span class="p">:])</span><span class="o">.</span><span class="n">T</span>
+        <span class="n">z_label</span> <span class="o">=</span> <span class="n">label</span><span class="p">[</span><span class="n">axis</span><span class="p">]</span>
+        <span class="n">title</span> <span class="o">=</span> <span class="n">z_label</span>
+    <span class="k">else</span><span class="p">:</span>
+        <span class="n">dimension_dict</span> <span class="o">=</span> <span class="p">{</span>
+            <span class="s2">&quot;x&quot;</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span>
+            <span class="s2">&quot;xp&quot;</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span>
+            <span class="s2">&quot;y&quot;</span><span class="p">:</span> <span class="mi">2</span><span class="p">,</span>
+            <span class="s2">&quot;yp&quot;</span><span class="p">:</span> <span class="mi">3</span><span class="p">,</span>
+            <span class="s2">&quot;tau&quot;</span><span class="p">:</span> <span class="mi">4</span><span class="p">,</span>
+            <span class="s2">&quot;delta&quot;</span><span class="p">:</span> <span class="mi">5</span>
+        <span class="p">}</span>
+        <span class="n">axis</span> <span class="o">=</span> <span class="n">dimension_dict</span><span class="p">[</span><span class="n">dimension</span><span class="p">]</span>
+        <span class="n">scale</span> <span class="o">=</span> <span class="p">[</span><span class="mf">1e6</span><span class="p">,</span> <span class="mf">1e6</span><span class="p">,</span> <span class="mf">1e6</span><span class="p">,</span> <span class="mf">1e6</span><span class="p">,</span> <span class="mf">1e12</span><span class="p">,</span> <span class="mi">1</span><span class="p">]</span>
+        <span class="n">label</span> <span class="o">=</span> <span class="p">[</span>
+            <span class="s2">&quot;x (um)&quot;</span><span class="p">,</span> <span class="s2">&quot;x&#39; ($</span><span class="se">\\</span><span class="s2">mu$rad)&quot;</span><span class="p">,</span> <span class="s2">&quot;y (um)&quot;</span><span class="p">,</span> <span class="s2">&quot;y&#39; ($</span><span class="se">\\</span><span class="s2">mu$rad)&quot;</span><span class="p">,</span>
+            <span class="s2">&quot;$</span><span class="se">\\</span><span class="s2">tau$ (ps)&quot;</span><span class="p">,</span> <span class="s2">&quot;$</span><span class="se">\\</span><span class="s2">delta$&quot;</span>
+        <span class="p">]</span>
+        <span class="n">z</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">data</span><span class="p">[</span><span class="n">dataset</span><span class="p">][</span><span class="n">axis</span><span class="p">,</span> <span class="p">:,</span> <span class="p">:])</span><span class="o">.</span><span class="n">T</span> <span class="o">*</span> <span class="n">scale</span><span class="p">[</span><span class="n">axis</span><span class="p">]</span>
+        <span class="n">z_label</span> <span class="o">=</span> <span class="n">label</span><span class="p">[</span><span class="n">axis</span><span class="p">]</span>
+        <span class="k">if</span> <span class="n">dataset</span> <span class="o">==</span> <span class="s2">&quot;mean&quot;</span><span class="p">:</span>
+            <span class="n">title</span> <span class="o">=</span> <span class="n">label</span><span class="p">[</span><span class="n">axis</span><span class="p">]</span> <span class="o">+</span> <span class="s2">&quot; CM&quot;</span>
+        <span class="k">elif</span> <span class="n">dataset</span> <span class="o">==</span> <span class="s2">&quot;std&quot;</span><span class="p">:</span>
+            <span class="n">title</span> <span class="o">=</span> <span class="n">label</span><span class="p">[</span><span class="n">axis</span><span class="p">]</span> <span class="o">+</span> <span class="s2">&quot; RMS&quot;</span>
+
+    <span class="n">fig</span><span class="p">,</span> <span class="n">ax</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">()</span>
+    <span class="n">ax</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="n">x_label</span><span class="p">)</span>
+    <span class="n">ax</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="n">y_label</span><span class="p">)</span>
+    <span class="n">ax</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="n">title</span><span class="p">)</span>
+
+    <span class="k">if</span> <span class="n">dataset</span> <span class="o">==</span> <span class="s2">&quot;mean&quot;</span><span class="p">:</span>
+        <span class="n">cmap</span> <span class="o">=</span> <span class="n">mpl</span><span class="o">.</span><span class="n">cm</span><span class="o">.</span><span class="n">coolwarm</span>  <span class="c1"># diverging</span>
+    <span class="k">else</span><span class="p">:</span>
+        <span class="n">cmap</span> <span class="o">=</span> <span class="n">mpl</span><span class="o">.</span><span class="n">cm</span><span class="o">.</span><span class="n">inferno</span>  <span class="c1"># sequential</span>
+
+    <span class="n">c</span> <span class="o">=</span> <span class="n">ax</span><span class="o">.</span><span class="n">imshow</span><span class="p">(</span><span class="n">z</span><span class="p">,</span>
+                  <span class="n">cmap</span><span class="o">=</span><span class="n">cmap</span><span class="p">,</span>
+                  <span class="n">origin</span><span class="o">=</span><span class="s1">&#39;lower&#39;</span><span class="p">,</span>
+                  <span class="n">aspect</span><span class="o">=</span><span class="s1">&#39;auto&#39;</span><span class="p">,</span>
+                  <span class="n">extent</span><span class="o">=</span><span class="p">[</span><span class="n">x</span><span class="o">.</span><span class="n">min</span><span class="p">(),</span> <span class="n">x</span><span class="o">.</span><span class="n">max</span><span class="p">(),</span> <span class="n">y</span><span class="o">.</span><span class="n">min</span><span class="p">(),</span>
+                          <span class="n">y</span><span class="o">.</span><span class="n">max</span><span class="p">()])</span>
+    <span class="k">if</span> <span class="n">cm_lim</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
+        <span class="n">c</span><span class="o">.</span><span class="n">set_clim</span><span class="p">(</span><span class="n">vmin</span><span class="o">=</span><span class="n">cm_lim</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">vmax</span><span class="o">=</span><span class="n">cm_lim</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
+    <span class="n">cbar</span> <span class="o">=</span> <span class="n">fig</span><span class="o">.</span><span class="n">colorbar</span><span class="p">(</span><span class="n">c</span><span class="p">,</span> <span class="n">ax</span><span class="o">=</span><span class="n">ax</span><span class="p">)</span>
+    <span class="n">cbar</span><span class="o">.</span><span class="n">set_label</span><span class="p">(</span><span class="n">z_label</span><span class="p">)</span>
+
+    <span class="n">file</span><span class="o">.</span><span class="n">close</span><span class="p">()</span>
+
+    <span class="k">return</span> <span class="n">fig</span></div>
+
+
+<div class="viewcode-block" id="plot_bunchdata"><a class="viewcode-back" href="../../../../mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.plotting.plot_bunchdata">[docs]</a><span class="k">def</span> <span class="nf">plot_bunchdata</span><span class="p">(</span><span class="n">filenames</span><span class="p">,</span>
+                   <span class="n">bunch_number</span><span class="p">,</span>
+                   <span class="n">dataset</span><span class="p">,</span>
+                   <span class="n">dimension</span><span class="o">=</span><span class="s2">&quot;x&quot;</span><span class="p">,</span>
+                   <span class="n">legend</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    Plot data recorded by BunchMonitor.</span>
+<span class="sd">    </span>
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">    filenames : str or list of str</span>
+<span class="sd">        Names of the HDF5 files to be plotted.</span>
+<span class="sd">    bunch_number : int or list of int</span>
+<span class="sd">        Bunch to plot. This has to be identical to &#39;bunch_number&#39; parameter in </span>
+<span class="sd">        &#39;BunchMonitor&#39; object.</span>
+<span class="sd">    dataset : {&quot;current&quot;, &quot;emit&quot;, &quot;mean&quot;, &quot;std&quot;, &quot;cs_invariant&quot;}</span>
+<span class="sd">        HDF5 file&#39;s dataset to be plotted.</span>
+<span class="sd">    dimension : str, optional</span>
+<span class="sd">        The dimension of the dataset to plot. Use &quot;None&quot; for &quot;current&quot;,</span>
+<span class="sd">        otherwise use the following : </span>
+<span class="sd">            for &quot;emit&quot;, dimension = {&quot;x&quot;,&quot;y&quot;,&quot;s&quot;},</span>
+<span class="sd">            for &quot;cs_invariant&quot;, dimension = {&quot;x&quot;,&quot;y&quot;,&quot;s&quot;},</span>
+<span class="sd">            for &quot;mean&quot; and &quot;std&quot;, dimension = {&quot;x&quot;,&quot;xp&quot;,&quot;y&quot;,&quot;yp&quot;,&quot;tau&quot;,&quot;delta&quot;},</span>
+<span class="sd">            for &quot;action&quot;, dimension = {&quot;x&quot;,&quot;y&quot;}.</span>
+<span class="sd">    legend : list of str, optional</span>
+<span class="sd">        Legend to add for each file.</span>
+<span class="sd">        </span>
+<span class="sd">    Return</span>
+<span class="sd">    ------</span>
+<span class="sd">    fig : Figure</span>
+<span class="sd">        Figure object with the plot on it.</span>
+
+<span class="sd">    &quot;&quot;&quot;</span>
+
+    <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">filenames</span><span class="p">,</span> <span class="nb">str</span><span class="p">):</span>
+        <span class="n">filenames</span> <span class="o">=</span> <span class="p">[</span><span class="n">filenames</span><span class="p">]</span>
+
+    <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">bunch_number</span><span class="p">,</span> <span class="nb">int</span><span class="p">):</span>
+        <span class="n">ll</span> <span class="o">=</span> <span class="p">[]</span>
+        <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">filenames</span><span class="p">)):</span>
+            <span class="n">ll</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">bunch_number</span><span class="p">)</span>
+        <span class="n">bunch_number</span> <span class="o">=</span> <span class="n">ll</span>
+
+    <span class="n">fig</span><span class="p">,</span> <span class="n">ax</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">()</span>
+
+    <span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">filename</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">filenames</span><span class="p">):</span>
+        <span class="n">file</span> <span class="o">=</span> <span class="n">hp</span><span class="o">.</span><span class="n">File</span><span class="p">(</span><span class="n">filename</span><span class="p">,</span> <span class="s2">&quot;r&quot;</span><span class="p">)</span>
+        <span class="n">group</span> <span class="o">=</span> <span class="s2">&quot;BunchData_</span><span class="si">{0}</span><span class="s2">&quot;</span><span class="o">.</span><span class="n">format</span><span class="p">(</span>
+            <span class="n">bunch_number</span><span class="p">[</span><span class="n">i</span><span class="p">])</span>  <span class="c1"># Data group of the HDF5 file</span>
+
+        <span class="k">if</span> <span class="n">dataset</span> <span class="o">==</span> <span class="s2">&quot;current&quot;</span><span class="p">:</span>
+            <span class="n">y_var</span> <span class="o">=</span> <span class="n">file</span><span class="p">[</span><span class="n">group</span><span class="p">][</span><span class="n">dataset</span><span class="p">][:]</span> <span class="o">*</span> <span class="mf">1e3</span>
+            <span class="n">label</span> <span class="o">=</span> <span class="s2">&quot;current (mA)&quot;</span>
+
+        <span class="k">elif</span> <span class="n">dataset</span> <span class="o">==</span> <span class="s2">&quot;emit&quot;</span><span class="p">:</span>
+            <span class="n">dimension_dict</span> <span class="o">=</span> <span class="p">{</span><span class="s2">&quot;x&quot;</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="s2">&quot;y&quot;</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span> <span class="s2">&quot;s&quot;</span><span class="p">:</span> <span class="mi">2</span><span class="p">}</span>
+
+            <span class="n">y_var</span> <span class="o">=</span> <span class="n">file</span><span class="p">[</span><span class="n">group</span><span class="p">][</span><span class="n">dataset</span><span class="p">][</span><span class="n">dimension_dict</span><span class="p">[</span><span class="n">dimension</span><span class="p">]]</span>
+
+            <span class="k">if</span> <span class="n">dimension</span> <span class="o">==</span> <span class="s2">&quot;x&quot;</span><span class="p">:</span> <span class="n">label</span> <span class="o">=</span> <span class="s2">&quot;hor. emittance (m.rad)&quot;</span>
+            <span class="k">elif</span> <span class="n">dimension</span> <span class="o">==</span> <span class="s2">&quot;y&quot;</span><span class="p">:</span> <span class="n">label</span> <span class="o">=</span> <span class="s2">&quot;ver. emittance (m.rad)&quot;</span>
+            <span class="k">elif</span> <span class="n">dimension</span> <span class="o">==</span> <span class="s2">&quot;s&quot;</span><span class="p">:</span> <span class="n">label</span> <span class="o">=</span> <span class="s2">&quot;long. emittance (s)&quot;</span>
+
+        <span class="k">elif</span> <span class="n">dataset</span> <span class="o">==</span> <span class="s2">&quot;mean&quot;</span> <span class="ow">or</span> <span class="n">dataset</span> <span class="o">==</span> <span class="s2">&quot;std&quot;</span><span class="p">:</span>
+            <span class="n">dimension_dict</span> <span class="o">=</span> <span class="p">{</span>
+                <span class="s2">&quot;x&quot;</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span>
+                <span class="s2">&quot;xp&quot;</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span>
+                <span class="s2">&quot;y&quot;</span><span class="p">:</span> <span class="mi">2</span><span class="p">,</span>
+                <span class="s2">&quot;yp&quot;</span><span class="p">:</span> <span class="mi">3</span><span class="p">,</span>
+                <span class="s2">&quot;tau&quot;</span><span class="p">:</span> <span class="mi">4</span><span class="p">,</span>
+                <span class="s2">&quot;delta&quot;</span><span class="p">:</span> <span class="mi">5</span>
+            <span class="p">}</span>
+            <span class="n">scale</span> <span class="o">=</span> <span class="p">[</span><span class="mf">1e6</span><span class="p">,</span> <span class="mf">1e6</span><span class="p">,</span> <span class="mf">1e6</span><span class="p">,</span> <span class="mf">1e6</span><span class="p">,</span> <span class="mf">1e12</span><span class="p">,</span> <span class="mi">1</span><span class="p">]</span>
+            <span class="n">axis_index</span> <span class="o">=</span> <span class="n">dimension_dict</span><span class="p">[</span><span class="n">dimension</span><span class="p">]</span>
+
+            <span class="n">y_var</span> <span class="o">=</span> <span class="n">file</span><span class="p">[</span><span class="n">group</span><span class="p">][</span><span class="n">dataset</span><span class="p">][</span><span class="n">axis_index</span><span class="p">]</span> <span class="o">*</span> <span class="n">scale</span><span class="p">[</span><span class="n">axis_index</span><span class="p">]</span>
+            <span class="k">if</span> <span class="n">dataset</span> <span class="o">==</span> <span class="s2">&quot;mean&quot;</span><span class="p">:</span>
+                <span class="n">label_list</span> <span class="o">=</span> <span class="p">[</span>
+                    <span class="s2">&quot;x ($</span><span class="se">\\</span><span class="s2">mu$m)&quot;</span><span class="p">,</span> <span class="s2">&quot;x&#39; ($</span><span class="se">\\</span><span class="s2">mu$rad)&quot;</span><span class="p">,</span> <span class="s2">&quot;y ($</span><span class="se">\\</span><span class="s2">mu$m)&quot;</span><span class="p">,</span>
+                    <span class="s2">&quot;y&#39; ($</span><span class="se">\\</span><span class="s2">mu$rad)&quot;</span><span class="p">,</span> <span class="s2">&quot;$</span><span class="se">\\</span><span class="s2">tau$ (ps)&quot;</span><span class="p">,</span> <span class="s2">&quot;$</span><span class="se">\\</span><span class="s2">delta$&quot;</span>
+                <span class="p">]</span>
+            <span class="k">else</span><span class="p">:</span>
+                <span class="n">label_list</span> <span class="o">=</span> <span class="p">[</span>
+                    <span class="s2">&quot;$</span><span class="se">\\</span><span class="s2">sigma_x$ ($</span><span class="se">\\</span><span class="s2">mu$m)&quot;</span><span class="p">,</span> <span class="s2">&quot;$</span><span class="se">\\</span><span class="s2">sigma_{x&#39;}$ ($</span><span class="se">\\</span><span class="s2">mu$rad)&quot;</span><span class="p">,</span>
+                    <span class="s2">&quot;$</span><span class="se">\\</span><span class="s2">sigma_y$ ($</span><span class="se">\\</span><span class="s2">mu$m)&quot;</span><span class="p">,</span> <span class="s2">&quot;$</span><span class="se">\\</span><span class="s2">sigma_{y&#39;}$ ($</span><span class="se">\\</span><span class="s2">mu$rad)&quot;</span><span class="p">,</span>
+                    <span class="s2">&quot;$</span><span class="se">\\</span><span class="s2">sigma_{</span><span class="se">\\</span><span class="s2">tau}$ (ps)&quot;</span><span class="p">,</span> <span class="s2">&quot;$</span><span class="se">\\</span><span class="s2">sigma_{</span><span class="se">\\</span><span class="s2">delta}$&quot;</span>
+                <span class="p">]</span>
+
+            <span class="n">label</span> <span class="o">=</span> <span class="n">label_list</span><span class="p">[</span><span class="n">axis_index</span><span class="p">]</span>
+
+        <span class="k">elif</span> <span class="n">dataset</span> <span class="o">==</span> <span class="s2">&quot;cs_invariant&quot;</span><span class="p">:</span>
+            <span class="n">dimension_dict</span> <span class="o">=</span> <span class="p">{</span><span class="s2">&quot;x&quot;</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="s2">&quot;y&quot;</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span> <span class="s2">&quot;s&quot;</span><span class="p">:</span> <span class="mi">2</span><span class="p">}</span>
+            <span class="n">axis_index</span> <span class="o">=</span> <span class="n">dimension_dict</span><span class="p">[</span><span class="n">dimension</span><span class="p">]</span>
+            <span class="n">y_var</span> <span class="o">=</span> <span class="n">file</span><span class="p">[</span><span class="n">group</span><span class="p">][</span><span class="n">dataset</span><span class="p">][</span><span class="n">axis_index</span><span class="p">]</span>
+            <span class="n">label_list</span> <span class="o">=</span> <span class="p">[</span><span class="s1">&#39;$J_x$ (m)&#39;</span><span class="p">,</span> <span class="s1">&#39;$J_y$ (m)&#39;</span><span class="p">,</span> <span class="s1">&#39;$J_s$ (s)&#39;</span><span class="p">]</span>
+            <span class="n">label</span> <span class="o">=</span> <span class="n">label_list</span><span class="p">[</span><span class="n">axis_index</span><span class="p">]</span>
+
+        <span class="n">x_axis</span> <span class="o">=</span> <span class="n">file</span><span class="p">[</span><span class="n">group</span><span class="p">][</span><span class="s2">&quot;time&quot;</span><span class="p">][:]</span>
+        <span class="n">xlabel</span> <span class="o">=</span> <span class="s2">&quot;Number of turns&quot;</span>
+
+        <span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x_axis</span><span class="p">,</span> <span class="n">y_var</span><span class="p">)</span>
+        <span class="n">ax</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="n">xlabel</span><span class="p">)</span>
+        <span class="n">ax</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="n">label</span><span class="p">)</span>
+        <span class="k">if</span> <span class="n">legend</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="n">plt</span><span class="o">.</span><span class="n">legend</span><span class="p">(</span><span class="n">legend</span><span class="p">)</span>
+
+        <span class="n">file</span><span class="o">.</span><span class="n">close</span><span class="p">()</span>
+
+    <span class="k">return</span> <span class="n">fig</span></div>
+
+
+<div class="viewcode-block" id="plot_phasespacedata"><a class="viewcode-back" href="../../../../mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.plotting.plot_phasespacedata">[docs]</a><span class="k">def</span> <span class="nf">plot_phasespacedata</span><span class="p">(</span><span class="n">filename</span><span class="p">,</span>
+                        <span class="n">bunch_number</span><span class="p">,</span>
+                        <span class="n">x_var</span><span class="p">,</span>
+                        <span class="n">y_var</span><span class="p">,</span>
+                        <span class="n">turn</span><span class="p">,</span>
+                        <span class="n">only_alive</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span>
+                        <span class="n">plot_size</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span>
+                        <span class="n">plot_kind</span><span class="o">=</span><span class="s1">&#39;kde&#39;</span><span class="p">):</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    Plot data recorded by PhaseSpaceMonitor.</span>
+
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">    filename : str</span>
+<span class="sd">        Name of the HDF5 file that contains the data.</span>
+<span class="sd">    bunch_number : int</span>
+<span class="sd">        Bunch to plot. This has to be identical to &#39;bunch_number&#39; parameter in </span>
+<span class="sd">        &#39;PhaseSpaceMonitor&#39; object.</span>
+<span class="sd">    x_var, y_var : str {&quot;x&quot;, &quot;xp&quot;, &quot;y&quot;, &quot;yp&quot;, &quot;tau&quot;, &quot;delta&quot;}</span>
+<span class="sd">        If dataset is &quot;particles&quot;, the variables to be plotted on the </span>
+<span class="sd">        horizontal and the vertical axes need to be specified.</span>
+<span class="sd">    turn : int</span>
+<span class="sd">        Turn at which the data will be extracted.</span>
+<span class="sd">    only_alive : bool, optional</span>
+<span class="sd">        When only_alive is True, only alive particles are plotted and dead </span>
+<span class="sd">        particles will be discarded.</span>
+<span class="sd">    plot_size : [0,1], optional</span>
+<span class="sd">        Number of macro-particles to plot relative to the total number </span>
+<span class="sd">        of macro-particles recorded. This option helps reduce processing time</span>
+<span class="sd">        when the data is big.</span>
+<span class="sd">    plot_kind : {&#39;scatter&#39;, &#39;kde&#39;, &#39;hex&#39;, &#39;reg&#39;, &#39;resid&#39;}, optional</span>
+<span class="sd">        The plot style. The default is &#39;kde&#39;. </span>
+<span class="sd">        </span>
+<span class="sd">    Return</span>
+<span class="sd">    ------</span>
+<span class="sd">    fig : Figure</span>
+<span class="sd">        Figure object with the plot on it.</span>
+<span class="sd">    &quot;&quot;&quot;</span>
+
+    <span class="n">file</span> <span class="o">=</span> <span class="n">hp</span><span class="o">.</span><span class="n">File</span><span class="p">(</span><span class="n">filename</span><span class="p">,</span> <span class="s2">&quot;r&quot;</span><span class="p">)</span>
+
+    <span class="n">group</span> <span class="o">=</span> <span class="s2">&quot;PhaseSpaceData_</span><span class="si">{0}</span><span class="s2">&quot;</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">bunch_number</span><span class="p">)</span>
+    <span class="n">dataset</span> <span class="o">=</span> <span class="s2">&quot;particles&quot;</span>
+
+    <span class="n">option_dict</span> <span class="o">=</span> <span class="p">{</span><span class="s2">&quot;x&quot;</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="s2">&quot;xp&quot;</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span> <span class="s2">&quot;y&quot;</span><span class="p">:</span> <span class="mi">2</span><span class="p">,</span> <span class="s2">&quot;yp&quot;</span><span class="p">:</span> <span class="mi">3</span><span class="p">,</span> <span class="s2">&quot;tau&quot;</span><span class="p">:</span> <span class="mi">4</span><span class="p">,</span> <span class="s2">&quot;delta&quot;</span><span class="p">:</span> <span class="mi">5</span><span class="p">}</span>
+    <span class="n">scale</span> <span class="o">=</span> <span class="p">[</span><span class="mf">1e3</span><span class="p">,</span> <span class="mf">1e3</span><span class="p">,</span> <span class="mf">1e3</span><span class="p">,</span> <span class="mf">1e3</span><span class="p">,</span> <span class="mf">1e12</span><span class="p">,</span> <span class="mi">1</span><span class="p">]</span>
+    <span class="n">label</span> <span class="o">=</span> <span class="p">[</span>
+        <span class="s2">&quot;x (mm)&quot;</span><span class="p">,</span> <span class="s2">&quot;x&#39; (mrad)&quot;</span><span class="p">,</span> <span class="s2">&quot;y (mm)&quot;</span><span class="p">,</span> <span class="s2">&quot;y&#39; (mrad)&quot;</span><span class="p">,</span> <span class="s2">&quot;$</span><span class="se">\\</span><span class="s2">tau$ (ps)&quot;</span><span class="p">,</span>
+        <span class="s2">&quot;$</span><span class="se">\\</span><span class="s2">delta$&quot;</span>
+    <span class="p">]</span>
+
+    <span class="c1"># find the index of &quot;turn&quot; in time array</span>
+    <span class="n">turn_index</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">where</span><span class="p">(</span><span class="n">file</span><span class="p">[</span><span class="n">group</span><span class="p">][</span><span class="s2">&quot;time&quot;</span><span class="p">][:]</span> <span class="o">==</span> <span class="n">turn</span><span class="p">)</span>
+
+    <span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">turn_index</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
+        <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">&quot;Turn </span><span class="si">{0}</span><span class="s2"> is not found. Enter turn from </span><span class="si">{1}</span><span class="s2">.&quot;</span><span class="o">.</span><span class="n">format</span><span class="p">(</span>
+            <span class="n">turn</span><span class="p">,</span> <span class="n">file</span><span class="p">[</span><span class="n">group</span><span class="p">][</span><span class="s2">&quot;time&quot;</span><span class="p">][:]))</span>
+
+    <span class="n">path</span> <span class="o">=</span> <span class="n">file</span><span class="p">[</span><span class="n">group</span><span class="p">][</span><span class="n">dataset</span><span class="p">]</span>
+    <span class="n">mp_number</span> <span class="o">=</span> <span class="n">path</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">size</span>
+
+    <span class="k">if</span> <span class="n">only_alive</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">:</span>
+        <span class="n">data</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">file</span><span class="p">[</span><span class="n">group</span><span class="p">][</span><span class="s2">&quot;alive&quot;</span><span class="p">])</span>
+        <span class="n">index</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">where</span><span class="p">(</span><span class="n">data</span><span class="p">[:,</span> <span class="n">turn_index</span><span class="p">])[</span><span class="mi">0</span><span class="p">]</span>
+    <span class="k">else</span><span class="p">:</span>
+        <span class="n">index</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="n">mp_number</span><span class="p">)</span>
+
+    <span class="k">if</span> <span class="n">plot_size</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
+        <span class="n">samples</span> <span class="o">=</span> <span class="n">index</span>
+    <span class="k">elif</span> <span class="n">plot_size</span> <span class="o">&lt;</span> <span class="mi">1</span><span class="p">:</span>
+        <span class="n">samples_meta</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">sample</span><span class="p">(</span><span class="nb">list</span><span class="p">(</span><span class="n">index</span><span class="p">),</span> <span class="nb">int</span><span class="p">(</span><span class="n">plot_size</span> <span class="o">*</span> <span class="n">mp_number</span><span class="p">))</span>
+        <span class="n">samples</span> <span class="o">=</span> <span class="nb">sorted</span><span class="p">(</span><span class="n">samples_meta</span><span class="p">)</span>
+    <span class="k">else</span><span class="p">:</span>
+        <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">&quot;plot_size must be in range [0,1].&quot;</span><span class="p">)</span>
+
+    <span class="c1"># format : sns.jointplot(x_axis, yaxis, kind)</span>
+    <span class="n">x_axis</span> <span class="o">=</span> <span class="n">path</span><span class="p">[</span><span class="n">samples</span><span class="p">,</span> <span class="n">option_dict</span><span class="p">[</span><span class="n">x_var</span><span class="p">],</span> <span class="n">turn_index</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="mi">0</span><span class="p">]]</span>
+    <span class="n">y_axis</span> <span class="o">=</span> <span class="n">path</span><span class="p">[</span><span class="n">samples</span><span class="p">,</span> <span class="n">option_dict</span><span class="p">[</span><span class="n">y_var</span><span class="p">],</span> <span class="n">turn_index</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="mi">0</span><span class="p">]]</span>
+
+    <span class="n">fig</span> <span class="o">=</span> <span class="n">sns</span><span class="o">.</span><span class="n">jointplot</span><span class="p">(</span><span class="n">x_axis</span> <span class="o">*</span> <span class="n">scale</span><span class="p">[</span><span class="n">option_dict</span><span class="p">[</span><span class="n">x_var</span><span class="p">]],</span>
+                        <span class="n">y_axis</span> <span class="o">*</span> <span class="n">scale</span><span class="p">[</span><span class="n">option_dict</span><span class="p">[</span><span class="n">y_var</span><span class="p">]],</span>
+                        <span class="n">kind</span><span class="o">=</span><span class="n">plot_kind</span><span class="p">)</span>
+
+    <span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="n">label</span><span class="p">[</span><span class="n">option_dict</span><span class="p">[</span><span class="n">x_var</span><span class="p">]])</span>
+    <span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="n">label</span><span class="p">[</span><span class="n">option_dict</span><span class="p">[</span><span class="n">y_var</span><span class="p">]])</span>
+
+    <span class="n">file</span><span class="o">.</span><span class="n">close</span><span class="p">()</span>
+    <span class="k">return</span> <span class="n">fig</span></div>
+
+
+<div class="viewcode-block" id="plot_profiledata"><a class="viewcode-back" href="../../../../mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.plotting.plot_profiledata">[docs]</a><span class="k">def</span> <span class="nf">plot_profiledata</span><span class="p">(</span><span class="n">filename</span><span class="p">,</span>
+                     <span class="n">bunch_number</span><span class="p">,</span>
+                     <span class="n">dimension</span><span class="o">=</span><span class="s2">&quot;tau&quot;</span><span class="p">,</span>
+                     <span class="n">start</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span>
+                     <span class="n">stop</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+                     <span class="n">step</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+                     <span class="n">profile_plot</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span>
+                     <span class="n">streak_plot</span><span class="o">=</span><span class="kc">True</span><span class="p">):</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    Plot data recorded by ProfileMonitor</span>
+
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">    filename : str</span>
+<span class="sd">        Name of the HDF5 file that contains the data.</span>
+<span class="sd">    bunch_number : int</span>
+<span class="sd">        Bunch to plot. This has to be identical to &#39;bunch_number&#39; parameter in </span>
+<span class="sd">        &#39;ProfileMonitor&#39; object.</span>
+<span class="sd">    dimension : str, optional</span>
+<span class="sd">        Dimension to plot. The default is &quot;tau&quot;</span>
+<span class="sd">    start : int, optional</span>
+<span class="sd">        First turn to plot. The default is 0.</span>
+<span class="sd">    stop : int, optional</span>
+<span class="sd">        Last turn to plot. If None, the last turn of the record is selected.</span>
+<span class="sd">    step : int, optional</span>
+<span class="sd">        Plotting step. This has to be divisible by &#39;save_every&#39; parameter in</span>
+<span class="sd">        &#39;ProfileMonitor&#39; object, i.e. step % save_every == 0. If None, step is</span>
+<span class="sd">        equivalent to save_every.</span>
+<span class="sd">    profile_plot : bool, optional</span>
+<span class="sd">        If Ture, bunch profile plot is plotted.</span>
+<span class="sd">    streak_plot : bool, optional</span>
+<span class="sd">        If True, strek plot is plotted.</span>
+
+<span class="sd">    Returns</span>
+<span class="sd">    -------</span>
+<span class="sd">    fig : Figure</span>
+<span class="sd">        Figure object with the plot on it.</span>
+
+<span class="sd">    &quot;&quot;&quot;</span>
+
+    <span class="n">file</span> <span class="o">=</span> <span class="n">hp</span><span class="o">.</span><span class="n">File</span><span class="p">(</span><span class="n">filename</span><span class="p">,</span> <span class="s2">&quot;r&quot;</span><span class="p">)</span>
+    <span class="n">path</span> <span class="o">=</span> <span class="n">file</span><span class="p">[</span><span class="s1">&#39;ProfileData_</span><span class="si">{0}</span><span class="s1">&#39;</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">bunch_number</span><span class="p">)]</span>
+    <span class="n">l_bound</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">path</span><span class="p">[</span><span class="s2">&quot;</span><span class="si">{0}</span><span class="s2">_bin&quot;</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">dimension</span><span class="p">)])</span>
+    <span class="n">data</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">path</span><span class="p">[</span><span class="n">dimension</span><span class="p">])</span>
+    <span class="n">time</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">path</span><span class="p">[</span><span class="s2">&quot;time&quot;</span><span class="p">])</span>
+
+    <span class="k">if</span> <span class="n">stop</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+        <span class="n">stop</span> <span class="o">=</span> <span class="n">time</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
+    <span class="k">elif</span> <span class="n">stop</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">time</span><span class="p">:</span>
+        <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">&quot;stop not found. Choose from </span><span class="si">{0}</span><span class="s2">&quot;</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">time</span><span class="p">[:]))</span>
+
+    <span class="k">if</span> <span class="n">start</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">time</span><span class="p">:</span>
+        <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">&quot;start not found. Choose from </span><span class="si">{0}</span><span class="s2">&quot;</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">time</span><span class="p">[:]))</span>
+
+    <span class="n">save_every</span> <span class="o">=</span> <span class="n">time</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="n">time</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
+
+    <span class="k">if</span> <span class="n">step</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+        <span class="n">step</span> <span class="o">=</span> <span class="n">save_every</span>
+
+    <span class="k">if</span> <span class="n">step</span> <span class="o">%</span> <span class="n">save_every</span> <span class="o">!=</span> <span class="mi">0</span><span class="p">:</span>
+        <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">&quot;step must be divisible by the recording step &quot;</span>
+                         <span class="s2">&quot;which is </span><span class="si">{0}</span><span class="s2">.&quot;</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">save_every</span><span class="p">))</span>
+
+    <span class="n">dimension_dict</span> <span class="o">=</span> <span class="p">{</span><span class="s2">&quot;x&quot;</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="s2">&quot;xp&quot;</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span> <span class="s2">&quot;y&quot;</span><span class="p">:</span> <span class="mi">2</span><span class="p">,</span> <span class="s2">&quot;yp&quot;</span><span class="p">:</span> <span class="mi">3</span><span class="p">,</span> <span class="s2">&quot;tau&quot;</span><span class="p">:</span> <span class="mi">4</span><span class="p">,</span> <span class="s2">&quot;delta&quot;</span><span class="p">:</span> <span class="mi">5</span><span class="p">}</span>
+    <span class="n">scale</span> <span class="o">=</span> <span class="p">[</span><span class="mf">1e6</span><span class="p">,</span> <span class="mf">1e6</span><span class="p">,</span> <span class="mf">1e6</span><span class="p">,</span> <span class="mf">1e6</span><span class="p">,</span> <span class="mf">1e12</span><span class="p">,</span> <span class="mi">1</span><span class="p">]</span>
+    <span class="n">label</span> <span class="o">=</span> <span class="p">[</span>
+        <span class="s2">&quot;x (um)&quot;</span><span class="p">,</span> <span class="s2">&quot;x&#39; ($</span><span class="se">\\</span><span class="s2">mu$rad)&quot;</span><span class="p">,</span> <span class="s2">&quot;y (um)&quot;</span><span class="p">,</span> <span class="s2">&quot;y&#39; ($</span><span class="se">\\</span><span class="s2">mu$rad)&quot;</span><span class="p">,</span> <span class="s2">&quot;$</span><span class="se">\\</span><span class="s2">tau$ (ps)&quot;</span><span class="p">,</span>
+        <span class="s2">&quot;$</span><span class="se">\\</span><span class="s2">delta$&quot;</span>
+    <span class="p">]</span>
+
+    <span class="n">num</span> <span class="o">=</span> <span class="nb">int</span><span class="p">((</span><span class="n">stop</span><span class="o">-</span><span class="n">start</span><span class="p">)</span> <span class="o">/</span> <span class="n">step</span><span class="p">)</span>
+    <span class="n">n_bin</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">data</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">])</span>
+
+    <span class="n">start_index</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">where</span><span class="p">(</span><span class="n">time</span><span class="p">[:]</span> <span class="o">==</span> <span class="n">start</span><span class="p">)[</span><span class="mi">0</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span>
+
+    <span class="n">x_var</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="n">num</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span> <span class="n">n_bin</span><span class="p">))</span>
+    <span class="n">turn_index_array</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="n">num</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span> <span class="p">),</span> <span class="n">dtype</span><span class="o">=</span><span class="nb">int</span><span class="p">)</span>
+    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">num</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
+        <span class="n">turn_index</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">start_index</span> <span class="o">+</span> <span class="n">i</span><span class="o">*</span><span class="n">step</span><span class="o">/</span><span class="n">save_every</span><span class="p">)</span>
+        <span class="n">turn_index_array</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="n">turn_index</span>
+        <span class="c1"># construct an array of bin mids</span>
+        <span class="n">x_var</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="p">:]</span> <span class="o">=</span> <span class="n">l_bound</span><span class="p">[:,</span> <span class="n">turn_index</span><span class="p">]</span>
+
+    <span class="k">if</span> <span class="n">profile_plot</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">:</span>
+        <span class="n">fig</span><span class="p">,</span> <span class="n">ax</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">()</span>
+        <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">num</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
+            <span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x_var</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">*</span> <span class="n">scale</span><span class="p">[</span><span class="n">dimension_dict</span><span class="p">[</span><span class="n">dimension</span><span class="p">]],</span>
+                    <span class="n">data</span><span class="p">[:,</span> <span class="n">turn_index_array</span><span class="p">[</span><span class="n">i</span><span class="p">]],</span>
+                    <span class="n">label</span><span class="o">=</span><span class="s2">&quot;turn </span><span class="si">{0}</span><span class="s2">&quot;</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">time</span><span class="p">[</span><span class="n">turn_index_array</span><span class="p">[</span><span class="n">i</span><span class="p">]]))</span>
+        <span class="n">ax</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="n">label</span><span class="p">[</span><span class="n">dimension_dict</span><span class="p">[</span><span class="n">dimension</span><span class="p">]])</span>
+        <span class="n">ax</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="s2">&quot;number of macro-particles&quot;</span><span class="p">)</span>
+        <span class="n">ax</span><span class="o">.</span><span class="n">legend</span><span class="p">()</span>
+
+    <span class="k">if</span> <span class="n">streak_plot</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">:</span>
+        <span class="n">turn</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">time</span><span class="p">[</span><span class="n">turn_index_array</span><span class="p">],</span> <span class="p">(</span><span class="n">num</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">))</span>
+        <span class="n">y_var</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">((</span><span class="n">num</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span> <span class="n">n_bin</span><span class="p">))</span> <span class="o">*</span> <span class="n">turn</span>
+        <span class="n">z_var</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">transpose</span><span class="p">(</span><span class="n">data</span><span class="p">[:,</span> <span class="n">turn_index_array</span><span class="p">])</span>
+        <span class="n">fig2</span><span class="p">,</span> <span class="n">ax2</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">()</span>
+        <span class="n">cmap</span> <span class="o">=</span> <span class="n">mpl</span><span class="o">.</span><span class="n">cm</span><span class="o">.</span><span class="n">inferno</span>  <span class="c1"># sequential</span>
+        <span class="n">c</span> <span class="o">=</span> <span class="n">ax2</span><span class="o">.</span><span class="n">imshow</span><span class="p">(</span><span class="n">z_var</span><span class="p">,</span>
+                       <span class="n">cmap</span><span class="o">=</span><span class="n">cmap</span><span class="p">,</span>
+                       <span class="n">origin</span><span class="o">=</span><span class="s1">&#39;lower&#39;</span><span class="p">,</span>
+                       <span class="n">aspect</span><span class="o">=</span><span class="s1">&#39;auto&#39;</span><span class="p">,</span>
+                       <span class="n">extent</span><span class="o">=</span><span class="p">[</span>
+                           <span class="n">x_var</span><span class="o">.</span><span class="n">min</span><span class="p">()</span> <span class="o">*</span> <span class="n">scale</span><span class="p">[</span><span class="n">dimension_dict</span><span class="p">[</span><span class="n">dimension</span><span class="p">]],</span>
+                           <span class="n">x_var</span><span class="o">.</span><span class="n">max</span><span class="p">()</span> <span class="o">*</span> <span class="n">scale</span><span class="p">[</span><span class="n">dimension_dict</span><span class="p">[</span><span class="n">dimension</span><span class="p">]],</span>
+                           <span class="n">y_var</span><span class="o">.</span><span class="n">min</span><span class="p">(),</span>
+                           <span class="n">y_var</span><span class="o">.</span><span class="n">max</span><span class="p">()</span>
+                       <span class="p">])</span>
+        <span class="n">ax2</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="n">label</span><span class="p">[</span><span class="n">dimension_dict</span><span class="p">[</span><span class="n">dimension</span><span class="p">]])</span>
+        <span class="n">ax2</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="s2">&quot;Number of turns&quot;</span><span class="p">)</span>
+        <span class="n">cbar</span> <span class="o">=</span> <span class="n">fig2</span><span class="o">.</span><span class="n">colorbar</span><span class="p">(</span><span class="n">c</span><span class="p">,</span> <span class="n">ax</span><span class="o">=</span><span class="n">ax2</span><span class="p">)</span>
+        <span class="n">cbar</span><span class="o">.</span><span class="n">set_label</span><span class="p">(</span><span class="s2">&quot;Number of macro-particles&quot;</span><span class="p">)</span>
+
+    <span class="n">file</span><span class="o">.</span><span class="n">close</span><span class="p">()</span>
+    <span class="k">if</span> <span class="n">profile_plot</span> <span class="ow">is</span> <span class="kc">True</span> <span class="ow">and</span> <span class="n">streak_plot</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">:</span>
+        <span class="k">return</span> <span class="n">fig</span><span class="p">,</span> <span class="n">fig2</span>
+    <span class="k">elif</span> <span class="n">profile_plot</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">:</span>
+        <span class="k">return</span> <span class="n">fig</span>
+    <span class="k">elif</span> <span class="n">streak_plot</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">:</span>
+        <span class="k">return</span> <span class="n">fig2</span></div>
+
+
+<div class="viewcode-block" id="plot_wakedata"><a class="viewcode-back" href="../../../../mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.plotting.plot_wakedata">[docs]</a><span class="k">def</span> <span class="nf">plot_wakedata</span><span class="p">(</span><span class="n">filename</span><span class="p">,</span>
+                  <span class="n">bunch_number</span><span class="p">,</span>
+                  <span class="n">wake_type</span><span class="o">=</span><span class="s2">&quot;Wlong&quot;</span><span class="p">,</span>
+                  <span class="n">start</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span>
+                  <span class="n">stop</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+                  <span class="n">step</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+                  <span class="n">profile_plot</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span>
+                  <span class="n">streak_plot</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span>
+                  <span class="n">bunch_profile</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span>
+                  <span class="n">dipole</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    Plot data recorded by WakePotentialMonitor</span>
+
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">    filename : str</span>
+<span class="sd">        Name of the HDF5 file that contains the data.</span>
+<span class="sd">    bunch_number : int</span>
+<span class="sd">        Bunch to plot. This has to be identical to &#39;bunch_number&#39; parameter in </span>
+<span class="sd">        &#39;WakePotentialMonitor&#39; object.</span>
+<span class="sd">    wake_type : str, optional</span>
+<span class="sd">        Wake type to plot: &quot;Wlong&quot;, &quot;Wxdip&quot;, ... </span>
+<span class="sd">    start : int, optional</span>
+<span class="sd">        First turn to plot. The default is 0.</span>
+<span class="sd">    stop : int, optional</span>
+<span class="sd">        Last turn to plot. If None, the last turn of the record is selected.</span>
+<span class="sd">    step : int, optional</span>
+<span class="sd">        Plotting step. This has to be divisible by &#39;save_every&#39; parameter in</span>
+<span class="sd">        &#39;WakePotentialMonitor&#39; object, i.e. step % save_every == 0. If None, </span>
+<span class="sd">        step is equivalent to save_every.</span>
+<span class="sd">    profile_plot : bool, optional</span>
+<span class="sd">        If Ture, wake potential profile plot is plotted.</span>
+<span class="sd">    streak_plot : bool, optional</span>
+<span class="sd">        If True, strek plot is plotted.</span>
+<span class="sd">    bunch_profile : bool, optional.</span>
+<span class="sd">        If True, the bunch profile is plotted.</span>
+<span class="sd">    dipole : bool, optional</span>
+<span class="sd">        If True, the dipole moment is plotted.</span>
+
+<span class="sd">    Returns</span>
+<span class="sd">    -------</span>
+<span class="sd">    fig : Figure</span>
+<span class="sd">        Figure object with the plot on it.</span>
+
+<span class="sd">    &quot;&quot;&quot;</span>
+
+    <span class="n">file</span> <span class="o">=</span> <span class="n">hp</span><span class="o">.</span><span class="n">File</span><span class="p">(</span><span class="n">filename</span><span class="p">,</span> <span class="s2">&quot;r&quot;</span><span class="p">)</span>
+    <span class="n">path</span> <span class="o">=</span> <span class="n">file</span><span class="p">[</span><span class="s1">&#39;WakePotentialData_</span><span class="si">{0}</span><span class="s1">&#39;</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">bunch_number</span><span class="p">)]</span>
+    <span class="n">time</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">path</span><span class="p">[</span><span class="s2">&quot;time&quot;</span><span class="p">])</span>
+
+    <span class="k">if</span> <span class="n">stop</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+        <span class="n">stop</span> <span class="o">=</span> <span class="n">time</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
+    <span class="k">elif</span> <span class="n">stop</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">time</span><span class="p">:</span>
+        <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">&quot;stop not found. Choose from </span><span class="si">{0}</span><span class="s2">&quot;</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">time</span><span class="p">[:]))</span>
+
+    <span class="k">if</span> <span class="n">start</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">time</span><span class="p">:</span>
+        <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">&quot;start not found. Choose from </span><span class="si">{0}</span><span class="s2">&quot;</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">time</span><span class="p">[:]))</span>
+
+    <span class="n">save_every</span> <span class="o">=</span> <span class="n">time</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="n">time</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
+
+    <span class="k">if</span> <span class="n">step</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+        <span class="n">step</span> <span class="o">=</span> <span class="n">save_every</span>
+
+    <span class="k">if</span> <span class="n">step</span> <span class="o">%</span> <span class="n">save_every</span> <span class="o">!=</span> <span class="mi">0</span><span class="p">:</span>
+        <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">&quot;step must be divisible by the recording step &quot;</span>
+                         <span class="s2">&quot;which is </span><span class="si">{0}</span><span class="s2">.&quot;</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">save_every</span><span class="p">))</span>
+
+    <span class="n">dimension_dict</span> <span class="o">=</span> <span class="p">{</span>
+        <span class="s2">&quot;Wlong&quot;</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span>
+        <span class="s2">&quot;Wxdip&quot;</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span>
+        <span class="s2">&quot;Wydip&quot;</span><span class="p">:</span> <span class="mi">2</span><span class="p">,</span>
+        <span class="s2">&quot;Wxquad&quot;</span><span class="p">:</span> <span class="mi">3</span><span class="p">,</span>
+        <span class="s2">&quot;Wyquad&quot;</span><span class="p">:</span> <span class="mi">4</span>
+    <span class="p">}</span>
+    <span class="n">scale</span> <span class="o">=</span> <span class="p">[</span><span class="mf">1e-12</span><span class="p">,</span> <span class="mf">1e-12</span><span class="p">,</span> <span class="mf">1e-12</span><span class="p">,</span> <span class="mf">1e-15</span><span class="p">,</span> <span class="mf">1e-15</span><span class="p">]</span>
+    <span class="n">label</span> <span class="o">=</span> <span class="p">[</span>
+        <span class="s2">&quot;$W_p$ (V/pC)&quot;</span><span class="p">,</span> <span class="s2">&quot;$W_{p,x}^D (V/pC)$&quot;</span><span class="p">,</span> <span class="s2">&quot;$W_{p,y}^D (V/pC)$&quot;</span><span class="p">,</span>
+        <span class="s2">&quot;$W_{p,x}^Q (V/pC/mm)$&quot;</span><span class="p">,</span> <span class="s2">&quot;$W_{p,y}^Q (V/pC/mm)$&quot;</span>
+    <span class="p">]</span>
+
+    <span class="k">if</span> <span class="n">bunch_profile</span> <span class="o">==</span> <span class="kc">True</span><span class="p">:</span>
+        <span class="n">tau_name</span> <span class="o">=</span> <span class="s2">&quot;tau_&quot;</span> <span class="o">+</span> <span class="n">wake_type</span>
+        <span class="n">wake_type</span> <span class="o">=</span> <span class="s2">&quot;profile_&quot;</span> <span class="o">+</span> <span class="n">wake_type</span>
+        <span class="n">dimension_dict</span> <span class="o">=</span> <span class="p">{</span><span class="n">wake_type</span><span class="p">:</span> <span class="mi">0</span><span class="p">}</span>
+        <span class="n">scale</span> <span class="o">=</span> <span class="p">[</span><span class="mi">1</span><span class="p">]</span>
+        <span class="n">label</span> <span class="o">=</span> <span class="p">[</span><span class="s2">&quot;$</span><span class="se">\\</span><span class="s2">rho$ (a.u.)&quot;</span><span class="p">]</span>
+        <span class="n">cmap</span> <span class="o">=</span> <span class="n">mpl</span><span class="o">.</span><span class="n">cm</span><span class="o">.</span><span class="n">inferno</span>  <span class="c1"># sequential</span>
+    <span class="k">elif</span> <span class="n">dipole</span> <span class="o">==</span> <span class="kc">True</span><span class="p">:</span>
+        <span class="n">tau_name</span> <span class="o">=</span> <span class="s2">&quot;tau_&quot;</span> <span class="o">+</span> <span class="n">wake_type</span>
+        <span class="n">wake_type</span> <span class="o">=</span> <span class="s2">&quot;dipole_&quot;</span> <span class="o">+</span> <span class="n">wake_type</span>
+        <span class="n">dimension_dict</span> <span class="o">=</span> <span class="p">{</span><span class="n">wake_type</span><span class="p">:</span> <span class="mi">0</span><span class="p">}</span>
+        <span class="n">scale</span> <span class="o">=</span> <span class="p">[</span><span class="mi">1</span><span class="p">]</span>
+        <span class="n">label</span> <span class="o">=</span> <span class="p">[</span><span class="s2">&quot;Dipole moment (m)&quot;</span><span class="p">]</span>
+        <span class="n">cmap</span> <span class="o">=</span> <span class="n">mpl</span><span class="o">.</span><span class="n">cm</span><span class="o">.</span><span class="n">coolwarm</span>  <span class="c1"># diverging</span>
+    <span class="k">else</span><span class="p">:</span>
+        <span class="n">tau_name</span> <span class="o">=</span> <span class="s2">&quot;tau_&quot;</span> <span class="o">+</span> <span class="n">wake_type</span>
+        <span class="n">cmap</span> <span class="o">=</span> <span class="n">mpl</span><span class="o">.</span><span class="n">cm</span><span class="o">.</span><span class="n">coolwarm</span>  <span class="c1"># diverging</span>
+
+    <span class="n">data</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">path</span><span class="p">[</span><span class="n">wake_type</span><span class="p">])</span>
+
+    <span class="n">num</span> <span class="o">=</span> <span class="nb">int</span><span class="p">((</span><span class="n">stop</span><span class="o">-</span><span class="n">start</span><span class="p">)</span> <span class="o">/</span> <span class="n">step</span><span class="p">)</span>
+    <span class="n">n_bin</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">data</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">])</span>
+
+    <span class="n">start_index</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">where</span><span class="p">(</span><span class="n">time</span><span class="p">[:]</span> <span class="o">==</span> <span class="n">start</span><span class="p">)[</span><span class="mi">0</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span>
+
+    <span class="n">x_var</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="n">num</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span> <span class="n">n_bin</span><span class="p">))</span>
+    <span class="n">turn_index_array</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="n">num</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span> <span class="p">),</span> <span class="n">dtype</span><span class="o">=</span><span class="nb">int</span><span class="p">)</span>
+    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">num</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
+        <span class="n">turn_index</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">start_index</span> <span class="o">+</span> <span class="n">i</span><span class="o">*</span><span class="n">step</span><span class="o">/</span><span class="n">save_every</span><span class="p">)</span>
+        <span class="n">turn_index_array</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="n">turn_index</span>
+        <span class="c1"># construct an array of bin mids</span>
+        <span class="n">x_var</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="p">:]</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">path</span><span class="p">[</span><span class="n">tau_name</span><span class="p">])[:,</span> <span class="n">turn_index</span><span class="p">]</span>
+
+    <span class="k">if</span> <span class="n">profile_plot</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">:</span>
+        <span class="n">fig</span><span class="p">,</span> <span class="n">ax</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">()</span>
+        <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">num</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
+            <span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x_var</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">*</span> <span class="mf">1e12</span><span class="p">,</span>
+                    <span class="n">data</span><span class="p">[:,</span> <span class="n">turn_index_array</span><span class="p">[</span><span class="n">i</span><span class="p">]]</span> <span class="o">*</span>
+                    <span class="n">scale</span><span class="p">[</span><span class="n">dimension_dict</span><span class="p">[</span><span class="n">wake_type</span><span class="p">]],</span>
+                    <span class="n">label</span><span class="o">=</span><span class="s2">&quot;turn </span><span class="si">{0}</span><span class="s2">&quot;</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">time</span><span class="p">[</span><span class="n">turn_index_array</span><span class="p">[</span><span class="n">i</span><span class="p">]]))</span>
+        <span class="n">ax</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="s2">&quot;$</span><span class="se">\\</span><span class="s2">tau$ (ps)&quot;</span><span class="p">)</span>
+        <span class="n">ax</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="n">label</span><span class="p">[</span><span class="n">dimension_dict</span><span class="p">[</span><span class="n">wake_type</span><span class="p">]])</span>
+        <span class="n">ax</span><span class="o">.</span><span class="n">legend</span><span class="p">()</span>
+
+    <span class="k">if</span> <span class="n">streak_plot</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">:</span>
+        <span class="n">turn</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">time</span><span class="p">[</span><span class="n">turn_index_array</span><span class="p">],</span> <span class="p">(</span><span class="n">num</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">))</span>
+        <span class="n">y_var</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">((</span><span class="n">num</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span> <span class="n">n_bin</span><span class="p">))</span> <span class="o">*</span> <span class="n">turn</span>
+        <span class="n">z_var</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">transpose</span><span class="p">(</span><span class="n">data</span><span class="p">[:,</span> <span class="n">turn_index_array</span><span class="p">]</span> <span class="o">*</span>
+                             <span class="n">scale</span><span class="p">[</span><span class="n">dimension_dict</span><span class="p">[</span><span class="n">wake_type</span><span class="p">]])</span>
+        <span class="n">fig2</span><span class="p">,</span> <span class="n">ax2</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">()</span>
+        <span class="n">c</span> <span class="o">=</span> <span class="n">ax2</span><span class="o">.</span><span class="n">imshow</span><span class="p">(</span><span class="n">z_var</span><span class="p">,</span>
+                       <span class="n">cmap</span><span class="o">=</span><span class="n">cmap</span><span class="p">,</span>
+                       <span class="n">origin</span><span class="o">=</span><span class="s1">&#39;lower&#39;</span><span class="p">,</span>
+                       <span class="n">aspect</span><span class="o">=</span><span class="s1">&#39;auto&#39;</span><span class="p">,</span>
+                       <span class="n">extent</span><span class="o">=</span><span class="p">[</span>
+                           <span class="n">x_var</span><span class="o">.</span><span class="n">min</span><span class="p">()</span> <span class="o">*</span> <span class="mf">1e12</span><span class="p">,</span>
+                           <span class="n">x_var</span><span class="o">.</span><span class="n">max</span><span class="p">()</span> <span class="o">*</span> <span class="mf">1e12</span><span class="p">,</span>
+                           <span class="n">y_var</span><span class="o">.</span><span class="n">min</span><span class="p">(),</span>
+                           <span class="n">y_var</span><span class="o">.</span><span class="n">max</span><span class="p">()</span>
+                       <span class="p">])</span>
+        <span class="n">ax2</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="s2">&quot;$</span><span class="se">\\</span><span class="s2">tau$ (ps)&quot;</span><span class="p">)</span>
+        <span class="n">ax2</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="s2">&quot;Number of turns&quot;</span><span class="p">)</span>
+        <span class="n">cbar</span> <span class="o">=</span> <span class="n">fig2</span><span class="o">.</span><span class="n">colorbar</span><span class="p">(</span><span class="n">c</span><span class="p">,</span> <span class="n">ax</span><span class="o">=</span><span class="n">ax2</span><span class="p">)</span>
+        <span class="n">cbar</span><span class="o">.</span><span class="n">set_label</span><span class="p">(</span><span class="n">label</span><span class="p">[</span><span class="n">dimension_dict</span><span class="p">[</span><span class="n">wake_type</span><span class="p">]])</span>
+
+    <span class="n">file</span><span class="o">.</span><span class="n">close</span><span class="p">()</span>
+    <span class="k">if</span> <span class="n">profile_plot</span> <span class="ow">is</span> <span class="kc">True</span> <span class="ow">and</span> <span class="n">streak_plot</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">:</span>
+        <span class="k">return</span> <span class="n">fig</span><span class="p">,</span> <span class="n">fig2</span>
+    <span class="k">elif</span> <span class="n">profile_plot</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">:</span>
+        <span class="k">return</span> <span class="n">fig</span>
+    <span class="k">elif</span> <span class="n">streak_plot</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">:</span>
+        <span class="k">return</span> <span class="n">fig2</span></div>
+
+
+<div class="viewcode-block" id="plot_bunchspectrum"><a class="viewcode-back" href="../../../../mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.plotting.plot_bunchspectrum">[docs]</a><span class="k">def</span> <span class="nf">plot_bunchspectrum</span><span class="p">(</span><span class="n">filenames</span><span class="p">,</span>
+                       <span class="n">bunch_number</span><span class="p">,</span>
+                       <span class="n">dataset</span><span class="o">=</span><span class="s2">&quot;incoherent&quot;</span><span class="p">,</span>
+                       <span class="n">dim</span><span class="o">=</span><span class="s2">&quot;tau&quot;</span><span class="p">,</span>
+                       <span class="n">turns</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+                       <span class="n">fs</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+                       <span class="n">log_scale</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span>
+                       <span class="n">legend</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+                       <span class="n">norm</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    Plot coherent and incoherent spectrum data.</span>
+
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">    filenames : str or list of str</span>
+<span class="sd">        Names of the HDF5 files to be plotted.</span>
+<span class="sd">    bunch_number : int or list of int</span>
+<span class="sd">        Bunch to plot. This has to be identical to &#39;bunch_number&#39; parameter in </span>
+<span class="sd">        &#39;BunchSpectrumMonitor&#39; object.</span>
+<span class="sd">    dataset : {&quot;mean_incoherent&quot;, &quot;coherent&quot;, &quot;incoherent&quot;}</span>
+<span class="sd">        HDF5 file&#39;s dataset to be plotted. </span>
+<span class="sd">        The default is &quot;incoherent&quot;.</span>
+<span class="sd">    dim :  {&quot;x&quot;,&quot;y&quot;,&quot;tau&quot;}, optional</span>
+<span class="sd">        The dimension of the dataset to plot.</span>
+<span class="sd">        The default is &quot;tau&quot;.</span>
+<span class="sd">    turns : array or None, optional</span>
+<span class="sd">        Numbers of the turns to plot.</span>
+<span class="sd">        If None, all turns are shown. </span>
+<span class="sd">        The default is None.</span>
+<span class="sd">    fs : float or None, optional</span>
+<span class="sd">        If not None, the frequency axis is noramlised by fs. </span>
+<span class="sd">        The default is None.</span>
+<span class="sd">    log_scale : bool, optional</span>
+<span class="sd">        If True, the spectrum plots are shown in y-log scale. </span>
+<span class="sd">        The default is True.</span>
+<span class="sd">    legend : list of str, optional</span>
+<span class="sd">        Legend to add for each file.</span>
+<span class="sd">        The default is None.</span>
+<span class="sd">    norm : bool, optional</span>
+<span class="sd">        If True, normalise the data of each spectrum by its geometric mean.</span>
+<span class="sd">        The default is False.</span>
+
+<span class="sd">    Return</span>
+<span class="sd">    ------</span>
+<span class="sd">    fig : Figure</span>
+
+<span class="sd">    &quot;&quot;&quot;</span>
+
+    <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">filenames</span><span class="p">,</span> <span class="nb">str</span><span class="p">):</span>
+        <span class="n">filenames</span> <span class="o">=</span> <span class="p">[</span><span class="n">filenames</span><span class="p">]</span>
+
+    <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">bunch_number</span><span class="p">,</span> <span class="nb">int</span><span class="p">):</span>
+        <span class="n">ll</span> <span class="o">=</span> <span class="p">[]</span>
+        <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">filenames</span><span class="p">)):</span>
+            <span class="n">ll</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">bunch_number</span><span class="p">)</span>
+        <span class="n">bunch_number</span> <span class="o">=</span> <span class="n">ll</span>
+
+    <span class="n">fig</span><span class="p">,</span> <span class="n">ax</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">()</span>
+
+    <span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">filename</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">filenames</span><span class="p">):</span>
+        <span class="n">file</span> <span class="o">=</span> <span class="n">hp</span><span class="o">.</span><span class="n">File</span><span class="p">(</span><span class="n">filename</span><span class="p">,</span> <span class="s2">&quot;r&quot;</span><span class="p">)</span>
+        <span class="n">group</span> <span class="o">=</span> <span class="n">file</span><span class="p">[</span><span class="s2">&quot;BunchSpectrum_</span><span class="si">{0}</span><span class="s2">&quot;</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">bunch_number</span><span class="p">[</span><span class="n">i</span><span class="p">])]</span>
+
+        <span class="n">time</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">group</span><span class="p">[</span><span class="s2">&quot;time&quot;</span><span class="p">])</span>
+        <span class="n">freq</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">group</span><span class="p">[</span><span class="s2">&quot;freq&quot;</span><span class="p">])</span>
+        <span class="n">dim_dict</span> <span class="o">=</span> <span class="p">{</span><span class="s2">&quot;x&quot;</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="s2">&quot;y&quot;</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span> <span class="s2">&quot;tau&quot;</span><span class="p">:</span> <span class="mi">2</span><span class="p">}</span>
+
+        <span class="k">if</span> <span class="n">dataset</span> <span class="o">==</span> <span class="s2">&quot;mean_incoherent&quot;</span><span class="p">:</span>
+            <span class="n">y_var</span> <span class="o">=</span> <span class="n">group</span><span class="p">[</span><span class="s2">&quot;mean_incoherent&quot;</span><span class="p">][</span><span class="n">dim_dict</span><span class="p">[</span><span class="n">dim</span><span class="p">],</span> <span class="p">:]</span>
+            <span class="n">y_err</span> <span class="o">=</span> <span class="n">group</span><span class="p">[</span><span class="s2">&quot;std_incoherent&quot;</span><span class="p">][</span><span class="n">dim_dict</span><span class="p">[</span><span class="n">dim</span><span class="p">],</span> <span class="p">:]</span>
+            <span class="n">ax</span><span class="o">.</span><span class="n">errorbar</span><span class="p">(</span><span class="n">time</span><span class="p">,</span> <span class="n">y_var</span><span class="p">,</span> <span class="n">y_err</span><span class="p">)</span>
+            <span class="n">xlabel</span> <span class="o">=</span> <span class="s2">&quot;Turn number&quot;</span>
+            <span class="n">ylabel</span> <span class="o">=</span> <span class="s2">&quot;Mean incoherent frequency [Hz]&quot;</span>
+        <span class="k">elif</span> <span class="n">dataset</span> <span class="o">==</span> <span class="s2">&quot;incoherent&quot;</span> <span class="ow">or</span> <span class="n">dataset</span> <span class="o">==</span> <span class="s2">&quot;coherent&quot;</span><span class="p">:</span>
+
+            <span class="k">if</span> <span class="n">turns</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+                <span class="n">turn_index</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">where</span><span class="p">(</span><span class="n">time</span> <span class="o">==</span> <span class="n">time</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span>
+            <span class="k">else</span><span class="p">:</span>
+                <span class="n">turn_index</span> <span class="o">=</span> <span class="p">[]</span>
+                <span class="k">for</span> <span class="n">turn</span> <span class="ow">in</span> <span class="n">turns</span><span class="p">:</span>
+                    <span class="n">idx</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">where</span><span class="p">(</span><span class="n">time</span> <span class="o">==</span> <span class="n">turn</span><span class="p">)[</span><span class="mi">0</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span>
+                    <span class="n">turn_index</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">idx</span><span class="p">)</span>
+                <span class="n">turn_index</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">turn_index</span><span class="p">)</span>
+
+            <span class="k">if</span> <span class="n">fs</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+                <span class="n">x_var</span> <span class="o">=</span> <span class="n">freq</span>
+                <span class="n">xlabel</span> <span class="o">=</span> <span class="s2">&quot;Frequency [Hz]&quot;</span>
+            <span class="k">else</span><span class="p">:</span>
+                <span class="n">x_var</span> <span class="o">=</span> <span class="n">freq</span> <span class="o">/</span> <span class="n">fs</span>
+                <span class="n">xlabel</span> <span class="o">=</span> <span class="sa">r</span><span class="s2">&quot;$f/f_</span><span class="si">{s}</span><span class="s2">$&quot;</span>
+
+            <span class="k">for</span> <span class="n">idx</span> <span class="ow">in</span> <span class="n">turn_index</span><span class="p">:</span>
+                <span class="n">y_var</span> <span class="o">=</span> <span class="n">group</span><span class="p">[</span><span class="n">dataset</span><span class="p">][</span><span class="n">dim_dict</span><span class="p">[</span><span class="n">dim</span><span class="p">],</span> <span class="p">:,</span> <span class="n">idx</span><span class="p">]</span>
+                <span class="k">if</span> <span class="n">norm</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">:</span>
+                    <span class="n">y_var</span> <span class="o">=</span> <span class="n">y_var</span> <span class="o">/</span> <span class="n">gmean</span><span class="p">(</span><span class="n">y_var</span><span class="p">)</span>
+                <span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x_var</span><span class="p">,</span> <span class="n">y_var</span><span class="p">)</span>
+
+            <span class="k">if</span> <span class="n">log_scale</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">:</span>
+                <span class="n">ax</span><span class="o">.</span><span class="n">set_yscale</span><span class="p">(</span><span class="s1">&#39;log&#39;</span><span class="p">)</span>
+
+            <span class="n">ylabel</span> <span class="o">=</span> <span class="s2">&quot;FFT amplitude [a.u.]&quot;</span>
+            <span class="k">if</span> <span class="n">dataset</span> <span class="o">==</span> <span class="s2">&quot;incoherent&quot;</span><span class="p">:</span>
+                <span class="n">ax</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s2">&quot;Incoherent spectrum&quot;</span><span class="p">)</span>
+            <span class="k">elif</span> <span class="n">dataset</span> <span class="o">==</span> <span class="s2">&quot;coherent&quot;</span><span class="p">:</span>
+                <span class="n">ax</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s2">&quot;Coherent spectrum&quot;</span><span class="p">)</span>
+
+        <span class="n">ax</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="n">xlabel</span><span class="p">)</span>
+        <span class="n">ax</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="n">ylabel</span><span class="p">)</span>
+        <span class="k">if</span> <span class="n">legend</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="n">plt</span><span class="o">.</span><span class="n">legend</span><span class="p">(</span><span class="n">legend</span><span class="p">)</span>
+        <span class="n">file</span><span class="o">.</span><span class="n">close</span><span class="p">()</span>
+
+    <span class="k">return</span> <span class="n">fig</span></div>
+
+
+<div class="viewcode-block" id="streak_bunchspectrum"><a class="viewcode-back" href="../../../../mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.plotting.streak_bunchspectrum">[docs]</a><span class="k">def</span> <span class="nf">streak_bunchspectrum</span><span class="p">(</span><span class="n">filename</span><span class="p">,</span>
+                         <span class="n">bunch_number</span><span class="p">,</span>
+                         <span class="n">dataset</span><span class="o">=</span><span class="s2">&quot;incoherent&quot;</span><span class="p">,</span>
+                         <span class="n">dim</span><span class="o">=</span><span class="s2">&quot;tau&quot;</span><span class="p">,</span>
+                         <span class="n">fs</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+                         <span class="n">log_scale</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span>
+                         <span class="n">fmin</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+                         <span class="n">fmax</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+                         <span class="n">turns</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+                         <span class="n">norm</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span>
+                         <span class="n">ylim</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    Plot 3D data recorded by the BunchSpectrumMonitor.</span>
+
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">    filenames : str</span>
+<span class="sd">        Name of the HDF5 file to be plotted.</span>
+<span class="sd">    bunch_number : int</span>
+<span class="sd">        Bunch to plot. This has to be identical to &#39;bunch_number&#39; parameter in </span>
+<span class="sd">        &#39;BunchSpectrumMonitor&#39; object.</span>
+<span class="sd">    dataset : {&quot;coherent&quot;, &quot;incoherent&quot;}</span>
+<span class="sd">        HDF5 file&#39;s dataset to be plotted. </span>
+<span class="sd">        The default is &quot;incoherent&quot;.</span>
+<span class="sd">    dim :  {&quot;x&quot;,&quot;y&quot;,&quot;tau&quot;}, optional</span>
+<span class="sd">        The dimension of the dataset to plot.</span>
+<span class="sd">        The default is &quot;tau&quot;.</span>
+<span class="sd">    fs : float or None, optional</span>
+<span class="sd">        If not None, the frequency axis is noramlised by fs. </span>
+<span class="sd">    log_scale : bool, optional</span>
+<span class="sd">        If True, the spectrum plots are shown in y-log scale. </span>
+<span class="sd">        The default is True.</span>
+<span class="sd">    fmin : float, optional</span>
+<span class="sd">        If not None, the plot is limitted to values bigger than fmin.</span>
+<span class="sd">    fmax : float, optional</span>
+<span class="sd">        If not None, the plot is limitted to values smaller than fmax.</span>
+<span class="sd">    turns : array, optional</span>
+<span class="sd">        If not None, only the turn numbers in the turns array are plotted.</span>
+<span class="sd">    norm : bool, optional</span>
+<span class="sd">        If True, normalise the data of each spectrum by its geometric mean.</span>
+<span class="sd">        The default is False.</span>
+<span class="sd">    ylim : array, optional</span>
+<span class="sd">        If not None, should be array like in the form [ymin, ymax] where ymin </span>
+<span class="sd">        and ymax are the minimum and maxmimum values used in the y axis.</span>
+<span class="sd">        </span>
+
+<span class="sd">    Returns</span>
+<span class="sd">    -------</span>
+<span class="sd">    fig : Figure</span>
+
+<span class="sd">    &quot;&quot;&quot;</span>
+
+    <span class="n">file</span> <span class="o">=</span> <span class="n">hp</span><span class="o">.</span><span class="n">File</span><span class="p">(</span><span class="n">filename</span><span class="p">,</span> <span class="s2">&quot;r&quot;</span><span class="p">)</span>
+    <span class="n">group</span> <span class="o">=</span> <span class="n">file</span><span class="p">[</span><span class="s2">&quot;BunchSpectrum_</span><span class="si">{0}</span><span class="s2">&quot;</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">bunch_number</span><span class="p">)]</span>
+
+    <span class="n">time</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">group</span><span class="p">[</span><span class="s2">&quot;time&quot;</span><span class="p">])</span>
+    <span class="n">freq</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">group</span><span class="p">[</span><span class="s2">&quot;freq&quot;</span><span class="p">])</span>
+    <span class="n">dim_dict</span> <span class="o">=</span> <span class="p">{</span><span class="s2">&quot;x&quot;</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="s2">&quot;y&quot;</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span> <span class="s2">&quot;tau&quot;</span><span class="p">:</span> <span class="mi">2</span><span class="p">}</span>
+
+    <span class="k">if</span> <span class="n">turns</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+        <span class="n">turn_index</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">where</span><span class="p">(</span><span class="n">time</span> <span class="o">==</span> <span class="n">time</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span>
+        <span class="k">if</span> <span class="n">ylim</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="n">tmin</span> <span class="o">=</span> <span class="n">time</span><span class="o">.</span><span class="n">min</span><span class="p">()</span>
+            <span class="n">tmax</span> <span class="o">=</span> <span class="n">time</span><span class="o">.</span><span class="n">max</span><span class="p">()</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="n">tmin</span> <span class="o">=</span> <span class="n">ylim</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
+            <span class="n">tmax</span> <span class="o">=</span> <span class="n">ylim</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span>
+    <span class="k">else</span><span class="p">:</span>
+        <span class="n">tmin</span> <span class="o">=</span> <span class="n">turns</span><span class="o">.</span><span class="n">min</span><span class="p">()</span>
+        <span class="n">tmax</span> <span class="o">=</span> <span class="n">turns</span><span class="o">.</span><span class="n">max</span><span class="p">()</span>
+        <span class="n">turn_index</span> <span class="o">=</span> <span class="p">[]</span>
+        <span class="k">for</span> <span class="n">turn</span> <span class="ow">in</span> <span class="n">turns</span><span class="p">:</span>
+            <span class="n">idx</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">where</span><span class="p">(</span><span class="n">time</span> <span class="o">==</span> <span class="n">turn</span><span class="p">)[</span><span class="mi">0</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span>
+            <span class="n">turn_index</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">idx</span><span class="p">)</span>
+        <span class="n">turn_index</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">turn_index</span><span class="p">)</span>
+
+    <span class="n">data</span> <span class="o">=</span> <span class="n">group</span><span class="p">[</span><span class="n">dataset</span><span class="p">][</span><span class="n">dim_dict</span><span class="p">[</span><span class="n">dim</span><span class="p">],</span> <span class="p">:,</span> <span class="n">turn_index</span><span class="p">]</span>
+
+    <span class="k">if</span> <span class="n">log_scale</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">:</span>
+        <span class="n">option</span> <span class="o">=</span> <span class="n">mpl</span><span class="o">.</span><span class="n">colors</span><span class="o">.</span><span class="n">LogNorm</span><span class="p">()</span>
+    <span class="k">else</span><span class="p">:</span>
+        <span class="n">option</span> <span class="o">=</span> <span class="kc">None</span>
+
+    <span class="k">if</span> <span class="n">fs</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+        <span class="n">x_var</span> <span class="o">=</span> <span class="n">freq</span>
+        <span class="n">xlabel</span> <span class="o">=</span> <span class="s2">&quot;Frequency [Hz]&quot;</span>
+    <span class="k">else</span><span class="p">:</span>
+        <span class="n">x_var</span> <span class="o">=</span> <span class="n">freq</span> <span class="o">/</span> <span class="n">fs</span>
+        <span class="n">xlabel</span> <span class="o">=</span> <span class="sa">r</span><span class="s2">&quot;$f/f_</span><span class="si">{s}</span><span class="s2">$&quot;</span>
+
+    <span class="k">if</span> <span class="n">fmin</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+        <span class="n">fmin</span> <span class="o">=</span> <span class="n">x_var</span><span class="o">.</span><span class="n">min</span><span class="p">()</span>
+    <span class="k">if</span> <span class="n">fmax</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+        <span class="n">fmax</span> <span class="o">=</span> <span class="n">x_var</span><span class="o">.</span><span class="n">max</span><span class="p">()</span>
+
+    <span class="n">ind</span> <span class="o">=</span> <span class="p">(</span><span class="n">x_var</span> <span class="o">&gt;</span> <span class="n">fmin</span><span class="p">)</span> <span class="o">&amp;</span> <span class="p">(</span><span class="n">x_var</span> <span class="o">&lt;</span> <span class="n">fmax</span><span class="p">)</span>
+    <span class="n">x_var</span> <span class="o">=</span> <span class="n">x_var</span><span class="p">[</span><span class="n">ind</span><span class="p">]</span>
+    <span class="n">data</span> <span class="o">=</span> <span class="n">data</span><span class="p">[</span><span class="n">ind</span><span class="p">,</span> <span class="p">:]</span>
+
+    <span class="k">if</span> <span class="n">norm</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">:</span>
+        <span class="n">data</span> <span class="o">=</span> <span class="n">data</span> <span class="o">/</span> <span class="n">gmean</span><span class="p">(</span><span class="n">data</span><span class="p">)</span>
+
+    <span class="k">if</span> <span class="n">ylim</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+        <span class="n">ylabel</span> <span class="o">=</span> <span class="s2">&quot;Turn number&quot;</span>
+    <span class="k">else</span><span class="p">:</span>
+        <span class="n">ylabel</span> <span class="o">=</span> <span class="s2">&quot;&quot;</span>
+
+    <span class="n">fig</span><span class="p">,</span> <span class="n">ax</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">()</span>
+    <span class="k">if</span> <span class="n">dataset</span> <span class="o">==</span> <span class="s2">&quot;incoherent&quot;</span><span class="p">:</span>
+        <span class="n">ax</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s2">&quot;Incoherent spectrum&quot;</span><span class="p">)</span>
+    <span class="k">elif</span> <span class="n">dataset</span> <span class="o">==</span> <span class="s2">&quot;coherent&quot;</span><span class="p">:</span>
+        <span class="n">ax</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s2">&quot;Coherent spectrum&quot;</span><span class="p">)</span>
+
+    <span class="n">cmap</span> <span class="o">=</span> <span class="n">mpl</span><span class="o">.</span><span class="n">cm</span><span class="o">.</span><span class="n">inferno</span>  <span class="c1"># sequential</span>
+    <span class="n">c</span> <span class="o">=</span> <span class="n">ax</span><span class="o">.</span><span class="n">imshow</span><span class="p">(</span><span class="n">data</span><span class="o">.</span><span class="n">T</span><span class="p">,</span>
+                  <span class="n">cmap</span><span class="o">=</span><span class="n">cmap</span><span class="p">,</span>
+                  <span class="n">origin</span><span class="o">=</span><span class="s1">&#39;lower&#39;</span><span class="p">,</span>
+                  <span class="n">aspect</span><span class="o">=</span><span class="s1">&#39;auto&#39;</span><span class="p">,</span>
+                  <span class="n">extent</span><span class="o">=</span><span class="p">[</span><span class="n">x_var</span><span class="o">.</span><span class="n">min</span><span class="p">(),</span> <span class="n">x_var</span><span class="o">.</span><span class="n">max</span><span class="p">(),</span> <span class="n">tmin</span><span class="p">,</span> <span class="n">tmax</span><span class="p">],</span>
+                  <span class="n">norm</span><span class="o">=</span><span class="n">option</span><span class="p">,</span>
+                  <span class="n">interpolation</span><span class="o">=</span><span class="s2">&quot;none&quot;</span><span class="p">)</span>
+    <span class="n">cbar</span> <span class="o">=</span> <span class="n">fig</span><span class="o">.</span><span class="n">colorbar</span><span class="p">(</span><span class="n">c</span><span class="p">,</span> <span class="n">ax</span><span class="o">=</span><span class="n">ax</span><span class="p">)</span>
+    <span class="n">cbar</span><span class="o">.</span><span class="n">ax</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="s2">&quot;FFT amplitude [a.u.]&quot;</span><span class="p">,</span> <span class="n">rotation</span><span class="o">=</span><span class="mi">270</span><span class="p">)</span>
+    <span class="n">ax</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="n">xlabel</span><span class="p">)</span>
+    <span class="n">ax</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="n">ylabel</span><span class="p">)</span>
+
+    <span class="k">return</span> <span class="n">fig</span></div>
+
+
+<div class="viewcode-block" id="plot_beamspectrum"><a class="viewcode-back" href="../../../../mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.plotting.plot_beamspectrum">[docs]</a><span class="k">def</span> <span class="nf">plot_beamspectrum</span><span class="p">(</span><span class="n">filenames</span><span class="p">,</span>
+                      <span class="n">dim</span><span class="o">=</span><span class="s2">&quot;tau&quot;</span><span class="p">,</span>
+                      <span class="n">turns</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+                      <span class="n">f0</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+                      <span class="n">log_scale</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span>
+                      <span class="n">legend</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+                      <span class="n">norm</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    Plot coherent beam spectrum data.</span>
+
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">    filenames : str or list of str</span>
+<span class="sd">        Names of the HDF5 files to be plotted.</span>
+<span class="sd">    dim :  {&quot;x&quot;,&quot;y&quot;,&quot;tau&quot;}, optional</span>
+<span class="sd">        The dimension of the dataset to plot.</span>
+<span class="sd">        The default is &quot;tau&quot;.</span>
+<span class="sd">    turns : array or None, optional</span>
+<span class="sd">        Numbers of the turns to plot.</span>
+<span class="sd">        If None, all turns are shown. </span>
+<span class="sd">        The default is None.</span>
+<span class="sd">    f0 : float or None, optional</span>
+<span class="sd">        If not None, the frequency axis is noramlised by f0. </span>
+<span class="sd">        The default is None.</span>
+<span class="sd">    log_scale : bool, optional</span>
+<span class="sd">        If True, the spectrum plots are shown in y-log scale. </span>
+<span class="sd">        The default is True.</span>
+<span class="sd">    legend : list of str, optional</span>
+<span class="sd">        Legend to add for each file.</span>
+<span class="sd">        The default is None.</span>
+<span class="sd">    norm : bool, optional</span>
+<span class="sd">        If True, normalise the data of each spectrum by its geometric mean.</span>
+<span class="sd">        The default is False.</span>
+
+<span class="sd">    Return</span>
+<span class="sd">    ------</span>
+<span class="sd">    fig : Figure</span>
+
+<span class="sd">    &quot;&quot;&quot;</span>
+
+    <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">filenames</span><span class="p">,</span> <span class="nb">str</span><span class="p">):</span>
+        <span class="n">filenames</span> <span class="o">=</span> <span class="p">[</span><span class="n">filenames</span><span class="p">]</span>
+
+    <span class="n">fig</span><span class="p">,</span> <span class="n">ax</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">()</span>
+
+    <span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">filename</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">filenames</span><span class="p">):</span>
+        <span class="n">file</span> <span class="o">=</span> <span class="n">hp</span><span class="o">.</span><span class="n">File</span><span class="p">(</span><span class="n">filename</span><span class="p">,</span> <span class="s2">&quot;r&quot;</span><span class="p">)</span>
+        <span class="n">group</span> <span class="o">=</span> <span class="n">file</span><span class="p">[</span><span class="s2">&quot;BeamSpectrum&quot;</span><span class="p">]</span>
+
+        <span class="n">dataset</span> <span class="o">=</span> <span class="s2">&quot;coherent&quot;</span>
+        <span class="n">time</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">group</span><span class="p">[</span><span class="s2">&quot;time&quot;</span><span class="p">])</span>
+        <span class="n">freq</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">group</span><span class="p">[</span><span class="s2">&quot;freq&quot;</span><span class="p">])</span>
+        <span class="n">dim_dict</span> <span class="o">=</span> <span class="p">{</span><span class="s2">&quot;x&quot;</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="s2">&quot;y&quot;</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span> <span class="s2">&quot;tau&quot;</span><span class="p">:</span> <span class="mi">2</span><span class="p">}</span>
+
+        <span class="k">if</span> <span class="n">turns</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="n">turn_index</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">where</span><span class="p">(</span><span class="n">time</span> <span class="o">==</span> <span class="n">time</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="n">turn_index</span> <span class="o">=</span> <span class="p">[]</span>
+            <span class="k">for</span> <span class="n">turn</span> <span class="ow">in</span> <span class="n">turns</span><span class="p">:</span>
+                <span class="n">idx</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">where</span><span class="p">(</span><span class="n">time</span> <span class="o">==</span> <span class="n">turn</span><span class="p">)[</span><span class="mi">0</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span>
+                <span class="n">turn_index</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">idx</span><span class="p">)</span>
+            <span class="n">turn_index</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">turn_index</span><span class="p">)</span>
+
+        <span class="k">if</span> <span class="n">f0</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="n">x_var</span> <span class="o">=</span> <span class="n">freq</span>
+            <span class="n">xlabel</span> <span class="o">=</span> <span class="s2">&quot;Frequency [Hz]&quot;</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="n">x_var</span> <span class="o">=</span> <span class="n">freq</span> <span class="o">/</span> <span class="n">f0</span>
+            <span class="n">xlabel</span> <span class="o">=</span> <span class="sa">r</span><span class="s2">&quot;$f/f_</span><span class="si">{0}</span><span class="s2">$&quot;</span>
+
+        <span class="k">for</span> <span class="n">idx</span> <span class="ow">in</span> <span class="n">turn_index</span><span class="p">:</span>
+            <span class="n">y_var</span> <span class="o">=</span> <span class="n">group</span><span class="p">[</span><span class="n">dataset</span><span class="p">][</span><span class="n">dim_dict</span><span class="p">[</span><span class="n">dim</span><span class="p">],</span> <span class="p">:,</span> <span class="n">idx</span><span class="p">]</span>
+            <span class="k">if</span> <span class="n">norm</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">:</span>
+                <span class="n">y_var</span> <span class="o">=</span> <span class="n">y_var</span> <span class="o">/</span> <span class="n">gmean</span><span class="p">(</span><span class="n">y_var</span><span class="p">)</span>
+            <span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x_var</span><span class="p">,</span> <span class="n">y_var</span><span class="p">)</span>
+
+        <span class="k">if</span> <span class="n">log_scale</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">:</span>
+            <span class="n">ax</span><span class="o">.</span><span class="n">set_yscale</span><span class="p">(</span><span class="s1">&#39;log&#39;</span><span class="p">)</span>
+
+        <span class="n">ylabel</span> <span class="o">=</span> <span class="s2">&quot;FFT amplitude [a.u.]&quot;</span>
+        <span class="n">ax</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s2">&quot;Beam coherent spectrum&quot;</span><span class="p">)</span>
+
+        <span class="n">ax</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="n">xlabel</span><span class="p">)</span>
+        <span class="n">ax</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="n">ylabel</span><span class="p">)</span>
+        <span class="k">if</span> <span class="n">legend</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="n">plt</span><span class="o">.</span><span class="n">legend</span><span class="p">(</span><span class="n">legend</span><span class="p">)</span>
+        <span class="n">file</span><span class="o">.</span><span class="n">close</span><span class="p">()</span>
+
+    <span class="k">return</span> <span class="n">fig</span></div>
+
+
+<div class="viewcode-block" id="streak_beamspectrum"><a class="viewcode-back" href="../../../../mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.plotting.streak_beamspectrum">[docs]</a><span class="k">def</span> <span class="nf">streak_beamspectrum</span><span class="p">(</span><span class="n">filename</span><span class="p">,</span>
+                        <span class="n">dim</span><span class="o">=</span><span class="s2">&quot;tau&quot;</span><span class="p">,</span>
+                        <span class="n">f0</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+                        <span class="n">log_scale</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span>
+                        <span class="n">fmin</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+                        <span class="n">fmax</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+                        <span class="n">turns</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+                        <span class="n">norm</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span>
+                        <span class="n">ylim</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    Plot 3D data recorded by the BeamSpectrumMonitor.</span>
+
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">    filenames : str</span>
+<span class="sd">        Name of the HDF5 file to be plotted.</span>
+<span class="sd">    dim :  {&quot;x&quot;,&quot;y&quot;,&quot;tau&quot;}, optional</span>
+<span class="sd">        The dimension of the dataset to plot.</span>
+<span class="sd">        The default is &quot;tau&quot;.</span>
+<span class="sd">    f0 : float or None, optional</span>
+<span class="sd">        If not None, the frequency axis is noramlised by f0. </span>
+<span class="sd">    log_scale : bool, optional</span>
+<span class="sd">        If True, the spectrum plots are shown in y-log scale. </span>
+<span class="sd">        The default is True.</span>
+<span class="sd">    fmin : float, optional</span>
+<span class="sd">        If not None, the plot is limitted to values bigger than fmin.</span>
+<span class="sd">    fmax : float, optional</span>
+<span class="sd">        If not None, the plot is limitted to values smaller than fmax.</span>
+<span class="sd">    turns : array, optional</span>
+<span class="sd">        If not None, only the turn numbers in the turns array are plotted.</span>
+<span class="sd">    norm : bool, optional</span>
+<span class="sd">        If True, normalise the data of each spectrum by its geometric mean.</span>
+<span class="sd">        The default is False.</span>
+<span class="sd">    ylim : array, optional</span>
+<span class="sd">        If not None, should be array like in the form [ymin, ymax] where ymin </span>
+<span class="sd">        and ymax are the minimum and maxmimum values used in the y axis.</span>
+
+<span class="sd">    Returns</span>
+<span class="sd">    -------</span>
+<span class="sd">    fig : Figure</span>
+
+<span class="sd">    &quot;&quot;&quot;</span>
+
+    <span class="n">file</span> <span class="o">=</span> <span class="n">hp</span><span class="o">.</span><span class="n">File</span><span class="p">(</span><span class="n">filename</span><span class="p">,</span> <span class="s2">&quot;r&quot;</span><span class="p">)</span>
+    <span class="n">group</span> <span class="o">=</span> <span class="n">file</span><span class="p">[</span><span class="s2">&quot;BeamSpectrum&quot;</span><span class="p">]</span>
+    <span class="n">dataset</span> <span class="o">=</span> <span class="s2">&quot;coherent&quot;</span>
+    <span class="n">time</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">group</span><span class="p">[</span><span class="s2">&quot;time&quot;</span><span class="p">])</span>
+    <span class="n">freq</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">group</span><span class="p">[</span><span class="s2">&quot;freq&quot;</span><span class="p">])</span>
+    <span class="n">dim_dict</span> <span class="o">=</span> <span class="p">{</span><span class="s2">&quot;x&quot;</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="s2">&quot;y&quot;</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span> <span class="s2">&quot;tau&quot;</span><span class="p">:</span> <span class="mi">2</span><span class="p">}</span>
+
+    <span class="k">if</span> <span class="n">turns</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+        <span class="n">turn_index</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">where</span><span class="p">(</span><span class="n">time</span> <span class="o">==</span> <span class="n">time</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span>
+        <span class="k">if</span> <span class="n">ylim</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="n">tmin</span> <span class="o">=</span> <span class="n">time</span><span class="o">.</span><span class="n">min</span><span class="p">()</span>
+            <span class="n">tmax</span> <span class="o">=</span> <span class="n">time</span><span class="o">.</span><span class="n">max</span><span class="p">()</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="n">tmin</span> <span class="o">=</span> <span class="n">ylim</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
+            <span class="n">tmax</span> <span class="o">=</span> <span class="n">ylim</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span>
+    <span class="k">else</span><span class="p">:</span>
+        <span class="n">tmin</span> <span class="o">=</span> <span class="n">turns</span><span class="o">.</span><span class="n">min</span><span class="p">()</span>
+        <span class="n">tmax</span> <span class="o">=</span> <span class="n">turns</span><span class="o">.</span><span class="n">max</span><span class="p">()</span>
+        <span class="n">turn_index</span> <span class="o">=</span> <span class="p">[]</span>
+        <span class="k">for</span> <span class="n">turn</span> <span class="ow">in</span> <span class="n">turns</span><span class="p">:</span>
+            <span class="n">idx</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">where</span><span class="p">(</span><span class="n">time</span> <span class="o">==</span> <span class="n">turn</span><span class="p">)[</span><span class="mi">0</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span>
+            <span class="n">turn_index</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">idx</span><span class="p">)</span>
+        <span class="n">turn_index</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">turn_index</span><span class="p">)</span>
+
+    <span class="n">data</span> <span class="o">=</span> <span class="n">group</span><span class="p">[</span><span class="n">dataset</span><span class="p">][</span><span class="n">dim_dict</span><span class="p">[</span><span class="n">dim</span><span class="p">],</span> <span class="p">:,</span> <span class="n">turn_index</span><span class="p">]</span>
+
+    <span class="k">if</span> <span class="n">log_scale</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">:</span>
+        <span class="n">option</span> <span class="o">=</span> <span class="n">mpl</span><span class="o">.</span><span class="n">colors</span><span class="o">.</span><span class="n">LogNorm</span><span class="p">()</span>
+    <span class="k">else</span><span class="p">:</span>
+        <span class="n">option</span> <span class="o">=</span> <span class="kc">None</span>
+
+    <span class="k">if</span> <span class="n">f0</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+        <span class="n">x_var</span> <span class="o">=</span> <span class="n">freq</span>
+        <span class="n">xlabel</span> <span class="o">=</span> <span class="s2">&quot;Frequency [Hz]&quot;</span>
+    <span class="k">else</span><span class="p">:</span>
+        <span class="n">x_var</span> <span class="o">=</span> <span class="n">freq</span> <span class="o">/</span> <span class="n">f0</span>
+        <span class="n">xlabel</span> <span class="o">=</span> <span class="sa">r</span><span class="s2">&quot;$f/f_</span><span class="si">{0}</span><span class="s2">$&quot;</span>
+
+    <span class="k">if</span> <span class="n">fmin</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+        <span class="n">fmin</span> <span class="o">=</span> <span class="n">x_var</span><span class="o">.</span><span class="n">min</span><span class="p">()</span>
+    <span class="k">if</span> <span class="n">fmax</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+        <span class="n">fmax</span> <span class="o">=</span> <span class="n">x_var</span><span class="o">.</span><span class="n">max</span><span class="p">()</span>
+
+    <span class="n">ind</span> <span class="o">=</span> <span class="p">(</span><span class="n">x_var</span> <span class="o">&gt;</span> <span class="n">fmin</span><span class="p">)</span> <span class="o">&amp;</span> <span class="p">(</span><span class="n">x_var</span> <span class="o">&lt;</span> <span class="n">fmax</span><span class="p">)</span>
+    <span class="n">x_var</span> <span class="o">=</span> <span class="n">x_var</span><span class="p">[</span><span class="n">ind</span><span class="p">]</span>
+    <span class="n">data</span> <span class="o">=</span> <span class="n">data</span><span class="p">[</span><span class="n">ind</span><span class="p">,</span> <span class="p">:]</span>
+
+    <span class="k">if</span> <span class="n">norm</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">:</span>
+        <span class="n">data</span> <span class="o">=</span> <span class="n">data</span> <span class="o">/</span> <span class="n">gmean</span><span class="p">(</span><span class="n">data</span><span class="p">)</span>
+
+    <span class="k">if</span> <span class="n">ylim</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+        <span class="n">ylabel</span> <span class="o">=</span> <span class="s2">&quot;Turn number&quot;</span>
+    <span class="k">else</span><span class="p">:</span>
+        <span class="n">ylabel</span> <span class="o">=</span> <span class="s2">&quot;&quot;</span>
+
+    <span class="n">fig</span><span class="p">,</span> <span class="n">ax</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">()</span>
+    <span class="n">ax</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s2">&quot;Beam coherent spectrum&quot;</span><span class="p">)</span>
+
+    <span class="n">cmap</span> <span class="o">=</span> <span class="n">mpl</span><span class="o">.</span><span class="n">cm</span><span class="o">.</span><span class="n">inferno</span>  <span class="c1"># sequential</span>
+    <span class="n">c</span> <span class="o">=</span> <span class="n">ax</span><span class="o">.</span><span class="n">imshow</span><span class="p">(</span><span class="n">data</span><span class="o">.</span><span class="n">T</span><span class="p">,</span>
+                  <span class="n">cmap</span><span class="o">=</span><span class="n">cmap</span><span class="p">,</span>
+                  <span class="n">origin</span><span class="o">=</span><span class="s1">&#39;lower&#39;</span><span class="p">,</span>
+                  <span class="n">aspect</span><span class="o">=</span><span class="s1">&#39;auto&#39;</span><span class="p">,</span>
+                  <span class="n">extent</span><span class="o">=</span><span class="p">[</span><span class="n">x_var</span><span class="o">.</span><span class="n">min</span><span class="p">(),</span> <span class="n">x_var</span><span class="o">.</span><span class="n">max</span><span class="p">(),</span> <span class="n">tmin</span><span class="p">,</span> <span class="n">tmax</span><span class="p">],</span>
+                  <span class="n">norm</span><span class="o">=</span><span class="n">option</span><span class="p">,</span>
+                  <span class="n">interpolation</span><span class="o">=</span><span class="s2">&quot;none&quot;</span><span class="p">)</span>
+    <span class="n">cbar</span> <span class="o">=</span> <span class="n">fig</span><span class="o">.</span><span class="n">colorbar</span><span class="p">(</span><span class="n">c</span><span class="p">,</span> <span class="n">ax</span><span class="o">=</span><span class="n">ax</span><span class="p">)</span>
+    <span class="n">cbar</span><span class="o">.</span><span class="n">ax</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="s2">&quot;FFT amplitude [a.u.]&quot;</span><span class="p">,</span> <span class="n">rotation</span><span class="o">=</span><span class="mi">270</span><span class="p">)</span>
+    <span class="n">ax</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="n">xlabel</span><span class="p">)</span>
+    <span class="n">ax</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="n">ylabel</span><span class="p">)</span>
+
+    <span class="k">return</span> <span class="n">fig</span></div>
+
+
+<div class="viewcode-block" id="plot_cavitydata"><a class="viewcode-back" href="../../../../mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.plotting.plot_cavitydata">[docs]</a><span class="k">def</span> <span class="nf">plot_cavitydata</span><span class="p">(</span><span class="n">filename</span><span class="p">,</span>
+                    <span class="n">cavity_name</span><span class="p">,</span>
+                    <span class="n">phasor</span><span class="o">=</span><span class="s2">&quot;cavity&quot;</span><span class="p">,</span>
+                    <span class="n">plot_type</span><span class="o">=</span><span class="s2">&quot;bunch&quot;</span><span class="p">,</span>
+                    <span class="n">bunch_number</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span>
+                    <span class="n">turn</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+                    <span class="n">cm_lim</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+                    <span class="n">show_objective</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    Plot data recorded by CavityMonitor.</span>
+
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">    filename : str </span>
+<span class="sd">        Name of the HDF5 file that contains the data.</span>
+<span class="sd">    cavity_name : str</span>
+<span class="sd">        Name of the CavityResonator object.</span>
+<span class="sd">    phasor : str, optional</span>
+<span class="sd">        Type of the phasor to plot. Can be &quot;beam&quot;, &quot;cavity&quot;, &quot;generator&quot; or </span>
+<span class="sd">        &quot;ig&quot;.</span>
+<span class="sd">    plot_type : str, optional</span>
+<span class="sd">        Type of plot:</span>
+<span class="sd">            - &quot;bunch&quot; plots the phasor voltage and angle versus time for a </span>
+<span class="sd">            given bunch.</span>
+<span class="sd">            - &quot;turn&quot; plots the phasor voltage and ange versus bunch index for</span>
+<span class="sd">            a given turn.</span>
+<span class="sd">            - &quot;streak_amplitude&quot; plots the phasor amplitude versus bunch index </span>
+<span class="sd">            and time.</span>
+<span class="sd">            - &quot;streak_angle&quot; plots the phasor angle versus bunch index and </span>
+<span class="sd">            time.</span>
+<span class="sd">            - &quot;detune&quot; or &quot;psi&quot; plots the detuning or tuning angle versus time.</span>
+<span class="sd">            - &quot;power&quot; plots the generator, cavity, beam and reflected power</span>
+<span class="sd">            versus time. Needs BeamMonitor data with same save_every as </span>
+<span class="sd">            CavityMonitor.</span>
+<span class="sd">            - &quot;mean&quot; plots the mean phasor voltage and angle versus time for </span>
+<span class="sd">            non empty bunches. Needs BeamMonitor data with same save_every as </span>
+<span class="sd">            CavityMonitor.</span>
+<span class="sd">            - &quot;tuner_diff&quot; plots the tuner difference from optimal tuning </span>
+<span class="sd">            condition (for a given bunch) and the tuning angle versus time.</span>
+<span class="sd">    bunch_number : int, optional</span>
+<span class="sd">        Bunch number to select. The default is 0.</span>
+<span class="sd">    turn : int, optional</span>
+<span class="sd">        Turn to plot. The default is None.</span>
+<span class="sd">    cm_lim : list [vmin, vmax], optional</span>
+<span class="sd">        Colormap scale for the &quot;streak&quot; plots.</span>
+<span class="sd">    show_objective : bool, optional</span>
+<span class="sd">        If True, shows the Cavity voltage and phase objective value (Vc and </span>
+<span class="sd">        theta) in plot type &quot;mean&quot; and &quot;bunch&quot; for &quot;cavity&quot; phasor.</span>
+<span class="sd">        Default is False.</span>
+
+<span class="sd">    Returns</span>
+<span class="sd">    -------</span>
+<span class="sd">    fig : Figure</span>
+<span class="sd">        Figure object with the plot on it.</span>
+
+<span class="sd">    &quot;&quot;&quot;</span>
+    <span class="n">file</span> <span class="o">=</span> <span class="n">hp</span><span class="o">.</span><span class="n">File</span><span class="p">(</span><span class="n">filename</span><span class="p">,</span> <span class="s2">&quot;r&quot;</span><span class="p">)</span>
+    <span class="n">cavity_data</span> <span class="o">=</span> <span class="n">file</span><span class="p">[</span><span class="n">cavity_name</span><span class="p">]</span>
+
+    <span class="n">time</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">cavity_data</span><span class="p">[</span><span class="s2">&quot;time&quot;</span><span class="p">])</span>
+
+    <span class="n">ph</span> <span class="o">=</span> <span class="p">{</span><span class="s2">&quot;cavity&quot;</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="s2">&quot;beam&quot;</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span> <span class="s2">&quot;generator&quot;</span><span class="p">:</span> <span class="mi">2</span><span class="p">,</span> <span class="s2">&quot;ig&quot;</span><span class="p">:</span> <span class="mi">3</span><span class="p">}</span>
+    <span class="n">labels</span> <span class="o">=</span> <span class="p">[</span><span class="s2">&quot;Cavity&quot;</span><span class="p">,</span> <span class="s2">&quot;Beam&quot;</span><span class="p">,</span> <span class="s2">&quot;Generator&quot;</span><span class="p">,</span> <span class="s2">&quot;Generator&quot;</span><span class="p">]</span>
+    <span class="n">units</span> <span class="o">=</span> <span class="p">[</span><span class="s2">&quot; voltage [MV]&quot;</span><span class="p">,</span> <span class="s2">&quot; voltage [MV]&quot;</span><span class="p">,</span> <span class="s2">&quot; voltage [MV]&quot;</span><span class="p">,</span> <span class="s2">&quot; current [A]&quot;</span><span class="p">]</span>
+    <span class="n">units_val</span> <span class="o">=</span> <span class="p">[</span><span class="mf">1e-6</span><span class="p">,</span> <span class="mf">1e-6</span><span class="p">,</span> <span class="mf">1e-6</span><span class="p">,</span> <span class="mi">1</span><span class="p">]</span>
+
+    <span class="k">if</span> <span class="p">(</span><span class="n">plot_type</span> <span class="o">==</span> <span class="s2">&quot;bunch&quot;</span><span class="p">)</span> <span class="ow">or</span> <span class="p">(</span><span class="n">plot_type</span> <span class="o">==</span> <span class="s2">&quot;mean&quot;</span><span class="p">):</span>
+
+        <span class="k">if</span> <span class="n">plot_type</span> <span class="o">==</span> <span class="s2">&quot;bunch&quot;</span><span class="p">:</span>
+            <span class="n">data</span> <span class="o">=</span> <span class="p">[</span>
+                <span class="n">cavity_data</span><span class="p">[</span><span class="s2">&quot;cavity_phasor_record&quot;</span><span class="p">][</span><span class="n">bunch_number</span><span class="p">,</span> <span class="p">:],</span>
+                <span class="n">cavity_data</span><span class="p">[</span><span class="s2">&quot;beam_phasor_record&quot;</span><span class="p">][</span><span class="n">bunch_number</span><span class="p">,</span> <span class="p">:],</span>
+                <span class="n">cavity_data</span><span class="p">[</span><span class="s2">&quot;generator_phasor_record&quot;</span><span class="p">][</span><span class="n">bunch_number</span><span class="p">,</span> <span class="p">:],</span>
+                <span class="n">cavity_data</span><span class="p">[</span><span class="s2">&quot;ig_phasor_record&quot;</span><span class="p">][</span><span class="n">bunch_number</span><span class="p">,</span> <span class="p">:]</span>
+            <span class="p">]</span>
+        <span class="k">elif</span> <span class="n">plot_type</span> <span class="o">==</span> <span class="s2">&quot;mean&quot;</span><span class="p">:</span>
+            <span class="k">try</span><span class="p">:</span>
+                <span class="n">bunch_index</span> <span class="o">=</span> <span class="p">(</span><span class="n">file</span><span class="p">[</span><span class="s2">&quot;Beam&quot;</span><span class="p">][</span><span class="s2">&quot;current&quot;</span><span class="p">][:,</span> <span class="mi">0</span><span class="p">]</span> <span class="o">!=</span> <span class="mi">0</span><span class="p">)</span><span class="o">.</span><span class="n">nonzero</span><span class="p">()[</span><span class="mi">0</span><span class="p">]</span>
+            <span class="k">except</span><span class="p">:</span>
+                <span class="ne">ValueError</span><span class="p">(</span><span class="s2">&quot;Beam monitor is needed to show mean voltage.&quot;</span><span class="p">)</span>
+            <span class="n">data</span> <span class="o">=</span> <span class="p">[</span>
+                <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">cavity_data</span><span class="p">[</span><span class="s2">&quot;cavity_phasor_record&quot;</span><span class="p">][</span><span class="n">bunch_index</span><span class="p">,</span> <span class="p">:],</span>
+                        <span class="mi">0</span><span class="p">),</span>
+                <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">cavity_data</span><span class="p">[</span><span class="s2">&quot;beam_phasor_record&quot;</span><span class="p">][</span><span class="n">bunch_index</span><span class="p">,</span> <span class="p">:],</span> <span class="mi">0</span><span class="p">),</span>
+                <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">cavity_data</span><span class="p">[</span><span class="s2">&quot;generator_phasor_record&quot;</span><span class="p">][</span><span class="n">bunch_index</span><span class="p">,</span> <span class="p">:],</span>
+                        <span class="mi">0</span><span class="p">),</span>
+                <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">cavity_data</span><span class="p">[</span><span class="s2">&quot;ig_phasor_record&quot;</span><span class="p">][</span><span class="n">bunch_index</span><span class="p">,</span> <span class="p">:],</span> <span class="mi">0</span><span class="p">)</span>
+            <span class="p">]</span>
+
+        <span class="n">ylabel1</span> <span class="o">=</span> <span class="n">labels</span><span class="p">[</span><span class="n">ph</span><span class="p">[</span><span class="n">phasor</span><span class="p">]]</span> <span class="o">+</span> <span class="n">units</span><span class="p">[</span><span class="n">ph</span><span class="p">[</span><span class="n">phasor</span><span class="p">]]</span>
+        <span class="n">ylabel2</span> <span class="o">=</span> <span class="n">labels</span><span class="p">[</span><span class="n">ph</span><span class="p">[</span><span class="n">phasor</span><span class="p">]]</span> <span class="o">+</span> <span class="s2">&quot; phase [rad]&quot;</span>
+
+        <span class="n">fig</span><span class="p">,</span> <span class="n">ax</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">()</span>
+        <span class="n">twin</span> <span class="o">=</span> <span class="n">ax</span><span class="o">.</span><span class="n">twinx</span><span class="p">()</span>
+        <span class="n">p1</span><span class="p">,</span> <span class="o">=</span> <span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">time</span><span class="p">,</span>
+                      <span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">data</span><span class="p">[</span><span class="n">ph</span><span class="p">[</span><span class="n">phasor</span><span class="p">]])</span> <span class="o">*</span> <span class="n">units_val</span><span class="p">[</span><span class="n">ph</span><span class="p">[</span><span class="n">phasor</span><span class="p">]],</span>
+                      <span class="n">color</span><span class="o">=</span><span class="s2">&quot;r&quot;</span><span class="p">,</span>
+                      <span class="n">label</span><span class="o">=</span><span class="n">ylabel1</span><span class="p">)</span>
+        <span class="n">p2</span><span class="p">,</span> <span class="o">=</span> <span class="n">twin</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">time</span><span class="p">,</span>
+                        <span class="n">np</span><span class="o">.</span><span class="n">angle</span><span class="p">(</span><span class="n">data</span><span class="p">[</span><span class="n">ph</span><span class="p">[</span><span class="n">phasor</span><span class="p">]]),</span>
+                        <span class="n">color</span><span class="o">=</span><span class="s2">&quot;b&quot;</span><span class="p">,</span>
+                        <span class="n">label</span><span class="o">=</span><span class="n">ylabel2</span><span class="p">)</span>
+        <span class="k">if</span> <span class="n">show_objective</span><span class="p">:</span>
+            <span class="n">o1</span><span class="p">,</span> <span class="o">=</span> <span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">time</span><span class="p">,</span>
+                          <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">cavity_data</span><span class="p">[</span><span class="s2">&quot;Vc&quot;</span><span class="p">])</span> <span class="o">*</span> <span class="mf">1e-6</span><span class="p">,</span>
+                          <span class="s2">&quot;r--&quot;</span><span class="p">,</span>
+                          <span class="n">label</span><span class="o">=</span><span class="s2">&quot;Cavity voltage objective value [MV]&quot;</span><span class="p">)</span>
+            <span class="n">o2</span><span class="p">,</span> <span class="o">=</span> <span class="n">twin</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">time</span><span class="p">,</span>
+                            <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">cavity_data</span><span class="p">[</span><span class="s2">&quot;theta&quot;</span><span class="p">]),</span>
+                            <span class="s2">&quot;b--&quot;</span><span class="p">,</span>
+                            <span class="n">label</span><span class="o">=</span><span class="s2">&quot;Cavity phase objective value [rad]&quot;</span><span class="p">)</span>
+        <span class="n">ax</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="s2">&quot;Turn number&quot;</span><span class="p">)</span>
+        <span class="n">ax</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="n">ylabel1</span><span class="p">)</span>
+        <span class="n">twin</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="n">ylabel2</span><span class="p">)</span>
+
+        <span class="k">if</span> <span class="n">show_objective</span><span class="p">:</span>
+            <span class="n">plots</span> <span class="o">=</span> <span class="p">[</span><span class="n">p1</span><span class="p">,</span> <span class="n">o1</span><span class="p">,</span> <span class="n">p2</span><span class="p">,</span> <span class="n">o2</span><span class="p">]</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="n">plots</span> <span class="o">=</span> <span class="p">[</span><span class="n">p1</span><span class="p">,</span> <span class="n">p2</span><span class="p">]</span>
+        <span class="n">ax</span><span class="o">.</span><span class="n">legend</span><span class="p">(</span><span class="n">handles</span><span class="o">=</span><span class="n">plots</span><span class="p">,</span> <span class="n">loc</span><span class="o">=</span><span class="s2">&quot;best&quot;</span><span class="p">)</span>
+
+        <span class="n">ax</span><span class="o">.</span><span class="n">yaxis</span><span class="o">.</span><span class="n">label</span><span class="o">.</span><span class="n">set_color</span><span class="p">(</span><span class="s2">&quot;r&quot;</span><span class="p">)</span>
+        <span class="n">twin</span><span class="o">.</span><span class="n">yaxis</span><span class="o">.</span><span class="n">label</span><span class="o">.</span><span class="n">set_color</span><span class="p">(</span><span class="s2">&quot;b&quot;</span><span class="p">)</span>
+
+    <span class="k">if</span> <span class="n">plot_type</span> <span class="o">==</span> <span class="s2">&quot;turn&quot;</span><span class="p">:</span>
+
+        <span class="n">index</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">time</span><span class="p">)</span> <span class="o">==</span> <span class="n">turn</span>
+        <span class="k">if</span> <span class="p">(</span><span class="n">index</span><span class="o">.</span><span class="n">size</span> <span class="o">==</span> <span class="mi">0</span><span class="p">):</span>
+            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">&quot;Turn is not valid.&quot;</span><span class="p">)</span>
+        <span class="n">data</span> <span class="o">=</span> <span class="p">[</span>
+            <span class="n">cavity_data</span><span class="p">[</span><span class="s2">&quot;cavity_phasor_record&quot;</span><span class="p">][:,</span> <span class="n">index</span><span class="p">],</span>
+            <span class="n">cavity_data</span><span class="p">[</span><span class="s2">&quot;beam_phasor_record&quot;</span><span class="p">][:,</span> <span class="n">index</span><span class="p">],</span>
+            <span class="n">cavity_data</span><span class="p">[</span><span class="s2">&quot;generator_phasor_record&quot;</span><span class="p">][:,</span> <span class="n">index</span><span class="p">],</span>
+            <span class="n">cavity_data</span><span class="p">[</span><span class="s2">&quot;ig_phasor_record&quot;</span><span class="p">][:,</span> <span class="n">index</span><span class="p">]</span>
+        <span class="p">]</span>
+
+        <span class="n">h</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">data</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
+        <span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="n">h</span><span class="p">)</span>
+
+        <span class="n">ylabel1</span> <span class="o">=</span> <span class="n">labels</span><span class="p">[</span><span class="n">ph</span><span class="p">[</span><span class="n">phasor</span><span class="p">]]</span> <span class="o">+</span> <span class="n">units</span><span class="p">[</span><span class="n">ph</span><span class="p">[</span><span class="n">phasor</span><span class="p">]]</span>
+        <span class="n">ylabel2</span> <span class="o">=</span> <span class="n">labels</span><span class="p">[</span><span class="n">ph</span><span class="p">[</span><span class="n">phasor</span><span class="p">]]</span> <span class="o">+</span> <span class="s2">&quot; phase [rad]&quot;</span>
+
+        <span class="n">fig</span><span class="p">,</span> <span class="n">ax</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">()</span>
+        <span class="n">twin</span> <span class="o">=</span> <span class="n">ax</span><span class="o">.</span><span class="n">twinx</span><span class="p">()</span>
+        <span class="n">p1</span><span class="p">,</span> <span class="o">=</span> <span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span>
+                      <span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">data</span><span class="p">[</span><span class="n">ph</span><span class="p">[</span><span class="n">phasor</span><span class="p">]])</span> <span class="o">*</span> <span class="n">units_val</span><span class="p">[</span><span class="n">ph</span><span class="p">[</span><span class="n">phasor</span><span class="p">]],</span>
+                      <span class="n">color</span><span class="o">=</span><span class="s2">&quot;r&quot;</span><span class="p">,</span>
+                      <span class="n">label</span><span class="o">=</span><span class="n">ylabel1</span><span class="p">)</span>
+        <span class="n">p2</span><span class="p">,</span> <span class="o">=</span> <span class="n">twin</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span>
+                        <span class="n">np</span><span class="o">.</span><span class="n">angle</span><span class="p">(</span><span class="n">data</span><span class="p">[</span><span class="n">ph</span><span class="p">[</span><span class="n">phasor</span><span class="p">]]),</span>
+                        <span class="n">color</span><span class="o">=</span><span class="s2">&quot;b&quot;</span><span class="p">,</span>
+                        <span class="n">label</span><span class="o">=</span><span class="n">ylabel2</span><span class="p">)</span>
+        <span class="n">ax</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="s2">&quot;Bunch index&quot;</span><span class="p">)</span>
+        <span class="n">ax</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="n">ylabel1</span><span class="p">)</span>
+        <span class="n">twin</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="n">ylabel2</span><span class="p">)</span>
+
+        <span class="n">plots</span> <span class="o">=</span> <span class="p">[</span><span class="n">p1</span><span class="p">,</span> <span class="n">p2</span><span class="p">]</span>
+        <span class="n">ax</span><span class="o">.</span><span class="n">legend</span><span class="p">(</span><span class="n">handles</span><span class="o">=</span><span class="n">plots</span><span class="p">,</span> <span class="n">loc</span><span class="o">=</span><span class="s2">&quot;best&quot;</span><span class="p">)</span>
+
+        <span class="n">ax</span><span class="o">.</span><span class="n">yaxis</span><span class="o">.</span><span class="n">label</span><span class="o">.</span><span class="n">set_color</span><span class="p">(</span><span class="s2">&quot;r&quot;</span><span class="p">)</span>
+        <span class="n">twin</span><span class="o">.</span><span class="n">yaxis</span><span class="o">.</span><span class="n">label</span><span class="o">.</span><span class="n">set_color</span><span class="p">(</span><span class="s2">&quot;b&quot;</span><span class="p">)</span>
+
+    <span class="k">if</span> <span class="n">plot_type</span> <span class="o">==</span> <span class="s2">&quot;streak_amplitude&quot;</span> <span class="ow">or</span> <span class="n">plot_type</span> <span class="o">==</span> <span class="s2">&quot;streak_phase&quot;</span><span class="p">:</span>
+
+        <span class="n">data</span> <span class="o">=</span> <span class="p">[</span>
+            <span class="n">cavity_data</span><span class="p">[</span><span class="s2">&quot;cavity_phasor_record&quot;</span><span class="p">][:,</span> <span class="p">:],</span>
+            <span class="n">cavity_data</span><span class="p">[</span><span class="s2">&quot;beam_phasor_record&quot;</span><span class="p">][:,</span> <span class="p">:],</span>
+            <span class="n">cavity_data</span><span class="p">[</span><span class="s2">&quot;generator_phasor_record&quot;</span><span class="p">][:,</span> <span class="p">:],</span>
+            <span class="n">cavity_data</span><span class="p">[</span><span class="s2">&quot;ig_phasor_record&quot;</span><span class="p">][:,</span> <span class="p">:]</span>
+        <span class="p">]</span>
+
+        <span class="k">if</span> <span class="n">plot_type</span> <span class="o">==</span> <span class="s2">&quot;streak_amplitude&quot;</span><span class="p">:</span>
+            <span class="n">data</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">transpose</span><span class="p">(</span>
+                <span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">data</span><span class="p">[</span><span class="n">ph</span><span class="p">[</span><span class="n">phasor</span><span class="p">]])</span> <span class="o">*</span> <span class="n">units_val</span><span class="p">[</span><span class="n">ph</span><span class="p">[</span><span class="n">phasor</span><span class="p">]])</span>
+            <span class="n">ylabel</span> <span class="o">=</span> <span class="n">labels</span><span class="p">[</span><span class="n">ph</span><span class="p">[</span><span class="n">phasor</span><span class="p">]]</span> <span class="o">+</span> <span class="n">units</span><span class="p">[</span><span class="n">ph</span><span class="p">[</span><span class="n">phasor</span><span class="p">]]</span>
+            <span class="n">cmap</span> <span class="o">=</span> <span class="n">mpl</span><span class="o">.</span><span class="n">cm</span><span class="o">.</span><span class="n">coolwarm</span>  <span class="c1"># diverging</span>
+        <span class="k">elif</span> <span class="n">plot_type</span> <span class="o">==</span> <span class="s2">&quot;streak_phase&quot;</span><span class="p">:</span>
+            <span class="n">data</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">transpose</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">angle</span><span class="p">(</span><span class="n">data</span><span class="p">[</span><span class="n">ph</span><span class="p">[</span><span class="n">phasor</span><span class="p">]]))</span>
+            <span class="n">ylabel</span> <span class="o">=</span> <span class="n">labels</span><span class="p">[</span><span class="n">ph</span><span class="p">[</span><span class="n">phasor</span><span class="p">]]</span> <span class="o">+</span> <span class="s2">&quot; phase [rad]&quot;</span>
+            <span class="n">cmap</span> <span class="o">=</span> <span class="n">mpl</span><span class="o">.</span><span class="n">cm</span><span class="o">.</span><span class="n">coolwarm</span>  <span class="c1"># diverging</span>
+
+        <span class="n">fig</span><span class="p">,</span> <span class="n">ax</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">()</span>
+        <span class="n">c</span> <span class="o">=</span> <span class="n">ax</span><span class="o">.</span><span class="n">imshow</span><span class="p">(</span><span class="n">data</span><span class="p">,</span> <span class="n">cmap</span><span class="o">=</span><span class="n">cmap</span><span class="p">,</span> <span class="n">origin</span><span class="o">=</span><span class="s1">&#39;lower&#39;</span><span class="p">,</span> <span class="n">aspect</span><span class="o">=</span><span class="s1">&#39;auto&#39;</span><span class="p">)</span>
+        <span class="k">if</span> <span class="n">cm_lim</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="n">c</span><span class="o">.</span><span class="n">set_clim</span><span class="p">(</span><span class="n">vmin</span><span class="o">=</span><span class="n">cm_lim</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">vmax</span><span class="o">=</span><span class="n">cm_lim</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
+        <span class="n">ax</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="s2">&quot;Bunch index&quot;</span><span class="p">)</span>
+        <span class="n">ax</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="s2">&quot;Number of turns&quot;</span><span class="p">)</span>
+        <span class="n">cbar</span> <span class="o">=</span> <span class="n">fig</span><span class="o">.</span><span class="n">colorbar</span><span class="p">(</span><span class="n">c</span><span class="p">,</span> <span class="n">ax</span><span class="o">=</span><span class="n">ax</span><span class="p">)</span>
+        <span class="n">cbar</span><span class="o">.</span><span class="n">set_label</span><span class="p">(</span><span class="n">ylabel</span><span class="p">)</span>
+
+    <span class="k">if</span> <span class="n">plot_type</span> <span class="o">==</span> <span class="s2">&quot;detune&quot;</span> <span class="ow">or</span> <span class="n">plot_type</span> <span class="o">==</span> <span class="s2">&quot;psi&quot;</span><span class="p">:</span>
+
+        <span class="n">fig</span><span class="p">,</span> <span class="n">ax</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">()</span>
+        <span class="k">if</span> <span class="n">plot_type</span> <span class="o">==</span> <span class="s2">&quot;detune&quot;</span><span class="p">:</span>
+            <span class="n">data</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">cavity_data</span><span class="p">[</span><span class="s2">&quot;detune&quot;</span><span class="p">])</span> <span class="o">*</span> <span class="mf">1e-3</span>
+            <span class="n">ylabel</span> <span class="o">=</span> <span class="sa">r</span><span class="s2">&quot;Detuning $\Delta f$ [kHz]&quot;</span>
+        <span class="k">elif</span> <span class="n">plot_type</span> <span class="o">==</span> <span class="s2">&quot;psi&quot;</span><span class="p">:</span>
+            <span class="n">data</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">cavity_data</span><span class="p">[</span><span class="s2">&quot;psi&quot;</span><span class="p">])</span>
+            <span class="n">ylabel</span> <span class="o">=</span> <span class="sa">r</span><span class="s2">&quot;Tuning angle $\psi$&quot;</span>
+
+        <span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">time</span><span class="p">,</span> <span class="n">data</span><span class="p">)</span>
+        <span class="n">ax</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="s2">&quot;Number of turns&quot;</span><span class="p">)</span>
+        <span class="n">ax</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="n">ylabel</span><span class="p">)</span>
+
+    <span class="k">if</span> <span class="n">plot_type</span> <span class="o">==</span> <span class="s2">&quot;power&quot;</span><span class="p">:</span>
+        <span class="n">Vc</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">cavity_data</span><span class="p">[</span><span class="s2">&quot;cavity_phasor_record&quot;</span><span class="p">]),</span> <span class="mi">0</span><span class="p">)</span>
+        <span class="n">theta</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">angle</span><span class="p">(</span><span class="n">cavity_data</span><span class="p">[</span><span class="s2">&quot;cavity_phasor_record&quot;</span><span class="p">]),</span> <span class="mi">0</span><span class="p">)</span>
+        <span class="k">try</span><span class="p">:</span>
+            <span class="n">bunch_index</span> <span class="o">=</span> <span class="p">(</span><span class="n">file</span><span class="p">[</span><span class="s2">&quot;Beam&quot;</span><span class="p">][</span><span class="s2">&quot;current&quot;</span><span class="p">][:,</span> <span class="mi">0</span><span class="p">]</span> <span class="o">!=</span> <span class="mi">0</span><span class="p">)</span><span class="o">.</span><span class="n">nonzero</span><span class="p">()[</span><span class="mi">0</span><span class="p">]</span>
+            <span class="n">I0</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">nansum</span><span class="p">(</span><span class="n">file</span><span class="p">[</span><span class="s2">&quot;Beam&quot;</span><span class="p">][</span><span class="s2">&quot;current&quot;</span><span class="p">][</span><span class="n">bunch_index</span><span class="p">,</span> <span class="p">:],</span> <span class="mi">0</span><span class="p">)</span>
+        <span class="k">except</span><span class="p">:</span>
+            <span class="nb">print</span><span class="p">(</span><span class="s2">&quot;Beam monitor is needed to compute power.&quot;</span><span class="p">)</span>
+
+        <span class="n">Rs</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">cavity_data</span><span class="p">[</span><span class="s2">&quot;Rs&quot;</span><span class="p">])</span>
+        <span class="n">Pc</span> <span class="o">=</span> <span class="n">Vc</span><span class="o">**</span><span class="mi">2</span> <span class="o">/</span> <span class="p">(</span><span class="mi">2</span><span class="o">*</span><span class="n">Rs</span><span class="p">)</span>
+        <span class="n">Pb</span> <span class="o">=</span> <span class="n">I0</span> <span class="o">*</span> <span class="n">Vc</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">theta</span><span class="p">)</span>
+        <span class="n">Pg</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">cavity_data</span><span class="p">[</span><span class="s2">&quot;Pg&quot;</span><span class="p">])</span>
+        <span class="n">Pr</span> <span class="o">=</span> <span class="n">Pg</span> <span class="o">-</span> <span class="n">Pb</span> <span class="o">-</span> <span class="n">Pc</span>
+
+        <span class="n">fig</span><span class="p">,</span> <span class="n">ax</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">()</span>
+        <span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">time</span><span class="p">,</span> <span class="n">Pg</span> <span class="o">*</span> <span class="mf">1e-3</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s2">&quot;Generator power $P_g$ [kW]&quot;</span><span class="p">)</span>
+        <span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">time</span><span class="p">,</span> <span class="n">Pb</span> <span class="o">*</span> <span class="mf">1e-3</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s2">&quot;Beam power $P_b$ [kW]&quot;</span><span class="p">)</span>
+        <span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">time</span><span class="p">,</span> <span class="n">Pc</span> <span class="o">*</span> <span class="mf">1e-3</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s2">&quot;Dissipated cavity power $P_c$ [kW]&quot;</span><span class="p">)</span>
+        <span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">time</span><span class="p">,</span> <span class="n">Pr</span> <span class="o">*</span> <span class="mf">1e-3</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s2">&quot;Reflected power $P_r$ [kW]&quot;</span><span class="p">)</span>
+        <span class="n">ax</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="s2">&quot;Number of turns&quot;</span><span class="p">)</span>
+        <span class="n">ax</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="s2">&quot;Power [kW]&quot;</span><span class="p">)</span>
+        <span class="n">plt</span><span class="o">.</span><span class="n">legend</span><span class="p">()</span>
+
+    <span class="k">if</span> <span class="n">plot_type</span> <span class="o">==</span> <span class="s2">&quot;tuner_diff&quot;</span><span class="p">:</span>
+        <span class="n">data0</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">angle</span><span class="p">(</span><span class="n">cavity_data</span><span class="p">[</span><span class="s2">&quot;cavity_phasor_record&quot;</span><span class="p">][</span><span class="n">bunch_number</span><span class="p">,</span> <span class="p">:])</span>
+        <span class="n">data1</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">cavity_data</span><span class="p">[</span><span class="s2">&quot;psi&quot;</span><span class="p">])</span>
+        <span class="n">data2</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">cavity_data</span><span class="p">[</span><span class="s2">&quot;theta_g&quot;</span><span class="p">])</span>
+
+        <span class="n">ylabel1</span> <span class="o">=</span> <span class="s2">&quot;Tuner diff. from optimal [rad]&quot;</span>
+        <span class="n">ylabel2</span> <span class="o">=</span> <span class="sa">r</span><span class="s2">&quot;Tuning angle $\psi$ [rad]&quot;</span>
+        <span class="n">fig</span><span class="p">,</span> <span class="n">ax</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">()</span>
+        <span class="n">twin</span> <span class="o">=</span> <span class="n">ax</span><span class="o">.</span><span class="n">twinx</span><span class="p">()</span>
+        <span class="n">p1</span><span class="p">,</span> <span class="o">=</span> <span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">time</span><span class="p">,</span> <span class="n">data0</span> <span class="o">-</span> <span class="n">data2</span> <span class="o">+</span> <span class="n">data1</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s2">&quot;r&quot;</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="n">ylabel1</span><span class="p">)</span>
+        <span class="n">p2</span><span class="p">,</span> <span class="o">=</span> <span class="n">twin</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">time</span><span class="p">,</span> <span class="n">data1</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s2">&quot;b&quot;</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="n">ylabel2</span><span class="p">)</span>
+        <span class="n">ax</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="s2">&quot;Turn number&quot;</span><span class="p">)</span>
+        <span class="n">ax</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="n">ylabel1</span><span class="p">)</span>
+        <span class="n">twin</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="n">ylabel2</span><span class="p">)</span>
+        <span class="n">plots</span> <span class="o">=</span> <span class="p">[</span><span class="n">p1</span><span class="p">,</span> <span class="n">p2</span><span class="p">]</span>
+        <span class="n">ax</span><span class="o">.</span><span class="n">legend</span><span class="p">(</span><span class="n">handles</span><span class="o">=</span><span class="n">plots</span><span class="p">,</span> <span class="n">loc</span><span class="o">=</span><span class="s2">&quot;best&quot;</span><span class="p">)</span>
+        <span class="n">ax</span><span class="o">.</span><span class="n">yaxis</span><span class="o">.</span><span class="n">label</span><span class="o">.</span><span class="n">set_color</span><span class="p">(</span><span class="s2">&quot;r&quot;</span><span class="p">)</span>
+        <span class="n">twin</span><span class="o">.</span><span class="n">yaxis</span><span class="o">.</span><span class="n">label</span><span class="o">.</span><span class="n">set_color</span><span class="p">(</span><span class="s2">&quot;b&quot;</span><span class="p">)</span>
+
+    <span class="n">file</span><span class="o">.</span><span class="n">close</span><span class="p">()</span>
+    <span class="k">return</span> <span class="n">fig</span></div>
+</pre></div>
+
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+        <li class="nav-item nav-item-this"><a href="">mbtrack2.tracking.monitors.plotting</a></li> 
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+
+<!DOCTYPE html>
+
+<html lang="en">
+  <head>
+    <meta charset="utf-8" />
+    <meta name="viewport" content="width=device-width, initial-scale=1.0" />
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+            
+  <h1>Source code for mbtrack2.tracking.monitors.tools</h1><div class="highlight"><pre>
+<span></span><span class="c1"># -*- coding: utf-8 -*-</span>
+<span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">This module defines utilities functions, helping to deals with tracking output </span>
+<span class="sd">and hdf5 files.</span>
+<span class="sd">&quot;&quot;&quot;</span>
+
+<span class="kn">import</span> <span class="nn">h5py</span> <span class="k">as</span> <span class="nn">hp</span>
+<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
+
+
+<div class="viewcode-block" id="merge_files"><a class="viewcode-back" href="../../../../mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.tools.merge_files">[docs]</a><span class="k">def</span> <span class="nf">merge_files</span><span class="p">(</span><span class="n">files_prefix</span><span class="p">,</span> <span class="n">files_number</span><span class="p">,</span> <span class="n">start_idx</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">file_name</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    Merge several hdf5 files into one.</span>
+<span class="sd">    </span>
+<span class="sd">    The function assumes that the files to merge have names in the follwing </span>
+<span class="sd">    format:</span>
+<span class="sd">        - &quot;files_prefix_0.hdf5&quot;</span>
+<span class="sd">        - &quot;files_prefix_1.hdf5&quot;</span>
+<span class="sd">        ...</span>
+<span class="sd">        - &quot;files_prefix_files_number.hdf5&quot;</span>
+
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">    files_prefix : str</span>
+<span class="sd">        Name of the files to merge.</span>
+<span class="sd">    files_number : int</span>
+<span class="sd">        Number of files to merge.</span>
+<span class="sd">    start_idx : int, optional</span>
+<span class="sd">        Start index of the hdf5 files.        </span>
+<span class="sd">    file_name : str, optional</span>
+<span class="sd">        Name of the file with the merged data. If None, files_prefix without</span>
+<span class="sd">        number is used.</span>
+
+<span class="sd">    &quot;&quot;&quot;</span>
+    <span class="k">if</span> <span class="n">file_name</span> <span class="o">==</span> <span class="kc">None</span><span class="p">:</span>
+        <span class="n">file_name</span> <span class="o">=</span> <span class="n">files_prefix</span>
+    <span class="n">f</span> <span class="o">=</span> <span class="n">hp</span><span class="o">.</span><span class="n">File</span><span class="p">(</span><span class="n">file_name</span> <span class="o">+</span> <span class="s2">&quot;.hdf5&quot;</span><span class="p">,</span> <span class="s2">&quot;a&quot;</span><span class="p">)</span>
+
+    <span class="c1">## Create file architecture</span>
+    <span class="n">f0</span> <span class="o">=</span> <span class="n">hp</span><span class="o">.</span><span class="n">File</span><span class="p">(</span><span class="n">files_prefix</span> <span class="o">+</span> <span class="s2">&quot;_&quot;</span> <span class="o">+</span> <span class="nb">str</span><span class="p">(</span><span class="n">start_idx</span><span class="p">)</span> <span class="o">+</span> <span class="s2">&quot;.hdf5&quot;</span><span class="p">,</span> <span class="s2">&quot;r&quot;</span><span class="p">)</span>
+    <span class="k">for</span> <span class="n">group</span> <span class="ow">in</span> <span class="nb">list</span><span class="p">(</span><span class="n">f0</span><span class="p">):</span>
+        <span class="n">f</span><span class="o">.</span><span class="n">require_group</span><span class="p">(</span><span class="n">group</span><span class="p">)</span>
+        <span class="k">for</span> <span class="n">dataset_name</span> <span class="ow">in</span> <span class="nb">list</span><span class="p">(</span><span class="n">f0</span><span class="p">[</span><span class="n">group</span><span class="p">]):</span>
+            <span class="k">if</span> <span class="n">dataset_name</span> <span class="o">==</span> <span class="s2">&quot;freq&quot;</span><span class="p">:</span>
+                <span class="n">f0</span><span class="p">[</span><span class="n">group</span><span class="p">]</span><span class="o">.</span><span class="n">copy</span><span class="p">(</span><span class="n">dataset_name</span><span class="p">,</span> <span class="n">f</span><span class="p">[</span><span class="n">group</span><span class="p">])</span>
+                <span class="k">continue</span>
+            <span class="n">shape</span> <span class="o">=</span> <span class="n">f0</span><span class="p">[</span><span class="n">group</span><span class="p">][</span><span class="n">dataset_name</span><span class="p">]</span><span class="o">.</span><span class="n">shape</span>
+            <span class="n">dtype</span> <span class="o">=</span> <span class="n">f0</span><span class="p">[</span><span class="n">group</span><span class="p">][</span><span class="n">dataset_name</span><span class="p">]</span><span class="o">.</span><span class="n">dtype</span>
+            <span class="n">shape_needed</span> <span class="o">=</span> <span class="nb">list</span><span class="p">(</span><span class="n">shape</span><span class="p">)</span>
+            <span class="n">shape_needed</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="n">shape_needed</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="n">files_number</span>
+            <span class="n">shape_needed</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">shape_needed</span><span class="p">)</span>
+            <span class="n">f</span><span class="p">[</span><span class="n">group</span><span class="p">]</span><span class="o">.</span><span class="n">create_dataset</span><span class="p">(</span><span class="n">dataset_name</span><span class="p">,</span> <span class="n">shape_needed</span><span class="p">,</span> <span class="n">dtype</span><span class="p">)</span>
+
+    <span class="n">f0</span><span class="o">.</span><span class="n">close</span><span class="p">()</span>
+
+    <span class="c1">## Copy data</span>
+    <span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">file_num</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="n">start_idx</span><span class="p">,</span> <span class="n">start_idx</span> <span class="o">+</span> <span class="n">files_number</span><span class="p">)):</span>
+        <span class="n">fi</span> <span class="o">=</span> <span class="n">hp</span><span class="o">.</span><span class="n">File</span><span class="p">(</span><span class="n">files_prefix</span> <span class="o">+</span> <span class="s2">&quot;_&quot;</span> <span class="o">+</span> <span class="nb">str</span><span class="p">(</span><span class="n">file_num</span><span class="p">)</span> <span class="o">+</span> <span class="s2">&quot;.hdf5&quot;</span><span class="p">,</span> <span class="s2">&quot;r&quot;</span><span class="p">)</span>
+        <span class="k">for</span> <span class="n">group</span> <span class="ow">in</span> <span class="nb">list</span><span class="p">(</span><span class="n">fi</span><span class="p">):</span>
+            <span class="k">for</span> <span class="n">dataset_name</span> <span class="ow">in</span> <span class="nb">list</span><span class="p">(</span><span class="n">fi</span><span class="p">[</span><span class="n">group</span><span class="p">]):</span>
+                <span class="n">shape</span> <span class="o">=</span> <span class="n">fi</span><span class="p">[</span><span class="n">group</span><span class="p">][</span><span class="n">dataset_name</span><span class="p">]</span><span class="o">.</span><span class="n">shape</span>
+                <span class="n">n_slice</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">shape</span><span class="p">)</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
+                <span class="n">length</span> <span class="o">=</span> <span class="n">shape</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
+                <span class="n">slice_list</span> <span class="o">=</span> <span class="p">[]</span>
+                <span class="k">for</span> <span class="n">n</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n_slice</span><span class="p">):</span>
+                    <span class="n">slice_list</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="nb">slice</span><span class="p">(</span><span class="kc">None</span><span class="p">))</span>
+                <span class="n">slice_list</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="nb">slice</span><span class="p">(</span><span class="n">length</span> <span class="o">*</span> <span class="n">i</span><span class="p">,</span> <span class="n">length</span> <span class="o">*</span> <span class="p">(</span><span class="n">i</span><span class="o">+</span><span class="mi">1</span><span class="p">)))</span>
+                <span class="k">if</span> <span class="p">(</span><span class="n">dataset_name</span> <span class="o">==</span> <span class="s2">&quot;freq&quot;</span><span class="p">):</span>
+                    <span class="k">continue</span>
+                <span class="k">if</span> <span class="p">(</span><span class="n">dataset_name</span> <span class="o">==</span> <span class="s2">&quot;time&quot;</span><span class="p">)</span> <span class="ow">and</span> <span class="p">(</span><span class="n">file_num</span> <span class="o">!=</span> <span class="n">start_idx</span><span class="p">):</span>
+                    <span class="n">f</span><span class="p">[</span><span class="n">group</span><span class="p">][</span><span class="n">dataset_name</span><span class="p">][</span><span class="nb">tuple</span><span class="p">(</span><span class="n">slice_list</span><span class="p">)]</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">max</span><span class="p">(</span>
+                        <span class="n">f</span><span class="p">[</span><span class="n">group</span><span class="p">][</span><span class="n">dataset_name</span><span class="p">][:])</span> <span class="o">+</span> <span class="n">fi</span><span class="p">[</span><span class="n">group</span><span class="p">][</span><span class="n">dataset_name</span><span class="p">]</span>
+                <span class="k">else</span><span class="p">:</span>
+                    <span class="n">f</span><span class="p">[</span><span class="n">group</span><span class="p">][</span><span class="n">dataset_name</span><span class="p">][</span><span class="nb">tuple</span><span class="p">(</span>
+                        <span class="n">slice_list</span><span class="p">)]</span> <span class="o">=</span> <span class="n">fi</span><span class="p">[</span><span class="n">group</span><span class="p">][</span><span class="n">dataset_name</span><span class="p">]</span>
+        <span class="n">fi</span><span class="o">.</span><span class="n">close</span><span class="p">()</span>
+    <span class="n">f</span><span class="o">.</span><span class="n">close</span><span class="p">()</span></div>
+
+
+<div class="viewcode-block" id="copy_files"><a class="viewcode-back" href="../../../../mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.tools.copy_files">[docs]</a><span class="k">def</span> <span class="nf">copy_files</span><span class="p">(</span><span class="n">source</span><span class="p">,</span> <span class="n">copy</span><span class="p">,</span> <span class="n">version</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    Copy a source hdf5 file into another hdf5 file using a different HDF5 </span>
+<span class="sd">    version.</span>
+<span class="sd">    </span>
+<span class="sd">    The function assumes that the source file has only a single group layer.</span>
+
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">    source : str</span>
+<span class="sd">        Name of the source file.</span>
+<span class="sd">    copy : str</span>
+<span class="sd">        Name of the copy file.</span>
+<span class="sd">    version : str, optional</span>
+<span class="sd">        Version number of the copy file.</span>
+
+<span class="sd">    &quot;&quot;&quot;</span>
+    <span class="k">if</span> <span class="n">version</span> <span class="o">==</span> <span class="kc">None</span><span class="p">:</span>
+        <span class="n">version</span> <span class="o">=</span> <span class="s1">&#39;v108&#39;</span>
+    <span class="n">f</span> <span class="o">=</span> <span class="n">hp</span><span class="o">.</span><span class="n">File</span><span class="p">(</span><span class="n">source</span> <span class="o">+</span> <span class="s2">&quot;.hdf5&quot;</span><span class="p">,</span> <span class="s2">&quot;r&quot;</span><span class="p">)</span>
+    <span class="n">h</span> <span class="o">=</span> <span class="n">hp</span><span class="o">.</span><span class="n">File</span><span class="p">(</span><span class="n">copy</span> <span class="o">+</span> <span class="s2">&quot;.hdf5&quot;</span><span class="p">,</span> <span class="s2">&quot;a&quot;</span><span class="p">,</span> <span class="n">libver</span><span class="o">=</span><span class="p">(</span><span class="s1">&#39;earliest&#39;</span><span class="p">,</span> <span class="n">version</span><span class="p">))</span>
+
+    <span class="c1">## Copy file</span>
+    <span class="k">for</span> <span class="n">group</span> <span class="ow">in</span> <span class="nb">list</span><span class="p">(</span><span class="n">f</span><span class="p">):</span>
+        <span class="n">h</span><span class="o">.</span><span class="n">require_group</span><span class="p">(</span><span class="n">group</span><span class="p">)</span>
+        <span class="k">for</span> <span class="n">dataset_name</span> <span class="ow">in</span> <span class="nb">list</span><span class="p">(</span><span class="n">f</span><span class="p">[</span><span class="n">group</span><span class="p">]):</span>
+            <span class="n">h</span><span class="p">[</span><span class="n">group</span><span class="p">][</span><span class="n">dataset_name</span><span class="p">]</span> <span class="o">=</span> <span class="n">f</span><span class="p">[</span><span class="n">group</span><span class="p">][</span><span class="n">dataset_name</span><span class="p">][()]</span>
+
+    <span class="n">f</span><span class="o">.</span><span class="n">close</span><span class="p">()</span>
+    <span class="n">h</span><span class="o">.</span><span class="n">close</span><span class="p">()</span></div>
+</pre></div>
+
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+            
+  <h1>Source code for mbtrack2.tracking.parallel</h1><div class="highlight"><pre>
+<span></span><span class="c1"># -*- coding: utf-8 -*-</span>
+<span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">Module to handle parallel computation</span>
+<span class="sd">&quot;&quot;&quot;</span>
+
+<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
+
+
+<div class="viewcode-block" id="Mpi"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.parallel.Mpi">[docs]</a><span class="k">class</span> <span class="nc">Mpi</span><span class="p">:</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    Class which handle parallel computation via the mpi4py module [1].</span>
+<span class="sd">    </span>
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">    filling_pattern : bool array of shape (h,)</span>
+<span class="sd">        Filling pattern of the beam, like Beam.filling_pattern</span>
+<span class="sd">        </span>
+<span class="sd">    Attributes</span>
+<span class="sd">    ----------</span>
+<span class="sd">    comm : MPI.Intracomm object</span>
+<span class="sd">        MPI intra-comminicator of the processor group, used to manage </span>
+<span class="sd">        communication between processors. </span>
+<span class="sd">    rank : int</span>
+<span class="sd">        Rank of the processor which run the program</span>
+<span class="sd">    size : int</span>
+<span class="sd">        Number of processor within the processor group (in fact in the </span>
+<span class="sd">        intra-comminicator group)</span>
+<span class="sd">    table : int array of shape (size, 2)</span>
+<span class="sd">        Table of correspondance between the rank of the processor and its </span>
+<span class="sd">        associated bunch number</span>
+<span class="sd">    bunch_num : int</span>
+<span class="sd">        Return the bunch number corresponding to the current processor</span>
+<span class="sd">    next_bunch : int</span>
+<span class="sd">        Return the rank of the next tracked bunch</span>
+<span class="sd">    previous_bunch : int</span>
+<span class="sd">        Return the rank of the previous tracked bunch</span>
+<span class="sd">        </span>
+<span class="sd">    Methods</span>
+<span class="sd">    -------</span>
+<span class="sd">    write_table(filling_pattern)</span>
+<span class="sd">        Write a table with the rank and the corresponding bunch number for each</span>
+<span class="sd">        bunch of the filling pattern</span>
+<span class="sd">    rank_to_bunch(rank)</span>
+<span class="sd">        Return the bunch number corresponding to rank</span>
+<span class="sd">    bunch_to_rank(bunch_num)</span>
+<span class="sd">        Return the rank corresponding to the bunch number bunch_num</span>
+<span class="sd">    share_distributions(beam)</span>
+<span class="sd">        Compute the bunch profiles and share it between the different bunches.</span>
+<span class="sd">    share_means(beam)</span>
+<span class="sd">        Compute the bunch means and share it between the different bunches.</span>
+<span class="sd">    share_stds(beam)</span>
+<span class="sd">        Compute the bunch standard deviations and share it between the </span>
+<span class="sd">        different bunches.</span>
+<span class="sd">        </span>
+<span class="sd">    References</span>
+<span class="sd">    ----------</span>
+<span class="sd">    [1] L. Dalcin, P. Kler, R. Paz, and A. Cosimo, Parallel Distributed </span>
+<span class="sd">    Computing using Python, Advances in Water Resources, 34(9):1124-1139, 2011.</span>
+<span class="sd">    </span>
+<span class="sd">    &quot;&quot;&quot;</span>
+
+    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">filling_pattern</span><span class="p">):</span>
+        <span class="kn">from</span> <span class="nn">mpi4py</span> <span class="kn">import</span> <span class="n">MPI</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">MPI</span> <span class="o">=</span> <span class="n">MPI</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">comm</span> <span class="o">=</span> <span class="n">MPI</span><span class="o">.</span><span class="n">COMM_WORLD</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">rank</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">comm</span><span class="o">.</span><span class="n">Get_rank</span><span class="p">()</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">size</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">comm</span><span class="o">.</span><span class="n">Get_size</span><span class="p">()</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">write_table</span><span class="p">(</span><span class="n">filling_pattern</span><span class="p">)</span>
+
+<div class="viewcode-block" id="Mpi.write_table"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.parallel.Mpi.write_table">[docs]</a>    <span class="k">def</span> <span class="nf">write_table</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">filling_pattern</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Write a table with the rank and the corresponding bunch number for each</span>
+<span class="sd">        bunch of the filling pattern</span>
+<span class="sd">        </span>
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        filling_pattern : bool array of shape (h,)</span>
+<span class="sd">            Filling pattern of the beam, like Beam.filling_pattern</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="k">if</span> <span class="p">(</span><span class="n">filling_pattern</span><span class="o">.</span><span class="n">sum</span><span class="p">()</span> <span class="o">!=</span> <span class="bp">self</span><span class="o">.</span><span class="n">size</span><span class="p">):</span>
+            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">&quot;The number of processors must be equal to the&quot;</span>
+                             <span class="s2">&quot;number of (non-empty) bunches.&quot;</span><span class="p">)</span>
+        <span class="n">table</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="bp">self</span><span class="o">.</span><span class="n">size</span><span class="p">,</span> <span class="mi">2</span><span class="p">),</span> <span class="n">dtype</span><span class="o">=</span><span class="nb">int</span><span class="p">)</span>
+        <span class="n">table</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">size</span><span class="p">)</span>
+        <span class="n">table</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">where</span><span class="p">(</span><span class="n">filling_pattern</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">table</span> <span class="o">=</span> <span class="n">table</span></div>
+
+<div class="viewcode-block" id="Mpi.rank_to_bunch"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.parallel.Mpi.rank_to_bunch">[docs]</a>    <span class="k">def</span> <span class="nf">rank_to_bunch</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">rank</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Return the bunch number corresponding to rank</span>
+<span class="sd">        </span>
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        rank : int</span>
+<span class="sd">            Rank of a processor</span>
+<span class="sd">            </span>
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        bunch_num : int</span>
+<span class="sd">            Bunch number corresponding to the input rank</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">table</span><span class="p">[</span><span class="n">rank</span><span class="p">,</span> <span class="mi">1</span><span class="p">]</span></div>
+
+<div class="viewcode-block" id="Mpi.bunch_to_rank"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.parallel.Mpi.bunch_to_rank">[docs]</a>    <span class="k">def</span> <span class="nf">bunch_to_rank</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">bunch_num</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Return the rank corresponding to the bunch number bunch_num</span>
+<span class="sd">        </span>
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        bunch_num : int</span>
+<span class="sd">            Bunch number</span>
+<span class="sd">            </span>
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        rank : int</span>
+<span class="sd">            Rank of the processor which tracks the input bunch number</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="k">try</span><span class="p">:</span>
+            <span class="n">rank</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">where</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">table</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">]</span> <span class="o">==</span> <span class="n">bunch_num</span><span class="p">)[</span><span class="mi">0</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span>
+        <span class="k">except</span> <span class="ne">IndexError</span><span class="p">:</span>
+            <span class="nb">print</span><span class="p">(</span><span class="s2">&quot;The bunch &quot;</span> <span class="o">+</span> <span class="nb">str</span><span class="p">(</span><span class="n">bunch_num</span><span class="p">)</span> <span class="o">+</span>
+                  <span class="s2">&quot; is not tracked on any processor.&quot;</span><span class="p">)</span>
+            <span class="n">rank</span> <span class="o">=</span> <span class="kc">None</span>
+        <span class="k">return</span> <span class="n">rank</span></div>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">bunch_num</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Return the bunch number corresponding to the current processor&quot;&quot;&quot;</span>
+        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">rank_to_bunch</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">rank</span><span class="p">)</span>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">next_bunch</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Return the rank of the next tracked bunch&quot;&quot;&quot;</span>
+        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">rank</span> <span class="o">+</span> <span class="mi">1</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">table</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">]:</span>
+            <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">rank</span> <span class="o">+</span> <span class="mi">1</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="k">return</span> <span class="mi">0</span>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">previous_bunch</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Return the rank of the previous tracked bunch&quot;&quot;&quot;</span>
+        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">rank</span> <span class="o">-</span> <span class="mi">1</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">table</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">]:</span>
+            <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">rank</span> <span class="o">-</span> <span class="mi">1</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="k">return</span> <span class="nb">max</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">table</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">])</span>
+
+<div class="viewcode-block" id="Mpi.share_distributions"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.parallel.Mpi.share_distributions">[docs]</a>    <span class="k">def</span> <span class="nf">share_distributions</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">beam</span><span class="p">,</span> <span class="n">dimensions</span><span class="o">=</span><span class="s2">&quot;tau&quot;</span><span class="p">,</span> <span class="n">n_bin</span><span class="o">=</span><span class="mi">75</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Compute the bunch profiles and share it between the different bunches.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        beam : Beam object</span>
+<span class="sd">        dimension : str or list of str, optional</span>
+<span class="sd">            Dimensions in which the binning is done. The default is &quot;tau&quot;.</span>
+<span class="sd">        n_bin : int or list of int, optional</span>
+<span class="sd">            Number of bins. The default is 75.</span>
+
+<span class="sd">        &quot;&quot;&quot;</span>
+
+        <span class="k">if</span> <span class="p">(</span><span class="n">beam</span><span class="o">.</span><span class="n">mpi_switch</span> <span class="o">==</span> <span class="kc">False</span><span class="p">):</span>
+            <span class="nb">print</span><span class="p">(</span><span class="s2">&quot;Error, mpi is not initialised.&quot;</span><span class="p">)</span>
+
+        <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">dimensions</span><span class="p">,</span> <span class="nb">str</span><span class="p">):</span>
+            <span class="n">dimensions</span> <span class="o">=</span> <span class="p">[</span><span class="n">dimensions</span><span class="p">]</span>
+
+        <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">n_bin</span><span class="p">,</span> <span class="nb">int</span><span class="p">):</span>
+            <span class="n">n_bin</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">((</span><span class="nb">len</span><span class="p">(</span><span class="n">dimensions</span><span class="p">),</span> <span class="p">),</span> <span class="n">dtype</span><span class="o">=</span><span class="nb">int</span><span class="p">)</span> <span class="o">*</span> <span class="n">n_bin</span>
+
+        <span class="n">bunch</span> <span class="o">=</span> <span class="n">beam</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">bunch_num</span><span class="p">]</span>
+
+        <span class="n">charge_per_mp_all</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">comm</span><span class="o">.</span><span class="n">allgather</span><span class="p">(</span><span class="n">bunch</span><span class="o">.</span><span class="n">charge_per_mp</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">charge_per_mp_all</span> <span class="o">=</span> <span class="n">charge_per_mp_all</span>
+
+        <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">dimensions</span><span class="p">)):</span>
+
+            <span class="n">dim</span> <span class="o">=</span> <span class="n">dimensions</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
+            <span class="n">n</span> <span class="o">=</span> <span class="n">n_bin</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
+
+            <span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">bunch</span><span class="p">)</span> <span class="o">!=</span> <span class="mi">0</span><span class="p">:</span>
+                <span class="n">bins</span><span class="p">,</span> <span class="n">sorted_index</span><span class="p">,</span> <span class="n">profile</span><span class="p">,</span> <span class="n">center</span> <span class="o">=</span> <span class="n">bunch</span><span class="o">.</span><span class="n">binning</span><span class="p">(</span>
+                    <span class="n">dimension</span><span class="o">=</span><span class="n">dim</span><span class="p">,</span> <span class="n">n_bin</span><span class="o">=</span><span class="n">n</span><span class="p">)</span>
+            <span class="k">else</span><span class="p">:</span>
+                <span class="n">sorted_index</span> <span class="o">=</span> <span class="kc">None</span>
+                <span class="n">profile</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="n">n</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="p">),</span> <span class="n">dtype</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">int64</span><span class="p">)</span>
+                <span class="n">center</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="n">n</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="p">),</span> <span class="n">dtype</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">float64</span><span class="p">)</span>
+                <span class="k">if</span> <span class="n">beam</span><span class="o">.</span><span class="n">filling_pattern</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">bunch_num</span><span class="p">]</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">:</span>
+                    <span class="n">beam</span><span class="o">.</span><span class="n">update_filling_pattern</span><span class="p">()</span>
+                    <span class="n">beam</span><span class="o">.</span><span class="n">update_distance_between_bunches</span><span class="p">()</span>
+
+            <span class="bp">self</span><span class="o">.</span><span class="fm">__setattr__</span><span class="p">(</span><span class="n">dim</span> <span class="o">+</span> <span class="s2">&quot;_center&quot;</span><span class="p">,</span>
+                             <span class="n">np</span><span class="o">.</span><span class="n">empty</span><span class="p">((</span><span class="bp">self</span><span class="o">.</span><span class="n">size</span><span class="p">,</span> <span class="n">n</span> <span class="o">-</span> <span class="mi">1</span><span class="p">),</span> <span class="n">dtype</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">float64</span><span class="p">))</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">comm</span><span class="o">.</span><span class="n">Allgather</span><span class="p">(</span>
+                <span class="p">[</span><span class="n">center</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">MPI</span><span class="o">.</span><span class="n">DOUBLE</span><span class="p">],</span>
+                <span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="fm">__getattribute__</span><span class="p">(</span><span class="n">dim</span> <span class="o">+</span> <span class="s2">&quot;_center&quot;</span><span class="p">),</span> <span class="bp">self</span><span class="o">.</span><span class="n">MPI</span><span class="o">.</span><span class="n">DOUBLE</span><span class="p">])</span>
+
+            <span class="bp">self</span><span class="o">.</span><span class="fm">__setattr__</span><span class="p">(</span><span class="n">dim</span> <span class="o">+</span> <span class="s2">&quot;_profile&quot;</span><span class="p">,</span>
+                             <span class="n">np</span><span class="o">.</span><span class="n">empty</span><span class="p">((</span><span class="bp">self</span><span class="o">.</span><span class="n">size</span><span class="p">,</span> <span class="n">n</span> <span class="o">-</span> <span class="mi">1</span><span class="p">),</span> <span class="n">dtype</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">int64</span><span class="p">))</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">comm</span><span class="o">.</span><span class="n">Allgather</span><span class="p">(</span>
+                <span class="p">[</span><span class="n">profile</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">MPI</span><span class="o">.</span><span class="n">INT64_T</span><span class="p">],</span>
+                <span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="fm">__getattribute__</span><span class="p">(</span><span class="n">dim</span> <span class="o">+</span> <span class="s2">&quot;_profile&quot;</span><span class="p">),</span> <span class="bp">self</span><span class="o">.</span><span class="n">MPI</span><span class="o">.</span><span class="n">INT64_T</span><span class="p">])</span>
+
+            <span class="bp">self</span><span class="o">.</span><span class="fm">__setattr__</span><span class="p">(</span><span class="n">dim</span> <span class="o">+</span> <span class="s2">&quot;_sorted_index&quot;</span><span class="p">,</span> <span class="n">sorted_index</span><span class="p">)</span></div>
+
+<div class="viewcode-block" id="Mpi.share_means"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.parallel.Mpi.share_means">[docs]</a>    <span class="k">def</span> <span class="nf">share_means</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">beam</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Compute the bunch means and share it between the different bunches.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        beam : Beam object</span>
+
+<span class="sd">        &quot;&quot;&quot;</span>
+
+        <span class="k">if</span> <span class="p">(</span><span class="n">beam</span><span class="o">.</span><span class="n">mpi_switch</span> <span class="o">==</span> <span class="kc">False</span><span class="p">):</span>
+            <span class="nb">print</span><span class="p">(</span><span class="s2">&quot;Error, mpi is not initialised.&quot;</span><span class="p">)</span>
+
+        <span class="n">bunch</span> <span class="o">=</span> <span class="n">beam</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">bunch_num</span><span class="p">]</span>
+
+        <span class="n">charge_all</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">comm</span><span class="o">.</span><span class="n">allgather</span><span class="p">(</span><span class="n">bunch</span><span class="o">.</span><span class="n">charge</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">charge_all</span> <span class="o">=</span> <span class="n">charge_all</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">mean_all</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">empty</span><span class="p">((</span><span class="bp">self</span><span class="o">.</span><span class="n">size</span><span class="p">,</span> <span class="mi">6</span><span class="p">),</span> <span class="n">dtype</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">float64</span><span class="p">)</span>
+        <span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">bunch</span><span class="p">)</span> <span class="o">!=</span> <span class="mi">0</span><span class="p">:</span>
+            <span class="n">mean</span> <span class="o">=</span> <span class="n">bunch</span><span class="o">.</span><span class="n">mean</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="n">mean</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="mi">6</span><span class="p">,</span> <span class="p">),</span> <span class="n">dtype</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">float64</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">comm</span><span class="o">.</span><span class="n">Allgather</span><span class="p">([</span><span class="n">mean</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">MPI</span><span class="o">.</span><span class="n">DOUBLE</span><span class="p">],</span>
+                            <span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">mean_all</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">MPI</span><span class="o">.</span><span class="n">DOUBLE</span><span class="p">])</span></div>
+
+<div class="viewcode-block" id="Mpi.share_stds"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.parallel.Mpi.share_stds">[docs]</a>    <span class="k">def</span> <span class="nf">share_stds</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">beam</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Compute the bunch standard deviations and share it between the </span>
+<span class="sd">        different bunches.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        beam : Beam object</span>
+
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="k">if</span> <span class="p">(</span><span class="n">beam</span><span class="o">.</span><span class="n">mpi_switch</span> <span class="o">==</span> <span class="kc">False</span><span class="p">):</span>
+            <span class="nb">print</span><span class="p">(</span><span class="s2">&quot;Error, mpi is not initialised.&quot;</span><span class="p">)</span>
+
+        <span class="n">bunch</span> <span class="o">=</span> <span class="n">beam</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">bunch_num</span><span class="p">]</span>
+
+        <span class="n">charge_all</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">comm</span><span class="o">.</span><span class="n">allgather</span><span class="p">(</span><span class="n">bunch</span><span class="o">.</span><span class="n">charge</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">charge_all</span> <span class="o">=</span> <span class="n">charge_all</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">std_all</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">empty</span><span class="p">((</span><span class="bp">self</span><span class="o">.</span><span class="n">size</span><span class="p">,</span> <span class="mi">6</span><span class="p">),</span> <span class="n">dtype</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">float64</span><span class="p">)</span>
+        <span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">bunch</span><span class="p">)</span> <span class="o">!=</span> <span class="mi">0</span><span class="p">:</span>
+            <span class="n">std</span> <span class="o">=</span> <span class="n">bunch</span><span class="o">.</span><span class="n">std</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="n">std</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="mi">6</span><span class="p">,</span> <span class="p">),</span> <span class="n">dtype</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">float64</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">comm</span><span class="o">.</span><span class="n">Allgather</span><span class="p">([</span><span class="n">std</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">MPI</span><span class="o">.</span><span class="n">DOUBLE</span><span class="p">],</span>
+                            <span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">std_all</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">MPI</span><span class="o">.</span><span class="n">DOUBLE</span><span class="p">])</span></div></div>
+</pre></div>
+
+            <div class="clearer"></div>
+          </div>
+        </div>
+      </div>
+      <div class="sphinxsidebar" role="navigation" aria-label="main navigation">
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+</div>
+<script>document.getElementById('searchbox').style.display = "block"</script>
+        </div>
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+    </div>
+    <div class="related" role="navigation" aria-label="related navigation">
+      <h3>Navigation</h3>
+      <ul>
+        <li class="right" style="margin-right: 10px">
+          <a href="../../../genindex.html" title="General Index"
+             >index</a></li>
+        <li class="right" >
+          <a href="../../../py-modindex.html" title="Python Module Index"
+             >modules</a> |</li>
+        <li class="nav-item nav-item-0"><a href="../../../index.html">mbtrack2 0.6.0 documentation</a> &#187;</li>
+          <li class="nav-item nav-item-1"><a href="../../index.html" >Module code</a> &#187;</li>
+        <li class="nav-item nav-item-this"><a href="">mbtrack2.tracking.parallel</a></li> 
+      </ul>
+    </div>
+    <div class="footer" role="contentinfo">
+        &#169; Copyright 2024, A. Gamelin et al.
+      Created using <a href="https://www.sphinx-doc.org/">Sphinx</a> 5.0.2.
+    </div>
+  </body>
+</html>
\ No newline at end of file
diff --git a/docs/build/html/_modules/mbtrack2/tracking/particles.html b/docs/build/html/_modules/mbtrack2/tracking/particles.html
new file mode 100644
index 0000000..ce38877
--- /dev/null
+++ b/docs/build/html/_modules/mbtrack2/tracking/particles.html
@@ -0,0 +1,1136 @@
+
+<!DOCTYPE html>
+
+<html lang="en">
+  <head>
+    <meta charset="utf-8" />
+    <meta name="viewport" content="width=device-width, initial-scale=1.0" />
+    <title>mbtrack2.tracking.particles &#8212; mbtrack2 0.6.0 documentation</title>
+    <link rel="stylesheet" type="text/css" href="../../../_static/pygments.css" />
+    <link rel="stylesheet" type="text/css" href="../../../_static/nature.css" />
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+    <script src="../../../_static/jquery.js"></script>
+    <script src="../../../_static/underscore.js"></script>
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+    <script src="../../../_static/doctools.js"></script>
+    <link rel="index" title="Index" href="../../../genindex.html" />
+    <link rel="search" title="Search" href="../../../search.html" /> 
+  </head><body>
+    <div class="related" role="navigation" aria-label="related navigation">
+      <h3>Navigation</h3>
+      <ul>
+        <li class="right" style="margin-right: 10px">
+          <a href="../../../genindex.html" title="General Index"
+             accesskey="I">index</a></li>
+        <li class="right" >
+          <a href="../../../py-modindex.html" title="Python Module Index"
+             >modules</a> |</li>
+        <li class="nav-item nav-item-0"><a href="../../../index.html">mbtrack2 0.6.0 documentation</a> &#187;</li>
+          <li class="nav-item nav-item-1"><a href="../../index.html" accesskey="U">Module code</a> &#187;</li>
+        <li class="nav-item nav-item-this"><a href="">mbtrack2.tracking.particles</a></li> 
+      </ul>
+    </div>  
+
+    <div class="document">
+      <div class="documentwrapper">
+        <div class="bodywrapper">
+          <div class="body" role="main">
+            
+  <h1>Source code for mbtrack2.tracking.particles</h1><div class="highlight"><pre>
+<span></span><span class="c1"># -*- coding: utf-8 -*-</span>
+<span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">Module where particles, bunches and beams are described as objects.</span>
+<span class="sd">&quot;&quot;&quot;</span>
+
+<span class="kn">import</span> <span class="nn">h5py</span> <span class="k">as</span> <span class="nn">hp</span>
+<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
+<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="kn">import</span> <span class="nn">pandas</span> <span class="k">as</span> <span class="nn">pd</span>
+<span class="kn">import</span> <span class="nn">seaborn</span> <span class="k">as</span> <span class="nn">sns</span>
+<span class="kn">from</span> <span class="nn">scipy.constants</span> <span class="kn">import</span> <span class="n">c</span><span class="p">,</span> <span class="n">e</span><span class="p">,</span> <span class="n">m_e</span><span class="p">,</span> <span class="n">m_p</span>
+
+
+<div class="viewcode-block" id="Particle"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.particles.Particle">[docs]</a><span class="k">class</span> <span class="nc">Particle</span><span class="p">:</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    Define a particle object.</span>
+
+<span class="sd">    Attributes</span>
+<span class="sd">    ----------</span>
+<span class="sd">    mass : float</span>
+<span class="sd">        total particle mass in [kg]</span>
+<span class="sd">    charge : float</span>
+<span class="sd">        electrical charge in [C]</span>
+<span class="sd">    E_rest : float</span>
+<span class="sd">        particle rest energy in [eV]</span>
+<span class="sd">    &quot;&quot;&quot;</span>
+
+    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">mass</span><span class="p">,</span> <span class="n">charge</span><span class="p">):</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">mass</span> <span class="o">=</span> <span class="n">mass</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">charge</span> <span class="o">=</span> <span class="n">charge</span>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">E_rest</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">mass</span> <span class="o">*</span> <span class="n">c</span><span class="o">**</span><span class="mi">2</span> <span class="o">/</span> <span class="n">e</span></div>
+
+
+<div class="viewcode-block" id="Electron"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.particles.Electron">[docs]</a><span class="k">class</span> <span class="nc">Electron</span><span class="p">(</span><span class="n">Particle</span><span class="p">):</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot; Define an electron&quot;&quot;&quot;</span>
+
+    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+        <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__init__</span><span class="p">(</span><span class="n">m_e</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span> <span class="o">*</span> <span class="n">e</span><span class="p">)</span></div>
+
+
+<div class="viewcode-block" id="Proton"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.particles.Proton">[docs]</a><span class="k">class</span> <span class="nc">Proton</span><span class="p">(</span><span class="n">Particle</span><span class="p">):</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot; Define a proton&quot;&quot;&quot;</span>
+
+    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+        <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__init__</span><span class="p">(</span><span class="n">m_p</span><span class="p">,</span> <span class="n">e</span><span class="p">)</span></div>
+
+
+<div class="viewcode-block" id="Bunch"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.particles.Bunch">[docs]</a><span class="k">class</span> <span class="nc">Bunch</span><span class="p">:</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    Define a bunch object.</span>
+<span class="sd">    </span>
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">    ring : Synchrotron object</span>
+<span class="sd">    mp_number : float, optional</span>
+<span class="sd">        Macro-particle number.</span>
+<span class="sd">    current : float, optional</span>
+<span class="sd">        Bunch current in [A].</span>
+<span class="sd">    track_alive : bool, optional</span>
+<span class="sd">        If False, the code no longer take into account alive/dead particles.</span>
+<span class="sd">        Should be set to True if element such as apertures are used.</span>
+<span class="sd">        Can be set to False to gain a speed increase.</span>
+<span class="sd">    alive : bool, optional</span>
+<span class="sd">        If False, the bunch is defined as empty.</span>
+<span class="sd">    load_from_file : str, optional</span>
+<span class="sd">        Name of bunch save file generated by save method.</span>
+<span class="sd">        If None, the bunch is initialized using the input parameters.</span>
+<span class="sd">        Otherwise, the bunch from the file is loaded and the other inputs are </span>
+<span class="sd">        ignored.</span>
+<span class="sd">        Default is None.</span>
+<span class="sd">    load_suffix : str or int, optional</span>
+<span class="sd">        Suffix to the group name used to load the data from the HDF5 file.</span>
+<span class="sd">        Default is None.</span>
+<span class="sd">        </span>
+<span class="sd">    Attributes</span>
+<span class="sd">    ----------</span>
+<span class="sd">    mp_number : int</span>
+<span class="sd">        Macro-particle number.</span>
+<span class="sd">    alive : array of bool of shape (mp_number,)</span>
+<span class="sd">        Array used to monitor which particle is dead or alive.</span>
+<span class="sd">    charge : float</span>
+<span class="sd">        Bunch charge in [C].</span>
+<span class="sd">    charge_per_mp : float</span>
+<span class="sd">        Charge per macro-particle in [C].</span>
+<span class="sd">    particle_number : int</span>
+<span class="sd">        Number of particles in the bunch.</span>
+<span class="sd">    current : float</span>
+<span class="sd">        Bunch current in [A].</span>
+<span class="sd">    is_empty : bool</span>
+<span class="sd">        Return True if the bunch is empty.</span>
+<span class="sd">    mean : array of shape (6,)</span>
+<span class="sd">        Mean position of alive particles for each coordinates.</span>
+<span class="sd">    std : array of shape (6,)</span>
+<span class="sd">        Standard deviation of the position of alive particles for each </span>
+<span class="sd">        coordinates.</span>
+<span class="sd">    emit : array of shape (3,)</span>
+<span class="sd">        Bunch emittance for each plane [1]. !!! -&gt; Correct for long ?</span>
+<span class="sd">        </span>
+<span class="sd">    Methods</span>
+<span class="sd">    -------</span>
+<span class="sd">    init_gaussian(cov=None, mean=None, **kwargs)</span>
+<span class="sd">        Initialize bunch particles with 6D gaussian phase space.</span>
+<span class="sd">    plot_phasespace(x_var=&quot;tau&quot;, y_var=&quot;delta&quot;, plot_type=&quot;j&quot;)</span>
+<span class="sd">        Plot phase space.</span>
+<span class="sd">    save(file_name)</span>
+<span class="sd">        Save bunch object data (6D phase space, current, and state) in an HDF5 </span>
+<span class="sd">        file format.</span>
+<span class="sd">    load(file_name)</span>
+<span class="sd">        Load data from a HDF5 file recorded by Bunch save method.</span>
+<span class="sd">    </span>
+<span class="sd">    References</span>
+<span class="sd">    ----------</span>
+<span class="sd">    [1] Wiedemann, H. (2015). Particle accelerator physics. 4th edition. </span>
+<span class="sd">    Springer, Eq.(8.39) of p224.</span>
+<span class="sd">    &quot;&quot;&quot;</span>
+
+    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span>
+                 <span class="n">ring</span><span class="p">,</span>
+                 <span class="n">mp_number</span><span class="o">=</span><span class="mf">1e3</span><span class="p">,</span>
+                 <span class="n">current</span><span class="o">=</span><span class="mf">1e-3</span><span class="p">,</span>
+                 <span class="n">track_alive</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span>
+                 <span class="n">alive</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span>
+                 <span class="n">load_from_file</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+                 <span class="n">load_suffix</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">ring</span> <span class="o">=</span> <span class="n">ring</span>
+        <span class="k">if</span> <span class="ow">not</span> <span class="n">alive</span><span class="p">:</span>
+            <span class="n">mp_number</span> <span class="o">=</span> <span class="mi">1</span>
+            <span class="n">current</span> <span class="o">=</span> <span class="mi">0</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">_mp_number</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">mp_number</span><span class="p">)</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">particles</span> <span class="o">=</span> <span class="p">{</span>
+            <span class="s2">&quot;x&quot;</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">mp_number</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">float64</span><span class="p">),</span>
+            <span class="s2">&quot;xp&quot;</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">mp_number</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">float64</span><span class="p">),</span>
+            <span class="s2">&quot;y&quot;</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">mp_number</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">float64</span><span class="p">),</span>
+            <span class="s2">&quot;yp&quot;</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">mp_number</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">float64</span><span class="p">),</span>
+            <span class="s2">&quot;tau&quot;</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">mp_number</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">float64</span><span class="p">),</span>
+            <span class="s2">&quot;delta&quot;</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">mp_number</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">float64</span><span class="p">),</span>
+        <span class="p">}</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">track_alive</span> <span class="o">=</span> <span class="n">track_alive</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">alive</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">((</span><span class="bp">self</span><span class="o">.</span><span class="n">mp_number</span><span class="p">,</span> <span class="p">),</span> <span class="n">dtype</span><span class="o">=</span><span class="nb">bool</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">current</span> <span class="o">=</span> <span class="n">current</span>
+        <span class="k">if</span> <span class="ow">not</span> <span class="n">alive</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">alive</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="bp">self</span><span class="o">.</span><span class="n">mp_number</span><span class="p">,</span> <span class="p">),</span> <span class="n">dtype</span><span class="o">=</span><span class="nb">bool</span><span class="p">)</span>
+
+        <span class="k">if</span> <span class="n">load_from_file</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">load</span><span class="p">(</span><span class="n">load_from_file</span><span class="p">,</span> <span class="n">load_suffix</span><span class="p">,</span> <span class="n">track_alive</span><span class="p">)</span>
+
+    <span class="k">def</span> <span class="fm">__len__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Return the number of alive particles&quot;&quot;&quot;</span>
+        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">alive</span><span class="o">.</span><span class="n">sum</span><span class="p">()</span>
+
+    <span class="k">def</span> <span class="fm">__getitem__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">label</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Return the columns label for alive particles&quot;&quot;&quot;</span>
+        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">track_alive</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">:</span>
+            <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">particles</span><span class="p">[</span><span class="n">label</span><span class="p">][</span><span class="bp">self</span><span class="o">.</span><span class="n">alive</span><span class="p">]</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">particles</span><span class="p">[</span><span class="n">label</span><span class="p">]</span>
+
+    <span class="k">def</span> <span class="fm">__setitem__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">label</span><span class="p">,</span> <span class="n">value</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Set value to the columns label for alive particles&quot;&quot;&quot;</span>
+        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">track_alive</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">particles</span><span class="p">[</span><span class="n">label</span><span class="p">][</span><span class="bp">self</span><span class="o">.</span><span class="n">alive</span><span class="p">]</span> <span class="o">=</span> <span class="n">value</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">particles</span><span class="p">[</span><span class="n">label</span><span class="p">]</span> <span class="o">=</span> <span class="n">value</span>
+
+    <span class="k">def</span> <span class="fm">__iter__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Iterate over labels&quot;&quot;&quot;</span>
+        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">particles</span><span class="o">.</span><span class="n">keys</span><span class="p">()</span><span class="o">.</span><span class="fm">__iter__</span><span class="p">()</span>
+
+    <span class="k">def</span> <span class="fm">__repr__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Return representation of alive particles&quot;&quot;&quot;</span>
+        <span class="n">rep</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">DataFrame</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="bp">self</span><span class="p">[</span><span class="n">l</span><span class="p">]</span> <span class="k">for</span> <span class="n">l</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="fm">__iter__</span><span class="p">()])</span><span class="o">.</span><span class="n">T</span><span class="p">,</span>
+                           <span class="n">columns</span><span class="o">=</span><span class="nb">list</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="fm">__iter__</span><span class="p">()))</span>
+        <span class="k">return</span> <span class="sa">f</span><span class="s1">&#39;Bunch with macro-particles: </span><span class="se">\n</span><span class="s1"> </span><span class="si">{</span><span class="n">rep</span><span class="si">!r}</span><span class="s1">&#39;</span>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">mp_number</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Macro-particle number&quot;&quot;&quot;</span>
+        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_mp_number</span>
+
+    <span class="nd">@mp_number</span><span class="o">.</span><span class="n">setter</span>
+    <span class="k">def</span> <span class="nf">mp_number</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">value</span><span class="p">):</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">_mp_number</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">value</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="p">,</span> <span class="n">value</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">charge</span><span class="p">)</span>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">charge_per_mp</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Charge per macro-particle [C]&quot;&quot;&quot;</span>
+        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_charge_per_mp</span>
+
+    <span class="nd">@charge_per_mp</span><span class="o">.</span><span class="n">setter</span>
+    <span class="k">def</span> <span class="nf">charge_per_mp</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">value</span><span class="p">):</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">_charge_per_mp</span> <span class="o">=</span> <span class="n">value</span>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">charge</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Bunch charge in [C]&quot;&quot;&quot;</span>
+        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="fm">__len__</span><span class="p">()</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">charge_per_mp</span>
+
+    <span class="nd">@charge</span><span class="o">.</span><span class="n">setter</span>
+    <span class="k">def</span> <span class="nf">charge</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">value</span><span class="p">):</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">charge_per_mp</span> <span class="o">=</span> <span class="n">value</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="fm">__len__</span><span class="p">()</span>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">particle_number</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Particle number&quot;&quot;&quot;</span>
+        <span class="k">return</span> <span class="nb">int</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">charge</span> <span class="o">/</span> <span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">particle</span><span class="o">.</span><span class="n">charge</span><span class="p">))</span>
+
+    <span class="nd">@particle_number</span><span class="o">.</span><span class="n">setter</span>
+    <span class="k">def</span> <span class="nf">particle_number</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">value</span><span class="p">):</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">charge_per_mp</span> <span class="o">=</span> <span class="n">value</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">particle</span><span class="o">.</span><span class="n">charge</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="fm">__len__</span><span class="p">()</span>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">current</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Bunch current [A]&quot;&quot;&quot;</span>
+        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">charge</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">T0</span>
+
+    <span class="nd">@current</span><span class="o">.</span><span class="n">setter</span>
+    <span class="k">def</span> <span class="nf">current</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">value</span><span class="p">):</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">charge_per_mp</span> <span class="o">=</span> <span class="n">value</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">T0</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="fm">__len__</span><span class="p">()</span>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">is_empty</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Return True if the bunch is empty.&quot;&quot;&quot;</span>
+        <span class="k">return</span> <span class="o">~</span><span class="n">np</span><span class="o">.</span><span class="n">any</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">alive</span><span class="p">)</span>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">mean</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Return the mean position of alive particles for each coordinates.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="n">mean</span> <span class="o">=</span> <span class="p">[[</span><span class="bp">self</span><span class="p">[</span><span class="n">name</span><span class="p">]</span><span class="o">.</span><span class="n">mean</span><span class="p">()]</span> <span class="k">for</span> <span class="n">name</span> <span class="ow">in</span> <span class="bp">self</span><span class="p">]</span>
+        <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">squeeze</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">mean</span><span class="p">))</span>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">std</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Return the standard deviation of the position of alive </span>
+<span class="sd">        particles for each coordinates.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="n">std</span> <span class="o">=</span> <span class="p">[[</span><span class="bp">self</span><span class="p">[</span><span class="n">name</span><span class="p">]</span><span class="o">.</span><span class="n">std</span><span class="p">()]</span> <span class="k">for</span> <span class="n">name</span> <span class="ow">in</span> <span class="bp">self</span><span class="p">]</span>
+        <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">squeeze</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">std</span><span class="p">))</span>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">emit</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Return the bunch emittance for each plane.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="n">cor</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">squeeze</span><span class="p">([[</span><span class="bp">self</span><span class="p">[</span><span class="n">name</span><span class="p">]</span> <span class="o">-</span> <span class="bp">self</span><span class="p">[</span><span class="n">name</span><span class="p">]</span><span class="o">.</span><span class="n">mean</span><span class="p">()]</span> <span class="k">for</span> <span class="n">name</span> <span class="ow">in</span> <span class="bp">self</span><span class="p">])</span>
+        <span class="n">emitX</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span>
+            <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">cor</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">cor</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span> <span class="o">-</span>
+            <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">cor</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">cor</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span>
+        <span class="n">emitY</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span>
+            <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">cor</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">cor</span><span class="p">[</span><span class="mi">3</span><span class="p">]</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span> <span class="o">-</span>
+            <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">cor</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="o">*</span> <span class="n">cor</span><span class="p">[</span><span class="mi">3</span><span class="p">])</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span>
+        <span class="n">emitS</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span>
+            <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">cor</span><span class="p">[</span><span class="mi">4</span><span class="p">]</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">cor</span><span class="p">[</span><span class="mi">5</span><span class="p">]</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span> <span class="o">-</span>
+            <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">cor</span><span class="p">[</span><span class="mi">4</span><span class="p">]</span> <span class="o">*</span> <span class="n">cor</span><span class="p">[</span><span class="mi">5</span><span class="p">])</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span>
+        <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="n">emitX</span><span class="p">,</span> <span class="n">emitY</span><span class="p">,</span> <span class="n">emitS</span><span class="p">])</span>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">cs_invariant</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Return the average Courant-Snyder invariant of each plane.</span>
+
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="n">Jx</span> <span class="o">=</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">optics</span><span class="o">.</span><span class="n">local_gamma</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="bp">self</span><span class="p">[</span><span class="s1">&#39;x&#39;</span><span class="p">]</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span> <span class="o">+</span> \
+              <span class="p">(</span><span class="mi">2</span><span class="o">*</span><span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">optics</span><span class="o">.</span><span class="n">local_alpha</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="bp">self</span><span class="p">[</span><span class="s1">&#39;x&#39;</span><span class="p">])</span><span class="o">*</span><span class="bp">self</span><span class="p">[</span><span class="s1">&#39;xp&#39;</span><span class="p">]</span> <span class="o">+</span> \
+              <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">optics</span><span class="o">.</span><span class="n">local_beta</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="bp">self</span><span class="p">[</span><span class="s1">&#39;xp&#39;</span><span class="p">]</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span>
+        <span class="n">Jy</span> <span class="o">=</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">optics</span><span class="o">.</span><span class="n">local_gamma</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="bp">self</span><span class="p">[</span><span class="s1">&#39;y&#39;</span><span class="p">]</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span> <span class="o">+</span> \
+              <span class="p">(</span><span class="mi">2</span><span class="o">*</span><span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">optics</span><span class="o">.</span><span class="n">local_alpha</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="bp">self</span><span class="p">[</span><span class="s1">&#39;y&#39;</span><span class="p">]</span><span class="o">*</span><span class="bp">self</span><span class="p">[</span><span class="s1">&#39;yp&#39;</span><span class="p">])</span> <span class="o">+</span> \
+              <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">optics</span><span class="o">.</span><span class="n">local_beta</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="bp">self</span><span class="p">[</span><span class="s1">&#39;yp&#39;</span><span class="p">]</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span>
+        <span class="n">Js</span> <span class="o">=</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">long_gamma</span> <span class="o">*</span> <span class="bp">self</span><span class="p">[</span><span class="s1">&#39;tau&#39;</span><span class="p">]</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span> <span class="o">+</span> \
+              <span class="p">(</span><span class="mi">2</span><span class="o">*</span><span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">long_alpha</span> <span class="o">*</span> <span class="bp">self</span><span class="p">[</span><span class="s1">&#39;tau&#39;</span><span class="p">]</span><span class="o">*</span><span class="bp">self</span><span class="p">[</span><span class="s1">&#39;delta&#39;</span><span class="p">])</span> <span class="o">+</span> \
+              <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">long_beta</span> <span class="o">*</span> <span class="bp">self</span><span class="p">[</span><span class="s1">&#39;delta&#39;</span><span class="p">]</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span>
+        <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">((</span><span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">Jx</span><span class="p">),</span> <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">Jy</span><span class="p">),</span> <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">Js</span><span class="p">)))</span>
+
+<div class="viewcode-block" id="Bunch.init_gaussian"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.particles.Bunch.init_gaussian">[docs]</a>    <span class="k">def</span> <span class="nf">init_gaussian</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">cov</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">mean</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Initialize bunch particles with 6D gaussian phase space.</span>
+<span class="sd">        Covariance matrix is taken from [1] and dispersion is added following</span>
+<span class="sd">        the method explained in [2].</span>
+<span class="sd">                </span>
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        cov : (6,6) array, optional</span>
+<span class="sd">            Covariance matrix of the bunch distribution</span>
+<span class="sd">        mean : (6,) array, optional</span>
+<span class="sd">            Mean of the bunch distribution</span>
+<span class="sd">        </span>
+<span class="sd">        References</span>
+<span class="sd">        ----------</span>
+<span class="sd">        [1] Wiedemann, H. (2015). Particle accelerator physics. 4th </span>
+<span class="sd">        edition. Springer, Eq.(8.38) of p223.</span>
+<span class="sd">        [2] http://www.pp.rhul.ac.uk/bdsim/manual-develop/dev_beamgeneration.html</span>
+
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="k">if</span> <span class="n">mean</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="n">mean</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="mi">6</span><span class="p">,</span> <span class="p">))</span>
+
+        <span class="k">if</span> <span class="n">cov</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="n">sigma_0</span> <span class="o">=</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s2">&quot;sigma_0&quot;</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">sigma_0</span><span class="p">)</span>
+            <span class="n">sigma_delta</span> <span class="o">=</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s2">&quot;sigma_delta&quot;</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">sigma_delta</span><span class="p">)</span>
+            <span class="n">optics</span> <span class="o">=</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s2">&quot;optics&quot;</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">optics</span><span class="p">)</span>
+
+            <span class="n">cov</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="mi">6</span><span class="p">,</span> <span class="mi">6</span><span class="p">))</span>
+            <span class="n">cov</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">emit</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">optics</span><span class="o">.</span><span class="n">local_beta</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">+</span> <span class="p">(</span>
+                <span class="n">optics</span><span class="o">.</span><span class="n">local_dispersion</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">sigma_delta</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span>
+            <span class="n">cov</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">emit</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">optics</span><span class="o">.</span><span class="n">local_gamma</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">+</span> <span class="p">(</span>
+                <span class="n">optics</span><span class="o">.</span><span class="n">local_dispersion</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">sigma_delta</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span>
+            <span class="n">cov</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="o">-</span><span class="mi">1</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">emit</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">optics</span><span class="o">.</span><span class="n">local_alpha</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">+</span> <span class="p">(</span>
+                <span class="n">optics</span><span class="o">.</span><span class="n">local_dispersion</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">optics</span><span class="o">.</span><span class="n">local_dispersion</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span>
+                <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">sigma_delta</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span>
+            <span class="n">cov</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="o">-</span><span class="mi">1</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">emit</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">optics</span><span class="o">.</span><span class="n">local_alpha</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">+</span> <span class="p">(</span>
+                <span class="n">optics</span><span class="o">.</span><span class="n">local_dispersion</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">optics</span><span class="o">.</span><span class="n">local_dispersion</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span>
+                <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">sigma_delta</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span>
+            <span class="n">cov</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">5</span><span class="p">]</span> <span class="o">=</span> <span class="n">optics</span><span class="o">.</span><span class="n">local_dispersion</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">sigma_delta</span><span class="o">**</span><span class="mi">2</span>
+            <span class="n">cov</span><span class="p">[</span><span class="mi">5</span><span class="p">,</span> <span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">optics</span><span class="o">.</span><span class="n">local_dispersion</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">sigma_delta</span><span class="o">**</span><span class="mi">2</span>
+            <span class="n">cov</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">5</span><span class="p">]</span> <span class="o">=</span> <span class="n">optics</span><span class="o">.</span><span class="n">local_dispersion</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">sigma_delta</span><span class="o">**</span><span class="mi">2</span>
+            <span class="n">cov</span><span class="p">[</span><span class="mi">5</span><span class="p">,</span> <span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="n">optics</span><span class="o">.</span><span class="n">local_dispersion</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">sigma_delta</span><span class="o">**</span><span class="mi">2</span>
+            <span class="n">cov</span><span class="p">[</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">emit</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="n">optics</span><span class="o">.</span><span class="n">local_beta</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">+</span> <span class="p">(</span>
+                <span class="n">optics</span><span class="o">.</span><span class="n">local_dispersion</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">sigma_delta</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span>
+            <span class="n">cov</span><span class="p">[</span><span class="mi">3</span><span class="p">,</span> <span class="mi">3</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">emit</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="n">optics</span><span class="o">.</span><span class="n">local_gamma</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">+</span> <span class="p">(</span>
+                <span class="n">optics</span><span class="o">.</span><span class="n">local_dispersion</span><span class="p">[</span><span class="mi">3</span><span class="p">]</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">sigma_delta</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span>
+            <span class="n">cov</span><span class="p">[</span><span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">]</span> <span class="o">=</span> <span class="o">-</span><span class="mi">1</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">emit</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="n">optics</span><span class="o">.</span><span class="n">local_alpha</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">+</span> <span class="p">(</span>
+                <span class="n">optics</span><span class="o">.</span><span class="n">local_dispersion</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="o">*</span> <span class="n">optics</span><span class="o">.</span><span class="n">local_dispersion</span><span class="p">[</span><span class="mi">3</span><span class="p">]</span> <span class="o">*</span>
+                <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">sigma_delta</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span>
+            <span class="n">cov</span><span class="p">[</span><span class="mi">3</span><span class="p">,</span> <span class="mi">2</span><span class="p">]</span> <span class="o">=</span> <span class="o">-</span><span class="mi">1</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">emit</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="n">optics</span><span class="o">.</span><span class="n">local_alpha</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">+</span> <span class="p">(</span>
+                <span class="n">optics</span><span class="o">.</span><span class="n">local_dispersion</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="o">*</span> <span class="n">optics</span><span class="o">.</span><span class="n">local_dispersion</span><span class="p">[</span><span class="mi">3</span><span class="p">]</span> <span class="o">*</span>
+                <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">sigma_delta</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span>
+            <span class="n">cov</span><span class="p">[</span><span class="mi">2</span><span class="p">,</span> <span class="mi">5</span><span class="p">]</span> <span class="o">=</span> <span class="n">optics</span><span class="o">.</span><span class="n">local_dispersion</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">sigma_delta</span><span class="o">**</span><span class="mi">2</span>
+            <span class="n">cov</span><span class="p">[</span><span class="mi">5</span><span class="p">,</span> <span class="mi">2</span><span class="p">]</span> <span class="o">=</span> <span class="n">optics</span><span class="o">.</span><span class="n">local_dispersion</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">sigma_delta</span><span class="o">**</span><span class="mi">2</span>
+            <span class="n">cov</span><span class="p">[</span><span class="mi">3</span><span class="p">,</span> <span class="mi">5</span><span class="p">]</span> <span class="o">=</span> <span class="n">optics</span><span class="o">.</span><span class="n">local_dispersion</span><span class="p">[</span><span class="mi">3</span><span class="p">]</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">sigma_delta</span><span class="o">**</span><span class="mi">2</span>
+            <span class="n">cov</span><span class="p">[</span><span class="mi">5</span><span class="p">,</span> <span class="mi">3</span><span class="p">]</span> <span class="o">=</span> <span class="n">optics</span><span class="o">.</span><span class="n">local_dispersion</span><span class="p">[</span><span class="mi">3</span><span class="p">]</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">sigma_delta</span><span class="o">**</span><span class="mi">2</span>
+            <span class="n">cov</span><span class="p">[</span><span class="mi">4</span><span class="p">,</span> <span class="mi">4</span><span class="p">]</span> <span class="o">=</span> <span class="n">sigma_0</span><span class="o">**</span><span class="mi">2</span>
+            <span class="n">cov</span><span class="p">[</span><span class="mi">5</span><span class="p">,</span> <span class="mi">5</span><span class="p">]</span> <span class="o">=</span> <span class="n">sigma_delta</span><span class="o">**</span><span class="mi">2</span>
+
+        <span class="n">values</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">multivariate_normal</span><span class="p">(</span><span class="n">mean</span><span class="p">,</span> <span class="n">cov</span><span class="p">,</span> <span class="n">size</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">mp_number</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">particles</span><span class="p">[</span><span class="s2">&quot;x&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="n">values</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">]</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">particles</span><span class="p">[</span><span class="s2">&quot;xp&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="n">values</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">]</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">particles</span><span class="p">[</span><span class="s2">&quot;y&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="n">values</span><span class="p">[:,</span> <span class="mi">2</span><span class="p">]</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">particles</span><span class="p">[</span><span class="s2">&quot;yp&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="n">values</span><span class="p">[:,</span> <span class="mi">3</span><span class="p">]</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">particles</span><span class="p">[</span><span class="s2">&quot;tau&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="n">values</span><span class="p">[:,</span> <span class="mi">4</span><span class="p">]</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">particles</span><span class="p">[</span><span class="s2">&quot;delta&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="n">values</span><span class="p">[:,</span> <span class="mi">5</span><span class="p">]</span></div>
+
+<div class="viewcode-block" id="Bunch.binning"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.particles.Bunch.binning">[docs]</a>    <span class="k">def</span> <span class="nf">binning</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">dimension</span><span class="o">=</span><span class="s2">&quot;tau&quot;</span><span class="p">,</span> <span class="n">n_bin</span><span class="o">=</span><span class="mi">75</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Bin macro-particles.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        dimension : str, optional</span>
+<span class="sd">            Dimension in which the binning is done. The default is &quot;tau&quot;.</span>
+<span class="sd">        n_bin : int, optional</span>
+<span class="sd">            Number of bins. The default is 75.</span>
+
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        bins : array of shape (n_bin,)</span>
+<span class="sd">            Bins where the particles are sorted.</span>
+<span class="sd">        sorted_index : array of shape (self.mp_number,)</span>
+<span class="sd">            Bin number of each macro-particles.</span>
+<span class="sd">        profile : array of shape (n_bin - 1,)</span>
+<span class="sd">            Number of marco-particles in each bin.</span>
+<span class="sd">        center : array of shape (n_bin - 1,)</span>
+<span class="sd">            Center of each bin.</span>
+
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="n">bin_min</span> <span class="o">=</span> <span class="bp">self</span><span class="p">[</span><span class="n">dimension</span><span class="p">]</span><span class="o">.</span><span class="n">min</span><span class="p">()</span>
+        <span class="n">bin_min</span> <span class="o">=</span> <span class="nb">min</span><span class="p">(</span><span class="n">bin_min</span> <span class="o">*</span> <span class="mf">0.99</span><span class="p">,</span> <span class="n">bin_min</span> <span class="o">*</span> <span class="mf">1.01</span><span class="p">)</span>
+        <span class="n">bin_max</span> <span class="o">=</span> <span class="bp">self</span><span class="p">[</span><span class="n">dimension</span><span class="p">]</span><span class="o">.</span><span class="n">max</span><span class="p">()</span>
+        <span class="n">bin_max</span> <span class="o">=</span> <span class="nb">max</span><span class="p">(</span><span class="n">bin_max</span> <span class="o">*</span> <span class="mf">0.99</span><span class="p">,</span> <span class="n">bin_max</span> <span class="o">*</span> <span class="mf">1.01</span><span class="p">)</span>
+
+        <span class="n">bins</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="n">bin_min</span><span class="p">,</span> <span class="n">bin_max</span><span class="p">,</span> <span class="n">n_bin</span><span class="p">)</span>
+        <span class="n">center</span> <span class="o">=</span> <span class="p">(</span><span class="n">bins</span><span class="p">[</span><span class="mi">1</span><span class="p">:]</span> <span class="o">+</span> <span class="n">bins</span><span class="p">[:</span><span class="o">-</span><span class="mi">1</span><span class="p">])</span> <span class="o">/</span> <span class="mi">2</span>
+        <span class="n">sorted_index</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">searchsorted</span><span class="p">(</span><span class="n">bins</span><span class="p">,</span> <span class="bp">self</span><span class="p">[</span><span class="n">dimension</span><span class="p">],</span> <span class="n">side</span><span class="o">=</span><span class="s1">&#39;left&#39;</span><span class="p">)</span>
+        <span class="n">sorted_index</span> <span class="o">-=</span> <span class="mi">1</span>
+        <span class="n">profile</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">bincount</span><span class="p">(</span><span class="n">sorted_index</span><span class="p">,</span> <span class="n">minlength</span><span class="o">=</span><span class="n">n_bin</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
+
+        <span class="k">return</span> <span class="p">(</span><span class="n">bins</span><span class="p">,</span> <span class="n">sorted_index</span><span class="p">,</span> <span class="n">profile</span><span class="p">,</span> <span class="n">center</span><span class="p">)</span></div>
+
+<div class="viewcode-block" id="Bunch.plot_profile"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.particles.Bunch.plot_profile">[docs]</a>    <span class="k">def</span> <span class="nf">plot_profile</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">dimension</span><span class="o">=</span><span class="s2">&quot;tau&quot;</span><span class="p">,</span> <span class="n">n_bin</span><span class="o">=</span><span class="mi">75</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Plot bunch profile.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        dimension : str, optional</span>
+<span class="sd">            Dimension to plot. The default is &quot;tau&quot;.</span>
+<span class="sd">        n_bin : int, optional</span>
+<span class="sd">            Number of bins. The default is 75.</span>
+
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="n">bins</span><span class="p">,</span> <span class="n">sorted_index</span><span class="p">,</span> <span class="n">profile</span><span class="p">,</span> <span class="n">center</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">binning</span><span class="p">(</span><span class="n">dimension</span><span class="p">,</span> <span class="n">n_bin</span><span class="p">)</span>
+        <span class="n">fig</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">()</span>
+        <span class="n">ax</span> <span class="o">=</span> <span class="n">fig</span><span class="o">.</span><span class="n">gca</span><span class="p">()</span>
+        <span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">center</span><span class="p">,</span> <span class="n">profile</span><span class="p">)</span></div>
+
+<div class="viewcode-block" id="Bunch.plot_phasespace"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.particles.Bunch.plot_phasespace">[docs]</a>    <span class="k">def</span> <span class="nf">plot_phasespace</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">x_var</span><span class="o">=</span><span class="s2">&quot;tau&quot;</span><span class="p">,</span> <span class="n">y_var</span><span class="o">=</span><span class="s2">&quot;delta&quot;</span><span class="p">,</span> <span class="n">kind</span><span class="o">=</span><span class="s2">&quot;scatter&quot;</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Plot phase space.</span>
+<span class="sd">        </span>
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        x_var : str </span>
+<span class="sd">            Dimension to plot on horizontal axis.</span>
+<span class="sd">        y_var : str </span>
+<span class="sd">            Dimension to plot on vertical axis.</span>
+<span class="sd">        kind : str, {&quot;scatter&quot;, &quot;kde&quot;, &quot;hist&quot;, &quot;hex&quot;, &quot;reg&quot;, &quot;resid&quot;}</span>
+<span class="sd">            Kind of plot to draw. See seeborn documentation.</span>
+<span class="sd">            The defualt value is &quot;scatter&quot;.</span>
+<span class="sd">            </span>
+<span class="sd">        Return</span>
+<span class="sd">        ------</span>
+<span class="sd">        fig : Figure</span>
+<span class="sd">            Figure object with the plot on it.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+
+        <span class="n">label_dict</span> <span class="o">=</span> <span class="p">{</span>
+            <span class="s2">&quot;x&quot;</span><span class="p">:</span> <span class="s2">&quot;x (mm)&quot;</span><span class="p">,</span>
+            <span class="s2">&quot;xp&quot;</span><span class="p">:</span> <span class="s2">&quot;x&#39; (mrad)&quot;</span><span class="p">,</span>
+            <span class="s2">&quot;y&quot;</span><span class="p">:</span> <span class="s2">&quot;y (mm)&quot;</span><span class="p">,</span>
+            <span class="s2">&quot;yp&quot;</span><span class="p">:</span> <span class="s2">&quot;y&#39; (mrad)&quot;</span><span class="p">,</span>
+            <span class="s2">&quot;tau&quot;</span><span class="p">:</span> <span class="s2">&quot;$</span><span class="se">\\</span><span class="s2">tau$ (ps)&quot;</span><span class="p">,</span>
+            <span class="s2">&quot;delta&quot;</span><span class="p">:</span> <span class="s2">&quot;$</span><span class="se">\\</span><span class="s2">delta$&quot;</span>
+        <span class="p">}</span>
+        <span class="n">scale</span> <span class="o">=</span> <span class="p">{</span>
+            <span class="s2">&quot;x&quot;</span><span class="p">:</span> <span class="mf">1e3</span><span class="p">,</span>
+            <span class="s2">&quot;xp&quot;</span><span class="p">:</span> <span class="mf">1e3</span><span class="p">,</span>
+            <span class="s2">&quot;y&quot;</span><span class="p">:</span> <span class="mf">1e3</span><span class="p">,</span>
+            <span class="s2">&quot;yp&quot;</span><span class="p">:</span> <span class="mf">1e3</span><span class="p">,</span>
+            <span class="s2">&quot;tau&quot;</span><span class="p">:</span> <span class="mf">1e12</span><span class="p">,</span>
+            <span class="s2">&quot;delta&quot;</span><span class="p">:</span> <span class="mi">1</span>
+        <span class="p">}</span>
+
+        <span class="n">fig</span> <span class="o">=</span> <span class="n">sns</span><span class="o">.</span><span class="n">jointplot</span><span class="p">(</span><span class="n">x</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">particles</span><span class="p">[</span><span class="n">x_var</span><span class="p">]</span> <span class="o">*</span> <span class="n">scale</span><span class="p">[</span><span class="n">x_var</span><span class="p">],</span>
+                            <span class="n">y</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">particles</span><span class="p">[</span><span class="n">y_var</span><span class="p">]</span> <span class="o">*</span> <span class="n">scale</span><span class="p">[</span><span class="n">y_var</span><span class="p">],</span>
+                            <span class="n">kind</span><span class="o">=</span><span class="n">kind</span><span class="p">)</span>
+        <span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="n">label_dict</span><span class="p">[</span><span class="n">x_var</span><span class="p">])</span>
+        <span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="n">label_dict</span><span class="p">[</span><span class="n">y_var</span><span class="p">])</span>
+
+        <span class="k">return</span> <span class="n">fig</span></div>
+
+<div class="viewcode-block" id="Bunch.save"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.particles.Bunch.save">[docs]</a>    <span class="k">def</span> <span class="nf">save</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">file_name</span><span class="p">,</span> <span class="n">suffix</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">mpi_comm</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Save bunch object data (6D phase space, current, and state) in an HDF5 </span>
+<span class="sd">        file format.</span>
+<span class="sd">        </span>
+<span class="sd">        The output file is named as &quot;&lt;file_name&gt;.hdf5&quot;.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        file_name : str</span>
+<span class="sd">            Name of the output file.</span>
+<span class="sd">        suffix : str or int, optional</span>
+<span class="sd">            Suffix to the group name used to save the data into the HDF5 file.</span>
+<span class="sd">            If None, it is not used.</span>
+<span class="sd">        mpi_comm : MPI communicator, optional</span>
+<span class="sd">            For internal use if mpi is used in Beam objects.</span>
+<span class="sd">            Default is None.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+
+        <span class="k">if</span> <span class="n">mpi_comm</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="n">f</span> <span class="o">=</span> <span class="n">hp</span><span class="o">.</span><span class="n">File</span><span class="p">(</span><span class="n">file_name</span> <span class="o">+</span> <span class="s2">&quot;.hdf5&quot;</span><span class="p">,</span> <span class="s2">&quot;a&quot;</span><span class="p">,</span> <span class="n">libver</span><span class="o">=</span><span class="s2">&quot;earliest&quot;</span><span class="p">)</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="n">f</span> <span class="o">=</span> <span class="n">hp</span><span class="o">.</span><span class="n">File</span><span class="p">(</span><span class="n">file_name</span> <span class="o">+</span> <span class="s2">&quot;.hdf5&quot;</span><span class="p">,</span>
+                        <span class="s2">&quot;a&quot;</span><span class="p">,</span>
+                        <span class="n">libver</span><span class="o">=</span><span class="s1">&#39;earliest&#39;</span><span class="p">,</span>
+                        <span class="n">driver</span><span class="o">=</span><span class="s1">&#39;mpio&#39;</span><span class="p">,</span>
+                        <span class="n">comm</span><span class="o">=</span><span class="n">mpi_comm</span><span class="p">)</span>
+
+        <span class="k">if</span> <span class="n">suffix</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="n">group_name</span> <span class="o">=</span> <span class="s2">&quot;Bunch&quot;</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="n">group_name</span> <span class="o">=</span> <span class="s2">&quot;Bunch_&quot;</span> <span class="o">+</span> <span class="nb">str</span><span class="p">(</span><span class="n">suffix</span><span class="p">)</span>
+
+        <span class="n">g</span> <span class="o">=</span> <span class="n">f</span><span class="o">.</span><span class="n">create_group</span><span class="p">(</span><span class="n">group_name</span><span class="p">)</span>
+        <span class="n">g</span><span class="o">.</span><span class="n">create_dataset</span><span class="p">(</span><span class="s2">&quot;alive&quot;</span><span class="p">,</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">mp_number</span><span class="p">,</span> <span class="p">),</span> <span class="n">dtype</span><span class="o">=</span><span class="nb">bool</span><span class="p">)</span>
+        <span class="n">g</span><span class="o">.</span><span class="n">create_dataset</span><span class="p">(</span><span class="s2">&quot;phasespace&quot;</span><span class="p">,</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">mp_number</span><span class="p">,</span> <span class="mi">6</span><span class="p">),</span> <span class="n">dtype</span><span class="o">=</span><span class="nb">float</span><span class="p">)</span>
+        <span class="n">g</span><span class="o">.</span><span class="n">create_dataset</span><span class="p">(</span><span class="s2">&quot;current&quot;</span><span class="p">,</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="p">),</span> <span class="n">dtype</span><span class="o">=</span><span class="nb">float</span><span class="p">)</span>
+
+        <span class="n">f</span><span class="p">[</span><span class="n">group_name</span><span class="p">][</span><span class="s2">&quot;alive&quot;</span><span class="p">][:]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">alive</span>
+        <span class="n">f</span><span class="p">[</span><span class="n">group_name</span><span class="p">][</span><span class="s2">&quot;current&quot;</span><span class="p">][:]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">current</span>
+        <span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">dim</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+            <span class="n">f</span><span class="p">[</span><span class="n">group_name</span><span class="p">][</span><span class="s2">&quot;phasespace&quot;</span><span class="p">][:,</span> <span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">particles</span><span class="p">[</span><span class="n">dim</span><span class="p">]</span>
+
+        <span class="n">f</span><span class="o">.</span><span class="n">close</span><span class="p">()</span></div>
+
+<div class="viewcode-block" id="Bunch.load"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.particles.Bunch.load">[docs]</a>    <span class="k">def</span> <span class="nf">load</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">file_name</span><span class="p">,</span> <span class="n">suffix</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">track_alive</span><span class="o">=</span><span class="kc">True</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Load data from a HDF5 file recorded by Bunch save method.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        file_name : str</span>
+<span class="sd">            Path to the HDF5 file where the Bunch data is stored.</span>
+<span class="sd">        suffix : str or int, optional</span>
+<span class="sd">            Suffix to the group name used to load the data from the HDF5 file.</span>
+<span class="sd">            If None, it is not used.</span>
+<span class="sd">        track_alive : bool, optional</span>
+<span class="sd">            If False, the code no longer take into account alive/dead particles.</span>
+<span class="sd">            Should be set to True if element such as apertures are used.</span>
+<span class="sd">            Can be set to False to gain a speed increase.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+
+        <span class="n">f</span> <span class="o">=</span> <span class="n">hp</span><span class="o">.</span><span class="n">File</span><span class="p">(</span><span class="n">file_name</span><span class="p">,</span> <span class="s2">&quot;r&quot;</span><span class="p">)</span>
+
+        <span class="k">if</span> <span class="n">suffix</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="n">group_name</span> <span class="o">=</span> <span class="s2">&quot;Bunch&quot;</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="n">group_name</span> <span class="o">=</span> <span class="s2">&quot;Bunch_&quot;</span> <span class="o">+</span> <span class="nb">str</span><span class="p">(</span><span class="n">suffix</span><span class="p">)</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">mp_number</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">f</span><span class="p">[</span><span class="n">group_name</span><span class="p">][</span><span class="s1">&#39;alive&#39;</span><span class="p">][:])</span>
+
+        <span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">dim</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">particles</span><span class="p">[</span><span class="n">dim</span><span class="p">]</span> <span class="o">=</span> <span class="n">f</span><span class="p">[</span><span class="n">group_name</span><span class="p">][</span><span class="s2">&quot;phasespace&quot;</span><span class="p">][:,</span> <span class="n">i</span><span class="p">]</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">alive</span> <span class="o">=</span> <span class="n">f</span><span class="p">[</span><span class="n">group_name</span><span class="p">][</span><span class="s1">&#39;alive&#39;</span><span class="p">][:]</span>
+        <span class="k">if</span> <span class="n">f</span><span class="p">[</span><span class="n">group_name</span><span class="p">][</span><span class="s1">&#39;current&#39;</span><span class="p">][:][</span><span class="mi">0</span><span class="p">]</span> <span class="o">!=</span> <span class="mi">0</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">current</span> <span class="o">=</span> <span class="n">f</span><span class="p">[</span><span class="n">group_name</span><span class="p">][</span><span class="s1">&#39;current&#39;</span><span class="p">][:][</span><span class="mi">0</span><span class="p">]</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">charge_per_mp</span> <span class="o">=</span> <span class="mi">0</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">track_alive</span> <span class="o">=</span> <span class="n">track_alive</span>
+
+        <span class="n">f</span><span class="o">.</span><span class="n">close</span><span class="p">()</span></div></div>
+
+
+<div class="viewcode-block" id="Beam"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.particles.Beam">[docs]</a><span class="k">class</span> <span class="nc">Beam</span><span class="p">:</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    Define a Beam object composed of several Bunch objects. </span>
+<span class="sd">    </span>
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">    ring : Synchrotron object</span>
+<span class="sd">    bunch_list : list of Bunch object, optional</span>
+
+<span class="sd">    Attributes</span>
+<span class="sd">    ----------</span>
+<span class="sd">    current : float</span>
+<span class="sd">        Total beam current in [A]</span>
+<span class="sd">    charge : float</span>
+<span class="sd">        Total bunch charge in [C]</span>
+<span class="sd">    particle_number : int</span>
+<span class="sd">        Total number of particle in the beam</span>
+<span class="sd">    filling_pattern : bool array of shape (ring.h,)</span>
+<span class="sd">        Filling pattern of the beam</span>
+<span class="sd">    bunch_current : array of shape (ring.h,)</span>
+<span class="sd">        Current in each bunch in [A]</span>
+<span class="sd">    bunch_charge : array of shape (ring.h,)</span>
+<span class="sd">        Charge in each bunch in [C]</span>
+<span class="sd">    bunch_particle : array of shape (ring.h,)</span>
+<span class="sd">        Particle number in each bunch</span>
+<span class="sd">    bunch_mean : array of shape (6, ring.h)</span>
+<span class="sd">        Mean position of alive particles for each bunch</span>
+<span class="sd">    bunch_std : array of shape (6, ring.h)</span>
+<span class="sd">        Standard deviation of the position of alive particles for each bunch        </span>
+<span class="sd">    bunch_emit : array of shape (6, ring.h)</span>
+<span class="sd">        Bunch emittance of alive particles for each bunch</span>
+<span class="sd">    mpi : Mpi object</span>
+<span class="sd">    mpi_switch : bool</span>
+<span class="sd">        Status of MPI parallelisation, should not be changed directly but with</span>
+<span class="sd">        mpi_init() and mpi_close()</span>
+<span class="sd">    bunch_index : array of shape (len(self,))</span>
+<span class="sd">        Return an array with the positions of the non-empty bunches</span>
+<span class="sd">        </span>
+<span class="sd">    Methods</span>
+<span class="sd">    ------</span>
+<span class="sd">    init_beam(filling_pattern, current_per_bunch=1e-3, mp_per_bunch=1e3)</span>
+<span class="sd">        Initialize beam with a given filling pattern and marco-particle number </span>
+<span class="sd">        per bunch. Then initialize the different bunches with a 6D gaussian</span>
+<span class="sd">        phase space.</span>
+<span class="sd">    mpi_init()</span>
+<span class="sd">        Switch on MPI parallelisation and initialise a Mpi object</span>
+<span class="sd">    mpi_gather()</span>
+<span class="sd">        Gather beam, all bunches of the different processors are sent to </span>
+<span class="sd">        all processors. Rather slow</span>
+<span class="sd">    mpi_share_distributions()</span>
+<span class="sd">        Compute the bunch profile and share it between the different bunches.</span>
+<span class="sd">    mpi_close()</span>
+<span class="sd">        Call mpi_gather and switch off MPI parallelisation</span>
+<span class="sd">    plot(var, option=None)</span>
+<span class="sd">        Plot variables with respect to bunch number.</span>
+<span class="sd">    save(file_name)</span>
+<span class="sd">        Save beam object data in an HDF5 file format.</span>
+<span class="sd">    load(file_name, mpi)</span>
+<span class="sd">        Load data from a HDF5 file recorded by Beam save method.</span>
+<span class="sd">    &quot;&quot;&quot;</span>
+
+    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">ring</span><span class="p">,</span> <span class="n">bunch_list</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">ring</span> <span class="o">=</span> <span class="n">ring</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">mpi_switch</span> <span class="o">=</span> <span class="kc">False</span>
+        <span class="k">if</span> <span class="n">bunch_list</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">init_beam</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">h</span><span class="p">,</span> <span class="mi">1</span><span class="p">),</span> <span class="n">dtype</span><span class="o">=</span><span class="nb">bool</span><span class="p">))</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="k">if</span> <span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">bunch_list</span><span class="p">)</span> <span class="o">!=</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">h</span><span class="p">):</span>
+                <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">((</span><span class="s2">&quot;The length of the bunch list is </span><span class="si">{}</span><span class="s2"> &quot;</span><span class="o">.</span><span class="n">format</span><span class="p">(</span>
+                    <span class="nb">len</span><span class="p">(</span><span class="n">bunch_list</span><span class="p">))</span> <span class="o">+</span> <span class="s2">&quot;but should be </span><span class="si">{}</span><span class="s2">&quot;</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">h</span><span class="p">)))</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">bunch_list</span> <span class="o">=</span> <span class="n">bunch_list</span>
+
+    <span class="k">def</span> <span class="fm">__len__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Return the number of (not empty) bunches&quot;&quot;&quot;</span>
+        <span class="n">length</span> <span class="o">=</span> <span class="mi">0</span>
+        <span class="k">for</span> <span class="n">bunch</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">not_empty</span><span class="p">:</span>
+            <span class="n">length</span> <span class="o">+=</span> <span class="mi">1</span>
+        <span class="k">return</span> <span class="n">length</span>
+
+    <span class="k">def</span> <span class="fm">__getitem__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">i</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Return the bunch number i&quot;&quot;&quot;</span>
+        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">bunch_list</span><span class="o">.</span><span class="fm">__getitem__</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>
+
+    <span class="k">def</span> <span class="fm">__setitem__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">i</span><span class="p">,</span> <span class="n">value</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Set value to the bunch number i&quot;&quot;&quot;</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">bunch_list</span><span class="o">.</span><span class="fm">__setitem__</span><span class="p">(</span><span class="n">i</span><span class="p">,</span> <span class="n">value</span><span class="p">)</span>
+
+    <span class="k">def</span> <span class="fm">__iter__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Iterate over all bunches&quot;&quot;&quot;</span>
+        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">bunch_list</span><span class="o">.</span><span class="fm">__iter__</span><span class="p">()</span>
+
+    <span class="k">def</span> <span class="fm">__repr__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Return representation of the beam filling pattern&quot;&quot;&quot;</span>
+        <span class="k">return</span> <span class="sa">f</span><span class="s1">&#39;Beam with bunch current:</span><span class="se">\n</span><span class="s1"> </span><span class="si">{</span><span class="nb">list</span><span class="p">((</span><span class="bp">self</span><span class="o">.</span><span class="n">bunch_current</span><span class="p">))</span><span class="si">!r}</span><span class="s1">&#39;</span>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">not_empty</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Return a generator to iterate over not empty bunches.&quot;&quot;&quot;</span>
+        <span class="k">for</span> <span class="n">index</span><span class="p">,</span> <span class="n">value</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">filling_pattern</span><span class="p">):</span>
+            <span class="k">if</span> <span class="n">value</span> <span class="o">==</span> <span class="kc">True</span><span class="p">:</span>
+                <span class="k">yield</span> <span class="bp">self</span><span class="p">[</span><span class="n">index</span><span class="p">]</span>
+            <span class="k">else</span><span class="p">:</span>
+                <span class="k">pass</span>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">distance_between_bunches</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Return an array which contains the distance to the next bunch in </span>
+<span class="sd">        units of the RF period (ring.T1)&quot;&quot;&quot;</span>
+        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_distance_between_bunches</span>
+
+<div class="viewcode-block" id="Beam.update_distance_between_bunches"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.particles.Beam.update_distance_between_bunches">[docs]</a>    <span class="k">def</span> <span class="nf">update_distance_between_bunches</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Update the distance_between_bunches array&quot;&quot;&quot;</span>
+        <span class="n">filling_pattern</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">filling_pattern</span>
+        <span class="n">distance</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">filling_pattern</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span>
+        <span class="n">last_value</span> <span class="o">=</span> <span class="mi">0</span>
+
+        <span class="c1"># All bunches</span>
+        <span class="k">for</span> <span class="n">index</span><span class="p">,</span> <span class="n">value</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">filling_pattern</span><span class="p">):</span>
+            <span class="k">if</span> <span class="n">value</span> <span class="o">==</span> <span class="kc">False</span><span class="p">:</span>
+                <span class="k">pass</span>
+            <span class="k">elif</span> <span class="n">value</span> <span class="o">==</span> <span class="kc">True</span><span class="p">:</span>
+                <span class="n">last_value</span> <span class="o">=</span> <span class="n">index</span>
+                <span class="n">count</span> <span class="o">=</span> <span class="mi">1</span>
+                <span class="k">for</span> <span class="n">value2</span> <span class="ow">in</span> <span class="n">filling_pattern</span><span class="p">[</span><span class="n">index</span> <span class="o">+</span> <span class="mi">1</span><span class="p">:]:</span>
+                    <span class="k">if</span> <span class="n">value2</span> <span class="o">==</span> <span class="kc">False</span><span class="p">:</span>
+                        <span class="n">count</span> <span class="o">+=</span> <span class="mi">1</span>
+                    <span class="k">elif</span> <span class="n">value2</span> <span class="o">==</span> <span class="kc">True</span><span class="p">:</span>
+                        <span class="k">break</span>
+                <span class="n">distance</span><span class="p">[</span><span class="n">index</span><span class="p">]</span> <span class="o">=</span> <span class="n">count</span>
+
+        <span class="c1"># Last bunch case</span>
+        <span class="n">count2</span> <span class="o">=</span> <span class="mi">0</span>
+        <span class="k">for</span> <span class="n">index2</span><span class="p">,</span> <span class="n">value2</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">filling_pattern</span><span class="p">):</span>
+            <span class="k">if</span> <span class="n">value2</span> <span class="o">==</span> <span class="kc">True</span><span class="p">:</span>
+                <span class="k">break</span>
+            <span class="k">if</span> <span class="n">value2</span> <span class="o">==</span> <span class="kc">False</span><span class="p">:</span>
+                <span class="n">count2</span> <span class="o">+=</span> <span class="mi">1</span>
+        <span class="n">distance</span><span class="p">[</span><span class="n">last_value</span><span class="p">]</span> <span class="o">+=</span> <span class="n">count2</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">_distance_between_bunches</span> <span class="o">=</span> <span class="n">distance</span></div>
+
+<div class="viewcode-block" id="Beam.init_beam"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.particles.Beam.init_beam">[docs]</a>    <span class="k">def</span> <span class="nf">init_beam</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span>
+                  <span class="n">filling_pattern</span><span class="p">,</span>
+                  <span class="n">current_per_bunch</span><span class="o">=</span><span class="mf">1e-3</span><span class="p">,</span>
+                  <span class="n">mp_per_bunch</span><span class="o">=</span><span class="mf">1e3</span><span class="p">,</span>
+                  <span class="n">track_alive</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span>
+                  <span class="n">mpi</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Initialize beam with a given filling pattern and marco-particle number </span>
+<span class="sd">        per bunch. Then initialize the different bunches with a 6D gaussian</span>
+<span class="sd">        phase space.</span>
+<span class="sd">        </span>
+<span class="sd">        If the filling pattern is an array of bool then the current per bunch </span>
+<span class="sd">        is uniform, else the filling pattern can be an array with the current</span>
+<span class="sd">        in each bunch.</span>
+<span class="sd">        </span>
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        filling_pattern : numpy array or list of length ring.h</span>
+<span class="sd">            Filling pattern of the beam, can be a list or an array of bool, </span>
+<span class="sd">            then current_per_bunch is used. Or can be an array with the current</span>
+<span class="sd">            in each bunch.</span>
+<span class="sd">        current_per_bunch : float, optional</span>
+<span class="sd">            Current per bunch in [A]</span>
+<span class="sd">        mp_per_bunch : float, optional</span>
+<span class="sd">            Macro-particle number per bunch</span>
+<span class="sd">        track_alive : bool, optional</span>
+<span class="sd">            If False, the code no longer take into account alive/dead particles.</span>
+<span class="sd">            Should be set to True if element such as apertures are used.</span>
+<span class="sd">            Can be set to False to gain a speed increase.</span>
+<span class="sd">        mpi : bool, optional</span>
+<span class="sd">            If True, only a single bunch is fully initialized on each core, the</span>
+<span class="sd">            other bunches are initialized with a single marco-particle.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+
+        <span class="k">if</span> <span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">filling_pattern</span><span class="p">)</span> <span class="o">!=</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">h</span><span class="p">):</span>
+            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">((</span><span class="s2">&quot;The length of filling pattern is </span><span class="si">{}</span><span class="s2"> &quot;</span><span class="o">.</span><span class="n">format</span><span class="p">(</span>
+                <span class="nb">len</span><span class="p">(</span><span class="n">filling_pattern</span><span class="p">))</span> <span class="o">+</span>
+                              <span class="s2">&quot;but should be </span><span class="si">{}</span><span class="s2">&quot;</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">h</span><span class="p">)))</span>
+
+        <span class="k">if</span> <span class="n">mpi</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">:</span>
+            <span class="n">mp_per_bunch_mpi</span> <span class="o">=</span> <span class="n">mp_per_bunch</span>
+            <span class="n">mp_per_bunch</span> <span class="o">=</span> <span class="mi">1</span>
+
+        <span class="n">filling_pattern</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">filling_pattern</span><span class="p">)</span>
+        <span class="n">bunch_list</span> <span class="o">=</span> <span class="p">[]</span>
+        <span class="k">if</span> <span class="n">filling_pattern</span><span class="o">.</span><span class="n">dtype</span> <span class="o">==</span> <span class="n">np</span><span class="o">.</span><span class="n">dtype</span><span class="p">(</span><span class="s2">&quot;bool&quot;</span><span class="p">):</span>
+            <span class="k">for</span> <span class="n">value</span> <span class="ow">in</span> <span class="n">filling_pattern</span><span class="p">:</span>
+                <span class="k">if</span> <span class="n">value</span> <span class="o">==</span> <span class="kc">True</span><span class="p">:</span>
+                    <span class="n">bunch_list</span><span class="o">.</span><span class="n">append</span><span class="p">(</span>
+                        <span class="n">Bunch</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="p">,</span> <span class="n">mp_per_bunch</span><span class="p">,</span> <span class="n">current_per_bunch</span><span class="p">,</span>
+                              <span class="n">track_alive</span><span class="p">))</span>
+                <span class="k">elif</span> <span class="n">value</span> <span class="o">==</span> <span class="kc">False</span><span class="p">:</span>
+                    <span class="n">bunch_list</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">Bunch</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="p">,</span> <span class="n">alive</span><span class="o">=</span><span class="kc">False</span><span class="p">))</span>
+        <span class="k">elif</span> <span class="n">filling_pattern</span><span class="o">.</span><span class="n">dtype</span> <span class="o">==</span> <span class="n">np</span><span class="o">.</span><span class="n">dtype</span><span class="p">(</span><span class="s2">&quot;float64&quot;</span><span class="p">):</span>
+            <span class="k">for</span> <span class="n">current</span> <span class="ow">in</span> <span class="n">filling_pattern</span><span class="p">:</span>
+                <span class="k">if</span> <span class="n">current</span> <span class="o">!=</span> <span class="mi">0</span><span class="p">:</span>
+                    <span class="n">bunch_list</span><span class="o">.</span><span class="n">append</span><span class="p">(</span>
+                        <span class="n">Bunch</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="p">,</span> <span class="n">mp_per_bunch</span><span class="p">,</span> <span class="n">current</span><span class="p">,</span> <span class="n">track_alive</span><span class="p">))</span>
+                <span class="k">elif</span> <span class="n">current</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
+                    <span class="n">bunch_list</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">Bunch</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="p">,</span> <span class="n">alive</span><span class="o">=</span><span class="kc">False</span><span class="p">))</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s2">&quot;</span><span class="si">{}</span><span class="s2"> should be bool or float64&quot;</span><span class="o">.</span><span class="n">format</span><span class="p">(</span>
+                <span class="n">filling_pattern</span><span class="o">.</span><span class="n">dtype</span><span class="p">))</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">bunch_list</span> <span class="o">=</span> <span class="n">bunch_list</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">update_filling_pattern</span><span class="p">()</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">update_distance_between_bunches</span><span class="p">()</span>
+
+        <span class="k">if</span> <span class="n">mpi</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">mpi_init</span><span class="p">()</span>
+            <span class="n">current</span> <span class="o">=</span> <span class="bp">self</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">mpi</span><span class="o">.</span><span class="n">rank_to_bunch</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">mpi</span><span class="o">.</span><span class="n">rank</span><span class="p">)]</span><span class="o">.</span><span class="n">current</span>
+            <span class="n">bunch</span> <span class="o">=</span> <span class="n">Bunch</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="p">,</span> <span class="n">mp_per_bunch_mpi</span><span class="p">,</span> <span class="n">current</span><span class="p">,</span> <span class="n">track_alive</span><span class="p">)</span>
+            <span class="n">bunch</span><span class="o">.</span><span class="n">init_gaussian</span><span class="p">()</span>
+            <span class="bp">self</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">mpi</span><span class="o">.</span><span class="n">rank_to_bunch</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">mpi</span><span class="o">.</span><span class="n">rank</span><span class="p">)]</span> <span class="o">=</span> <span class="n">bunch</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="k">for</span> <span class="n">bunch</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">not_empty</span><span class="p">:</span>
+                <span class="n">bunch</span><span class="o">.</span><span class="n">init_gaussian</span><span class="p">()</span></div>
+
+<div class="viewcode-block" id="Beam.update_filling_pattern"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.particles.Beam.update_filling_pattern">[docs]</a>    <span class="k">def</span> <span class="nf">update_filling_pattern</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Update the beam filling pattern.&quot;&quot;&quot;</span>
+        <span class="n">filling_pattern</span> <span class="o">=</span> <span class="p">[]</span>
+        <span class="k">for</span> <span class="n">bunch</span> <span class="ow">in</span> <span class="bp">self</span><span class="p">:</span>
+            <span class="k">if</span> <span class="n">bunch</span><span class="o">.</span><span class="n">current</span> <span class="o">!=</span> <span class="mi">0</span><span class="p">:</span>
+                <span class="n">filling_pattern</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="kc">True</span><span class="p">)</span>
+            <span class="k">else</span><span class="p">:</span>
+                <span class="n">filling_pattern</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="kc">False</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">_filling_pattern</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">filling_pattern</span><span class="p">)</span></div>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">filling_pattern</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Return an array with the filling pattern of the beam as bool&quot;&quot;&quot;</span>
+        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_filling_pattern</span>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">bunch_index</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Return an array with the positions of the non-empty bunches.&quot;&quot;&quot;</span>
+        <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">where</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">filling_pattern</span> <span class="o">==</span> <span class="kc">True</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">bunch_current</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Return an array with the current in each bunch in [A]&quot;&quot;&quot;</span>
+        <span class="n">bunch_current</span> <span class="o">=</span> <span class="p">[</span><span class="n">bunch</span><span class="o">.</span><span class="n">current</span> <span class="k">for</span> <span class="n">bunch</span> <span class="ow">in</span> <span class="bp">self</span><span class="p">]</span>
+        <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">bunch_current</span><span class="p">)</span>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">bunch_charge</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Return an array with the charge in each bunch in [C]&quot;&quot;&quot;</span>
+        <span class="n">bunch_charge</span> <span class="o">=</span> <span class="p">[</span><span class="n">bunch</span><span class="o">.</span><span class="n">charge</span> <span class="k">for</span> <span class="n">bunch</span> <span class="ow">in</span> <span class="bp">self</span><span class="p">]</span>
+        <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">bunch_charge</span><span class="p">)</span>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">bunch_particle</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Return an array with the particle number in each bunch&quot;&quot;&quot;</span>
+        <span class="n">bunch_particle</span> <span class="o">=</span> <span class="p">[</span><span class="n">bunch</span><span class="o">.</span><span class="n">particle_number</span> <span class="k">for</span> <span class="n">bunch</span> <span class="ow">in</span> <span class="bp">self</span><span class="p">]</span>
+        <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">bunch_particle</span><span class="p">)</span>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">current</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Total beam current in [A]&quot;&quot;&quot;</span>
+        <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">bunch_current</span><span class="p">)</span>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">charge</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Total beam charge in [C]&quot;&quot;&quot;</span>
+        <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">bunch_charge</span><span class="p">)</span>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">particle_number</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Total number of particles in the beam&quot;&quot;&quot;</span>
+        <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">bunch_particle</span><span class="p">)</span>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">bunch_mean</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Return an array with the mean position of alive particles for each</span>
+<span class="sd">        bunches&quot;&quot;&quot;</span>
+        <span class="n">bunch_mean</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="mi">6</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">h</span><span class="p">))</span>
+        <span class="k">for</span> <span class="n">idx</span><span class="p">,</span> <span class="n">bunch</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">not_empty</span><span class="p">):</span>
+            <span class="n">index</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">bunch_index</span><span class="p">[</span><span class="n">idx</span><span class="p">]</span>
+            <span class="n">bunch_mean</span><span class="p">[:,</span> <span class="n">index</span><span class="p">]</span> <span class="o">=</span> <span class="n">bunch</span><span class="o">.</span><span class="n">mean</span>
+        <span class="k">return</span> <span class="n">bunch_mean</span>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">bunch_std</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Return an array with the standard deviation of the position of alive </span>
+<span class="sd">        particles for each bunches&quot;&quot;&quot;</span>
+        <span class="n">bunch_std</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="mi">6</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">h</span><span class="p">))</span>
+        <span class="k">for</span> <span class="n">idx</span><span class="p">,</span> <span class="n">bunch</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">not_empty</span><span class="p">):</span>
+            <span class="n">index</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">bunch_index</span><span class="p">[</span><span class="n">idx</span><span class="p">]</span>
+            <span class="n">bunch_std</span><span class="p">[:,</span> <span class="n">index</span><span class="p">]</span> <span class="o">=</span> <span class="n">bunch</span><span class="o">.</span><span class="n">std</span>
+        <span class="k">return</span> <span class="n">bunch_std</span>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">bunch_emit</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Return an array with the bunch emittance of alive particles for each</span>
+<span class="sd">        bunches and each plane&quot;&quot;&quot;</span>
+        <span class="n">bunch_emit</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="mi">3</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">h</span><span class="p">))</span>
+        <span class="k">for</span> <span class="n">idx</span><span class="p">,</span> <span class="n">bunch</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">not_empty</span><span class="p">):</span>
+            <span class="n">index</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">bunch_index</span><span class="p">[</span><span class="n">idx</span><span class="p">]</span>
+            <span class="n">bunch_emit</span><span class="p">[:,</span> <span class="n">index</span><span class="p">]</span> <span class="o">=</span> <span class="n">bunch</span><span class="o">.</span><span class="n">emit</span>
+        <span class="k">return</span> <span class="n">bunch_emit</span>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">bunch_cs</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Return an array with the average Courant-Snyder invariant for each </span>
+<span class="sd">        bunch&quot;&quot;&quot;</span>
+        <span class="n">bunch_cs</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="mi">3</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">h</span><span class="p">))</span>
+        <span class="k">for</span> <span class="n">idx</span><span class="p">,</span> <span class="n">bunch</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">not_empty</span><span class="p">):</span>
+            <span class="n">index</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">bunch_index</span><span class="p">[</span><span class="n">idx</span><span class="p">]</span>
+            <span class="n">bunch_cs</span><span class="p">[:,</span> <span class="n">index</span><span class="p">]</span> <span class="o">=</span> <span class="n">bunch</span><span class="o">.</span><span class="n">cs_invariant</span>
+        <span class="k">return</span> <span class="n">bunch_cs</span>
+
+<div class="viewcode-block" id="Beam.mpi_init"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.particles.Beam.mpi_init">[docs]</a>    <span class="k">def</span> <span class="nf">mpi_init</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Switch on MPI parallelisation and initialise a Mpi object&quot;&quot;&quot;</span>
+        <span class="kn">from</span> <span class="nn">mbtrack2.tracking.parallel</span> <span class="kn">import</span> <span class="n">Mpi</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">mpi</span> <span class="o">=</span> <span class="n">Mpi</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">filling_pattern</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">mpi_switch</span> <span class="o">=</span> <span class="kc">True</span></div>
+
+<div class="viewcode-block" id="Beam.mpi_gather"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.particles.Beam.mpi_gather">[docs]</a>    <span class="k">def</span> <span class="nf">mpi_gather</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Gather beam, all bunches of the different processors are sent to </span>
+<span class="sd">        all processors. Rather slow&quot;&quot;&quot;</span>
+
+        <span class="k">if</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">mpi_switch</span> <span class="o">==</span> <span class="kc">False</span><span class="p">):</span>
+            <span class="nb">print</span><span class="p">(</span><span class="s2">&quot;Error, mpi is not initialised.&quot;</span><span class="p">)</span>
+
+        <span class="n">bunch</span> <span class="o">=</span> <span class="bp">self</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">mpi</span><span class="o">.</span><span class="n">bunch_num</span><span class="p">]</span>
+        <span class="n">bunches</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">mpi</span><span class="o">.</span><span class="n">comm</span><span class="o">.</span><span class="n">allgather</span><span class="p">(</span><span class="n">bunch</span><span class="p">)</span>
+        <span class="k">for</span> <span class="n">rank</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">mpi</span><span class="o">.</span><span class="n">size</span><span class="p">):</span>
+            <span class="bp">self</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">mpi</span><span class="o">.</span><span class="n">rank_to_bunch</span><span class="p">(</span><span class="n">rank</span><span class="p">)]</span> <span class="o">=</span> <span class="n">bunches</span><span class="p">[</span><span class="n">rank</span><span class="p">]</span></div>
+
+<div class="viewcode-block" id="Beam.mpi_close"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.particles.Beam.mpi_close">[docs]</a>    <span class="k">def</span> <span class="nf">mpi_close</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Call mpi_gather and switch off MPI parallelisation&quot;&quot;&quot;</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">mpi_gather</span><span class="p">()</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">mpi_switch</span> <span class="o">=</span> <span class="kc">False</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">mpi</span> <span class="o">=</span> <span class="kc">None</span></div>
+
+<div class="viewcode-block" id="Beam.plot"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.particles.Beam.plot">[docs]</a>    <span class="k">def</span> <span class="nf">plot</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">var</span><span class="p">,</span> <span class="n">option</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Plot variables with respect to bunch number.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        var : str {&quot;bunch_current&quot;, &quot;bunch_charge&quot;, &quot;bunch_particle&quot;, </span>
+<span class="sd">                   &quot;bunch_mean&quot;, &quot;bunch_std&quot;, &quot;bunch_emit&quot;}</span>
+<span class="sd">            Variable to be plotted.</span>
+<span class="sd">        option : str, optional</span>
+<span class="sd">            If var is &quot;bunch_mean&quot;, &quot;bunch_std&quot;, or &quot;bunch_emit, option needs </span>
+<span class="sd">            to be specified.</span>
+<span class="sd">            For &quot;bunch_mean&quot; and &quot;bunch_std&quot;, </span>
+<span class="sd">                option = {&quot;x&quot;,&quot;xp&quot;,&quot;y&quot;,&quot;yp&quot;,&quot;tau&quot;,&quot;delta&quot;}.</span>
+<span class="sd">            For &quot;bunch_emit&quot;, option = {&quot;x&quot;,&quot;y&quot;,&quot;s&quot;}.</span>
+<span class="sd">            The default is None.</span>
+<span class="sd">            </span>
+<span class="sd">        Return</span>
+<span class="sd">        ------</span>
+<span class="sd">        fig : Figure</span>
+<span class="sd">            Figure object with the plot on it.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+
+        <span class="n">var_dict</span> <span class="o">=</span> <span class="p">{</span>
+            <span class="s2">&quot;bunch_current&quot;</span><span class="p">:</span> <span class="bp">self</span><span class="o">.</span><span class="n">bunch_current</span><span class="p">,</span>
+            <span class="s2">&quot;bunch_charge&quot;</span><span class="p">:</span> <span class="bp">self</span><span class="o">.</span><span class="n">bunch_charge</span><span class="p">,</span>
+            <span class="s2">&quot;bunch_particle&quot;</span><span class="p">:</span> <span class="bp">self</span><span class="o">.</span><span class="n">bunch_particle</span><span class="p">,</span>
+            <span class="s2">&quot;bunch_mean&quot;</span><span class="p">:</span> <span class="bp">self</span><span class="o">.</span><span class="n">bunch_mean</span><span class="p">,</span>
+            <span class="s2">&quot;bunch_std&quot;</span><span class="p">:</span> <span class="bp">self</span><span class="o">.</span><span class="n">bunch_std</span><span class="p">,</span>
+            <span class="s2">&quot;bunch_emit&quot;</span><span class="p">:</span> <span class="bp">self</span><span class="o">.</span><span class="n">bunch_emit</span>
+        <span class="p">}</span>
+
+        <span class="n">fig</span><span class="p">,</span> <span class="n">ax</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">()</span>
+
+        <span class="k">if</span> <span class="n">var</span> <span class="o">==</span> <span class="s2">&quot;bunch_mean&quot;</span> <span class="ow">or</span> <span class="n">var</span> <span class="o">==</span> <span class="s2">&quot;bunch_std&quot;</span><span class="p">:</span>
+            <span class="n">value_dict</span> <span class="o">=</span> <span class="p">{</span>
+                <span class="s2">&quot;x&quot;</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span>
+                <span class="s2">&quot;xp&quot;</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span>
+                <span class="s2">&quot;y&quot;</span><span class="p">:</span> <span class="mi">2</span><span class="p">,</span>
+                <span class="s2">&quot;yp&quot;</span><span class="p">:</span> <span class="mi">3</span><span class="p">,</span>
+                <span class="s2">&quot;tau&quot;</span><span class="p">:</span> <span class="mi">4</span><span class="p">,</span>
+                <span class="s2">&quot;delta&quot;</span><span class="p">:</span> <span class="mi">5</span>
+            <span class="p">}</span>
+            <span class="n">scale</span> <span class="o">=</span> <span class="p">[</span><span class="mf">1e6</span><span class="p">,</span> <span class="mf">1e6</span><span class="p">,</span> <span class="mf">1e6</span><span class="p">,</span> <span class="mf">1e6</span><span class="p">,</span> <span class="mf">1e12</span><span class="p">,</span> <span class="mi">1</span><span class="p">]</span>
+            <span class="n">label_mean</span> <span class="o">=</span> <span class="p">[</span>
+                <span class="s2">&quot;x (um)&quot;</span><span class="p">,</span> <span class="s2">&quot;x&#39; ($</span><span class="se">\\</span><span class="s2">mu$rad)&quot;</span><span class="p">,</span> <span class="s2">&quot;y (um)&quot;</span><span class="p">,</span> <span class="s2">&quot;y&#39; ($</span><span class="se">\\</span><span class="s2">mu$rad)&quot;</span><span class="p">,</span>
+                <span class="s2">&quot;$</span><span class="se">\\</span><span class="s2">tau$ (ps)&quot;</span><span class="p">,</span> <span class="s2">&quot;$</span><span class="se">\\</span><span class="s2">delta$&quot;</span>
+            <span class="p">]</span>
+            <span class="n">label_std</span> <span class="o">=</span> <span class="p">[</span>
+                <span class="s2">&quot;std x (um)&quot;</span><span class="p">,</span> <span class="s2">&quot;std x&#39; ($</span><span class="se">\\</span><span class="s2">mu$rad)&quot;</span><span class="p">,</span> <span class="s2">&quot;std y (um)&quot;</span><span class="p">,</span>
+                <span class="s2">&quot;std y&#39; ($</span><span class="se">\\</span><span class="s2">mu$rad)&quot;</span><span class="p">,</span> <span class="s2">&quot;std $</span><span class="se">\\</span><span class="s2">tau$ (ps)&quot;</span><span class="p">,</span> <span class="s2">&quot;std $</span><span class="se">\\</span><span class="s2">delta$&quot;</span>
+            <span class="p">]</span>
+
+            <span class="n">y_axis</span> <span class="o">=</span> <span class="n">var_dict</span><span class="p">[</span><span class="n">var</span><span class="p">][</span><span class="n">value_dict</span><span class="p">[</span><span class="n">option</span><span class="p">]]</span>
+
+            <span class="c1"># Convert NaN in y_axis array into zero</span>
+            <span class="n">where_is_nan</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">isnan</span><span class="p">(</span><span class="n">y_axis</span><span class="p">)</span>
+            <span class="n">y_axis</span><span class="p">[</span><span class="n">where_is_nan</span><span class="p">]</span> <span class="o">=</span> <span class="mi">0</span>
+
+            <span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">filling_pattern</span><span class="p">)),</span>
+                    <span class="n">y_axis</span> <span class="o">*</span> <span class="n">scale</span><span class="p">[</span><span class="n">value_dict</span><span class="p">[</span><span class="n">option</span><span class="p">]])</span>
+            <span class="n">ax</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="s1">&#39;bunch number&#39;</span><span class="p">)</span>
+            <span class="k">if</span> <span class="n">var</span> <span class="o">==</span> <span class="s2">&quot;bunch_mean&quot;</span><span class="p">:</span>
+                <span class="n">ax</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="n">label_mean</span><span class="p">[</span><span class="n">value_dict</span><span class="p">[</span><span class="n">option</span><span class="p">]])</span>
+            <span class="k">else</span><span class="p">:</span>
+                <span class="n">ax</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="n">label_std</span><span class="p">[</span><span class="n">value_dict</span><span class="p">[</span><span class="n">option</span><span class="p">]])</span>
+
+        <span class="k">elif</span> <span class="n">var</span> <span class="o">==</span> <span class="s2">&quot;bunch_emit&quot;</span><span class="p">:</span>
+            <span class="n">value_dict</span> <span class="o">=</span> <span class="p">{</span><span class="s2">&quot;x&quot;</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="s2">&quot;y&quot;</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span> <span class="s2">&quot;s&quot;</span><span class="p">:</span> <span class="mi">2</span><span class="p">}</span>
+            <span class="n">scale</span> <span class="o">=</span> <span class="p">[</span><span class="mf">1e9</span><span class="p">,</span> <span class="mf">1e9</span><span class="p">,</span> <span class="mf">1e15</span><span class="p">]</span>
+
+            <span class="n">y_axis</span> <span class="o">=</span> <span class="n">var_dict</span><span class="p">[</span><span class="n">var</span><span class="p">][</span><span class="n">value_dict</span><span class="p">[</span><span class="n">option</span><span class="p">]]</span>
+
+            <span class="c1"># Convert NaN in y_axis array into zero</span>
+            <span class="n">where_is_nan</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">isnan</span><span class="p">(</span><span class="n">y_axis</span><span class="p">)</span>
+            <span class="n">y_axis</span><span class="p">[</span><span class="n">where_is_nan</span><span class="p">]</span> <span class="o">=</span> <span class="mi">0</span>
+
+            <span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">filling_pattern</span><span class="p">)),</span>
+                    <span class="n">y_axis</span> <span class="o">*</span> <span class="n">scale</span><span class="p">[</span><span class="n">value_dict</span><span class="p">[</span><span class="n">option</span><span class="p">]])</span>
+
+            <span class="k">if</span> <span class="n">option</span> <span class="o">==</span> <span class="s2">&quot;x&quot;</span><span class="p">:</span> <span class="n">label_y</span> <span class="o">=</span> <span class="s2">&quot;hor. emittance (nm.rad)&quot;</span>
+            <span class="k">elif</span> <span class="n">option</span> <span class="o">==</span> <span class="s2">&quot;y&quot;</span><span class="p">:</span> <span class="n">label_y</span> <span class="o">=</span> <span class="s2">&quot;ver. emittance (nm.rad)&quot;</span>
+            <span class="k">elif</span> <span class="n">option</span> <span class="o">==</span> <span class="s2">&quot;s&quot;</span><span class="p">:</span> <span class="n">label_y</span> <span class="o">=</span> <span class="s2">&quot;long. emittance (fm.rad)&quot;</span>
+
+            <span class="n">ax</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="s1">&#39;bunch number&#39;</span><span class="p">)</span>
+            <span class="n">ax</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="n">label_y</span><span class="p">)</span>
+
+        <span class="k">elif</span> <span class="n">var</span> <span class="o">==</span> <span class="s2">&quot;bunch_current&quot;</span> <span class="ow">or</span> <span class="n">var</span> <span class="o">==</span> <span class="s2">&quot;bunch_charge&quot;</span> <span class="ow">or</span> <span class="n">var</span> <span class="o">==</span> <span class="s2">&quot;bunch_particle&quot;</span><span class="p">:</span>
+            <span class="n">scale</span> <span class="o">=</span> <span class="p">{</span>
+                <span class="s2">&quot;bunch_current&quot;</span><span class="p">:</span> <span class="mf">1e3</span><span class="p">,</span>
+                <span class="s2">&quot;bunch_charge&quot;</span><span class="p">:</span> <span class="mf">1e9</span><span class="p">,</span>
+                <span class="s2">&quot;bunch_particle&quot;</span><span class="p">:</span> <span class="mi">1</span>
+            <span class="p">}</span>
+
+            <span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">filling_pattern</span><span class="p">)),</span>
+                    <span class="n">var_dict</span><span class="p">[</span><span class="n">var</span><span class="p">]</span> <span class="o">*</span> <span class="n">scale</span><span class="p">[</span><span class="n">var</span><span class="p">])</span>
+            <span class="n">ax</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="s1">&#39;bunch number&#39;</span><span class="p">)</span>
+
+            <span class="k">if</span> <span class="n">var</span> <span class="o">==</span> <span class="s2">&quot;bunch_current&quot;</span><span class="p">:</span> <span class="n">label_y</span> <span class="o">=</span> <span class="s2">&quot;bunch current (mA)&quot;</span>
+            <span class="k">elif</span> <span class="n">var</span> <span class="o">==</span> <span class="s2">&quot;bunch_charge&quot;</span><span class="p">:</span> <span class="n">label_y</span> <span class="o">=</span> <span class="s2">&quot;bunch chagre (nC)&quot;</span>
+            <span class="k">else</span><span class="p">:</span> <span class="n">label_y</span> <span class="o">=</span> <span class="s2">&quot;number of particles&quot;</span>
+
+            <span class="n">ax</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="n">label_y</span><span class="p">)</span>
+
+        <span class="k">elif</span> <span class="n">var</span> <span class="o">==</span> <span class="s2">&quot;current&quot;</span> <span class="ow">or</span> <span class="n">var</span> <span class="o">==</span> <span class="s2">&quot;charge&quot;</span> <span class="ow">or</span> <span class="n">var</span> <span class="o">==</span> <span class="s2">&quot;particle_number&quot;</span><span class="p">:</span>
+            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span>
+                <span class="s2">&quot;&#39;</span><span class="si">{0}</span><span class="s2">&#39;is a total value and cannot be plotted.&quot;</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">var</span><span class="p">))</span>
+
+        <span class="k">return</span> <span class="n">fig</span></div>
+
+<div class="viewcode-block" id="Beam.save"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.particles.Beam.save">[docs]</a>    <span class="k">def</span> <span class="nf">save</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">file_name</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Save beam object data in an HDF5 file format.</span>
+<span class="sd">        </span>
+<span class="sd">        The output file is named as &quot;&lt;file_name&gt;.hdf5&quot;.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        file_name : str</span>
+<span class="sd">            Name of the output file.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">mpi_switch</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">:</span>
+            <span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">bunch</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+                <span class="k">if</span> <span class="n">i</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">mpi</span><span class="o">.</span><span class="n">table</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">]:</span>
+                    <span class="k">if</span> <span class="n">i</span> <span class="o">==</span> <span class="bp">self</span><span class="o">.</span><span class="n">mpi</span><span class="o">.</span><span class="n">bunch_num</span><span class="p">:</span>
+                        <span class="n">mp_number</span> <span class="o">=</span> <span class="bp">self</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">mpi</span><span class="o">.</span><span class="n">bunch_num</span><span class="p">]</span><span class="o">.</span><span class="n">mp_number</span>
+                        <span class="bp">self</span><span class="o">.</span><span class="n">mpi</span><span class="o">.</span><span class="n">comm</span><span class="o">.</span><span class="n">bcast</span><span class="p">(</span><span class="n">mp_number</span><span class="p">,</span> <span class="n">root</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">mpi</span><span class="o">.</span><span class="n">rank</span><span class="p">)</span>
+                        <span class="bp">self</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">mpi</span><span class="o">.</span><span class="n">bunch_num</span><span class="p">]</span><span class="o">.</span><span class="n">save</span><span class="p">(</span><span class="n">file_name</span><span class="p">,</span>
+                                                      <span class="bp">self</span><span class="o">.</span><span class="n">mpi</span><span class="o">.</span><span class="n">bunch_num</span><span class="p">,</span>
+                                                      <span class="bp">self</span><span class="o">.</span><span class="n">mpi</span><span class="o">.</span><span class="n">comm</span><span class="p">)</span>
+                    <span class="k">else</span><span class="p">:</span>
+                        <span class="n">mp_number</span> <span class="o">=</span> <span class="kc">None</span>
+                        <span class="n">mp_number</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">mpi</span><span class="o">.</span><span class="n">comm</span><span class="o">.</span><span class="n">bcast</span><span class="p">(</span>
+                            <span class="n">mp_number</span><span class="p">,</span> <span class="n">root</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">mpi</span><span class="o">.</span><span class="n">bunch_to_rank</span><span class="p">(</span><span class="n">i</span><span class="p">))</span>
+                        <span class="n">f</span> <span class="o">=</span> <span class="n">hp</span><span class="o">.</span><span class="n">File</span><span class="p">(</span><span class="n">file_name</span> <span class="o">+</span> <span class="s2">&quot;.hdf5&quot;</span><span class="p">,</span>
+                                    <span class="s2">&quot;a&quot;</span><span class="p">,</span>
+                                    <span class="n">libver</span><span class="o">=</span><span class="s1">&#39;earliest&#39;</span><span class="p">,</span>
+                                    <span class="n">driver</span><span class="o">=</span><span class="s1">&#39;mpio&#39;</span><span class="p">,</span>
+                                    <span class="n">comm</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">mpi</span><span class="o">.</span><span class="n">comm</span><span class="p">)</span>
+                        <span class="n">group_name</span> <span class="o">=</span> <span class="s2">&quot;Bunch_&quot;</span> <span class="o">+</span> <span class="nb">str</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>
+                        <span class="n">g</span> <span class="o">=</span> <span class="n">f</span><span class="o">.</span><span class="n">create_group</span><span class="p">(</span><span class="n">group_name</span><span class="p">)</span>
+                        <span class="n">g</span><span class="o">.</span><span class="n">create_dataset</span><span class="p">(</span><span class="s2">&quot;alive&quot;</span><span class="p">,</span> <span class="p">(</span><span class="n">mp_number</span><span class="p">,</span> <span class="p">),</span> <span class="n">dtype</span><span class="o">=</span><span class="nb">bool</span><span class="p">)</span>
+                        <span class="n">g</span><span class="o">.</span><span class="n">create_dataset</span><span class="p">(</span><span class="s2">&quot;phasespace&quot;</span><span class="p">,</span> <span class="p">(</span><span class="n">mp_number</span><span class="p">,</span> <span class="mi">6</span><span class="p">),</span>
+                                         <span class="n">dtype</span><span class="o">=</span><span class="nb">float</span><span class="p">)</span>
+                        <span class="n">g</span><span class="o">.</span><span class="n">create_dataset</span><span class="p">(</span><span class="s2">&quot;current&quot;</span><span class="p">,</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="p">),</span> <span class="n">dtype</span><span class="o">=</span><span class="nb">float</span><span class="p">)</span>
+                        <span class="n">f</span><span class="o">.</span><span class="n">close</span><span class="p">()</span>
+                <span class="k">else</span><span class="p">:</span>
+                    <span class="n">bunch</span><span class="o">.</span><span class="n">save</span><span class="p">(</span><span class="n">file_name</span><span class="p">,</span> <span class="n">i</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">mpi</span><span class="o">.</span><span class="n">comm</span><span class="p">)</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">bunch</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+                <span class="n">bunch</span><span class="o">.</span><span class="n">save</span><span class="p">(</span><span class="n">file_name</span><span class="p">,</span> <span class="n">i</span><span class="p">)</span></div>
+
+<div class="viewcode-block" id="Beam.load"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.particles.Beam.load">[docs]</a>    <span class="k">def</span> <span class="nf">load</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">file_name</span><span class="p">,</span> <span class="n">mpi</span><span class="p">,</span> <span class="n">track_alive</span><span class="o">=</span><span class="kc">True</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Load data from a HDF5 file recorded by Beam save method.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        file_name : str</span>
+<span class="sd">            Path to the HDF5 file where the Beam data is stored.</span>
+<span class="sd">        mpi : bool</span>
+<span class="sd">            If True, only a single bunch is fully initialized on each core, the</span>
+<span class="sd">            other bunches are initialized with a single marco-particle.</span>
+<span class="sd">        track_alive : bool, optional</span>
+<span class="sd">            If False, the code no longer take into account alive/dead particles.</span>
+<span class="sd">            Should be set to True if element such as apertures are used.</span>
+<span class="sd">            Can be set to False to gain a speed increase.</span>
+<span class="sd">            The default is True.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="k">if</span> <span class="n">mpi</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="p">)</span>
+            <span class="n">f</span> <span class="o">=</span> <span class="n">hp</span><span class="o">.</span><span class="n">File</span><span class="p">(</span><span class="n">file_name</span><span class="p">,</span> <span class="s2">&quot;r&quot;</span><span class="p">)</span>
+            <span class="n">filling_pattern</span> <span class="o">=</span> <span class="p">[]</span>
+            <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">h</span><span class="p">):</span>
+                <span class="n">current</span> <span class="o">=</span> <span class="n">f</span><span class="p">[</span><span class="s2">&quot;Bunch_&quot;</span> <span class="o">+</span> <span class="nb">str</span><span class="p">(</span><span class="n">i</span><span class="p">)][</span><span class="s1">&#39;current&#39;</span><span class="p">][:][</span><span class="mi">0</span><span class="p">]</span>
+                <span class="n">filling_pattern</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">current</span><span class="p">)</span>
+
+            <span class="bp">self</span><span class="o">.</span><span class="n">init_beam</span><span class="p">(</span><span class="n">filling_pattern</span><span class="p">,</span>
+                           <span class="n">mp_per_bunch</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span>
+                           <span class="n">track_alive</span><span class="o">=</span><span class="n">track_alive</span><span class="p">,</span>
+                           <span class="n">mpi</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
+            <span class="bp">self</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">mpi</span><span class="o">.</span><span class="n">bunch_num</span><span class="p">]</span><span class="o">.</span><span class="n">load</span><span class="p">(</span><span class="n">file_name</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">mpi</span><span class="o">.</span><span class="n">bunch_num</span><span class="p">)</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">bunch</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+                <span class="n">bunch</span><span class="o">.</span><span class="n">load</span><span class="p">(</span><span class="n">file_name</span><span class="p">,</span> <span class="n">i</span><span class="p">,</span> <span class="n">track_alive</span><span class="p">)</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">update_filling_pattern</span><span class="p">()</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">update_distance_between_bunches</span><span class="p">()</span></div></div>
+</pre></div>
+
+            <div class="clearer"></div>
+          </div>
+        </div>
+      </div>
+      <div class="sphinxsidebar" role="navigation" aria-label="main navigation">
+        <div class="sphinxsidebarwrapper">
+<div id="searchbox" style="display: none" role="search">
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+    </form>
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+<script>document.getElementById('searchbox').style.display = "block"</script>
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+    <div class="related" role="navigation" aria-label="related navigation">
+      <h3>Navigation</h3>
+      <ul>
+        <li class="right" style="margin-right: 10px">
+          <a href="../../../genindex.html" title="General Index"
+             >index</a></li>
+        <li class="right" >
+          <a href="../../../py-modindex.html" title="Python Module Index"
+             >modules</a> |</li>
+        <li class="nav-item nav-item-0"><a href="../../../index.html">mbtrack2 0.6.0 documentation</a> &#187;</li>
+          <li class="nav-item nav-item-1"><a href="../../index.html" >Module code</a> &#187;</li>
+        <li class="nav-item nav-item-this"><a href="">mbtrack2.tracking.particles</a></li> 
+      </ul>
+    </div>
+    <div class="footer" role="contentinfo">
+        &#169; Copyright 2024, A. Gamelin et al.
+      Created using <a href="https://www.sphinx-doc.org/">Sphinx</a> 5.0.2.
+    </div>
+  </body>
+</html>
\ No newline at end of file
diff --git a/docs/build/html/_modules/mbtrack2/tracking/rf.html b/docs/build/html/_modules/mbtrack2/tracking/rf.html
new file mode 100644
index 0000000..f341313
--- /dev/null
+++ b/docs/build/html/_modules/mbtrack2/tracking/rf.html
@@ -0,0 +1,1889 @@
+
+<!DOCTYPE html>
+
+<html lang="en">
+  <head>
+    <meta charset="utf-8" />
+    <meta name="viewport" content="width=device-width, initial-scale=1.0" />
+    <title>mbtrack2.tracking.rf &#8212; mbtrack2 0.6.0 documentation</title>
+    <link rel="stylesheet" type="text/css" href="../../../_static/pygments.css" />
+    <link rel="stylesheet" type="text/css" href="../../../_static/nature.css" />
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+    <script src="../../../_static/jquery.js"></script>
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+    <link rel="index" title="Index" href="../../../genindex.html" />
+    <link rel="search" title="Search" href="../../../search.html" /> 
+  </head><body>
+    <div class="related" role="navigation" aria-label="related navigation">
+      <h3>Navigation</h3>
+      <ul>
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+          <a href="../../../genindex.html" title="General Index"
+             accesskey="I">index</a></li>
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+          <a href="../../../py-modindex.html" title="Python Module Index"
+             >modules</a> |</li>
+        <li class="nav-item nav-item-0"><a href="../../../index.html">mbtrack2 0.6.0 documentation</a> &#187;</li>
+          <li class="nav-item nav-item-1"><a href="../../index.html" accesskey="U">Module code</a> &#187;</li>
+        <li class="nav-item nav-item-this"><a href="">mbtrack2.tracking.rf</a></li> 
+      </ul>
+    </div>  
+
+    <div class="document">
+      <div class="documentwrapper">
+        <div class="bodywrapper">
+          <div class="body" role="main">
+            
+  <h1>Source code for mbtrack2.tracking.rf</h1><div class="highlight"><pre>
+<span></span><span class="c1"># -*- coding: utf-8 -*-</span>
+<span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">This module handles radio-frequency (RF) cavitiy elements. </span>
+<span class="sd">&quot;&quot;&quot;</span>
+
+<span class="kn">import</span> <span class="nn">matplotlib.patches</span> <span class="k">as</span> <span class="nn">mpatches</span>
+<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
+<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="kn">from</span> <span class="nn">matplotlib.legend_handler</span> <span class="kn">import</span> <span class="n">HandlerPatch</span>
+
+<span class="kn">from</span> <span class="nn">mbtrack2.instability</span> <span class="kn">import</span> <span class="n">lcbi_growth_rate</span>
+<span class="kn">from</span> <span class="nn">mbtrack2.tracking.element</span> <span class="kn">import</span> <span class="n">Element</span>
+
+
+<div class="viewcode-block" id="RFCavity"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.rf.RFCavity">[docs]</a><span class="k">class</span> <span class="nc">RFCavity</span><span class="p">(</span><span class="n">Element</span><span class="p">):</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    Perfect RF cavity class for main and harmonic RF cavities.</span>
+<span class="sd">    Use cosine definition.</span>
+<span class="sd">    </span>
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">    ring : Synchrotron object</span>
+<span class="sd">    m : int</span>
+<span class="sd">        Harmonic number of the cavity</span>
+<span class="sd">    Vc : float</span>
+<span class="sd">        Amplitude of cavity voltage [V]</span>
+<span class="sd">    theta : float</span>
+<span class="sd">        Phase of Cavity voltage</span>
+<span class="sd">    &quot;&quot;&quot;</span>
+
+    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">ring</span><span class="p">,</span> <span class="n">m</span><span class="p">,</span> <span class="n">Vc</span><span class="p">,</span> <span class="n">theta</span><span class="p">):</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">ring</span> <span class="o">=</span> <span class="n">ring</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">m</span> <span class="o">=</span> <span class="n">m</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">Vc</span> <span class="o">=</span> <span class="n">Vc</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">theta</span> <span class="o">=</span> <span class="n">theta</span>
+
+<div class="viewcode-block" id="RFCavity.track"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.rf.RFCavity.track">[docs]</a>    <span class="nd">@Element</span><span class="o">.</span><span class="n">parallel</span>
+    <span class="k">def</span> <span class="nf">track</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">bunch</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Tracking method for the element.</span>
+<span class="sd">        No bunch to bunch interaction, so written for Bunch objects and</span>
+<span class="sd">        @Element.parallel is used to handle Beam objects.</span>
+<span class="sd">        </span>
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        bunch : Bunch or Beam object</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="n">bunch</span><span class="p">[</span><span class="s2">&quot;delta&quot;</span><span class="p">]</span> <span class="o">+=</span> <span class="bp">self</span><span class="o">.</span><span class="n">Vc</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">E0</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">m</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">omega1</span> <span class="o">*</span> <span class="n">bunch</span><span class="p">[</span><span class="s2">&quot;tau&quot;</span><span class="p">]</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">theta</span><span class="p">)</span></div>
+
+<div class="viewcode-block" id="RFCavity.value"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.rf.RFCavity.value">[docs]</a>    <span class="k">def</span> <span class="nf">value</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">val</span><span class="p">):</span>
+        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">Vc</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">E0</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">m</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">omega1</span> <span class="o">*</span>
+                                               <span class="n">val</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">theta</span><span class="p">)</span></div></div>
+
+
+<div class="viewcode-block" id="CavityResonator"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.rf.CavityResonator">[docs]</a><span class="k">class</span> <span class="nc">CavityResonator</span><span class="p">():</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;Cavity resonator class for active or passive RF cavity with beam</span>
+<span class="sd">    loading or HOM, based on [1,2].</span>
+<span class="sd">    </span>
+<span class="sd">    Use cosine definition.</span>
+<span class="sd">    </span>
+<span class="sd">    If used with mpi, beam.mpi.share_distributions must be called before the </span>
+<span class="sd">    track method call.</span>
+<span class="sd">    </span>
+<span class="sd">    Different kind of RF feeback and loops can be added using:</span>
+<span class="sd">        cavity_resonator.feedback.append(loop)</span>
+<span class="sd">    </span>
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">    ring : Synchrotron object</span>
+<span class="sd">    m : int or float</span>
+<span class="sd">        Harmonic number of the cavity.</span>
+<span class="sd">    Rs : float</span>
+<span class="sd">        Shunt impedance of the cavities in [Ohm], defined as 0.5*Vc*Vc/Pc.</span>
+<span class="sd">        If Ncav = 1, used for the total shunt impedance.</span>
+<span class="sd">        If Ncav &gt; 1, used for the shunt impedance per cavity.</span>
+<span class="sd">    Q : float</span>
+<span class="sd">        Quality factor of the cavity.</span>
+<span class="sd">    QL : float</span>
+<span class="sd">        Loaded quality factor of the cavity.</span>
+<span class="sd">    detune : float</span>
+<span class="sd">        Detuing of the cavity in [Hz], defined as (fr - m*ring.f1).</span>
+<span class="sd">    Ncav : int, optional</span>
+<span class="sd">        Number of cavities.</span>
+<span class="sd">    Vc : float, optinal</span>
+<span class="sd">        Total cavity voltage objective value in [V].</span>
+<span class="sd">    theta : float, optional</span>
+<span class="sd">        Total cavity phase objective value in [rad].</span>
+<span class="sd">    n_bin : int, optional</span>
+<span class="sd">        Number of bins used for the beam loading computation. </span>
+<span class="sd">        Only used if MPI is not used, otherwise n_bin must be specified in the </span>
+<span class="sd">        beam.mpi.share_distributions method.</span>
+<span class="sd">        The default is 75.</span>
+<span class="sd">        </span>
+<span class="sd">    Attributes</span>
+<span class="sd">    ----------</span>
+<span class="sd">    beam_phasor : complex</span>
+<span class="sd">        Beam phasor in [V].</span>
+<span class="sd">    beam_phasor_record : array of complex</span>
+<span class="sd">        Last beam phasor value of each bunch in [V].</span>
+<span class="sd">    generator_phasor : complex</span>
+<span class="sd">        Generator phasor in [V].</span>
+<span class="sd">    generator_phasor_record : array of complex</span>
+<span class="sd">        Last generator phasor value of each bunch in [V].</span>
+<span class="sd">    cavity_phasor : complex</span>
+<span class="sd">        Cavity phasor in [V].</span>
+<span class="sd">    cavity_phasor_record : array of complex</span>
+<span class="sd">        Last cavity phasor value of each bunch in [V].</span>
+<span class="sd">    ig_phasor_record : array of complex</span>
+<span class="sd">        Last current generator phasor of each bunch in [A].</span>
+<span class="sd">        Only used for some feedback types.</span>
+<span class="sd">    cavity_voltage : float</span>
+<span class="sd">        Cavity total voltage in [V].</span>
+<span class="sd">    cavity_phase : float</span>
+<span class="sd">        Cavity total phase in [rad].</span>
+<span class="sd">    loss_factor : float</span>
+<span class="sd">        Cavity loss factor in [V/C].</span>
+<span class="sd">    Rs_per_cavity : float</span>
+<span class="sd">        Shunt impedance of a single cavity in [Ohm], defined as 0.5*Vc*Vc/Pc.</span>
+<span class="sd">    beta : float</span>
+<span class="sd">        Coupling coefficient of the cavity.</span>
+<span class="sd">    fr : float</span>
+<span class="sd">        Resonance frequency of the cavity in [Hz].</span>
+<span class="sd">    wr : float</span>
+<span class="sd">        Angular resonance frequency in [Hz.rad].</span>
+<span class="sd">    psi : float</span>
+<span class="sd">        Tuning angle in [rad].</span>
+<span class="sd">    filling_time : float</span>
+<span class="sd">        Cavity filling time in [s].</span>
+<span class="sd">    Pc : float</span>
+<span class="sd">        Power dissipated in the cavity walls in [W].</span>
+<span class="sd">    Pg : float</span>
+<span class="sd">        Generator power in [W].</span>
+<span class="sd">    Vgr : float</span>
+<span class="sd">        Generator voltage at resonance in [V].</span>
+<span class="sd">    theta_gr : float</span>
+<span class="sd">        Generator phase at resonance in [rad].</span>
+<span class="sd">    Vg : float</span>
+<span class="sd">        Generator voltage in [V].</span>
+<span class="sd">    theta_g : float</span>
+<span class="sd">        Generator phase in [rad].</span>
+<span class="sd">    tracking : bool</span>
+<span class="sd">        True if the tracking has been initialized.</span>
+<span class="sd">    bunch_index : int</span>
+<span class="sd">        Number of the tracked bunch in the current core.</span>
+<span class="sd">    distance : array</span>
+<span class="sd">        Distance between bunches.</span>
+<span class="sd">    valid_bunch_index : array</span>
+<span class="sd">    </span>
+<span class="sd">    Methods</span>
+<span class="sd">    -------</span>
+<span class="sd">    Vbr(I0)</span>
+<span class="sd">        Return beam voltage at resonance in [V].</span>
+<span class="sd">    Vb(I0)</span>
+<span class="sd">        Return beam voltage in [V].</span>
+<span class="sd">    Pb(I0)</span>
+<span class="sd">        Return power transmitted to the beam in [W].</span>
+<span class="sd">    Pr(I0)</span>
+<span class="sd">        Return power reflected back to the generator in [W].</span>
+<span class="sd">    Z(f)</span>
+<span class="sd">        Cavity impedance in [Ohm] for a given frequency f in [Hz].</span>
+<span class="sd">    set_optimal_coupling(I0)</span>
+<span class="sd">        Set coupling to optimal value.</span>
+<span class="sd">    set_optimal_detune(I0)</span>
+<span class="sd">        Set detuning to optimal conditions.</span>
+<span class="sd">    set_generator(I0)</span>
+<span class="sd">        Set generator parameters.</span>
+<span class="sd">    plot_phasor(I0)</span>
+<span class="sd">        Plot phasor diagram.</span>
+<span class="sd">    is_DC_Robinson_stable(I0)</span>
+<span class="sd">        Check DC Robinson stability.</span>
+<span class="sd">    plot_DC_Robinson_stability()</span>
+<span class="sd">        Plot DC Robinson stability limit.</span>
+<span class="sd">    init_tracking(beam)</span>
+<span class="sd">        Initialization of the tracking.</span>
+<span class="sd">    track(beam)</span>
+<span class="sd">        Tracking method.</span>
+<span class="sd">    phasor_decay(time)</span>
+<span class="sd">        Compute the beam phasor decay during a given time span.</span>
+<span class="sd">    phasor_evol(profile, bin_length, charge_per_mp)</span>
+<span class="sd">        Compute the beam phasor evolution during the crossing of a bunch.</span>
+<span class="sd">    VRF(z, I0)</span>
+<span class="sd">        Return the total RF voltage.</span>
+<span class="sd">    dVRF(z, I0)</span>
+<span class="sd">        Return derivative of total RF voltage.</span>
+<span class="sd">    ddVRF(z, I0)</span>
+<span class="sd">        Return the second derivative of total RF voltage.</span>
+<span class="sd">    deltaVRF(z, I0)</span>
+<span class="sd">        Return the generator voltage minus beam loading voltage.</span>
+<span class="sd">    update_feedback()</span>
+<span class="sd">        Force feedback update from current CavityResonator parameters.</span>
+<span class="sd">    sample_voltage()</span>
+<span class="sd">        Sample the voltage seen by a zero charge particle during an RF period.</span>
+<span class="sd">    </span>
+<span class="sd">    References</span>
+<span class="sd">    ----------</span>
+<span class="sd">    [1] Wilson, P. B. (1994). Fundamental-mode rf design in e+ e− storage ring </span>
+<span class="sd">    factories. In Frontiers of Particle Beams: Factories with e+ e-Rings </span>
+<span class="sd">    (pp. 293-311). Springer, Berlin, Heidelberg.</span>
+<span class="sd">    </span>
+<span class="sd">    [2] Naoto Yamamoto, Alexis Gamelin, and Ryutaro Nagaoka. &quot;Investigation </span>
+<span class="sd">    of Longitudinal Beam Dynamics With Harmonic Cavities by Using the Code </span>
+<span class="sd">    Mbtrack.&quot; IPAC’19, Melbourne, Australia, 2019.</span>
+<span class="sd">    &quot;&quot;&quot;</span>
+
+    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span>
+                 <span class="n">ring</span><span class="p">,</span>
+                 <span class="n">m</span><span class="p">,</span>
+                 <span class="n">Rs</span><span class="p">,</span>
+                 <span class="n">Q</span><span class="p">,</span>
+                 <span class="n">QL</span><span class="p">,</span>
+                 <span class="n">detune</span><span class="p">,</span>
+                 <span class="n">Ncav</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span>
+                 <span class="n">Vc</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span>
+                 <span class="n">theta</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span>
+                 <span class="n">n_bin</span><span class="o">=</span><span class="mi">75</span><span class="p">):</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">ring</span> <span class="o">=</span> <span class="n">ring</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">feedback</span> <span class="o">=</span> <span class="p">[]</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">m</span> <span class="o">=</span> <span class="n">m</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">Ncav</span> <span class="o">=</span> <span class="n">Ncav</span>
+        <span class="k">if</span> <span class="n">Ncav</span> <span class="o">!=</span> <span class="mi">1</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">Rs_per_cavity</span> <span class="o">=</span> <span class="n">Rs</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">Rs</span> <span class="o">=</span> <span class="n">Rs</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">Q</span> <span class="o">=</span> <span class="n">Q</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">QL</span> <span class="o">=</span> <span class="n">QL</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">detune</span> <span class="o">=</span> <span class="n">detune</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">Vc</span> <span class="o">=</span> <span class="n">Vc</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">theta</span> <span class="o">=</span> <span class="n">theta</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">beam_phasor</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="nb">complex</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">beam_phasor_record</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">h</span><span class="p">),</span> <span class="n">dtype</span><span class="o">=</span><span class="nb">complex</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">generator_phasor_record</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">h</span><span class="p">),</span> <span class="n">dtype</span><span class="o">=</span><span class="nb">complex</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">tracking</span> <span class="o">=</span> <span class="kc">False</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">Vg</span> <span class="o">=</span> <span class="mi">0</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">theta_g</span> <span class="o">=</span> <span class="mi">0</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">Vgr</span> <span class="o">=</span> <span class="mi">0</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">theta_gr</span> <span class="o">=</span> <span class="mi">0</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">Pg</span> <span class="o">=</span> <span class="mi">0</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">n_bin</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">n_bin</span><span class="p">)</span>
+
+<div class="viewcode-block" id="CavityResonator.init_tracking"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.rf.CavityResonator.init_tracking">[docs]</a>    <span class="k">def</span> <span class="nf">init_tracking</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">beam</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Initialization of the tracking.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        beam : Beam object</span>
+
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="k">if</span> <span class="n">beam</span><span class="o">.</span><span class="n">mpi_switch</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">bunch_index</span> <span class="o">=</span> <span class="n">beam</span><span class="o">.</span><span class="n">mpi</span><span class="o">.</span><span class="n">bunch_num</span>  <span class="c1"># Number of the tracked bunch in this processor</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">distance</span> <span class="o">=</span> <span class="n">beam</span><span class="o">.</span><span class="n">distance_between_bunches</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">valid_bunch_index</span> <span class="o">=</span> <span class="n">beam</span><span class="o">.</span><span class="n">bunch_index</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">tracking</span> <span class="o">=</span> <span class="kc">True</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">nturn</span> <span class="o">=</span> <span class="mi">0</span></div>
+
+<div class="viewcode-block" id="CavityResonator.track"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.rf.CavityResonator.track">[docs]</a>    <span class="k">def</span> <span class="nf">track</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">beam</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Track a Beam object through the CavityResonator object.</span>
+<span class="sd">        </span>
+<span class="sd">        Can be used with or without mpi.</span>
+<span class="sd">        If used with mpi, beam.mpi.share_distributions must be called before.</span>
+<span class="sd">        </span>
+<span class="sd">        The beam phasor is given at t=0 (synchronous particle) of the first </span>
+<span class="sd">        non empty bunch.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        beam : Beam object</span>
+
+<span class="sd">        &quot;&quot;&quot;</span>
+
+        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">tracking</span> <span class="ow">is</span> <span class="kc">False</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">init_tracking</span><span class="p">(</span><span class="n">beam</span><span class="p">)</span>
+
+        <span class="k">for</span> <span class="n">index</span><span class="p">,</span> <span class="n">bunch</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">beam</span><span class="p">):</span>
+
+            <span class="k">if</span> <span class="n">beam</span><span class="o">.</span><span class="n">filling_pattern</span><span class="p">[</span><span class="n">index</span><span class="p">]:</span>
+
+                <span class="k">if</span> <span class="n">beam</span><span class="o">.</span><span class="n">mpi_switch</span><span class="p">:</span>
+                    <span class="c1"># get rank of bunch n° index</span>
+                    <span class="n">rank</span> <span class="o">=</span> <span class="n">beam</span><span class="o">.</span><span class="n">mpi</span><span class="o">.</span><span class="n">bunch_to_rank</span><span class="p">(</span><span class="n">index</span><span class="p">)</span>
+                    <span class="c1"># mpi -&gt; get shared bunch profile for current bunch</span>
+                    <span class="n">center</span> <span class="o">=</span> <span class="n">beam</span><span class="o">.</span><span class="n">mpi</span><span class="o">.</span><span class="n">tau_center</span><span class="p">[</span><span class="n">rank</span><span class="p">]</span>
+                    <span class="n">profile</span> <span class="o">=</span> <span class="n">beam</span><span class="o">.</span><span class="n">mpi</span><span class="o">.</span><span class="n">tau_profile</span><span class="p">[</span><span class="n">rank</span><span class="p">]</span>
+                    <span class="n">bin_length</span> <span class="o">=</span> <span class="n">center</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="n">center</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
+                    <span class="n">charge_per_mp</span> <span class="o">=</span> <span class="n">beam</span><span class="o">.</span><span class="n">mpi</span><span class="o">.</span><span class="n">charge_per_mp_all</span><span class="p">[</span><span class="n">rank</span><span class="p">]</span>
+                    <span class="k">if</span> <span class="n">index</span> <span class="o">==</span> <span class="bp">self</span><span class="o">.</span><span class="n">bunch_index</span><span class="p">:</span>
+                        <span class="n">sorted_index</span> <span class="o">=</span> <span class="n">beam</span><span class="o">.</span><span class="n">mpi</span><span class="o">.</span><span class="n">tau_sorted_index</span>
+                <span class="k">else</span><span class="p">:</span>
+                    <span class="c1"># no mpi -&gt; get bunch profile for current bunch</span>
+                    <span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">bunch</span><span class="p">)</span> <span class="o">!=</span> <span class="mi">0</span><span class="p">:</span>
+                        <span class="p">(</span><span class="n">bins</span><span class="p">,</span> <span class="n">sorted_index</span><span class="p">,</span> <span class="n">profile</span><span class="p">,</span>
+                         <span class="n">center</span><span class="p">)</span> <span class="o">=</span> <span class="n">bunch</span><span class="o">.</span><span class="n">binning</span><span class="p">(</span><span class="n">n_bin</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">n_bin</span><span class="p">)</span>
+                        <span class="n">bin_length</span> <span class="o">=</span> <span class="n">center</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="n">center</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
+                        <span class="n">charge_per_mp</span> <span class="o">=</span> <span class="n">bunch</span><span class="o">.</span><span class="n">charge_per_mp</span>
+                        <span class="bp">self</span><span class="o">.</span><span class="n">bunch_index</span> <span class="o">=</span> <span class="n">index</span>
+                    <span class="k">else</span><span class="p">:</span>
+                        <span class="c1"># Update filling pattern</span>
+                        <span class="n">beam</span><span class="o">.</span><span class="n">update_filling_pattern</span><span class="p">()</span>
+                        <span class="n">beam</span><span class="o">.</span><span class="n">update_distance_between_bunches</span><span class="p">()</span>
+                        <span class="c1"># save beam phasor value</span>
+                        <span class="bp">self</span><span class="o">.</span><span class="n">beam_phasor_record</span><span class="p">[</span><span class="n">index</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">beam_phasor</span>
+                        <span class="c1"># phasor decay to be at t=0 of the next bunch</span>
+                        <span class="bp">self</span><span class="o">.</span><span class="n">phasor_decay</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">T1</span><span class="p">,</span> <span class="n">ref_frame</span><span class="o">=</span><span class="s2">&quot;beam&quot;</span><span class="p">)</span>
+                        <span class="k">continue</span>
+
+                <span class="n">energy_change</span> <span class="o">=</span> <span class="n">bunch</span><span class="p">[</span><span class="s2">&quot;tau&quot;</span><span class="p">]</span> <span class="o">*</span> <span class="mi">0</span>
+
+                <span class="c1"># remove part of beam phasor decay to be at the start of the binning (=bins[0])</span>
+                <span class="bp">self</span><span class="o">.</span><span class="n">phasor_decay</span><span class="p">(</span><span class="n">center</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">-</span> <span class="n">bin_length</span><span class="o">/</span><span class="mi">2</span><span class="p">,</span> <span class="n">ref_frame</span><span class="o">=</span><span class="s2">&quot;beam&quot;</span><span class="p">)</span>
+
+                <span class="k">if</span> <span class="n">index</span> <span class="o">!=</span> <span class="bp">self</span><span class="o">.</span><span class="n">bunch_index</span><span class="p">:</span>
+                    <span class="bp">self</span><span class="o">.</span><span class="n">phasor_evol</span><span class="p">(</span><span class="n">profile</span><span class="p">,</span>
+                                     <span class="n">bin_length</span><span class="p">,</span>
+                                     <span class="n">charge_per_mp</span><span class="p">,</span>
+                                     <span class="n">ref_frame</span><span class="o">=</span><span class="s2">&quot;beam&quot;</span><span class="p">)</span>
+                <span class="k">else</span><span class="p">:</span>
+                    <span class="c1"># modify beam phasor</span>
+                    <span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">center0</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">center</span><span class="p">):</span>
+                        <span class="n">mp_per_bin</span> <span class="o">=</span> <span class="n">profile</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
+
+                        <span class="k">if</span> <span class="n">mp_per_bin</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
+                            <span class="bp">self</span><span class="o">.</span><span class="n">phasor_decay</span><span class="p">(</span><span class="n">bin_length</span><span class="p">,</span> <span class="n">ref_frame</span><span class="o">=</span><span class="s2">&quot;beam&quot;</span><span class="p">)</span>
+                            <span class="k">continue</span>
+
+                        <span class="n">ind</span> <span class="o">=</span> <span class="p">(</span><span class="n">sorted_index</span> <span class="o">==</span> <span class="n">i</span><span class="p">)</span>
+                        <span class="n">phase</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">m</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">omega1</span> <span class="o">*</span> <span class="p">(</span>
+                            <span class="n">center0</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">T1</span> <span class="o">*</span>
+                            <span class="p">(</span><span class="n">index</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">h</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">nturn</span><span class="p">))</span>
+                        <span class="n">Vgene</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">real</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">generator_phasor_record</span><span class="p">[</span><span class="n">index</span><span class="p">]</span> <span class="o">*</span>
+                                        <span class="n">np</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="mi">1</span><span class="n">j</span> <span class="o">*</span> <span class="n">phase</span><span class="p">))</span>
+                        <span class="n">Vbeam</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">real</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">beam_phasor</span><span class="p">)</span>
+                        <span class="n">Vtot</span> <span class="o">=</span> <span class="n">Vgene</span> <span class="o">+</span> <span class="n">Vbeam</span> <span class="o">-</span> <span class="n">charge_per_mp</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">loss_factor</span> <span class="o">*</span> <span class="n">mp_per_bin</span>
+                        <span class="n">energy_change</span><span class="p">[</span><span class="n">ind</span><span class="p">]</span> <span class="o">=</span> <span class="n">Vtot</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">E0</span>
+
+                        <span class="bp">self</span><span class="o">.</span><span class="n">beam_phasor</span> <span class="o">-=</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">charge_per_mp</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">loss_factor</span> <span class="o">*</span> <span class="n">mp_per_bin</span>
+                        <span class="bp">self</span><span class="o">.</span><span class="n">phasor_decay</span><span class="p">(</span><span class="n">bin_length</span><span class="p">,</span> <span class="n">ref_frame</span><span class="o">=</span><span class="s2">&quot;beam&quot;</span><span class="p">)</span>
+
+                <span class="c1"># phasor decay to be at t=0 of the current bunch (=-1*bins[-1])</span>
+                <span class="bp">self</span><span class="o">.</span><span class="n">phasor_decay</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span> <span class="o">*</span> <span class="p">(</span><span class="n">center</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">+</span> <span class="n">bin_length</span><span class="o">/</span><span class="mi">2</span><span class="p">),</span>
+                                  <span class="n">ref_frame</span><span class="o">=</span><span class="s2">&quot;beam&quot;</span><span class="p">)</span>
+
+                <span class="k">if</span> <span class="n">index</span> <span class="o">==</span> <span class="bp">self</span><span class="o">.</span><span class="n">bunch_index</span><span class="p">:</span>
+                    <span class="c1"># apply kick</span>
+                    <span class="n">bunch</span><span class="p">[</span><span class="s2">&quot;delta&quot;</span><span class="p">]</span> <span class="o">+=</span> <span class="n">energy_change</span>
+
+            <span class="c1"># save beam phasor value</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">beam_phasor_record</span><span class="p">[</span><span class="n">index</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">beam_phasor</span>
+
+            <span class="c1"># phasor decay to be at t=0 of the next bunch</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">phasor_decay</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">T1</span><span class="p">,</span> <span class="n">ref_frame</span><span class="o">=</span><span class="s2">&quot;beam&quot;</span><span class="p">)</span>
+
+        <span class="c1"># apply different kind of RF feedback</span>
+        <span class="k">for</span> <span class="n">fb</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">feedback</span><span class="p">:</span>
+            <span class="n">fb</span><span class="o">.</span><span class="n">track</span><span class="p">()</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">nturn</span> <span class="o">+=</span> <span class="mi">1</span></div>
+
+<div class="viewcode-block" id="CavityResonator.init_phasor_track"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.rf.CavityResonator.init_phasor_track">[docs]</a>    <span class="k">def</span> <span class="nf">init_phasor_track</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">beam</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Initialize the beam phasor for a given beam distribution using a</span>
+<span class="sd">        tracking like method.</span>
+<span class="sd">        </span>
+<span class="sd">        Follow the same steps as the track method but in the &quot;rf&quot; reference </span>
+<span class="sd">        frame and without any modifications on the beam.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        beam : Beam object</span>
+
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">tracking</span> <span class="ow">is</span> <span class="kc">False</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">init_tracking</span><span class="p">(</span><span class="n">beam</span><span class="p">)</span>
+
+        <span class="n">n_turn</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">filling_time</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">T0</span> <span class="o">*</span> <span class="mi">10</span><span class="p">)</span>
+
+        <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n_turn</span><span class="p">):</span>
+            <span class="k">for</span> <span class="n">j</span><span class="p">,</span> <span class="n">bunch</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">beam</span><span class="o">.</span><span class="n">not_empty</span><span class="p">):</span>
+
+                <span class="n">index</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">valid_bunch_index</span><span class="p">[</span><span class="n">j</span><span class="p">]</span>
+
+                <span class="k">if</span> <span class="n">beam</span><span class="o">.</span><span class="n">mpi_switch</span><span class="p">:</span>
+                    <span class="c1"># get shared bunch profile for current bunch</span>
+                    <span class="n">center</span> <span class="o">=</span> <span class="n">beam</span><span class="o">.</span><span class="n">mpi</span><span class="o">.</span><span class="n">tau_center</span><span class="p">[</span><span class="n">j</span><span class="p">]</span>
+                    <span class="n">profile</span> <span class="o">=</span> <span class="n">beam</span><span class="o">.</span><span class="n">mpi</span><span class="o">.</span><span class="n">tau_profile</span><span class="p">[</span><span class="n">j</span><span class="p">]</span>
+                    <span class="n">bin_length</span> <span class="o">=</span> <span class="n">center</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="n">center</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
+                    <span class="n">charge_per_mp</span> <span class="o">=</span> <span class="n">beam</span><span class="o">.</span><span class="n">mpi</span><span class="o">.</span><span class="n">charge_per_mp_all</span><span class="p">[</span><span class="n">j</span><span class="p">]</span>
+                <span class="k">else</span><span class="p">:</span>
+                    <span class="k">if</span> <span class="n">i</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
+                        <span class="c1"># get bunch profile for current bunch</span>
+                        <span class="p">(</span><span class="n">bins</span><span class="p">,</span> <span class="n">sorted_index</span><span class="p">,</span> <span class="n">profile</span><span class="p">,</span>
+                         <span class="n">center</span><span class="p">)</span> <span class="o">=</span> <span class="n">bunch</span><span class="o">.</span><span class="n">binning</span><span class="p">(</span><span class="n">n_bin</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">n_bin</span><span class="p">)</span>
+                        <span class="k">if</span> <span class="n">j</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
+                            <span class="bp">self</span><span class="o">.</span><span class="n">profile_save</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span>
+                                <span class="nb">len</span><span class="p">(</span><span class="n">beam</span><span class="p">),</span>
+                                <span class="nb">len</span><span class="p">(</span><span class="n">profile</span><span class="p">),</span>
+                            <span class="p">))</span>
+                            <span class="bp">self</span><span class="o">.</span><span class="n">center_save</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span>
+                                <span class="nb">len</span><span class="p">(</span><span class="n">beam</span><span class="p">),</span>
+                                <span class="nb">len</span><span class="p">(</span><span class="n">center</span><span class="p">),</span>
+                            <span class="p">))</span>
+                        <span class="bp">self</span><span class="o">.</span><span class="n">profile_save</span><span class="p">[</span><span class="n">j</span><span class="p">,</span> <span class="p">:]</span> <span class="o">=</span> <span class="n">profile</span>
+                        <span class="bp">self</span><span class="o">.</span><span class="n">center_save</span><span class="p">[</span><span class="n">j</span><span class="p">,</span> <span class="p">:]</span> <span class="o">=</span> <span class="n">center</span>
+                    <span class="k">else</span><span class="p">:</span>
+                        <span class="n">profile</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">profile_save</span><span class="p">[</span><span class="n">j</span><span class="p">,</span> <span class="p">:]</span>
+                        <span class="n">center</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">center_save</span><span class="p">[</span><span class="n">j</span><span class="p">,</span> <span class="p">:]</span>
+
+                    <span class="n">bin_length</span> <span class="o">=</span> <span class="n">center</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="n">center</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
+                    <span class="n">charge_per_mp</span> <span class="o">=</span> <span class="n">bunch</span><span class="o">.</span><span class="n">charge_per_mp</span>
+
+                <span class="bp">self</span><span class="o">.</span><span class="n">phasor_decay</span><span class="p">(</span><span class="n">center</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">-</span> <span class="n">bin_length</span><span class="o">/</span><span class="mi">2</span><span class="p">,</span> <span class="n">ref_frame</span><span class="o">=</span><span class="s2">&quot;rf&quot;</span><span class="p">)</span>
+                <span class="bp">self</span><span class="o">.</span><span class="n">phasor_evol</span><span class="p">(</span><span class="n">profile</span><span class="p">,</span>
+                                 <span class="n">bin_length</span><span class="p">,</span>
+                                 <span class="n">charge_per_mp</span><span class="p">,</span>
+                                 <span class="n">ref_frame</span><span class="o">=</span><span class="s2">&quot;rf&quot;</span><span class="p">)</span>
+                <span class="bp">self</span><span class="o">.</span><span class="n">phasor_decay</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span> <span class="o">*</span> <span class="p">(</span><span class="n">center</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">+</span> <span class="n">bin_length</span><span class="o">/</span><span class="mi">2</span><span class="p">),</span>
+                                  <span class="n">ref_frame</span><span class="o">=</span><span class="s2">&quot;rf&quot;</span><span class="p">)</span>
+                <span class="bp">self</span><span class="o">.</span><span class="n">phasor_decay</span><span class="p">((</span><span class="bp">self</span><span class="o">.</span><span class="n">distance</span><span class="p">[</span><span class="n">index</span><span class="p">]</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">T1</span><span class="p">),</span>
+                                  <span class="n">ref_frame</span><span class="o">=</span><span class="s2">&quot;rf&quot;</span><span class="p">)</span></div>
+
+<div class="viewcode-block" id="CavityResonator.phasor_decay"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.rf.CavityResonator.phasor_decay">[docs]</a>    <span class="k">def</span> <span class="nf">phasor_decay</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">time</span><span class="p">,</span> <span class="n">ref_frame</span><span class="o">=</span><span class="s2">&quot;beam&quot;</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Compute the beam phasor decay during a given time span, assuming that </span>
+<span class="sd">        no particles are crossing the cavity during the time span.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        time : float</span>
+<span class="sd">            Time span in [s], can be positive or negative.</span>
+<span class="sd">        ref_frame : string, optional</span>
+<span class="sd">            Reference frame to be used, can be &quot;beam&quot; or &quot;rf&quot;.</span>
+
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="k">if</span> <span class="n">ref_frame</span> <span class="o">==</span> <span class="s2">&quot;beam&quot;</span><span class="p">:</span>
+            <span class="n">delta</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">wr</span>
+        <span class="k">elif</span> <span class="n">ref_frame</span> <span class="o">==</span> <span class="s2">&quot;rf&quot;</span><span class="p">:</span>
+            <span class="n">delta</span> <span class="o">=</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">wr</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">m</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">omega1</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">beam_phasor</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">beam_phasor</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span>
+            <span class="p">(</span><span class="o">-</span><span class="mi">1</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">filling_time</span> <span class="o">+</span> <span class="mi">1</span><span class="n">j</span><span class="o">*</span><span class="n">delta</span><span class="p">)</span> <span class="o">*</span> <span class="n">time</span><span class="p">)</span></div>
+
+<div class="viewcode-block" id="CavityResonator.phasor_evol"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.rf.CavityResonator.phasor_evol">[docs]</a>    <span class="k">def</span> <span class="nf">phasor_evol</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span>
+                    <span class="n">profile</span><span class="p">,</span>
+                    <span class="n">bin_length</span><span class="p">,</span>
+                    <span class="n">charge_per_mp</span><span class="p">,</span>
+                    <span class="n">ref_frame</span><span class="o">=</span><span class="s2">&quot;beam&quot;</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Compute the beam phasor evolution during the crossing of a bunch using </span>
+<span class="sd">        an analytic formula [1].</span>
+<span class="sd">        </span>
+<span class="sd">        Assume that the phasor decay happens before the beam loading.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        profile : array</span>
+<span class="sd">            Longitudinal profile of the bunch in [number of macro-particle].</span>
+<span class="sd">        bin_length : float</span>
+<span class="sd">            Length of a bin in [s].</span>
+<span class="sd">        charge_per_mp : float</span>
+<span class="sd">            Charge per macro-particle in [C].</span>
+<span class="sd">        ref_frame : string, optional</span>
+<span class="sd">            Reference frame to be used, can be &quot;beam&quot; or &quot;rf&quot;.</span>
+<span class="sd">            </span>
+<span class="sd">        References</span>
+<span class="sd">        ----------</span>
+<span class="sd">        [1] mbtrack2 manual.</span>
+<span class="sd">            </span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="k">if</span> <span class="n">ref_frame</span> <span class="o">==</span> <span class="s2">&quot;beam&quot;</span><span class="p">:</span>
+            <span class="n">delta</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">wr</span>
+        <span class="k">elif</span> <span class="n">ref_frame</span> <span class="o">==</span> <span class="s2">&quot;rf&quot;</span><span class="p">:</span>
+            <span class="n">delta</span> <span class="o">=</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">wr</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">m</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">omega1</span><span class="p">)</span>
+
+        <span class="n">n_bin</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">profile</span><span class="p">)</span>
+
+        <span class="c1"># Phasor decay during crossing time</span>
+        <span class="n">deltaT</span> <span class="o">=</span> <span class="n">n_bin</span> <span class="o">*</span> <span class="n">bin_length</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">phasor_decay</span><span class="p">(</span><span class="n">deltaT</span><span class="p">,</span> <span class="n">ref_frame</span><span class="p">)</span>
+
+        <span class="c1"># Phasor evolution due to induced voltage by marco-particles</span>
+        <span class="n">k</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">n_bin</span><span class="p">)</span>
+        <span class="n">var</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span>
+            <span class="p">(</span><span class="o">-</span><span class="mi">1</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">filling_time</span> <span class="o">+</span> <span class="mi">1</span><span class="n">j</span><span class="o">*</span><span class="n">delta</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="n">n_bin</span><span class="o">-</span><span class="n">k</span><span class="p">)</span> <span class="o">*</span> <span class="n">bin_length</span><span class="p">)</span>
+        <span class="n">sum_tot</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">profile</span> <span class="o">*</span> <span class="n">var</span><span class="p">)</span>
+        <span class="n">sum_val</span> <span class="o">=</span> <span class="o">-</span><span class="mi">2</span> <span class="o">*</span> <span class="n">sum_tot</span> <span class="o">*</span> <span class="n">charge_per_mp</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">loss_factor</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">beam_phasor</span> <span class="o">+=</span> <span class="n">sum_val</span></div>
+
+<div class="viewcode-block" id="CavityResonator.init_phasor"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.rf.CavityResonator.init_phasor">[docs]</a>    <span class="k">def</span> <span class="nf">init_phasor</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">beam</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Initialize the beam phasor for a given beam distribution using an</span>
+<span class="sd">        analytic formula [1].</span>
+<span class="sd">        </span>
+<span class="sd">        No modifications on the Beam object.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        beam : Beam object</span>
+<span class="sd">            </span>
+<span class="sd">        References</span>
+<span class="sd">        ----------</span>
+<span class="sd">        [1] mbtrack2 manual.</span>
+
+<span class="sd">        &quot;&quot;&quot;</span>
+
+        <span class="c1"># Initialization</span>
+        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">tracking</span> <span class="ow">is</span> <span class="kc">False</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">init_tracking</span><span class="p">(</span><span class="n">beam</span><span class="p">)</span>
+
+        <span class="n">N</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">n_bin</span> <span class="o">-</span> <span class="mi">1</span>
+        <span class="n">delta</span> <span class="o">=</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">wr</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">m</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">omega1</span><span class="p">)</span>
+        <span class="n">n_turn</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">filling_time</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">T0</span> <span class="o">*</span> <span class="mi">10</span><span class="p">)</span>
+
+        <span class="n">T</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">h</span><span class="p">)</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">T1</span>
+        <span class="n">bin_length</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">h</span><span class="p">)</span>
+        <span class="n">charge_per_mp</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">h</span><span class="p">)</span>
+        <span class="n">profile</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="n">N</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">h</span><span class="p">))</span>
+        <span class="n">center</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="n">N</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">h</span><span class="p">))</span>
+
+        <span class="c1"># Gather beam distribution data</span>
+        <span class="k">for</span> <span class="n">j</span><span class="p">,</span> <span class="n">bunch</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">beam</span><span class="o">.</span><span class="n">not_empty</span><span class="p">):</span>
+            <span class="n">index</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">valid_bunch_index</span><span class="p">[</span><span class="n">j</span><span class="p">]</span>
+            <span class="k">if</span> <span class="n">beam</span><span class="o">.</span><span class="n">mpi_switch</span><span class="p">:</span>
+                <span class="n">beam</span><span class="o">.</span><span class="n">mpi</span><span class="o">.</span><span class="n">share_distributions</span><span class="p">(</span><span class="n">beam</span><span class="p">,</span> <span class="n">n_bin</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">n_bin</span><span class="p">)</span>
+                <span class="n">center</span><span class="p">[:,</span> <span class="n">index</span><span class="p">]</span> <span class="o">=</span> <span class="n">beam</span><span class="o">.</span><span class="n">mpi</span><span class="o">.</span><span class="n">tau_center</span><span class="p">[</span><span class="n">j</span><span class="p">]</span>
+                <span class="n">profile</span><span class="p">[:,</span> <span class="n">index</span><span class="p">]</span> <span class="o">=</span> <span class="n">beam</span><span class="o">.</span><span class="n">mpi</span><span class="o">.</span><span class="n">tau_profile</span><span class="p">[</span><span class="n">j</span><span class="p">]</span>
+                <span class="n">bin_length</span><span class="p">[</span><span class="n">index</span><span class="p">]</span> <span class="o">=</span> <span class="n">center</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="n">index</span><span class="p">]</span> <span class="o">-</span> <span class="n">center</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="n">index</span><span class="p">]</span>
+                <span class="n">charge_per_mp</span><span class="p">[</span><span class="n">index</span><span class="p">]</span> <span class="o">=</span> <span class="n">beam</span><span class="o">.</span><span class="n">mpi</span><span class="o">.</span><span class="n">charge_per_mp_all</span><span class="p">[</span><span class="n">j</span><span class="p">]</span>
+            <span class="k">else</span><span class="p">:</span>
+                <span class="p">(</span><span class="n">bins</span><span class="p">,</span> <span class="n">sorted_index</span><span class="p">,</span> <span class="n">profile</span><span class="p">[:,</span> <span class="n">index</span><span class="p">],</span>
+                 <span class="n">center</span><span class="p">[:,</span> <span class="n">index</span><span class="p">])</span> <span class="o">=</span> <span class="n">bunch</span><span class="o">.</span><span class="n">binning</span><span class="p">(</span><span class="n">n_bin</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">n_bin</span><span class="p">)</span>
+                <span class="n">bin_length</span><span class="p">[</span><span class="n">index</span><span class="p">]</span> <span class="o">=</span> <span class="n">center</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="n">index</span><span class="p">]</span> <span class="o">-</span> <span class="n">center</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="n">index</span><span class="p">]</span>
+                <span class="n">charge_per_mp</span><span class="p">[</span><span class="n">index</span><span class="p">]</span> <span class="o">=</span> <span class="n">bunch</span><span class="o">.</span><span class="n">charge_per_mp</span>
+            <span class="n">T</span><span class="p">[</span><span class="n">index</span><span class="p">]</span> <span class="o">-=</span> <span class="p">(</span><span class="n">center</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="n">index</span><span class="p">]</span> <span class="o">+</span> <span class="n">bin_length</span><span class="p">[</span><span class="n">index</span><span class="p">]</span> <span class="o">/</span> <span class="mi">2</span><span class="p">)</span>
+            <span class="k">if</span> <span class="n">index</span> <span class="o">!=</span> <span class="mi">0</span><span class="p">:</span>
+                <span class="n">T</span><span class="p">[</span><span class="n">index</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span> <span class="o">+=</span> <span class="p">(</span><span class="n">center</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="n">index</span><span class="p">]</span> <span class="o">-</span> <span class="n">bin_length</span><span class="p">[</span><span class="n">index</span><span class="p">]</span> <span class="o">/</span> <span class="mi">2</span><span class="p">)</span>
+        <span class="n">T</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">h</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span> <span class="o">+=</span> <span class="p">(</span><span class="n">center</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">]</span> <span class="o">-</span> <span class="n">bin_length</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">/</span> <span class="mi">2</span><span class="p">)</span>
+
+        <span class="c1"># Compute matrix coefficients</span>
+        <span class="n">k</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">N</span><span class="p">)</span>
+        <span class="n">Tkj</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="n">N</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">h</span><span class="p">))</span>
+        <span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">h</span><span class="p">):</span>
+            <span class="n">sum_t</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span>
+                <span class="p">[</span><span class="n">T</span><span class="p">[</span><span class="n">n</span><span class="p">]</span> <span class="o">+</span> <span class="n">N</span> <span class="o">*</span> <span class="n">bin_length</span><span class="p">[</span><span class="n">n</span><span class="p">]</span> <span class="k">for</span> <span class="n">n</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">j</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">h</span><span class="p">)])</span>
+            <span class="n">Tkj</span><span class="p">[:,</span> <span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="p">(</span><span class="n">N</span><span class="o">-</span><span class="n">k</span><span class="p">)</span> <span class="o">*</span> <span class="n">bin_length</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o">+</span> <span class="n">T</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o">+</span> <span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">sum_t</span><span class="p">)</span>
+
+        <span class="n">var</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">exp</span><span class="p">((</span><span class="o">-</span><span class="mi">1</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">filling_time</span> <span class="o">+</span> <span class="mi">1</span><span class="n">j</span><span class="o">*</span><span class="n">delta</span><span class="p">)</span> <span class="o">*</span> <span class="n">Tkj</span><span class="p">)</span>
+        <span class="n">sum_tot</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">((</span><span class="n">profile</span><span class="o">*</span><span class="n">charge_per_mp</span><span class="p">)</span> <span class="o">*</span> <span class="n">var</span><span class="p">)</span>
+
+        <span class="c1"># Use the formula n_turn times</span>
+        <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n_turn</span><span class="p">):</span>
+            <span class="c1"># Phasor decay during one turn</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">phasor_decay</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">T0</span><span class="p">,</span> <span class="n">ref_frame</span><span class="o">=</span><span class="s2">&quot;rf&quot;</span><span class="p">)</span>
+            <span class="c1"># Phasor evolution due to induced voltage by marco-particles during one turn</span>
+            <span class="n">sum_val</span> <span class="o">=</span> <span class="o">-</span><span class="mi">2</span> <span class="o">*</span> <span class="n">sum_tot</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">loss_factor</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">beam_phasor</span> <span class="o">+=</span> <span class="n">sum_val</span>
+
+        <span class="c1"># Replace phasor at t=0 (synchronous particle) of the first non empty bunch.</span>
+        <span class="n">idx0</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">valid_bunch_index</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">phasor_decay</span><span class="p">(</span><span class="n">center</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="n">idx0</span><span class="p">]</span> <span class="o">+</span> <span class="n">bin_length</span><span class="p">[</span><span class="n">idx0</span><span class="p">]</span> <span class="o">/</span> <span class="mi">2</span><span class="p">,</span>
+                          <span class="n">ref_frame</span><span class="o">=</span><span class="s2">&quot;rf&quot;</span><span class="p">)</span></div>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">generator_phasor</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Generator phasor in [V]&quot;&quot;&quot;</span>
+        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">Vg</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="mi">1</span><span class="n">j</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">theta_g</span><span class="p">)</span>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">cavity_phasor</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Cavity total phasor in [V]&quot;&quot;&quot;</span>
+        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">generator_phasor</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">beam_phasor</span>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">cavity_phasor_record</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Last cavity phasor value of each bunch in [V]&quot;&quot;&quot;</span>
+        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">generator_phasor_record</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">beam_phasor_record</span>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">ig_phasor_record</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Last current generator phasor of each bunch in [A]&quot;&quot;&quot;</span>
+        <span class="k">for</span> <span class="n">FB</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">feedback</span><span class="p">:</span>
+            <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">FB</span><span class="p">,</span> <span class="p">(</span><span class="n">ProportionalIntegralLoop</span><span class="p">,</span> <span class="n">DirectFeedback</span><span class="p">)):</span>
+                <span class="k">return</span> <span class="n">FB</span><span class="o">.</span><span class="n">ig_phasor_record</span>
+        <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">h</span><span class="p">)</span>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">DFB_ig_phasor</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Last direct feedback current generator phasor of each bunch in [A]&quot;&quot;&quot;</span>
+        <span class="k">for</span> <span class="n">FB</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">feedback</span><span class="p">:</span>
+            <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">FB</span><span class="p">,</span> <span class="n">DirectFeedback</span><span class="p">):</span>
+                <span class="k">return</span> <span class="n">FB</span><span class="o">.</span><span class="n">DFB_ig_phasor</span>
+        <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">h</span><span class="p">)</span>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">cavity_voltage</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Cavity total voltage in [V]&quot;&quot;&quot;</span>
+        <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">cavity_phasor</span><span class="p">)</span>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">cavity_phase</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Cavity total phase in [rad]&quot;&quot;&quot;</span>
+        <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">angle</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">cavity_phasor</span><span class="p">)</span>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">beam_voltage</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Beam loading voltage in [V]&quot;&quot;&quot;</span>
+        <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">beam_phasor</span><span class="p">)</span>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">beam_phase</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Beam loading phase in [rad]&quot;&quot;&quot;</span>
+        <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">angle</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">beam_phasor</span><span class="p">)</span>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">loss_factor</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Cavity loss factor in [V/C]&quot;&quot;&quot;</span>
+        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">wr</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">Rs</span> <span class="o">/</span> <span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">Q</span><span class="p">)</span>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">m</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Harmonic number of the cavity&quot;&quot;&quot;</span>
+        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_m</span>
+
+    <span class="nd">@m</span><span class="o">.</span><span class="n">setter</span>
+    <span class="k">def</span> <span class="nf">m</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">value</span><span class="p">):</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">_m</span> <span class="o">=</span> <span class="n">value</span>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">Ncav</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Number of cavities&quot;&quot;&quot;</span>
+        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_Ncav</span>
+
+    <span class="nd">@Ncav</span><span class="o">.</span><span class="n">setter</span>
+    <span class="k">def</span> <span class="nf">Ncav</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">value</span><span class="p">):</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">_Ncav</span> <span class="o">=</span> <span class="n">value</span>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">Rs_per_cavity</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Shunt impedance of a single cavity in [Ohm], defined as </span>
+<span class="sd">        0.5*Vc*Vc/Pc.&quot;&quot;&quot;</span>
+        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_Rs_per_cavity</span>
+
+    <span class="nd">@Rs_per_cavity</span><span class="o">.</span><span class="n">setter</span>
+    <span class="k">def</span> <span class="nf">Rs_per_cavity</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">value</span><span class="p">):</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">_Rs_per_cavity</span> <span class="o">=</span> <span class="n">value</span>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">Rs</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Shunt impedance [ohm]&quot;&quot;&quot;</span>
+        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">Rs_per_cavity</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">Ncav</span>
+
+    <span class="nd">@Rs</span><span class="o">.</span><span class="n">setter</span>
+    <span class="k">def</span> <span class="nf">Rs</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">value</span><span class="p">):</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">Rs_per_cavity</span> <span class="o">=</span> <span class="n">value</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">Ncav</span>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">RL</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Loaded shunt impedance [ohm]&quot;&quot;&quot;</span>
+        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">Rs</span> <span class="o">/</span> <span class="p">(</span><span class="mi">1</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">beta</span><span class="p">)</span>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">Q</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Quality factor&quot;&quot;&quot;</span>
+        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_Q</span>
+
+    <span class="nd">@Q</span><span class="o">.</span><span class="n">setter</span>
+    <span class="k">def</span> <span class="nf">Q</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">value</span><span class="p">):</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">_Q</span> <span class="o">=</span> <span class="n">value</span>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">QL</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Loaded quality factor&quot;&quot;&quot;</span>
+        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_QL</span>
+
+    <span class="nd">@QL</span><span class="o">.</span><span class="n">setter</span>
+    <span class="k">def</span> <span class="nf">QL</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">value</span><span class="p">):</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">_QL</span> <span class="o">=</span> <span class="n">value</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">_beta</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">Q</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">QL</span> <span class="o">-</span> <span class="mi">1</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">update_feedback</span><span class="p">()</span>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">beta</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Coupling coefficient&quot;&quot;&quot;</span>
+        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_beta</span>
+
+    <span class="nd">@beta</span><span class="o">.</span><span class="n">setter</span>
+    <span class="k">def</span> <span class="nf">beta</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">value</span><span class="p">):</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">QL</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">Q</span> <span class="o">/</span> <span class="p">(</span><span class="mi">1</span><span class="o">+</span><span class="n">value</span><span class="p">)</span>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">detune</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Cavity detuning [Hz] - defined as (fr - m*f1)&quot;&quot;&quot;</span>
+        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_detune</span>
+
+    <span class="nd">@detune</span><span class="o">.</span><span class="n">setter</span>
+    <span class="k">def</span> <span class="nf">detune</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">value</span><span class="p">):</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">_detune</span> <span class="o">=</span> <span class="n">value</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">_fr</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">detune</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">m</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">f1</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">_wr</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">fr</span> <span class="o">*</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">_psi</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arctan</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">QL</span> <span class="o">*</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">fr</span> <span class="o">/</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">m</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">f1</span><span class="p">)</span> <span class="o">-</span>
+                                         <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">m</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">f1</span><span class="p">)</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">fr</span><span class="p">))</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">update_feedback</span><span class="p">()</span>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">fr</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Resonance frequency of the cavity in [Hz]&quot;&quot;&quot;</span>
+        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_fr</span>
+
+    <span class="nd">@fr</span><span class="o">.</span><span class="n">setter</span>
+    <span class="k">def</span> <span class="nf">fr</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">value</span><span class="p">):</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">detune</span> <span class="o">=</span> <span class="n">value</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">m</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">f1</span>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">wr</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Angular resonance frequency in [Hz.rad]&quot;&quot;&quot;</span>
+        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_wr</span>
+
+    <span class="nd">@wr</span><span class="o">.</span><span class="n">setter</span>
+    <span class="k">def</span> <span class="nf">wr</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">value</span><span class="p">):</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">detune</span> <span class="o">=</span> <span class="p">(</span><span class="n">value</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">m</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">f1</span><span class="p">)</span> <span class="o">*</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">psi</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Tuning angle in [rad]&quot;&quot;&quot;</span>
+        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_psi</span>
+
+    <span class="nd">@psi</span><span class="o">.</span><span class="n">setter</span>
+    <span class="k">def</span> <span class="nf">psi</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">value</span><span class="p">):</span>
+        <span class="n">delta</span> <span class="o">=</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">f1</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">m</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">tan</span><span class="p">(</span><span class="n">value</span><span class="p">)</span> <span class="o">/</span>
+                 <span class="bp">self</span><span class="o">.</span><span class="n">QL</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span> <span class="o">+</span> <span class="mi">4</span> <span class="o">*</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">f1</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">m</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span>
+        <span class="n">fr</span> <span class="o">=</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">f1</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">m</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">tan</span><span class="p">(</span><span class="n">value</span><span class="p">)</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">QL</span> <span class="o">+</span>
+              <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">delta</span><span class="p">))</span> <span class="o">/</span> <span class="mi">2</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">detune</span> <span class="o">=</span> <span class="n">fr</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">m</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">f1</span>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">filling_time</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Cavity filling time in [s]&quot;&quot;&quot;</span>
+        <span class="k">return</span> <span class="mi">2</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">QL</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">wr</span>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">Pc</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Power dissipated in the cavity walls in [W]&quot;&quot;&quot;</span>
+        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">Vc</span><span class="o">**</span><span class="mi">2</span> <span class="o">/</span> <span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">Rs</span><span class="p">)</span>
+
+<div class="viewcode-block" id="CavityResonator.Pb"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.rf.CavityResonator.Pb">[docs]</a>    <span class="k">def</span> <span class="nf">Pb</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">I0</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Return power transmitted to the beam in [W] - near Eq. (4.2.3) in [1].</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        I0 : float</span>
+<span class="sd">            Beam current in [A].</span>
+
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        float</span>
+<span class="sd">            Power transmitted to the beam in [W].</span>
+
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="k">return</span> <span class="n">I0</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">Vc</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">theta</span><span class="p">)</span></div>
+
+<div class="viewcode-block" id="CavityResonator.Pr"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.rf.CavityResonator.Pr">[docs]</a>    <span class="k">def</span> <span class="nf">Pr</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">I0</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Power reflected back to the generator in [W].</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        I0 : float</span>
+<span class="sd">            Beam current in [A].</span>
+
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        float</span>
+<span class="sd">            Power reflected back to the generator in [W].</span>
+
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">Pg</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">Pb</span><span class="p">(</span><span class="n">I0</span><span class="p">)</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">Pc</span></div>
+
+<div class="viewcode-block" id="CavityResonator.Vbr"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.rf.CavityResonator.Vbr">[docs]</a>    <span class="k">def</span> <span class="nf">Vbr</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">I0</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Return beam voltage at resonance in [V].</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        I0 : float</span>
+<span class="sd">            Beam current in [A].</span>
+
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        float</span>
+<span class="sd">            Beam voltage at resonance in [V].</span>
+
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="k">return</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">I0</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">Rs</span> <span class="o">/</span> <span class="p">(</span><span class="mi">1</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">beta</span><span class="p">)</span></div>
+
+<div class="viewcode-block" id="CavityResonator.Vb"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.rf.CavityResonator.Vb">[docs]</a>    <span class="k">def</span> <span class="nf">Vb</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">I0</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Return beam voltage in [V].</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        I0 : float</span>
+<span class="sd">            Beam current in [A].</span>
+
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        float</span>
+<span class="sd">            Beam voltage in [V].</span>
+
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">Vbr</span><span class="p">(</span><span class="n">I0</span><span class="p">)</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">psi</span><span class="p">)</span></div>
+
+<div class="viewcode-block" id="CavityResonator.Z"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.rf.CavityResonator.Z">[docs]</a>    <span class="k">def</span> <span class="nf">Z</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">f</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Cavity impedance in [Ohm] for a given frequency f in [Hz]&quot;&quot;&quot;</span>
+        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">RL</span> <span class="o">/</span> <span class="p">(</span><span class="mi">1</span> <span class="o">+</span> <span class="mi">1</span><span class="n">j</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">QL</span> <span class="o">*</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">fr</span> <span class="o">/</span> <span class="n">f</span> <span class="o">-</span> <span class="n">f</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">fr</span><span class="p">))</span></div>
+
+<div class="viewcode-block" id="CavityResonator.set_optimal_detune"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.rf.CavityResonator.set_optimal_detune">[docs]</a>    <span class="k">def</span> <span class="nf">set_optimal_detune</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">I0</span><span class="p">,</span> <span class="n">F</span><span class="o">=</span><span class="mi">1</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Set detuning to optimal conditions - second Eq. (4.2.1) in [1].</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        I0 : float</span>
+<span class="sd">            Beam current in [A].</span>
+
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">psi</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arctan</span><span class="p">(</span><span class="o">-</span><span class="bp">self</span><span class="o">.</span><span class="n">Vbr</span><span class="p">(</span><span class="n">I0</span><span class="p">)</span> <span class="o">*</span> <span class="n">F</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">Vc</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">theta</span><span class="p">))</span></div>
+
+<div class="viewcode-block" id="CavityResonator.set_optimal_coupling"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.rf.CavityResonator.set_optimal_coupling">[docs]</a>    <span class="k">def</span> <span class="nf">set_optimal_coupling</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">I0</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Set coupling to optimal value - Eq. (4.2.3) in [1].</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        I0 : float</span>
+<span class="sd">            Beam current in [A].</span>
+
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">beta</span> <span class="o">=</span> <span class="mi">1</span> <span class="o">+</span> <span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">I0</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">Rs</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">theta</span><span class="p">)</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">Vc</span><span class="p">)</span></div>
+
+<div class="viewcode-block" id="CavityResonator.set_generator"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.rf.CavityResonator.set_generator">[docs]</a>    <span class="k">def</span> <span class="nf">set_generator</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">I0</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Set generator parameters (Pg, Vgr, theta_gr, Vg and theta_g) for a </span>
+<span class="sd">        given current and set of parameters.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        I0 : float</span>
+<span class="sd">            Beam current in [A].</span>
+
+<span class="sd">        &quot;&quot;&quot;</span>
+
+        <span class="c1"># Generator power [W] - Eq. (4.1.2) [1] corrected with factor (1+beta)**2 instead of (1+beta**2)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">Pg</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">Vc</span><span class="o">**</span><span class="mi">2</span> <span class="o">*</span> <span class="p">(</span><span class="mi">1</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">beta</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span> <span class="o">/</span> <span class="p">(</span>
+            <span class="mi">2</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">Rs</span> <span class="o">*</span> <span class="mi">4</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">beta</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">psi</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span>
+                <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">theta</span><span class="p">)</span> <span class="o">+</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">I0</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">Rs</span> <span class="o">/</span>
+                 <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">Vc</span> <span class="o">*</span> <span class="p">(</span><span class="mi">1</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">beta</span><span class="p">))</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">psi</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span> <span class="o">+</span>
+                <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">theta</span><span class="p">)</span> <span class="o">+</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">I0</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">Rs</span> <span class="o">/</span>
+                 <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">Vc</span> <span class="o">*</span>
+                  <span class="p">(</span><span class="mi">1</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">beta</span><span class="p">))</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">psi</span><span class="p">)</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">psi</span><span class="p">))</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span>
+        <span class="c1"># Generator voltage at resonance [V] - Eq. (3.2.2) [1]</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">Vgr</span> <span class="o">=</span> <span class="mi">2</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">beta</span><span class="o">**</span><span class="p">(</span><span class="mi">1</span> <span class="o">/</span> <span class="mi">2</span><span class="p">)</span> <span class="o">/</span> <span class="p">(</span><span class="mi">1</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">beta</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span>
+            <span class="mi">2</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">Rs</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">Pg</span><span class="p">)</span><span class="o">**</span><span class="p">(</span><span class="mi">1</span> <span class="o">/</span> <span class="mi">2</span><span class="p">)</span>
+        <span class="c1"># Generator phase at resonance [rad] - from Eq. (4.1.1)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">theta_gr</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arctan</span><span class="p">(</span>
+            <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">Vc</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">theta</span><span class="p">)</span> <span class="o">+</span>
+             <span class="bp">self</span><span class="o">.</span><span class="n">Vbr</span><span class="p">(</span><span class="n">I0</span><span class="p">)</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">psi</span><span class="p">)</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">psi</span><span class="p">))</span> <span class="o">/</span>
+            <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">Vc</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">theta</span><span class="p">)</span> <span class="o">+</span>
+             <span class="bp">self</span><span class="o">.</span><span class="n">Vbr</span><span class="p">(</span><span class="n">I0</span><span class="p">)</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">psi</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span><span class="p">))</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">psi</span>
+        <span class="c1"># Generator voltage [V]</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">Vg</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">Vgr</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">psi</span><span class="p">)</span>
+        <span class="c1"># Generator phase [rad]</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">theta_g</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">theta_gr</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">psi</span>
+        <span class="c1"># Set generator_phasor_record</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">generator_phasor_record</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">(</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">h</span><span class="p">)</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">generator_phasor</span></div>
+
+<div class="viewcode-block" id="CavityResonator.plot_phasor"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.rf.CavityResonator.plot_phasor">[docs]</a>    <span class="k">def</span> <span class="nf">plot_phasor</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">I0</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Plot phasor diagram showing the vector addition of generator and beam </span>
+<span class="sd">        loading voltage.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        I0 : float</span>
+<span class="sd">            Beam current in [A].</span>
+<span class="sd">            </span>
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        Figure.</span>
+
+<span class="sd">        &quot;&quot;&quot;</span>
+
+        <span class="k">def</span> <span class="nf">make_legend_arrow</span><span class="p">(</span><span class="n">legend</span><span class="p">,</span> <span class="n">orig_handle</span><span class="p">,</span> <span class="n">xdescent</span><span class="p">,</span> <span class="n">ydescent</span><span class="p">,</span> <span class="n">width</span><span class="p">,</span>
+                              <span class="n">height</span><span class="p">,</span> <span class="n">fontsize</span><span class="p">):</span>
+            <span class="n">p</span> <span class="o">=</span> <span class="n">mpatches</span><span class="o">.</span><span class="n">FancyArrow</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span>
+                                    <span class="mf">0.5</span> <span class="o">*</span> <span class="n">height</span><span class="p">,</span>
+                                    <span class="n">width</span><span class="p">,</span>
+                                    <span class="mi">0</span><span class="p">,</span>
+                                    <span class="n">length_includes_head</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span>
+                                    <span class="n">head_width</span><span class="o">=</span><span class="mf">0.75</span> <span class="o">*</span> <span class="n">height</span><span class="p">)</span>
+            <span class="k">return</span> <span class="n">p</span>
+
+        <span class="n">fig</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">()</span>
+        <span class="n">ax</span> <span class="o">=</span> <span class="n">fig</span><span class="o">.</span><span class="n">add_subplot</span><span class="p">(</span><span class="mi">111</span><span class="p">,</span> <span class="n">polar</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
+        <span class="n">ax</span><span class="o">.</span><span class="n">set_rmax</span><span class="p">(</span>
+            <span class="nb">max</span><span class="p">([</span><span class="mf">1.2</span><span class="p">,</span>
+                 <span class="bp">self</span><span class="o">.</span><span class="n">Vb</span><span class="p">(</span><span class="n">I0</span><span class="p">)</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">Vc</span> <span class="o">*</span> <span class="mf">1.2</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">Vg</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">Vc</span> <span class="o">*</span> <span class="mf">1.2</span><span class="p">]))</span>
+        <span class="n">arr1</span> <span class="o">=</span> <span class="n">ax</span><span class="o">.</span><span class="n">arrow</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">theta</span><span class="p">,</span>
+                        <span class="mi">0</span><span class="p">,</span>
+                        <span class="mi">0</span><span class="p">,</span>
+                        <span class="mi">1</span><span class="p">,</span>
+                        <span class="n">alpha</span><span class="o">=</span><span class="mf">0.5</span><span class="p">,</span>
+                        <span class="n">width</span><span class="o">=</span><span class="mf">0.015</span><span class="p">,</span>
+                        <span class="n">edgecolor</span><span class="o">=</span><span class="s1">&#39;black&#39;</span><span class="p">,</span>
+                        <span class="n">lw</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
+
+        <span class="n">arr2</span> <span class="o">=</span> <span class="n">ax</span><span class="o">.</span><span class="n">arrow</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">psi</span> <span class="o">+</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span><span class="p">,</span>
+                        <span class="mi">0</span><span class="p">,</span>
+                        <span class="mi">0</span><span class="p">,</span>
+                        <span class="bp">self</span><span class="o">.</span><span class="n">Vb</span><span class="p">(</span><span class="n">I0</span><span class="p">)</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">Vc</span><span class="p">,</span>
+                        <span class="n">alpha</span><span class="o">=</span><span class="mf">0.5</span><span class="p">,</span>
+                        <span class="n">width</span><span class="o">=</span><span class="mf">0.015</span><span class="p">,</span>
+                        <span class="n">edgecolor</span><span class="o">=</span><span class="s1">&#39;red&#39;</span><span class="p">,</span>
+                        <span class="n">lw</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
+
+        <span class="n">arr3</span> <span class="o">=</span> <span class="n">ax</span><span class="o">.</span><span class="n">arrow</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">theta_g</span><span class="p">,</span>
+                        <span class="mi">0</span><span class="p">,</span>
+                        <span class="mi">0</span><span class="p">,</span>
+                        <span class="bp">self</span><span class="o">.</span><span class="n">Vg</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">Vc</span><span class="p">,</span>
+                        <span class="n">alpha</span><span class="o">=</span><span class="mf">0.5</span><span class="p">,</span>
+                        <span class="n">width</span><span class="o">=</span><span class="mf">0.015</span><span class="p">,</span>
+                        <span class="n">edgecolor</span><span class="o">=</span><span class="s1">&#39;blue&#39;</span><span class="p">,</span>
+                        <span class="n">lw</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
+
+        <span class="n">ax</span><span class="o">.</span><span class="n">set_rticks</span><span class="p">([])</span>  <span class="c1"># less radial ticks</span>
+        <span class="n">plt</span><span class="o">.</span><span class="n">legend</span><span class="p">([</span><span class="n">arr1</span><span class="p">,</span> <span class="n">arr2</span><span class="p">,</span> <span class="n">arr3</span><span class="p">],</span> <span class="p">[</span><span class="s1">&#39;Vc&#39;</span><span class="p">,</span> <span class="s1">&#39;Vb&#39;</span><span class="p">,</span> <span class="s1">&#39;Vg&#39;</span><span class="p">],</span>
+                   <span class="n">handler_map</span><span class="o">=</span><span class="p">{</span>
+                       <span class="n">mpatches</span><span class="o">.</span><span class="n">FancyArrow</span><span class="p">:</span>
+                       <span class="n">HandlerPatch</span><span class="p">(</span><span class="n">patch_func</span><span class="o">=</span><span class="n">make_legend_arrow</span><span class="p">),</span>
+                   <span class="p">})</span>
+
+        <span class="k">return</span> <span class="n">fig</span></div>
+
+<div class="viewcode-block" id="CavityResonator.is_CBI_stable"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.rf.CavityResonator.is_CBI_stable">[docs]</a>    <span class="k">def</span> <span class="nf">is_CBI_stable</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span>
+                      <span class="n">I0</span><span class="p">,</span>
+                      <span class="n">synchrotron_tune</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+                      <span class="n">modes</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+                      <span class="n">bool_return</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Check Coupled-Bunch-Instability stability, </span>
+<span class="sd">        Effect of Direct RF feedback is not included.</span>
+
+<span class="sd">        This method is a wraper around lcbi_growth_rate to caluclate the CBI </span>
+<span class="sd">        growth rate from the CavityResonator own impedance.</span>
+<span class="sd">        </span>
+<span class="sd">        See lcbi_growth_rate for details.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        I0 : float</span>
+<span class="sd">            Beam current in [A].</span>
+<span class="sd">        synchrotron_tune : float, optinal</span>
+<span class="sd">            Fractional number of longitudinal tune.</span>
+<span class="sd">            If None, synchrotron_tune is computed using self.Vc as total </span>
+<span class="sd">            voltage.</span>
+<span class="sd">            Default is None.</span>
+<span class="sd">        modes : float or list of float, optional</span>
+<span class="sd">            Coupled Bunch Instability mode numbers to consider.</span>
+<span class="sd">            If not None, return growth_rates of the input coupled bunch modes.</span>
+<span class="sd">            Default is None.</span>
+<span class="sd">        bool_return : bool, optional</span>
+<span class="sd">            If True:</span>
+<span class="sd">                - return True if the most unstable mode is stronger than </span>
+<span class="sd">                longitudinal damping time.</span>
+<span class="sd">                - return False if it is not the case.</span>
+<span class="sd">            Default is False.</span>
+<span class="sd">            </span>
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        growth_rate : float</span>
+<span class="sd">            Maximum coupled bunch instability growth rate in [s-1].</span>
+<span class="sd">        mu : int</span>
+<span class="sd">            Coupled bunch mode number corresponding to the maximum coupled bunch </span>
+<span class="sd">            instability growth rate.</span>
+
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="n">growth_rate</span><span class="p">,</span> <span class="n">mu</span><span class="p">,</span> <span class="n">growth_rates</span> <span class="o">=</span> <span class="n">lcbi_growth_rate</span><span class="p">(</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="p">,</span>
+            <span class="n">I0</span><span class="p">,</span>
+            <span class="n">M</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">h</span><span class="p">,</span>
+            <span class="n">synchrotron_tune</span><span class="o">=</span><span class="n">synchrotron_tune</span><span class="p">,</span>
+            <span class="n">Vrf</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">Vc</span><span class="p">,</span>
+            <span class="n">fr</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">fr</span><span class="p">,</span>
+            <span class="n">RL</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">RL</span><span class="p">,</span>
+            <span class="n">QL</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">QL</span><span class="p">)</span>
+
+        <span class="k">if</span> <span class="n">modes</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="n">growth_rates</span> <span class="o">=</span> <span class="n">growth_rates</span><span class="p">[</span><span class="n">modes</span><span class="p">]</span>
+            <span class="k">return</span> <span class="n">growth_rates</span>
+
+        <span class="k">if</span> <span class="n">bool_return</span><span class="p">:</span>
+            <span class="k">if</span> <span class="n">growth_rate</span> <span class="o">&gt;</span> <span class="mi">1</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">tau</span><span class="p">[</span><span class="mi">2</span><span class="p">]:</span>
+                <span class="k">return</span> <span class="kc">True</span>
+            <span class="k">else</span><span class="p">:</span>
+                <span class="k">return</span> <span class="kc">False</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="k">return</span> <span class="n">growth_rate</span><span class="p">,</span> <span class="n">mu</span></div>
+
+<div class="viewcode-block" id="CavityResonator.is_DC_Robinson_stable"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.rf.CavityResonator.is_DC_Robinson_stable">[docs]</a>    <span class="k">def</span> <span class="nf">is_DC_Robinson_stable</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">I0</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Check DC Robinson stability - Eq. (6.1.1) [1]</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        I0 : float</span>
+<span class="sd">            Beam current in [A].</span>
+
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        bool</span>
+
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="k">return</span> <span class="mi">2</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">Vc</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">theta</span><span class="p">)</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">Vbr</span><span class="p">(</span><span class="n">I0</span><span class="p">)</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span>
+            <span class="mi">2</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">psi</span><span class="p">)</span> <span class="o">&gt;</span> <span class="mi">0</span></div>
+
+<div class="viewcode-block" id="CavityResonator.plot_DC_Robinson_stability"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.rf.CavityResonator.plot_DC_Robinson_stability">[docs]</a>    <span class="k">def</span> <span class="nf">plot_DC_Robinson_stability</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">detune_range</span><span class="o">=</span><span class="p">[</span><span class="o">-</span><span class="mf">1e5</span><span class="p">,</span> <span class="mf">1e5</span><span class="p">]):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Plot DC Robinson stability limit.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        detune_range : list or array, optional</span>
+<span class="sd">            Range of tuning to plot in [Hz].</span>
+
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        Figure.</span>
+
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="n">old_detune</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">psi</span>
+
+        <span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="n">detune_range</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">detune_range</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="mi">1000</span><span class="p">)</span>
+        <span class="n">y</span> <span class="o">=</span> <span class="p">[]</span>
+        <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">x</span><span class="o">.</span><span class="n">size</span><span class="p">):</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">detune</span> <span class="o">=</span> <span class="n">x</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
+            <span class="n">y</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="o">-</span><span class="bp">self</span><span class="o">.</span><span class="n">Vc</span> <span class="o">*</span> <span class="p">(</span><span class="mi">1</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">beta</span><span class="p">)</span> <span class="o">/</span>
+                     <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">Rs</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">psi</span><span class="p">))</span> <span class="o">*</span>
+                     <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">theta</span><span class="p">))</span>  <span class="c1"># droite de stabilité</span>
+
+        <span class="n">fig</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">()</span>
+        <span class="n">ax</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">gca</span><span class="p">()</span>
+        <span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span>
+        <span class="n">ax</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="s2">&quot;Detune [Hz]&quot;</span><span class="p">)</span>
+        <span class="n">ax</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="s2">&quot;Threshold current [A]&quot;</span><span class="p">)</span>
+        <span class="n">ax</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s2">&quot;DC Robinson stability limit&quot;</span><span class="p">)</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">psi</span> <span class="o">=</span> <span class="n">old_detune</span>
+
+        <span class="k">return</span> <span class="n">fig</span></div>
+
+<div class="viewcode-block" id="CavityResonator.VRF"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.rf.CavityResonator.VRF">[docs]</a>    <span class="k">def</span> <span class="nf">VRF</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">z</span><span class="p">,</span> <span class="n">I0</span><span class="p">,</span> <span class="n">F</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">PHI</span><span class="o">=</span><span class="mi">0</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Total RF voltage taking into account form factor amplitude F and form factor phase PHI&quot;&quot;&quot;</span>
+        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">Vg</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">k1</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">m</span> <span class="o">*</span> <span class="n">z</span> <span class="o">+</span>
+                                <span class="bp">self</span><span class="o">.</span><span class="n">theta_g</span><span class="p">)</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">Vb</span><span class="p">(</span><span class="n">I0</span><span class="p">)</span> <span class="o">*</span> <span class="n">F</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span>
+                                    <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">k1</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">m</span> <span class="o">*</span> <span class="n">z</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">psi</span> <span class="o">-</span> <span class="n">PHI</span><span class="p">)</span></div>
+
+<div class="viewcode-block" id="CavityResonator.dVRF"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.rf.CavityResonator.dVRF">[docs]</a>    <span class="k">def</span> <span class="nf">dVRF</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">z</span><span class="p">,</span> <span class="n">I0</span><span class="p">,</span> <span class="n">F</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">PHI</span><span class="o">=</span><span class="mi">0</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Return derivative of total RF voltage taking into account form factor amplitude F and form factor phase PHI&quot;&quot;&quot;</span>
+        <span class="k">return</span> <span class="o">-</span><span class="mi">1</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">Vg</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">k1</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">m</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">k1</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">m</span> <span class="o">*</span> <span class="n">z</span> <span class="o">+</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">theta_g</span><span class="p">)</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">Vb</span><span class="p">(</span><span class="n">I0</span><span class="p">)</span> <span class="o">*</span> <span class="n">F</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">k1</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">m</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span>
+                <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">k1</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">m</span> <span class="o">*</span> <span class="n">z</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">psi</span> <span class="o">-</span> <span class="n">PHI</span><span class="p">)</span></div>
+
+<div class="viewcode-block" id="CavityResonator.ddVRF"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.rf.CavityResonator.ddVRF">[docs]</a>    <span class="k">def</span> <span class="nf">ddVRF</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">z</span><span class="p">,</span> <span class="n">I0</span><span class="p">,</span> <span class="n">F</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">PHI</span><span class="o">=</span><span class="mi">0</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Return the second derivative of total RF voltage taking into account form factor amplitude F and form factor phase PHI&quot;&quot;&quot;</span>
+        <span class="k">return</span> <span class="o">-</span><span class="mi">1</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">Vg</span> <span class="o">*</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">k1</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">m</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">k1</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">m</span> <span class="o">*</span> <span class="n">z</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">theta_g</span><span class="p">)</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">Vb</span><span class="p">(</span><span class="n">I0</span><span class="p">)</span> <span class="o">*</span> <span class="n">F</span> <span class="o">*</span> <span class="p">(</span>
+                <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">k1</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">m</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">k1</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">m</span> <span class="o">*</span> <span class="n">z</span> <span class="o">+</span>
+                                                   <span class="bp">self</span><span class="o">.</span><span class="n">psi</span> <span class="o">-</span> <span class="n">PHI</span><span class="p">)</span></div>
+
+<div class="viewcode-block" id="CavityResonator.deltaVRF"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.rf.CavityResonator.deltaVRF">[docs]</a>    <span class="k">def</span> <span class="nf">deltaVRF</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">z</span><span class="p">,</span> <span class="n">I0</span><span class="p">,</span> <span class="n">F</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">PHI</span><span class="o">=</span><span class="mi">0</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Return the generator voltage minus beam loading voltage taking into account form factor amplitude F and form factor phase PHI&quot;&quot;&quot;</span>
+        <span class="k">return</span> <span class="o">-</span><span class="mi">1</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">Vg</span> <span class="o">*</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">k1</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">m</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">k1</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">m</span> <span class="o">*</span> <span class="n">z</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">theta_g</span><span class="p">)</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">Vb</span><span class="p">(</span><span class="n">I0</span><span class="p">)</span> <span class="o">*</span> <span class="n">F</span> <span class="o">*</span> <span class="p">(</span>
+                <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">k1</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">m</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">k1</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">m</span> <span class="o">*</span> <span class="n">z</span> <span class="o">+</span>
+                                                   <span class="bp">self</span><span class="o">.</span><span class="n">psi</span> <span class="o">-</span> <span class="n">PHI</span><span class="p">)</span></div>
+
+<div class="viewcode-block" id="CavityResonator.update_feedback"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.rf.CavityResonator.update_feedback">[docs]</a>    <span class="k">def</span> <span class="nf">update_feedback</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Force feedback update from current CavityResonator parameters.&quot;&quot;&quot;</span>
+        <span class="k">for</span> <span class="n">FB</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">feedback</span><span class="p">:</span>
+            <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">FB</span><span class="p">,</span> <span class="p">(</span><span class="n">ProportionalIntegralLoop</span><span class="p">,</span> <span class="n">DirectFeedback</span><span class="p">)):</span>
+                <span class="n">FB</span><span class="o">.</span><span class="n">init_Ig2Vg_matrix</span><span class="p">()</span></div>
+
+<div class="viewcode-block" id="CavityResonator.sample_voltage"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.rf.CavityResonator.sample_voltage">[docs]</a>    <span class="k">def</span> <span class="nf">sample_voltage</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">n_points</span><span class="o">=</span><span class="mf">1e4</span><span class="p">,</span> <span class="n">index</span><span class="o">=</span><span class="mi">0</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Sample the voltage seen by a zero charge particle during an RF period.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        n_points : int or float, optional</span>
+<span class="sd">            Number of sample points. The default is 1e4.</span>
+<span class="sd">        index : int, optional</span>
+<span class="sd">            RF bucket number to sample. Be carful if index &gt; 0 as no new beam </span>
+<span class="sd">            loading is not taken into account here.</span>
+<span class="sd">            The default is 0.</span>
+
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        pos : array of float</span>
+<span class="sd">            Array of position from -T1/2 to T1/2.</span>
+<span class="sd">        voltage_rec : array of float</span>
+<span class="sd">            Recoring of the voltage.</span>
+
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="c1"># Init</span>
+        <span class="n">n_points</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">n_points</span><span class="p">)</span>
+        <span class="n">index</span> <span class="o">=</span> <span class="mi">0</span>
+        <span class="n">voltage_rec</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">n_points</span><span class="p">)</span>
+        <span class="n">pos</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="o">-</span><span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">T1</span> <span class="o">/</span> <span class="mi">2</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">T1</span> <span class="o">/</span> <span class="mi">2</span><span class="p">,</span> <span class="n">n_points</span><span class="p">)</span>
+        <span class="n">DeltaT</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">T1</span> <span class="o">/</span> <span class="p">(</span><span class="n">n_points</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span>
+
+        <span class="c1"># From t=0 of first non empty bunch to -T1/2</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">phasor_decay</span><span class="p">(</span><span class="o">-</span><span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">T1</span> <span class="o">/</span> <span class="mi">2</span> <span class="o">+</span> <span class="n">index</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">T1</span><span class="p">,</span>
+                          <span class="n">ref_frame</span><span class="o">=</span><span class="s2">&quot;beam&quot;</span><span class="p">)</span>
+
+        <span class="c1"># Goes from (-T1/2) to (T1/2 + DeltaT) in n_points steps</span>
+        <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n_points</span><span class="p">):</span>
+            <span class="n">phase</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">m</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">omega1</span> <span class="o">*</span> <span class="p">(</span>
+                <span class="n">pos</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">T1</span> <span class="o">*</span> <span class="p">(</span><span class="n">index</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">h</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">nturn</span><span class="p">))</span>
+            <span class="n">Vgene</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">real</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">generator_phasor_record</span><span class="p">[</span><span class="n">index</span><span class="p">]</span> <span class="o">*</span>
+                            <span class="n">np</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="mi">1</span><span class="n">j</span> <span class="o">*</span> <span class="n">phase</span><span class="p">))</span>
+            <span class="n">Vbeam</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">real</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">beam_phasor</span><span class="p">)</span>
+            <span class="n">Vtot</span> <span class="o">=</span> <span class="n">Vgene</span> <span class="o">+</span> <span class="n">Vbeam</span>
+            <span class="n">voltage_rec</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="n">Vtot</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">phasor_decay</span><span class="p">(</span><span class="n">DeltaT</span><span class="p">,</span> <span class="n">ref_frame</span><span class="o">=</span><span class="s2">&quot;beam&quot;</span><span class="p">)</span>
+
+        <span class="c1"># Get back to t=0</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">phasor_decay</span><span class="p">(</span><span class="o">-</span><span class="n">DeltaT</span> <span class="o">*</span> <span class="n">n_points</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">T1</span> <span class="o">/</span> <span class="mi">2</span> <span class="o">-</span>
+                          <span class="n">index</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">T1</span><span class="p">,</span>
+                          <span class="n">ref_frame</span><span class="o">=</span><span class="s2">&quot;beam&quot;</span><span class="p">)</span>
+
+        <span class="k">return</span> <span class="n">pos</span><span class="p">,</span> <span class="n">voltage_rec</span></div></div>
+
+
+<div class="viewcode-block" id="ProportionalLoop"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.rf.ProportionalLoop">[docs]</a><span class="k">class</span> <span class="nc">ProportionalLoop</span><span class="p">():</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    Proportional feedback loop to control a CavityResonator amplitude and phase.</span>
+<span class="sd">    </span>
+<span class="sd">    Feedback setpoints are cav_res.Vc and cav_res.theta.</span>
+<span class="sd">    </span>
+<span class="sd">    The loop must be added to the CavityResonator object using:</span>
+<span class="sd">        cav_res.feedback.append(loop)</span>
+
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">    ring : Synchrotron object</span>
+<span class="sd">    cav_res : CavityResonator</span>
+<span class="sd">        The CavityResonator which is to be controlled.</span>
+<span class="sd">    gain_A : float</span>
+<span class="sd">        Amplitude (voltage) gain of the feedback.</span>
+<span class="sd">    gain_P : float</span>
+<span class="sd">        Phase gain of the feedback.</span>
+<span class="sd">    delay : int</span>
+<span class="sd">        Feedback delay in unit of turns.</span>
+<span class="sd">        Must be supperior or equal to 1.</span>
+
+<span class="sd">    &quot;&quot;&quot;</span>
+
+    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">ring</span><span class="p">,</span> <span class="n">cav_res</span><span class="p">,</span> <span class="n">gain_A</span><span class="p">,</span> <span class="n">gain_P</span><span class="p">,</span> <span class="n">delay</span><span class="p">):</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">ring</span> <span class="o">=</span> <span class="n">ring</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">cav_res</span> <span class="o">=</span> <span class="n">cav_res</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">gain_A</span> <span class="o">=</span> <span class="n">gain_A</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">gain_P</span> <span class="o">=</span> <span class="n">gain_P</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">delay</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">delay</span><span class="p">)</span>
+        <span class="k">if</span> <span class="n">delay</span> <span class="o">&lt;</span> <span class="mi">1</span><span class="p">:</span>
+            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">&quot;delay must be &gt;= 1.&quot;</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">volt_delay</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">delay</span><span class="p">)</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">cav_res</span><span class="o">.</span><span class="n">Vc</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">phase_delay</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">delay</span><span class="p">)</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">cav_res</span><span class="o">.</span><span class="n">theta</span>
+
+<div class="viewcode-block" id="ProportionalLoop.track"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.rf.ProportionalLoop.track">[docs]</a>    <span class="k">def</span> <span class="nf">track</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Tracking method for the amplitude and phase loop.</span>
+
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        None.</span>
+
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="n">diff_A</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">volt_delay</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">cav_res</span><span class="o">.</span><span class="n">Vc</span>
+        <span class="n">diff_P</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">phase_delay</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">cav_res</span><span class="o">.</span><span class="n">theta</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">cav_res</span><span class="o">.</span><span class="n">Vg</span> <span class="o">-=</span> <span class="bp">self</span><span class="o">.</span><span class="n">gain_A</span> <span class="o">*</span> <span class="n">diff_A</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">cav_res</span><span class="o">.</span><span class="n">theta_g</span> <span class="o">-=</span> <span class="bp">self</span><span class="o">.</span><span class="n">gain_P</span> <span class="o">*</span> <span class="n">diff_P</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">cav_res</span><span class="o">.</span><span class="n">generator_phasor_record</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">(</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">h</span><span class="p">)</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">cav_res</span><span class="o">.</span><span class="n">generator_phasor</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">volt_delay</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">roll</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">volt_delay</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">phase_delay</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">roll</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">phase_delay</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">volt_delay</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">cav_res</span><span class="o">.</span><span class="n">cavity_voltage</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">phase_delay</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">cav_res</span><span class="o">.</span><span class="n">cavity_phase</span></div></div>
+
+
+<div class="viewcode-block" id="TunerLoop"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.rf.TunerLoop">[docs]</a><span class="k">class</span> <span class="nc">TunerLoop</span><span class="p">():</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    Cavity tuner loop used to control a CavityResonator tuning (psi or detune)</span>
+<span class="sd">    in order to keep the phase between cavity and generator current constant.</span>
+<span class="sd">    </span>
+<span class="sd">    Only a proportional controller is assumed.</span>
+<span class="sd">    </span>
+<span class="sd">    The loop must be added to the CavityResonator object using:</span>
+<span class="sd">        cav_res.feedback.append(loop)</span>
+
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">    ring : Synchrotron object</span>
+<span class="sd">    cav_res : CavityResonator</span>
+<span class="sd">        The CavityResonator which is to be controlled.</span>
+<span class="sd">    gain : float</span>
+<span class="sd">        Proportional gain of the tuner loop.</span>
+<span class="sd">        If not specified, 0.01 is used.</span>
+<span class="sd">    avering_period:</span>
+<span class="sd">        Period during which the phase difference is monitored and averaged. </span>
+<span class="sd">        Then the feedback correction is applied every avering_period turn.</span>
+<span class="sd">        Unit is turn number.</span>
+<span class="sd">        A value longer than one synchrotron period (1/fs) is recommended.</span>
+<span class="sd">        If not specified, 2-synchrotron period (2/fs) is used, although it is</span>
+<span class="sd">        too fast compared to the actual situation.</span>
+<span class="sd">    offset : float</span>
+<span class="sd">        Tuning offset in [rad].</span>
+<span class="sd">        </span>
+<span class="sd">    &quot;&quot;&quot;</span>
+
+    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">ring</span><span class="p">,</span> <span class="n">cav_res</span><span class="p">,</span> <span class="n">gain</span><span class="o">=</span><span class="mf">0.01</span><span class="p">,</span> <span class="n">avering_period</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">offset</span><span class="o">=</span><span class="mi">0</span><span class="p">):</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">ring</span> <span class="o">=</span> <span class="n">ring</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">cav_res</span> <span class="o">=</span> <span class="n">cav_res</span>
+        <span class="k">if</span> <span class="n">avering_period</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
+            <span class="n">fs</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">synchrotron_tune</span><span class="p">(</span>
+                <span class="bp">self</span><span class="o">.</span><span class="n">cav_res</span><span class="o">.</span><span class="n">Vc</span><span class="p">)</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">f1</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">h</span>
+            <span class="n">avering_period</span> <span class="o">=</span> <span class="mi">2</span> <span class="o">/</span> <span class="n">fs</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">T0</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">Pgain</span> <span class="o">=</span> <span class="n">gain</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">offset</span> <span class="o">=</span> <span class="n">offset</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">avering_period</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">avering_period</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">diff</span> <span class="o">=</span> <span class="mi">0</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">count</span> <span class="o">=</span> <span class="mi">0</span>
+
+<div class="viewcode-block" id="TunerLoop.track"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.rf.TunerLoop.track">[docs]</a>    <span class="k">def</span> <span class="nf">track</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Tracking method for the tuner loop.</span>
+<span class="sd">    </span>
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        None.</span>
+<span class="sd">    </span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">count</span> <span class="o">==</span> <span class="bp">self</span><span class="o">.</span><span class="n">avering_period</span><span class="p">:</span>
+            <span class="n">diff</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">diff</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">avering_period</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">offset</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">cav_res</span><span class="o">.</span><span class="n">psi</span> <span class="o">-=</span> <span class="n">diff</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">Pgain</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">count</span> <span class="o">=</span> <span class="mi">0</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">diff</span> <span class="o">=</span> <span class="mi">0</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">diff</span> <span class="o">+=</span> <span class="bp">self</span><span class="o">.</span><span class="n">cav_res</span><span class="o">.</span><span class="n">cavity_phase</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">cav_res</span><span class="o">.</span><span class="n">theta_g</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">cav_res</span><span class="o">.</span><span class="n">psi</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">count</span> <span class="o">+=</span> <span class="mi">1</span></div></div>
+
+
+<div class="viewcode-block" id="ProportionalIntegralLoop"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.rf.ProportionalIntegralLoop">[docs]</a><span class="k">class</span> <span class="nc">ProportionalIntegralLoop</span><span class="p">():</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    Proportional Integral (PI) loop to control a CavityResonator amplitude and </span>
+<span class="sd">    phase via generator current (ig) [1,2].</span>
+<span class="sd">    </span>
+<span class="sd">    Feedback reference targets (setpoints) are cav_res.Vc and cav_res.theta.</span>
+<span class="sd">    </span>
+<span class="sd">    The ProportionalIntegralLoop should be initialized only after generator </span>
+<span class="sd">    parameters are set.</span>
+<span class="sd">    </span>
+<span class="sd">    The loop must be added to the CavityResonator object using:</span>
+<span class="sd">        cav_res.feedback.append(loop)</span>
+<span class="sd">        </span>
+<span class="sd">    When the reference target is changed, it might be needed to re-initialize </span>
+<span class="sd">    the feedforward constant by calling init_FFconst().</span>
+
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">    ring : Synchrotron object</span>
+<span class="sd">    cav_res : CavityResonator object</span>
+<span class="sd">        CavityResonator in which the loop will be added. </span>
+<span class="sd">    gain : float list</span>
+<span class="sd">        Proportional gain (Pgain) and integral gain (Igain) of the feedback </span>
+<span class="sd">        system in the form of a list [Pgain, Igain].</span>
+<span class="sd">        In case of normal conducting cavity (QL~1e4), the Pgain of ~1.0 and </span>
+<span class="sd">        Igain of ~1e4(5) are usually used.</span>
+<span class="sd">        In case of super conducting cavity (QL &gt; 1e6), the Pgain of ~100 </span>
+<span class="sd">        can be used.</span>
+<span class="sd">        In a &quot;bad&quot; parameter set, unstable oscillation of the cavity voltage </span>
+<span class="sd">        can be caused. So, a parameter scan of the gain should be made.</span>
+<span class="sd">        Igain * ring.T1 / dtau is Ki defined as a the coefficients for </span>
+<span class="sd">        integral part in of [1], where dtau is a clock period of the PI controller.</span>
+<span class="sd">    sample_num : int</span>
+<span class="sd">        Number of bunch over which the mean cavity voltage is computed.</span>
+<span class="sd">        Units are in bucket numbers.</span>
+<span class="sd">    every : int</span>
+<span class="sd">        Sampling and clock period of the feedback controller</span>
+<span class="sd">        Time interval between two cavity voltage monitoring and feedback.</span>
+<span class="sd">        Units are in bucket numbers.</span>
+<span class="sd">    delay : int</span>
+<span class="sd">        Loop delay of the PI feedback system. </span>
+<span class="sd">        Units are in bucket numbers.</span>
+<span class="sd">    IIR_cutoff : float, optinal</span>
+<span class="sd">        Cutoff frequency of the IIR filter in [Hz].</span>
+<span class="sd">        If 0, cutoff frequency is infinity.</span>
+<span class="sd">        Default is 0.</span>
+<span class="sd">    FF : bool, optional</span>
+<span class="sd">        Boolean switch to use feedforward constant.</span>
+<span class="sd">        True is recommended to prevent a cavity voltage drop in the beginning </span>
+<span class="sd">        of the tracking.</span>
+<span class="sd">        In case of small Pgain (QL ~ 1e4), cavity voltage drop may cause </span>
+<span class="sd">        beam loss due to static Robinson.</span>
+<span class="sd">        Default is True.</span>
+<span class="sd">        </span>
+<span class="sd">    Methods</span>
+<span class="sd">    -------</span>
+<span class="sd">    track()</span>
+<span class="sd">        Tracking method for the Cavity PI control feedback.</span>
+<span class="sd">    init_Ig2Vg_matrix()</span>
+<span class="sd">        Initialize matrix for Ig2Vg_matrix.</span>
+<span class="sd">    init_FFconst()</span>
+<span class="sd">        Initialize feedforward constant.</span>
+<span class="sd">    Ig2Vg_matrix()</span>
+<span class="sd">        Return Vg from Ig using matrix formalism.</span>
+<span class="sd">    Ig2Vg()</span>
+<span class="sd">        Go from Ig to Vg and apply values.</span>
+<span class="sd">    Vg2Ig(Vg)</span>
+<span class="sd">        Return Ig from Vg (assuming constant Vg).</span>
+<span class="sd">    IIR_init(cutoff)</span>
+<span class="sd">        Initialization for the IIR filter.</span>
+<span class="sd">    IIR(input)</span>
+<span class="sd">        Return IIR filter output.</span>
+<span class="sd">    IIRcutoff()</span>
+<span class="sd">        Return IIR cutoff frequency in [Hz].</span>
+
+<span class="sd">    Notes</span>
+<span class="sd">    -----</span>
+<span class="sd">    Assumption : delay &gt;&gt; every ~ sample_num</span>
+<span class="sd">    </span>
+<span class="sd">    Adjusting ig(Vg) parameter to keep the cavity voltage constant (to target values).</span>
+<span class="sd">    The &quot;track&quot; method is</span>
+<span class="sd">       1) Monitoring the cavity voltage phasor</span>
+<span class="sd">       Mean cavity voltage value between specified bunch number (sample_num) is monitored</span>
+<span class="sd">       with specified interval period (every).</span>
+<span class="sd">       2) Changing the ig phasor</span>
+<span class="sd">       The ig phasor is changed according the difference of the specified</span>
+<span class="sd">       reference values with specified gain (gain).</span>
+<span class="sd">       By using ig instead of Vg, the cavity response can be taken account.</span>
+<span class="sd">       3) ig changes are reflected to Vg after the specifed delay (delay) of the system</span>
+
+<span class="sd">    Vc--&gt;(rot)--&gt;IIR--&gt;(-)--&gt;(V-&gt;I,fac)--&gt;PI--&gt;Ig --&gt; Vg</span>
+<span class="sd">                        |</span>
+<span class="sd">                       Ref</span>
+
+<span class="sd">    Examples</span>
+<span class="sd">    --------</span>
+<span class="sd">    PF; E0=2.5GeV, C=187m, frf=500MHz</span>
+<span class="sd">        QL=11800, fs0=23kHz</span>
+<span class="sd">        ==&gt; gain=[0.5,1e4], sample_num=8, every=7(13ns), delay=500(1us)</span>
+<span class="sd">                     is one reasonable parameter set.</span>
+<span class="sd">        The practical clock period is 13ns.</span>
+<span class="sd">            ==&gt; Igain_PF = Igain_mbtrack * Trf / 13ns = Igain_mbtrack * 0.153</span>
+<span class="sd">     </span>
+<span class="sd">    References</span>
+<span class="sd">    ----------</span>
+<span class="sd">    [1] : https://en.wikipedia.org/wiki/PID_controller</span>
+<span class="sd">    [2] : Yamamoto, N., Takahashi, T., &amp; Sakanaka, S. (2018). Reduction and </span>
+<span class="sd">    compensation of the transient beam loading effect in a double rf system </span>
+<span class="sd">    of synchrotron light sources. PRAB, 21(1), 012001.</span>
+<span class="sd">    </span>
+<span class="sd">    &quot;&quot;&quot;</span>
+
+    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span>
+                 <span class="n">ring</span><span class="p">,</span>
+                 <span class="n">cav_res</span><span class="p">,</span>
+                 <span class="n">gain</span><span class="p">,</span>
+                 <span class="n">sample_num</span><span class="p">,</span>
+                 <span class="n">every</span><span class="p">,</span>
+                 <span class="n">delay</span><span class="p">,</span>
+                 <span class="n">IIR_cutoff</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span>
+                 <span class="n">FF</span><span class="o">=</span><span class="kc">True</span><span class="p">):</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">ring</span> <span class="o">=</span> <span class="n">ring</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">cav_res</span> <span class="o">=</span> <span class="n">cav_res</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">Ig2Vg_mat</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">h</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">h</span><span class="p">),</span> <span class="n">dtype</span><span class="o">=</span><span class="nb">complex</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">ig_modulation_signal</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">h</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="nb">complex</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">gain</span> <span class="o">=</span> <span class="n">gain</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">FF</span> <span class="o">=</span> <span class="n">FF</span>
+
+        <span class="k">if</span> <span class="n">delay</span> <span class="o">&gt;</span> <span class="mi">0</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">delay</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">delay</span><span class="p">)</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">delay</span> <span class="o">=</span> <span class="mi">1</span>
+        <span class="k">if</span> <span class="n">every</span> <span class="o">&gt;</span> <span class="mi">0</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">every</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">every</span><span class="p">)</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">every</span> <span class="o">=</span> <span class="mi">1</span>
+        <span class="n">record_size</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">ceil</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">delay</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">every</span><span class="p">))</span>
+        <span class="k">if</span> <span class="n">record_size</span> <span class="o">&lt;</span> <span class="mi">1</span><span class="p">:</span>
+            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">&quot;Bad parameter set : delay or every&quot;</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">sample_num</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">sample_num</span><span class="p">)</span>
+
+        <span class="c1"># init lists for FB process</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">ig_phasor</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">h</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="nb">complex</span><span class="p">)</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">Vg2Ig</span><span class="p">(</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">cav_res</span><span class="o">.</span><span class="n">generator_phasor</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">ig_phasor_record</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">ig_phasor</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">vc_previous</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">(</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">sample_num</span><span class="p">)</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">cav_res</span><span class="o">.</span><span class="n">cavity_phasor</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">diff_record</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">record_size</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="nb">complex</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">I_record</span> <span class="o">=</span> <span class="mi">0</span> <span class="o">+</span> <span class="mi">0</span><span class="n">j</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">sample_list</span> <span class="o">=</span> <span class="nb">range</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">h</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">every</span><span class="p">)</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">IIR_init</span><span class="p">(</span><span class="n">IIR_cutoff</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">init_FFconst</span><span class="p">()</span>
+
+        <span class="c1"># Pre caclulation for Ig2Vg</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">init_Ig2Vg_matrix</span><span class="p">()</span>
+
+<div class="viewcode-block" id="ProportionalIntegralLoop.track"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.rf.ProportionalIntegralLoop.track">[docs]</a>    <span class="k">def</span> <span class="nf">track</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">apply_changes</span><span class="o">=</span><span class="kc">True</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Tracking method for the Cavity PI control feedback.</span>
+
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        None.</span>
+
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="n">vc_list</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">([</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">vc_previous</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">cav_res</span><span class="o">.</span><span class="n">cavity_phasor_record</span>
+        <span class="p">])</span>  <span class="c1">#This line is slowing down the process.</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">ig_phasor</span><span class="o">.</span><span class="n">fill</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">ig_phasor</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">])</span>
+
+        <span class="k">for</span> <span class="n">index</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">sample_list</span><span class="p">:</span>
+            <span class="c1"># 2) updating Ig using last item of the list</span>
+            <span class="n">diff</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">diff_record</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">FFconst</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">I_record</span> <span class="o">+=</span> <span class="n">diff</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">f1</span>
+            <span class="n">fb_value</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">gain</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">diff</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">gain</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">I_record</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">ig_phasor</span><span class="p">[</span><span class="n">index</span><span class="p">:]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">Vg2Ig</span><span class="p">(</span><span class="n">fb_value</span><span class="p">)</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">FFconst</span>
+            <span class="c1"># Shift the record</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">diff_record</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">roll</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">diff_record</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
+            <span class="c1"># 1) recording diff as a first item of the list</span>
+            <span class="n">mean_vc</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">vc_list</span><span class="p">[</span><span class="n">index</span><span class="p">:</span><span class="bp">self</span><span class="o">.</span><span class="n">sample_num</span> <span class="o">+</span> <span class="n">index</span><span class="p">])</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span>
+                <span class="o">-</span><span class="mi">1</span><span class="n">j</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">cav_res</span><span class="o">.</span><span class="n">theta</span><span class="p">)</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">diff_record</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">cav_res</span><span class="o">.</span><span class="n">Vc</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">IIR</span><span class="p">(</span><span class="n">mean_vc</span><span class="p">)</span>
+        <span class="c1"># update sample_list for next turn</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">sample_list</span> <span class="o">=</span> <span class="nb">range</span><span class="p">(</span><span class="n">index</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">every</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">h</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">h</span><span class="p">,</span>
+                                 <span class="bp">self</span><span class="o">.</span><span class="n">every</span><span class="p">)</span>
+        <span class="c1"># update vc_previous for next turn</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">vc_previous</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">cav_res</span><span class="o">.</span><span class="n">cavity_phasor_record</span><span class="p">[</span><span class="o">-</span><span class="bp">self</span><span class="o">.</span><span class="n">sample_num</span><span class="p">:]</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">ig_phasor</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">ig_phasor</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">ig_modulation_signal</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">ig_phasor_record</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">ig_phasor</span>
+
+        <span class="k">if</span> <span class="n">apply_changes</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">Ig2Vg</span><span class="p">()</span></div>
+
+<div class="viewcode-block" id="ProportionalIntegralLoop.init_Ig2Vg_matrix"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.rf.ProportionalIntegralLoop.init_Ig2Vg_matrix">[docs]</a>    <span class="k">def</span> <span class="nf">init_Ig2Vg_matrix</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Initialize matrix for Ig2Vg_matrix.</span>
+<span class="sd">        </span>
+<span class="sd">        Shoud be called before first use of Ig2Vg_matrix and after each cavity </span>
+<span class="sd">        parameter change.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="n">k</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">h</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">Ig2Vg_vec</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">cav_res</span><span class="o">.</span><span class="n">filling_time</span> <span class="o">*</span>
+                                <span class="p">(</span><span class="mi">1</span> <span class="o">-</span> <span class="mi">1</span><span class="n">j</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">tan</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">cav_res</span><span class="o">.</span><span class="n">psi</span><span class="p">))</span> <span class="o">*</span>
+                                <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">T1</span> <span class="o">*</span> <span class="p">(</span><span class="n">k</span><span class="o">+</span><span class="mi">1</span><span class="p">))</span>
+        <span class="n">tempV</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">cav_res</span><span class="o">.</span><span class="n">filling_time</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">T1</span> <span class="o">*</span> <span class="n">k</span> <span class="o">*</span>
+                       <span class="p">(</span><span class="mi">1</span> <span class="o">-</span> <span class="mi">1</span><span class="n">j</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">tan</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">cav_res</span><span class="o">.</span><span class="n">psi</span><span class="p">)))</span>
+        <span class="k">for</span> <span class="n">idx</span> <span class="ow">in</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">h</span><span class="p">):</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">Ig2Vg_mat</span><span class="p">[</span><span class="n">idx</span><span class="p">:,</span> <span class="n">idx</span><span class="p">]</span> <span class="o">=</span> <span class="n">tempV</span><span class="p">[:</span><span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">h</span> <span class="o">-</span> <span class="n">idx</span><span class="p">]</span></div>
+
+<div class="viewcode-block" id="ProportionalIntegralLoop.init_FFconst"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.rf.ProportionalIntegralLoop.init_FFconst">[docs]</a>    <span class="k">def</span> <span class="nf">init_FFconst</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Initialize feedforward constant.&quot;&quot;&quot;</span>
+        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">FF</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">FFconst</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">ig_phasor</span><span class="p">)</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">FFconst</span> <span class="o">=</span> <span class="mi">0</span></div>
+
+<div class="viewcode-block" id="ProportionalIntegralLoop.Ig2Vg_matrix"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.rf.ProportionalIntegralLoop.Ig2Vg_matrix">[docs]</a>    <span class="k">def</span> <span class="nf">Ig2Vg_matrix</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Return Vg from Ig using matrix formalism.</span>
+<span class="sd">        Warning: self.init_Ig2Vg should be called after each CavityResonator </span>
+<span class="sd">        parameter change.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="n">generator_phasor_record</span> <span class="o">=</span> <span class="p">(</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">Ig2Vg_vec</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">cav_res</span><span class="o">.</span><span class="n">generator_phasor_record</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">+</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">Ig2Vg_mat</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">ig_phasor_record</span><span class="p">)</span> <span class="o">*</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">cav_res</span><span class="o">.</span><span class="n">loss_factor</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">T1</span><span class="p">)</span>
+        <span class="k">return</span> <span class="n">generator_phasor_record</span></div>
+
+<div class="viewcode-block" id="ProportionalIntegralLoop.Ig2Vg"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.rf.ProportionalIntegralLoop.Ig2Vg">[docs]</a>    <span class="k">def</span> <span class="nf">Ig2Vg</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Go from Ig to Vg.</span>
+<span class="sd">        </span>
+<span class="sd">        Apply new values to cav_res.generator_phasor_record, cav_res.Vg and</span>
+<span class="sd">        cav_res.theta_g from ig_phasor_record.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">cav_res</span><span class="o">.</span><span class="n">generator_phasor_record</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">Ig2Vg_matrix</span><span class="p">()</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">cav_res</span><span class="o">.</span><span class="n">Vg</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">cav_res</span><span class="o">.</span><span class="n">generator_phasor_record</span><span class="p">))</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">cav_res</span><span class="o">.</span><span class="n">theta_g</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span>
+            <span class="n">np</span><span class="o">.</span><span class="n">angle</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">cav_res</span><span class="o">.</span><span class="n">generator_phasor_record</span><span class="p">))</span></div>
+
+<div class="viewcode-block" id="ProportionalIntegralLoop.Vg2Ig"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.rf.ProportionalIntegralLoop.Vg2Ig">[docs]</a>    <span class="k">def</span> <span class="nf">Vg2Ig</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">Vg</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Return Ig from Vg (assuming constant Vg).</span>
+
+<span class="sd">        Eq.25 of ref [2] assuming the dVg/dt = 0.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="k">return</span> <span class="n">Vg</span> <span class="o">*</span> <span class="p">(</span><span class="mi">1</span> <span class="o">-</span> <span class="mi">1</span><span class="n">j</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">tan</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">cav_res</span><span class="o">.</span><span class="n">psi</span><span class="p">))</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">cav_res</span><span class="o">.</span><span class="n">RL</span></div>
+
+<div class="viewcode-block" id="ProportionalIntegralLoop.IIR_init"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.rf.ProportionalIntegralLoop.IIR_init">[docs]</a>    <span class="k">def</span> <span class="nf">IIR_init</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">cutoff</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Initialization for the IIR filter.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        cutoff : float</span>
+<span class="sd">            Cutoff frequency of the IIR filter in [Hz].</span>
+<span class="sd">            If 0, cutoff frequency is infinity.</span>
+<span class="sd">            </span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="k">if</span> <span class="n">cutoff</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">IIRcoef</span> <span class="o">=</span> <span class="mf">1.0</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="n">omega</span> <span class="o">=</span> <span class="mf">2.0</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="n">cutoff</span>
+            <span class="n">T</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">T1</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">every</span>
+            <span class="n">alpha</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">omega</span> <span class="o">*</span> <span class="n">T</span><span class="p">)</span> <span class="o">-</span> <span class="mi">1</span>
+            <span class="n">tmp</span> <span class="o">=</span> <span class="n">alpha</span><span class="o">*</span><span class="n">alpha</span> <span class="o">-</span> <span class="mi">2</span><span class="o">*</span><span class="n">alpha</span>
+            <span class="k">if</span> <span class="n">tmp</span> <span class="o">&gt;</span> <span class="mi">0</span><span class="p">:</span>
+                <span class="bp">self</span><span class="o">.</span><span class="n">IIRcoef</span> <span class="o">=</span> <span class="n">alpha</span> <span class="o">+</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">tmp</span><span class="p">)</span>
+            <span class="k">else</span><span class="p">:</span>
+                <span class="bp">self</span><span class="o">.</span><span class="n">IIRcoef</span> <span class="o">=</span> <span class="n">T</span> <span class="o">*</span> <span class="n">cutoff</span> <span class="o">*</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">IIRout</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">cav_res</span><span class="o">.</span><span class="n">Vc</span></div>
+
+<div class="viewcode-block" id="ProportionalIntegralLoop.IIR"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.rf.ProportionalIntegralLoop.IIR">[docs]</a>    <span class="k">def</span> <span class="nf">IIR</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="nb">input</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Return IIR filter output.&quot;&quot;&quot;</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">IIRout</span> <span class="o">=</span> <span class="p">(</span><span class="mi">1</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">IIRcoef</span><span class="p">)</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">IIRout</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">IIRcoef</span> <span class="o">*</span> <span class="nb">input</span>
+        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">IIRout</span></div>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">IIRcutoff</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Return IIR cutoff frequency in [Hz].&quot;&quot;&quot;</span>
+        <span class="n">T</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">T1</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">every</span>
+        <span class="k">return</span> <span class="mf">1.0</span> <span class="o">/</span> <span class="mf">2.0</span> <span class="o">/</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">/</span> <span class="n">T</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">arccos</span><span class="p">(</span>
+            <span class="p">(</span><span class="mi">2</span> <span class="o">-</span> <span class="mi">2</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">IIRcoef</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">IIRcoef</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">IIRcoef</span><span class="p">)</span> <span class="o">/</span> <span class="mi">2</span> <span class="o">/</span>
+            <span class="p">(</span><span class="mi">1</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">IIRcoef</span><span class="p">))</span></div>
+
+
+<div class="viewcode-block" id="DirectFeedback"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.rf.DirectFeedback">[docs]</a><span class="k">class</span> <span class="nc">DirectFeedback</span><span class="p">(</span><span class="n">ProportionalIntegralLoop</span><span class="p">):</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    Direct RF FB (DFB) via generator current (ig) using PI controller [1,2].</span>
+<span class="sd">    </span>
+<span class="sd">    The DirectFeedback inherits from ProportionalIntegralLoop so all </span>
+<span class="sd">    mandatory parameters from ProportionalIntegralLoop should be passed as</span>
+<span class="sd">    kwargs when initializing a DirectFeedback object.</span>
+<span class="sd">        </span>
+<span class="sd">    To avoid cavity-beam unmatching (large synchrotron oscilation of beam),</span>
+<span class="sd">    the CavityResonator generator parameters should be set before </span>
+<span class="sd">    initialization.</span>
+<span class="sd">    </span>
+<span class="sd">    The loop must be added to the CavityResonator object using:</span>
+<span class="sd">        cav_res.feedback.append(loop)</span>
+<span class="sd">    </span>
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">    DFB_gain : float</span>
+<span class="sd">        Gain of the DFB.</span>
+<span class="sd">    DFB_phase_shift : float</span>
+<span class="sd">        Phase shift of the DFB.</span>
+<span class="sd">    DFB_sample_num : int, optional</span>
+<span class="sd">        Sample number to monitor Vc for the DFB.</span>
+<span class="sd">        The averaged Vc value in DFB_sample_num is monitored.</span>
+<span class="sd">        Units are in bucket numbers.</span>
+<span class="sd">        If None, value from the ProportionalIntegralLoop is used.</span>
+<span class="sd">        Default is None.</span>
+<span class="sd">    DFB_every : int, optional</span>
+<span class="sd">        Interval to monitor and change Vc for the DFB.</span>
+<span class="sd">        Units are in bucket numbers.</span>
+<span class="sd">        If None, value from the ProportionalIntegralLoop is used.</span>
+<span class="sd">        Default is None.</span>
+<span class="sd">    DFB_delay : int, optional</span>
+<span class="sd">        Loop delay of the DFB.</span>
+<span class="sd">        Units are in bucket numbers.</span>
+<span class="sd">        If None, value from the ProportionalIntegralLoop is used.</span>
+<span class="sd">        Default is None.</span>
+<span class="sd">        </span>
+<span class="sd">    Attributes</span>
+<span class="sd">    ----------</span>
+<span class="sd">    phase_shift : float</span>
+<span class="sd">        Phase shift applied to DFB, defined as psi - DFB_phase_shift.</span>
+<span class="sd">    DFB_psi: float</span>
+<span class="sd">        Return detuning angle value with Direct RF feedback in [rad].</span>
+<span class="sd">    DFB_alpha : float</span>
+<span class="sd">        Return the amplitude ratio alpha of the DFB.</span>
+<span class="sd">    DFB_gamma : float</span>
+<span class="sd">        Return the gain gamma of the DFB.</span>
+<span class="sd">    DFB_Rs : float</span>
+<span class="sd">        Return the shunt impedance of the DFB in [ohm].</span>
+<span class="sd">    </span>
+<span class="sd">    Methods</span>
+<span class="sd">    -------</span>
+<span class="sd">    DFB_parameter_set(DFB_gain, DFB_phase_shift)</span>
+<span class="sd">        Set DFB gain and phase shift parameters.</span>
+<span class="sd">    track()</span>
+<span class="sd">        Tracking method for the Direct RF feedback.</span>
+<span class="sd">    DFB_Vg()</span>
+<span class="sd">        Return the generator voltage main and DFB components in [V].</span>
+<span class="sd">    DFB_fs()</span>
+<span class="sd">        Return the modified synchrotron frequency in [Hz].</span>
+<span class="sd">        </span>
+<span class="sd">    References</span>
+<span class="sd">    ----------</span>
+<span class="sd">    [1] : Akai, K. (2022). Stability analysis of rf accelerating mode with </span>
+<span class="sd">    feedback loops under heavy beam loading in SuperKEKB. PRAB, 25(10), </span>
+<span class="sd">    102002.</span>
+<span class="sd">    [2] : N. Yamamoto et al. (2023). Stability survey of a double RF system </span>
+<span class="sd">    with RF feedback loops for bunch lengthening in a low-emittance synchrotron </span>
+<span class="sd">    ring. In Proc. IPAC&#39;23. doi:10.18429/JACoW-IPAC2023-WEPL161</span>
+
+<span class="sd">    &quot;&quot;&quot;</span>
+
+    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span>
+                 <span class="n">DFB_gain</span><span class="p">,</span>
+                 <span class="n">DFB_phase_shift</span><span class="p">,</span>
+                 <span class="n">DFB_sample_num</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+                 <span class="n">DFB_every</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+                 <span class="n">DFB_delay</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+                 <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
+        <span class="nb">super</span><span class="p">(</span><span class="n">DirectFeedback</span><span class="p">,</span> <span class="bp">self</span><span class="p">)</span><span class="o">.</span><span class="fm">__init__</span><span class="p">(</span><span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
+
+        <span class="k">if</span> <span class="n">DFB_delay</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">DFB_delay</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">DFB_delay</span><span class="p">)</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">DFB_delay</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">delay</span>
+
+        <span class="k">if</span> <span class="n">DFB_sample_num</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">DFB_sample_num</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">DFB_sample_num</span><span class="p">)</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">DFB_sample_num</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">sample_num</span>
+
+        <span class="k">if</span> <span class="n">DFB_every</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">DFB_every</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">DFB_every</span><span class="p">)</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">DFB_every</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">every</span>
+
+        <span class="n">record_size</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">ceil</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">DFB_delay</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">DFB_every</span><span class="p">))</span>
+        <span class="k">if</span> <span class="n">record_size</span> <span class="o">&lt;</span> <span class="mi">1</span><span class="p">:</span>
+            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">&quot;Bad parameter set : DFB_delay or DFB_every&quot;</span><span class="p">)</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">DFB_parameter_set</span><span class="p">(</span><span class="n">DFB_gain</span><span class="p">,</span> <span class="n">DFB_phase_shift</span><span class="p">)</span>
+        <span class="k">if</span> <span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">cav_res</span><span class="o">.</span><span class="n">beam_phasor</span><span class="p">))</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
+            <span class="n">cavity_phasor</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">cav_res</span><span class="o">.</span><span class="n">Vc</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="mi">1</span><span class="n">j</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">cav_res</span><span class="o">.</span><span class="n">theta</span><span class="p">)</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="n">cavity_phasor</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">cav_res</span><span class="o">.</span><span class="n">cavity_phasor_record</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">DFB_VcRecord</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">(</span><span class="n">record_size</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="nb">complex</span><span class="p">)</span> <span class="o">*</span> <span class="n">cavity_phasor</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">DFB_vc_previous</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">DFB_sample_num</span><span class="p">,</span>
+                                       <span class="n">dtype</span><span class="o">=</span><span class="nb">complex</span><span class="p">)</span> <span class="o">*</span> <span class="n">cavity_phasor</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">DFB_sample_list</span> <span class="o">=</span> <span class="nb">range</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">h</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">DFB_every</span><span class="p">)</span>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">DFB_phase_shift</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Return DFB phase shift.&quot;&quot;&quot;</span>
+        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_DFB_phase_shift</span>
+
+    <span class="nd">@DFB_phase_shift</span><span class="o">.</span><span class="n">setter</span>
+    <span class="k">def</span> <span class="nf">DFB_phase_shift</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">value</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Set DFB_phase_shift and phase_shift&quot;&quot;&quot;</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">_DFB_phase_shift</span> <span class="o">=</span> <span class="n">value</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">_phase_shift</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">cav_res</span><span class="o">.</span><span class="n">psi</span> <span class="o">-</span> <span class="n">value</span>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">phase_shift</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Return phase shift applied to DFB.</span>
+<span class="sd">        Defined as self.cav_res.psi - self.DFB_phase_shift.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_phase_shift</span>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">DFB_psi</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Return detuning angle value with Direct RF feedback in [rad].</span>
+<span class="sd">    </span>
+<span class="sd">        Fig.4 of ref [1].</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="k">return</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">angle</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">cav_res</span><span class="o">.</span><span class="n">cavity_phasor_record</span><span class="p">))</span> <span class="o">-</span>
+                <span class="n">np</span><span class="o">.</span><span class="n">angle</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">ig_phasor_record</span><span class="p">)))</span>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">DFB_alpha</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Return the amplitude ratio alpha of the DFB.</span>
+<span class="sd">        </span>
+<span class="sd">        Near Eq. (13) of [1].</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="n">fac</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span>
+            <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">DFB_ig_phasor</span><span class="p">)</span> <span class="o">/</span> <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">ig_phasor_record</span><span class="p">))</span>
+        <span class="k">return</span> <span class="mi">20</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">log10</span><span class="p">(</span><span class="n">fac</span><span class="p">)</span>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">DFB_gamma</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Return the gain gamma of the DFB.</span>
+<span class="sd">        </span>
+<span class="sd">        Near Eq. (13) of [1].</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="n">fac</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span>
+            <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">DFB_ig_phasor</span><span class="p">)</span> <span class="o">/</span> <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">ig_phasor_record</span><span class="p">))</span>
+        <span class="k">return</span> <span class="n">fac</span> <span class="o">/</span> <span class="p">(</span><span class="mi">1</span><span class="o">-</span><span class="n">fac</span><span class="p">)</span>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">DFB_Rs</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Return the shunt impedance of the DFB in [ohm].</span>
+<span class="sd">        </span>
+<span class="sd">        Eq. (15) of [1].</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">cav_res</span><span class="o">.</span><span class="n">Rs</span> <span class="o">/</span> <span class="p">(</span><span class="mi">1</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">DFB_gamma</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">DFB_psi</span><span class="p">))</span>
+
+<div class="viewcode-block" id="DirectFeedback.DFB_parameter_set"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.rf.DirectFeedback.DFB_parameter_set">[docs]</a>    <span class="k">def</span> <span class="nf">DFB_parameter_set</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">DFB_gain</span><span class="p">,</span> <span class="n">DFB_phase_shift</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Set DFB gain and phase shift parameters.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        DFB_gain : float</span>
+<span class="sd">            Gain of the DFB.</span>
+<span class="sd">        DFB_phase_shift : float</span>
+<span class="sd">            Phase shift of the DFB.</span>
+
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">DFB_gain</span> <span class="o">=</span> <span class="n">DFB_gain</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">DFB_phase_shift</span> <span class="o">=</span> <span class="n">DFB_phase_shift</span>
+
+        <span class="k">if</span> <span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">cav_res</span><span class="o">.</span><span class="n">beam_phasor</span><span class="p">))</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
+            <span class="n">vc</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">h</span><span class="p">)</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">cav_res</span><span class="o">.</span><span class="n">Vc</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span>
+                <span class="mi">1</span><span class="n">j</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">cav_res</span><span class="o">.</span><span class="n">theta</span><span class="p">)</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="n">vc</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">cav_res</span><span class="o">.</span><span class="n">cavity_phasor_record</span>
+        <span class="n">vg_drf</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">DFB_gain</span> <span class="o">*</span> <span class="n">vc</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="mi">1</span><span class="n">j</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">phase_shift</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">DFB_ig_phasor</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">Vg2Ig</span><span class="p">(</span><span class="n">vg_drf</span><span class="p">)</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">ig_phasor</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">ig_phasor_record</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">DFB_ig_phasor</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">init_FFconst</span><span class="p">()</span></div>
+
+<div class="viewcode-block" id="DirectFeedback.track"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.rf.DirectFeedback.track">[docs]</a>    <span class="k">def</span> <span class="nf">track</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Tracking method for the Direct RF feedback.</span>
+
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        None.</span>
+
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="nb">super</span><span class="p">(</span><span class="n">DirectFeedback</span><span class="p">,</span> <span class="bp">self</span><span class="p">)</span><span class="o">.</span><span class="n">track</span><span class="p">(</span><span class="kc">False</span><span class="p">)</span>
+
+        <span class="n">vc_list</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">(</span>
+            <span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">DFB_vc_previous</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">cav_res</span><span class="o">.</span><span class="n">cavity_phasor_record</span><span class="p">])</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">DFB_ig_phasor</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">roll</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">DFB_ig_phasor</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
+        <span class="k">for</span> <span class="n">index</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">DFB_sample_list</span><span class="p">:</span>
+            <span class="c1"># 2) updating Ig using last item of the list</span>
+            <span class="n">vg_drf</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">DFB_gain</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">DFB_VcRecord</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span>
+                <span class="mi">1</span><span class="n">j</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">phase_shift</span><span class="p">)</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">DFB_ig_phasor</span><span class="p">[</span><span class="n">index</span><span class="p">:]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">Vg2Ig</span><span class="p">(</span><span class="n">vg_drf</span><span class="p">)</span>
+            <span class="c1"># Shift the record</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">DFB_VcRecord</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">roll</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">DFB_VcRecord</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
+            <span class="c1"># 1) recording Vc</span>
+            <span class="n">mean_vc</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">vc_list</span><span class="p">[</span><span class="n">index</span><span class="p">:</span><span class="bp">self</span><span class="o">.</span><span class="n">DFB_sample_num</span> <span class="o">+</span> <span class="n">index</span><span class="p">])</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">DFB_VcRecord</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">mean_vc</span>
+        <span class="c1"># update sample_list for next turn</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">DFB_sample_list</span> <span class="o">=</span> <span class="nb">range</span><span class="p">(</span><span class="n">index</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">DFB_every</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">h</span><span class="p">,</span>
+                                     <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">h</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">DFB_every</span><span class="p">)</span>
+        <span class="c1"># update vc_previous for next turn</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">DFB_vc_previous</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">cav_res</span><span class="o">.</span><span class="n">cavity_phasor_record</span><span class="p">[</span>
+            <span class="o">-</span><span class="bp">self</span><span class="o">.</span><span class="n">DFB_sample_num</span><span class="p">:]</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">ig_phasor_record</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">ig_phasor</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">DFB_ig_phasor</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">Ig2Vg</span><span class="p">()</span></div>
+
+<div class="viewcode-block" id="DirectFeedback.DFB_Vg"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.rf.DirectFeedback.DFB_Vg">[docs]</a>    <span class="k">def</span> <span class="nf">DFB_Vg</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">vc</span><span class="o">=-</span><span class="mi">1</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Return the generator voltage main and DFB components in [V].&quot;&quot;&quot;</span>
+        <span class="k">if</span> <span class="n">vc</span> <span class="o">==</span> <span class="o">-</span><span class="mi">1</span><span class="p">:</span>
+            <span class="n">vc</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">cav_res</span><span class="o">.</span><span class="n">cavity_phasor_record</span><span class="p">)</span>
+        <span class="n">vg_drf</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">DFB_gain</span> <span class="o">*</span> <span class="n">vc</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="mi">1</span><span class="n">j</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">phase_shift</span><span class="p">)</span>
+        <span class="n">vg_main</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">cav_res</span><span class="o">.</span><span class="n">generator_phasor_record</span><span class="p">)</span> <span class="o">-</span> <span class="n">vg_drf</span>
+        <span class="k">return</span> <span class="n">vg_main</span><span class="p">,</span> <span class="n">vg_drf</span></div>
+
+<div class="viewcode-block" id="DirectFeedback.DFB_fs"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.rf.DirectFeedback.DFB_fs">[docs]</a>    <span class="k">def</span> <span class="nf">DFB_fs</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">vg_main</span><span class="o">=-</span><span class="mi">1</span><span class="p">,</span> <span class="n">vg_drf</span><span class="o">=-</span><span class="mi">1</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Return the modified synchrotron frequency in [Hz].&quot;&quot;&quot;</span>
+        <span class="n">vc</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">cav_res</span><span class="o">.</span><span class="n">cavity_phasor_record</span><span class="p">)</span>
+        <span class="k">if</span> <span class="n">vg_drf</span> <span class="o">==</span> <span class="o">-</span><span class="mi">1</span><span class="p">:</span>
+            <span class="n">vg_drf</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">DFB_gain</span> <span class="o">*</span> <span class="n">vc</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="mi">1</span><span class="n">j</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">phase_shift</span><span class="p">)</span>
+        <span class="k">if</span> <span class="n">vg_main</span> <span class="o">==</span> <span class="o">-</span><span class="mi">1</span><span class="p">:</span>
+            <span class="n">vg_main</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">cav_res</span><span class="o">.</span><span class="n">generator_phasor_record</span><span class="p">)</span> <span class="o">-</span> <span class="n">vg_drf</span>
+        <span class="n">vg_sum</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">vg_main</span><span class="p">)</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span>
+            <span class="n">np</span><span class="o">.</span><span class="n">angle</span><span class="p">(</span><span class="n">vg_main</span><span class="p">))</span> <span class="o">+</span> <span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">vg_drf</span><span class="p">)</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">angle</span><span class="p">(</span><span class="n">vg_drf</span><span class="p">))</span>
+        <span class="n">omega_s</span> <span class="o">=</span> <span class="mi">0</span>
+        <span class="k">if</span> <span class="p">(</span><span class="n">vg_sum</span><span class="p">)</span> <span class="o">&gt;</span> <span class="mf">0.0</span><span class="p">:</span>
+            <span class="n">omega_s</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">ac</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">omega1</span> <span class="o">*</span> <span class="p">(</span><span class="n">vg_sum</span><span class="p">)</span> <span class="o">/</span>
+                              <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">E0</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">T0</span><span class="p">)</span>
+        <span class="k">return</span> <span class="n">omega_s</span> <span class="o">/</span> <span class="mi">2</span> <span class="o">/</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span></div></div>
+</pre></div>
+
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+          <li class="nav-item nav-item-1"><a href="../../index.html" accesskey="U">Module code</a> &#187;</li>
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+  <h1>Source code for mbtrack2.tracking.synchrotron</h1><div class="highlight"><pre>
+<span></span><span class="c1"># -*- coding: utf-8 -*-</span>
+<span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">Module where the Synchrotron class is defined.</span>
+<span class="sd">&quot;&quot;&quot;</span>
+
+<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
+<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="kn">from</span> <span class="nn">scipy.constants</span> <span class="kn">import</span> <span class="n">c</span><span class="p">,</span> <span class="n">e</span>
+
+
+<div class="viewcode-block" id="Synchrotron"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.synchrotron.Synchrotron">[docs]</a><span class="k">class</span> <span class="nc">Synchrotron</span><span class="p">:</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    Synchrotron class to store main properties.</span>
+<span class="sd">    </span>
+<span class="sd">    Optional parameters are optional only if the Optics object passed to the </span>
+<span class="sd">    class uses a loaded lattice.</span>
+<span class="sd">    </span>
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">    h : int</span>
+<span class="sd">        Harmonic number of the accelerator.</span>
+<span class="sd">    optics : Optics object</span>
+<span class="sd">        Object where the optic functions are stored.</span>
+<span class="sd">    particle : Particle object</span>
+<span class="sd">        Particle which is accelerated.</span>
+<span class="sd">    tau : array of shape (3,)</span>
+<span class="sd">        Horizontal, vertical and longitudinal damping times in [s].</span>
+<span class="sd">    sigma_delta : float</span>
+<span class="sd">        Equilibrium energy spread.</span>
+<span class="sd">    sigma_0 : float</span>
+<span class="sd">        Natural bunch length in [s].</span>
+<span class="sd">    emit : array of shape (2,)</span>
+<span class="sd">        Horizontal and vertical equilibrium emittance in [m.rad].</span>
+<span class="sd">    L : float, optional</span>
+<span class="sd">        Ring circumference in [m].</span>
+<span class="sd">    E0 : float, optional</span>
+<span class="sd">        Nominal (total) energy of the ring in [eV].</span>
+<span class="sd">    ac : float, optional</span>
+<span class="sd">        Momentum compaction factor.</span>
+<span class="sd">    tune : array of shape (2,), optional</span>
+<span class="sd">        Horizontal and vertical tunes.</span>
+<span class="sd">    chro : array of shape (2,), optional</span>
+<span class="sd">        Horizontal and vertical (non-normalized) chromaticities.</span>
+<span class="sd">    U0 : float, optional</span>
+<span class="sd">        Energy loss per turn in [eV].</span>
+<span class="sd">    adts : list of arrays or None, optional</span>
+<span class="sd">        List that contains arrays of polynomial&#39;s coefficients, in decreasing </span>
+<span class="sd">        powers, used to determine Amplitude-Dependent Tune Shifts (ADTS). </span>
+<span class="sd">        The order of the elements strictly needs to be</span>
+<span class="sd">        [coef_xx, coef_yx, coef_xy, coef_yy], where x and y denote the horizontal</span>
+<span class="sd">        and the vertical plane, respectively, and coef_PQ means the polynomial&#39;s</span>
+<span class="sd">        coefficients of the ADTS in plane P due to the amplitude in plane Q.</span>
+
+<span class="sd">        For example, if the tune shift in y due to the Courant-Snyder invariant </span>
+<span class="sd">        Jx is characterized by the equation dQy(x) = 3*Jx**2 + 2*Jx + 1, then </span>
+<span class="sd">        coef_yx takes the form np.array([3, 2, 1]).</span>
+<span class="sd">        </span>
+<span class="sd">        Use None, to exclude the ADTS from calculation.</span>
+<span class="sd">    mcf_order : array, optional</span>
+<span class="sd">        Higher-orders momentum compaction factor in decreasing powers.</span>
+<span class="sd">        Input here the coefficients considering only the derivatives and which</span>
+<span class="sd">        do not include any factorial factor.</span>
+<span class="sd">        The 1st order should be included in the array and be at the last </span>
+<span class="sd">        position.</span>
+<span class="sd">        </span>
+<span class="sd">    Attributes</span>
+<span class="sd">    ----------</span>
+<span class="sd">    T0 : float</span>
+<span class="sd">        Revolution time in [s].</span>
+<span class="sd">    f0 : float</span>
+<span class="sd">        Revolution frequency in [Hz].</span>
+<span class="sd">    omega0 : float</span>
+<span class="sd">        Angular revolution frequency in [Hz.rad]</span>
+<span class="sd">    T1 : flaot</span>
+<span class="sd">        Fundamental RF period in [s].</span>
+<span class="sd">    f1 : float</span>
+<span class="sd">        Fundamental RF frequency in [Hz].</span>
+<span class="sd">    omega1 : float</span>
+<span class="sd">        Fundamental RF angular frequency in [Hz.rad].</span>
+<span class="sd">    k1 : float</span>
+<span class="sd">        Fundamental RF wave number in [m**-1].</span>
+<span class="sd">    gamma : float</span>
+<span class="sd">        Relativistic Lorentz gamma.</span>
+<span class="sd">    beta : float</span>
+<span class="sd">        Relativistic Lorentz beta.</span>
+<span class="sd">    long_alpha : float</span>
+<span class="sd">        Longitudinal alpha Twiss parameter at the tracking location.</span>
+<span class="sd">        Initialized at zero.</span>
+<span class="sd">    long_beta : float</span>
+<span class="sd">        Longitudinal beta Twiss parameter at the tracking location in [s].</span>
+<span class="sd">        Initialized at zero.</span>
+<span class="sd">    long_gamma : float</span>
+<span class="sd">        Longitudinal gamma Twiss parameter at the tracking location in [s-1].</span>
+<span class="sd">        Initialized at zero.</span>
+<span class="sd">        </span>
+<span class="sd">        </span>
+<span class="sd">    Methods</span>
+<span class="sd">    -------</span>
+<span class="sd">    synchrotron_tune(V)</span>
+<span class="sd">        Compute the (unperturbed) synchrotron tune from main RF voltage.</span>
+<span class="sd">    sigma(position)</span>
+<span class="sd">        Return the RMS beam size at equilibrium in [m].</span>
+<span class="sd">    eta(delta)</span>
+<span class="sd">        Momentum compaction taking into account higher orders if provided in</span>
+<span class="sd">        mcf_order.</span>
+<span class="sd">    mcf(delta)</span>
+<span class="sd">        Momentum compaction factor taking into account higher orders if </span>
+<span class="sd">        provided in mcf_order.</span>
+<span class="sd">    get_adts()</span>
+<span class="sd">        Compute and add Amplitude-Dependent Tune Shifts (ADTS) sextupolar </span>
+<span class="sd">        componenet from AT lattice.</span>
+<span class="sd">    get_mcf_order()</span>
+<span class="sd">        Compute momentum compaction factor up to 3rd order from AT lattice.</span>
+<span class="sd">    get_longitudinal_twiss(V)</span>
+<span class="sd">        Compute the longitudinal Twiss parameters and the synchrotron tune for </span>
+<span class="sd">        single or multi-harmonic RF systems.</span>
+<span class="sd">    to_pyat(Vrf)</span>
+<span class="sd">        Return a pyAT simple_ring element from the Synchrotron element data.</span>
+<span class="sd">    &quot;&quot;&quot;</span>
+
+    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">h</span><span class="p">,</span> <span class="n">optics</span><span class="p">,</span> <span class="n">particle</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">_h</span> <span class="o">=</span> <span class="n">h</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">particle</span> <span class="o">=</span> <span class="n">particle</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">optics</span> <span class="o">=</span> <span class="n">optics</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">long_alpha</span> <span class="o">=</span> <span class="mi">0</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">long_beta</span> <span class="o">=</span> <span class="mi">0</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">long_gamma</span> <span class="o">=</span> <span class="mi">0</span>
+
+        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">optics</span><span class="o">.</span><span class="n">use_local_values</span> <span class="o">==</span> <span class="kc">False</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">L</span> <span class="o">=</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">&#39;L&#39;</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">optics</span><span class="o">.</span><span class="n">lattice</span><span class="o">.</span><span class="n">circumference</span><span class="p">)</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">E0</span> <span class="o">=</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">&#39;E0&#39;</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">optics</span><span class="o">.</span><span class="n">lattice</span><span class="o">.</span><span class="n">energy</span><span class="p">)</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">ac</span> <span class="o">=</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">&#39;ac&#39;</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">optics</span><span class="o">.</span><span class="n">ac</span><span class="p">)</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">tune</span> <span class="o">=</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">&#39;tune&#39;</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">optics</span><span class="o">.</span><span class="n">tune</span><span class="p">)</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">chro</span> <span class="o">=</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">&#39;chro&#39;</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">optics</span><span class="o">.</span><span class="n">chro</span><span class="p">)</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">U0</span> <span class="o">=</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">&#39;U0&#39;</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">optics</span><span class="o">.</span><span class="n">lattice</span><span class="o">.</span><span class="n">energy_loss</span><span class="p">)</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">L</span> <span class="o">=</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">&#39;L&#39;</span><span class="p">)</span>  <span class="c1"># Ring circumference [m]</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">E0</span> <span class="o">=</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span>
+                <span class="s1">&#39;E0&#39;</span><span class="p">)</span>  <span class="c1"># Nominal (total) energy of the ring [eV]</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">ac</span> <span class="o">=</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">&#39;ac&#39;</span><span class="p">)</span>  <span class="c1"># Momentum compaction factor</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">tune</span> <span class="o">=</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">&#39;tune&#39;</span><span class="p">)</span>  <span class="c1"># X/Y/S tunes</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">chro</span> <span class="o">=</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span>
+                <span class="s1">&#39;chro&#39;</span><span class="p">)</span>  <span class="c1"># X/Y (non-normalized) chromaticities</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">U0</span> <span class="o">=</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">&#39;U0&#39;</span><span class="p">)</span>  <span class="c1"># Energy loss per turn [eV]</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">tau</span> <span class="o">=</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">&#39;tau&#39;</span><span class="p">)</span>  <span class="c1"># X/Y/S damping times [s]</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">sigma_delta</span> <span class="o">=</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span>
+            <span class="s1">&#39;sigma_delta&#39;</span><span class="p">)</span>  <span class="c1"># Equilibrium energy spread</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">sigma_0</span> <span class="o">=</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">&#39;sigma_0&#39;</span><span class="p">)</span>  <span class="c1"># Natural bunch length [s]</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">emit</span> <span class="o">=</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">&#39;emit&#39;</span><span class="p">)</span>  <span class="c1"># X/Y emittances in [m.rad]</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">adts</span> <span class="o">=</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">&#39;adts&#39;</span><span class="p">)</span>  <span class="c1"># Amplitude-Dependent Tune Shift (ADTS)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">mcf_order</span> <span class="o">=</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span>
+            <span class="s1">&#39;mcf_order&#39;</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">ac</span><span class="p">)</span>  <span class="c1"># Higher-orders momentum compaction factor</span>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">h</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Harmonic number&quot;&quot;&quot;</span>
+        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_h</span>
+
+    <span class="nd">@h</span><span class="o">.</span><span class="n">setter</span>
+    <span class="k">def</span> <span class="nf">h</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">value</span><span class="p">):</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">_h</span> <span class="o">=</span> <span class="n">value</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">L</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">L</span>  <span class="c1"># call setter</span>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">L</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Ring circumference [m]&quot;&quot;&quot;</span>
+        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_L</span>
+
+    <span class="nd">@L</span><span class="o">.</span><span class="n">setter</span>
+    <span class="k">def</span> <span class="nf">L</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">value</span><span class="p">):</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">_L</span> <span class="o">=</span> <span class="n">value</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">_T0</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">L</span> <span class="o">/</span> <span class="n">c</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">_T1</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">T0</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">h</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">_f0</span> <span class="o">=</span> <span class="mi">1</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">T0</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">_omega0</span> <span class="o">=</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">f0</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">_f1</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">h</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">f0</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">_omega1</span> <span class="o">=</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">f1</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">_k1</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">omega1</span> <span class="o">/</span> <span class="n">c</span>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">T0</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Revolution time [s]&quot;&quot;&quot;</span>
+        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_T0</span>
+
+    <span class="nd">@T0</span><span class="o">.</span><span class="n">setter</span>
+    <span class="k">def</span> <span class="nf">T0</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">value</span><span class="p">):</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">L</span> <span class="o">=</span> <span class="n">c</span> <span class="o">*</span> <span class="n">value</span>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">T1</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;&quot;Fundamental RF period [s]&quot;&quot;&quot;</span>
+        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_T1</span>
+
+    <span class="nd">@T1</span><span class="o">.</span><span class="n">setter</span>
+    <span class="k">def</span> <span class="nf">T1</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">value</span><span class="p">):</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">L</span> <span class="o">=</span> <span class="n">c</span> <span class="o">*</span> <span class="n">value</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">h</span>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">f0</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Revolution frequency [Hz]&quot;&quot;&quot;</span>
+        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_f0</span>
+
+    <span class="nd">@f0</span><span class="o">.</span><span class="n">setter</span>
+    <span class="k">def</span> <span class="nf">f0</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">value</span><span class="p">):</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">L</span> <span class="o">=</span> <span class="n">c</span> <span class="o">/</span> <span class="n">value</span>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">omega0</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Angular revolution frequency [Hz rad]&quot;&quot;&quot;</span>
+        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_omega0</span>
+
+    <span class="nd">@omega0</span><span class="o">.</span><span class="n">setter</span>
+    <span class="k">def</span> <span class="nf">omega0</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">value</span><span class="p">):</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">L</span> <span class="o">=</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="n">c</span> <span class="o">/</span> <span class="n">value</span>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">f1</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Fundamental RF frequency [Hz]&quot;&quot;&quot;</span>
+        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_f1</span>
+
+    <span class="nd">@f1</span><span class="o">.</span><span class="n">setter</span>
+    <span class="k">def</span> <span class="nf">f1</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">value</span><span class="p">):</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">L</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">h</span> <span class="o">*</span> <span class="n">c</span> <span class="o">/</span> <span class="n">value</span>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">omega1</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Fundamental RF angular frequency[Hz rad]&quot;&quot;&quot;</span>
+        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_omega1</span>
+
+    <span class="nd">@omega1</span><span class="o">.</span><span class="n">setter</span>
+    <span class="k">def</span> <span class="nf">omega1</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">value</span><span class="p">):</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">L</span> <span class="o">=</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">h</span> <span class="o">*</span> <span class="n">c</span> <span class="o">/</span> <span class="n">value</span>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">k1</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Fundamental RF wave number [m**-1]&quot;&quot;&quot;</span>
+        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_k1</span>
+
+    <span class="nd">@k1</span><span class="o">.</span><span class="n">setter</span>
+    <span class="k">def</span> <span class="nf">k1</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">value</span><span class="p">):</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">L</span> <span class="o">=</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">h</span> <span class="o">/</span> <span class="n">value</span>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">gamma</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Relativistic gamma&quot;&quot;&quot;</span>
+        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_gamma</span>
+
+    <span class="nd">@gamma</span><span class="o">.</span><span class="n">setter</span>
+    <span class="k">def</span> <span class="nf">gamma</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">value</span><span class="p">):</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">_gamma</span> <span class="o">=</span> <span class="n">value</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">_beta</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="mi">1</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">gamma</span><span class="o">**-</span><span class="mi">2</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">_E0</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">gamma</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">particle</span><span class="o">.</span><span class="n">mass</span> <span class="o">*</span> <span class="n">c</span><span class="o">**</span><span class="mi">2</span> <span class="o">/</span> <span class="n">e</span>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">beta</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Relativistic beta&quot;&quot;&quot;</span>
+        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_beta</span>
+
+    <span class="nd">@beta</span><span class="o">.</span><span class="n">setter</span>
+    <span class="k">def</span> <span class="nf">beta</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">value</span><span class="p">):</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">gamma</span> <span class="o">=</span> <span class="mi">1</span> <span class="o">/</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="mi">1</span> <span class="o">-</span> <span class="n">value</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">E0</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Nominal (total) energy of the ring [eV]&quot;&quot;&quot;</span>
+        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_E0</span>
+
+    <span class="nd">@E0</span><span class="o">.</span><span class="n">setter</span>
+    <span class="k">def</span> <span class="nf">E0</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">value</span><span class="p">):</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">gamma</span> <span class="o">=</span> <span class="n">value</span> <span class="o">/</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">particle</span><span class="o">.</span><span class="n">mass</span> <span class="o">*</span> <span class="n">c</span><span class="o">**</span><span class="mi">2</span> <span class="o">/</span> <span class="n">e</span><span class="p">)</span>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">mcf_order</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Higher-orders momentum compaction factor&quot;&quot;&quot;</span>
+        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_mcf_order</span>
+
+    <span class="nd">@mcf_order</span><span class="o">.</span><span class="n">setter</span>
+    <span class="k">def</span> <span class="nf">mcf_order</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">value</span><span class="p">):</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">_mcf_order</span> <span class="o">=</span> <span class="n">value</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">mcf</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">poly1d</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">mcf_order</span><span class="p">)</span>
+
+<div class="viewcode-block" id="Synchrotron.eta"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.synchrotron.Synchrotron.eta">[docs]</a>    <span class="k">def</span> <span class="nf">eta</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">delta</span><span class="o">=</span><span class="mi">0</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Momentum compaction taking into account higher orders if provided in</span>
+<span class="sd">        mcf_order.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        delta : float or array like bunch[&quot;delta&quot;], optional</span>
+<span class="sd">            Relative energy deviation. The default is 0.</span>
+
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        float or array</span>
+<span class="sd">            Momentum compaction.</span>
+
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">mcf</span><span class="p">(</span><span class="n">delta</span><span class="p">)</span> <span class="o">-</span> <span class="mi">1</span> <span class="o">/</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">gamma</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span></div>
+
+<div class="viewcode-block" id="Synchrotron.sigma"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.synchrotron.Synchrotron.sigma">[docs]</a>    <span class="k">def</span> <span class="nf">sigma</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">position</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Return the RMS beam size at equilibrium in [m].</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        position : float or array, optional</span>
+<span class="sd">            Longitudinal position in [m] where the beam size is computed. </span>
+<span class="sd">            If None, the local values are used.</span>
+
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        sigma : array</span>
+<span class="sd">            RMS beam size in [m] at position location or at local positon if </span>
+<span class="sd">            position is None.</span>
+
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="k">if</span> <span class="n">position</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="n">sigma</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="mi">4</span><span class="p">,</span> <span class="p">))</span>
+            <span class="n">sigma</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="p">(</span>
+                <span class="bp">self</span><span class="o">.</span><span class="n">emit</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">optics</span><span class="o">.</span><span class="n">local_beta</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">+</span>
+                <span class="bp">self</span><span class="o">.</span><span class="n">optics</span><span class="o">.</span><span class="n">local_dispersion</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">**</span><span class="mi">2</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">sigma_delta</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span><span class="o">**</span><span class="mf">0.5</span>
+            <span class="n">sigma</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="p">(</span>
+                <span class="bp">self</span><span class="o">.</span><span class="n">emit</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">optics</span><span class="o">.</span><span class="n">local_gamma</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">+</span>
+                <span class="bp">self</span><span class="o">.</span><span class="n">optics</span><span class="o">.</span><span class="n">local_dispersion</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">**</span><span class="mi">2</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">sigma_delta</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span><span class="o">**</span><span class="mf">0.5</span>
+            <span class="n">sigma</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="o">=</span> <span class="p">(</span>
+                <span class="bp">self</span><span class="o">.</span><span class="n">emit</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">optics</span><span class="o">.</span><span class="n">local_beta</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">+</span>
+                <span class="bp">self</span><span class="o">.</span><span class="n">optics</span><span class="o">.</span><span class="n">local_dispersion</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span><span class="o">**</span><span class="mi">2</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">sigma_delta</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span><span class="o">**</span><span class="mf">0.5</span>
+            <span class="n">sigma</span><span class="p">[</span><span class="mi">3</span><span class="p">]</span> <span class="o">=</span> <span class="p">(</span>
+                <span class="bp">self</span><span class="o">.</span><span class="n">emit</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">optics</span><span class="o">.</span><span class="n">local_gamma</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">+</span>
+                <span class="bp">self</span><span class="o">.</span><span class="n">optics</span><span class="o">.</span><span class="n">local_dispersion</span><span class="p">[</span><span class="mi">3</span><span class="p">]</span><span class="o">**</span><span class="mi">2</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">sigma_delta</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span><span class="o">**</span><span class="mf">0.5</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">position</span><span class="p">,</span> <span class="p">(</span><span class="nb">float</span><span class="p">,</span> <span class="nb">int</span><span class="p">)):</span>
+                <span class="n">n</span> <span class="o">=</span> <span class="mi">1</span>
+            <span class="k">else</span><span class="p">:</span>
+                <span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">position</span><span class="p">)</span>
+            <span class="n">sigma</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="mi">4</span><span class="p">,</span> <span class="n">n</span><span class="p">))</span>
+            <span class="n">sigma</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="p">:]</span> <span class="o">=</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">emit</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">optics</span><span class="o">.</span><span class="n">beta</span><span class="p">(</span><span class="n">position</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span> <span class="o">+</span>
+                           <span class="bp">self</span><span class="o">.</span><span class="n">optics</span><span class="o">.</span><span class="n">dispersion</span><span class="p">(</span><span class="n">position</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span><span class="o">**</span><span class="mi">2</span> <span class="o">*</span>
+                           <span class="bp">self</span><span class="o">.</span><span class="n">sigma_delta</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span><span class="o">**</span><span class="mf">0.5</span>
+            <span class="n">sigma</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="p">:]</span> <span class="o">=</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">emit</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">optics</span><span class="o">.</span><span class="n">gamma</span><span class="p">(</span><span class="n">position</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span> <span class="o">+</span>
+                           <span class="bp">self</span><span class="o">.</span><span class="n">optics</span><span class="o">.</span><span class="n">dispersion</span><span class="p">(</span><span class="n">position</span><span class="p">)[</span><span class="mi">1</span><span class="p">]</span><span class="o">**</span><span class="mi">2</span> <span class="o">*</span>
+                           <span class="bp">self</span><span class="o">.</span><span class="n">sigma_delta</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span><span class="o">**</span><span class="mf">0.5</span>
+            <span class="n">sigma</span><span class="p">[</span><span class="mi">2</span><span class="p">,</span> <span class="p">:]</span> <span class="o">=</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">emit</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">optics</span><span class="o">.</span><span class="n">beta</span><span class="p">(</span><span class="n">position</span><span class="p">)[</span><span class="mi">1</span><span class="p">]</span> <span class="o">+</span>
+                           <span class="bp">self</span><span class="o">.</span><span class="n">optics</span><span class="o">.</span><span class="n">dispersion</span><span class="p">(</span><span class="n">position</span><span class="p">)[</span><span class="mi">2</span><span class="p">]</span><span class="o">**</span><span class="mi">2</span> <span class="o">*</span>
+                           <span class="bp">self</span><span class="o">.</span><span class="n">sigma_delta</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span><span class="o">**</span><span class="mf">0.5</span>
+            <span class="n">sigma</span><span class="p">[</span><span class="mi">3</span><span class="p">,</span> <span class="p">:]</span> <span class="o">=</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">emit</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">optics</span><span class="o">.</span><span class="n">gamma</span><span class="p">(</span><span class="n">position</span><span class="p">)[</span><span class="mi">1</span><span class="p">]</span> <span class="o">+</span>
+                           <span class="bp">self</span><span class="o">.</span><span class="n">optics</span><span class="o">.</span><span class="n">dispersion</span><span class="p">(</span><span class="n">position</span><span class="p">)[</span><span class="mi">3</span><span class="p">]</span><span class="o">**</span><span class="mi">2</span> <span class="o">*</span>
+                           <span class="bp">self</span><span class="o">.</span><span class="n">sigma_delta</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span><span class="o">**</span><span class="mf">0.5</span>
+        <span class="k">return</span> <span class="n">sigma</span></div>
+
+<div class="viewcode-block" id="Synchrotron.synchrotron_tune"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.synchrotron.Synchrotron.synchrotron_tune">[docs]</a>    <span class="k">def</span> <span class="nf">synchrotron_tune</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">V</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Compute the (unperturbed) synchrotron tune from main RF voltage.</span>
+<span class="sd">        </span>
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        V : float</span>
+<span class="sd">            Main RF voltage in [V].</span>
+
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        tuneS : float</span>
+<span class="sd">            Synchrotron tune.</span>
+<span class="sd">            </span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="n">Vsum</span> <span class="o">=</span> <span class="n">V</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">arccos</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">U0</span> <span class="o">/</span> <span class="n">V</span><span class="p">))</span>
+        <span class="n">phi</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arccos</span><span class="p">(</span><span class="mi">1</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">eta</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">h</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">E0</span> <span class="o">*</span> <span class="n">Vsum</span><span class="p">)</span>
+        <span class="n">tuneS</span> <span class="o">=</span> <span class="n">phi</span> <span class="o">/</span> <span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span><span class="p">)</span>
+        <span class="k">return</span> <span class="n">tuneS</span></div>
+
+<div class="viewcode-block" id="Synchrotron.get_adts"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.synchrotron.Synchrotron.get_adts">[docs]</a>    <span class="k">def</span> <span class="nf">get_adts</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Compute and add Amplitude-Dependent Tune Shifts (ADTS) sextupolar </span>
+<span class="sd">        componenet from AT lattice.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="kn">import</span> <span class="nn">at</span>
+        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">optics</span><span class="o">.</span><span class="n">use_local_values</span><span class="p">:</span>
+            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">&quot;ADTS needs to be provided manualy as no AT&quot;</span> <span class="o">+</span>
+                             <span class="s2">&quot; lattice file is loaded.&quot;</span><span class="p">)</span>
+
+        <span class="n">det</span> <span class="o">=</span> <span class="n">at</span><span class="o">.</span><span class="n">physics</span><span class="o">.</span><span class="n">nonlinear</span><span class="o">.</span><span class="n">gen_detuning_elem</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">optics</span><span class="o">.</span><span class="n">lattice</span><span class="p">)</span>
+        <span class="n">coef_xx</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="n">det</span><span class="o">.</span><span class="n">A1</span> <span class="o">/</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">0</span><span class="p">])</span>
+        <span class="n">coef_yx</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="n">det</span><span class="o">.</span><span class="n">A2</span> <span class="o">/</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">0</span><span class="p">])</span>
+        <span class="n">coef_xy</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="n">det</span><span class="o">.</span><span class="n">A2</span> <span class="o">/</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">0</span><span class="p">])</span>
+        <span class="n">coef_yy</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="n">det</span><span class="o">.</span><span class="n">A3</span> <span class="o">/</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">0</span><span class="p">])</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">adts</span> <span class="o">=</span> <span class="p">[</span><span class="n">coef_xx</span><span class="p">,</span> <span class="n">coef_yx</span><span class="p">,</span> <span class="n">coef_xy</span><span class="p">,</span> <span class="n">coef_yy</span><span class="p">]</span></div>
+
+<div class="viewcode-block" id="Synchrotron.get_mcf_order"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.synchrotron.Synchrotron.get_mcf_order">[docs]</a>    <span class="k">def</span> <span class="nf">get_mcf_order</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">add</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span> <span class="n">show_fit</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Compute momentum compaction factor up to 3rd order from AT lattice.</span>
+<span class="sd">        </span>
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        add : bool, optional</span>
+<span class="sd">            If True, add the computed coefficient to the Synchrotron object.</span>
+<span class="sd">            If False, the result is returned.</span>
+<span class="sd">            The default is True.</span>
+<span class="sd">        show_fit : bool, optional</span>
+<span class="sd">            If True, show a plot with the data and fit.</span>
+<span class="sd">            The default is False.</span>
+<span class="sd">            </span>
+<span class="sd">        Return</span>
+<span class="sd">        ------</span>
+<span class="sd">        pvalue : array, optional</span>
+<span class="sd">            Momentum compaction factor up to 3rd order</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="kn">import</span> <span class="nn">at</span>
+        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">optics</span><span class="o">.</span><span class="n">use_local_values</span><span class="p">:</span>
+            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">&quot;ADTS needs to be provided manualy as no AT&quot;</span> <span class="o">+</span>
+                             <span class="s2">&quot; lattice file is loaded.&quot;</span><span class="p">)</span>
+        <span class="n">deltamin</span> <span class="o">=</span> <span class="o">-</span><span class="mf">1e-4</span>
+        <span class="n">deltamax</span> <span class="o">=</span> <span class="mf">1e-4</span>
+
+        <span class="n">delta</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="n">deltamin</span><span class="p">,</span> <span class="n">deltamax</span><span class="p">,</span> <span class="mi">7</span><span class="p">)</span>
+        <span class="n">delta4eval</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="n">deltamin</span><span class="p">,</span> <span class="n">deltamax</span><span class="p">,</span> <span class="mi">21</span><span class="p">)</span>
+        <span class="n">alpha</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros_like</span><span class="p">(</span><span class="n">delta</span><span class="p">)</span>
+
+        <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">delta</span><span class="p">)):</span>
+            <span class="n">alpha</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="n">at</span><span class="o">.</span><span class="n">physics</span><span class="o">.</span><span class="n">revolution</span><span class="o">.</span><span class="n">get_mcf</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">optics</span><span class="o">.</span><span class="n">lattice</span><span class="p">,</span>
+                                                     <span class="n">delta</span><span class="p">[</span><span class="n">i</span><span class="p">])</span>
+        <span class="n">pvalue</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">polyfit</span><span class="p">(</span><span class="n">delta</span><span class="p">,</span> <span class="n">alpha</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
+
+        <span class="k">if</span> <span class="n">show_fit</span><span class="p">:</span>
+            <span class="n">pvalue</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">polyfit</span><span class="p">(</span><span class="n">delta</span><span class="p">,</span> <span class="n">alpha</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
+            <span class="n">palpha</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">polyval</span><span class="p">(</span><span class="n">pvalue</span><span class="p">,</span> <span class="n">delta4eval</span><span class="p">)</span>
+
+            <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">delta</span> <span class="o">*</span> <span class="mi">100</span><span class="p">,</span> <span class="n">alpha</span><span class="p">,</span> <span class="s1">&#39;k.&#39;</span><span class="p">)</span>
+            <span class="n">plt</span><span class="o">.</span><span class="n">grid</span><span class="p">()</span>
+            <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">delta4eval</span> <span class="o">*</span> <span class="mi">100</span><span class="p">,</span> <span class="n">palpha</span><span class="p">,</span> <span class="s1">&#39;r&#39;</span><span class="p">)</span>
+            <span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="s1">&#39;Energy (%)&#39;</span><span class="p">)</span>
+            <span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="s1">&#39;Momemtum compaction factor&#39;</span><span class="p">)</span>
+            <span class="n">plt</span><span class="o">.</span><span class="n">legend</span><span class="p">([</span><span class="s1">&#39;Data&#39;</span><span class="p">,</span> <span class="s1">&#39;polyfit&#39;</span><span class="p">])</span>
+
+        <span class="k">if</span> <span class="n">add</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">mcf_order</span> <span class="o">=</span> <span class="n">pvalue</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="k">return</span> <span class="n">pvalue</span></div>
+
+<div class="viewcode-block" id="Synchrotron.get_longitudinal_twiss"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.synchrotron.Synchrotron.get_longitudinal_twiss">[docs]</a>    <span class="k">def</span> <span class="nf">get_longitudinal_twiss</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">V</span><span class="p">,</span> <span class="n">phase</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">harmonics</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">add</span><span class="o">=</span><span class="kc">True</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Compute the longitudinal Twiss parameters and the synchrotron tune for </span>
+<span class="sd">        single or multi-harmonic RF systems.</span>
+<span class="sd">        </span>
+<span class="sd">        Hypthesis:</span>
+<span class="sd">        - Use the linear approximation (tau ~ 0).</span>
+<span class="sd">        - For higher haromics only, cos(phi) ~ 0 must be true.</span>
+<span class="sd">        </span>
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        V : float or array-like of float</span>
+<span class="sd">            RF voltage in [V].</span>
+<span class="sd">        phase : float or array-like of float, optional</span>
+<span class="sd">            RF phase using cosine convention in [rad].</span>
+<span class="sd">            Default is None.</span>
+<span class="sd">        harmonics : int or array-like of int, optional</span>
+<span class="sd">            Harmonics of the cavities to consider.</span>
+<span class="sd">            Default is None.</span>
+<span class="sd">        add : bool, optional</span>
+<span class="sd">            If True, </span>
+<span class="sd">            </span>
+<span class="sd">        Usage</span>
+<span class="sd">        -----</span>
+<span class="sd">        - If a single voltage value is given, assume a single RF system set at </span>
+<span class="sd">        the synchronous phase.</span>
+<span class="sd">        - If a single pair of voltage/phase value is given, assume a single RF </span>
+<span class="sd">        system at this setting.</span>
+<span class="sd">        - Otherwise, compute the synchrotron tune for a multi-harmonic RF </span>
+<span class="sd">        system.</span>
+<span class="sd">            </span>
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        tuneS : float</span>
+<span class="sd">            Synchrotron tune in the linear approximation.</span>
+<span class="sd">        long_alpha : float</span>
+<span class="sd">            Longitudinal alpha Twiss parameter at the tracking location.</span>
+<span class="sd">        long_beta : float</span>
+<span class="sd">            Longitudinal beta Twiss parameter at the tracking location in [s].   </span>
+<span class="sd">        long_gamma : float</span>
+<span class="sd">            Longitudinal gamma Twiss parameter at the tracking location in [s-1].</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+
+        <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">V</span><span class="p">,</span> <span class="nb">float</span><span class="p">)</span> <span class="ow">or</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">V</span><span class="p">,</span> <span class="nb">int</span><span class="p">):</span>
+            <span class="n">V</span> <span class="o">=</span> <span class="p">[</span><span class="n">V</span><span class="p">]</span>
+            <span class="k">if</span> <span class="n">phase</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+                <span class="n">phase</span> <span class="o">=</span> <span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">arccos</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">U0</span> <span class="o">/</span> <span class="n">V</span><span class="p">[</span><span class="mi">0</span><span class="p">])]</span>
+            <span class="k">elif</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">phase</span><span class="p">,</span> <span class="nb">float</span><span class="p">)</span> <span class="ow">or</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">phase</span><span class="p">,</span> <span class="nb">int</span><span class="p">):</span>
+                <span class="n">phase</span> <span class="o">=</span> <span class="p">[</span><span class="n">phase</span><span class="p">]</span>
+            <span class="k">if</span> <span class="n">harmonics</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+                <span class="n">harmonics</span> <span class="o">=</span> <span class="p">[</span><span class="mi">1</span><span class="p">]</span>
+
+        <span class="k">if</span> <span class="ow">not</span> <span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">V</span><span class="p">)</span> <span class="o">==</span> <span class="nb">len</span><span class="p">(</span><span class="n">phase</span><span class="p">)</span> <span class="o">==</span> <span class="nb">len</span><span class="p">(</span><span class="n">harmonics</span><span class="p">)):</span>
+            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">&quot;You must provide array of the same length for&quot;</span>
+                             <span class="s2">&quot; V, phase and harmonics&quot;</span><span class="p">)</span>
+
+        <span class="n">Vsum</span> <span class="o">=</span> <span class="mi">0</span>
+        <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">V</span><span class="p">)):</span>
+            <span class="n">Vsum</span> <span class="o">+=</span> <span class="n">harmonics</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">*</span> <span class="n">V</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">phase</span><span class="p">[</span><span class="n">i</span><span class="p">])</span>
+        <span class="n">phi</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arccos</span><span class="p">(</span><span class="mi">1</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">eta</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">h</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">E0</span> <span class="o">*</span> <span class="n">Vsum</span><span class="p">)</span>
+        <span class="n">long_alpha</span> <span class="o">=</span> <span class="o">-</span><span class="bp">self</span><span class="o">.</span><span class="n">eta</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">h</span> <span class="o">/</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">E0</span> <span class="o">*</span>
+                                                      <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">phi</span><span class="p">))</span> <span class="o">*</span> <span class="n">Vsum</span>
+        <span class="n">long_beta</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">eta</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">T0</span> <span class="o">/</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">phi</span><span class="p">)</span>
+        <span class="n">long_gamma</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">omega1</span> <span class="o">*</span> <span class="n">Vsum</span> <span class="o">/</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">E0</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">phi</span><span class="p">))</span>
+        <span class="n">tuneS</span> <span class="o">=</span> <span class="n">phi</span> <span class="o">/</span> <span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span><span class="p">)</span>
+        <span class="k">if</span> <span class="n">add</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">tuneS</span> <span class="o">=</span> <span class="n">tuneS</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">long_alpha</span> <span class="o">=</span> <span class="n">long_alpha</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">long_beta</span> <span class="o">=</span> <span class="n">long_beta</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">long_gamma</span> <span class="o">=</span> <span class="n">long_gamma</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="k">return</span> <span class="n">tuneS</span><span class="p">,</span> <span class="n">long_alpha</span><span class="p">,</span> <span class="n">long_beta</span><span class="p">,</span> <span class="n">long_gamma</span></div>
+
+<div class="viewcode-block" id="Synchrotron.to_pyat"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.synchrotron.Synchrotron.to_pyat">[docs]</a>    <span class="k">def</span> <span class="nf">to_pyat</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">Vrf</span><span class="p">,</span> <span class="n">harmonic_number</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">TimeLag</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Return a pyAT simple_ring element from the Synchrotron element data.</span>
+<span class="sd">        </span>
+<span class="sd">        See pyAT documentation for informations about simple_ring.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        Vrf : float or array-like of float</span>
+<span class="sd">            RF Voltage in [V]. If sevral cavities are provided, harmonic_number</span>
+<span class="sd">            and TimeLag should be provided.</span>
+<span class="sd">        harmonic_number : float or array-like of float, optional</span>
+<span class="sd">            Harmonic numbers of the RF cavities. The default is None.</span>
+<span class="sd">        TimeLag : float or array-like of float, optional</span>
+<span class="sd">            Set the timelag of the cavities in pyAT definition. </span>
+<span class="sd">            The default is False.</span>
+
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        at_simple_ring : at.physics.fastring.simple_ring</span>
+<span class="sd">            A pyAT simple_ring element.</span>
+
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="kn">from</span> <span class="nn">at</span> <span class="kn">import</span> <span class="n">simple_ring</span>
+        <span class="n">optics</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">optics</span>
+
+        <span class="k">if</span> <span class="p">(</span><span class="n">harmonic_number</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">)</span> <span class="ow">and</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">Vrf</span><span class="p">,</span> <span class="p">(</span><span class="nb">float</span><span class="p">,</span> <span class="nb">int</span><span class="p">)):</span>
+            <span class="n">harmonic_number</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">h</span>
+
+        <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">Vrf</span><span class="p">,</span> <span class="p">(</span><span class="nb">list</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">)):</span>
+            <span class="k">if</span> <span class="p">(</span><span class="n">harmonic_number</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">)</span> <span class="ow">or</span> <span class="p">(</span><span class="n">TimeLag</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">):</span>
+                <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span>
+                    <span class="s2">&quot;If sevral cavities are provided, &quot;</span>
+                    <span class="s2">&quot;harmonic_number and TimeLag should be provided.&quot;</span><span class="p">)</span>
+
+        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">adts</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="k">try</span><span class="p">:</span>
+                <span class="n">A1</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">adts</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="o">-</span><span class="mi">2</span><span class="p">]</span> <span class="o">*</span> <span class="mi">2</span>
+                <span class="n">A2</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">adts</span><span class="p">[</span><span class="mi">1</span><span class="p">][</span><span class="o">-</span><span class="mi">2</span><span class="p">]</span> <span class="o">*</span> <span class="mi">2</span>
+                <span class="n">A3</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">adts</span><span class="p">[</span><span class="mi">3</span><span class="p">][</span><span class="o">-</span><span class="mi">2</span><span class="p">]</span> <span class="o">*</span> <span class="mi">2</span>
+            <span class="k">except</span> <span class="ne">IndexError</span><span class="p">:</span>
+                <span class="n">A1</span> <span class="o">=</span> <span class="kc">None</span>
+                <span class="n">A2</span> <span class="o">=</span> <span class="kc">None</span>
+                <span class="n">A3</span> <span class="o">=</span> <span class="kc">None</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="n">A1</span> <span class="o">=</span> <span class="kc">None</span>
+            <span class="n">A2</span> <span class="o">=</span> <span class="kc">None</span>
+            <span class="n">A3</span> <span class="o">=</span> <span class="kc">None</span>
+
+        <span class="n">at_simple_ring</span> <span class="o">=</span> <span class="n">simple_ring</span><span class="p">(</span><span class="n">energy</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">E0</span><span class="p">,</span>
+                                     <span class="n">circumference</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">L</span><span class="p">,</span>
+                                     <span class="n">harmonic_number</span><span class="o">=</span><span class="n">harmonic_number</span><span class="p">,</span>
+                                     <span class="n">Qx</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">tune</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span>
+                                     <span class="n">Qy</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">tune</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span>
+                                     <span class="n">Vrf</span><span class="o">=</span><span class="n">Vrf</span><span class="p">,</span>
+                                     <span class="n">alpha</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">ac</span><span class="p">,</span>
+                                     <span class="n">betax</span><span class="o">=</span><span class="n">optics</span><span class="o">.</span><span class="n">local_beta</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span>
+                                     <span class="n">betay</span><span class="o">=</span><span class="n">optics</span><span class="o">.</span><span class="n">local_beta</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span>
+                                     <span class="n">alphax</span><span class="o">=</span><span class="n">optics</span><span class="o">.</span><span class="n">local_alpha</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span>
+                                     <span class="n">alphay</span><span class="o">=</span><span class="n">optics</span><span class="o">.</span><span class="n">local_alpha</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span>
+                                     <span class="n">Qpx</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">chro</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span>
+                                     <span class="n">Qpy</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">chro</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span>
+                                     <span class="n">A1</span><span class="o">=</span><span class="n">A1</span><span class="p">,</span>
+                                     <span class="n">A2</span><span class="o">=</span><span class="n">A2</span><span class="p">,</span>
+                                     <span class="n">A3</span><span class="o">=</span><span class="n">A3</span><span class="p">,</span>
+                                     <span class="n">emitx</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">emit</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span>
+                                     <span class="n">emity</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">emit</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span>
+                                     <span class="n">espread</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">sigma_delta</span><span class="p">,</span>
+                                     <span class="n">taux</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">tau</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">T0</span><span class="p">,</span>
+                                     <span class="n">tauy</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">tau</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">T0</span><span class="p">,</span>
+                                     <span class="n">tauz</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">tau</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">T0</span><span class="p">,</span>
+                                     <span class="n">U0</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">U0</span><span class="p">,</span>
+                                     <span class="n">TimeLag</span><span class="o">=</span><span class="n">TimeLag</span><span class="p">)</span>
+        <span class="k">return</span> <span class="n">at_simple_ring</span></div></div>
+</pre></div>
+
+            <div class="clearer"></div>
+          </div>
+        </div>
+      </div>
+      <div class="sphinxsidebar" role="navigation" aria-label="main navigation">
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+             >modules</a> |</li>
+        <li class="nav-item nav-item-0"><a href="../../../index.html">mbtrack2 0.6.0 documentation</a> &#187;</li>
+          <li class="nav-item nav-item-1"><a href="../../index.html" >Module code</a> &#187;</li>
+        <li class="nav-item nav-item-this"><a href="">mbtrack2.tracking.synchrotron</a></li> 
+      </ul>
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+    <div class="footer" role="contentinfo">
+        &#169; Copyright 2024, A. Gamelin et al.
+      Created using <a href="https://www.sphinx-doc.org/">Sphinx</a> 5.0.2.
+    </div>
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+</html>
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diff --git a/docs/build/html/_modules/mbtrack2/tracking/wakepotential.html b/docs/build/html/_modules/mbtrack2/tracking/wakepotential.html
new file mode 100644
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@@ -0,0 +1,964 @@
+
+<!DOCTYPE html>
+
+<html lang="en">
+  <head>
+    <meta charset="utf-8" />
+    <meta name="viewport" content="width=device-width, initial-scale=1.0" />
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+        <li class="nav-item nav-item-this"><a href="">mbtrack2.tracking.wakepotential</a></li> 
+      </ul>
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+
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+        <div class="bodywrapper">
+          <div class="body" role="main">
+            
+  <h1>Source code for mbtrack2.tracking.wakepotential</h1><div class="highlight"><pre>
+<span></span><span class="c1"># -*- coding: utf-8 -*-</span>
+<span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">This module defines the WakePotential and LongRangeResistiveWall classes which </span>
+<span class="sd">deal with the single bunch and multi-bunch wakes.</span>
+<span class="sd">&quot;&quot;&quot;</span>
+
+<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
+<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="kn">import</span> <span class="nn">pandas</span> <span class="k">as</span> <span class="nn">pd</span>
+<span class="kn">from</span> <span class="nn">scipy</span> <span class="kn">import</span> <span class="n">signal</span>
+<span class="kn">from</span> <span class="nn">scipy.constants</span> <span class="kn">import</span> <span class="n">c</span><span class="p">,</span> <span class="n">mu_0</span><span class="p">,</span> <span class="n">pi</span>
+<span class="kn">from</span> <span class="nn">scipy.interpolate</span> <span class="kn">import</span> <span class="n">interp1d</span>
+
+<span class="kn">from</span> <span class="nn">mbtrack2.tracking.element</span> <span class="kn">import</span> <span class="n">Element</span>
+<span class="kn">from</span> <span class="nn">mbtrack2.utilities.spectrum</span> <span class="kn">import</span> <span class="n">gaussian_bunch</span>
+
+
+<div class="viewcode-block" id="WakePotential"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.wakepotential.WakePotential">[docs]</a><span class="k">class</span> <span class="nc">WakePotential</span><span class="p">(</span><span class="n">Element</span><span class="p">):</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    Compute a wake potential from uniformly sampled wake functions by </span>
+<span class="sd">    performing a convolution with a bunch charge profile.</span>
+<span class="sd">    </span>
+<span class="sd">    Two different time bases are used. The first one is controled by the n_bin</span>
+<span class="sd">    parameter and is used to compute the bunch profile. Then the bunch profile</span>
+<span class="sd">    is interpolated on the wake function time base which is used to perform the</span>
+<span class="sd">    convolution to get the wake potential.</span>
+<span class="sd">    </span>
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">    ring : Synchrotron object</span>
+<span class="sd">    wakefield : Wakefield object</span>
+<span class="sd">        Wakefield object which contains the wake functions to be used. The wake</span>
+<span class="sd">        functions must be uniformly sampled!</span>
+<span class="sd">    n_bin : int, optional</span>
+<span class="sd">        Number of bins for constructing the longitudinal bunch profile.</span>
+<span class="sd">    interp_on_postion : bool, optional</span>
+<span class="sd">        If True, the computed wake potential is interpolated on the exact </span>
+<span class="sd">        particle location. If False, the wake potential is interpolated on the </span>
+<span class="sd">        bin center and each particle of the bin get the same value.</span>
+<span class="sd">        Default is True.</span>
+<span class="sd">        </span>
+<span class="sd">    Attributes</span>
+<span class="sd">    ----------</span>
+<span class="sd">    rho : array of shape (n_bin, )</span>
+<span class="sd">        Bunch charge density profile in the unit [1/s].</span>
+<span class="sd">    Wp : array </span>
+<span class="sd">        Wake potential profile.</span>
+<span class="sd">    Wp_interp : array of shape (mp_number, )</span>
+<span class="sd">        Wake potential, obtained from interpolating Wp, exerted on each macro-particle.</span>
+<span class="sd">    </span>
+<span class="sd">    Methods</span>
+<span class="sd">    -------</span>
+<span class="sd">    charge_density(bunch)</span>
+<span class="sd">        Compute bunch charge density profile in [1/s].</span>
+<span class="sd">    dipole_moment(bunch, plane, tau0)</span>
+<span class="sd">        Return the dipole moment of the bunch computed on the same time array </span>
+<span class="sd">        as the wake function.</span>
+<span class="sd">    prepare_wakefunction(wake_type)</span>
+<span class="sd">        Prepare the wake function of a given wake_type to be used for the wake</span>
+<span class="sd">        potential computation. </span>
+<span class="sd">    get_wakepotential(bunch, wake_type)</span>
+<span class="sd">        Return the wake potential computed on the wake function time array </span>
+<span class="sd">        limited to the bunch profile.</span>
+<span class="sd">    track(bunch)</span>
+<span class="sd">        Tracking method for the element.</span>
+<span class="sd">    plot_last_wake(wake_type)</span>
+<span class="sd">        Plot the last wake potential of a given type computed during the last</span>
+<span class="sd">        call of the track method.</span>
+<span class="sd">    reference_loss(bunch)</span>
+<span class="sd">        Calculate the loss factor and kick factor from the wake potential and </span>
+<span class="sd">        compare it to a reference value assuming a Gaussian bunch computed in </span>
+<span class="sd">        the frequency domain.</span>
+<span class="sd">    check_sampling()</span>
+<span class="sd">        Check if the wake function sampling is uniform.</span>
+<span class="sd">    reduce_sampling(factor)</span>
+<span class="sd">        Reduce wake function samping by an integer factor.</span>
+<span class="sd">        </span>
+<span class="sd">    &quot;&quot;&quot;</span>
+
+    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">ring</span><span class="p">,</span> <span class="n">wakefield</span><span class="p">,</span> <span class="n">n_bin</span><span class="o">=</span><span class="mi">80</span><span class="p">,</span> <span class="n">interp_on_postion</span><span class="o">=</span><span class="kc">True</span><span class="p">):</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">wakefield</span> <span class="o">=</span> <span class="n">wakefield</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">types</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">wakefield</span><span class="o">.</span><span class="n">wake_components</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">n_types</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">wakefield</span><span class="o">.</span><span class="n">wake_components</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">ring</span> <span class="o">=</span> <span class="n">ring</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">n_bin</span> <span class="o">=</span> <span class="n">n_bin</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">check_sampling</span><span class="p">()</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">interp_on_postion</span> <span class="o">=</span> <span class="n">interp_on_postion</span>
+
+        <span class="c1"># Suppress numpy warning for floating-point operations.</span>
+        <span class="n">np</span><span class="o">.</span><span class="n">seterr</span><span class="p">(</span><span class="n">invalid</span><span class="o">=</span><span class="s1">&#39;ignore&#39;</span><span class="p">)</span>
+
+<div class="viewcode-block" id="WakePotential.charge_density"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.wakepotential.WakePotential.charge_density">[docs]</a>    <span class="k">def</span> <span class="nf">charge_density</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">bunch</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Compute bunch charge density profile in [1/s].</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        bunch : Bunch object</span>
+
+<span class="sd">        &quot;&quot;&quot;</span>
+
+        <span class="c1"># Get binning data</span>
+        <span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">,</span> <span class="n">c</span><span class="p">,</span> <span class="n">d</span> <span class="o">=</span> <span class="n">bunch</span><span class="o">.</span><span class="n">binning</span><span class="p">(</span><span class="n">n_bin</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">n_bin</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">bins</span> <span class="o">=</span> <span class="n">a</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">sorted_index</span> <span class="o">=</span> <span class="n">b</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">profile</span> <span class="o">=</span> <span class="n">c</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">center</span> <span class="o">=</span> <span class="n">d</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">bin_size</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">bins</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">bins</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
+
+        <span class="c1"># Compute charge density</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">rho</span> <span class="o">=</span> <span class="n">bunch</span><span class="o">.</span><span class="n">charge_per_mp</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">profile</span> <span class="o">/</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">bin_size</span> <span class="o">*</span>
+                                                         <span class="n">bunch</span><span class="o">.</span><span class="n">charge</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">rho</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">rho</span><span class="p">)</span>
+
+        <span class="c1"># Compute time array</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">tau</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">center</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">dtau</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">tau</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">tau</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
+
+        <span class="c1"># Add N values before and after rho and tau</span>
+        <span class="n">N</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">n_bin</span> <span class="o">/</span> <span class="mi">2</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">tau</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">tau</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">dtau</span> <span class="o">*</span> <span class="n">N</span><span class="p">,</span>
+                             <span class="bp">self</span><span class="o">.</span><span class="n">tau</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">dtau</span> <span class="o">*</span> <span class="n">N</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">dtau</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">rho</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">pad</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">rho</span><span class="p">,</span> <span class="p">(</span><span class="n">N</span><span class="p">,</span> <span class="n">N</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">n_bin</span> <span class="o">%</span> <span class="mi">2</span><span class="p">),</span>
+                          <span class="n">mode</span><span class="o">=</span><span class="s2">&quot;constant&quot;</span><span class="p">,</span>
+                          <span class="n">constant_values</span><span class="o">=</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">))</span>
+
+        <span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">tau</span><span class="p">)</span> <span class="o">!=</span> <span class="nb">len</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">rho</span><span class="p">):</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">tau</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">tau</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">tau</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">dtau</span><span class="p">)</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">tau_mean</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">tau</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">tau</span> <span class="o">-=</span> <span class="bp">self</span><span class="o">.</span><span class="n">tau_mean</span></div>
+
+<div class="viewcode-block" id="WakePotential.dipole_moment"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.wakepotential.WakePotential.dipole_moment">[docs]</a>    <span class="k">def</span> <span class="nf">dipole_moment</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">bunch</span><span class="p">,</span> <span class="n">plane</span><span class="p">,</span> <span class="n">tau0</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Return the dipole moment of the bunch computed on the same time array </span>
+<span class="sd">        as the wake function.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        bunch : Bunch object</span>
+<span class="sd">        plane : str</span>
+<span class="sd">            Plane on which the dipole moment is computed, &quot;x&quot; or &quot;y&quot;.</span>
+<span class="sd">        tau0 : array</span>
+<span class="sd">            Time array on which the dipole moment will be interpolated, in [s].</span>
+
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        dipole : array</span>
+<span class="sd">            Dipole moment of the bunch.</span>
+
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="n">dipole</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">empty</span><span class="p">((</span><span class="bp">self</span><span class="o">.</span><span class="n">n_bin</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="p">))</span>
+        <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">n_bin</span> <span class="o">-</span> <span class="mi">1</span><span class="p">):</span>
+            <span class="n">dipole</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="n">bunch</span><span class="p">[</span><span class="n">plane</span><span class="p">][</span><span class="bp">self</span><span class="o">.</span><span class="n">sorted_index</span> <span class="o">==</span> <span class="n">i</span><span class="p">]</span><span class="o">.</span><span class="n">sum</span><span class="p">()</span>
+        <span class="n">dipole</span> <span class="o">=</span> <span class="n">dipole</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">profile</span>
+        <span class="n">dipole</span><span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">isnan</span><span class="p">(</span><span class="n">dipole</span><span class="p">)]</span> <span class="o">=</span> <span class="mi">0</span>
+
+        <span class="c1"># Add N values to get same size as tau/profile</span>
+        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">n_bin</span> <span class="o">%</span> <span class="mi">2</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
+            <span class="n">N</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">n_bin</span> <span class="o">/</span> <span class="mi">2</span><span class="p">)</span>
+            <span class="n">dipole</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">dipole</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">N</span><span class="p">))</span>
+            <span class="n">dipole</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">insert</span><span class="p">(</span><span class="n">dipole</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">N</span><span class="p">))</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="n">N</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">floor</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">n_bin</span> <span class="o">/</span> <span class="mi">2</span><span class="p">))</span>
+            <span class="n">dipole</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">dipole</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">N</span><span class="p">))</span>
+            <span class="n">dipole</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">insert</span><span class="p">(</span><span class="n">dipole</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">N</span> <span class="o">+</span> <span class="mi">1</span><span class="p">))</span>
+
+        <span class="c1"># Interpole on tau0 to get the same size as W0</span>
+        <span class="n">dipole0</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">interp</span><span class="p">(</span><span class="n">tau0</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">tau</span><span class="p">,</span> <span class="n">dipole</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span>
+
+        <span class="nb">setattr</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="s2">&quot;dipole_&quot;</span> <span class="o">+</span> <span class="n">plane</span><span class="p">,</span> <span class="n">dipole0</span><span class="p">)</span>
+        <span class="k">return</span> <span class="n">dipole0</span></div>
+
+<div class="viewcode-block" id="WakePotential.prepare_wakefunction"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.wakepotential.WakePotential.prepare_wakefunction">[docs]</a>    <span class="k">def</span> <span class="nf">prepare_wakefunction</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">wake_type</span><span class="p">,</span> <span class="n">tau</span><span class="p">,</span> <span class="n">save_data</span><span class="o">=</span><span class="kc">True</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Prepare the wake function of a given wake_type to be used for the wake</span>
+<span class="sd">        potential computation. </span>
+<span class="sd">        </span>
+<span class="sd">        The new time array keeps the same sampling time as given in the </span>
+<span class="sd">        WakeFunction definition but is restricted to the bunch profile time </span>
+<span class="sd">        array.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        wake_type : str</span>
+<span class="sd">            Type of the wake function to prepare: &quot;Wlong&quot;, &quot;Wxdip&quot;, ...</span>
+<span class="sd">        tau : array</span>
+<span class="sd">            Time domain array of the bunch profile in [s].</span>
+<span class="sd">        save_data : bool, optional</span>
+<span class="sd">            If True, the results are saved as atributes.</span>
+
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        tau0 : array</span>
+<span class="sd">            Time base of the wake function in [s].</span>
+<span class="sd">        dtau0 : float</span>
+<span class="sd">            Difference between two points of the wake function time base in </span>
+<span class="sd">            [s].</span>
+<span class="sd">        W0 : array</span>
+<span class="sd">            Wake function array in [V/C] or [V/C/m].</span>
+
+<span class="sd">        &quot;&quot;&quot;</span>
+
+        <span class="n">tau0</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="nb">getattr</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">wakefield</span><span class="p">,</span> <span class="n">wake_type</span><span class="p">)</span><span class="o">.</span><span class="n">data</span><span class="o">.</span><span class="n">index</span><span class="p">)</span>
+        <span class="n">dtau0</span> <span class="o">=</span> <span class="n">tau0</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="n">tau0</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
+        <span class="n">W0</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="nb">getattr</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">wakefield</span><span class="p">,</span> <span class="n">wake_type</span><span class="p">)</span><span class="o">.</span><span class="n">data</span><span class="p">[</span><span class="s2">&quot;real&quot;</span><span class="p">])</span>
+
+        <span class="c1"># Keep only the wake function on the rho window</span>
+        <span class="n">ind</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">all</span><span class="p">([</span><span class="nb">min</span><span class="p">(</span><span class="n">tau</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="mi">0</span><span class="p">)</span> <span class="o">&lt;</span> <span class="n">tau0</span><span class="p">,</span> <span class="nb">max</span><span class="p">(</span><span class="n">tau</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">],</span> <span class="mi">0</span><span class="p">)</span> <span class="o">&gt;</span> <span class="n">tau0</span><span class="p">],</span> <span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
+        <span class="n">tau0</span> <span class="o">=</span> <span class="n">tau0</span><span class="p">[</span><span class="n">ind</span><span class="p">]</span>
+        <span class="n">W0</span> <span class="o">=</span> <span class="n">W0</span><span class="p">[</span><span class="n">ind</span><span class="p">]</span>
+
+        <span class="c1"># Check the wake function window for assymetry</span>
+        <span class="n">assym</span> <span class="o">=</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">tau0</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">])</span> <span class="o">-</span> <span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">tau0</span><span class="p">[</span><span class="mi">0</span><span class="p">]))</span> <span class="o">/</span> <span class="n">dtau0</span>
+        <span class="n">n_assym</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">floor</span><span class="p">(</span><span class="n">assym</span><span class="p">))</span>
+        <span class="k">if</span> <span class="n">np</span><span class="o">.</span><span class="n">floor</span><span class="p">(</span><span class="n">assym</span><span class="p">)</span> <span class="o">&gt;</span> <span class="mi">1</span><span class="p">:</span>
+
+            <span class="c1"># add at head</span>
+            <span class="k">if</span> <span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">tau0</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">])</span> <span class="o">&gt;</span> <span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">tau0</span><span class="p">[</span><span class="mi">0</span><span class="p">]):</span>
+                <span class="n">tau0</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="n">tau0</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">-</span> <span class="n">dtau0</span><span class="o">*</span><span class="n">n_assym</span><span class="p">,</span> <span class="n">tau0</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">+</span> <span class="n">dtau0</span><span class="p">,</span>
+                                 <span class="n">dtau0</span><span class="p">)</span>
+                <span class="n">n_to_add</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">tau0</span><span class="p">)</span> <span class="o">-</span> <span class="nb">len</span><span class="p">(</span><span class="n">W0</span><span class="p">)</span>
+                <span class="n">W0</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">((</span><span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">n_to_add</span><span class="p">),</span> <span class="n">W0</span><span class="p">))</span>
+
+            <span class="c1"># add at tail</span>
+            <span class="k">elif</span> <span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">tau0</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span> <span class="o">&gt;</span> <span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">tau0</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]):</span>
+                <span class="n">tau0</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="n">tau0</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">tau0</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">+</span> <span class="n">dtau0</span> <span class="o">*</span> <span class="p">(</span><span class="n">n_assym</span><span class="o">+</span><span class="mi">1</span><span class="p">),</span>
+                                 <span class="n">dtau0</span><span class="p">)</span>
+                <span class="n">n_to_add</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">tau0</span><span class="p">)</span> <span class="o">-</span> <span class="nb">len</span><span class="p">(</span><span class="n">W0</span><span class="p">)</span>
+                <span class="n">W0</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">((</span><span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">n_to_add</span><span class="p">),</span> <span class="n">W0</span><span class="p">))</span>
+
+        <span class="c1"># Check is the wf is shorter than rho then add zeros</span>
+        <span class="k">if</span> <span class="p">(</span><span class="n">tau0</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">&gt;</span> <span class="n">tau</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span> <span class="ow">or</span> <span class="p">(</span><span class="n">tau0</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">&lt;</span> <span class="n">tau</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]):</span>
+            <span class="n">n</span> <span class="o">=</span> <span class="nb">max</span><span class="p">(</span><span class="nb">int</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">ceil</span><span class="p">((</span><span class="n">tau0</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">-</span> <span class="n">tau</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span> <span class="o">/</span> <span class="n">dtau0</span><span class="p">)),</span>
+                    <span class="nb">int</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">ceil</span><span class="p">((</span><span class="n">tau</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="n">tau0</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">])</span> <span class="o">/</span> <span class="n">dtau0</span><span class="p">)))</span>
+
+            <span class="n">tau0</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="n">tau0</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">-</span> <span class="n">dtau0</span><span class="o">*</span><span class="n">n</span><span class="p">,</span> <span class="n">tau0</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">+</span> <span class="n">dtau0</span> <span class="o">*</span> <span class="p">(</span><span class="n">n</span><span class="o">+</span><span class="mi">1</span><span class="p">),</span>
+                             <span class="n">dtau0</span><span class="p">)</span>
+            <span class="n">W0</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">insert</span><span class="p">(</span><span class="n">W0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">n</span><span class="p">))</span>
+            <span class="n">n_to_add</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">tau0</span><span class="p">)</span> <span class="o">-</span> <span class="nb">len</span><span class="p">(</span><span class="n">W0</span><span class="p">)</span>
+            <span class="n">W0</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">pad</span><span class="p">(</span><span class="n">W0</span><span class="p">,</span> <span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">n_to_add</span><span class="p">),</span>
+                        <span class="n">mode</span><span class="o">=</span><span class="s2">&quot;constant&quot;</span><span class="p">,</span>
+                        <span class="n">constant_values</span><span class="o">=</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">))</span>
+
+        <span class="k">if</span> <span class="n">save_data</span><span class="p">:</span>
+            <span class="nb">setattr</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="s2">&quot;tau0_&quot;</span> <span class="o">+</span> <span class="n">wake_type</span><span class="p">,</span> <span class="n">tau0</span><span class="p">)</span>
+            <span class="nb">setattr</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="s2">&quot;dtau0_&quot;</span> <span class="o">+</span> <span class="n">wake_type</span><span class="p">,</span> <span class="n">dtau0</span><span class="p">)</span>
+            <span class="nb">setattr</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="s2">&quot;W0_&quot;</span> <span class="o">+</span> <span class="n">wake_type</span><span class="p">,</span> <span class="n">W0</span><span class="p">)</span>
+
+        <span class="k">return</span> <span class="p">(</span><span class="n">tau0</span><span class="p">,</span> <span class="n">dtau0</span><span class="p">,</span> <span class="n">W0</span><span class="p">)</span></div>
+
+<div class="viewcode-block" id="WakePotential.get_wakepotential"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.wakepotential.WakePotential.get_wakepotential">[docs]</a>    <span class="k">def</span> <span class="nf">get_wakepotential</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">bunch</span><span class="p">,</span> <span class="n">wake_type</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Return the wake potential computed on the wake function time array </span>
+<span class="sd">        limited to the bunch profile.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        bunch : Bunch object</span>
+<span class="sd">        wake_type : str</span>
+<span class="sd">            Wake function type: &quot;Wlong&quot;, &quot;Wxdip&quot;, ...</span>
+
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        Wp : array</span>
+<span class="sd">            Wake potential.</span>
+
+<span class="sd">        &quot;&quot;&quot;</span>
+
+        <span class="p">(</span><span class="n">tau0</span><span class="p">,</span> <span class="n">dtau0</span><span class="p">,</span> <span class="n">W0</span><span class="p">)</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">prepare_wakefunction</span><span class="p">(</span><span class="n">wake_type</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">tau</span><span class="p">)</span>
+
+        <span class="n">profile0</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">interp</span><span class="p">(</span><span class="n">tau0</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">tau</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">rho</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span>
+
+        <span class="k">if</span> <span class="n">wake_type</span> <span class="o">==</span> <span class="s2">&quot;Wlong&quot;</span> <span class="ow">or</span> <span class="n">wake_type</span> <span class="o">==</span> <span class="s2">&quot;Wxquad&quot;</span> <span class="ow">or</span> <span class="n">wake_type</span> <span class="o">==</span> <span class="s2">&quot;Wyquad&quot;</span> <span class="ow">or</span> <span class="n">wake_type</span> <span class="o">==</span> <span class="s2">&quot;Wxcst&quot;</span> <span class="ow">or</span> <span class="n">wake_type</span> <span class="o">==</span> <span class="s2">&quot;Wycst&quot;</span><span class="p">:</span>
+            <span class="n">Wp</span> <span class="o">=</span> <span class="n">signal</span><span class="o">.</span><span class="n">convolve</span><span class="p">(</span><span class="n">profile0</span><span class="p">,</span> <span class="n">W0</span> <span class="o">*</span> <span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="n">mode</span><span class="o">=</span><span class="s1">&#39;same&#39;</span><span class="p">)</span> <span class="o">*</span> <span class="n">dtau0</span>
+        <span class="k">elif</span> <span class="n">wake_type</span> <span class="o">==</span> <span class="s2">&quot;Wxdip&quot;</span><span class="p">:</span>
+            <span class="n">dipole0</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">dipole_moment</span><span class="p">(</span><span class="n">bunch</span><span class="p">,</span> <span class="s2">&quot;x&quot;</span><span class="p">,</span> <span class="n">tau0</span><span class="p">)</span>
+            <span class="n">Wp</span> <span class="o">=</span> <span class="n">signal</span><span class="o">.</span><span class="n">convolve</span><span class="p">(</span><span class="n">profile0</span> <span class="o">*</span> <span class="n">dipole0</span><span class="p">,</span> <span class="n">W0</span><span class="p">,</span> <span class="n">mode</span><span class="o">=</span><span class="s1">&#39;same&#39;</span><span class="p">)</span> <span class="o">*</span> <span class="n">dtau0</span>
+        <span class="k">elif</span> <span class="n">wake_type</span> <span class="o">==</span> <span class="s2">&quot;Wydip&quot;</span><span class="p">:</span>
+            <span class="n">dipole0</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">dipole_moment</span><span class="p">(</span><span class="n">bunch</span><span class="p">,</span> <span class="s2">&quot;y&quot;</span><span class="p">,</span> <span class="n">tau0</span><span class="p">)</span>
+            <span class="n">Wp</span> <span class="o">=</span> <span class="n">signal</span><span class="o">.</span><span class="n">convolve</span><span class="p">(</span><span class="n">profile0</span> <span class="o">*</span> <span class="n">dipole0</span><span class="p">,</span> <span class="n">W0</span><span class="p">,</span> <span class="n">mode</span><span class="o">=</span><span class="s1">&#39;same&#39;</span><span class="p">)</span> <span class="o">*</span> <span class="n">dtau0</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">&quot;This type of wake is not taken into account.&quot;</span><span class="p">)</span>
+
+        <span class="nb">setattr</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="s2">&quot;profile0_&quot;</span> <span class="o">+</span> <span class="n">wake_type</span><span class="p">,</span> <span class="n">profile0</span><span class="p">)</span>
+        <span class="nb">setattr</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">wake_type</span><span class="p">,</span> <span class="n">Wp</span><span class="p">)</span>
+        <span class="k">return</span> <span class="n">tau0</span><span class="p">,</span> <span class="n">Wp</span></div>
+
+<div class="viewcode-block" id="WakePotential.track"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.wakepotential.WakePotential.track">[docs]</a>    <span class="nd">@Element</span><span class="o">.</span><span class="n">parallel</span>
+    <span class="k">def</span> <span class="nf">track</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">bunch</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Tracking method for the element.</span>
+<span class="sd">        No bunch to bunch interaction, so written for Bunch objects and</span>
+<span class="sd">        @Element.parallel is used to handle Beam objects.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        bunch : Bunch or Beam object.</span>
+<span class="sd">        </span>
+<span class="sd">        &quot;&quot;&quot;</span>
+
+        <span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">bunch</span><span class="p">)</span> <span class="o">!=</span> <span class="mi">0</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">charge_density</span><span class="p">(</span><span class="n">bunch</span><span class="p">)</span>
+            <span class="k">for</span> <span class="n">wake_type</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">types</span><span class="p">:</span>
+                <span class="n">tau0</span><span class="p">,</span> <span class="n">Wp</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">get_wakepotential</span><span class="p">(</span><span class="n">bunch</span><span class="p">,</span> <span class="n">wake_type</span><span class="p">)</span>
+                <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">interp_on_postion</span><span class="p">:</span>
+                    <span class="n">Wp_interp</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">interp</span><span class="p">(</span><span class="n">bunch</span><span class="p">[</span><span class="s2">&quot;tau&quot;</span><span class="p">],</span> <span class="n">tau0</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">tau_mean</span><span class="p">,</span>
+                                          <span class="n">Wp</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span>
+                <span class="k">else</span><span class="p">:</span>
+                    <span class="n">Wp_interp</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">interp</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">center</span><span class="p">,</span> <span class="n">tau0</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">tau_mean</span><span class="p">,</span>
+                                          <span class="n">Wp</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span>
+                    <span class="n">Wp_interp</span> <span class="o">=</span> <span class="n">Wp_interp</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">sorted_index</span><span class="p">]</span>
+                <span class="k">if</span> <span class="n">wake_type</span> <span class="o">==</span> <span class="s2">&quot;Wlong&quot;</span><span class="p">:</span>
+                    <span class="n">bunch</span><span class="p">[</span><span class="s2">&quot;delta&quot;</span><span class="p">]</span> <span class="o">+=</span> <span class="n">Wp_interp</span> <span class="o">*</span> <span class="n">bunch</span><span class="o">.</span><span class="n">charge</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">E0</span>
+                <span class="k">elif</span> <span class="n">wake_type</span> <span class="o">==</span> <span class="s2">&quot;Wxdip&quot;</span><span class="p">:</span>
+                    <span class="n">bunch</span><span class="p">[</span><span class="s2">&quot;xp&quot;</span><span class="p">]</span> <span class="o">+=</span> <span class="n">Wp_interp</span> <span class="o">*</span> <span class="n">bunch</span><span class="o">.</span><span class="n">charge</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">E0</span>
+                <span class="k">elif</span> <span class="n">wake_type</span> <span class="o">==</span> <span class="s2">&quot;Wydip&quot;</span><span class="p">:</span>
+                    <span class="n">bunch</span><span class="p">[</span><span class="s2">&quot;yp&quot;</span><span class="p">]</span> <span class="o">+=</span> <span class="n">Wp_interp</span> <span class="o">*</span> <span class="n">bunch</span><span class="o">.</span><span class="n">charge</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">E0</span>
+                <span class="k">elif</span> <span class="n">wake_type</span> <span class="o">==</span> <span class="s2">&quot;Wxquad&quot;</span><span class="p">:</span>
+                    <span class="n">bunch</span><span class="p">[</span><span class="s2">&quot;xp&quot;</span><span class="p">]</span> <span class="o">+=</span> <span class="p">(</span><span class="n">bunch</span><span class="p">[</span><span class="s2">&quot;x&quot;</span><span class="p">]</span> <span class="o">*</span> <span class="n">Wp_interp</span> <span class="o">*</span> <span class="n">bunch</span><span class="o">.</span><span class="n">charge</span> <span class="o">/</span>
+                                    <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">E0</span><span class="p">)</span>
+                <span class="k">elif</span> <span class="n">wake_type</span> <span class="o">==</span> <span class="s2">&quot;Wyquad&quot;</span><span class="p">:</span>
+                    <span class="n">bunch</span><span class="p">[</span><span class="s2">&quot;yp&quot;</span><span class="p">]</span> <span class="o">+=</span> <span class="p">(</span><span class="n">bunch</span><span class="p">[</span><span class="s2">&quot;y&quot;</span><span class="p">]</span> <span class="o">*</span> <span class="n">Wp_interp</span> <span class="o">*</span> <span class="n">bunch</span><span class="o">.</span><span class="n">charge</span> <span class="o">/</span>
+                                    <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">E0</span><span class="p">)</span>
+                <span class="k">elif</span> <span class="n">wake_type</span> <span class="o">==</span> <span class="s2">&quot;Wxcst&quot;</span><span class="p">:</span>
+                    <span class="n">bunch</span><span class="p">[</span><span class="s2">&quot;xp&quot;</span><span class="p">]</span> <span class="o">+=</span> <span class="n">Wp_interp</span> <span class="o">*</span> <span class="n">bunch</span><span class="o">.</span><span class="n">charge</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">E0</span>
+                <span class="k">elif</span> <span class="n">wake_type</span> <span class="o">==</span> <span class="s2">&quot;Wycst&quot;</span><span class="p">:</span>
+                    <span class="n">bunch</span><span class="p">[</span><span class="s2">&quot;yp&quot;</span><span class="p">]</span> <span class="o">+=</span> <span class="n">Wp_interp</span> <span class="o">*</span> <span class="n">bunch</span><span class="o">.</span><span class="n">charge</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">E0</span></div>
+
+<div class="viewcode-block" id="WakePotential.plot_last_wake"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.wakepotential.WakePotential.plot_last_wake">[docs]</a>    <span class="k">def</span> <span class="nf">plot_last_wake</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span>
+                       <span class="n">wake_type</span><span class="p">,</span>
+                       <span class="n">plot_rho</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span>
+                       <span class="n">plot_dipole</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span>
+                       <span class="n">plot_wake_function</span><span class="o">=</span><span class="kc">True</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Plot the last wake potential of a given type computed during the last</span>
+<span class="sd">        call of the track method.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        wake_type : str</span>
+<span class="sd">            Type of the wake to plot: &quot;Wlong&quot;, &quot;Wxdip&quot;, ...</span>
+<span class="sd">        plot_rho : bool, optional</span>
+<span class="sd">            Plot the normalised bunch profile. The default is True.</span>
+<span class="sd">        plot_dipole : bool, optional</span>
+<span class="sd">            Plot the normalised dipole moment. The default is False.</span>
+<span class="sd">        plot_wake_function : bool, optional</span>
+<span class="sd">            Plot the normalised wake function. The default is True.</span>
+
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        fig : figure</span>
+
+<span class="sd">        &quot;&quot;&quot;</span>
+
+        <span class="n">labels</span> <span class="o">=</span> <span class="p">{</span>
+            <span class="s2">&quot;Wlong&quot;</span><span class="p">:</span> <span class="sa">r</span><span class="s2">&quot;$W_{p,long}$ (V/pC)&quot;</span><span class="p">,</span>
+            <span class="s2">&quot;Wxdip&quot;</span><span class="p">:</span> <span class="sa">r</span><span class="s2">&quot;$W_{p,x}^</span><span class="si">{D}</span><span class="s2"> (V/pC)$&quot;</span><span class="p">,</span>
+            <span class="s2">&quot;Wydip&quot;</span><span class="p">:</span> <span class="sa">r</span><span class="s2">&quot;$W_{p,y}^</span><span class="si">{D}</span><span class="s2"> (V/pC)$&quot;</span><span class="p">,</span>
+            <span class="s2">&quot;Wxquad&quot;</span><span class="p">:</span> <span class="sa">r</span><span class="s2">&quot;$W_{p,x}^</span><span class="si">{Q}</span><span class="s2"> (V/pC/m)$&quot;</span><span class="p">,</span>
+            <span class="s2">&quot;Wyquad&quot;</span><span class="p">:</span> <span class="sa">r</span><span class="s2">&quot;$W_{p,y}^</span><span class="si">{Q}</span><span class="s2"> (V/pC/m)$&quot;</span><span class="p">,</span>
+            <span class="s2">&quot;Wxcst&quot;</span><span class="p">:</span> <span class="sa">r</span><span class="s2">&quot;$W_{p,x}^</span><span class="si">{M}</span><span class="s2">$ (V/pC)&quot;</span><span class="p">,</span>
+            <span class="s2">&quot;Wycst&quot;</span><span class="p">:</span> <span class="sa">r</span><span class="s2">&quot;$W_{p,y}^</span><span class="si">{M}</span><span class="s2">$ (V/pC)&quot;</span><span class="p">,</span>
+        <span class="p">}</span>
+
+        <span class="n">Wp</span> <span class="o">=</span> <span class="nb">getattr</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">wake_type</span><span class="p">)</span>
+        <span class="n">tau0</span> <span class="o">=</span> <span class="nb">getattr</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="s2">&quot;tau0_&quot;</span> <span class="o">+</span> <span class="n">wake_type</span><span class="p">)</span>
+
+        <span class="n">fig</span><span class="p">,</span> <span class="n">ax</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">()</span>
+        <span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">tau0</span> <span class="o">*</span> <span class="mf">1e12</span><span class="p">,</span> <span class="n">Wp</span> <span class="o">*</span> <span class="mf">1e-12</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="n">labels</span><span class="p">[</span><span class="n">wake_type</span><span class="p">])</span>
+        <span class="n">ax</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="s2">&quot;$</span><span class="se">\\</span><span class="s2">tau$ (ps)&quot;</span><span class="p">)</span>
+        <span class="n">ax</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="n">labels</span><span class="p">[</span><span class="n">wake_type</span><span class="p">])</span>
+
+        <span class="k">if</span> <span class="n">plot_rho</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">:</span>
+            <span class="n">profile0</span> <span class="o">=</span> <span class="nb">getattr</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="s2">&quot;profile0_&quot;</span> <span class="o">+</span> <span class="n">wake_type</span><span class="p">)</span>
+            <span class="n">profile_rescaled</span> <span class="o">=</span> <span class="n">profile0</span> <span class="o">/</span> <span class="nb">max</span><span class="p">(</span><span class="n">profile0</span><span class="p">)</span> <span class="o">*</span> <span class="nb">max</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">Wp</span><span class="p">))</span>
+            <span class="n">rho_rescaled</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">rho</span> <span class="o">/</span> <span class="nb">max</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">rho</span><span class="p">)</span> <span class="o">*</span> <span class="nb">max</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">Wp</span><span class="p">))</span>
+            <span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">tau0</span> <span class="o">*</span> <span class="mf">1e12</span><span class="p">,</span>
+                    <span class="n">profile_rescaled</span> <span class="o">*</span> <span class="mf">1e-12</span><span class="p">,</span>
+                    <span class="n">label</span><span class="o">=</span><span class="sa">r</span><span class="s2">&quot;$\rho$ interpolated (a.u.)&quot;</span><span class="p">)</span>
+            <span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">((</span><span class="bp">self</span><span class="o">.</span><span class="n">tau</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">tau_mean</span><span class="p">)</span> <span class="o">*</span> <span class="mf">1e12</span><span class="p">,</span>
+                    <span class="n">rho_rescaled</span> <span class="o">*</span> <span class="mf">1e-12</span><span class="p">,</span>
+                    <span class="n">label</span><span class="o">=</span><span class="sa">r</span><span class="s2">&quot;$\rho$ (a.u.)&quot;</span><span class="p">,</span>
+                    <span class="n">linestyle</span><span class="o">=</span><span class="s1">&#39;dashed&#39;</span><span class="p">)</span>
+            <span class="n">plt</span><span class="o">.</span><span class="n">legend</span><span class="p">()</span>
+
+        <span class="k">if</span> <span class="n">plot_wake_function</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">:</span>
+            <span class="n">W0</span> <span class="o">=</span> <span class="nb">getattr</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="s2">&quot;W0_&quot;</span> <span class="o">+</span> <span class="n">wake_type</span><span class="p">)</span>
+            <span class="n">W0_rescaled</span> <span class="o">=</span> <span class="n">W0</span> <span class="o">/</span> <span class="nb">max</span><span class="p">(</span><span class="n">W0</span><span class="p">)</span> <span class="o">*</span> <span class="nb">max</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">Wp</span><span class="p">))</span>
+            <span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">tau0</span> <span class="o">*</span> <span class="mf">1e12</span><span class="p">,</span>
+                    <span class="n">W0_rescaled</span> <span class="o">*</span> <span class="mf">1e-12</span><span class="p">,</span>
+                    <span class="n">label</span><span class="o">=</span><span class="sa">r</span><span class="s2">&quot;$W_</span><span class="si">{function}</span><span class="s2">$ (a.u.)&quot;</span><span class="p">)</span>
+            <span class="n">plt</span><span class="o">.</span><span class="n">legend</span><span class="p">()</span>
+
+        <span class="k">if</span> <span class="n">plot_dipole</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">:</span>
+            <span class="n">dipole</span> <span class="o">=</span> <span class="nb">getattr</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="s2">&quot;dipole_&quot;</span> <span class="o">+</span> <span class="n">wake_type</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
+            <span class="n">dipole_rescaled</span> <span class="o">=</span> <span class="n">dipole</span> <span class="o">/</span> <span class="nb">max</span><span class="p">(</span><span class="n">dipole</span><span class="p">)</span> <span class="o">*</span> <span class="nb">max</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">Wp</span><span class="p">))</span>
+            <span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">tau0</span> <span class="o">*</span> <span class="mf">1e12</span><span class="p">,</span>
+                    <span class="n">dipole_rescaled</span> <span class="o">*</span> <span class="mf">1e-12</span><span class="p">,</span>
+                    <span class="n">label</span><span class="o">=</span><span class="sa">r</span><span class="s2">&quot;Dipole moment (a.u.)&quot;</span><span class="p">)</span>
+            <span class="n">plt</span><span class="o">.</span><span class="n">legend</span><span class="p">()</span>
+
+        <span class="k">return</span> <span class="n">fig</span></div>
+
+<div class="viewcode-block" id="WakePotential.get_gaussian_wakepotential"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.wakepotential.WakePotential.get_gaussian_wakepotential">[docs]</a>    <span class="k">def</span> <span class="nf">get_gaussian_wakepotential</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">sigma</span><span class="p">,</span> <span class="n">wake_type</span><span class="p">,</span> <span class="n">dipole</span><span class="o">=</span><span class="mf">1e-3</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Return the wake potential computed using a perfect gaussian profile.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        sigma : float</span>
+<span class="sd">            RMS bunch length in [s].</span>
+<span class="sd">        wake_type : str</span>
+<span class="sd">            Wake function type: &quot;Wlong&quot;, &quot;Wxdip&quot;, ...</span>
+<span class="sd">        dipole : float, optional</span>
+<span class="sd">            Dipole moment to consider in [m], (uniform dipole moment).</span>
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        tau0 : array</span>
+<span class="sd">            Time base in [s].</span>
+<span class="sd">        W0 : array</span>
+<span class="sd">            Wake function.</span>
+<span class="sd">        Wp : array</span>
+<span class="sd">            Wake potential.</span>
+<span class="sd">        profile0 : array</span>
+<span class="sd">            Gaussian bunch profile.</span>
+<span class="sd">        dipole0 : array</span>
+<span class="sd">            Dipole moment.</span>
+
+<span class="sd">        &quot;&quot;&quot;</span>
+
+        <span class="n">tau</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="o">-</span><span class="mi">10</span> <span class="o">*</span> <span class="n">sigma</span><span class="p">,</span> <span class="mi">10</span> <span class="o">*</span> <span class="n">sigma</span><span class="p">,</span> <span class="nb">int</span><span class="p">(</span><span class="mf">1e3</span><span class="p">))</span>
+        <span class="p">(</span><span class="n">tau0</span><span class="p">,</span> <span class="n">dtau0</span><span class="p">,</span> <span class="n">W0</span><span class="p">)</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">prepare_wakefunction</span><span class="p">(</span><span class="n">wake_type</span><span class="p">,</span> <span class="n">tau</span><span class="p">,</span> <span class="kc">False</span><span class="p">)</span>
+
+        <span class="n">profile0</span> <span class="o">=</span> <span class="n">gaussian_bunch</span><span class="p">(</span><span class="n">tau0</span><span class="p">,</span> <span class="n">sigma</span><span class="p">)</span>
+        <span class="n">dipole0</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">ones_like</span><span class="p">(</span><span class="n">profile0</span><span class="p">)</span> <span class="o">*</span> <span class="n">dipole</span>
+
+        <span class="k">if</span> <span class="n">wake_type</span> <span class="o">==</span> <span class="s2">&quot;Wlong&quot;</span> <span class="ow">or</span> <span class="n">wake_type</span> <span class="o">==</span> <span class="s2">&quot;Wxquad&quot;</span> <span class="ow">or</span> <span class="n">wake_type</span> <span class="o">==</span> <span class="s2">&quot;Wyquad&quot;</span><span class="p">:</span>
+            <span class="n">Wp</span> <span class="o">=</span> <span class="n">signal</span><span class="o">.</span><span class="n">convolve</span><span class="p">(</span><span class="n">profile0</span><span class="p">,</span> <span class="n">W0</span> <span class="o">*</span> <span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="n">mode</span><span class="o">=</span><span class="s1">&#39;same&#39;</span><span class="p">)</span> <span class="o">*</span> <span class="n">dtau0</span>
+        <span class="k">elif</span> <span class="n">wake_type</span> <span class="o">==</span> <span class="s2">&quot;Wxdip&quot;</span><span class="p">:</span>
+            <span class="n">Wp</span> <span class="o">=</span> <span class="n">signal</span><span class="o">.</span><span class="n">convolve</span><span class="p">(</span><span class="n">profile0</span> <span class="o">*</span> <span class="n">dipole0</span><span class="p">,</span> <span class="n">W0</span><span class="p">,</span> <span class="n">mode</span><span class="o">=</span><span class="s1">&#39;same&#39;</span><span class="p">)</span> <span class="o">*</span> <span class="n">dtau0</span>
+        <span class="k">elif</span> <span class="n">wake_type</span> <span class="o">==</span> <span class="s2">&quot;Wydip&quot;</span><span class="p">:</span>
+            <span class="n">Wp</span> <span class="o">=</span> <span class="n">signal</span><span class="o">.</span><span class="n">convolve</span><span class="p">(</span><span class="n">profile0</span> <span class="o">*</span> <span class="n">dipole0</span><span class="p">,</span> <span class="n">W0</span><span class="p">,</span> <span class="n">mode</span><span class="o">=</span><span class="s1">&#39;same&#39;</span><span class="p">)</span> <span class="o">*</span> <span class="n">dtau0</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">&quot;This type of wake is not taken into account.&quot;</span><span class="p">)</span>
+
+        <span class="k">return</span> <span class="n">tau0</span><span class="p">,</span> <span class="n">W0</span><span class="p">,</span> <span class="n">Wp</span><span class="p">,</span> <span class="n">profile0</span><span class="p">,</span> <span class="n">dipole0</span></div>
+
+<div class="viewcode-block" id="WakePotential.plot_gaussian_wake"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.wakepotential.WakePotential.plot_gaussian_wake">[docs]</a>    <span class="k">def</span> <span class="nf">plot_gaussian_wake</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span>
+                           <span class="n">sigma</span><span class="p">,</span>
+                           <span class="n">wake_type</span><span class="p">,</span>
+                           <span class="n">dipole</span><span class="o">=</span><span class="mf">1e-3</span><span class="p">,</span>
+                           <span class="n">plot_rho</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span>
+                           <span class="n">plot_dipole</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span>
+                           <span class="n">plot_wake_function</span><span class="o">=</span><span class="kc">True</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Plot the wake potential of a given type for a perfect gaussian bunch.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        sigma : float</span>
+<span class="sd">            RMS bunch length in [s].</span>
+<span class="sd">        wake_type : str</span>
+<span class="sd">            Type of the wake to plot: &quot;Wlong&quot;, &quot;Wxdip&quot;, ...</span>
+<span class="sd">        dipole : float, optional</span>
+<span class="sd">            Dipole moment to consider in [m], (uniform dipole moment).</span>
+<span class="sd">        plot_rho : bool, optional</span>
+<span class="sd">            Plot the normalised bunch profile. The default is True.</span>
+<span class="sd">        plot_dipole : bool, optional</span>
+<span class="sd">            Plot the normalised dipole moment. The default is False.</span>
+<span class="sd">        plot_wake_function : bool, optional</span>
+<span class="sd">            Plot the normalised wake function. The default is True.</span>
+
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        fig : figure</span>
+
+<span class="sd">        &quot;&quot;&quot;</span>
+
+        <span class="n">labels</span> <span class="o">=</span> <span class="p">{</span>
+            <span class="s2">&quot;Wlong&quot;</span><span class="p">:</span> <span class="sa">r</span><span class="s2">&quot;$W_{p,long}$ (V/pC)&quot;</span><span class="p">,</span>
+            <span class="s2">&quot;Wxdip&quot;</span><span class="p">:</span> <span class="sa">r</span><span class="s2">&quot;$W_{p,x}^</span><span class="si">{D}</span><span class="s2"> (V/pC)$&quot;</span><span class="p">,</span>
+            <span class="s2">&quot;Wydip&quot;</span><span class="p">:</span> <span class="sa">r</span><span class="s2">&quot;$W_{p,y}^</span><span class="si">{D}</span><span class="s2"> (V/pC)$&quot;</span><span class="p">,</span>
+            <span class="s2">&quot;Wxquad&quot;</span><span class="p">:</span> <span class="sa">r</span><span class="s2">&quot;$W_{p,x}^</span><span class="si">{Q}</span><span class="s2"> (V/pC/m)$&quot;</span><span class="p">,</span>
+            <span class="s2">&quot;Wyquad&quot;</span><span class="p">:</span> <span class="sa">r</span><span class="s2">&quot;$W_{p,y}^</span><span class="si">{Q}</span><span class="s2"> (V/pC/m)$&quot;</span>
+        <span class="p">}</span>
+
+        <span class="n">tau0</span><span class="p">,</span> <span class="n">W0</span><span class="p">,</span> <span class="n">Wp</span><span class="p">,</span> <span class="n">profile0</span><span class="p">,</span> <span class="n">dipole0</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">get_gaussian_wakepotential</span><span class="p">(</span>
+            <span class="n">sigma</span><span class="p">,</span> <span class="n">wake_type</span><span class="p">,</span> <span class="n">dipole</span><span class="p">)</span>
+
+        <span class="n">fig</span><span class="p">,</span> <span class="n">ax</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">()</span>
+        <span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">tau0</span> <span class="o">*</span> <span class="mf">1e12</span><span class="p">,</span> <span class="n">Wp</span> <span class="o">*</span> <span class="mf">1e-12</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="n">labels</span><span class="p">[</span><span class="n">wake_type</span><span class="p">])</span>
+        <span class="n">ax</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="s2">&quot;$</span><span class="se">\\</span><span class="s2">tau$ (ps)&quot;</span><span class="p">)</span>
+        <span class="n">ax</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="n">labels</span><span class="p">[</span><span class="n">wake_type</span><span class="p">])</span>
+
+        <span class="k">if</span> <span class="n">plot_rho</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">:</span>
+            <span class="n">profile_rescaled</span> <span class="o">=</span> <span class="n">profile0</span> <span class="o">/</span> <span class="nb">max</span><span class="p">(</span><span class="n">profile0</span><span class="p">)</span> <span class="o">*</span> <span class="nb">max</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">Wp</span><span class="p">))</span>
+            <span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">tau0</span> <span class="o">*</span> <span class="mf">1e12</span><span class="p">,</span>
+                    <span class="n">profile_rescaled</span> <span class="o">*</span> <span class="mf">1e-12</span><span class="p">,</span>
+                    <span class="n">label</span><span class="o">=</span><span class="sa">r</span><span class="s2">&quot;$\rho$ (a.u.)&quot;</span><span class="p">)</span>
+            <span class="n">plt</span><span class="o">.</span><span class="n">legend</span><span class="p">()</span>
+
+        <span class="k">if</span> <span class="n">plot_wake_function</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">:</span>
+            <span class="n">W0_rescaled</span> <span class="o">=</span> <span class="n">W0</span> <span class="o">/</span> <span class="nb">max</span><span class="p">(</span><span class="n">W0</span><span class="p">)</span> <span class="o">*</span> <span class="nb">max</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">Wp</span><span class="p">))</span>
+            <span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">tau0</span> <span class="o">*</span> <span class="mf">1e12</span><span class="p">,</span>
+                    <span class="n">W0_rescaled</span> <span class="o">*</span> <span class="mf">1e-12</span><span class="p">,</span>
+                    <span class="n">label</span><span class="o">=</span><span class="sa">r</span><span class="s2">&quot;$W_</span><span class="si">{function}</span><span class="s2">$ (a.u.)&quot;</span><span class="p">)</span>
+            <span class="n">plt</span><span class="o">.</span><span class="n">legend</span><span class="p">()</span>
+
+        <span class="k">if</span> <span class="n">plot_dipole</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">:</span>
+            <span class="n">dipole_rescaled</span> <span class="o">=</span> <span class="n">dipole0</span> <span class="o">/</span> <span class="nb">max</span><span class="p">(</span><span class="n">dipole0</span><span class="p">)</span> <span class="o">*</span> <span class="nb">max</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">Wp</span><span class="p">))</span>
+            <span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">tau0</span> <span class="o">*</span> <span class="mf">1e12</span><span class="p">,</span>
+                    <span class="n">dipole_rescaled</span> <span class="o">*</span> <span class="mf">1e-12</span><span class="p">,</span>
+                    <span class="n">label</span><span class="o">=</span><span class="sa">r</span><span class="s2">&quot;Dipole moment (a.u.)&quot;</span><span class="p">)</span>
+            <span class="n">plt</span><span class="o">.</span><span class="n">legend</span><span class="p">()</span>
+
+        <span class="k">return</span> <span class="n">fig</span></div>
+
+<div class="viewcode-block" id="WakePotential.reference_loss"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.wakepotential.WakePotential.reference_loss">[docs]</a>    <span class="k">def</span> <span class="nf">reference_loss</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">bunch</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Calculate the loss factor and kick factor from the wake potential and </span>
+<span class="sd">        compare it to a reference value assuming a Gaussian bunch computed in </span>
+<span class="sd">        the frequency domain.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        bunch : Bunch object</span>
+
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        loss_data : DataFrame</span>
+<span class="sd">            An output showing the loss/kick factors compared to the reference </span>
+<span class="sd">            values.</span>
+
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="n">loss</span> <span class="o">=</span> <span class="p">[]</span>
+        <span class="n">loss_0</span> <span class="o">=</span> <span class="p">[]</span>
+        <span class="n">delta_loss</span> <span class="o">=</span> <span class="p">[]</span>
+        <span class="n">index</span> <span class="o">=</span> <span class="p">[]</span>
+        <span class="k">for</span> <span class="n">wake_type</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">types</span><span class="p">:</span>
+            <span class="n">tau0</span><span class="p">,</span> <span class="n">Wp</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">get_wakepotential</span><span class="p">(</span><span class="n">bunch</span><span class="p">,</span> <span class="n">wake_type</span><span class="p">)</span>
+            <span class="n">profile0</span> <span class="o">=</span> <span class="nb">getattr</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="s2">&quot;profile0_&quot;</span> <span class="o">+</span> <span class="n">wake_type</span><span class="p">)</span>
+            <span class="n">factorTD</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">trapz</span><span class="p">(</span><span class="n">Wp</span> <span class="o">*</span> <span class="n">profile0</span><span class="p">,</span> <span class="n">tau0</span><span class="p">)</span>
+
+            <span class="k">if</span> <span class="n">wake_type</span> <span class="o">==</span> <span class="s2">&quot;Wlong&quot;</span><span class="p">:</span>
+                <span class="n">factorTD</span> <span class="o">*=</span> <span class="o">-</span><span class="mi">1</span>
+            <span class="k">if</span> <span class="n">wake_type</span> <span class="o">==</span> <span class="s2">&quot;Wxdip&quot;</span><span class="p">:</span>
+                <span class="n">factorTD</span> <span class="o">/=</span> <span class="n">bunch</span><span class="p">[</span><span class="s2">&quot;x&quot;</span><span class="p">]</span><span class="o">.</span><span class="n">mean</span><span class="p">()</span>
+            <span class="k">if</span> <span class="n">wake_type</span> <span class="o">==</span> <span class="s2">&quot;Wydip&quot;</span><span class="p">:</span>
+                <span class="n">factorTD</span> <span class="o">/=</span> <span class="n">bunch</span><span class="p">[</span><span class="s2">&quot;y&quot;</span><span class="p">]</span><span class="o">.</span><span class="n">mean</span><span class="p">()</span>
+
+            <span class="n">Z</span> <span class="o">=</span> <span class="nb">getattr</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">wakefield</span><span class="p">,</span> <span class="s2">&quot;Z&quot;</span> <span class="o">+</span> <span class="n">wake_type</span><span class="p">[</span><span class="mi">1</span><span class="p">:])</span>
+            <span class="n">sigma</span> <span class="o">=</span> <span class="n">bunch</span><span class="p">[</span><span class="s1">&#39;tau&#39;</span><span class="p">]</span><span class="o">.</span><span class="n">std</span><span class="p">()</span>
+            <span class="n">factorFD</span> <span class="o">=</span> <span class="n">Z</span><span class="o">.</span><span class="n">loss_factor</span><span class="p">(</span><span class="n">sigma</span><span class="p">)</span>
+
+            <span class="n">loss</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">factorTD</span><span class="p">)</span>
+            <span class="n">loss_0</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">factorFD</span><span class="p">)</span>
+            <span class="n">delta_loss</span><span class="o">.</span><span class="n">append</span><span class="p">((</span><span class="n">factorTD</span><span class="o">-</span><span class="n">factorFD</span><span class="p">)</span> <span class="o">/</span> <span class="n">factorFD</span> <span class="o">*</span> <span class="mi">100</span><span class="p">)</span>
+            <span class="k">if</span> <span class="n">wake_type</span> <span class="o">==</span> <span class="s2">&quot;Wlong&quot;</span><span class="p">:</span>
+                <span class="n">index</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="s2">&quot;Wlong [V/C]&quot;</span><span class="p">)</span>
+            <span class="k">else</span><span class="p">:</span>
+                <span class="n">index</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">wake_type</span> <span class="o">+</span> <span class="s2">&quot; [V/C/m]&quot;</span><span class="p">)</span>
+
+            <span class="n">column</span> <span class="o">=</span> <span class="p">[</span><span class="s1">&#39;TD factor&#39;</span><span class="p">,</span> <span class="s1">&#39;FD factor&#39;</span><span class="p">,</span> <span class="s1">&#39;Relative error [%]&#39;</span><span class="p">]</span>
+
+        <span class="n">loss_data</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">DataFrame</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="n">loss</span><span class="p">,</span> <span class="n">loss_0</span><span class="p">,</span> <span class="n">delta_loss</span><span class="p">])</span><span class="o">.</span><span class="n">T</span><span class="p">,</span>
+                                 <span class="n">columns</span><span class="o">=</span><span class="n">column</span><span class="p">,</span>
+                                 <span class="n">index</span><span class="o">=</span><span class="n">index</span><span class="p">)</span>
+        <span class="k">return</span> <span class="n">loss_data</span></div>
+
+<div class="viewcode-block" id="WakePotential.check_sampling"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.wakepotential.WakePotential.check_sampling">[docs]</a>    <span class="k">def</span> <span class="nf">check_sampling</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Check if the wake function sampling is uniform.</span>
+
+<span class="sd">        Raises</span>
+<span class="sd">        ------</span>
+<span class="sd">        ValueError</span>
+
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="k">for</span> <span class="n">wake_type</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">types</span><span class="p">:</span>
+            <span class="n">idx</span> <span class="o">=</span> <span class="nb">getattr</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">wakefield</span><span class="p">,</span> <span class="n">wake_type</span><span class="p">)</span><span class="o">.</span><span class="n">data</span><span class="o">.</span><span class="n">index</span>
+            <span class="n">diff</span> <span class="o">=</span> <span class="n">idx</span><span class="p">[</span><span class="mi">1</span><span class="p">:]</span> <span class="o">-</span> <span class="n">idx</span><span class="p">[:</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
+            <span class="n">result</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">all</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">isclose</span><span class="p">(</span><span class="n">diff</span><span class="p">,</span> <span class="n">diff</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">atol</span><span class="o">=</span><span class="mf">1e-15</span><span class="p">))</span>
+            <span class="k">if</span> <span class="n">result</span> <span class="ow">is</span> <span class="kc">False</span><span class="p">:</span>
+                <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span>
+                    <span class="s2">&quot;The wake function must be uniformly sampled.&quot;</span><span class="p">)</span></div>
+
+<div class="viewcode-block" id="WakePotential.reduce_sampling"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.wakepotential.WakePotential.reduce_sampling">[docs]</a>    <span class="k">def</span> <span class="nf">reduce_sampling</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">factor</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Reduce wake function samping by an integer factor.</span>
+<span class="sd">        </span>
+<span class="sd">        Used to reduce computation time for long bunches.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        factor : int</span>
+
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="k">for</span> <span class="n">wake_type</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">types</span><span class="p">:</span>
+            <span class="n">idx</span> <span class="o">=</span> <span class="nb">getattr</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">wakefield</span><span class="p">,</span> <span class="n">wake_type</span><span class="p">)</span><span class="o">.</span><span class="n">data</span><span class="o">.</span><span class="n">index</span><span class="p">[::</span><span class="n">factor</span><span class="p">]</span>
+            <span class="nb">getattr</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">wakefield</span><span class="p">,</span>
+                    <span class="n">wake_type</span><span class="p">)</span><span class="o">.</span><span class="n">data</span> <span class="o">=</span> <span class="nb">getattr</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">wakefield</span><span class="p">,</span>
+                                              <span class="n">wake_type</span><span class="p">)</span><span class="o">.</span><span class="n">data</span><span class="o">.</span><span class="n">loc</span><span class="p">[</span><span class="n">idx</span><span class="p">]</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">check_sampling</span><span class="p">()</span></div></div>
+
+
+<div class="viewcode-block" id="LongRangeResistiveWall"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.wakepotential.LongRangeResistiveWall">[docs]</a><span class="k">class</span> <span class="nc">LongRangeResistiveWall</span><span class="p">(</span><span class="n">Element</span><span class="p">):</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    Element to deal with multi-bunch and multi-turn wakes from resistive wall </span>
+<span class="sd">    using the algorithm defined in [1].</span>
+<span class="sd">    </span>
+<span class="sd">    Main approximations:</span>
+<span class="sd">        - Bunches are treated as point charge.</span>
+<span class="sd">        - Assymptotic expression for the resistive wall wake functions are </span>
+<span class="sd">        used.</span>
+<span class="sd">        - Multi-turn wakes are limited to nt turns.</span>
+<span class="sd">    </span>
+<span class="sd">    Self-bunch interaction is not included in this element and should be dealed</span>
+<span class="sd">    with the WakePotential class.</span>
+<span class="sd">    </span>
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">    ring : Synchrotron object</span>
+<span class="sd">    beam : Beam object</span>
+<span class="sd">    length : float</span>
+<span class="sd">        Length of the resistive pipe to consider in [m].</span>
+<span class="sd">    rho : float</span>
+<span class="sd">        Effective resistivity to consider in [ohm.m] as in [1].</span>
+<span class="sd">    radius : float</span>
+<span class="sd">        Beam pipe radius to consider in [m].</span>
+<span class="sd">    types : str or list, optional</span>
+<span class="sd">        Wake types to consider. </span>
+<span class="sd">        The default is [&quot;Wlong&quot;,&quot;Wxdip&quot;,&quot;Wydip&quot;].</span>
+<span class="sd">    nt : int or float, optional</span>
+<span class="sd">        Number of turns to consider for the long range wakes. </span>
+<span class="sd">        The default is 50.</span>
+<span class="sd">    x3 : float, optional</span>
+<span class="sd">        Horizontal effective radius of the 3rd power in [m], as Eq.27 in [1].</span>
+<span class="sd">        The default is radius.</span>
+<span class="sd">    y3 : float, optional</span>
+<span class="sd">        Vertical effective radius of the 3rd power in [m], as Eq.27 in [1].</span>
+<span class="sd">        The default is radius.</span>
+<span class="sd">    </span>
+<span class="sd">    References</span>
+<span class="sd">    ----------</span>
+<span class="sd">    [1] : Skripka, Galina, et al. &quot;Simultaneous computation of intrabunch and </span>
+<span class="sd">    interbunch collective beam motions in storage rings.&quot; NIM.A (2016).</span>
+<span class="sd">    &quot;&quot;&quot;</span>
+
+    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span>
+                 <span class="n">ring</span><span class="p">,</span>
+                 <span class="n">beam</span><span class="p">,</span>
+                 <span class="n">length</span><span class="p">,</span>
+                 <span class="n">rho</span><span class="p">,</span>
+                 <span class="n">radius</span><span class="p">,</span>
+                 <span class="n">types</span><span class="o">=</span><span class="p">[</span><span class="s2">&quot;Wlong&quot;</span><span class="p">,</span> <span class="s2">&quot;Wxdip&quot;</span><span class="p">,</span> <span class="s2">&quot;Wydip&quot;</span><span class="p">],</span>
+                 <span class="n">nt</span><span class="o">=</span><span class="mi">50</span><span class="p">,</span>
+                 <span class="n">x3</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+                 <span class="n">y3</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
+        <span class="c1"># parameters</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">ring</span> <span class="o">=</span> <span class="n">ring</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">length</span> <span class="o">=</span> <span class="n">length</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">rho</span> <span class="o">=</span> <span class="n">rho</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">nt</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">nt</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">nb</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">beam</span><span class="p">)</span>
+        <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">types</span><span class="p">,</span> <span class="nb">str</span><span class="p">):</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">types</span> <span class="o">=</span> <span class="p">[</span><span class="n">types</span><span class="p">]</span>
+        <span class="k">elif</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">types</span><span class="p">,</span> <span class="nb">list</span><span class="p">):</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">types</span> <span class="o">=</span> <span class="n">types</span>
+
+        <span class="c1"># effective radius for RW</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">radius</span> <span class="o">=</span> <span class="n">radius</span>
+        <span class="k">if</span> <span class="n">x3</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">x3</span> <span class="o">=</span> <span class="n">x3</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">x3</span> <span class="o">=</span> <span class="n">radius</span>
+        <span class="k">if</span> <span class="n">y3</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">y3</span> <span class="o">=</span> <span class="n">y3</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">y3</span> <span class="o">=</span> <span class="n">radius</span>
+
+        <span class="c1"># constants</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">Z0</span> <span class="o">=</span> <span class="n">mu_0</span> <span class="o">*</span> <span class="n">c</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">t0</span> <span class="o">=</span> <span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">rho</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">radius</span><span class="o">**</span><span class="mi">2</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">Z0</span><span class="p">)</span><span class="o">**</span><span class="p">(</span><span class="mi">1</span> <span class="o">/</span> <span class="mi">3</span><span class="p">)</span> <span class="o">/</span> <span class="n">c</span>
+
+        <span class="c1"># check approximation</span>
+        <span class="k">if</span> <span class="mi">20</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">t0</span> <span class="o">&gt;</span> <span class="n">ring</span><span class="o">.</span><span class="n">T1</span><span class="p">:</span>
+            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">&quot;The approximated wake functions are not valid.&quot;</span><span class="p">)</span>
+
+        <span class="c1"># init tables</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">tau</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">((</span><span class="bp">self</span><span class="o">.</span><span class="n">nb</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">nt</span><span class="p">))</span> <span class="o">*</span> <span class="mf">1e100</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="bp">self</span><span class="o">.</span><span class="n">nb</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">nt</span><span class="p">))</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">y</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="bp">self</span><span class="o">.</span><span class="n">nb</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">nt</span><span class="p">))</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">charge</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="bp">self</span><span class="o">.</span><span class="n">nb</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">nt</span><span class="p">))</span>
+
+<div class="viewcode-block" id="LongRangeResistiveWall.Wlong"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.wakepotential.LongRangeResistiveWall.Wlong">[docs]</a>    <span class="k">def</span> <span class="nf">Wlong</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">t</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Approxmiate expression for the longitudinal resistive wall wake </span>
+<span class="sd">        function - Eq.24 of [1].</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        t : float</span>
+<span class="sd">            Time in [s].</span>
+
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        wl : float</span>
+<span class="sd">            Wake function in [V/C].</span>
+
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="n">wl</span> <span class="o">=</span> <span class="p">(</span><span class="mi">1</span> <span class="o">/</span> <span class="p">(</span><span class="mi">4</span> <span class="o">*</span> <span class="n">pi</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">radius</span><span class="p">)</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">Z0</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">rho</span> <span class="o">/</span>
+                                                   <span class="p">(</span><span class="n">c</span><span class="o">*</span><span class="n">pi</span><span class="p">))</span> <span class="o">/</span>
+              <span class="n">t</span><span class="o">**</span><span class="p">(</span><span class="mi">3</span> <span class="o">/</span> <span class="mi">2</span><span class="p">))</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">length</span> <span class="o">*</span> <span class="o">-</span><span class="mi">1</span>
+        <span class="k">return</span> <span class="n">wl</span></div>
+
+<div class="viewcode-block" id="LongRangeResistiveWall.Wdip"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.wakepotential.LongRangeResistiveWall.Wdip">[docs]</a>    <span class="k">def</span> <span class="nf">Wdip</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">t</span><span class="p">,</span> <span class="n">plane</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Approxmiate expression for the transverse resistive wall wake </span>
+<span class="sd">        function - Eq.26 of [1].</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        t : float</span>
+<span class="sd">            Time in [s].</span>
+<span class="sd">        plane : str</span>
+<span class="sd">            &quot;x&quot; or &quot;y&quot;.</span>
+
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        wdip : float</span>
+<span class="sd">            Wake function in [V/C/m].</span>
+
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="k">if</span> <span class="n">plane</span> <span class="o">==</span> <span class="s2">&quot;x&quot;</span><span class="p">:</span>
+            <span class="n">r3</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">x3</span>
+        <span class="k">elif</span> <span class="n">plane</span> <span class="o">==</span> <span class="s2">&quot;y&quot;</span><span class="p">:</span>
+            <span class="n">r3</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">y3</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">()</span>
+
+        <span class="n">wdip</span> <span class="o">=</span> <span class="p">(</span><span class="mi">1</span> <span class="o">/</span> <span class="p">(</span><span class="n">pi</span> <span class="o">*</span> <span class="n">r3</span><span class="o">**</span><span class="mi">3</span><span class="p">)</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">Z0</span> <span class="o">*</span> <span class="n">c</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">rho</span> <span class="o">/</span> <span class="n">pi</span><span class="p">)</span> <span class="o">/</span>
+                <span class="n">t</span><span class="o">**</span><span class="p">(</span><span class="mi">1</span> <span class="o">/</span> <span class="mi">2</span><span class="p">)</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">length</span><span class="p">)</span>
+        <span class="k">return</span> <span class="n">wdip</span></div>
+
+<div class="viewcode-block" id="LongRangeResistiveWall.update_tables"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.wakepotential.LongRangeResistiveWall.update_tables">[docs]</a>    <span class="k">def</span> <span class="nf">update_tables</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">beam</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Update tables.</span>
+<span class="sd">        </span>
+<span class="sd">        Table tau[i,j] is defined as the time difference of the bunch i center </span>
+<span class="sd">        of mass with respect to center of the RF bucket number 0 at turn j.</span>
+<span class="sd">        Turn 0 corresponds to the tracked turn.</span>
+<span class="sd">        </span>
+<span class="sd">        Positive time corresponds to past events and negative time to future </span>
+<span class="sd">        events.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        beam : Beam object</span>
+
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        None.</span>
+
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="c1"># shift tables to next turn</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">tau</span> <span class="o">+=</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">T0</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">tau</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">roll</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">tau</span><span class="p">,</span> <span class="n">shift</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">roll</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">x</span><span class="p">,</span> <span class="n">shift</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">y</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">roll</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">y</span><span class="p">,</span> <span class="n">shift</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">charge</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">roll</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">charge</span><span class="p">,</span> <span class="n">shift</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
+
+        <span class="c1"># update tables</span>
+        <span class="k">if</span> <span class="n">beam</span><span class="o">.</span><span class="n">mpi_switch</span><span class="p">:</span>
+            <span class="n">beam</span><span class="o">.</span><span class="n">mpi</span><span class="o">.</span><span class="n">share_means</span><span class="p">(</span><span class="n">beam</span><span class="p">)</span>
+            <span class="c1"># negative sign as when bunch 0 is tracked, the others are not yet passed</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">tau</span><span class="p">[:,</span>
+                     <span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">beam</span><span class="o">.</span><span class="n">mpi</span><span class="o">.</span><span class="n">mean_all</span><span class="p">[:,</span>
+                                            <span class="mi">4</span><span class="p">]</span> <span class="o">-</span> <span class="n">beam</span><span class="o">.</span><span class="n">bunch_index</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">T1</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">x</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">beam</span><span class="o">.</span><span class="n">mpi</span><span class="o">.</span><span class="n">mean_all</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">]</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">y</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">beam</span><span class="o">.</span><span class="n">mpi</span><span class="o">.</span><span class="n">mean_all</span><span class="p">[:,</span> <span class="mi">2</span><span class="p">]</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">charge</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">beam</span><span class="o">.</span><span class="n">mpi</span><span class="o">.</span><span class="n">charge_all</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="n">mean_all</span> <span class="o">=</span> <span class="n">beam</span><span class="o">.</span><span class="n">bunch_mean</span>
+            <span class="n">charge_all</span> <span class="o">=</span> <span class="n">beam</span><span class="o">.</span><span class="n">bunch_charge</span>
+            <span class="c1"># negative sign as when bunch 0 is tracked, the others are not yet passed</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">tau</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">mean_all</span><span class="p">[</span>
+                <span class="mi">4</span><span class="p">,</span> <span class="n">beam</span><span class="o">.</span><span class="n">filling_pattern</span><span class="p">]</span> <span class="o">-</span> <span class="n">beam</span><span class="o">.</span><span class="n">bunch_index</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">T1</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">x</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">mean_all</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="n">beam</span><span class="o">.</span><span class="n">filling_pattern</span><span class="p">]</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">y</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">mean_all</span><span class="p">[</span><span class="mi">2</span><span class="p">,</span> <span class="n">beam</span><span class="o">.</span><span class="n">filling_pattern</span><span class="p">]</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">charge</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">charge_all</span><span class="p">[</span><span class="n">beam</span><span class="o">.</span><span class="n">filling_pattern</span><span class="p">]</span></div>
+
+<div class="viewcode-block" id="LongRangeResistiveWall.get_kick"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.wakepotential.LongRangeResistiveWall.get_kick">[docs]</a>    <span class="k">def</span> <span class="nf">get_kick</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">rank</span><span class="p">,</span> <span class="n">wake_type</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Compute the wake kick to apply.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        rank : int</span>
+<span class="sd">            Rank of the bunch, as defined in Mpi class.</span>
+<span class="sd">        wake_type : float</span>
+<span class="sd">            Type of the wake to compute.</span>
+
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        sum_kick : float</span>
+<span class="sd">            Sum of the kicks from the different bunches at different turns.</span>
+
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="n">sum_kick</span> <span class="o">=</span> <span class="mi">0</span>
+        <span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">nt</span><span class="p">):</span>
+            <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">nb</span><span class="p">):</span>
+                <span class="k">if</span> <span class="p">(</span><span class="n">j</span> <span class="o">==</span> <span class="mi">0</span><span class="p">)</span> <span class="ow">and</span> <span class="p">(</span><span class="n">rank</span> <span class="o">&lt;=</span> <span class="n">i</span><span class="p">):</span>
+                    <span class="k">continue</span>
+                <span class="n">deltaT</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">tau</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">]</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">tau</span><span class="p">[</span><span class="n">rank</span><span class="p">,</span> <span class="mi">0</span><span class="p">]</span>
+                <span class="k">if</span> <span class="n">wake_type</span> <span class="o">==</span> <span class="s2">&quot;Wlong&quot;</span><span class="p">:</span>
+                    <span class="n">sum_kick</span> <span class="o">+=</span> <span class="bp">self</span><span class="o">.</span><span class="n">Wlong</span><span class="p">(</span><span class="n">deltaT</span><span class="p">)</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">charge</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">]</span>
+                <span class="k">elif</span> <span class="n">wake_type</span> <span class="o">==</span> <span class="s2">&quot;Wxdip&quot;</span><span class="p">:</span>
+                    <span class="n">sum_kick</span> <span class="o">+=</span> <span class="bp">self</span><span class="o">.</span><span class="n">Wdip</span><span class="p">(</span>
+                        <span class="n">deltaT</span><span class="p">,</span> <span class="s2">&quot;x&quot;</span><span class="p">)</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">charge</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">]</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">x</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">]</span>
+                <span class="k">elif</span> <span class="n">wake_type</span> <span class="o">==</span> <span class="s2">&quot;Wydip&quot;</span><span class="p">:</span>
+                    <span class="n">sum_kick</span> <span class="o">+=</span> <span class="bp">self</span><span class="o">.</span><span class="n">Wdip</span><span class="p">(</span>
+                        <span class="n">deltaT</span><span class="p">,</span> <span class="s2">&quot;y&quot;</span><span class="p">)</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">charge</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">]</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">y</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">]</span>
+                <span class="k">elif</span> <span class="n">wake_type</span> <span class="o">==</span> <span class="s2">&quot;Wxquad&quot;</span><span class="p">:</span>
+                    <span class="k">raise</span> <span class="ne">NotImplementedError</span><span class="p">()</span>
+                <span class="k">elif</span> <span class="n">wake_type</span> <span class="o">==</span> <span class="s2">&quot;Wyquad&quot;</span><span class="p">:</span>
+                    <span class="k">raise</span> <span class="ne">NotImplementedError</span><span class="p">()</span>
+
+        <span class="k">return</span> <span class="n">sum_kick</span></div>
+
+<div class="viewcode-block" id="LongRangeResistiveWall.track_bunch"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.wakepotential.LongRangeResistiveWall.track_bunch">[docs]</a>    <span class="k">def</span> <span class="nf">track_bunch</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">bunch</span><span class="p">,</span> <span class="n">rank</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Track a bunch.</span>
+<span class="sd">        </span>
+<span class="sd">        Should only be used within the track method and not standalone.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        bunch : Bunch object</span>
+<span class="sd">        rank : int</span>
+<span class="sd">            Rank of the bunch, as defined in Mpi class.</span>
+
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        None.</span>
+
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="k">for</span> <span class="n">wake_type</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">types</span><span class="p">:</span>
+            <span class="n">kick</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">get_kick</span><span class="p">(</span><span class="n">rank</span><span class="p">,</span> <span class="n">wake_type</span><span class="p">)</span>
+            <span class="k">if</span> <span class="n">wake_type</span> <span class="o">==</span> <span class="s2">&quot;Wlong&quot;</span><span class="p">:</span>
+                <span class="n">bunch</span><span class="p">[</span><span class="s2">&quot;delta&quot;</span><span class="p">]</span> <span class="o">-=</span> <span class="n">kick</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">E0</span>
+            <span class="k">elif</span> <span class="n">wake_type</span> <span class="o">==</span> <span class="s2">&quot;Wxdip&quot;</span><span class="p">:</span>
+                <span class="n">bunch</span><span class="p">[</span><span class="s2">&quot;xp&quot;</span><span class="p">]</span> <span class="o">+=</span> <span class="n">kick</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">E0</span>
+            <span class="k">elif</span> <span class="n">wake_type</span> <span class="o">==</span> <span class="s2">&quot;Wydip&quot;</span><span class="p">:</span>
+                <span class="n">bunch</span><span class="p">[</span><span class="s2">&quot;yp&quot;</span><span class="p">]</span> <span class="o">+=</span> <span class="n">kick</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">E0</span>
+            <span class="k">elif</span> <span class="n">wake_type</span> <span class="o">==</span> <span class="s2">&quot;Wxquad&quot;</span><span class="p">:</span>
+                <span class="n">bunch</span><span class="p">[</span><span class="s2">&quot;xp&quot;</span><span class="p">]</span> <span class="o">+=</span> <span class="p">(</span><span class="n">bunch</span><span class="p">[</span><span class="s2">&quot;x&quot;</span><span class="p">]</span> <span class="o">*</span> <span class="n">kick</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">E0</span><span class="p">)</span>
+            <span class="k">elif</span> <span class="n">wake_type</span> <span class="o">==</span> <span class="s2">&quot;Wyquad&quot;</span><span class="p">:</span>
+                <span class="n">bunch</span><span class="p">[</span><span class="s2">&quot;yp&quot;</span><span class="p">]</span> <span class="o">+=</span> <span class="p">(</span><span class="n">bunch</span><span class="p">[</span><span class="s2">&quot;y&quot;</span><span class="p">]</span> <span class="o">*</span> <span class="n">kick</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">E0</span><span class="p">)</span></div>
+
+<div class="viewcode-block" id="LongRangeResistiveWall.track"><a class="viewcode-back" href="../../../mbtrack2.tracking.html#mbtrack2.tracking.wakepotential.LongRangeResistiveWall.track">[docs]</a>    <span class="k">def</span> <span class="nf">track</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">beam</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Track a beam.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        beam : Beam object</span>
+
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        None.</span>
+
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">update_tables</span><span class="p">(</span><span class="n">beam</span><span class="p">)</span>
+
+        <span class="k">if</span> <span class="n">beam</span><span class="o">.</span><span class="n">mpi_switch</span><span class="p">:</span>
+            <span class="n">rank</span> <span class="o">=</span> <span class="n">beam</span><span class="o">.</span><span class="n">mpi</span><span class="o">.</span><span class="n">rank</span>
+            <span class="n">bunch_index</span> <span class="o">=</span> <span class="n">beam</span><span class="o">.</span><span class="n">mpi</span><span class="o">.</span><span class="n">bunch_num</span>  <span class="c1"># Number of the tracked bunch in this processor</span>
+            <span class="n">bunch</span> <span class="o">=</span> <span class="n">beam</span><span class="p">[</span><span class="n">bunch_index</span><span class="p">]</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">track_bunch</span><span class="p">(</span><span class="n">bunch</span><span class="p">,</span> <span class="n">rank</span><span class="p">)</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="k">for</span> <span class="n">rank</span><span class="p">,</span> <span class="n">bunch</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">beam</span><span class="o">.</span><span class="n">not_empty</span><span class="p">):</span>
+                <span class="bp">self</span><span class="o">.</span><span class="n">track_bunch</span><span class="p">(</span><span class="n">bunch</span><span class="p">,</span> <span class="n">rank</span><span class="p">)</span></div></div>
+</pre></div>
+
+            <div class="clearer"></div>
+          </div>
+        </div>
+      </div>
+      <div class="sphinxsidebar" role="navigation" aria-label="main navigation">
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+<script>document.getElementById('searchbox').style.display = "block"</script>
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+    <div class="related" role="navigation" aria-label="related navigation">
+      <h3>Navigation</h3>
+      <ul>
+        <li class="right" style="margin-right: 10px">
+          <a href="../../../genindex.html" title="General Index"
+             >index</a></li>
+        <li class="right" >
+          <a href="../../../py-modindex.html" title="Python Module Index"
+             >modules</a> |</li>
+        <li class="nav-item nav-item-0"><a href="../../../index.html">mbtrack2 0.6.0 documentation</a> &#187;</li>
+          <li class="nav-item nav-item-1"><a href="../../index.html" >Module code</a> &#187;</li>
+        <li class="nav-item nav-item-this"><a href="">mbtrack2.tracking.wakepotential</a></li> 
+      </ul>
+    </div>
+    <div class="footer" role="contentinfo">
+        &#169; Copyright 2024, A. Gamelin et al.
+      Created using <a href="https://www.sphinx-doc.org/">Sphinx</a> 5.0.2.
+    </div>
+  </body>
+</html>
\ No newline at end of file
diff --git a/docs/build/html/_modules/mbtrack2/utilities/beamloading.html b/docs/build/html/_modules/mbtrack2/utilities/beamloading.html
new file mode 100644
index 0000000..fa7a4a8
--- /dev/null
+++ b/docs/build/html/_modules/mbtrack2/utilities/beamloading.html
@@ -0,0 +1,487 @@
+
+<!DOCTYPE html>
+
+<html lang="en">
+  <head>
+    <meta charset="utf-8" />
+    <meta name="viewport" content="width=device-width, initial-scale=1.0" />
+    <title>mbtrack2.utilities.beamloading &#8212; mbtrack2 0.6.0 documentation</title>
+    <link rel="stylesheet" type="text/css" href="../../../_static/pygments.css" />
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+    <link rel="index" title="Index" href="../../../genindex.html" />
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+             accesskey="I">index</a></li>
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+          <a href="../../../py-modindex.html" title="Python Module Index"
+             >modules</a> |</li>
+        <li class="nav-item nav-item-0"><a href="../../../index.html">mbtrack2 0.6.0 documentation</a> &#187;</li>
+          <li class="nav-item nav-item-1"><a href="../../index.html" accesskey="U">Module code</a> &#187;</li>
+        <li class="nav-item nav-item-this"><a href="">mbtrack2.utilities.beamloading</a></li> 
+      </ul>
+    </div>  
+
+    <div class="document">
+      <div class="documentwrapper">
+        <div class="bodywrapper">
+          <div class="body" role="main">
+            
+  <h1>Source code for mbtrack2.utilities.beamloading</h1><div class="highlight"><pre>
+<span></span><span class="c1"># -*- coding: utf-8 -*-</span>
+<span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">Module where the BeamLoadingEquilibrium class is defined.</span>
+<span class="sd">&quot;&quot;&quot;</span>
+
+<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
+<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="kn">from</span> <span class="nn">scipy.constants</span> <span class="kn">import</span> <span class="n">c</span>
+<span class="kn">from</span> <span class="nn">scipy.integrate</span> <span class="kn">import</span> <span class="n">quad</span>
+<span class="kn">from</span> <span class="nn">scipy.optimize</span> <span class="kn">import</span> <span class="n">root</span>
+
+
+<div class="viewcode-block" id="BeamLoadingEquilibrium"><a class="viewcode-back" href="../../../mbtrack2.utilities.html#mbtrack2.utilities.beamloading.BeamLoadingEquilibrium">[docs]</a><span class="k">class</span> <span class="nc">BeamLoadingEquilibrium</span><span class="p">():</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;Class used to compute beam equilibrium profile for a given storage ring </span>
+<span class="sd">    and a list of RF cavities of any harmonic. The class assumes an uniform </span>
+<span class="sd">    filling of the storage ring. Based on an extension of [1].</span>
+
+<span class="sd">    [1] Venturini, M. (2018). Passive higher-harmonic rf cavities with general</span>
+<span class="sd">    settings and multibunch instabilities in electron storage rings.</span>
+<span class="sd">    Physical Review Accelerators and Beams, 21(11), 114404.</span>
+
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">    ring : Synchrotron object</span>
+<span class="sd">    cavity_list : list of CavityResonator objects</span>
+<span class="sd">    I0 : beam current in [A].</span>
+<span class="sd">    auto_set_MC_theta : if True, allow class to change cavity phase for</span>
+<span class="sd">        CavityResonator objetcs with m = 1 (i.e. main cavities)</span>
+<span class="sd">    F : list of form factor amplitude</span>
+<span class="sd">    PHI : list of form factor phase</span>
+<span class="sd">    B1 : lower intergration boundary</span>
+<span class="sd">    B2 : upper intergration boundary</span>
+<span class="sd">    &quot;&quot;&quot;</span>
+
+    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span>
+                 <span class="n">ring</span><span class="p">,</span>
+                 <span class="n">cavity_list</span><span class="p">,</span>
+                 <span class="n">I0</span><span class="p">,</span>
+                 <span class="n">auto_set_MC_theta</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span>
+                 <span class="n">F</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+                 <span class="n">PHI</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+                 <span class="n">B1</span><span class="o">=-</span><span class="mf">0.2</span><span class="p">,</span>
+                 <span class="n">B2</span><span class="o">=</span><span class="mf">0.2</span><span class="p">):</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">ring</span> <span class="o">=</span> <span class="n">ring</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">cavity_list</span> <span class="o">=</span> <span class="n">cavity_list</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">I0</span> <span class="o">=</span> <span class="n">I0</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">n_cavity</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">cavity_list</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">auto_set_MC_theta</span> <span class="o">=</span> <span class="n">auto_set_MC_theta</span>
+        <span class="k">if</span> <span class="n">F</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">F</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">((</span><span class="bp">self</span><span class="o">.</span><span class="n">n_cavity</span><span class="p">,</span> <span class="p">))</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">F</span> <span class="o">=</span> <span class="n">F</span>
+        <span class="k">if</span> <span class="n">PHI</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">PHI</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="bp">self</span><span class="o">.</span><span class="n">n_cavity</span><span class="p">,</span> <span class="p">))</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">PHI</span> <span class="o">=</span> <span class="n">PHI</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">B1</span> <span class="o">=</span> <span class="n">B1</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">B2</span> <span class="o">=</span> <span class="n">B2</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">mpi</span> <span class="o">=</span> <span class="kc">False</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">__version__</span> <span class="o">=</span> <span class="s2">&quot;1.0&quot;</span>
+
+        <span class="c1"># Define constants for scaled potential u(z)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">u0</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">U0</span> <span class="o">/</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">ac</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">sigma_delta</span><span class="o">**</span><span class="mi">2</span> <span class="o">*</span>
+                                  <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">E0</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">L</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">ug</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="bp">self</span><span class="o">.</span><span class="n">n_cavity</span><span class="p">,</span> <span class="p">))</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">ub</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="bp">self</span><span class="o">.</span><span class="n">n_cavity</span><span class="p">,</span> <span class="p">))</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">update_potentials</span><span class="p">()</span>
+
+<div class="viewcode-block" id="BeamLoadingEquilibrium.update_potentials"><a class="viewcode-back" href="../../../mbtrack2.utilities.html#mbtrack2.utilities.beamloading.BeamLoadingEquilibrium.update_potentials">[docs]</a>    <span class="k">def</span> <span class="nf">update_potentials</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Update potentials with cavity and ring data.&quot;&quot;&quot;</span>
+        <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">n_cavity</span><span class="p">):</span>
+            <span class="n">cavity</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">cavity_list</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">ug</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="n">cavity</span><span class="o">.</span><span class="n">Vg</span> <span class="o">/</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">ac</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">sigma_delta</span><span class="o">**</span><span class="mi">2</span> <span class="o">*</span>
+                                      <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">E0</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">L</span> <span class="o">*</span>
+                                      <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">k1</span> <span class="o">*</span> <span class="n">cavity</span><span class="o">.</span><span class="n">m</span><span class="p">)</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">ub</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="mi">2</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">I0</span> <span class="o">*</span> <span class="n">cavity</span><span class="o">.</span><span class="n">Rs</span> <span class="o">/</span> <span class="p">(</span>
+                <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">ac</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">sigma_delta</span><span class="o">**</span><span class="mi">2</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">E0</span> <span class="o">*</span>
+                <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">L</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">k1</span> <span class="o">*</span> <span class="n">cavity</span><span class="o">.</span><span class="n">m</span> <span class="o">*</span> <span class="p">(</span><span class="mi">1</span> <span class="o">+</span> <span class="n">cavity</span><span class="o">.</span><span class="n">beta</span><span class="p">))</span></div>
+
+<div class="viewcode-block" id="BeamLoadingEquilibrium.energy_balance"><a class="viewcode-back" href="../../../mbtrack2.utilities.html#mbtrack2.utilities.beamloading.BeamLoadingEquilibrium.energy_balance">[docs]</a>    <span class="k">def</span> <span class="nf">energy_balance</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Return energy balance for the synchronous particle</span>
+<span class="sd">        (z = 0 ,delta = 0).&quot;&quot;&quot;</span>
+        <span class="n">delta</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">U0</span>
+        <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">n_cavity</span><span class="p">):</span>
+            <span class="n">cavity</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">cavity_list</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
+            <span class="n">delta</span> <span class="o">+=</span> <span class="n">cavity</span><span class="o">.</span><span class="n">Vb</span><span class="p">(</span>
+                <span class="bp">self</span><span class="o">.</span><span class="n">I0</span><span class="p">)</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">F</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">cavity</span><span class="o">.</span><span class="n">psi</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">PHI</span><span class="p">[</span><span class="n">i</span><span class="p">])</span>
+            <span class="n">delta</span> <span class="o">-=</span> <span class="n">cavity</span><span class="o">.</span><span class="n">Vg</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">cavity</span><span class="o">.</span><span class="n">theta_g</span><span class="p">)</span>
+        <span class="k">return</span> <span class="n">delta</span></div>
+
+<div class="viewcode-block" id="BeamLoadingEquilibrium.center_of_mass"><a class="viewcode-back" href="../../../mbtrack2.utilities.html#mbtrack2.utilities.beamloading.BeamLoadingEquilibrium.center_of_mass">[docs]</a>    <span class="k">def</span> <span class="nf">center_of_mass</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Return center of mass position in [s]&quot;&quot;&quot;</span>
+        <span class="n">z0</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">B1</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">B2</span><span class="p">,</span> <span class="mi">1000</span><span class="p">)</span>
+        <span class="n">rho</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">rho</span><span class="p">(</span><span class="n">z0</span><span class="p">)</span>
+        <span class="n">CM</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">average</span><span class="p">(</span><span class="n">z0</span><span class="p">,</span> <span class="n">weights</span><span class="o">=</span><span class="n">rho</span><span class="p">)</span>
+        <span class="k">return</span> <span class="n">CM</span> <span class="o">/</span> <span class="n">c</span></div>
+
+<div class="viewcode-block" id="BeamLoadingEquilibrium.u"><a class="viewcode-back" href="../../../mbtrack2.utilities.html#mbtrack2.utilities.beamloading.BeamLoadingEquilibrium.u">[docs]</a>    <span class="k">def</span> <span class="nf">u</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">z</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Scaled potential u(z)&quot;&quot;&quot;</span>
+        <span class="n">pot</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">u0</span> <span class="o">*</span> <span class="n">z</span>
+        <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">n_cavity</span><span class="p">):</span>
+            <span class="n">cavity</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">cavity_list</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
+            <span class="n">pot</span> <span class="o">+=</span> <span class="o">-</span><span class="bp">self</span><span class="o">.</span><span class="n">ug</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">*</span> <span class="p">(</span>
+                <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">k1</span> <span class="o">*</span> <span class="n">cavity</span><span class="o">.</span><span class="n">m</span> <span class="o">*</span> <span class="n">z</span> <span class="o">+</span> <span class="n">cavity</span><span class="o">.</span><span class="n">theta_g</span><span class="p">)</span> <span class="o">-</span>
+                <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">cavity</span><span class="o">.</span><span class="n">theta_g</span><span class="p">))</span>
+            <span class="n">pot</span> <span class="o">+=</span> <span class="bp">self</span><span class="o">.</span><span class="n">ub</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">F</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">cavity</span><span class="o">.</span><span class="n">psi</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span>
+                <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">k1</span> <span class="o">*</span> <span class="n">cavity</span><span class="o">.</span><span class="n">m</span> <span class="o">*</span> <span class="n">z</span> <span class="o">+</span> <span class="n">cavity</span><span class="o">.</span><span class="n">psi</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">PHI</span><span class="p">[</span><span class="n">i</span><span class="p">])</span>
+                <span class="o">-</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">cavity</span><span class="o">.</span><span class="n">psi</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">PHI</span><span class="p">[</span><span class="n">i</span><span class="p">]))</span>
+        <span class="k">return</span> <span class="n">pot</span></div>
+
+<div class="viewcode-block" id="BeamLoadingEquilibrium.du_dz"><a class="viewcode-back" href="../../../mbtrack2.utilities.html#mbtrack2.utilities.beamloading.BeamLoadingEquilibrium.du_dz">[docs]</a>    <span class="k">def</span> <span class="nf">du_dz</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">z</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Partial derivative of the scaled potential u(z) by z&quot;&quot;&quot;</span>
+        <span class="n">pot</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">u0</span>
+        <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">n_cavity</span><span class="p">):</span>
+            <span class="n">cavity</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">cavity_list</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
+            <span class="n">pot</span> <span class="o">+=</span> <span class="o">-</span><span class="bp">self</span><span class="o">.</span><span class="n">ug</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">k1</span> <span class="o">*</span> <span class="n">cavity</span><span class="o">.</span><span class="n">m</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span>
+                <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">k1</span> <span class="o">*</span> <span class="n">cavity</span><span class="o">.</span><span class="n">m</span> <span class="o">*</span> <span class="n">z</span> <span class="o">+</span> <span class="n">cavity</span><span class="o">.</span><span class="n">theta_g</span><span class="p">)</span>
+            <span class="n">pot</span> <span class="o">+=</span> <span class="bp">self</span><span class="o">.</span><span class="n">ub</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">F</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">k1</span> <span class="o">*</span> <span class="n">cavity</span><span class="o">.</span><span class="n">m</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span>
+                <span class="n">cavity</span><span class="o">.</span><span class="n">psi</span><span class="p">)</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">k1</span> <span class="o">*</span> <span class="n">cavity</span><span class="o">.</span><span class="n">m</span> <span class="o">*</span> <span class="n">z</span> <span class="o">+</span> <span class="n">cavity</span><span class="o">.</span><span class="n">psi</span> <span class="o">-</span>
+                                     <span class="bp">self</span><span class="o">.</span><span class="n">PHI</span><span class="p">[</span><span class="n">i</span><span class="p">])</span>
+        <span class="k">return</span> <span class="n">pot</span></div>
+
+<div class="viewcode-block" id="BeamLoadingEquilibrium.uexp"><a class="viewcode-back" href="../../../mbtrack2.utilities.html#mbtrack2.utilities.beamloading.BeamLoadingEquilibrium.uexp">[docs]</a>    <span class="k">def</span> <span class="nf">uexp</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">z</span><span class="p">):</span>
+        <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">u</span><span class="p">(</span><span class="n">z</span><span class="p">))</span></div>
+
+<div class="viewcode-block" id="BeamLoadingEquilibrium.integrate_func"><a class="viewcode-back" href="../../../mbtrack2.utilities.html#mbtrack2.utilities.beamloading.BeamLoadingEquilibrium.integrate_func">[docs]</a>    <span class="k">def</span> <span class="nf">integrate_func</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">f</span><span class="p">,</span> <span class="n">g</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Return Integral[f*g]/Integral[f] between B1 and B2&quot;&quot;&quot;</span>
+        <span class="n">A</span> <span class="o">=</span> <span class="n">quad</span><span class="p">(</span><span class="k">lambda</span> <span class="n">x</span><span class="p">:</span> <span class="n">f</span><span class="p">(</span><span class="n">x</span><span class="p">)</span> <span class="o">*</span> <span class="n">g</span><span class="p">(</span><span class="n">x</span><span class="p">),</span> <span class="bp">self</span><span class="o">.</span><span class="n">B1</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">B2</span><span class="p">)</span>
+        <span class="n">B</span> <span class="o">=</span> <span class="n">quad</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">B1</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">B2</span><span class="p">)</span>
+        <span class="k">return</span> <span class="n">A</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">/</span> <span class="n">B</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span></div>
+
+<div class="viewcode-block" id="BeamLoadingEquilibrium.to_solve"><a class="viewcode-back" href="../../../mbtrack2.utilities.html#mbtrack2.utilities.beamloading.BeamLoadingEquilibrium.to_solve">[docs]</a>    <span class="k">def</span> <span class="nf">to_solve</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">x</span><span class="p">,</span> <span class="n">CM</span><span class="o">=</span><span class="kc">True</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;System of non-linear equation to solve to find the form factors F</span>
+<span class="sd">        and PHI at equilibrum.</span>
+<span class="sd">        The system is composed of Eq. (B6) and (B7) of [1] for each cavity.</span>
+<span class="sd">        If auto_set_MC_theta == True, the system also find the main cavity </span>
+<span class="sd">        phase to impose energy balance or cancel center of mass offset.</span>
+<span class="sd">        If CM is True, the system imposes zero center of mass offset,</span>
+<span class="sd">        if False, the system imposes energy balance.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="c1"># Update values of F, PHI and theta</span>
+        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">auto_set_MC_theta</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">F</span> <span class="o">=</span> <span class="n">x</span><span class="p">[:</span><span class="o">-</span><span class="mi">1</span><span class="p">:</span><span class="mi">2</span><span class="p">]</span>
+            <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">n_cavity</span><span class="p">):</span>
+                <span class="n">cavity</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">cavity_list</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
+                <span class="k">if</span> <span class="n">cavity</span><span class="o">.</span><span class="n">m</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
+                    <span class="n">cavity</span><span class="o">.</span><span class="n">theta</span> <span class="o">=</span> <span class="n">x</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
+                    <span class="n">cavity</span><span class="o">.</span><span class="n">set_generator</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">I0</span><span class="p">)</span>
+                    <span class="bp">self</span><span class="o">.</span><span class="n">update_potentials</span><span class="p">()</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">F</span> <span class="o">=</span> <span class="n">x</span><span class="p">[::</span><span class="mi">2</span><span class="p">]</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">PHI</span> <span class="o">=</span> <span class="n">x</span><span class="p">[</span><span class="mi">1</span><span class="p">::</span><span class="mi">2</span><span class="p">]</span>
+
+        <span class="c1"># Compute system</span>
+        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">auto_set_MC_theta</span><span class="p">:</span>
+            <span class="n">res</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="bp">self</span><span class="o">.</span><span class="n">n_cavity</span> <span class="o">*</span> <span class="mi">2</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span> <span class="p">))</span>
+            <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">n_cavity</span><span class="p">):</span>
+                <span class="n">cavity</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">cavity_list</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
+                <span class="n">res</span><span class="p">[</span><span class="mi">2</span> <span class="o">*</span>
+                    <span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">F</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">PHI</span><span class="p">[</span><span class="n">i</span><span class="p">])</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">integrate_func</span><span class="p">(</span>
+                        <span class="k">lambda</span> <span class="n">y</span><span class="p">:</span> <span class="bp">self</span><span class="o">.</span><span class="n">uexp</span><span class="p">(</span><span class="n">y</span><span class="p">),</span>
+                        <span class="k">lambda</span> <span class="n">y</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">k1</span> <span class="o">*</span> <span class="n">cavity</span><span class="o">.</span><span class="n">m</span> <span class="o">*</span> <span class="n">y</span><span class="p">))</span>
+                <span class="n">res</span><span class="p">[</span><span class="mi">2</span><span class="o">*</span><span class="n">i</span> <span class="o">+</span>
+                    <span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">F</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">PHI</span><span class="p">[</span><span class="n">i</span><span class="p">])</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">integrate_func</span><span class="p">(</span>
+                        <span class="k">lambda</span> <span class="n">y</span><span class="p">:</span> <span class="bp">self</span><span class="o">.</span><span class="n">uexp</span><span class="p">(</span><span class="n">y</span><span class="p">),</span>
+                        <span class="k">lambda</span> <span class="n">y</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">k1</span> <span class="o">*</span> <span class="n">cavity</span><span class="o">.</span><span class="n">m</span> <span class="o">*</span> <span class="n">y</span><span class="p">))</span>
+            <span class="c1"># Factor 1e-8 or 1e12 for better convergence</span>
+            <span class="k">if</span> <span class="n">CM</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">:</span>
+                <span class="n">res</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">n_cavity</span> <span class="o">*</span> <span class="mi">2</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">center_of_mass</span><span class="p">()</span> <span class="o">*</span> <span class="mf">1e12</span>
+            <span class="k">else</span><span class="p">:</span>
+                <span class="n">res</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">n_cavity</span> <span class="o">*</span> <span class="mi">2</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">energy_balance</span><span class="p">()</span> <span class="o">*</span> <span class="mf">1e-8</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="n">res</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="bp">self</span><span class="o">.</span><span class="n">n_cavity</span> <span class="o">*</span> <span class="mi">2</span><span class="p">,</span> <span class="p">))</span>
+            <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">n_cavity</span><span class="p">):</span>
+                <span class="n">cavity</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">cavity_list</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
+                <span class="n">res</span><span class="p">[</span><span class="mi">2</span> <span class="o">*</span>
+                    <span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">F</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">PHI</span><span class="p">[</span><span class="n">i</span><span class="p">])</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">integrate_func</span><span class="p">(</span>
+                        <span class="k">lambda</span> <span class="n">y</span><span class="p">:</span> <span class="bp">self</span><span class="o">.</span><span class="n">uexp</span><span class="p">(</span><span class="n">y</span><span class="p">),</span>
+                        <span class="k">lambda</span> <span class="n">y</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">k1</span> <span class="o">*</span> <span class="n">cavity</span><span class="o">.</span><span class="n">m</span> <span class="o">*</span> <span class="n">y</span><span class="p">))</span>
+                <span class="n">res</span><span class="p">[</span><span class="mi">2</span><span class="o">*</span><span class="n">i</span> <span class="o">+</span>
+                    <span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">F</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">PHI</span><span class="p">[</span><span class="n">i</span><span class="p">])</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">integrate_func</span><span class="p">(</span>
+                        <span class="k">lambda</span> <span class="n">y</span><span class="p">:</span> <span class="bp">self</span><span class="o">.</span><span class="n">uexp</span><span class="p">(</span><span class="n">y</span><span class="p">),</span>
+                        <span class="k">lambda</span> <span class="n">y</span><span class="p">:</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">k1</span> <span class="o">*</span> <span class="n">cavity</span><span class="o">.</span><span class="n">m</span> <span class="o">*</span> <span class="n">y</span><span class="p">))</span>
+        <span class="k">return</span> <span class="n">res</span></div>
+
+<div class="viewcode-block" id="BeamLoadingEquilibrium.rho"><a class="viewcode-back" href="../../../mbtrack2.utilities.html#mbtrack2.utilities.beamloading.BeamLoadingEquilibrium.rho">[docs]</a>    <span class="k">def</span> <span class="nf">rho</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">z</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Return bunch equilibrium profile at postion z&quot;&quot;&quot;</span>
+        <span class="n">A</span> <span class="o">=</span> <span class="n">quad</span><span class="p">(</span><span class="k">lambda</span> <span class="n">y</span><span class="p">:</span> <span class="bp">self</span><span class="o">.</span><span class="n">uexp</span><span class="p">(</span><span class="n">y</span><span class="p">),</span> <span class="bp">self</span><span class="o">.</span><span class="n">B1</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">B2</span><span class="p">)</span>
+        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">uexp</span><span class="p">(</span><span class="n">z</span><span class="p">)</span> <span class="o">/</span> <span class="n">A</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span></div>
+
+<div class="viewcode-block" id="BeamLoadingEquilibrium.plot_rho"><a class="viewcode-back" href="../../../mbtrack2.utilities.html#mbtrack2.utilities.beamloading.BeamLoadingEquilibrium.plot_rho">[docs]</a>    <span class="k">def</span> <span class="nf">plot_rho</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">z1</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">z2</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Plot the bunch equilibrium profile between z1 and z2&quot;&quot;&quot;</span>
+        <span class="k">if</span> <span class="n">z1</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="n">z1</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">B1</span>
+        <span class="k">if</span> <span class="n">z2</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="n">z2</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">B2</span>
+        <span class="n">z0</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="n">z1</span><span class="p">,</span> <span class="n">z2</span><span class="p">,</span> <span class="mi">1000</span><span class="p">)</span>
+        <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">z0</span> <span class="o">/</span> <span class="n">c</span> <span class="o">*</span> <span class="mf">1e12</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">rho</span><span class="p">(</span><span class="n">z0</span><span class="p">))</span>
+        <span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="sa">r</span><span class="s2">&quot;$\tau$ [ps]&quot;</span><span class="p">)</span>
+        <span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s2">&quot;Equilibrium bunch profile&quot;</span><span class="p">)</span></div>
+
+<div class="viewcode-block" id="BeamLoadingEquilibrium.voltage"><a class="viewcode-back" href="../../../mbtrack2.utilities.html#mbtrack2.utilities.beamloading.BeamLoadingEquilibrium.voltage">[docs]</a>    <span class="k">def</span> <span class="nf">voltage</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">z</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Return the RF system total voltage at position z&quot;&quot;&quot;</span>
+        <span class="n">Vtot</span> <span class="o">=</span> <span class="mi">0</span>
+        <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">n_cavity</span><span class="p">):</span>
+            <span class="n">cavity</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">cavity_list</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
+            <span class="n">Vtot</span> <span class="o">+=</span> <span class="n">cavity</span><span class="o">.</span><span class="n">VRF</span><span class="p">(</span><span class="n">z</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">I0</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">F</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="bp">self</span><span class="o">.</span><span class="n">PHI</span><span class="p">[</span><span class="n">i</span><span class="p">])</span>
+        <span class="k">return</span> <span class="n">Vtot</span></div>
+
+<div class="viewcode-block" id="BeamLoadingEquilibrium.dV"><a class="viewcode-back" href="../../../mbtrack2.utilities.html#mbtrack2.utilities.beamloading.BeamLoadingEquilibrium.dV">[docs]</a>    <span class="k">def</span> <span class="nf">dV</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">z</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Return derivative of the RF system total voltage at position z&quot;&quot;&quot;</span>
+        <span class="n">Vtot</span> <span class="o">=</span> <span class="mi">0</span>
+        <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">n_cavity</span><span class="p">):</span>
+            <span class="n">cavity</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">cavity_list</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
+            <span class="n">Vtot</span> <span class="o">+=</span> <span class="n">cavity</span><span class="o">.</span><span class="n">dVRF</span><span class="p">(</span><span class="n">z</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">I0</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">F</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="bp">self</span><span class="o">.</span><span class="n">PHI</span><span class="p">[</span><span class="n">i</span><span class="p">])</span>
+        <span class="k">return</span> <span class="n">Vtot</span></div>
+
+<div class="viewcode-block" id="BeamLoadingEquilibrium.ddV"><a class="viewcode-back" href="../../../mbtrack2.utilities.html#mbtrack2.utilities.beamloading.BeamLoadingEquilibrium.ddV">[docs]</a>    <span class="k">def</span> <span class="nf">ddV</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">z</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Return the second derivative of the RF system total voltage at position z&quot;&quot;&quot;</span>
+        <span class="n">Vtot</span> <span class="o">=</span> <span class="mi">0</span>
+        <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">n_cavity</span><span class="p">):</span>
+            <span class="n">cavity</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">cavity_list</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
+            <span class="n">Vtot</span> <span class="o">+=</span> <span class="n">cavity</span><span class="o">.</span><span class="n">ddVRF</span><span class="p">(</span><span class="n">z</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">I0</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">F</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="bp">self</span><span class="o">.</span><span class="n">PHI</span><span class="p">[</span><span class="n">i</span><span class="p">])</span>
+        <span class="k">return</span> <span class="n">Vtot</span></div>
+
+<div class="viewcode-block" id="BeamLoadingEquilibrium.deltaVRF"><a class="viewcode-back" href="../../../mbtrack2.utilities.html#mbtrack2.utilities.beamloading.BeamLoadingEquilibrium.deltaVRF">[docs]</a>    <span class="k">def</span> <span class="nf">deltaVRF</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">z</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Return the generator voltage minus beam loading voltage of the total RF system at position z&quot;&quot;&quot;</span>
+        <span class="n">Vtot</span> <span class="o">=</span> <span class="mi">0</span>
+        <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">n_cavity</span><span class="p">):</span>
+            <span class="n">cavity</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">cavity_list</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
+            <span class="n">Vtot</span> <span class="o">+=</span> <span class="n">cavity</span><span class="o">.</span><span class="n">deltaVRF</span><span class="p">(</span><span class="n">z</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">I0</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">F</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="bp">self</span><span class="o">.</span><span class="n">PHI</span><span class="p">[</span><span class="n">i</span><span class="p">])</span>
+        <span class="k">return</span> <span class="n">Vtot</span></div>
+
+<div class="viewcode-block" id="BeamLoadingEquilibrium.plot_dV"><a class="viewcode-back" href="../../../mbtrack2.utilities.html#mbtrack2.utilities.beamloading.BeamLoadingEquilibrium.plot_dV">[docs]</a>    <span class="k">def</span> <span class="nf">plot_dV</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">z1</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">z2</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Plot the derivative of RF system total voltage between z1 and z2&quot;&quot;&quot;</span>
+        <span class="k">if</span> <span class="n">z1</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="n">z1</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">B1</span>
+        <span class="k">if</span> <span class="n">z2</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="n">z2</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">B2</span>
+        <span class="n">z0</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="n">z1</span><span class="p">,</span> <span class="n">z2</span><span class="p">,</span> <span class="mi">1000</span><span class="p">)</span>
+        <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">z0</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">dV</span><span class="p">(</span><span class="n">z0</span><span class="p">))</span>
+        <span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="s2">&quot;z [m]&quot;</span><span class="p">)</span>
+        <span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="s2">&quot;Total RF voltage (V)&quot;</span><span class="p">)</span></div>
+
+<div class="viewcode-block" id="BeamLoadingEquilibrium.plot_voltage"><a class="viewcode-back" href="../../../mbtrack2.utilities.html#mbtrack2.utilities.beamloading.BeamLoadingEquilibrium.plot_voltage">[docs]</a>    <span class="k">def</span> <span class="nf">plot_voltage</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">z1</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">z2</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Plot the RF system total voltage between z1 and z2&quot;&quot;&quot;</span>
+        <span class="k">if</span> <span class="n">z1</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="n">z1</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">B1</span>
+        <span class="k">if</span> <span class="n">z2</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="n">z2</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">B2</span>
+        <span class="n">z0</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="n">z1</span><span class="p">,</span> <span class="n">z2</span><span class="p">,</span> <span class="mi">1000</span><span class="p">)</span>
+        <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">z0</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">voltage</span><span class="p">(</span><span class="n">z0</span><span class="p">))</span>
+        <span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="s2">&quot;z [m]&quot;</span><span class="p">)</span>
+        <span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="s2">&quot;Total RF voltage (V)&quot;</span><span class="p">)</span></div>
+
+<div class="viewcode-block" id="BeamLoadingEquilibrium.std_rho"><a class="viewcode-back" href="../../../mbtrack2.utilities.html#mbtrack2.utilities.beamloading.BeamLoadingEquilibrium.std_rho">[docs]</a>    <span class="k">def</span> <span class="nf">std_rho</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">z1</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">z2</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Return the rms bunch equilibrium size in [m]&quot;&quot;&quot;</span>
+        <span class="k">if</span> <span class="n">z1</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="n">z1</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">B1</span>
+        <span class="k">if</span> <span class="n">z2</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="n">z2</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">B2</span>
+        <span class="n">z0</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="n">z1</span><span class="p">,</span> <span class="n">z2</span><span class="p">,</span> <span class="mi">1000</span><span class="p">)</span>
+        <span class="n">values</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">rho</span><span class="p">(</span><span class="n">z0</span><span class="p">)</span>
+        <span class="n">average</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">average</span><span class="p">(</span><span class="n">z0</span><span class="p">,</span> <span class="n">weights</span><span class="o">=</span><span class="n">values</span><span class="p">)</span>
+        <span class="n">variance</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">average</span><span class="p">((</span><span class="n">z0</span> <span class="o">-</span> <span class="n">average</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span><span class="p">,</span> <span class="n">weights</span><span class="o">=</span><span class="n">values</span><span class="p">)</span>
+        <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">variance</span><span class="p">)</span></div>
+
+<div class="viewcode-block" id="BeamLoadingEquilibrium.beam_equilibrium"><a class="viewcode-back" href="../../../mbtrack2.utilities.html#mbtrack2.utilities.beamloading.BeamLoadingEquilibrium.beam_equilibrium">[docs]</a>    <span class="k">def</span> <span class="nf">beam_equilibrium</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span>
+                         <span class="n">x0</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+                         <span class="n">tol</span><span class="o">=</span><span class="mf">1e-4</span><span class="p">,</span>
+                         <span class="n">method</span><span class="o">=</span><span class="s1">&#39;hybr&#39;</span><span class="p">,</span>
+                         <span class="n">options</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+                         <span class="n">plot</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span>
+                         <span class="n">CM</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span>
+                         <span class="n">verbiose</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Solve system of non-linear equation to find the form factors F</span>
+<span class="sd">        and PHI at equilibrum. Can be used to compute the equilibrium bunch</span>
+<span class="sd">        profile.</span>
+<span class="sd">        </span>
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        x0 : initial guess</span>
+<span class="sd">        tol : tolerance for termination of the algorithm</span>
+<span class="sd">        method : method used by scipy.optimize.root to solve the system</span>
+<span class="sd">        options : options given to scipy.optimize.root</span>
+<span class="sd">        plot : if True, plot the equilibrium bunch profile</span>
+<span class="sd">        CM : if True, the system imposes zero center of mass offset,</span>
+<span class="sd">        if False, the system imposes energy balance.</span>
+<span class="sd">        verbiose : if True, print out informations about convergence.</span>
+<span class="sd">        </span>
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        sol : OptimizeResult object representing the solution</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="k">if</span> <span class="n">x0</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="n">x0</span> <span class="o">=</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">n_cavity</span>
+            <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">auto_set_MC_theta</span><span class="p">:</span>
+                <span class="n">x0</span> <span class="o">=</span> <span class="n">x0</span> <span class="o">+</span> <span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">cavity_list</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">theta</span><span class="p">]</span>
+
+        <span class="k">if</span> <span class="n">verbiose</span><span class="p">:</span>
+            <span class="k">if</span> <span class="n">CM</span><span class="p">:</span>
+                <span class="nb">print</span><span class="p">(</span><span class="s2">&quot;The initial center of mass offset is &quot;</span> <span class="o">+</span>
+                      <span class="nb">str</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">center_of_mass</span><span class="p">()</span> <span class="o">*</span> <span class="mf">1e12</span><span class="p">)</span> <span class="o">+</span> <span class="s2">&quot; ps&quot;</span><span class="p">)</span>
+            <span class="k">else</span><span class="p">:</span>
+                <span class="nb">print</span><span class="p">(</span><span class="s2">&quot;The initial energy balance is &quot;</span> <span class="o">+</span>
+                      <span class="nb">str</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">energy_balance</span><span class="p">())</span> <span class="o">+</span> <span class="s2">&quot; eV&quot;</span><span class="p">)</span>
+
+        <span class="n">sol</span> <span class="o">=</span> <span class="n">root</span><span class="p">(</span><span class="k">lambda</span> <span class="n">x</span><span class="p">:</span> <span class="bp">self</span><span class="o">.</span><span class="n">to_solve</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">CM</span><span class="p">),</span>
+                   <span class="n">x0</span><span class="p">,</span>
+                   <span class="n">tol</span><span class="o">=</span><span class="n">tol</span><span class="p">,</span>
+                   <span class="n">method</span><span class="o">=</span><span class="n">method</span><span class="p">,</span>
+                   <span class="n">options</span><span class="o">=</span><span class="n">options</span><span class="p">)</span>
+
+        <span class="c1"># Update values of F, PHI and theta_g</span>
+        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">auto_set_MC_theta</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">F</span> <span class="o">=</span> <span class="n">sol</span><span class="o">.</span><span class="n">x</span><span class="p">[:</span><span class="o">-</span><span class="mi">1</span><span class="p">:</span><span class="mi">2</span><span class="p">]</span>
+            <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">n_cavity</span><span class="p">):</span>
+                <span class="n">cavity</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">cavity_list</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
+                <span class="k">if</span> <span class="n">cavity</span><span class="o">.</span><span class="n">m</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
+                    <span class="n">cavity</span><span class="o">.</span><span class="n">theta</span> <span class="o">=</span> <span class="n">sol</span><span class="o">.</span><span class="n">x</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">F</span> <span class="o">=</span> <span class="n">sol</span><span class="o">.</span><span class="n">x</span><span class="p">[::</span><span class="mi">2</span><span class="p">]</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">PHI</span> <span class="o">=</span> <span class="n">sol</span><span class="o">.</span><span class="n">x</span><span class="p">[</span><span class="mi">1</span><span class="p">::</span><span class="mi">2</span><span class="p">]</span>
+
+        <span class="k">if</span> <span class="n">verbiose</span><span class="p">:</span>
+            <span class="k">if</span> <span class="n">CM</span><span class="p">:</span>
+                <span class="nb">print</span><span class="p">(</span><span class="s2">&quot;The final center of mass offset is &quot;</span> <span class="o">+</span>
+                      <span class="nb">str</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">center_of_mass</span><span class="p">()</span> <span class="o">*</span> <span class="mf">1e12</span><span class="p">)</span> <span class="o">+</span> <span class="s2">&quot; ps&quot;</span><span class="p">)</span>
+            <span class="k">else</span><span class="p">:</span>
+                <span class="nb">print</span><span class="p">(</span><span class="s2">&quot;The final energy balance is &quot;</span> <span class="o">+</span>
+                      <span class="nb">str</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">energy_balance</span><span class="p">())</span> <span class="o">+</span> <span class="s2">&quot; eV&quot;</span><span class="p">)</span>
+            <span class="k">if</span> <span class="ow">not</span> <span class="n">sol</span><span class="o">.</span><span class="n">success</span><span class="p">:</span>
+                <span class="nb">print</span><span class="p">(</span><span class="s2">&quot;The algorithm has converged: &quot;</span> <span class="o">+</span> <span class="nb">str</span><span class="p">(</span><span class="n">sol</span><span class="o">.</span><span class="n">success</span><span class="p">))</span>
+
+        <span class="k">if</span> <span class="n">plot</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">plot_rho</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">B1</span> <span class="o">/</span> <span class="mi">4</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">B2</span> <span class="o">/</span> <span class="mi">4</span><span class="p">)</span>
+
+        <span class="k">return</span> <span class="n">sol</span></div>
+
+<div class="viewcode-block" id="BeamLoadingEquilibrium.PTBL_threshold"><a class="viewcode-back" href="../../../mbtrack2.utilities.html#mbtrack2.utilities.beamloading.BeamLoadingEquilibrium.PTBL_threshold">[docs]</a>    <span class="k">def</span> <span class="nf">PTBL_threshold</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">I0</span><span class="p">,</span> <span class="n">m</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">MC_index</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">HC_index</span><span class="o">=</span><span class="mi">1</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Compute the periodic transient beam loading (PTBL) instability </span>
+<span class="sd">        threshold based on [1].</span>
+<span class="sd">        </span>
+<span class="sd">        The beam_equilibrium method should be called before the PTBL_threshold </span>
+<span class="sd">        one.</span>
+<span class="sd">        </span>
+<span class="sd">        Eq. (22) and (23) have been modified for cosine voltage convention </span>
+<span class="sd">        for the main cavity.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        I0 : float</span>
+<span class="sd">            Beam total current in [A].</span>
+<span class="sd">        m : int, optional</span>
+<span class="sd">            Number of bunches in the beam. </span>
+<span class="sd">            The default is None. If None, uniform filling is assumed.</span>
+<span class="sd">        MC_index : int, optional</span>
+<span class="sd">            Index of the main cavity in cavity_list. The default is 0.</span>
+<span class="sd">        HC_index : int, optional</span>
+<span class="sd">            Index of the harmonic cavity in cavity_list. The default is 1.</span>
+
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        eta : float</span>
+<span class="sd">            Amplification factor, if bigger than 1 then the beam is possibly </span>
+<span class="sd">            in the PTBL regime, Eq. (22) of [1].</span>
+<span class="sd">        RQth : float</span>
+<span class="sd">            R/Q threshold, Eq. (24) of [1].</span>
+<span class="sd">        f : float</span>
+<span class="sd">            f function, Eq. (23) of [1].</span>
+<span class="sd">            </span>
+<span class="sd">        Reference</span>
+<span class="sd">        ---------</span>
+<span class="sd">        [1] : He, T. (2022). Novel perturbation method for judging the </span>
+<span class="sd">        stability of the equilibrium solution in the presence of passive </span>
+<span class="sd">        harmonic cavities. Physical Review Accelerators and Beams, 25(9), </span>
+<span class="sd">        094402.</span>
+
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="k">if</span> <span class="n">m</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="n">m</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">h</span>
+
+        <span class="n">MC</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">cavity_list</span><span class="p">[</span><span class="n">MC_index</span><span class="p">]</span>
+        <span class="n">HC</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">cavity_list</span><span class="p">[</span><span class="n">HC_index</span><span class="p">]</span>
+        <span class="n">a</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="o">-</span><span class="n">HC</span><span class="o">.</span><span class="n">wr</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">T0</span> <span class="o">/</span> <span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">HC</span><span class="o">.</span><span class="n">Q</span><span class="p">))</span>
+        <span class="n">theta</span> <span class="o">=</span> <span class="n">HC</span><span class="o">.</span><span class="n">detune</span> <span class="o">*</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">T0</span>
+        <span class="n">dtheta</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arcsin</span><span class="p">((</span><span class="mi">1</span><span class="o">-</span><span class="n">a</span><span class="p">)</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">theta</span> <span class="o">/</span> <span class="mi">2</span><span class="p">)</span> <span class="o">/</span>
+                           <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="mi">1</span> <span class="o">+</span> <span class="n">a</span><span class="o">**</span><span class="mi">2</span> <span class="o">-</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">a</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">theta</span><span class="p">))))</span>
+
+        <span class="n">k</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">m</span><span class="p">)</span>
+        <span class="n">d_k</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span> <span class="o">*</span> <span class="n">HC</span><span class="o">.</span><span class="n">wr</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">T0</span> <span class="o">*</span> <span class="p">(</span><span class="n">k</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span> <span class="o">/</span> <span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">HC</span><span class="o">.</span><span class="n">Q</span> <span class="o">*</span> <span class="n">m</span><span class="p">))</span>
+        <span class="n">theta_k</span> <span class="o">=</span> <span class="p">(</span><span class="n">theta</span><span class="o">/</span><span class="mi">2</span> <span class="o">+</span> <span class="n">dtheta</span> <span class="o">-</span> <span class="p">(</span><span class="n">k</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span> <span class="o">/</span> <span class="n">m</span> <span class="o">*</span> <span class="n">theta</span><span class="p">)</span>
+        <span class="n">eps_k</span> <span class="o">=</span> <span class="mi">1</span> <span class="o">-</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">/</span> <span class="mi">2</span> <span class="o">-</span> <span class="n">k</span> <span class="o">*</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">/</span> <span class="n">m</span><span class="p">)</span>
+
+        <span class="n">num</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">eps_k</span> <span class="o">*</span> <span class="n">d_k</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">theta_k</span><span class="p">))</span>
+        <span class="n">f</span> <span class="o">=</span> <span class="n">num</span> <span class="o">/</span> <span class="p">(</span><span class="n">m</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="mi">1</span> <span class="o">+</span> <span class="n">a</span><span class="o">**</span><span class="mi">2</span> <span class="o">-</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">a</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">theta</span><span class="p">)))</span>
+
+        <span class="n">eta</span> <span class="o">=</span> <span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="n">HC</span><span class="o">.</span><span class="n">m</span><span class="o">**</span><span class="mi">2</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">F</span><span class="p">[</span><span class="n">HC_index</span><span class="p">]</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">h</span> <span class="o">*</span> <span class="n">I0</span> <span class="o">*</span>
+               <span class="n">HC</span><span class="o">.</span><span class="n">Rs</span> <span class="o">/</span> <span class="n">HC</span><span class="o">.</span><span class="n">Q</span> <span class="o">*</span> <span class="n">f</span> <span class="o">/</span>
+               <span class="p">(</span><span class="n">MC</span><span class="o">.</span><span class="n">Vc</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">MC</span><span class="o">.</span><span class="n">theta</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">PHI</span><span class="p">[</span><span class="n">HC_index</span><span class="p">]</span> <span class="o">/</span> <span class="n">HC</span><span class="o">.</span><span class="n">m</span><span class="p">)))</span>
+
+        <span class="n">RQth</span> <span class="o">=</span> <span class="p">(</span><span class="n">MC</span><span class="o">.</span><span class="n">Vc</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">MC</span><span class="o">.</span><span class="n">theta</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">PHI</span><span class="p">[</span><span class="n">HC_index</span><span class="p">]</span> <span class="o">/</span> <span class="n">HC</span><span class="o">.</span><span class="n">m</span><span class="p">)</span> <span class="o">/</span>
+                <span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="n">HC</span><span class="o">.</span><span class="n">m</span><span class="o">**</span><span class="mi">2</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">F</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">ring</span><span class="o">.</span><span class="n">h</span> <span class="o">*</span> <span class="n">I0</span> <span class="o">*</span> <span class="n">f</span><span class="p">))</span>
+
+        <span class="k">return</span> <span class="p">(</span><span class="n">eta</span><span class="p">,</span> <span class="n">RQth</span><span class="p">,</span> <span class="n">f</span><span class="p">)</span></div></div>
+</pre></div>
+
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+
+<!DOCTYPE html>
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+  <head>
+    <meta charset="utf-8" />
+    <meta name="viewport" content="width=device-width, initial-scale=1.0" />
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+            
+  <h1>Source code for mbtrack2.utilities.misc</h1><div class="highlight"><pre>
+<span></span><span class="c1"># -*- coding: utf-8 -*-</span>
+<span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">This module defines miscellaneous utilities functions.</span>
+<span class="sd">&quot;&quot;&quot;</span>
+
+<span class="kn">from</span> <span class="nn">pathlib</span> <span class="kn">import</span> <span class="n">Path</span>
+
+<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="kn">import</span> <span class="nn">pandas</span> <span class="k">as</span> <span class="nn">pd</span>
+<span class="kn">from</span> <span class="nn">scipy.interpolate</span> <span class="kn">import</span> <span class="n">interp1d</span>
+
+<span class="kn">from</span> <span class="nn">mbtrack2.impedance.wakefield</span> <span class="kn">import</span> <span class="n">Impedance</span>
+<span class="kn">from</span> <span class="nn">mbtrack2.utilities.spectrum</span> <span class="kn">import</span> <span class="n">spectral_density</span>
+
+
+<div class="viewcode-block" id="effective_impedance"><a class="viewcode-back" href="../../../mbtrack2.utilities.html#mbtrack2.utilities.misc.effective_impedance">[docs]</a><span class="k">def</span> <span class="nf">effective_impedance</span><span class="p">(</span><span class="n">ring</span><span class="p">,</span>
+                        <span class="n">imp</span><span class="p">,</span>
+                        <span class="n">m</span><span class="p">,</span>
+                        <span class="n">mu</span><span class="p">,</span>
+                        <span class="n">sigma</span><span class="p">,</span>
+                        <span class="n">M</span><span class="p">,</span>
+                        <span class="n">tuneS</span><span class="p">,</span>
+                        <span class="n">xi</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+                        <span class="n">mode</span><span class="o">=</span><span class="s2">&quot;Hermite&quot;</span><span class="p">):</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    Compute the effective (longitudinal or transverse) impedance. </span>
+<span class="sd">    Formulas from Eq. (1) and (2) p238 of [1].</span>
+
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">    ring : Synchrotron object</span>
+<span class="sd">    imp : Impedance object</span>
+<span class="sd">    mu : int</span>
+<span class="sd">        coupled bunch mode number, goes from 0 to (M-1) where M is the</span>
+<span class="sd">        number of bunches</span>
+<span class="sd">    m : int</span>
+<span class="sd">        head-tail (or azimutal/synchrotron) mode number</span>
+<span class="sd">    sigma : float</span>
+<span class="sd">        RMS bunch length in [s]</span>
+<span class="sd">    M : int</span>
+<span class="sd">        Number of bunches.</span>
+<span class="sd">    tuneS : float</span>
+<span class="sd">        Synchrotron tune.</span>
+<span class="sd">    xi : float, optional</span>
+<span class="sd">        (non-normalized) chromaticity</span>
+<span class="sd">    mode: str, optional</span>
+<span class="sd">        type of the mode taken into account for the computation:</span>
+<span class="sd">        -&quot;Hermite&quot; modes for Gaussian bunches</span>
+
+<span class="sd">    Returns</span>
+<span class="sd">    -------</span>
+<span class="sd">    Zeff : float </span>
+<span class="sd">        effective impedance in [ohm] or in [ohm/m] depanding on the impedance</span>
+<span class="sd">        type.</span>
+
+<span class="sd">    References</span>
+<span class="sd">    ----------</span>
+<span class="sd">    [1] : Handbook of accelerator physics and engineering, 3rd printing.</span>
+<span class="sd">    &quot;&quot;&quot;</span>
+
+    <span class="k">if</span> <span class="ow">not</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">imp</span><span class="p">,</span> <span class="n">Impedance</span><span class="p">):</span>
+        <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s2">&quot;</span><span class="si">{}</span><span class="s2"> should be an Impedance object.&quot;</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">imp</span><span class="p">))</span>
+
+    <span class="n">fmin</span> <span class="o">=</span> <span class="n">imp</span><span class="o">.</span><span class="n">data</span><span class="o">.</span><span class="n">index</span><span class="o">.</span><span class="n">min</span><span class="p">()</span>
+    <span class="n">fmax</span> <span class="o">=</span> <span class="n">imp</span><span class="o">.</span><span class="n">data</span><span class="o">.</span><span class="n">index</span><span class="o">.</span><span class="n">max</span><span class="p">()</span>
+    <span class="k">if</span> <span class="n">fmin</span> <span class="o">&gt;</span> <span class="mi">0</span><span class="p">:</span>
+        <span class="n">double_sided_impedance</span><span class="p">(</span><span class="n">imp</span><span class="p">)</span>
+
+    <span class="k">if</span> <span class="n">mode</span> <span class="ow">in</span> <span class="p">[</span><span class="s2">&quot;Hermite&quot;</span><span class="p">,</span> <span class="s2">&quot;Legendre&quot;</span><span class="p">,</span> <span class="s2">&quot;Sinusoidal&quot;</span><span class="p">,</span> <span class="s2">&quot;Sacherer&quot;</span><span class="p">,</span> <span class="s2">&quot;Chebyshev&quot;</span><span class="p">]:</span>
+
+        <span class="k">def</span> <span class="nf">h</span><span class="p">(</span><span class="n">f</span><span class="p">):</span>
+            <span class="k">return</span> <span class="n">spectral_density</span><span class="p">(</span><span class="n">frequency</span><span class="o">=</span><span class="n">f</span><span class="p">,</span> <span class="n">sigma</span><span class="o">=</span><span class="n">sigma</span><span class="p">,</span> <span class="n">m</span><span class="o">=</span><span class="n">m</span><span class="p">,</span> <span class="n">mode</span><span class="o">=</span><span class="n">mode</span><span class="p">)</span>
+    <span class="k">else</span><span class="p">:</span>
+        <span class="k">raise</span> <span class="ne">NotImplementedError</span><span class="p">(</span><span class="s2">&quot;Not implemanted yet.&quot;</span><span class="p">)</span>
+
+    <span class="k">if</span> <span class="n">imp</span><span class="o">.</span><span class="n">component_type</span> <span class="o">==</span> <span class="s2">&quot;long&quot;</span><span class="p">:</span>
+        <span class="n">pmax</span> <span class="o">=</span> <span class="n">fmax</span> <span class="o">/</span> <span class="p">(</span><span class="n">ring</span><span class="o">.</span><span class="n">f0</span> <span class="o">*</span> <span class="n">M</span><span class="p">)</span> <span class="o">-</span> <span class="mi">1</span>
+        <span class="n">pmin</span> <span class="o">=</span> <span class="n">fmin</span> <span class="o">/</span> <span class="p">(</span><span class="n">ring</span><span class="o">.</span><span class="n">f0</span> <span class="o">*</span> <span class="n">M</span><span class="p">)</span> <span class="o">+</span> <span class="mi">1</span>
+        <span class="n">p</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="n">pmin</span><span class="p">,</span> <span class="n">pmax</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span>
+
+        <span class="n">fp</span> <span class="o">=</span> <span class="n">ring</span><span class="o">.</span><span class="n">f0</span> <span class="o">*</span> <span class="p">(</span><span class="n">p</span><span class="o">*</span><span class="n">M</span> <span class="o">+</span> <span class="n">mu</span> <span class="o">+</span> <span class="n">m</span><span class="o">*</span><span class="n">tuneS</span><span class="p">)</span>
+        <span class="n">fp</span> <span class="o">=</span> <span class="n">fp</span><span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">nonzero</span><span class="p">(</span><span class="n">fp</span><span class="p">)]</span>  <span class="c1"># Avoid division by 0</span>
+        <span class="n">num</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">imp</span><span class="p">(</span><span class="n">fp</span><span class="p">)</span> <span class="o">*</span> <span class="n">h</span><span class="p">(</span><span class="n">fp</span><span class="p">)</span> <span class="o">/</span> <span class="p">(</span><span class="n">fp</span> <span class="o">*</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span><span class="p">))</span>
+        <span class="n">den</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">h</span><span class="p">(</span><span class="n">fp</span><span class="p">))</span>
+        <span class="n">Zeff</span> <span class="o">=</span> <span class="n">num</span> <span class="o">/</span> <span class="n">den</span>
+
+    <span class="k">elif</span> <span class="n">imp</span><span class="o">.</span><span class="n">component_type</span> <span class="o">==</span> <span class="s2">&quot;xdip&quot;</span> <span class="ow">or</span> <span class="n">imp</span><span class="o">.</span><span class="n">component_type</span> <span class="o">==</span> <span class="s2">&quot;ydip&quot;</span><span class="p">:</span>
+        <span class="k">if</span> <span class="n">imp</span><span class="o">.</span><span class="n">component_type</span> <span class="o">==</span> <span class="s2">&quot;xdip&quot;</span><span class="p">:</span>
+            <span class="n">tuneXY</span> <span class="o">=</span> <span class="n">ring</span><span class="o">.</span><span class="n">tune</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">-</span> <span class="n">np</span><span class="o">.</span><span class="n">floor</span><span class="p">(</span><span class="n">ring</span><span class="o">.</span><span class="n">tune</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
+            <span class="k">if</span> <span class="n">xi</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+                <span class="n">xi</span> <span class="o">=</span> <span class="n">ring</span><span class="o">.</span><span class="n">chro</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
+        <span class="k">elif</span> <span class="n">imp</span><span class="o">.</span><span class="n">component_type</span> <span class="o">==</span> <span class="s2">&quot;ydip&quot;</span><span class="p">:</span>
+            <span class="n">tuneXY</span> <span class="o">=</span> <span class="n">ring</span><span class="o">.</span><span class="n">tune</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="n">np</span><span class="o">.</span><span class="n">floor</span><span class="p">(</span><span class="n">ring</span><span class="o">.</span><span class="n">tune</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
+            <span class="k">if</span> <span class="n">xi</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+                <span class="n">xi</span> <span class="o">=</span> <span class="n">ring</span><span class="o">.</span><span class="n">chro</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span>
+        <span class="n">pmax</span> <span class="o">=</span> <span class="n">fmax</span> <span class="o">/</span> <span class="p">(</span><span class="n">ring</span><span class="o">.</span><span class="n">f0</span> <span class="o">*</span> <span class="n">M</span><span class="p">)</span> <span class="o">-</span> <span class="mi">1</span>
+        <span class="n">pmin</span> <span class="o">=</span> <span class="n">fmin</span> <span class="o">/</span> <span class="p">(</span><span class="n">ring</span><span class="o">.</span><span class="n">f0</span> <span class="o">*</span> <span class="n">M</span><span class="p">)</span> <span class="o">+</span> <span class="mi">1</span>
+        <span class="n">p</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="n">pmin</span><span class="p">,</span> <span class="n">pmax</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span>
+        <span class="n">fp</span> <span class="o">=</span> <span class="n">ring</span><span class="o">.</span><span class="n">f0</span> <span class="o">*</span> <span class="p">(</span><span class="n">p</span><span class="o">*</span><span class="n">M</span> <span class="o">+</span> <span class="n">mu</span> <span class="o">+</span> <span class="n">tuneXY</span> <span class="o">+</span> <span class="n">m</span><span class="o">*</span><span class="n">tuneS</span><span class="p">)</span>
+        <span class="n">f_xi</span> <span class="o">=</span> <span class="n">xi</span> <span class="o">/</span> <span class="n">ring</span><span class="o">.</span><span class="n">eta</span><span class="p">()</span> <span class="o">*</span> <span class="n">ring</span><span class="o">.</span><span class="n">f0</span>
+        <span class="n">num</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">imp</span><span class="p">(</span><span class="n">fp</span><span class="p">)</span> <span class="o">*</span> <span class="n">h</span><span class="p">(</span><span class="n">fp</span> <span class="o">-</span> <span class="n">f_xi</span><span class="p">))</span>
+        <span class="n">den</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">h</span><span class="p">(</span><span class="n">fp</span> <span class="o">-</span> <span class="n">f_xi</span><span class="p">))</span>
+        <span class="n">Zeff</span> <span class="o">=</span> <span class="n">num</span> <span class="o">/</span> <span class="n">den</span>
+    <span class="k">else</span><span class="p">:</span>
+        <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s2">&quot;Effective impedance is only defined for long, xdip&quot;</span>
+                        <span class="s2">&quot; and ydip impedance type.&quot;</span><span class="p">)</span>
+
+    <span class="k">return</span> <span class="n">Zeff</span></div>
+
+
+<div class="viewcode-block" id="head_tail_form_factor"><a class="viewcode-back" href="../../../mbtrack2.utilities.html#mbtrack2.utilities.misc.head_tail_form_factor">[docs]</a><span class="k">def</span> <span class="nf">head_tail_form_factor</span><span class="p">(</span><span class="n">ring</span><span class="p">,</span>
+                          <span class="n">imp</span><span class="p">,</span>
+                          <span class="n">m</span><span class="p">,</span>
+                          <span class="n">sigma</span><span class="p">,</span>
+                          <span class="n">tuneS</span><span class="p">,</span>
+                          <span class="n">xi</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+                          <span class="n">mode</span><span class="o">=</span><span class="s2">&quot;Hermite&quot;</span><span class="p">,</span>
+                          <span class="n">mu</span><span class="o">=</span><span class="mi">0</span><span class="p">):</span>
+    <span class="n">M</span> <span class="o">=</span> <span class="mi">1</span>
+    <span class="k">if</span> <span class="ow">not</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">imp</span><span class="p">,</span> <span class="n">Impedance</span><span class="p">):</span>
+        <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s2">&quot;</span><span class="si">{}</span><span class="s2"> should be an Impedance object.&quot;</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">imp</span><span class="p">))</span>
+
+    <span class="n">fmin</span> <span class="o">=</span> <span class="n">imp</span><span class="o">.</span><span class="n">data</span><span class="o">.</span><span class="n">index</span><span class="o">.</span><span class="n">min</span><span class="p">()</span>
+    <span class="n">fmax</span> <span class="o">=</span> <span class="n">imp</span><span class="o">.</span><span class="n">data</span><span class="o">.</span><span class="n">index</span><span class="o">.</span><span class="n">max</span><span class="p">()</span>
+    <span class="k">if</span> <span class="n">fmin</span> <span class="o">&gt;</span> <span class="mi">0</span><span class="p">:</span>
+        <span class="n">double_sided_impedance</span><span class="p">(</span><span class="n">imp</span><span class="p">)</span>
+
+    <span class="k">if</span> <span class="n">mode</span> <span class="ow">in</span> <span class="p">[</span><span class="s2">&quot;Hermite&quot;</span><span class="p">,</span> <span class="s2">&quot;Legendre&quot;</span><span class="p">,</span> <span class="s2">&quot;Sinusoidal&quot;</span><span class="p">,</span> <span class="s2">&quot;Sacherer&quot;</span><span class="p">,</span> <span class="s2">&quot;Chebyshev&quot;</span><span class="p">]:</span>
+
+        <span class="k">def</span> <span class="nf">h</span><span class="p">(</span><span class="n">f</span><span class="p">):</span>
+            <span class="k">return</span> <span class="n">spectral_density</span><span class="p">(</span><span class="n">frequency</span><span class="o">=</span><span class="n">f</span><span class="p">,</span> <span class="n">sigma</span><span class="o">=</span><span class="n">sigma</span><span class="p">,</span> <span class="n">m</span><span class="o">=</span><span class="n">m</span><span class="p">,</span> <span class="n">mode</span><span class="o">=</span><span class="n">mode</span><span class="p">)</span>
+    <span class="k">else</span><span class="p">:</span>
+        <span class="k">raise</span> <span class="ne">NotImplementedError</span><span class="p">(</span><span class="s2">&quot;Not implemanted yet.&quot;</span><span class="p">)</span>
+
+    <span class="n">pmax</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">floor</span><span class="p">(</span><span class="n">fmax</span> <span class="o">/</span> <span class="p">(</span><span class="n">ring</span><span class="o">.</span><span class="n">f0</span> <span class="o">*</span> <span class="n">M</span><span class="p">))</span>
+    <span class="n">pmin</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">ceil</span><span class="p">(</span><span class="n">fmin</span> <span class="o">/</span> <span class="p">(</span><span class="n">ring</span><span class="o">.</span><span class="n">f0</span> <span class="o">*</span> <span class="n">M</span><span class="p">))</span>
+
+    <span class="n">p</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="n">pmin</span><span class="p">,</span> <span class="n">pmax</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span>
+
+    <span class="k">if</span> <span class="n">imp</span><span class="o">.</span><span class="n">component_type</span> <span class="o">==</span> <span class="s2">&quot;long&quot;</span><span class="p">:</span>
+        <span class="n">fp</span> <span class="o">=</span> <span class="n">ring</span><span class="o">.</span><span class="n">f0</span> <span class="o">*</span> <span class="p">(</span><span class="n">p</span><span class="o">*</span><span class="n">M</span> <span class="o">+</span> <span class="n">mu</span> <span class="o">+</span> <span class="n">m</span><span class="o">*</span><span class="n">tuneS</span><span class="p">)</span>
+        <span class="n">fp</span> <span class="o">=</span> <span class="n">fp</span><span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">nonzero</span><span class="p">(</span><span class="n">fp</span><span class="p">)]</span>  <span class="c1"># Avoid division by 0</span>
+        <span class="n">den</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">h</span><span class="p">(</span><span class="n">fp</span><span class="p">))</span>
+
+    <span class="k">elif</span> <span class="n">imp</span><span class="o">.</span><span class="n">component_type</span> <span class="o">==</span> <span class="s2">&quot;xdip&quot;</span> <span class="ow">or</span> <span class="n">imp</span><span class="o">.</span><span class="n">component_type</span> <span class="o">==</span> <span class="s2">&quot;ydip&quot;</span><span class="p">:</span>
+        <span class="k">if</span> <span class="n">imp</span><span class="o">.</span><span class="n">component_type</span> <span class="o">==</span> <span class="s2">&quot;xdip&quot;</span><span class="p">:</span>
+            <span class="n">tuneXY</span> <span class="o">=</span> <span class="n">ring</span><span class="o">.</span><span class="n">tune</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">-</span> <span class="n">np</span><span class="o">.</span><span class="n">floor</span><span class="p">(</span><span class="n">ring</span><span class="o">.</span><span class="n">tune</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
+            <span class="k">if</span> <span class="n">xi</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+                <span class="n">xi</span> <span class="o">=</span> <span class="n">ring</span><span class="o">.</span><span class="n">chro</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
+        <span class="k">elif</span> <span class="n">imp</span><span class="o">.</span><span class="n">component_type</span> <span class="o">==</span> <span class="s2">&quot;ydip&quot;</span><span class="p">:</span>
+            <span class="n">tuneXY</span> <span class="o">=</span> <span class="n">ring</span><span class="o">.</span><span class="n">tune</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="n">np</span><span class="o">.</span><span class="n">floor</span><span class="p">(</span><span class="n">ring</span><span class="o">.</span><span class="n">tune</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
+            <span class="k">if</span> <span class="n">xi</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+                <span class="n">xi</span> <span class="o">=</span> <span class="n">ring</span><span class="o">.</span><span class="n">chro</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span>
+        <span class="n">fp</span> <span class="o">=</span> <span class="n">ring</span><span class="o">.</span><span class="n">f0</span> <span class="o">*</span> <span class="p">(</span><span class="n">p</span><span class="o">*</span><span class="n">M</span> <span class="o">+</span> <span class="n">mu</span> <span class="o">+</span> <span class="n">tuneXY</span> <span class="o">+</span> <span class="n">m</span><span class="o">*</span><span class="n">tuneS</span><span class="p">)</span>
+        <span class="n">f_xi</span> <span class="o">=</span> <span class="n">xi</span> <span class="o">/</span> <span class="n">ring</span><span class="o">.</span><span class="n">eta</span><span class="p">()</span> <span class="o">*</span> <span class="n">ring</span><span class="o">.</span><span class="n">f0</span>
+        <span class="n">den</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">h</span><span class="p">(</span><span class="n">fp</span> <span class="o">-</span> <span class="n">f_xi</span><span class="p">))</span>
+    <span class="k">else</span><span class="p">:</span>
+        <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s2">&quot;Effective impedance is only defined for long, xdip&quot;</span>
+                        <span class="s2">&quot; and ydip impedance type.&quot;</span><span class="p">)</span>
+
+    <span class="k">return</span> <span class="n">den</span></div>
+
+
+<div class="viewcode-block" id="tune_shift_from_effective_impedance"><a class="viewcode-back" href="../../../mbtrack2.utilities.html#mbtrack2.utilities.misc.tune_shift_from_effective_impedance">[docs]</a><span class="k">def</span> <span class="nf">tune_shift_from_effective_impedance</span><span class="p">(</span><span class="n">Zeff</span><span class="p">):</span>
+    <span class="k">pass</span></div>
+
+
+<div class="viewcode-block" id="yokoya_elliptic"><a class="viewcode-back" href="../../../mbtrack2.utilities.html#mbtrack2.utilities.misc.yokoya_elliptic">[docs]</a><span class="k">def</span> <span class="nf">yokoya_elliptic</span><span class="p">(</span><span class="n">x_radius</span><span class="p">,</span> <span class="n">y_radius</span><span class="p">):</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    Compute Yokoya factors for an elliptic beam pipe.</span>
+<span class="sd">    Function adapted from N. Mounet IW2D.</span>
+
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">    x_radius : float</span>
+<span class="sd">        Horizontal semi-axis of the ellipse in [m].</span>
+<span class="sd">    y_radius : float</span>
+<span class="sd">        Vertical semi-axis of the ellipse in [m].</span>
+
+<span class="sd">    Returns</span>
+<span class="sd">    -------</span>
+<span class="sd">    yoklong : float</span>
+<span class="sd">        Yokoya factor for the longitudinal impedance.</span>
+<span class="sd">    yokxdip : float</span>
+<span class="sd">        Yokoya factor for the dipolar horizontal impedance.</span>
+<span class="sd">    yokydip : float</span>
+<span class="sd">        Yokoya factor for the dipolar vertical impedance.</span>
+<span class="sd">    yokxquad : float</span>
+<span class="sd">        Yokoya factor for the quadrupolar horizontal impedance.</span>
+<span class="sd">    yokyquad : float</span>
+<span class="sd">        Yokoya factor for the quadrupolar vertical impedance.</span>
+<span class="sd">    &quot;&quot;&quot;</span>
+    <span class="k">if</span> <span class="n">y_radius</span> <span class="o">&lt;</span> <span class="n">x_radius</span><span class="p">:</span>
+        <span class="n">small_semiaxis</span> <span class="o">=</span> <span class="n">y_radius</span>
+        <span class="n">large_semiaxis</span> <span class="o">=</span> <span class="n">x_radius</span>
+    <span class="k">else</span><span class="p">:</span>
+        <span class="n">small_semiaxis</span> <span class="o">=</span> <span class="n">x_radius</span>
+        <span class="n">large_semiaxis</span> <span class="o">=</span> <span class="n">y_radius</span>
+
+    <span class="n">path_to_file</span> <span class="o">=</span> <span class="n">Path</span><span class="p">(</span><span class="vm">__file__</span><span class="p">)</span><span class="o">.</span><span class="n">parent</span>
+    <span class="n">file</span> <span class="o">=</span> <span class="n">path_to_file</span> <span class="o">/</span> <span class="s2">&quot;data&quot;</span> <span class="o">/</span> <span class="s2">&quot;Yokoya_elliptic_from_Elias_USPAS.csv&quot;</span>
+
+    <span class="c1"># read Yokoya factors interpolation file</span>
+    <span class="c1"># BEWARE: columns are ratio, dipy, dipx, quady, quadx</span>
+    <span class="n">yokoya_file</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">read_csv</span><span class="p">(</span><span class="n">file</span><span class="p">)</span>
+    <span class="n">ratio_col</span> <span class="o">=</span> <span class="n">yokoya_file</span><span class="p">[</span><span class="s2">&quot;x&quot;</span><span class="p">]</span>
+    <span class="c1"># compute semi-axes ratio (first column of this file)</span>
+    <span class="n">ratio</span> <span class="o">=</span> <span class="p">(</span><span class="n">large_semiaxis</span><span class="o">-</span><span class="n">small_semiaxis</span><span class="p">)</span> <span class="o">/</span> <span class="p">(</span><span class="n">large_semiaxis</span><span class="o">+</span><span class="n">small_semiaxis</span><span class="p">)</span>
+
+    <span class="c1"># interpolate Yokoya file at the correct ratio</span>
+    <span class="n">yoklong</span> <span class="o">=</span> <span class="mi">1</span>
+
+    <span class="k">if</span> <span class="n">y_radius</span> <span class="o">&lt;</span> <span class="n">x_radius</span><span class="p">:</span>
+        <span class="n">yokydip</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">interp</span><span class="p">(</span><span class="n">ratio</span><span class="p">,</span> <span class="n">ratio_col</span><span class="p">,</span> <span class="n">yokoya_file</span><span class="p">[</span><span class="s2">&quot;dipy&quot;</span><span class="p">])</span>
+        <span class="n">yokxdip</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">interp</span><span class="p">(</span><span class="n">ratio</span><span class="p">,</span> <span class="n">ratio_col</span><span class="p">,</span> <span class="n">yokoya_file</span><span class="p">[</span><span class="s2">&quot;dipx&quot;</span><span class="p">])</span>
+        <span class="n">yokyquad</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">interp</span><span class="p">(</span><span class="n">ratio</span><span class="p">,</span> <span class="n">ratio_col</span><span class="p">,</span> <span class="n">yokoya_file</span><span class="p">[</span><span class="s2">&quot;quady&quot;</span><span class="p">])</span>
+        <span class="n">yokxquad</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">interp</span><span class="p">(</span><span class="n">ratio</span><span class="p">,</span> <span class="n">ratio_col</span><span class="p">,</span> <span class="n">yokoya_file</span><span class="p">[</span><span class="s2">&quot;quadx&quot;</span><span class="p">])</span>
+    <span class="k">else</span><span class="p">:</span>
+        <span class="n">yokxdip</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">interp</span><span class="p">(</span><span class="n">ratio</span><span class="p">,</span> <span class="n">ratio_col</span><span class="p">,</span> <span class="n">yokoya_file</span><span class="p">[</span><span class="s2">&quot;dipy&quot;</span><span class="p">])</span>
+        <span class="n">yokydip</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">interp</span><span class="p">(</span><span class="n">ratio</span><span class="p">,</span> <span class="n">ratio_col</span><span class="p">,</span> <span class="n">yokoya_file</span><span class="p">[</span><span class="s2">&quot;dipx&quot;</span><span class="p">])</span>
+        <span class="n">yokxquad</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">interp</span><span class="p">(</span><span class="n">ratio</span><span class="p">,</span> <span class="n">ratio_col</span><span class="p">,</span> <span class="n">yokoya_file</span><span class="p">[</span><span class="s2">&quot;quady&quot;</span><span class="p">])</span>
+        <span class="n">yokyquad</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">interp</span><span class="p">(</span><span class="n">ratio</span><span class="p">,</span> <span class="n">ratio_col</span><span class="p">,</span> <span class="n">yokoya_file</span><span class="p">[</span><span class="s2">&quot;quadx&quot;</span><span class="p">])</span>
+
+    <span class="k">return</span> <span class="p">(</span><span class="n">yoklong</span><span class="p">,</span> <span class="n">yokxdip</span><span class="p">,</span> <span class="n">yokydip</span><span class="p">,</span> <span class="n">yokxquad</span><span class="p">,</span> <span class="n">yokyquad</span><span class="p">)</span></div>
+
+
+<div class="viewcode-block" id="beam_loss_factor"><a class="viewcode-back" href="../../../mbtrack2.utilities.html#mbtrack2.utilities.misc.beam_loss_factor">[docs]</a><span class="k">def</span> <span class="nf">beam_loss_factor</span><span class="p">(</span><span class="n">impedance</span><span class="p">,</span> <span class="n">frequency</span><span class="p">,</span> <span class="n">spectrum</span><span class="p">,</span> <span class="n">ring</span><span class="p">):</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    Compute &quot;beam&quot; loss factor using the beam spectrum, uses a sum instead of </span>
+<span class="sd">    integral compared to loss_factor [1].</span>
+
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">    impedance : Impedance of type &quot;long&quot;</span>
+<span class="sd">    frequency : array</span>
+<span class="sd">        Sample points of spectrum.</span>
+<span class="sd">    spectrum : array</span>
+<span class="sd">        Beam spectrum to consider.</span>
+<span class="sd">    ring : Synchrotron object</span>
+
+<span class="sd">    Returns</span>
+<span class="sd">    -------</span>
+<span class="sd">    kloss_beam : float</span>
+<span class="sd">        Beam loss factor in [V/C].</span>
+
+<span class="sd">    References</span>
+<span class="sd">    ----------</span>
+<span class="sd">    [1] : Handbook of accelerator physics and engineering, 3rd printing. </span>
+<span class="sd">        Eq (3) p239.</span>
+<span class="sd">    &quot;&quot;&quot;</span>
+    <span class="n">pmax</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">floor</span><span class="p">(</span><span class="n">impedance</span><span class="o">.</span><span class="n">data</span><span class="o">.</span><span class="n">index</span><span class="o">.</span><span class="n">max</span><span class="p">()</span> <span class="o">/</span> <span class="n">ring</span><span class="o">.</span><span class="n">f0</span><span class="p">)</span>
+    <span class="n">pmin</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">floor</span><span class="p">(</span><span class="n">impedance</span><span class="o">.</span><span class="n">data</span><span class="o">.</span><span class="n">index</span><span class="o">.</span><span class="n">min</span><span class="p">()</span> <span class="o">/</span> <span class="n">ring</span><span class="o">.</span><span class="n">f0</span><span class="p">)</span>
+
+    <span class="k">if</span> <span class="n">pmin</span> <span class="o">&gt;=</span> <span class="mi">0</span><span class="p">:</span>
+        <span class="n">double_sided_impedance</span><span class="p">(</span><span class="n">impedance</span><span class="p">)</span>
+        <span class="n">pmin</span> <span class="o">=</span> <span class="o">-</span><span class="mi">1</span> <span class="o">*</span> <span class="n">pmax</span>
+
+    <span class="n">p</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="n">pmin</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span> <span class="n">pmax</span><span class="p">)</span>
+    <span class="n">pf0</span> <span class="o">=</span> <span class="n">p</span> <span class="o">*</span> <span class="n">ring</span><span class="o">.</span><span class="n">f0</span>
+    <span class="n">ReZ</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">real</span><span class="p">(</span><span class="n">impedance</span><span class="p">(</span><span class="n">pf0</span><span class="p">))</span>
+    <span class="n">spectral_density</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">spectrum</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span>
+    <span class="c1"># interpolation of the spectrum is needed to avoid problems liked to</span>
+    <span class="c1"># division by 0</span>
+    <span class="c1"># computing the spectrum directly to the frequency points gives</span>
+    <span class="c1"># wrong results</span>
+    <span class="n">spect</span> <span class="o">=</span> <span class="n">interp1d</span><span class="p">(</span><span class="n">frequency</span><span class="p">,</span> <span class="n">spectral_density</span><span class="p">)</span>
+    <span class="n">kloss_beam</span> <span class="o">=</span> <span class="n">ring</span><span class="o">.</span><span class="n">f0</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">ReZ</span> <span class="o">*</span> <span class="n">spect</span><span class="p">(</span><span class="n">pf0</span><span class="p">))</span>
+
+    <span class="k">return</span> <span class="n">kloss_beam</span></div>
+
+
+<div class="viewcode-block" id="double_sided_impedance"><a class="viewcode-back" href="../../../mbtrack2.utilities.html#mbtrack2.utilities.misc.double_sided_impedance">[docs]</a><span class="k">def</span> <span class="nf">double_sided_impedance</span><span class="p">(</span><span class="n">impedance</span><span class="p">):</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    Add negative frequency points to single sided impedance spectrum following</span>
+<span class="sd">    symetries depending on impedance type.</span>
+
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">    impedance : Impedance object</span>
+<span class="sd">        Single sided impedance.</span>
+<span class="sd">    &quot;&quot;&quot;</span>
+    <span class="n">fmin</span> <span class="o">=</span> <span class="n">impedance</span><span class="o">.</span><span class="n">data</span><span class="o">.</span><span class="n">index</span><span class="o">.</span><span class="n">min</span><span class="p">()</span>
+
+    <span class="k">if</span> <span class="n">fmin</span> <span class="o">&gt;=</span> <span class="mi">0</span><span class="p">:</span>
+        <span class="n">negative_index</span> <span class="o">=</span> <span class="n">impedance</span><span class="o">.</span><span class="n">data</span><span class="o">.</span><span class="n">index</span> <span class="o">*</span> <span class="o">-</span><span class="mi">1</span>
+        <span class="n">negative_data</span> <span class="o">=</span> <span class="n">impedance</span><span class="o">.</span><span class="n">data</span><span class="o">.</span><span class="n">set_index</span><span class="p">(</span><span class="n">negative_index</span><span class="p">)</span>
+
+        <span class="n">imp_type</span> <span class="o">=</span> <span class="n">impedance</span><span class="o">.</span><span class="n">component_type</span>
+
+        <span class="k">if</span> <span class="n">imp_type</span> <span class="o">==</span> <span class="s2">&quot;long&quot;</span><span class="p">:</span>
+            <span class="n">negative_data</span><span class="p">[</span><span class="s2">&quot;imag&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="o">-</span><span class="mi">1</span> <span class="o">*</span> <span class="n">negative_data</span><span class="p">[</span><span class="s2">&quot;imag&quot;</span><span class="p">]</span>
+
+        <span class="k">elif</span> <span class="p">(</span><span class="n">imp_type</span> <span class="o">==</span> <span class="s2">&quot;xdip&quot;</span><span class="p">)</span> <span class="ow">or</span> <span class="p">(</span><span class="n">imp_type</span> <span class="o">==</span> <span class="s2">&quot;ydip&quot;</span><span class="p">):</span>
+            <span class="n">negative_data</span><span class="p">[</span><span class="s2">&quot;real&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="o">-</span><span class="mi">1</span> <span class="o">*</span> <span class="n">negative_data</span><span class="p">[</span><span class="s2">&quot;real&quot;</span><span class="p">]</span>
+
+        <span class="k">elif</span> <span class="p">(</span><span class="n">imp_type</span> <span class="o">==</span> <span class="s2">&quot;xquad&quot;</span><span class="p">)</span> <span class="ow">or</span> <span class="p">(</span><span class="n">imp_type</span> <span class="o">==</span> <span class="s2">&quot;yquad&quot;</span><span class="p">):</span>
+            <span class="n">negative_data</span><span class="p">[</span><span class="s2">&quot;real&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="o">-</span><span class="mi">1</span> <span class="o">*</span> <span class="n">negative_data</span><span class="p">[</span><span class="s2">&quot;real&quot;</span><span class="p">]</span>
+
+        <span class="k">else</span><span class="p">:</span>
+            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">&quot;Wrong impedance type&quot;</span><span class="p">)</span>
+
+        <span class="k">try</span><span class="p">:</span>
+            <span class="n">negative_data</span> <span class="o">=</span> <span class="n">negative_data</span><span class="o">.</span><span class="n">drop</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
+        <span class="k">except</span> <span class="ne">KeyError</span><span class="p">:</span>
+            <span class="k">pass</span>
+
+        <span class="n">all_data</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">concat</span><span class="p">([</span><span class="n">impedance</span><span class="o">.</span><span class="n">data</span><span class="p">,</span> <span class="n">negative_data</span><span class="p">])</span>
+        <span class="n">all_data</span> <span class="o">=</span> <span class="n">all_data</span><span class="o">.</span><span class="n">sort_index</span><span class="p">()</span>
+        <span class="n">impedance</span><span class="o">.</span><span class="n">data</span> <span class="o">=</span> <span class="n">all_data</span></div>
+</pre></div>
+
+            <div class="clearer"></div>
+          </div>
+        </div>
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+        &#169; Copyright 2024, A. Gamelin et al.
+      Created using <a href="https://www.sphinx-doc.org/">Sphinx</a> 5.0.2.
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diff --git a/docs/build/html/_modules/mbtrack2/utilities/optics.html b/docs/build/html/_modules/mbtrack2/utilities/optics.html
new file mode 100644
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--- /dev/null
+++ b/docs/build/html/_modules/mbtrack2/utilities/optics.html
@@ -0,0 +1,865 @@
+
+<!DOCTYPE html>
+
+<html lang="en">
+  <head>
+    <meta charset="utf-8" />
+    <meta name="viewport" content="width=device-width, initial-scale=1.0" />
+    <title>mbtrack2.utilities.optics &#8212; mbtrack2 0.6.0 documentation</title>
+    <link rel="stylesheet" type="text/css" href="../../../_static/pygments.css" />
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+          <li class="nav-item nav-item-1"><a href="../../index.html" accesskey="U">Module code</a> &#187;</li>
+        <li class="nav-item nav-item-this"><a href="">mbtrack2.utilities.optics</a></li> 
+      </ul>
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+
+    <div class="document">
+      <div class="documentwrapper">
+        <div class="bodywrapper">
+          <div class="body" role="main">
+            
+  <h1>Source code for mbtrack2.utilities.optics</h1><div class="highlight"><pre>
+<span></span><span class="c1"># -*- coding: utf-8 -*-</span>
+<span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">Module where the class to store the optic functions and the lattice physical </span>
+<span class="sd">parameters are defined.</span>
+<span class="sd">&quot;&quot;&quot;</span>
+
+<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
+<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="kn">from</span> <span class="nn">scipy.interpolate</span> <span class="kn">import</span> <span class="n">interp1d</span>
+
+
+<div class="viewcode-block" id="Optics"><a class="viewcode-back" href="../../../mbtrack2.utilities.html#mbtrack2.utilities.optics.Optics">[docs]</a><span class="k">class</span> <span class="nc">Optics</span><span class="p">:</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    Class used to handle optic functions.</span>
+<span class="sd">    </span>
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">    lattice_file : str, optional if local_beta, local_alpha and </span>
+<span class="sd">        local_dispersion are specified.</span>
+<span class="sd">        AT lattice file path.</span>
+<span class="sd">    local_beta : array of shape (2,), optional if lattice_file is specified.</span>
+<span class="sd">        Beta function at the location of the tracking. Default is mean beta if</span>
+<span class="sd">        lattice has been loaded.</span>
+<span class="sd">    local_alpha : array of shape (2,), optional if lattice_file is specified.</span>
+<span class="sd">        Alpha function at the location of the tracking. Default is mean alpha </span>
+<span class="sd">        if lattice has been loaded.</span>
+<span class="sd">    local_dispersion : array of shape (4,), optional if lattice_file is </span>
+<span class="sd">        specified.</span>
+<span class="sd">        Dispersion function and derivative at the location of the tracking. </span>
+<span class="sd">        Default is zero if lattice has been loaded.  </span>
+<span class="sd">        </span>
+<span class="sd">    Attributes</span>
+<span class="sd">    ----------</span>
+<span class="sd">    use_local_values : bool</span>
+<span class="sd">        True if no lattice has been loaded.</span>
+<span class="sd">    local_gamma : array of shape (2,)</span>
+<span class="sd">        Gamma function at the location of the tracking.</span>
+<span class="sd">    lattice : AT lattice</span>
+<span class="sd">        </span>
+<span class="sd">    Methods</span>
+<span class="sd">    -------</span>
+<span class="sd">    load_from_AT(lattice_file, **kwargs)</span>
+<span class="sd">        Load a lattice from accelerator toolbox (AT).</span>
+<span class="sd">    setup_interpolation()</span>
+<span class="sd">        Setup interpolation of the optic functions.</span>
+<span class="sd">    beta(position)</span>
+<span class="sd">        Return beta functions at specific locations given by position.</span>
+<span class="sd">    alpha(position)</span>
+<span class="sd">        Return alpha functions at specific locations given by position.</span>
+<span class="sd">    gamma(position)</span>
+<span class="sd">        Return gamma functions at specific locations given by position.</span>
+<span class="sd">    dispersion(position)</span>
+<span class="sd">        Return dispersion functions at specific locations given by position.</span>
+<span class="sd">    plot(self, var, option, n_points=1000)</span>
+<span class="sd">        Plot optical variables.</span>
+<span class="sd">    &quot;&quot;&quot;</span>
+
+    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span>
+                 <span class="n">lattice_file</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+                 <span class="n">local_beta</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+                 <span class="n">local_alpha</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+                 <span class="n">local_dispersion</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+                 <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
+
+        <span class="k">if</span> <span class="n">lattice_file</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">use_local_values</span> <span class="o">=</span> <span class="kc">False</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">load_from_AT</span><span class="p">(</span><span class="n">lattice_file</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
+            <span class="k">if</span> <span class="n">local_beta</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+                <span class="bp">self</span><span class="o">.</span><span class="n">_local_beta</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">beta_array</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
+            <span class="k">else</span><span class="p">:</span>
+                <span class="bp">self</span><span class="o">.</span><span class="n">_local_beta</span> <span class="o">=</span> <span class="n">local_beta</span>
+            <span class="k">if</span> <span class="n">local_alpha</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+                <span class="bp">self</span><span class="o">.</span><span class="n">_local_alpha</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">alpha_array</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
+            <span class="k">else</span><span class="p">:</span>
+                <span class="bp">self</span><span class="o">.</span><span class="n">_local_alpha</span> <span class="o">=</span> <span class="n">local_alpha</span>
+            <span class="k">if</span> <span class="n">local_dispersion</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+                <span class="bp">self</span><span class="o">.</span><span class="n">local_dispersion</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="mi">4</span><span class="p">,</span> <span class="p">))</span>
+            <span class="k">else</span><span class="p">:</span>
+                <span class="bp">self</span><span class="o">.</span><span class="n">local_dispersion</span> <span class="o">=</span> <span class="n">local_dispersion</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">_local_gamma</span> <span class="o">=</span> <span class="p">(</span><span class="mi">1</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">_local_alpha</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">_local_beta</span>
+
+        <span class="k">else</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">use_local_values</span> <span class="o">=</span> <span class="kc">True</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">_local_beta</span> <span class="o">=</span> <span class="n">local_beta</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">_local_alpha</span> <span class="o">=</span> <span class="n">local_alpha</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">_local_gamma</span> <span class="o">=</span> <span class="p">(</span><span class="mi">1</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">_local_alpha</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">_local_beta</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">local_dispersion</span> <span class="o">=</span> <span class="n">local_dispersion</span>
+
+<div class="viewcode-block" id="Optics.load_from_AT"><a class="viewcode-back" href="../../../mbtrack2.utilities.html#mbtrack2.utilities.optics.Optics.load_from_AT">[docs]</a>    <span class="k">def</span> <span class="nf">load_from_AT</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">lattice_file</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Load a lattice from accelerator toolbox (AT).</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        lattice_file : str</span>
+<span class="sd">            AT lattice file path.</span>
+<span class="sd">        n_points : int or float, optional</span>
+<span class="sd">            Minimum number of points to use for the optic function arrays.</span>
+<span class="sd">        periodicity : int, optional</span>
+<span class="sd">            Lattice periodicity, if not specified the AT lattice periodicity is</span>
+<span class="sd">            used.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="kn">import</span> <span class="nn">at</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">n_points</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s2">&quot;n_points&quot;</span><span class="p">,</span> <span class="mf">1e3</span><span class="p">))</span>
+        <span class="n">periodicity</span> <span class="o">=</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s2">&quot;periodicity&quot;</span><span class="p">)</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">lattice</span> <span class="o">=</span> <span class="n">at</span><span class="o">.</span><span class="n">load_lattice</span><span class="p">(</span><span class="n">lattice_file</span><span class="p">)</span>
+        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">lattice</span><span class="o">.</span><span class="n">radiation</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">lattice</span><span class="o">.</span><span class="n">radiation_off</span><span class="p">()</span>
+        <span class="n">lattice</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">lattice</span><span class="o">.</span><span class="n">slice</span><span class="p">(</span><span class="n">slices</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">n_points</span><span class="p">)</span>
+        <span class="n">refpts</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">lattice</span><span class="p">))</span>
+        <span class="n">twiss0</span><span class="p">,</span> <span class="n">tune</span><span class="p">,</span> <span class="n">chrom</span><span class="p">,</span> <span class="n">twiss</span> <span class="o">=</span> <span class="n">at</span><span class="o">.</span><span class="n">linopt</span><span class="p">(</span><span class="n">lattice</span><span class="p">,</span>
+                                               <span class="n">refpts</span><span class="o">=</span><span class="n">refpts</span><span class="p">,</span>
+                                               <span class="n">get_chrom</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
+
+        <span class="k">if</span> <span class="n">periodicity</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">periodicity</span> <span class="o">=</span> <span class="n">lattice</span><span class="o">.</span><span class="n">periodicity</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">periodicity</span> <span class="o">=</span> <span class="n">periodicity</span>
+
+        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">periodicity</span> <span class="o">&gt;</span> <span class="mi">1</span><span class="p">:</span>
+            <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">periodicity</span> <span class="o">-</span> <span class="mi">1</span><span class="p">):</span>
+                <span class="n">pos</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">twiss</span><span class="o">.</span><span class="n">s_pos</span><span class="p">,</span>
+                                <span class="n">twiss</span><span class="o">.</span><span class="n">s_pos</span> <span class="o">+</span> <span class="n">twiss</span><span class="o">.</span><span class="n">s_pos</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="p">(</span><span class="n">i</span><span class="o">+</span><span class="mi">1</span><span class="p">))</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="n">pos</span> <span class="o">=</span> <span class="n">twiss</span><span class="o">.</span><span class="n">s_pos</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">position</span> <span class="o">=</span> <span class="n">pos</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">beta_array</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">tile</span><span class="p">(</span><span class="n">twiss</span><span class="o">.</span><span class="n">beta</span><span class="o">.</span><span class="n">T</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">periodicity</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">alpha_array</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">tile</span><span class="p">(</span><span class="n">twiss</span><span class="o">.</span><span class="n">alpha</span><span class="o">.</span><span class="n">T</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">periodicity</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">dispersion_array</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">tile</span><span class="p">(</span><span class="n">twiss</span><span class="o">.</span><span class="n">dispersion</span><span class="o">.</span><span class="n">T</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">periodicity</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">mu_array</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">tile</span><span class="p">(</span><span class="n">twiss</span><span class="o">.</span><span class="n">mu</span><span class="o">.</span><span class="n">T</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">periodicity</span><span class="p">)</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">position</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">position</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">lattice</span><span class="o">.</span><span class="n">circumference</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">beta_array</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">beta_array</span><span class="p">,</span>
+                                    <span class="bp">self</span><span class="o">.</span><span class="n">beta_array</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">:</span><span class="mi">1</span><span class="p">],</span>
+                                    <span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">alpha_array</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">alpha_array</span><span class="p">,</span>
+                                     <span class="bp">self</span><span class="o">.</span><span class="n">alpha_array</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">:</span><span class="mi">1</span><span class="p">],</span>
+                                     <span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">dispersion_array</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">dispersion_array</span><span class="p">,</span>
+                                          <span class="bp">self</span><span class="o">.</span><span class="n">dispersion_array</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">:</span><span class="mi">1</span><span class="p">],</span>
+                                          <span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">mu_array</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">mu_array</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">mu_array</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">:</span><span class="mi">1</span><span class="p">],</span> <span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">gamma_array</span> <span class="o">=</span> <span class="p">(</span><span class="mi">1</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">alpha_array</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">beta_array</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">tune</span> <span class="o">=</span> <span class="n">tune</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">periodicity</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">chro</span> <span class="o">=</span> <span class="n">chrom</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">periodicity</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">ac</span> <span class="o">=</span> <span class="n">at</span><span class="o">.</span><span class="n">get_mcf</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">lattice</span><span class="p">)</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">mu_array</span><span class="p">[:,</span> <span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">floor</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">mu_array</span><span class="p">[:,</span> <span class="o">-</span><span class="mi">2</span><span class="p">]</span> <span class="o">/</span>
+                                         <span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span><span class="p">))</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">tune</span><span class="p">)</span> <span class="o">*</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">setup_interpolation</span><span class="p">()</span></div>
+
+<div class="viewcode-block" id="Optics.setup_interpolation"><a class="viewcode-back" href="../../../mbtrack2.utilities.html#mbtrack2.utilities.optics.Optics.setup_interpolation">[docs]</a>    <span class="k">def</span> <span class="nf">setup_interpolation</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Setup interpolation of the optic functions.&quot;&quot;&quot;</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">betaX</span> <span class="o">=</span> <span class="n">interp1d</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">position</span><span class="p">,</span>
+                              <span class="bp">self</span><span class="o">.</span><span class="n">beta_array</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="p">:],</span>
+                              <span class="n">kind</span><span class="o">=</span><span class="s1">&#39;linear&#39;</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">betaY</span> <span class="o">=</span> <span class="n">interp1d</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">position</span><span class="p">,</span>
+                              <span class="bp">self</span><span class="o">.</span><span class="n">beta_array</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="p">:],</span>
+                              <span class="n">kind</span><span class="o">=</span><span class="s1">&#39;linear&#39;</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">alphaX</span> <span class="o">=</span> <span class="n">interp1d</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">position</span><span class="p">,</span>
+                               <span class="bp">self</span><span class="o">.</span><span class="n">alpha_array</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="p">:],</span>
+                               <span class="n">kind</span><span class="o">=</span><span class="s1">&#39;linear&#39;</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">alphaY</span> <span class="o">=</span> <span class="n">interp1d</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">position</span><span class="p">,</span>
+                               <span class="bp">self</span><span class="o">.</span><span class="n">alpha_array</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="p">:],</span>
+                               <span class="n">kind</span><span class="o">=</span><span class="s1">&#39;linear&#39;</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">gammaX</span> <span class="o">=</span> <span class="n">interp1d</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">position</span><span class="p">,</span>
+                               <span class="bp">self</span><span class="o">.</span><span class="n">gamma_array</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="p">:],</span>
+                               <span class="n">kind</span><span class="o">=</span><span class="s1">&#39;linear&#39;</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">gammaY</span> <span class="o">=</span> <span class="n">interp1d</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">position</span><span class="p">,</span>
+                               <span class="bp">self</span><span class="o">.</span><span class="n">gamma_array</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="p">:],</span>
+                               <span class="n">kind</span><span class="o">=</span><span class="s1">&#39;linear&#39;</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">dispX</span> <span class="o">=</span> <span class="n">interp1d</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">position</span><span class="p">,</span>
+                              <span class="bp">self</span><span class="o">.</span><span class="n">dispersion_array</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="p">:],</span>
+                              <span class="n">kind</span><span class="o">=</span><span class="s1">&#39;linear&#39;</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">disppX</span> <span class="o">=</span> <span class="n">interp1d</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">position</span><span class="p">,</span>
+                               <span class="bp">self</span><span class="o">.</span><span class="n">dispersion_array</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="p">:],</span>
+                               <span class="n">kind</span><span class="o">=</span><span class="s1">&#39;linear&#39;</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">dispY</span> <span class="o">=</span> <span class="n">interp1d</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">position</span><span class="p">,</span>
+                              <span class="bp">self</span><span class="o">.</span><span class="n">dispersion_array</span><span class="p">[</span><span class="mi">2</span><span class="p">,</span> <span class="p">:],</span>
+                              <span class="n">kind</span><span class="o">=</span><span class="s1">&#39;linear&#39;</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">disppY</span> <span class="o">=</span> <span class="n">interp1d</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">position</span><span class="p">,</span>
+                               <span class="bp">self</span><span class="o">.</span><span class="n">dispersion_array</span><span class="p">[</span><span class="mi">3</span><span class="p">,</span> <span class="p">:],</span>
+                               <span class="n">kind</span><span class="o">=</span><span class="s1">&#39;linear&#39;</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">muX</span> <span class="o">=</span> <span class="n">interp1d</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">position</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">mu_array</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="p">:],</span> <span class="n">kind</span><span class="o">=</span><span class="s1">&#39;linear&#39;</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">muY</span> <span class="o">=</span> <span class="n">interp1d</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">position</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">mu_array</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="p">:],</span> <span class="n">kind</span><span class="o">=</span><span class="s1">&#39;linear&#39;</span><span class="p">)</span></div>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">local_beta</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Return beta function at the location defined by the lattice file.</span>
+
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_local_beta</span>
+
+    <span class="nd">@local_beta</span><span class="o">.</span><span class="n">setter</span>
+    <span class="k">def</span> <span class="nf">local_beta</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">beta_array</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Set the values of beta function. Gamma function is automatically </span>
+<span class="sd">        recalculated after the new value of beta function is set.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        beta_array : array of shape (2,)</span>
+<span class="sd">            Beta function in the horizontal and vertical plane.</span>
+
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">_local_beta</span> <span class="o">=</span> <span class="n">beta_array</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">_local_gamma</span> <span class="o">=</span> <span class="p">(</span><span class="mi">1</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">_local_alpha</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">_local_beta</span>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">local_alpha</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Return alpha function at the location defined by the lattice file.</span>
+
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_local_alpha</span>
+
+    <span class="nd">@local_alpha</span><span class="o">.</span><span class="n">setter</span>
+    <span class="k">def</span> <span class="nf">local_alpha</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">alpha_array</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Set the value of beta functions. Gamma function is automatically </span>
+<span class="sd">        recalculated after the new value of alpha function is set.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        alpha_array : array of shape (2,)</span>
+<span class="sd">            Alpha function in the horizontal and vertical plane.</span>
+
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">_local_alpha</span> <span class="o">=</span> <span class="n">alpha_array</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">_local_gamma</span> <span class="o">=</span> <span class="p">(</span><span class="mi">1</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">_local_alpha</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">_local_beta</span>
+
+    <span class="nd">@property</span>
+    <span class="k">def</span> <span class="nf">local_gamma</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Return beta function at the location defined by the lattice file.</span>
+
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_local_gamma</span>
+
+<div class="viewcode-block" id="Optics.beta"><a class="viewcode-back" href="../../../mbtrack2.utilities.html#mbtrack2.utilities.optics.Optics.beta">[docs]</a>    <span class="k">def</span> <span class="nf">beta</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">position</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Return beta functions at specific locations given by position. If no</span>
+<span class="sd">        lattice has been loaded, local values are returned.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        position : array or float</span>
+<span class="sd">            Longitudinal position at which the beta functions are returned.</span>
+
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        beta : array</span>
+<span class="sd">            Beta functions.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">use_local_values</span><span class="p">:</span>
+            <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">outer</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">local_beta</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">ones_like</span><span class="p">(</span><span class="n">position</span><span class="p">))</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="n">beta</span> <span class="o">=</span> <span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">betaX</span><span class="p">(</span><span class="n">position</span><span class="p">),</span> <span class="bp">self</span><span class="o">.</span><span class="n">betaY</span><span class="p">(</span><span class="n">position</span><span class="p">)]</span>
+            <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">beta</span><span class="p">)</span></div>
+
+<div class="viewcode-block" id="Optics.alpha"><a class="viewcode-back" href="../../../mbtrack2.utilities.html#mbtrack2.utilities.optics.Optics.alpha">[docs]</a>    <span class="k">def</span> <span class="nf">alpha</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">position</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Return alpha functions at specific locations given by position. If no</span>
+<span class="sd">        lattice has been loaded, local values are returned.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        position : array or float</span>
+<span class="sd">            Longitudinal position at which the alpha functions are returned.</span>
+
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        alpha : array</span>
+<span class="sd">            Alpha functions.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">use_local_values</span><span class="p">:</span>
+            <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">outer</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">local_alpha</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">ones_like</span><span class="p">(</span><span class="n">position</span><span class="p">))</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="n">alpha</span> <span class="o">=</span> <span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">alphaX</span><span class="p">(</span><span class="n">position</span><span class="p">),</span> <span class="bp">self</span><span class="o">.</span><span class="n">alphaY</span><span class="p">(</span><span class="n">position</span><span class="p">)]</span>
+            <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">alpha</span><span class="p">)</span></div>
+
+<div class="viewcode-block" id="Optics.gamma"><a class="viewcode-back" href="../../../mbtrack2.utilities.html#mbtrack2.utilities.optics.Optics.gamma">[docs]</a>    <span class="k">def</span> <span class="nf">gamma</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">position</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Return gamma functions at specific locations given by position. If no</span>
+<span class="sd">        lattice has been loaded, local values are returned.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        position : array or float</span>
+<span class="sd">            Longitudinal position at which the gamma functions are returned.</span>
+
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        gamma : array</span>
+<span class="sd">            Gamma functions.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">use_local_values</span><span class="p">:</span>
+            <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">outer</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">local_gamma</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">ones_like</span><span class="p">(</span><span class="n">position</span><span class="p">))</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="n">gamma</span> <span class="o">=</span> <span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">gammaX</span><span class="p">(</span><span class="n">position</span><span class="p">),</span> <span class="bp">self</span><span class="o">.</span><span class="n">gammaY</span><span class="p">(</span><span class="n">position</span><span class="p">)]</span>
+            <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">gamma</span><span class="p">)</span></div>
+
+<div class="viewcode-block" id="Optics.dispersion"><a class="viewcode-back" href="../../../mbtrack2.utilities.html#mbtrack2.utilities.optics.Optics.dispersion">[docs]</a>    <span class="k">def</span> <span class="nf">dispersion</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">position</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Return dispersion functions at specific locations given by position. </span>
+<span class="sd">        If no lattice has been loaded, local values are returned.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        position : array or float</span>
+<span class="sd">            Longitudinal position at which the dispersion functions are </span>
+<span class="sd">            returned.</span>
+
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        dispersion : array</span>
+<span class="sd">            Dispersion functions.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">use_local_values</span><span class="p">:</span>
+            <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">outer</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">local_dispersion</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">ones_like</span><span class="p">(</span><span class="n">position</span><span class="p">))</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="n">dispersion</span> <span class="o">=</span> <span class="p">[</span>
+                <span class="bp">self</span><span class="o">.</span><span class="n">dispX</span><span class="p">(</span><span class="n">position</span><span class="p">),</span>
+                <span class="bp">self</span><span class="o">.</span><span class="n">disppX</span><span class="p">(</span><span class="n">position</span><span class="p">),</span>
+                <span class="bp">self</span><span class="o">.</span><span class="n">dispY</span><span class="p">(</span><span class="n">position</span><span class="p">),</span>
+                <span class="bp">self</span><span class="o">.</span><span class="n">disppY</span><span class="p">(</span><span class="n">position</span><span class="p">)</span>
+            <span class="p">]</span>
+            <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">dispersion</span><span class="p">)</span></div>
+
+<div class="viewcode-block" id="Optics.mu"><a class="viewcode-back" href="../../../mbtrack2.utilities.html#mbtrack2.utilities.optics.Optics.mu">[docs]</a>    <span class="k">def</span> <span class="nf">mu</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">position</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Return phase advances at specific locations given by position. </span>
+<span class="sd">        If no lattice has been loaded, None is returned.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        position : array or float</span>
+<span class="sd">            Longitudinal position at which the phase advances are returned.</span>
+
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        mu : array</span>
+<span class="sd">            Phase advances.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">use_local_values</span><span class="p">:</span>
+            <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">outer</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">]),</span> <span class="n">np</span><span class="o">.</span><span class="n">ones_like</span><span class="p">(</span><span class="n">position</span><span class="p">))</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="n">mu</span> <span class="o">=</span> <span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">muX</span><span class="p">(</span><span class="n">position</span><span class="p">),</span> <span class="bp">self</span><span class="o">.</span><span class="n">muY</span><span class="p">(</span><span class="n">position</span><span class="p">)]</span>
+            <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">mu</span><span class="p">)</span></div>
+
+<div class="viewcode-block" id="Optics.plot"><a class="viewcode-back" href="../../../mbtrack2.utilities.html#mbtrack2.utilities.optics.Optics.plot">[docs]</a>    <span class="k">def</span> <span class="nf">plot</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">var</span><span class="p">,</span> <span class="n">option</span><span class="p">,</span> <span class="n">n_points</span><span class="o">=</span><span class="mi">1000</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Plot optical variables.</span>
+<span class="sd">    </span>
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        var : {&quot;beta&quot;, &quot;alpha&quot;, &quot;gamma&quot;, &quot;dispersion&quot;, &quot;mu&quot;}</span>
+<span class="sd">            Optical variable to be plotted.</span>
+<span class="sd">        option : str</span>
+<span class="sd">            If var = &quot;beta&quot;, &quot;alpha&quot; and &quot;gamma&quot;, option = {&quot;x&quot;,&quot;y&quot;} specifying</span>
+<span class="sd">            the axis of interest.</span>
+<span class="sd">            If var = &quot;dispersion&quot;, option = {&quot;x&quot;,&quot;px&quot;,&quot;y&quot;,&quot;py&quot;} specifying the </span>
+<span class="sd">            axis of interest for the dispersion function or its derivative.</span>
+<span class="sd">        n_points : int</span>
+<span class="sd">            Number of points on the plot. The default value is 1000.</span>
+<span class="sd">    </span>
+<span class="sd">        &quot;&quot;&quot;</span>
+
+        <span class="n">var_dict</span> <span class="o">=</span> <span class="p">{</span>
+            <span class="s2">&quot;beta&quot;</span><span class="p">:</span> <span class="bp">self</span><span class="o">.</span><span class="n">beta</span><span class="p">,</span>
+            <span class="s2">&quot;alpha&quot;</span><span class="p">:</span> <span class="bp">self</span><span class="o">.</span><span class="n">alpha</span><span class="p">,</span>
+            <span class="s2">&quot;gamma&quot;</span><span class="p">:</span> <span class="bp">self</span><span class="o">.</span><span class="n">gamma</span><span class="p">,</span>
+            <span class="s2">&quot;dispersion&quot;</span><span class="p">:</span> <span class="bp">self</span><span class="o">.</span><span class="n">dispersion</span><span class="p">,</span>
+            <span class="s2">&quot;mu&quot;</span><span class="p">:</span> <span class="bp">self</span><span class="o">.</span><span class="n">mu</span>
+        <span class="p">}</span>
+
+        <span class="k">if</span> <span class="n">var</span> <span class="o">==</span> <span class="s2">&quot;dispersion&quot;</span><span class="p">:</span>
+            <span class="n">option_dict</span> <span class="o">=</span> <span class="p">{</span><span class="s2">&quot;x&quot;</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="s2">&quot;px&quot;</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span> <span class="s2">&quot;y&quot;</span><span class="p">:</span> <span class="mi">2</span><span class="p">,</span> <span class="s2">&quot;py&quot;</span><span class="p">:</span> <span class="mi">3</span><span class="p">}</span>
+
+            <span class="n">label</span> <span class="o">=</span> <span class="p">[</span><span class="s2">&quot;D$_</span><span class="si">{x}</span><span class="s2">$ (m)&quot;</span><span class="p">,</span> <span class="s2">&quot;D&#39;$_</span><span class="si">{x}</span><span class="s2">$&quot;</span><span class="p">,</span> <span class="s2">&quot;D$_</span><span class="si">{y}</span><span class="s2">$ (m)&quot;</span><span class="p">,</span> <span class="s2">&quot;D&#39;$_</span><span class="si">{y}</span><span class="s2">$&quot;</span><span class="p">]</span>
+
+            <span class="n">ylabel</span> <span class="o">=</span> <span class="n">label</span><span class="p">[</span><span class="n">option_dict</span><span class="p">[</span><span class="n">option</span><span class="p">]]</span>
+
+        <span class="k">elif</span> <span class="n">var</span> <span class="o">==</span> <span class="s2">&quot;beta&quot;</span> <span class="ow">or</span> <span class="n">var</span> <span class="o">==</span> <span class="s2">&quot;alpha&quot;</span> <span class="ow">or</span> <span class="n">var</span> <span class="o">==</span> <span class="s2">&quot;gamma&quot;</span> <span class="ow">or</span> <span class="n">var</span> <span class="o">==</span> <span class="s2">&quot;mu&quot;</span><span class="p">:</span>
+            <span class="n">option_dict</span> <span class="o">=</span> <span class="p">{</span><span class="s2">&quot;x&quot;</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="s2">&quot;y&quot;</span><span class="p">:</span> <span class="mi">1</span><span class="p">}</span>
+            <span class="n">label_dict</span> <span class="o">=</span> <span class="p">{</span>
+                <span class="s2">&quot;beta&quot;</span><span class="p">:</span> <span class="s2">&quot;$</span><span class="se">\\</span><span class="s2">beta$&quot;</span><span class="p">,</span>
+                <span class="s2">&quot;alpha&quot;</span><span class="p">:</span> <span class="s2">&quot;$</span><span class="se">\\</span><span class="s2">alpha$&quot;</span><span class="p">,</span>
+                <span class="s2">&quot;gamma&quot;</span><span class="p">:</span> <span class="s2">&quot;$</span><span class="se">\\</span><span class="s2">gamma$&quot;</span><span class="p">,</span>
+                <span class="s2">&quot;mu&quot;</span><span class="p">:</span> <span class="s2">&quot;$</span><span class="se">\\</span><span class="s2">mu$&quot;</span>
+            <span class="p">}</span>
+
+            <span class="k">if</span> <span class="n">option</span> <span class="o">==</span> <span class="s2">&quot;x&quot;</span><span class="p">:</span> <span class="n">label_sup</span> <span class="o">=</span> <span class="s2">&quot;$_</span><span class="si">{x}</span><span class="s2">$&quot;</span>
+            <span class="k">elif</span> <span class="n">option</span> <span class="o">==</span> <span class="s2">&quot;y&quot;</span><span class="p">:</span> <span class="n">label_sup</span> <span class="o">=</span> <span class="s2">&quot;$_</span><span class="si">{y}</span><span class="s2">$&quot;</span>
+
+            <span class="n">unit</span> <span class="o">=</span> <span class="p">{</span>
+                <span class="s2">&quot;beta&quot;</span><span class="p">:</span> <span class="s2">&quot; (m)&quot;</span><span class="p">,</span>
+                <span class="s2">&quot;alpha&quot;</span><span class="p">:</span> <span class="s2">&quot;&quot;</span><span class="p">,</span>
+                <span class="s2">&quot;gamma&quot;</span><span class="p">:</span> <span class="s2">&quot; (m$^{-1}$)&quot;</span><span class="p">,</span>
+                <span class="s2">&quot;mu&quot;</span><span class="p">:</span> <span class="s2">&quot;&quot;</span>
+            <span class="p">}</span>
+
+            <span class="n">ylabel</span> <span class="o">=</span> <span class="n">label_dict</span><span class="p">[</span><span class="n">var</span><span class="p">]</span> <span class="o">+</span> <span class="n">label_sup</span> <span class="o">+</span> <span class="n">unit</span><span class="p">[</span><span class="n">var</span><span class="p">]</span>
+
+        <span class="k">else</span><span class="p">:</span>
+            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">&quot;Variable name is not found.&quot;</span><span class="p">)</span>
+
+        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">use_local_values</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">True</span><span class="p">:</span>
+            <span class="n">position</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">lattice</span><span class="o">.</span><span class="n">circumference</span><span class="p">,</span>
+                                   <span class="nb">int</span><span class="p">(</span><span class="n">n_points</span><span class="p">))</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="n">position</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
+
+        <span class="n">var_list</span> <span class="o">=</span> <span class="n">var_dict</span><span class="p">[</span><span class="n">var</span><span class="p">](</span><span class="n">position</span><span class="p">)[</span><span class="n">option_dict</span><span class="p">[</span><span class="n">option</span><span class="p">]]</span>
+        <span class="n">fig</span><span class="p">,</span> <span class="n">ax</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">()</span>
+        <span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">position</span><span class="p">,</span> <span class="n">var_list</span><span class="p">)</span>
+
+        <span class="n">ax</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="s2">&quot;position (m)&quot;</span><span class="p">)</span>
+        <span class="n">ax</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="n">ylabel</span><span class="p">)</span>
+
+        <span class="k">return</span> <span class="n">fig</span></div></div>
+
+
+<div class="viewcode-block" id="PhysicalModel"><a class="viewcode-back" href="../../../mbtrack2.utilities.html#mbtrack2.utilities.optics.PhysicalModel">[docs]</a><span class="k">class</span> <span class="nc">PhysicalModel</span><span class="p">:</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    Store the lattice physical parameters such as apperture and resistivity.</span>
+<span class="sd">    </span>
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">    ring : Synchrotron object</span>
+<span class="sd">    x_right : float</span>
+<span class="sd">        Default value for the right horizontal aperture in [m].</span>
+<span class="sd">    y_top : float</span>
+<span class="sd">        Default value for the top vertical aperture in [m].</span>
+<span class="sd">    shape : str</span>
+<span class="sd">        Default value for the shape of the chamber cross section </span>
+<span class="sd">        (elli/circ/rect).</span>
+<span class="sd">    rho : float</span>
+<span class="sd">        Default value for the resistivity of the chamber material [ohm.m].</span>
+<span class="sd">    x_left : float, optional</span>
+<span class="sd">        Default value for the left horizontal aperture in [m].</span>
+<span class="sd">    y_bottom : float, optional</span>
+<span class="sd">        Default value for the bottom vertical aperture in [m]. </span>
+<span class="sd">    n_points : int or float, optional</span>
+<span class="sd">        Number of points to use in class arrays</span>
+<span class="sd">        </span>
+<span class="sd">    Attributes</span>
+<span class="sd">    ----------</span>
+<span class="sd">    position : array of shape (n_points,)</span>
+<span class="sd">        Longitudinal position in [m].</span>
+<span class="sd">    x_right : array of shape (n_points,)</span>
+<span class="sd">        Right horizontal aperture in [m].</span>
+<span class="sd">    y_top : array of shape (n_points,)</span>
+<span class="sd">        Top vertical aperture in [m].</span>
+<span class="sd">    shape : array of shape (n_points - 1,)</span>
+<span class="sd">        Shape of the chamber cross section (elli/circ/rect).</span>
+<span class="sd">    rho : array of shape (n_points - 1,)</span>
+<span class="sd">        Resistivity of the chamber material in [ohm.m].</span>
+<span class="sd">    x_left : array of shape (n_points,)</span>
+<span class="sd">        Left horizontal aperture in [m].</span>
+<span class="sd">    y_bottom : array of shape (n_points,)</span>
+<span class="sd">        Bottom vertical aperture in [m].</span>
+<span class="sd">    length : array of shape (n_points - 1,)</span>
+<span class="sd">        Length of each segments between two longitudinal positions in [m].</span>
+<span class="sd">    center : array of shape (n_points - 1,)</span>
+<span class="sd">        Center of each segments between two longitudinal positions in [m].</span>
+<span class="sd">        </span>
+<span class="sd">    Methods</span>
+<span class="sd">    -------</span>
+<span class="sd">    change_values(start_position, end_position, x_right, y_top, shape, rho)</span>
+<span class="sd">        Change the physical parameters between start_position and end_position.</span>
+<span class="sd">    taper(start_position, end_position, x_right_start, x_right_end, </span>
+<span class="sd">          y_top_start, y_top_end, shape, rho)</span>
+<span class="sd">        Change the physical parameters to have a tapered transition between </span>
+<span class="sd">        start_position and end_position.</span>
+<span class="sd">    plot_aperture()</span>
+<span class="sd">        Plot horizontal and vertical apertures.</span>
+<span class="sd">    resistive_wall_effective_radius(optics)</span>
+<span class="sd">        Return the effective radius of the chamber for resistive wall </span>
+<span class="sd">        calculations.</span>
+<span class="sd">    &quot;&quot;&quot;</span>
+
+    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span>
+                 <span class="n">ring</span><span class="p">,</span>
+                 <span class="n">x_right</span><span class="p">,</span>
+                 <span class="n">y_top</span><span class="p">,</span>
+                 <span class="n">shape</span><span class="p">,</span>
+                 <span class="n">rho</span><span class="p">,</span>
+                 <span class="n">x_left</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+                 <span class="n">y_bottom</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+                 <span class="n">n_points</span><span class="o">=</span><span class="mf">1e4</span><span class="p">):</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">n_points</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">n_points</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">position</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">ring</span><span class="o">.</span><span class="n">L</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">n_points</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">x_right</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">ones_like</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">position</span><span class="p">)</span> <span class="o">*</span> <span class="n">x_right</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">y_top</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">ones_like</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">position</span><span class="p">)</span> <span class="o">*</span> <span class="n">y_top</span>
+
+        <span class="k">if</span> <span class="n">x_left</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">x_left</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">ones_like</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">position</span><span class="p">)</span> <span class="o">*</span> <span class="o">-</span><span class="mi">1</span> <span class="o">*</span> <span class="n">x_right</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">x_left</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">ones_like</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">position</span><span class="p">)</span> <span class="o">*</span> <span class="n">x_left</span>
+
+        <span class="k">if</span> <span class="n">y_bottom</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">y_bottom</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">ones_like</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">position</span><span class="p">)</span> <span class="o">*</span> <span class="o">-</span><span class="mi">1</span> <span class="o">*</span> <span class="n">y_top</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">y_bottom</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">ones_like</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">position</span><span class="p">)</span> <span class="o">*</span> <span class="n">y_bottom</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">length</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">position</span><span class="p">[</span><span class="mi">1</span><span class="p">:]</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">position</span><span class="p">[:</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">center</span> <span class="o">=</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">position</span><span class="p">[</span><span class="mi">1</span><span class="p">:]</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">position</span><span class="p">[:</span><span class="o">-</span><span class="mi">1</span><span class="p">])</span> <span class="o">/</span> <span class="mi">2</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">rho</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">ones_like</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">center</span><span class="p">)</span> <span class="o">*</span> <span class="n">rho</span>
+
+        <span class="bp">self</span><span class="o">.</span><span class="n">shape</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">repeat</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="n">shape</span><span class="p">]),</span> <span class="bp">self</span><span class="o">.</span><span class="n">n_points</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
+
+<div class="viewcode-block" id="PhysicalModel.resistive_wall_effective_radius"><a class="viewcode-back" href="../../../mbtrack2.utilities.html#mbtrack2.utilities.optics.PhysicalModel.resistive_wall_effective_radius">[docs]</a>    <span class="k">def</span> <span class="nf">resistive_wall_effective_radius</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span>
+                                        <span class="n">optics</span><span class="p">,</span>
+                                        <span class="n">x_right</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span>
+                                        <span class="n">y_top</span><span class="o">=</span><span class="kc">True</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Return the effective radius of the chamber for resistive wall </span>
+<span class="sd">        calculations as defined in Eq. 27 of [1].</span>
+<span class="sd">        </span>
+<span class="sd">        Section with rho = 0 ohm.m are not considered in this calculation.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        optics : Optics object</span>
+<span class="sd">        x_right : bool, optional</span>
+<span class="sd">            If True, x_right is used, if Fasle, x_left is used.</span>
+<span class="sd">        y_top : bool, optional</span>
+<span class="sd">            If True, y_top is used, if Fasle, y_bottom is used.</span>
+
+<span class="sd">        Returns</span>
+<span class="sd">        -------</span>
+<span class="sd">        L : float</span>
+<span class="sd">            Total length considered in [m].</span>
+<span class="sd">        rho_star : float</span>
+<span class="sd">            Effective resistivity of the chamber material in [ohm.m].</span>
+<span class="sd">        a1_L : float</span>
+<span class="sd">            Effective longitudinal radius of the chamber of the first power in</span>
+<span class="sd">            [m].</span>
+<span class="sd">        a2_L : float</span>
+<span class="sd">            Effective longitudinal radius of the chamber of the second power </span>
+<span class="sd">            in [m].</span>
+<span class="sd">        a3_H : float</span>
+<span class="sd">            Effective horizontal radius of the chamber of the third power in</span>
+<span class="sd">            [m].</span>
+<span class="sd">        a4_H : float</span>
+<span class="sd">            Effective horizontal radius of the chamber of the fourth power in</span>
+<span class="sd">            [m].</span>
+<span class="sd">        a3_V : float</span>
+<span class="sd">            Effective vertical radius of the chamber of the third power in [m].</span>
+<span class="sd">        a4_V : float</span>
+<span class="sd">            Effective vertical radius of the chamber of the fourth power in </span>
+<span class="sd">            [m].</span>
+
+<span class="sd">        References  </span>
+<span class="sd">        ----------</span>
+<span class="sd">        [1] Skripka, Galina, et al. &quot;Simultaneous computation of intrabunch </span>
+<span class="sd">        and interbunch collective beam motions in storage rings.&quot; Nuclear </span>
+<span class="sd">        Instruments and Methods in Physics Research Section A: Accelerators, </span>
+<span class="sd">        Spectrometers, Detectors and Associated Equipment 806 (2016): 221-230.         </span>
+<span class="sd">        &quot;&quot;&quot;</span>
+
+        <span class="n">idx</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">rho</span> <span class="o">!=</span> <span class="mi">0</span>
+
+        <span class="k">if</span> <span class="n">x_right</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">:</span>
+            <span class="n">a0</span> <span class="o">=</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">x_right</span><span class="p">[</span><span class="mi">1</span><span class="p">:]</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">x_right</span><span class="p">[:</span><span class="o">-</span><span class="mi">1</span><span class="p">])</span> <span class="o">/</span> <span class="mi">2</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="n">a0</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">((</span><span class="bp">self</span><span class="o">.</span><span class="n">x_left</span><span class="p">[</span><span class="mi">1</span><span class="p">:]</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">x_left</span><span class="p">[:</span><span class="o">-</span><span class="mi">1</span><span class="p">])</span> <span class="o">/</span> <span class="mi">2</span><span class="p">)</span>
+
+        <span class="k">if</span> <span class="n">y_top</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">:</span>
+            <span class="n">b0</span> <span class="o">=</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">y_top</span><span class="p">[</span><span class="mi">1</span><span class="p">:]</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">y_top</span><span class="p">[:</span><span class="o">-</span><span class="mi">1</span><span class="p">])</span> <span class="o">/</span> <span class="mi">2</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="n">b0</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">((</span><span class="bp">self</span><span class="o">.</span><span class="n">y_bottom</span><span class="p">[</span><span class="mi">1</span><span class="p">:]</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">y_bottom</span><span class="p">[:</span><span class="o">-</span><span class="mi">1</span><span class="p">])</span> <span class="o">/</span> <span class="mi">2</span><span class="p">)</span>
+
+        <span class="n">a0</span> <span class="o">=</span> <span class="n">a0</span><span class="p">[</span><span class="n">idx</span><span class="p">]</span>
+        <span class="n">b0</span> <span class="o">=</span> <span class="n">b0</span><span class="p">[</span><span class="n">idx</span><span class="p">]</span>
+
+        <span class="n">beta</span> <span class="o">=</span> <span class="n">optics</span><span class="o">.</span><span class="n">beta</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">center</span><span class="p">[</span><span class="n">idx</span><span class="p">])</span>
+        <span class="n">length</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">length</span><span class="p">[</span><span class="n">idx</span><span class="p">]</span>
+
+        <span class="n">L</span> <span class="o">=</span> <span class="n">length</span><span class="o">.</span><span class="n">sum</span><span class="p">()</span>
+        <span class="n">sigma</span> <span class="o">=</span> <span class="mi">1</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">rho</span><span class="p">[</span><span class="n">idx</span><span class="p">]</span>
+        <span class="n">beta_H_star</span> <span class="o">=</span> <span class="mi">1</span> <span class="o">/</span> <span class="n">L</span> <span class="o">*</span> <span class="p">(</span><span class="n">length</span> <span class="o">*</span> <span class="n">beta</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="p">:])</span><span class="o">.</span><span class="n">sum</span><span class="p">()</span>
+        <span class="n">beta_V_star</span> <span class="o">=</span> <span class="mi">1</span> <span class="o">/</span> <span class="n">L</span> <span class="o">*</span> <span class="p">(</span><span class="n">length</span> <span class="o">*</span> <span class="n">beta</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="p">:])</span><span class="o">.</span><span class="n">sum</span><span class="p">()</span>
+        <span class="n">sigma_star</span> <span class="o">=</span> <span class="mi">1</span> <span class="o">/</span> <span class="n">L</span> <span class="o">*</span> <span class="p">(</span><span class="n">length</span> <span class="o">*</span> <span class="n">sigma</span><span class="p">)</span><span class="o">.</span><span class="n">sum</span><span class="p">()</span>
+
+        <span class="n">a1_H</span> <span class="o">=</span> <span class="p">(((</span><span class="n">length</span> <span class="o">*</span> <span class="n">beta</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="p">:]</span> <span class="o">/</span>
+                  <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">sigma</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="n">a0</span><span class="p">)</span><span class="o">**</span><span class="mi">1</span><span class="p">))</span><span class="o">.</span><span class="n">sum</span><span class="p">())</span><span class="o">**</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span> <span class="o">*</span> <span class="n">L</span> <span class="o">*</span> <span class="n">beta_H_star</span> <span class="o">/</span>
+                <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">sigma_star</span><span class="p">))</span><span class="o">**</span><span class="p">(</span><span class="mi">1</span> <span class="o">/</span> <span class="mi">1</span><span class="p">)</span>
+        <span class="n">a2_H</span> <span class="o">=</span> <span class="p">(((</span><span class="n">length</span> <span class="o">*</span> <span class="n">beta</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="p">:]</span> <span class="o">/</span>
+                  <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">sigma</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="n">a0</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span><span class="p">))</span><span class="o">.</span><span class="n">sum</span><span class="p">())</span><span class="o">**</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span> <span class="o">*</span> <span class="n">L</span> <span class="o">*</span> <span class="n">beta_H_star</span> <span class="o">/</span>
+                <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">sigma_star</span><span class="p">))</span><span class="o">**</span><span class="p">(</span><span class="mi">1</span> <span class="o">/</span> <span class="mi">2</span><span class="p">)</span>
+
+        <span class="n">a1_V</span> <span class="o">=</span> <span class="p">(((</span><span class="n">length</span> <span class="o">*</span> <span class="n">beta</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="p">:]</span> <span class="o">/</span>
+                  <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">sigma</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="n">b0</span><span class="p">)</span><span class="o">**</span><span class="mi">1</span><span class="p">))</span><span class="o">.</span><span class="n">sum</span><span class="p">())</span><span class="o">**</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span> <span class="o">*</span> <span class="n">L</span> <span class="o">*</span> <span class="n">beta_V_star</span> <span class="o">/</span>
+                <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">sigma_star</span><span class="p">))</span><span class="o">**</span><span class="p">(</span><span class="mi">1</span> <span class="o">/</span> <span class="mi">1</span><span class="p">)</span>
+        <span class="n">a2_V</span> <span class="o">=</span> <span class="p">(((</span><span class="n">length</span> <span class="o">*</span> <span class="n">beta</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="p">:]</span> <span class="o">/</span>
+                  <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">sigma</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="n">b0</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span><span class="p">))</span><span class="o">.</span><span class="n">sum</span><span class="p">())</span><span class="o">**</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span> <span class="o">*</span> <span class="n">L</span> <span class="o">*</span> <span class="n">beta_V_star</span> <span class="o">/</span>
+                <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">sigma_star</span><span class="p">))</span><span class="o">**</span><span class="p">(</span><span class="mi">1</span> <span class="o">/</span> <span class="mi">2</span><span class="p">)</span>
+
+        <span class="n">a3_H</span> <span class="o">=</span> <span class="p">(((</span><span class="n">length</span> <span class="o">*</span> <span class="n">beta</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="p">:]</span> <span class="o">/</span>
+                  <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">sigma</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="n">a0</span><span class="p">)</span><span class="o">**</span><span class="mi">3</span><span class="p">))</span><span class="o">.</span><span class="n">sum</span><span class="p">())</span><span class="o">**</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span> <span class="o">*</span> <span class="n">L</span> <span class="o">*</span> <span class="n">beta_H_star</span> <span class="o">/</span>
+                <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">sigma_star</span><span class="p">))</span><span class="o">**</span><span class="p">(</span><span class="mi">1</span> <span class="o">/</span> <span class="mi">3</span><span class="p">)</span>
+        <span class="n">a4_H</span> <span class="o">=</span> <span class="p">(((</span><span class="n">length</span> <span class="o">*</span> <span class="n">beta</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="p">:]</span> <span class="o">/</span>
+                  <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">sigma</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="n">a0</span><span class="p">)</span><span class="o">**</span><span class="mi">4</span><span class="p">))</span><span class="o">.</span><span class="n">sum</span><span class="p">())</span><span class="o">**</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span> <span class="o">*</span> <span class="n">L</span> <span class="o">*</span> <span class="n">beta_H_star</span> <span class="o">/</span>
+                <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">sigma_star</span><span class="p">))</span><span class="o">**</span><span class="p">(</span><span class="mi">1</span> <span class="o">/</span> <span class="mi">4</span><span class="p">)</span>
+
+        <span class="n">a3_V</span> <span class="o">=</span> <span class="p">(((</span><span class="n">length</span> <span class="o">*</span> <span class="n">beta</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="p">:]</span> <span class="o">/</span>
+                  <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">sigma</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="n">b0</span><span class="p">)</span><span class="o">**</span><span class="mi">3</span><span class="p">))</span><span class="o">.</span><span class="n">sum</span><span class="p">())</span><span class="o">**</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span> <span class="o">*</span> <span class="n">L</span> <span class="o">*</span> <span class="n">beta_V_star</span> <span class="o">/</span>
+                <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">sigma_star</span><span class="p">))</span><span class="o">**</span><span class="p">(</span><span class="mi">1</span> <span class="o">/</span> <span class="mi">3</span><span class="p">)</span>
+        <span class="n">a4_V</span> <span class="o">=</span> <span class="p">(((</span><span class="n">length</span> <span class="o">*</span> <span class="n">beta</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="p">:]</span> <span class="o">/</span>
+                  <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">sigma</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="n">b0</span><span class="p">)</span><span class="o">**</span><span class="mi">4</span><span class="p">))</span><span class="o">.</span><span class="n">sum</span><span class="p">())</span><span class="o">**</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span> <span class="o">*</span> <span class="n">L</span> <span class="o">*</span> <span class="n">beta_V_star</span> <span class="o">/</span>
+                <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">sigma_star</span><span class="p">))</span><span class="o">**</span><span class="p">(</span><span class="mi">1</span> <span class="o">/</span> <span class="mi">4</span><span class="p">)</span>
+
+        <span class="n">a1_L</span> <span class="o">=</span> <span class="nb">min</span><span class="p">((</span><span class="n">a1_H</span><span class="p">,</span> <span class="n">a1_V</span><span class="p">))</span>
+        <span class="n">a2_L</span> <span class="o">=</span> <span class="nb">min</span><span class="p">((</span><span class="n">a2_H</span><span class="p">,</span> <span class="n">a2_V</span><span class="p">))</span>
+
+        <span class="k">return</span> <span class="p">(</span><span class="n">L</span><span class="p">,</span> <span class="mi">1</span> <span class="o">/</span> <span class="n">sigma_star</span><span class="p">,</span> <span class="n">beta_H_star</span><span class="p">,</span> <span class="n">beta_V_star</span><span class="p">,</span> <span class="n">a1_L</span><span class="p">,</span> <span class="n">a2_L</span><span class="p">,</span> <span class="n">a3_H</span><span class="p">,</span>
+                <span class="n">a4_H</span><span class="p">,</span> <span class="n">a3_V</span><span class="p">,</span> <span class="n">a4_V</span><span class="p">)</span></div>
+
+<div class="viewcode-block" id="PhysicalModel.change_values"><a class="viewcode-back" href="../../../mbtrack2.utilities.html#mbtrack2.utilities.optics.PhysicalModel.change_values">[docs]</a>    <span class="k">def</span> <span class="nf">change_values</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span>
+                      <span class="n">start_position</span><span class="p">,</span>
+                      <span class="n">end_position</span><span class="p">,</span>
+                      <span class="n">x_right</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+                      <span class="n">y_top</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+                      <span class="n">shape</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+                      <span class="n">rho</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+                      <span class="n">x_left</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+                      <span class="n">y_bottom</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+                      <span class="n">sym</span><span class="o">=</span><span class="kc">True</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Change the physical parameters between start_position and end_position.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        start_position : float</span>
+<span class="sd">        end_position : float</span>
+<span class="sd">        x_right : float, optional</span>
+<span class="sd">            Right horizontal aperture in [m].</span>
+<span class="sd">        y_top : float, optional</span>
+<span class="sd">            Top vertical aperture in [m].</span>
+<span class="sd">        shape : str, optional</span>
+<span class="sd">            Shape of the chamber cross section (elli/circ/rect).</span>
+<span class="sd">        rho : float, optional</span>
+<span class="sd">            Resistivity of the chamber material [ohm.m].</span>
+<span class="sd">        x_left : float, optional</span>
+<span class="sd">            Left horizontal aperture in [m].</span>
+<span class="sd">        y_bottom : float, optional</span>
+<span class="sd">            Bottom vertical aperture in [m].</span>
+<span class="sd">        sym : bool, optional</span>
+<span class="sd">            If True, right/left and top/bottum symmetry is applied.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="n">ind</span> <span class="o">=</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">position</span> <span class="o">&gt;</span> <span class="n">start_position</span><span class="p">)</span> <span class="o">&amp;</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">position</span> <span class="o">&lt;</span> <span class="n">end_position</span><span class="p">)</span>
+        <span class="k">if</span> <span class="n">x_right</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">x_right</span><span class="p">[</span><span class="n">ind</span><span class="p">]</span> <span class="o">=</span> <span class="n">x_right</span>
+        <span class="k">if</span> <span class="n">y_top</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">y_top</span><span class="p">[</span><span class="n">ind</span><span class="p">]</span> <span class="o">=</span> <span class="n">y_top</span>
+        <span class="k">if</span> <span class="n">x_left</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">x_left</span><span class="p">[</span><span class="n">ind</span><span class="p">]</span> <span class="o">=</span> <span class="n">x_left</span>
+        <span class="k">elif</span> <span class="p">(</span><span class="n">x_right</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">)</span> <span class="ow">and</span> <span class="p">(</span><span class="n">sym</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">):</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">x_left</span><span class="p">[</span><span class="n">ind</span><span class="p">]</span> <span class="o">=</span> <span class="o">-</span><span class="mi">1</span> <span class="o">*</span> <span class="n">x_right</span>
+        <span class="k">if</span> <span class="n">y_bottom</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">y_bottom</span><span class="p">[</span><span class="n">ind</span><span class="p">]</span> <span class="o">=</span> <span class="n">y_bottom</span>
+        <span class="k">elif</span> <span class="p">(</span><span class="n">y_top</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">)</span> <span class="ow">and</span> <span class="p">(</span><span class="n">sym</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">):</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">y_bottom</span><span class="p">[</span><span class="n">ind</span><span class="p">]</span> <span class="o">=</span> <span class="o">-</span><span class="mi">1</span> <span class="o">*</span> <span class="n">y_top</span>
+
+        <span class="n">ind2</span> <span class="o">=</span> <span class="p">((</span><span class="bp">self</span><span class="o">.</span><span class="n">position</span><span class="p">[:</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">&gt;</span> <span class="n">start_position</span><span class="p">)</span> <span class="o">&amp;</span>
+                <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">position</span><span class="p">[</span><span class="mi">1</span><span class="p">:]</span> <span class="o">&lt;</span> <span class="n">end_position</span><span class="p">))</span>
+        <span class="k">if</span> <span class="n">rho</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">rho</span><span class="p">[</span><span class="n">ind2</span><span class="p">]</span> <span class="o">=</span> <span class="n">rho</span>
+        <span class="k">if</span> <span class="n">shape</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="n">ind2</span><span class="p">]</span> <span class="o">=</span> <span class="n">shape</span></div>
+
+<div class="viewcode-block" id="PhysicalModel.taper"><a class="viewcode-back" href="../../../mbtrack2.utilities.html#mbtrack2.utilities.optics.PhysicalModel.taper">[docs]</a>    <span class="k">def</span> <span class="nf">taper</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span>
+              <span class="n">start_position</span><span class="p">,</span>
+              <span class="n">end_position</span><span class="p">,</span>
+              <span class="n">x_right_start</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+              <span class="n">x_right_end</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+              <span class="n">y_top_start</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+              <span class="n">y_top_end</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+              <span class="n">shape</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+              <span class="n">rho</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+              <span class="n">x_left_start</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+              <span class="n">x_left_end</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+              <span class="n">y_bottom_start</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+              <span class="n">y_bottom_end</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+              <span class="n">sym</span><span class="o">=</span><span class="kc">True</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">        Change the physical parameters to have a tapered transition between </span>
+<span class="sd">        start_position and end_position.</span>
+
+<span class="sd">        Parameters</span>
+<span class="sd">        ----------</span>
+<span class="sd">        start_position : float</span>
+<span class="sd">        end_position : float</span>
+<span class="sd">        x_right_start : float</span>
+<span class="sd">            Right horizontal aperture at the start of the taper in [m].</span>
+<span class="sd">        x_right_end : float</span>
+<span class="sd">            Right horizontal aperture at the end of the taper in [m].</span>
+<span class="sd">        y_top_start : float</span>
+<span class="sd">            Top vertical aperture at the start of the taper in [m].</span>
+<span class="sd">        y_top_end : float</span>
+<span class="sd">            Top vertical aperture at the end of the taper in [m].</span>
+<span class="sd">        shape : str</span>
+<span class="sd">            Shape of the chamber cross section (elli/circ/rect).</span>
+<span class="sd">        rho : float</span>
+<span class="sd">            Resistivity of the chamber material [ohm.m].</span>
+<span class="sd">        x_left_start : float, optional</span>
+<span class="sd">            Left horizontal aperture at the start of the taper in [m].</span>
+<span class="sd">        x_left_end : float, optional</span>
+<span class="sd">            Left horizontal aperture at the end of the taper in [m].</span>
+<span class="sd">        y_bottom_start : float, optional</span>
+<span class="sd">            Bottom vertical aperture at the start of the taper in [m].</span>
+<span class="sd">        y_bottom_end : float, optional</span>
+<span class="sd">            Bottom vertical aperture at the end of the taper in [m].</span>
+<span class="sd">        sym : bool, optional</span>
+<span class="sd">            If True, right/left and top/bottum symmetry is applied.</span>
+<span class="sd">        &quot;&quot;&quot;</span>
+        <span class="n">ind</span> <span class="o">=</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">position</span> <span class="o">&gt;</span> <span class="n">start_position</span><span class="p">)</span> <span class="o">&amp;</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">position</span> <span class="o">&lt;</span> <span class="n">end_position</span><span class="p">)</span>
+        <span class="k">if</span> <span class="p">(</span><span class="n">x_right_start</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">)</span> <span class="ow">and</span> <span class="p">(</span><span class="n">x_right_end</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">):</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">x_right</span><span class="p">[</span><span class="n">ind</span><span class="p">]</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="n">x_right_start</span><span class="p">,</span> <span class="n">x_right_end</span><span class="p">,</span>
+                                            <span class="nb">sum</span><span class="p">(</span><span class="n">ind</span><span class="p">))</span>
+            <span class="k">if</span> <span class="n">sym</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">:</span>
+                <span class="bp">self</span><span class="o">.</span><span class="n">x_left</span><span class="p">[</span><span class="n">ind</span><span class="p">]</span> <span class="o">=</span> <span class="o">-</span><span class="mi">1</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="n">x_right_start</span><span class="p">,</span> <span class="n">x_right_end</span><span class="p">,</span>
+                                                    <span class="nb">sum</span><span class="p">(</span><span class="n">ind</span><span class="p">))</span>
+
+        <span class="k">if</span> <span class="p">(</span><span class="n">y_top_start</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">)</span> <span class="ow">and</span> <span class="p">(</span><span class="n">y_top_end</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">):</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">y_top</span><span class="p">[</span><span class="n">ind</span><span class="p">]</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="n">y_top_start</span><span class="p">,</span> <span class="n">y_top_end</span><span class="p">,</span> <span class="nb">sum</span><span class="p">(</span><span class="n">ind</span><span class="p">))</span>
+            <span class="k">if</span> <span class="n">sym</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">:</span>
+                <span class="bp">self</span><span class="o">.</span><span class="n">y_bottom</span><span class="p">[</span><span class="n">ind</span><span class="p">]</span> <span class="o">=</span> <span class="o">-</span><span class="mi">1</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="n">y_top_start</span><span class="p">,</span> <span class="n">y_top_end</span><span class="p">,</span>
+                                                      <span class="nb">sum</span><span class="p">(</span><span class="n">ind</span><span class="p">))</span>
+
+        <span class="k">if</span> <span class="p">(</span><span class="n">x_left_start</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">)</span> <span class="ow">and</span> <span class="p">(</span><span class="n">x_left_end</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">):</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">x_left</span><span class="p">[</span><span class="n">ind</span><span class="p">]</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="n">x_left_start</span><span class="p">,</span> <span class="n">x_left_end</span><span class="p">,</span> <span class="nb">sum</span><span class="p">(</span><span class="n">ind</span><span class="p">))</span>
+        <span class="k">if</span> <span class="p">(</span><span class="n">y_bottom_start</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">)</span> <span class="ow">and</span> <span class="p">(</span><span class="n">y_bottom_end</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">):</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">y_bottom</span><span class="p">[</span><span class="n">ind</span><span class="p">]</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="n">y_bottom_start</span><span class="p">,</span> <span class="n">y_bottom_end</span><span class="p">,</span>
+                                             <span class="nb">sum</span><span class="p">(</span><span class="n">ind</span><span class="p">))</span>
+
+        <span class="n">ind2</span> <span class="o">=</span> <span class="p">((</span><span class="bp">self</span><span class="o">.</span><span class="n">position</span><span class="p">[:</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">&gt;</span> <span class="n">start_position</span><span class="p">)</span> <span class="o">&amp;</span>
+                <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">position</span><span class="p">[</span><span class="mi">1</span><span class="p">:]</span> <span class="o">&lt;</span> <span class="n">end_position</span><span class="p">))</span>
+        <span class="k">if</span> <span class="n">rho</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">rho</span><span class="p">[</span><span class="n">ind2</span><span class="p">]</span> <span class="o">=</span> <span class="n">rho</span>
+        <span class="k">if</span> <span class="n">shape</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="bp">self</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="n">ind2</span><span class="p">]</span> <span class="o">=</span> <span class="n">shape</span></div>
+
+<div class="viewcode-block" id="PhysicalModel.plot_aperture"><a class="viewcode-back" href="../../../mbtrack2.utilities.html#mbtrack2.utilities.optics.PhysicalModel.plot_aperture">[docs]</a>    <span class="k">def</span> <span class="nf">plot_aperture</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Plot horizontal and vertical apertures.&quot;&quot;&quot;</span>
+        <span class="n">fig</span><span class="p">,</span> <span class="n">axs</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span>
+        <span class="n">axs</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">position</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">x_right</span> <span class="o">*</span> <span class="mf">1e3</span><span class="p">)</span>
+        <span class="n">axs</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">position</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">x_left</span> <span class="o">*</span> <span class="mf">1e3</span><span class="p">)</span>
+        <span class="n">axs</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">set</span><span class="p">(</span><span class="n">xlabel</span><span class="o">=</span><span class="s2">&quot;Longitudinal position [m]&quot;</span><span class="p">,</span>
+                   <span class="n">ylabel</span><span class="o">=</span><span class="s2">&quot;Horizontal aperture [mm]&quot;</span><span class="p">)</span>
+        <span class="n">axs</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">legend</span><span class="p">([</span><span class="s2">&quot;Right&quot;</span><span class="p">,</span> <span class="s2">&quot;Left&quot;</span><span class="p">])</span>
+
+        <span class="n">axs</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">position</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">y_top</span> <span class="o">*</span> <span class="mf">1e3</span><span class="p">)</span>
+        <span class="n">axs</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">position</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">y_bottom</span> <span class="o">*</span> <span class="mf">1e3</span><span class="p">)</span>
+        <span class="n">axs</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">set</span><span class="p">(</span><span class="n">xlabel</span><span class="o">=</span><span class="s2">&quot;Longitudinal position [m]&quot;</span><span class="p">,</span>
+                   <span class="n">ylabel</span><span class="o">=</span><span class="s2">&quot;Vertical aperture [mm]&quot;</span><span class="p">)</span>
+        <span class="n">axs</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">legend</span><span class="p">([</span><span class="s2">&quot;Top&quot;</span><span class="p">,</span> <span class="s2">&quot;Bottom&quot;</span><span class="p">])</span>
+
+        <span class="k">return</span> <span class="p">(</span><span class="n">fig</span><span class="p">,</span> <span class="n">axs</span><span class="p">)</span></div>
+
+<div class="viewcode-block" id="PhysicalModel.get_aperture"><a class="viewcode-back" href="../../../mbtrack2.utilities.html#mbtrack2.utilities.optics.PhysicalModel.get_aperture">[docs]</a>    <span class="k">def</span> <span class="nf">get_aperture</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">s</span><span class="p">):</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">xp</span> <span class="o">=</span> <span class="n">interp1d</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">position</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">x_right</span><span class="p">,</span> <span class="n">kind</span><span class="o">=</span><span class="s1">&#39;linear&#39;</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">xm</span> <span class="o">=</span> <span class="n">interp1d</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">position</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">x_left</span><span class="p">,</span> <span class="n">kind</span><span class="o">=</span><span class="s1">&#39;linear&#39;</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">yp</span> <span class="o">=</span> <span class="n">interp1d</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">position</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">y_top</span><span class="p">,</span> <span class="n">kind</span><span class="o">=</span><span class="s1">&#39;linear&#39;</span><span class="p">)</span>
+        <span class="bp">self</span><span class="o">.</span><span class="n">ym</span> <span class="o">=</span> <span class="n">interp1d</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">position</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">y_bottom</span><span class="p">,</span> <span class="n">kind</span><span class="o">=</span><span class="s1">&#39;linear&#39;</span><span class="p">)</span>
+        <span class="n">aperture</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="bp">self</span><span class="o">.</span><span class="n">xp</span><span class="p">(</span><span class="n">s</span><span class="p">),</span> <span class="bp">self</span><span class="o">.</span><span class="n">xm</span><span class="p">(</span><span class="n">s</span><span class="p">),</span> <span class="bp">self</span><span class="o">.</span><span class="n">yp</span><span class="p">(</span><span class="n">s</span><span class="p">),</span> <span class="bp">self</span><span class="o">.</span><span class="n">ym</span><span class="p">(</span><span class="n">s</span><span class="p">)])</span>
+        <span class="k">return</span> <span class="n">aperture</span></div>
+
+<div class="viewcode-block" id="PhysicalModel.plot_resistivity"><a class="viewcode-back" href="../../../mbtrack2.utilities.html#mbtrack2.utilities.optics.PhysicalModel.plot_resistivity">[docs]</a>    <span class="k">def</span> <span class="nf">plot_resistivity</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w">        </span><span class="sd">&quot;&quot;&quot;Plot resistivity along the ring.&quot;&quot;&quot;</span>
+        <span class="n">fig</span><span class="p">,</span> <span class="n">ax</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
+        <span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">position</span><span class="p">[</span><span class="mi">1</span><span class="p">:],</span> <span class="bp">self</span><span class="o">.</span><span class="n">rho</span><span class="p">)</span>
+        <span class="n">ax</span><span class="o">.</span><span class="n">set</span><span class="p">(</span><span class="n">xlabel</span><span class="o">=</span><span class="s2">&quot;Longitudinal position [m]&quot;</span><span class="p">,</span>
+               <span class="n">ylabel</span><span class="o">=</span><span class="s2">&quot;Resistivity [ohm.m]&quot;</span><span class="p">)</span>
+
+        <span class="k">return</span> <span class="p">(</span><span class="n">fig</span><span class="p">,</span> <span class="n">ax</span><span class="p">)</span></div></div>
+</pre></div>
+
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+  <h1>Source code for mbtrack2.utilities.read_impedance</h1><div class="highlight"><pre>
+<span></span><span class="c1"># -*- coding: utf-8 -*-</span>
+<span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">Module where function used to import impedance and wakes from other codes are</span>
+<span class="sd">defined.</span>
+<span class="sd">&quot;&quot;&quot;</span>
+
+<span class="kn">import</span> <span class="nn">os</span>
+<span class="kn">import</span> <span class="nn">re</span>
+<span class="kn">from</span> <span class="nn">pathlib</span> <span class="kn">import</span> <span class="n">Path</span>
+<span class="kn">from</span> <span class="nn">tempfile</span> <span class="kn">import</span> <span class="n">NamedTemporaryFile</span>
+
+<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="kn">import</span> <span class="nn">pandas</span> <span class="k">as</span> <span class="nn">pd</span>
+<span class="kn">from</span> <span class="nn">scipy.constants</span> <span class="kn">import</span> <span class="n">c</span>
+
+<span class="kn">from</span> <span class="nn">mbtrack2.impedance.wakefield</span> <span class="kn">import</span> <span class="n">Impedance</span><span class="p">,</span> <span class="n">WakeField</span><span class="p">,</span> <span class="n">WakeFunction</span>
+
+
+<div class="viewcode-block" id="read_CST"><a class="viewcode-back" href="../../../mbtrack2.utilities.html#mbtrack2.utilities.read_impedance.read_CST">[docs]</a><span class="k">def</span> <span class="nf">read_CST</span><span class="p">(</span><span class="n">file</span><span class="p">,</span> <span class="n">component_type</span><span class="o">=</span><span class="s1">&#39;long&#39;</span><span class="p">,</span> <span class="n">divide_by</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">imp</span><span class="o">=</span><span class="kc">True</span><span class="p">):</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    Read CST text file format into an Impedance or WakeFunction object.</span>
+
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">    file : str</span>
+<span class="sd">        Path to the text file to read.</span>
+<span class="sd">    component_type : str, optional</span>
+<span class="sd">        Type of the Impedance or WakeFunction object to load.</span>
+<span class="sd">        Default is &#39;long&#39;.</span>
+<span class="sd">    divide_by : float, optional</span>
+<span class="sd">        Divide the impedance by a value. Mainly used to normalize transverse</span>
+<span class="sd">        impedance by displacement.</span>
+<span class="sd">        Default is None.</span>
+<span class="sd">    imp : bool, optional.</span>
+<span class="sd">        If True a Impedance object is loaded, if False a WakeFunction object is</span>
+<span class="sd">        loaded.</span>
+<span class="sd">        Default is True.</span>
+
+<span class="sd">    Returns</span>
+<span class="sd">    -------</span>
+<span class="sd">    result : Impedance or WakeFunction object.</span>
+<span class="sd">        Data from file.</span>
+<span class="sd">    &quot;&quot;&quot;</span>
+    <span class="k">if</span> <span class="n">imp</span><span class="p">:</span>
+        <span class="n">df</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">read_csv</span><span class="p">(</span><span class="n">file</span><span class="p">,</span>
+                         <span class="n">comment</span><span class="o">=</span><span class="s2">&quot;#&quot;</span><span class="p">,</span>
+                         <span class="n">header</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+                         <span class="n">sep</span><span class="o">=</span><span class="s2">&quot;</span><span class="se">\t</span><span class="s2">&quot;</span><span class="p">,</span>
+                         <span class="n">names</span><span class="o">=</span><span class="p">[</span><span class="s2">&quot;Frequency&quot;</span><span class="p">,</span> <span class="s2">&quot;Real&quot;</span><span class="p">,</span> <span class="s2">&quot;Imaginary&quot;</span><span class="p">])</span>
+        <span class="n">df</span><span class="p">[</span><span class="s2">&quot;Frequency&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="n">df</span><span class="p">[</span><span class="s2">&quot;Frequency&quot;</span><span class="p">]</span> <span class="o">*</span> <span class="mf">1e9</span>
+        <span class="k">if</span> <span class="n">divide_by</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="n">df</span><span class="p">[</span><span class="s2">&quot;Real&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="n">df</span><span class="p">[</span><span class="s2">&quot;Real&quot;</span><span class="p">]</span> <span class="o">/</span> <span class="n">divide_by</span>
+            <span class="n">df</span><span class="p">[</span><span class="s2">&quot;Imaginary&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="n">df</span><span class="p">[</span><span class="s2">&quot;Imaginary&quot;</span><span class="p">]</span> <span class="o">/</span> <span class="n">divide_by</span>
+        <span class="k">if</span> <span class="n">component_type</span> <span class="o">==</span> <span class="s2">&quot;long&quot;</span><span class="p">:</span>
+            <span class="n">df</span><span class="p">[</span><span class="s2">&quot;Real&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">df</span><span class="p">[</span><span class="s2">&quot;Real&quot;</span><span class="p">])</span>
+        <span class="n">df</span><span class="o">.</span><span class="n">set_index</span><span class="p">(</span><span class="s2">&quot;Frequency&quot;</span><span class="p">,</span> <span class="n">inplace</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
+        <span class="n">result</span> <span class="o">=</span> <span class="n">Impedance</span><span class="p">(</span><span class="n">variable</span><span class="o">=</span><span class="n">df</span><span class="o">.</span><span class="n">index</span><span class="p">,</span>
+                           <span class="n">function</span><span class="o">=</span><span class="n">df</span><span class="p">[</span><span class="s2">&quot;Real&quot;</span><span class="p">]</span> <span class="o">+</span> <span class="mi">1</span><span class="n">j</span> <span class="o">*</span> <span class="n">df</span><span class="p">[</span><span class="s2">&quot;Imaginary&quot;</span><span class="p">],</span>
+                           <span class="n">component_type</span><span class="o">=</span><span class="n">component_type</span><span class="p">)</span>
+    <span class="k">else</span><span class="p">:</span>
+        <span class="n">df</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">read_csv</span><span class="p">(</span><span class="n">file</span><span class="p">,</span>
+                         <span class="n">comment</span><span class="o">=</span><span class="s2">&quot;#&quot;</span><span class="p">,</span>
+                         <span class="n">header</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+                         <span class="n">sep</span><span class="o">=</span><span class="s2">&quot;</span><span class="se">\t</span><span class="s2">&quot;</span><span class="p">,</span>
+                         <span class="n">names</span><span class="o">=</span><span class="p">[</span><span class="s2">&quot;Distance&quot;</span><span class="p">,</span> <span class="s2">&quot;Wake&quot;</span><span class="p">])</span>
+        <span class="n">df</span><span class="p">[</span><span class="s2">&quot;Time&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="n">df</span><span class="p">[</span><span class="s2">&quot;Distance&quot;</span><span class="p">]</span> <span class="o">*</span> <span class="mf">1e-3</span> <span class="o">/</span> <span class="n">c</span>
+        <span class="n">df</span><span class="p">[</span><span class="s2">&quot;Wake&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="n">df</span><span class="p">[</span><span class="s2">&quot;Wake&quot;</span><span class="p">]</span> <span class="o">*</span> <span class="mf">1e12</span>
+        <span class="k">if</span> <span class="n">divide_by</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
+            <span class="n">df</span><span class="p">[</span><span class="s2">&quot;Wake&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="n">df</span><span class="p">[</span><span class="s2">&quot;Wake&quot;</span><span class="p">]</span> <span class="o">/</span> <span class="n">divide_by</span>
+        <span class="n">df</span><span class="o">.</span><span class="n">set_index</span><span class="p">(</span><span class="s2">&quot;Time&quot;</span><span class="p">,</span> <span class="n">inplace</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
+        <span class="n">result</span> <span class="o">=</span> <span class="n">WakeFunction</span><span class="p">(</span><span class="n">variable</span><span class="o">=</span><span class="n">df</span><span class="o">.</span><span class="n">index</span><span class="p">,</span>
+                              <span class="n">function</span><span class="o">=</span><span class="n">df</span><span class="p">[</span><span class="s2">&quot;Wake&quot;</span><span class="p">],</span>
+                              <span class="n">component_type</span><span class="o">=</span><span class="n">component_type</span><span class="p">)</span>
+    <span class="k">return</span> <span class="n">result</span></div>
+
+
+<div class="viewcode-block" id="read_IW2D"><a class="viewcode-back" href="../../../mbtrack2.utilities.html#mbtrack2.utilities.read_impedance.read_IW2D">[docs]</a><span class="k">def</span> <span class="nf">read_IW2D</span><span class="p">(</span><span class="n">file</span><span class="p">,</span> <span class="n">file_type</span><span class="o">=</span><span class="s1">&#39;Zlong&#39;</span><span class="p">,</span> <span class="n">output</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    Read IW2D file format into an Impedance object or a WakeField object.</span>
+
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">    file : str</span>
+<span class="sd">        Path to the file to read.</span>
+<span class="sd">    file_type : str, optional</span>
+<span class="sd">        Type of the Impedance or WakeField object.</span>
+<span class="sd">    output : bool, optional</span>
+<span class="sd">        If True, print out the interpolated values.</span>
+<span class="sd">        Default is False.</span>
+
+<span class="sd">    Returns</span>
+<span class="sd">    -------</span>
+<span class="sd">    result : Impedance or WakeField object</span>
+<span class="sd">        Data from file.</span>
+<span class="sd">    &quot;&quot;&quot;</span>
+    <span class="k">if</span> <span class="n">file_type</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">==</span> <span class="s2">&quot;Z&quot;</span><span class="p">:</span>
+        <span class="n">df</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">read_csv</span><span class="p">(</span><span class="n">file</span><span class="p">,</span>
+                         <span class="n">delim_whitespace</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span>
+                         <span class="n">header</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+                         <span class="n">names</span><span class="o">=</span><span class="p">[</span><span class="s2">&quot;Frequency&quot;</span><span class="p">,</span> <span class="s2">&quot;Real&quot;</span><span class="p">,</span> <span class="s2">&quot;Imaginary&quot;</span><span class="p">],</span>
+                         <span class="n">skiprows</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
+        <span class="n">df</span><span class="o">.</span><span class="n">set_index</span><span class="p">(</span><span class="s2">&quot;Frequency&quot;</span><span class="p">,</span> <span class="n">inplace</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
+        <span class="n">df</span> <span class="o">=</span> <span class="n">df</span><span class="p">[</span><span class="n">df</span><span class="p">[</span><span class="s2">&quot;Real&quot;</span><span class="p">]</span><span class="o">.</span><span class="n">notna</span><span class="p">()]</span>
+        <span class="n">df</span> <span class="o">=</span> <span class="n">df</span><span class="p">[</span><span class="n">df</span><span class="p">[</span><span class="s2">&quot;Imaginary&quot;</span><span class="p">]</span><span class="o">.</span><span class="n">notna</span><span class="p">()]</span>
+        <span class="n">result</span> <span class="o">=</span> <span class="n">Impedance</span><span class="p">(</span><span class="n">variable</span><span class="o">=</span><span class="n">df</span><span class="o">.</span><span class="n">index</span><span class="p">,</span>
+                           <span class="n">function</span><span class="o">=</span><span class="n">df</span><span class="p">[</span><span class="s2">&quot;Real&quot;</span><span class="p">]</span> <span class="o">+</span> <span class="mi">1</span><span class="n">j</span> <span class="o">*</span> <span class="n">df</span><span class="p">[</span><span class="s2">&quot;Imaginary&quot;</span><span class="p">],</span>
+                           <span class="n">component_type</span><span class="o">=</span><span class="n">file_type</span><span class="p">[</span><span class="mi">1</span><span class="p">:])</span>
+    <span class="k">elif</span> <span class="n">file_type</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">==</span> <span class="s2">&quot;W&quot;</span><span class="p">:</span>
+        <span class="n">df</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">read_csv</span><span class="p">(</span><span class="n">file</span><span class="p">,</span>
+                         <span class="n">delim_whitespace</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span>
+                         <span class="n">header</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+                         <span class="n">names</span><span class="o">=</span><span class="p">[</span><span class="s2">&quot;Distance&quot;</span><span class="p">,</span> <span class="s2">&quot;Wake&quot;</span><span class="p">],</span>
+                         <span class="n">skiprows</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
+        <span class="n">df</span><span class="p">[</span><span class="s2">&quot;Time&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="n">df</span><span class="p">[</span><span class="s2">&quot;Distance&quot;</span><span class="p">]</span> <span class="o">/</span> <span class="n">c</span>
+        <span class="n">df</span><span class="o">.</span><span class="n">set_index</span><span class="p">(</span><span class="s2">&quot;Time&quot;</span><span class="p">,</span> <span class="n">inplace</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
+        <span class="k">if</span> <span class="n">np</span><span class="o">.</span><span class="n">any</span><span class="p">(</span><span class="n">df</span><span class="o">.</span><span class="n">isna</span><span class="p">()):</span>
+            <span class="n">index</span> <span class="o">=</span> <span class="n">df</span><span class="o">.</span><span class="n">isna</span><span class="p">()</span><span class="o">.</span><span class="n">values</span>
+            <span class="n">df</span> <span class="o">=</span> <span class="n">df</span><span class="o">.</span><span class="n">interpolate</span><span class="p">()</span>
+            <span class="k">if</span> <span class="n">output</span><span class="p">:</span>
+                <span class="nb">print</span><span class="p">(</span><span class="s2">&quot;Nan values have been interpolated to:&quot;</span><span class="p">)</span>
+                <span class="nb">print</span><span class="p">(</span><span class="n">df</span><span class="p">[</span><span class="n">index</span><span class="p">])</span>
+        <span class="n">result</span> <span class="o">=</span> <span class="n">WakeFunction</span><span class="p">(</span><span class="n">variable</span><span class="o">=</span><span class="n">df</span><span class="o">.</span><span class="n">index</span><span class="p">,</span>
+                              <span class="n">function</span><span class="o">=</span><span class="n">df</span><span class="p">[</span><span class="s2">&quot;Wake&quot;</span><span class="p">],</span>
+                              <span class="n">component_type</span><span class="o">=</span><span class="n">file_type</span><span class="p">[</span><span class="mi">1</span><span class="p">:])</span>
+    <span class="k">else</span><span class="p">:</span>
+        <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">&quot;file_type should begin by Z or W.&quot;</span><span class="p">)</span>
+    <span class="k">return</span> <span class="n">result</span></div>
+
+
+<div class="viewcode-block" id="read_IW2D_folder"><a class="viewcode-back" href="../../../mbtrack2.utilities.html#mbtrack2.utilities.read_impedance.read_IW2D_folder">[docs]</a><span class="k">def</span> <span class="nf">read_IW2D_folder</span><span class="p">(</span><span class="n">folder</span><span class="p">,</span> <span class="n">suffix</span><span class="p">,</span> <span class="n">select</span><span class="o">=</span><span class="s2">&quot;WZ&quot;</span><span class="p">,</span> <span class="n">output</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    Read IW2D results into a WakeField object.</span>
+
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">    folder : str</span>
+<span class="sd">        Path to the folder to read.</span>
+<span class="sd">    suffix : str</span>
+<span class="sd">        End of the name of each files. For example, in &quot;Zlong_test.dat&quot; the</span>
+<span class="sd">        suffix should be &quot;_test.dat&quot;.</span>
+<span class="sd">    select : str, optional</span>
+<span class="sd">        Select which object to load. &quot;W&quot; for WakeFunction, &quot;Z&quot; for Impedance</span>
+<span class="sd">        and &quot;WZ&quot; or &quot;ZW&quot; for both.</span>
+<span class="sd">    output : bool, optional</span>
+<span class="sd">        If True, print out the interpolated values.</span>
+<span class="sd">        Default is False.</span>
+
+<span class="sd">    Returns</span>
+<span class="sd">    -------</span>
+<span class="sd">    result : WakeField object</span>
+<span class="sd">        WakeField object with Impedance and WakeFunction objects from the</span>
+<span class="sd">        different files.</span>
+<span class="sd">    &quot;&quot;&quot;</span>
+    <span class="k">if</span> <span class="p">(</span><span class="n">select</span> <span class="o">==</span> <span class="s2">&quot;WZ&quot;</span><span class="p">)</span> <span class="ow">or</span> <span class="p">(</span><span class="n">select</span> <span class="o">==</span> <span class="s2">&quot;ZW&quot;</span><span class="p">):</span>
+        <span class="n">types</span> <span class="o">=</span> <span class="p">{</span><span class="s2">&quot;W&quot;</span><span class="p">:</span> <span class="n">WakeFunction</span><span class="p">,</span> <span class="s2">&quot;Z&quot;</span><span class="p">:</span> <span class="n">Impedance</span><span class="p">}</span>
+    <span class="k">elif</span> <span class="p">(</span><span class="n">select</span> <span class="o">==</span> <span class="s2">&quot;W&quot;</span><span class="p">):</span>
+        <span class="n">types</span> <span class="o">=</span> <span class="p">{</span><span class="s2">&quot;W&quot;</span><span class="p">:</span> <span class="n">WakeFunction</span><span class="p">}</span>
+    <span class="k">elif</span> <span class="p">(</span><span class="n">select</span> <span class="o">==</span> <span class="s2">&quot;Z&quot;</span><span class="p">):</span>
+        <span class="n">types</span> <span class="o">=</span> <span class="p">{</span><span class="s2">&quot;Z&quot;</span><span class="p">:</span> <span class="n">Impedance</span><span class="p">}</span>
+    <span class="k">else</span><span class="p">:</span>
+        <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">&quot;select should be W, Z or WZ.&quot;</span><span class="p">)</span>
+
+    <span class="n">components</span> <span class="o">=</span> <span class="p">[</span><span class="s2">&quot;long&quot;</span><span class="p">,</span> <span class="s2">&quot;xdip&quot;</span><span class="p">,</span> <span class="s2">&quot;ydip&quot;</span><span class="p">,</span> <span class="s2">&quot;xquad&quot;</span><span class="p">,</span> <span class="s2">&quot;yquad&quot;</span><span class="p">]</span>
+
+    <span class="n">data_folder</span> <span class="o">=</span> <span class="n">Path</span><span class="p">(</span><span class="n">folder</span><span class="p">)</span>
+
+    <span class="n">list_for_wakefield</span> <span class="o">=</span> <span class="p">[]</span>
+    <span class="k">for</span> <span class="n">key</span><span class="p">,</span> <span class="n">item</span> <span class="ow">in</span> <span class="n">types</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
+        <span class="k">for</span> <span class="n">component</span> <span class="ow">in</span> <span class="n">components</span><span class="p">:</span>
+            <span class="n">name</span> <span class="o">=</span> <span class="n">data_folder</span> <span class="o">/</span> <span class="p">(</span><span class="n">key</span><span class="o">+</span><span class="n">component</span><span class="o">+</span><span class="n">suffix</span><span class="p">)</span>
+            <span class="n">res</span> <span class="o">=</span> <span class="n">read_IW2D</span><span class="p">(</span><span class="n">file</span><span class="o">=</span><span class="n">name</span><span class="p">,</span>
+                            <span class="n">file_type</span><span class="o">=</span><span class="n">key</span> <span class="o">+</span> <span class="n">component</span><span class="p">,</span>
+                            <span class="n">output</span><span class="o">=</span><span class="n">output</span><span class="p">)</span>
+            <span class="n">list_for_wakefield</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">res</span><span class="p">)</span>
+
+    <span class="n">wake</span> <span class="o">=</span> <span class="n">WakeField</span><span class="p">(</span><span class="n">list_for_wakefield</span><span class="p">)</span>
+
+    <span class="k">return</span> <span class="n">wake</span></div>
+
+
+<div class="viewcode-block" id="read_ABCI"><a class="viewcode-back" href="../../../mbtrack2.utilities.html#mbtrack2.utilities.read_impedance.read_ABCI">[docs]</a><span class="k">def</span> <span class="nf">read_ABCI</span><span class="p">(</span><span class="n">file</span><span class="p">,</span> <span class="n">azimuthal</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="n">output</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    Read ABCI output files [1].</span>
+
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">    file : str</span>
+<span class="sd">        Path to ABCI .pot file.</span>
+<span class="sd">    azimuthal : bool, optional</span>
+<span class="sd">        If True, the transverse wake potential and impedance is loaded from the</span>
+<span class="sd">        &quot;AZIMUTHAL&quot; data.</span>
+<span class="sd">        If False, it is loaded from the &quot;TRANSVERSE&quot; data. In that case, a -1</span>
+<span class="sd">        factor is applied on the wake to agree with mbtrack2 sign convention.</span>
+<span class="sd">        The default is False.</span>
+<span class="sd">    output : bool, optional</span>
+<span class="sd">        If True, print out the loaded components header.</span>
+<span class="sd">        Default is False.</span>
+
+<span class="sd">    Returns</span>
+<span class="sd">    -------</span>
+<span class="sd">    wake : WakeField</span>
+<span class="sd">        Object where the ABCI computed impedance and wake are stored.</span>
+
+<span class="sd">    References</span>
+<span class="sd">    ----------</span>
+<span class="sd">    [1] : ABCI - https://abci.kek.jp/abci.htm</span>
+
+<span class="sd">    &quot;&quot;&quot;</span>
+
+    <span class="k">if</span> <span class="n">azimuthal</span><span class="p">:</span>
+        <span class="n">source</span> <span class="o">=</span> <span class="s2">&quot;AZIMUTHAL&quot;</span>
+    <span class="k">else</span><span class="p">:</span>
+        <span class="n">source</span> <span class="o">=</span> <span class="s2">&quot;TRANSVERSE&quot;</span>
+
+    <span class="k">def</span> <span class="nf">_read_temp</span><span class="p">(</span><span class="n">file</span><span class="p">,</span> <span class="n">file_type</span><span class="p">,</span> <span class="n">file2</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
+        <span class="k">if</span> <span class="n">file_type</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">==</span> <span class="s2">&quot;Z&quot;</span><span class="p">:</span>
+            <span class="n">df</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">read_csv</span><span class="p">(</span><span class="n">file</span><span class="p">,</span>
+                             <span class="n">delim_whitespace</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span>
+                             <span class="n">names</span><span class="o">=</span><span class="p">[</span><span class="s2">&quot;Frequency&quot;</span><span class="p">,</span> <span class="s2">&quot;Real&quot;</span><span class="p">])</span>
+            <span class="n">df</span><span class="p">[</span><span class="s2">&quot;Real&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="n">df</span><span class="p">[</span><span class="s2">&quot;Real&quot;</span><span class="p">]</span> <span class="o">*</span> <span class="mf">1e3</span>
+            <span class="n">df</span><span class="p">[</span><span class="s2">&quot;Frequency&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="n">df</span><span class="p">[</span><span class="s2">&quot;Frequency&quot;</span><span class="p">]</span> <span class="o">*</span> <span class="mf">1e9</span>
+            <span class="n">df2</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">read_csv</span><span class="p">(</span><span class="n">file2</span><span class="p">,</span>
+                              <span class="n">delim_whitespace</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span>
+                              <span class="n">names</span><span class="o">=</span><span class="p">[</span><span class="s2">&quot;Frequency&quot;</span><span class="p">,</span> <span class="s2">&quot;Imaginary&quot;</span><span class="p">])</span>
+            <span class="n">df2</span><span class="p">[</span><span class="s2">&quot;Imaginary&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="n">df2</span><span class="p">[</span><span class="s2">&quot;Imaginary&quot;</span><span class="p">]</span> <span class="o">*</span> <span class="mf">1e3</span>
+            <span class="n">df2</span><span class="p">[</span><span class="s2">&quot;Frequency&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="n">df2</span><span class="p">[</span><span class="s2">&quot;Frequency&quot;</span><span class="p">]</span> <span class="o">*</span> <span class="mf">1e9</span>
+            <span class="n">df</span><span class="o">.</span><span class="n">set_index</span><span class="p">(</span><span class="s2">&quot;Frequency&quot;</span><span class="p">,</span> <span class="n">inplace</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
+            <span class="n">df2</span><span class="o">.</span><span class="n">set_index</span><span class="p">(</span><span class="s2">&quot;Frequency&quot;</span><span class="p">,</span> <span class="n">inplace</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
+            <span class="n">result</span> <span class="o">=</span> <span class="n">Impedance</span><span class="p">(</span><span class="n">variable</span><span class="o">=</span><span class="n">df</span><span class="o">.</span><span class="n">index</span><span class="p">,</span>
+                               <span class="n">function</span><span class="o">=</span><span class="n">df</span><span class="p">[</span><span class="s2">&quot;Real&quot;</span><span class="p">]</span> <span class="o">+</span> <span class="mi">1</span><span class="n">j</span> <span class="o">*</span> <span class="n">df2</span><span class="p">[</span><span class="s2">&quot;Imaginary&quot;</span><span class="p">],</span>
+                               <span class="n">component_type</span><span class="o">=</span><span class="n">file_type</span><span class="p">[</span><span class="mi">1</span><span class="p">:])</span>
+        <span class="k">elif</span> <span class="n">file_type</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">==</span> <span class="s2">&quot;W&quot;</span><span class="p">:</span>
+            <span class="n">df</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">read_csv</span><span class="p">(</span><span class="n">file</span><span class="p">,</span>
+                             <span class="n">delim_whitespace</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span>
+                             <span class="n">names</span><span class="o">=</span><span class="p">[</span><span class="s2">&quot;Time&quot;</span><span class="p">,</span> <span class="s2">&quot;Wake&quot;</span><span class="p">])</span>
+            <span class="n">df</span><span class="p">[</span><span class="s2">&quot;Time&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="n">df</span><span class="p">[</span><span class="s2">&quot;Time&quot;</span><span class="p">]</span> <span class="o">/</span> <span class="n">c</span>
+            <span class="n">df</span><span class="p">[</span><span class="s2">&quot;Wake&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="n">df</span><span class="p">[</span><span class="s2">&quot;Wake&quot;</span><span class="p">]</span> <span class="o">*</span> <span class="mf">1e12</span>
+            <span class="k">if</span> <span class="p">(</span><span class="ow">not</span> <span class="n">azimuthal</span><span class="p">)</span> <span class="ow">and</span> <span class="p">(</span><span class="n">file_type</span><span class="p">[</span><span class="o">-</span><span class="mi">3</span><span class="p">:]</span> <span class="o">==</span> <span class="s2">&quot;dip&quot;</span><span class="p">):</span>
+                <span class="n">df</span><span class="p">[</span><span class="s2">&quot;Wake&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="n">df</span><span class="p">[</span><span class="s2">&quot;Wake&quot;</span><span class="p">]</span> <span class="o">*</span> <span class="o">-</span><span class="mi">1</span>
+            <span class="n">df</span><span class="o">.</span><span class="n">set_index</span><span class="p">(</span><span class="s2">&quot;Time&quot;</span><span class="p">,</span> <span class="n">inplace</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
+            <span class="n">result</span> <span class="o">=</span> <span class="n">WakeFunction</span><span class="p">(</span><span class="n">variable</span><span class="o">=</span><span class="n">df</span><span class="o">.</span><span class="n">index</span><span class="p">,</span>
+                                  <span class="n">function</span><span class="o">=</span><span class="n">df</span><span class="p">[</span><span class="s2">&quot;Wake&quot;</span><span class="p">],</span>
+                                  <span class="n">component_type</span><span class="o">=</span><span class="n">file_type</span><span class="p">[</span><span class="mi">1</span><span class="p">:])</span>
+        <span class="k">return</span> <span class="n">result</span>
+
+    <span class="n">abci_dict</span> <span class="o">=</span> <span class="p">{</span>
+        <span class="s1">&#39;  TITLE: LONGITUDINAL WAKE POTENTIAL             </span><span class="se">\n</span><span class="s1">&#39;</span><span class="p">:</span>
+        <span class="s1">&#39;Wlong&#39;</span><span class="p">,</span>
+        <span class="s1">&#39;  TITLE: REAL PART OF LONGITUDINAL IMPEDANCE                      </span><span class="se">\n</span><span class="s1">&#39;</span><span class="p">:</span>
+        <span class="s1">&#39;Zlong_re&#39;</span><span class="p">,</span>
+        <span class="s1">&#39;  TITLE: IMAGINARY PART OF LONGITUDINAL IMPEDANCE                 </span><span class="se">\n</span><span class="s1">&#39;</span><span class="p">:</span>
+        <span class="s1">&#39;Zlong_im&#39;</span><span class="p">,</span>
+        <span class="sa">f</span><span class="s1">&#39;  TITLE: </span><span class="si">{</span><span class="n">source</span><span class="si">}</span><span class="s1"> WAKE POTENTIAL               </span><span class="se">\n</span><span class="s1">&#39;</span><span class="p">:</span>
+        <span class="s1">&#39;Wxdip&#39;</span><span class="p">,</span>
+        <span class="sa">f</span><span class="s1">&#39;  TITLE: REAL PART OF </span><span class="si">{</span><span class="n">source</span><span class="si">}</span><span class="s1"> IMPEDANCE                        </span><span class="se">\n</span><span class="s1">&#39;</span><span class="p">:</span>
+        <span class="s1">&#39;Zxdip_re&#39;</span><span class="p">,</span>
+        <span class="sa">f</span><span class="s1">&#39;  TITLE: IMAGINARY PART OF </span><span class="si">{</span><span class="n">source</span><span class="si">}</span><span class="s1"> IMPEDANCE                   </span><span class="se">\n</span><span class="s1">&#39;</span><span class="p">:</span>
+        <span class="s1">&#39;Zxdip_im&#39;</span>
+    <span class="p">}</span>
+
+    <span class="n">wake_list</span> <span class="o">=</span> <span class="p">[]</span>
+    <span class="n">start</span> <span class="o">=</span> <span class="kc">True</span>
+    <span class="k">with</span> <span class="nb">open</span><span class="p">(</span><span class="n">file</span><span class="p">)</span> <span class="k">as</span> <span class="n">f</span><span class="p">:</span>
+        <span class="k">while</span> <span class="kc">True</span><span class="p">:</span>
+            <span class="k">if</span> <span class="n">start</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">:</span>
+                <span class="c1"># read the header</span>
+                <span class="n">header</span> <span class="o">=</span> <span class="p">[</span><span class="nb">next</span><span class="p">(</span><span class="n">f</span><span class="p">)</span> <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">5</span><span class="p">)]</span>
+                <span class="n">start</span> <span class="o">=</span> <span class="kc">False</span>
+            <span class="k">elif</span> <span class="n">line</span> <span class="o">==</span> <span class="s1">&#39;&#39;</span><span class="p">:</span>
+                <span class="c1"># check if file is over</span>
+                <span class="k">break</span>
+            <span class="k">else</span><span class="p">:</span>
+                <span class="c1"># read the header</span>
+                <span class="n">header</span> <span class="o">=</span> <span class="p">[</span><span class="nb">next</span><span class="p">(</span><span class="n">f</span><span class="p">)</span> <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">4</span><span class="p">)]</span>
+                <span class="n">header</span><span class="o">.</span><span class="n">insert</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">line</span><span class="p">)</span>
+            <span class="k">if</span> <span class="n">output</span><span class="p">:</span>
+                <span class="nb">print</span><span class="p">(</span><span class="n">header</span><span class="p">)</span>
+            <span class="c1"># read the body until next TITLE field or end of file</span>
+            <span class="n">body</span> <span class="o">=</span> <span class="p">[]</span>
+            <span class="k">while</span> <span class="kc">True</span><span class="p">:</span>
+                <span class="n">line</span> <span class="o">=</span> <span class="n">f</span><span class="o">.</span><span class="n">readline</span><span class="p">()</span>
+                <span class="k">try</span><span class="p">:</span>
+                    <span class="k">if</span> <span class="n">line</span><span class="p">[:</span><span class="mi">8</span><span class="p">]</span> <span class="o">==</span> <span class="s2">&quot;  TITLE:&quot;</span><span class="p">:</span>
+                        <span class="k">break</span>
+                    <span class="k">if</span> <span class="n">line</span> <span class="o">==</span> <span class="s1">&#39;&#39;</span><span class="p">:</span>
+                        <span class="k">break</span>
+                <span class="k">except</span><span class="p">:</span>
+                    <span class="k">pass</span>
+                <span class="n">body</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">line</span><span class="p">)</span>
+            <span class="c1"># write body in temp file and then process it into wake/imp</span>
+            <span class="n">impedance_type</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">re</span><span class="o">.</span><span class="n">split</span><span class="p">(</span><span class="s1">&#39;\s+&#39;</span><span class="p">,</span> <span class="n">header</span><span class="p">[</span><span class="o">-</span><span class="mi">2</span><span class="p">])[</span><span class="o">-</span><span class="mi">3</span><span class="p">])</span>
+            <span class="k">try</span><span class="p">:</span>
+                <span class="k">if</span> <span class="n">abci_dict</span><span class="p">[</span><span class="n">header</span><span class="p">[</span><span class="mi">0</span><span class="p">]][</span><span class="mi">0</span><span class="p">]</span> <span class="o">==</span> <span class="s2">&quot;W&quot;</span><span class="p">:</span>
+                    <span class="n">tmp</span> <span class="o">=</span> <span class="n">NamedTemporaryFile</span><span class="p">(</span><span class="n">delete</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="n">mode</span><span class="o">=</span><span class="s2">&quot;w+&quot;</span><span class="p">)</span>
+                    <span class="n">tmp</span><span class="o">.</span><span class="n">writelines</span><span class="p">(</span><span class="n">body</span><span class="p">)</span>
+                    <span class="n">tmp</span><span class="o">.</span><span class="n">flush</span><span class="p">()</span>
+                    <span class="n">tmp</span><span class="o">.</span><span class="n">close</span><span class="p">()</span>
+                    <span class="k">if</span> <span class="n">abci_dict</span><span class="p">[</span>
+                            <span class="n">header</span><span class="p">[</span><span class="mi">0</span><span class="p">]][</span><span class="mi">1</span><span class="p">:]</span> <span class="o">==</span> <span class="s2">&quot;long&quot;</span> <span class="ow">and</span> <span class="n">impedance_type</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
+                        <span class="n">comp</span> <span class="o">=</span> <span class="n">_read_temp</span><span class="p">(</span><span class="n">tmp</span><span class="o">.</span><span class="n">name</span><span class="p">,</span> <span class="n">abci_dict</span><span class="p">[</span><span class="n">header</span><span class="p">[</span><span class="mi">0</span><span class="p">]])</span>
+                        <span class="n">wake_list</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">comp</span><span class="p">)</span>
+                    <span class="k">elif</span> <span class="n">abci_dict</span><span class="p">[</span>
+                            <span class="n">header</span><span class="p">[</span><span class="mi">0</span><span class="p">]][</span><span class="mi">1</span><span class="p">:]</span> <span class="o">==</span> <span class="s2">&quot;long&quot;</span> <span class="ow">and</span> <span class="n">impedance_type</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
+                        <span class="k">pass</span>
+                        <span class="c1"># Wlongxdip &amp; Wlongydip not implemented yet</span>
+                        <span class="c1"># comp = _read_temp(tmp.name, abci_dict[header[0]]+&#39;dip&#39;)</span>
+                        <span class="c1"># wake_list.append(comp)</span>
+                    <span class="k">else</span><span class="p">:</span>
+                        <span class="n">comp_x</span> <span class="o">=</span> <span class="n">_read_temp</span><span class="p">(</span><span class="n">tmp</span><span class="o">.</span><span class="n">name</span><span class="p">,</span> <span class="s2">&quot;Wxdip&quot;</span><span class="p">)</span>
+                        <span class="n">comp_y</span> <span class="o">=</span> <span class="n">_read_temp</span><span class="p">(</span><span class="n">tmp</span><span class="o">.</span><span class="n">name</span><span class="p">,</span> <span class="s2">&quot;Wydip&quot;</span><span class="p">)</span>
+                        <span class="n">wake_list</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">comp_x</span><span class="p">)</span>
+                        <span class="n">wake_list</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">comp_y</span><span class="p">)</span>
+                    <span class="n">os</span><span class="o">.</span><span class="n">unlink</span><span class="p">(</span><span class="n">tmp</span><span class="o">.</span><span class="n">name</span><span class="p">)</span>
+                <span class="k">elif</span> <span class="p">(</span><span class="n">abci_dict</span><span class="p">[</span><span class="n">header</span><span class="p">[</span><span class="mi">0</span><span class="p">]][</span><span class="mi">0</span><span class="p">]</span>
+                      <span class="o">==</span> <span class="s2">&quot;Z&quot;</span><span class="p">)</span> <span class="ow">and</span> <span class="p">(</span><span class="n">abci_dict</span><span class="p">[</span><span class="n">header</span><span class="p">[</span><span class="mi">0</span><span class="p">]][</span><span class="o">-</span><span class="mi">2</span><span class="p">:]</span> <span class="o">==</span> <span class="s2">&quot;re&quot;</span><span class="p">):</span>
+                    <span class="n">tmp1</span> <span class="o">=</span> <span class="n">NamedTemporaryFile</span><span class="p">(</span><span class="n">delete</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="n">mode</span><span class="o">=</span><span class="s2">&quot;w+&quot;</span><span class="p">)</span>
+                    <span class="n">tmp1</span><span class="o">.</span><span class="n">writelines</span><span class="p">(</span><span class="n">body</span><span class="p">)</span>
+                    <span class="n">tmp1</span><span class="o">.</span><span class="n">flush</span><span class="p">()</span>
+                    <span class="n">tmp1</span><span class="o">.</span><span class="n">close</span><span class="p">()</span>
+                <span class="k">elif</span> <span class="p">(</span><span class="n">abci_dict</span><span class="p">[</span><span class="n">header</span><span class="p">[</span><span class="mi">0</span><span class="p">]][</span><span class="mi">0</span><span class="p">]</span>
+                      <span class="o">==</span> <span class="s2">&quot;Z&quot;</span><span class="p">)</span> <span class="ow">and</span> <span class="p">(</span><span class="n">abci_dict</span><span class="p">[</span><span class="n">header</span><span class="p">[</span><span class="mi">0</span><span class="p">]][</span><span class="o">-</span><span class="mi">2</span><span class="p">:]</span> <span class="o">==</span> <span class="s2">&quot;im&quot;</span><span class="p">):</span>
+                    <span class="n">tmp2</span> <span class="o">=</span> <span class="n">NamedTemporaryFile</span><span class="p">(</span><span class="n">delete</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="n">mode</span><span class="o">=</span><span class="s2">&quot;w+&quot;</span><span class="p">)</span>
+                    <span class="n">tmp2</span><span class="o">.</span><span class="n">writelines</span><span class="p">(</span><span class="n">body</span><span class="p">)</span>
+                    <span class="n">tmp2</span><span class="o">.</span><span class="n">flush</span><span class="p">()</span>
+                    <span class="n">tmp2</span><span class="o">.</span><span class="n">close</span><span class="p">()</span>
+                    <span class="k">if</span> <span class="n">abci_dict</span><span class="p">[</span>
+                            <span class="n">header</span><span class="p">[</span><span class="mi">0</span><span class="p">]][</span><span class="mi">1</span><span class="p">:</span><span class="o">-</span><span class="mi">3</span><span class="p">]</span> <span class="o">==</span> <span class="s2">&quot;long&quot;</span> <span class="ow">and</span> <span class="n">impedance_type</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
+                        <span class="n">comp</span> <span class="o">=</span> <span class="n">_read_temp</span><span class="p">(</span><span class="n">tmp1</span><span class="o">.</span><span class="n">name</span><span class="p">,</span> <span class="s2">&quot;Zlong&quot;</span><span class="p">,</span> <span class="n">tmp2</span><span class="o">.</span><span class="n">name</span><span class="p">)</span>
+                        <span class="n">wake_list</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">comp</span><span class="p">)</span>
+                    <span class="k">elif</span> <span class="n">abci_dict</span><span class="p">[</span>
+                            <span class="n">header</span><span class="p">[</span><span class="mi">0</span><span class="p">]][</span><span class="mi">1</span><span class="p">:</span><span class="o">-</span><span class="mi">3</span><span class="p">]</span> <span class="o">==</span> <span class="s2">&quot;long&quot;</span> <span class="ow">and</span> <span class="n">impedance_type</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
+                        <span class="k">pass</span>
+                        <span class="c1"># Zlongxdip &amp; Zlongydip not implemented yet</span>
+                        <span class="c1"># comp = _read_temp(tmp1.name, &quot;Zlongdip&quot;, tmp2.name)</span>
+                        <span class="c1"># wake_list.append(comp)</span>
+                    <span class="k">else</span><span class="p">:</span>
+                        <span class="n">comp_x</span> <span class="o">=</span> <span class="n">_read_temp</span><span class="p">(</span><span class="n">tmp1</span><span class="o">.</span><span class="n">name</span><span class="p">,</span> <span class="s2">&quot;Zxdip&quot;</span><span class="p">,</span> <span class="n">tmp2</span><span class="o">.</span><span class="n">name</span><span class="p">)</span>
+                        <span class="n">comp_y</span> <span class="o">=</span> <span class="n">_read_temp</span><span class="p">(</span><span class="n">tmp1</span><span class="o">.</span><span class="n">name</span><span class="p">,</span> <span class="s2">&quot;Zydip&quot;</span><span class="p">,</span> <span class="n">tmp2</span><span class="o">.</span><span class="n">name</span><span class="p">)</span>
+                        <span class="n">wake_list</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">comp_x</span><span class="p">)</span>
+                        <span class="n">wake_list</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">comp_y</span><span class="p">)</span>
+                    <span class="n">os</span><span class="o">.</span><span class="n">unlink</span><span class="p">(</span><span class="n">tmp1</span><span class="o">.</span><span class="n">name</span><span class="p">)</span>
+                    <span class="n">os</span><span class="o">.</span><span class="n">unlink</span><span class="p">(</span><span class="n">tmp2</span><span class="o">.</span><span class="n">name</span><span class="p">)</span>
+            <span class="k">except</span> <span class="ne">KeyError</span><span class="p">:</span>
+                <span class="k">pass</span>
+
+    <span class="n">wake</span> <span class="o">=</span> <span class="n">WakeField</span><span class="p">(</span><span class="n">wake_list</span><span class="p">)</span>
+
+    <span class="k">return</span> <span class="n">wake</span></div>
+
+
+<div class="viewcode-block" id="read_ECHO2D"><a class="viewcode-back" href="../../../mbtrack2.utilities.html#mbtrack2.utilities.read_impedance.read_ECHO2D">[docs]</a><span class="k">def</span> <span class="nf">read_ECHO2D</span><span class="p">(</span><span class="n">file</span><span class="p">,</span> <span class="n">component_type</span><span class="o">=</span><span class="s1">&#39;long&#39;</span><span class="p">):</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    Read ECHO2D text file format (after matlab post-processing) into a</span>
+<span class="sd">    WakeFunction object.</span>
+
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">    file : str</span>
+<span class="sd">        Path to the text file to read.</span>
+<span class="sd">    component_type : str, optional</span>
+<span class="sd">        Type of the WakeFunction object to load.</span>
+<span class="sd">        Default is &#39;long&#39;.</span>
+
+<span class="sd">    Returns</span>
+<span class="sd">    -------</span>
+<span class="sd">    result : WakeFunction object.</span>
+<span class="sd">        Data from file.</span>
+<span class="sd">    &quot;&quot;&quot;</span>
+
+    <span class="n">df</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">read_csv</span><span class="p">(</span><span class="n">file</span><span class="p">,</span>
+                     <span class="n">delim_whitespace</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span>
+                     <span class="n">header</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+                     <span class="n">names</span><span class="o">=</span><span class="p">[</span><span class="s2">&quot;Distance&quot;</span><span class="p">,</span> <span class="s2">&quot;Wake&quot;</span><span class="p">])</span>
+    <span class="n">df</span><span class="p">[</span><span class="s2">&quot;Time&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="n">df</span><span class="p">[</span><span class="s2">&quot;Distance&quot;</span><span class="p">]</span> <span class="o">/</span> <span class="mi">100</span> <span class="o">/</span> <span class="n">c</span>
+    <span class="n">df</span><span class="p">[</span><span class="s2">&quot;Wake&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="n">df</span><span class="p">[</span><span class="s2">&quot;Wake&quot;</span><span class="p">]</span> <span class="o">*</span> <span class="mf">1e12</span>
+    <span class="k">if</span> <span class="n">component_type</span> <span class="o">!=</span> <span class="s1">&#39;long&#39;</span><span class="p">:</span>
+        <span class="n">df</span><span class="p">[</span><span class="s2">&quot;Wake&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="n">df</span><span class="p">[</span><span class="s2">&quot;Wake&quot;</span><span class="p">]</span> <span class="o">*</span> <span class="o">-</span><span class="mi">1</span>
+    <span class="n">df</span><span class="o">.</span><span class="n">set_index</span><span class="p">(</span><span class="s2">&quot;Time&quot;</span><span class="p">,</span> <span class="n">inplace</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
+    <span class="n">result</span> <span class="o">=</span> <span class="n">WakeFunction</span><span class="p">(</span><span class="n">variable</span><span class="o">=</span><span class="n">df</span><span class="o">.</span><span class="n">index</span><span class="p">,</span>
+                          <span class="n">function</span><span class="o">=</span><span class="n">df</span><span class="p">[</span><span class="s2">&quot;Wake&quot;</span><span class="p">],</span>
+                          <span class="n">component_type</span><span class="o">=</span><span class="n">component_type</span><span class="p">)</span>
+
+    <span class="k">return</span> <span class="n">result</span></div>
+</pre></div>
+
+            <div class="clearer"></div>
+          </div>
+        </div>
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+             >modules</a> |</li>
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+          <li class="nav-item nav-item-1"><a href="../../index.html" >Module code</a> &#187;</li>
+        <li class="nav-item nav-item-this"><a href="">mbtrack2.utilities.read_impedance</a></li> 
+      </ul>
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+    <div class="footer" role="contentinfo">
+        &#169; Copyright 2024, A. Gamelin et al.
+      Created using <a href="https://www.sphinx-doc.org/">Sphinx</a> 5.0.2.
+    </div>
+  </body>
+</html>
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diff --git a/docs/build/html/_modules/mbtrack2/utilities/spectrum.html b/docs/build/html/_modules/mbtrack2/utilities/spectrum.html
new file mode 100644
index 0000000..56dfd20
--- /dev/null
+++ b/docs/build/html/_modules/mbtrack2/utilities/spectrum.html
@@ -0,0 +1,225 @@
+
+<!DOCTYPE html>
+
+<html lang="en">
+  <head>
+    <meta charset="utf-8" />
+    <meta name="viewport" content="width=device-width, initial-scale=1.0" />
+    <title>mbtrack2.utilities.spectrum &#8212; mbtrack2 0.6.0 documentation</title>
+    <link rel="stylesheet" type="text/css" href="../../../_static/pygments.css" />
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+             accesskey="I">index</a></li>
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+             >modules</a> |</li>
+        <li class="nav-item nav-item-0"><a href="../../../index.html">mbtrack2 0.6.0 documentation</a> &#187;</li>
+          <li class="nav-item nav-item-1"><a href="../../index.html" accesskey="U">Module code</a> &#187;</li>
+        <li class="nav-item nav-item-this"><a href="">mbtrack2.utilities.spectrum</a></li> 
+      </ul>
+    </div>  
+
+    <div class="document">
+      <div class="documentwrapper">
+        <div class="bodywrapper">
+          <div class="body" role="main">
+            
+  <h1>Source code for mbtrack2.utilities.spectrum</h1><div class="highlight"><pre>
+<span></span><span class="c1"># -*- coding: utf-8 -*-</span>
+<span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">Module where bunch and beam spectrums and profile are defined.</span>
+<span class="sd">&quot;&quot;&quot;</span>
+
+<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="kn">from</span> <span class="nn">scipy.special</span> <span class="kn">import</span> <span class="n">jv</span><span class="p">,</span> <span class="n">spherical_jn</span>
+
+
+<div class="viewcode-block" id="spectral_density"><a class="viewcode-back" href="../../../mbtrack2.utilities.html#mbtrack2.utilities.spectrum.spectral_density">[docs]</a><span class="k">def</span> <span class="nf">spectral_density</span><span class="p">(</span><span class="n">frequency</span><span class="p">,</span> <span class="n">sigma</span><span class="p">,</span> <span class="n">m</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">k</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">mode</span><span class="o">=</span><span class="s2">&quot;Hermite&quot;</span><span class="p">):</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    Compute the spectral density of different modes for various values of the</span>
+<span class="sd">    head-tail mode number, based on Table 1 p238 of [1].</span>
+
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">    frequency : list or numpy array</span>
+<span class="sd">        sample points of the spectral density in [Hz]</span>
+<span class="sd">    sigma : float</span>
+<span class="sd">        RMS bunch length in [s]</span>
+<span class="sd">    m : int, optional</span>
+<span class="sd">        head-tail (or azimutal/synchrotron) mode number</span>
+<span class="sd">    k : int, optional</span>
+<span class="sd">        radial mode number (such that |q|=m+2k, where |q| is the head-tail mode number)</span>
+<span class="sd">    mode: str, optional</span>
+<span class="sd">        type of the mode taken into account for the computation:</span>
+<span class="sd">        -&quot;Hermite&quot; modes for Gaussian bunches (typical for electrons)</span>
+<span class="sd">        -&quot;Chebyshev&quot; for airbag bunches</span>
+<span class="sd">        -&quot;Legendre&quot; for parabolic bunches (typical for protons)</span>
+<span class="sd">        -&quot;Sacherer&quot; or &quot;Sinusoidal&quot; simplifying approximation of Legendre modes from [3]</span>
+
+<span class="sd">    Returns</span>
+<span class="sd">    -------</span>
+<span class="sd">    numpy array</span>
+
+<span class="sd">    References</span>
+<span class="sd">    ----------</span>
+<span class="sd">    [1] : Handbook of accelerator physics and engineering, 3rd printing.</span>
+<span class="sd">    [2] : Ng, K. Y. (2005). Physics of intensity dependent beam instabilities. WORLD SCIENTIFIC. https://doi.org/10.1142/5835</span>
+<span class="sd">    [3] : Sacherer, F. J. (1972). Methods for computing bunched beam instabilities. CERN Tech. rep. CERN/SI-BR/72-5 https://cds.cern.ch/record/2291670?ln=en</span>
+<span class="sd">    &quot;&quot;&quot;</span>
+
+    <span class="k">if</span> <span class="n">mode</span> <span class="o">==</span> <span class="s2">&quot;Hermite&quot;</span><span class="p">:</span>
+        <span class="k">return</span> <span class="mi">1</span> <span class="o">/</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">math</span><span class="o">.</span><span class="n">factorial</span><span class="p">(</span><span class="n">m</span><span class="p">)</span> <span class="o">*</span>
+                    <span class="mi">2</span><span class="o">**</span><span class="n">m</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="n">frequency</span> <span class="o">*</span> <span class="n">sigma</span><span class="p">)</span><span class="o">**</span><span class="p">(</span>
+                        <span class="mi">2</span> <span class="o">*</span> <span class="n">m</span><span class="p">)</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="o">-</span><span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="n">frequency</span> <span class="o">*</span> <span class="n">sigma</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span>
+    <span class="k">elif</span> <span class="n">mode</span> <span class="o">==</span> <span class="s2">&quot;Chebyshev&quot;</span><span class="p">:</span>
+        <span class="n">tau_l</span> <span class="o">=</span> <span class="mi">4</span> <span class="o">*</span> <span class="n">sigma</span>
+        <span class="k">return</span> <span class="p">(</span><span class="n">jv</span><span class="p">(</span><span class="n">m</span><span class="p">,</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="n">frequency</span> <span class="o">*</span> <span class="n">tau_l</span><span class="p">))</span><span class="o">**</span><span class="mi">2</span>
+    <span class="k">elif</span> <span class="n">mode</span> <span class="o">==</span> <span class="s2">&quot;Legendre&quot;</span><span class="p">:</span>
+        <span class="n">tau_l</span> <span class="o">=</span> <span class="mi">4</span> <span class="o">*</span> <span class="n">sigma</span>
+        <span class="k">return</span> <span class="p">(</span><span class="n">spherical_jn</span><span class="p">(</span><span class="n">m</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="n">frequency</span> <span class="o">*</span> <span class="n">tau_l</span><span class="p">)))</span><span class="o">**</span><span class="mi">2</span>
+    <span class="k">elif</span> <span class="n">mode</span> <span class="o">==</span> <span class="s2">&quot;Sacherer&quot;</span> <span class="ow">or</span> <span class="n">mode</span> <span class="o">==</span> <span class="s2">&quot;Sinusoidal&quot;</span><span class="p">:</span>
+        <span class="n">y</span> <span class="o">=</span> <span class="mi">4</span> <span class="o">*</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="n">frequency</span> <span class="o">*</span> <span class="n">sigma</span> <span class="o">/</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span>
+        <span class="k">return</span> <span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="p">(</span><span class="n">m</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span> <span class="o">/</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="mi">1</span> <span class="o">/</span> <span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">y</span><span class="o">**</span><span class="mi">2</span> <span class="o">-</span> <span class="p">(</span><span class="n">m</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span> <span class="o">*</span>
+                <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="mi">1</span> <span class="o">+</span> <span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span><span class="o">**</span><span class="n">m</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="n">y</span><span class="p">)))</span><span class="o">**</span><span class="mi">2</span>
+    <span class="k">else</span><span class="p">:</span>
+        <span class="k">raise</span> <span class="ne">NotImplementedError</span><span class="p">(</span><span class="s2">&quot;Not implemanted yet.&quot;</span><span class="p">)</span></div>
+
+
+<div class="viewcode-block" id="gaussian_bunch_spectrum"><a class="viewcode-back" href="../../../mbtrack2.utilities.html#mbtrack2.utilities.spectrum.gaussian_bunch_spectrum">[docs]</a><span class="k">def</span> <span class="nf">gaussian_bunch_spectrum</span><span class="p">(</span><span class="n">frequency</span><span class="p">,</span> <span class="n">sigma</span><span class="p">):</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    Compute a Gaussian bunch spectrum [1].</span>
+
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">    frequency : array</span>
+<span class="sd">        sample points of the beam spectrum in [Hz].</span>
+<span class="sd">    sigma : float</span>
+<span class="sd">        RMS bunch length in [s].</span>
+
+<span class="sd">    Returns</span>
+<span class="sd">    -------</span>
+<span class="sd">    bunch_spectrum : array</span>
+<span class="sd">        Bunch spectrum sampled at points given in frequency.</span>
+
+<span class="sd">    References</span>
+<span class="sd">    ----------</span>
+<span class="sd">    [1] : Gamelin, A. (2018). Collective effects in a transient microbunching </span>
+<span class="sd">    regime and ion cloud mitigation in ThomX. p86, Eq. 4.19</span>
+<span class="sd">    &quot;&quot;&quot;</span>
+    <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span> <span class="o">/</span> <span class="mi">2</span> <span class="o">*</span> <span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="n">frequency</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span> <span class="o">*</span> <span class="n">sigma</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span></div>
+
+
+<div class="viewcode-block" id="gaussian_bunch"><a class="viewcode-back" href="../../../mbtrack2.utilities.html#mbtrack2.utilities.spectrum.gaussian_bunch">[docs]</a><span class="k">def</span> <span class="nf">gaussian_bunch</span><span class="p">(</span><span class="n">time</span><span class="p">,</span> <span class="n">sigma</span><span class="p">):</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    Compute a Gaussian bunch profile.</span>
+
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">    time : array</span>
+<span class="sd">        sample points of the bunch profile in [s].</span>
+<span class="sd">    sigma : float</span>
+<span class="sd">        RMS bunch length in [s].</span>
+
+<span class="sd">    Returns</span>
+<span class="sd">    -------</span>
+<span class="sd">    bunch_profile : array</span>
+<span class="sd">        Bunch profile in [s**-1] sampled at points given in time.</span>
+<span class="sd">    &quot;&quot;&quot;</span>
+    <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span> <span class="o">/</span> <span class="mi">2</span> <span class="o">*</span> <span class="p">(</span><span class="n">time</span><span class="o">**</span><span class="mi">2</span> <span class="o">/</span> <span class="n">sigma</span><span class="o">**</span><span class="mi">2</span><span class="p">))</span> <span class="o">/</span> <span class="p">(</span><span class="n">sigma</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span><span class="p">))</span></div>
+
+
+<div class="viewcode-block" id="beam_spectrum"><a class="viewcode-back" href="../../../mbtrack2.utilities.html#mbtrack2.utilities.spectrum.beam_spectrum">[docs]</a><span class="k">def</span> <span class="nf">beam_spectrum</span><span class="p">(</span><span class="n">frequency</span><span class="p">,</span>
+                  <span class="n">M</span><span class="p">,</span>
+                  <span class="n">bunch_spacing</span><span class="p">,</span>
+                  <span class="n">sigma</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+                  <span class="n">bunch_spectrum</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
+<span class="sd">    Compute the beam spectrum assuming constant spacing between bunches [1].</span>
+
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">    frequency : list or numpy array</span>
+<span class="sd">        sample points of the beam spectrum in [Hz].</span>
+<span class="sd">    M : int</span>
+<span class="sd">        Number of bunches.</span>
+<span class="sd">    bunch_spacing : float</span>
+<span class="sd">        Time between two bunches in [s].</span>
+<span class="sd">    sigma : float, optional</span>
+<span class="sd">        If bunch_spectrum is None then a Gaussian bunch with sigma RMS bunch </span>
+<span class="sd">        length in [s] is assumed.</span>
+<span class="sd">    bunch_spectrum : array, optional</span>
+<span class="sd">        Bunch spectrum sampled at points given in frequency.</span>
+
+<span class="sd">    Returns</span>
+<span class="sd">    -------</span>
+<span class="sd">    beam_spectrum : array</span>
+
+<span class="sd">    References</span>
+<span class="sd">    ----------</span>
+<span class="sd">    [1] Rumolo, G - Beam Instabilities - CAS - CERN Accelerator School: </span>
+<span class="sd">        Advanced Accelerator Physics Course - 2014, Eq. 9</span>
+<span class="sd">    &quot;&quot;&quot;</span>
+
+    <span class="k">if</span> <span class="n">bunch_spectrum</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+        <span class="n">bunch_spectrum</span> <span class="o">=</span> <span class="n">gaussian_bunch_spectrum</span><span class="p">(</span><span class="n">frequency</span><span class="p">,</span> <span class="n">sigma</span><span class="p">)</span>
+
+    <span class="n">beam_spectrum</span> <span class="o">=</span> <span class="p">(</span><span class="n">bunch_spectrum</span> <span class="o">*</span>
+                     <span class="n">np</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="mi">1</span><span class="n">j</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="n">frequency</span> <span class="o">*</span> <span class="n">bunch_spacing</span> <span class="o">*</span> <span class="p">(</span><span class="n">M</span><span class="o">-</span><span class="mi">1</span><span class="p">))</span> <span class="o">*</span>
+                     <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">M</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="n">frequency</span> <span class="o">*</span> <span class="n">bunch_spacing</span><span class="p">)</span> <span class="o">/</span>
+                     <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="n">frequency</span> <span class="o">*</span> <span class="n">bunch_spacing</span><span class="p">))</span>
+
+    <span class="k">return</span> <span class="n">beam_spectrum</span></div>
+</pre></div>
+
+            <div class="clearer"></div>
+          </div>
+        </div>
+      </div>
+      <div class="sphinxsidebar" role="navigation" aria-label="main navigation">
+        <div class="sphinxsidebarwrapper">
+<div id="searchbox" style="display: none" role="search">
+  <h3 id="searchlabel">Quick search</h3>
+    <div class="searchformwrapper">
+    <form class="search" action="../../../search.html" method="get">
+      <input type="text" name="q" aria-labelledby="searchlabel" autocomplete="off" autocorrect="off" autocapitalize="off" spellcheck="false"/>
+      <input type="submit" value="Go" />
+    </form>
+    </div>
+</div>
+<script>document.getElementById('searchbox').style.display = "block"</script>
+        </div>
+      </div>
+      <div class="clearer"></div>
+    </div>
+    <div class="related" role="navigation" aria-label="related navigation">
+      <h3>Navigation</h3>
+      <ul>
+        <li class="right" style="margin-right: 10px">
+          <a href="../../../genindex.html" title="General Index"
+             >index</a></li>
+        <li class="right" >
+          <a href="../../../py-modindex.html" title="Python Module Index"
+             >modules</a> |</li>
+        <li class="nav-item nav-item-0"><a href="../../../index.html">mbtrack2 0.6.0 documentation</a> &#187;</li>
+          <li class="nav-item nav-item-1"><a href="../../index.html" >Module code</a> &#187;</li>
+        <li class="nav-item nav-item-this"><a href="">mbtrack2.utilities.spectrum</a></li> 
+      </ul>
+    </div>
+    <div class="footer" role="contentinfo">
+        &#169; Copyright 2024, A. Gamelin et al.
+      Created using <a href="https://www.sphinx-doc.org/">Sphinx</a> 5.0.2.
+    </div>
+  </body>
+</html>
\ No newline at end of file
diff --git a/docs/build/html/_sources/index.rst.txt b/docs/build/html/_sources/index.rst.txt
new file mode 100644
index 0000000..e4a144e
--- /dev/null
+++ b/docs/build/html/_sources/index.rst.txt
@@ -0,0 +1,20 @@
+.. mbtrack2 documentation master file, created by
+   sphinx-quickstart on Sun Apr 28 19:57:17 2024.
+   You can adapt this file completely to your liking, but it should at least
+   contain the root `toctree` directive.
+
+Welcome to mbtrack2's documentation!
+====================================
+
+.. toctree::
+   :maxdepth: 2
+   :caption: Contents:
+
+
+
+Indices and tables
+==================
+
+* :ref:`genindex`
+* :ref:`modindex`
+* :ref:`search`
diff --git a/docs/build/html/_sources/mbtrack2.impedance.rst.txt b/docs/build/html/_sources/mbtrack2.impedance.rst.txt
new file mode 100644
index 0000000..2d40343
--- /dev/null
+++ b/docs/build/html/_sources/mbtrack2.impedance.rst.txt
@@ -0,0 +1,61 @@
+mbtrack2.impedance package
+==========================
+
+Submodules
+----------
+
+mbtrack2.impedance.csr module
+-----------------------------
+
+.. automodule:: mbtrack2.impedance.csr
+   :members:
+   :undoc-members:
+   :show-inheritance:
+
+mbtrack2.impedance.impedance\_model module
+------------------------------------------
+
+.. automodule:: mbtrack2.impedance.impedance_model
+   :members:
+   :undoc-members:
+   :show-inheritance:
+
+mbtrack2.impedance.resistive\_wall module
+-----------------------------------------
+
+.. automodule:: mbtrack2.impedance.resistive_wall
+   :members:
+   :undoc-members:
+   :show-inheritance:
+
+mbtrack2.impedance.resonator module
+-----------------------------------
+
+.. automodule:: mbtrack2.impedance.resonator
+   :members:
+   :undoc-members:
+   :show-inheritance:
+
+mbtrack2.impedance.tapers module
+--------------------------------
+
+.. automodule:: mbtrack2.impedance.tapers
+   :members:
+   :undoc-members:
+   :show-inheritance:
+
+mbtrack2.impedance.wakefield module
+-----------------------------------
+
+.. automodule:: mbtrack2.impedance.wakefield
+   :members:
+   :undoc-members:
+   :show-inheritance:
+
+Module contents
+---------------
+
+.. automodule:: mbtrack2.impedance
+   :members:
+   :undoc-members:
+   :show-inheritance:
diff --git a/docs/build/html/_sources/mbtrack2.instability.rst.txt b/docs/build/html/_sources/mbtrack2.instability.rst.txt
new file mode 100644
index 0000000..7b7e8f4
--- /dev/null
+++ b/docs/build/html/_sources/mbtrack2.instability.rst.txt
@@ -0,0 +1,29 @@
+mbtrack2.instability package
+============================
+
+Submodules
+----------
+
+mbtrack2.instability.instabilities module
+-----------------------------------------
+
+.. automodule:: mbtrack2.instability.instabilities
+   :members:
+   :undoc-members:
+   :show-inheritance:
+
+mbtrack2.instability.ions module
+--------------------------------
+
+.. automodule:: mbtrack2.instability.ions
+   :members:
+   :undoc-members:
+   :show-inheritance:
+
+Module contents
+---------------
+
+.. automodule:: mbtrack2.instability
+   :members:
+   :undoc-members:
+   :show-inheritance:
diff --git a/docs/build/html/_sources/mbtrack2.rst.txt b/docs/build/html/_sources/mbtrack2.rst.txt
new file mode 100644
index 0000000..7d99aeb
--- /dev/null
+++ b/docs/build/html/_sources/mbtrack2.rst.txt
@@ -0,0 +1,21 @@
+mbtrack2 package
+================
+
+Subpackages
+-----------
+
+.. toctree::
+   :maxdepth: 4
+
+   mbtrack2.impedance
+   mbtrack2.instability
+   mbtrack2.tracking
+   mbtrack2.utilities
+
+Module contents
+---------------
+
+.. automodule:: mbtrack2
+   :members:
+   :undoc-members:
+   :show-inheritance:
diff --git a/docs/build/html/_sources/mbtrack2.tracking.monitors.rst.txt b/docs/build/html/_sources/mbtrack2.tracking.monitors.rst.txt
new file mode 100644
index 0000000..36cd62a
--- /dev/null
+++ b/docs/build/html/_sources/mbtrack2.tracking.monitors.rst.txt
@@ -0,0 +1,37 @@
+mbtrack2.tracking.monitors package
+==================================
+
+Submodules
+----------
+
+mbtrack2.tracking.monitors.monitors module
+------------------------------------------
+
+.. automodule:: mbtrack2.tracking.monitors.monitors
+   :members:
+   :undoc-members:
+   :show-inheritance:
+
+mbtrack2.tracking.monitors.plotting module
+------------------------------------------
+
+.. automodule:: mbtrack2.tracking.monitors.plotting
+   :members:
+   :undoc-members:
+   :show-inheritance:
+
+mbtrack2.tracking.monitors.tools module
+---------------------------------------
+
+.. automodule:: mbtrack2.tracking.monitors.tools
+   :members:
+   :undoc-members:
+   :show-inheritance:
+
+Module contents
+---------------
+
+.. automodule:: mbtrack2.tracking.monitors
+   :members:
+   :undoc-members:
+   :show-inheritance:
diff --git a/docs/build/html/_sources/mbtrack2.tracking.rst.txt b/docs/build/html/_sources/mbtrack2.tracking.rst.txt
new file mode 100644
index 0000000..36df13c
--- /dev/null
+++ b/docs/build/html/_sources/mbtrack2.tracking.rst.txt
@@ -0,0 +1,85 @@
+mbtrack2.tracking package
+=========================
+
+Subpackages
+-----------
+
+.. toctree::
+   :maxdepth: 4
+
+   mbtrack2.tracking.monitors
+
+Submodules
+----------
+
+mbtrack2.tracking.aperture module
+---------------------------------
+
+.. automodule:: mbtrack2.tracking.aperture
+   :members:
+   :undoc-members:
+   :show-inheritance:
+
+mbtrack2.tracking.element module
+--------------------------------
+
+.. automodule:: mbtrack2.tracking.element
+   :members:
+   :undoc-members:
+   :show-inheritance:
+
+mbtrack2.tracking.feedback module
+---------------------------------
+
+.. automodule:: mbtrack2.tracking.feedback
+   :members:
+   :undoc-members:
+   :show-inheritance:
+
+mbtrack2.tracking.parallel module
+---------------------------------
+
+.. automodule:: mbtrack2.tracking.parallel
+   :members:
+   :undoc-members:
+   :show-inheritance:
+
+mbtrack2.tracking.particles module
+----------------------------------
+
+.. automodule:: mbtrack2.tracking.particles
+   :members:
+   :undoc-members:
+   :show-inheritance:
+
+mbtrack2.tracking.rf module
+---------------------------
+
+.. automodule:: mbtrack2.tracking.rf
+   :members:
+   :undoc-members:
+   :show-inheritance:
+
+mbtrack2.tracking.synchrotron module
+------------------------------------
+
+.. automodule:: mbtrack2.tracking.synchrotron
+   :members:
+   :undoc-members:
+   :show-inheritance:
+
+mbtrack2.tracking.wakepotential module
+--------------------------------------
+
+.. automodule:: mbtrack2.tracking.wakepotential
+   :members:
+   :undoc-members:
+   :show-inheritance:
+
+Module contents
+---------------
+
+.. automodule:: mbtrack2.tracking
+   :members:
+   :undoc-members:
+   :show-inheritance:
diff --git a/docs/build/html/_sources/mbtrack2.utilities.rst.txt b/docs/build/html/_sources/mbtrack2.utilities.rst.txt
new file mode 100644
index 0000000..e23f1f6
--- /dev/null
+++ b/docs/build/html/_sources/mbtrack2.utilities.rst.txt
@@ -0,0 +1,53 @@
+mbtrack2.utilities package
+==========================
+
+Submodules
+----------
+
+mbtrack2.utilities.beamloading module
+-------------------------------------
+
+.. automodule:: mbtrack2.utilities.beamloading
+   :members:
+   :undoc-members:
+   :show-inheritance:
+
+mbtrack2.utilities.misc module
+------------------------------
+
+.. automodule:: mbtrack2.utilities.misc
+   :members:
+   :undoc-members:
+   :show-inheritance:
+
+mbtrack2.utilities.optics module
+--------------------------------
+
+.. automodule:: mbtrack2.utilities.optics
+   :members:
+   :undoc-members:
+   :show-inheritance:
+
+mbtrack2.utilities.read\_impedance module
+-----------------------------------------
+
+.. automodule:: mbtrack2.utilities.read_impedance
+   :members:
+   :undoc-members:
+   :show-inheritance:
+
+mbtrack2.utilities.spectrum module
+----------------------------------
+
+.. automodule:: mbtrack2.utilities.spectrum
+   :members:
+   :undoc-members:
+   :show-inheritance:
+
+Module contents
+---------------
+
+.. automodule:: mbtrack2.utilities
+   :members:
+   :undoc-members:
+   :show-inheritance:
diff --git a/docs/build/html/_static/_sphinx_javascript_frameworks_compat.js b/docs/build/html/_static/_sphinx_javascript_frameworks_compat.js
new file mode 100644
index 0000000..8549469
--- /dev/null
+++ b/docs/build/html/_static/_sphinx_javascript_frameworks_compat.js
@@ -0,0 +1,134 @@
+/*
+ * _sphinx_javascript_frameworks_compat.js
+ * ~~~~~~~~~~
+ *
+ * Compatability shim for jQuery and underscores.js.
+ *
+ * WILL BE REMOVED IN Sphinx 6.0
+ * xref RemovedInSphinx60Warning
+ *
+ */
+
+/**
+ * select a different prefix for underscore
+ */
+$u = _.noConflict();
+
+
+/**
+ * small helper function to urldecode strings
+ *
+ * See https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/decodeURIComponent#Decoding_query_parameters_from_a_URL
+ */
+jQuery.urldecode = function(x) {
+    if (!x) {
+        return x
+    }
+    return decodeURIComponent(x.replace(/\+/g, ' '));
+};
+
+/**
+ * small helper function to urlencode strings
+ */
+jQuery.urlencode = encodeURIComponent;
+
+/**
+ * This function returns the parsed url parameters of the
+ * current request. Multiple values per key are supported,
+ * it will always return arrays of strings for the value parts.
+ */
+jQuery.getQueryParameters = function(s) {
+    if (typeof s === 'undefined')
+        s = document.location.search;
+    var parts = s.substr(s.indexOf('?') + 1).split('&');
+    var result = {};
+    for (var i = 0; i < parts.length; i++) {
+        var tmp = parts[i].split('=', 2);
+        var key = jQuery.urldecode(tmp[0]);
+        var value = jQuery.urldecode(tmp[1]);
+        if (key in result)
+            result[key].push(value);
+        else
+            result[key] = [value];
+    }
+    return result;
+};
+
+/**
+ * highlight a given string on a jquery object by wrapping it in
+ * span elements with the given class name.
+ */
+jQuery.fn.highlightText = function(text, className) {
+    function highlight(node, addItems) {
+        if (node.nodeType === 3) {
+            var val = node.nodeValue;
+            var pos = val.toLowerCase().indexOf(text);
+            if (pos >= 0 &&
+                !jQuery(node.parentNode).hasClass(className) &&
+                !jQuery(node.parentNode).hasClass("nohighlight")) {
+                var span;
+                var isInSVG = jQuery(node).closest("body, svg, foreignObject").is("svg");
+                if (isInSVG) {
+                    span = document.createElementNS("http://www.w3.org/2000/svg", "tspan");
+                } else {
+                    span = document.createElement("span");
+                    span.className = className;
+                }
+                span.appendChild(document.createTextNode(val.substr(pos, text.length)));
+                node.parentNode.insertBefore(span, node.parentNode.insertBefore(
+                    document.createTextNode(val.substr(pos + text.length)),
+                    node.nextSibling));
+                node.nodeValue = val.substr(0, pos);
+                if (isInSVG) {
+                    var rect = document.createElementNS("http://www.w3.org/2000/svg", "rect");
+                    var bbox = node.parentElement.getBBox();
+                    rect.x.baseVal.value = bbox.x;
+                    rect.y.baseVal.value = bbox.y;
+                    rect.width.baseVal.value = bbox.width;
+                    rect.height.baseVal.value = bbox.height;
+                    rect.setAttribute('class', className);
+                    addItems.push({
+                        "parent": node.parentNode,
+                        "target": rect});
+                }
+            }
+        }
+        else if (!jQuery(node).is("button, select, textarea")) {
+            jQuery.each(node.childNodes, function() {
+                highlight(this, addItems);
+            });
+        }
+    }
+    var addItems = [];
+    var result = this.each(function() {
+        highlight(this, addItems);
+    });
+    for (var i = 0; i < addItems.length; ++i) {
+        jQuery(addItems[i].parent).before(addItems[i].target);
+    }
+    return result;
+};
+
+/*
+ * backward compatibility for jQuery.browser
+ * This will be supported until firefox bug is fixed.
+ */
+if (!jQuery.browser) {
+    jQuery.uaMatch = function(ua) {
+        ua = ua.toLowerCase();
+
+        var match = /(chrome)[ \/]([\w.]+)/.exec(ua) ||
+            /(webkit)[ \/]([\w.]+)/.exec(ua) ||
+            /(opera)(?:.*version|)[ \/]([\w.]+)/.exec(ua) ||
+            /(msie) ([\w.]+)/.exec(ua) ||
+            ua.indexOf("compatible") < 0 && /(mozilla)(?:.*? rv:([\w.]+)|)/.exec(ua) ||
+            [];
+
+        return {
+            browser: match[ 1 ] || "",
+            version: match[ 2 ] || "0"
+        };
+    };
+    jQuery.browser = {};
+    jQuery.browser[jQuery.uaMatch(navigator.userAgent).browser] = true;
+}
diff --git a/docs/build/html/_static/basic.css b/docs/build/html/_static/basic.css
new file mode 100644
index 0000000..0889677
--- /dev/null
+++ b/docs/build/html/_static/basic.css
@@ -0,0 +1,930 @@
+/*
+ * basic.css
+ * ~~~~~~~~~
+ *
+ * Sphinx stylesheet -- basic theme.
+ *
+ * :copyright: Copyright 2007-2022 by the Sphinx team, see AUTHORS.
+ * :license: BSD, see LICENSE for details.
+ *
+ */
+
+/* -- main layout ----------------------------------------------------------- */
+
+div.clearer {
+    clear: both;
+}
+
+div.section::after {
+    display: block;
+    content: '';
+    clear: left;
+}
+
+/* -- relbar ---------------------------------------------------------------- */
+
+div.related {
+    width: 100%;
+    font-size: 90%;
+}
+
+div.related h3 {
+    display: none;
+}
+
+div.related ul {
+    margin: 0;
+    padding: 0 0 0 10px;
+    list-style: none;
+}
+
+div.related li {
+    display: inline;
+}
+
+div.related li.right {
+    float: right;
+    margin-right: 5px;
+}
+
+/* -- sidebar --------------------------------------------------------------- */
+
+div.sphinxsidebarwrapper {
+    padding: 10px 5px 0 10px;
+}
+
+div.sphinxsidebar {
+    float: left;
+    width: 230px;
+    margin-left: -100%;
+    font-size: 90%;
+    word-wrap: break-word;
+    overflow-wrap : break-word;
+}
+
+div.sphinxsidebar ul {
+    list-style: none;
+}
+
+div.sphinxsidebar ul ul,
+div.sphinxsidebar ul.want-points {
+    margin-left: 20px;
+    list-style: square;
+}
+
+div.sphinxsidebar ul ul {
+    margin-top: 0;
+    margin-bottom: 0;
+}
+
+div.sphinxsidebar form {
+    margin-top: 10px;
+}
+
+div.sphinxsidebar input {
+    border: 1px solid #98dbcc;
+    font-family: sans-serif;
+    font-size: 1em;
+}
+
+div.sphinxsidebar #searchbox form.search {
+    overflow: hidden;
+}
+
+div.sphinxsidebar #searchbox input[type="text"] {
+    float: left;
+    width: 80%;
+    padding: 0.25em;
+    box-sizing: border-box;
+}
+
+div.sphinxsidebar #searchbox input[type="submit"] {
+    float: left;
+    width: 20%;
+    border-left: none;
+    padding: 0.25em;
+    box-sizing: border-box;
+}
+
+
+img {
+    border: 0;
+    max-width: 100%;
+}
+
+/* -- search page ----------------------------------------------------------- */
+
+ul.search {
+    margin: 10px 0 0 20px;
+    padding: 0;
+}
+
+ul.search li {
+    padding: 5px 0 5px 20px;
+    background-image: url(file.png);
+    background-repeat: no-repeat;
+    background-position: 0 7px;
+}
+
+ul.search li a {
+    font-weight: bold;
+}
+
+ul.search li p.context {
+    color: #888;
+    margin: 2px 0 0 30px;
+    text-align: left;
+}
+
+ul.keywordmatches li.goodmatch a {
+    font-weight: bold;
+}
+
+/* -- index page ------------------------------------------------------------ */
+
+table.contentstable {
+    width: 90%;
+    margin-left: auto;
+    margin-right: auto;
+}
+
+table.contentstable p.biglink {
+    line-height: 150%;
+}
+
+a.biglink {
+    font-size: 1.3em;
+}
+
+span.linkdescr {
+    font-style: italic;
+    padding-top: 5px;
+    font-size: 90%;
+}
+
+/* -- general index --------------------------------------------------------- */
+
+table.indextable {
+    width: 100%;
+}
+
+table.indextable td {
+    text-align: left;
+    vertical-align: top;
+}
+
+table.indextable ul {
+    margin-top: 0;
+    margin-bottom: 0;
+    list-style-type: none;
+}
+
+table.indextable > tbody > tr > td > ul {
+    padding-left: 0em;
+}
+
+table.indextable tr.pcap {
+    height: 10px;
+}
+
+table.indextable tr.cap {
+    margin-top: 10px;
+    background-color: #f2f2f2;
+}
+
+img.toggler {
+    margin-right: 3px;
+    margin-top: 3px;
+    cursor: pointer;
+}
+
+div.modindex-jumpbox {
+    border-top: 1px solid #ddd;
+    border-bottom: 1px solid #ddd;
+    margin: 1em 0 1em 0;
+    padding: 0.4em;
+}
+
+div.genindex-jumpbox {
+    border-top: 1px solid #ddd;
+    border-bottom: 1px solid #ddd;
+    margin: 1em 0 1em 0;
+    padding: 0.4em;
+}
+
+/* -- domain module index --------------------------------------------------- */
+
+table.modindextable td {
+    padding: 2px;
+    border-collapse: collapse;
+}
+
+/* -- general body styles --------------------------------------------------- */
+
+div.body {
+    min-width: 360px;
+    max-width: 800px;
+}
+
+div.body p, div.body dd, div.body li, div.body blockquote {
+    -moz-hyphens: auto;
+    -ms-hyphens: auto;
+    -webkit-hyphens: auto;
+    hyphens: auto;
+}
+
+a.headerlink {
+    visibility: hidden;
+}
+
+h1:hover > a.headerlink,
+h2:hover > a.headerlink,
+h3:hover > a.headerlink,
+h4:hover > a.headerlink,
+h5:hover > a.headerlink,
+h6:hover > a.headerlink,
+dt:hover > a.headerlink,
+caption:hover > a.headerlink,
+p.caption:hover > a.headerlink,
+div.code-block-caption:hover > a.headerlink {
+    visibility: visible;
+}
+
+div.body p.caption {
+    text-align: inherit;
+}
+
+div.body td {
+    text-align: left;
+}
+
+.first {
+    margin-top: 0 !important;
+}
+
+p.rubric {
+    margin-top: 30px;
+    font-weight: bold;
+}
+
+img.align-left, figure.align-left, .figure.align-left, object.align-left {
+    clear: left;
+    float: left;
+    margin-right: 1em;
+}
+
+img.align-right, figure.align-right, .figure.align-right, object.align-right {
+    clear: right;
+    float: right;
+    margin-left: 1em;
+}
+
+img.align-center, figure.align-center, .figure.align-center, object.align-center {
+  display: block;
+  margin-left: auto;
+  margin-right: auto;
+}
+
+img.align-default, figure.align-default, .figure.align-default {
+  display: block;
+  margin-left: auto;
+  margin-right: auto;
+}
+
+.align-left {
+    text-align: left;
+}
+
+.align-center {
+    text-align: center;
+}
+
+.align-default {
+    text-align: center;
+}
+
+.align-right {
+    text-align: right;
+}
+
+/* -- sidebars -------------------------------------------------------------- */
+
+div.sidebar,
+aside.sidebar {
+    margin: 0 0 0.5em 1em;
+    border: 1px solid #ddb;
+    padding: 7px;
+    background-color: #ffe;
+    width: 40%;
+    float: right;
+    clear: right;
+    overflow-x: auto;
+}
+
+p.sidebar-title {
+    font-weight: bold;
+}
+nav.contents,
+aside.topic,
+
+div.admonition, div.topic, blockquote {
+    clear: left;
+}
+
+/* -- topics ---------------------------------------------------------------- */
+nav.contents,
+aside.topic,
+
+div.topic {
+    border: 1px solid #ccc;
+    padding: 7px;
+    margin: 10px 0 10px 0;
+}
+
+p.topic-title {
+    font-size: 1.1em;
+    font-weight: bold;
+    margin-top: 10px;
+}
+
+/* -- admonitions ----------------------------------------------------------- */
+
+div.admonition {
+    margin-top: 10px;
+    margin-bottom: 10px;
+    padding: 7px;
+}
+
+div.admonition dt {
+    font-weight: bold;
+}
+
+p.admonition-title {
+    margin: 0px 10px 5px 0px;
+    font-weight: bold;
+}
+
+div.body p.centered {
+    text-align: center;
+    margin-top: 25px;
+}
+
+/* -- content of sidebars/topics/admonitions -------------------------------- */
+
+div.sidebar > :last-child,
+aside.sidebar > :last-child,
+nav.contents > :last-child,
+aside.topic > :last-child,
+
+div.topic > :last-child,
+div.admonition > :last-child {
+    margin-bottom: 0;
+}
+
+div.sidebar::after,
+aside.sidebar::after,
+nav.contents::after,
+aside.topic::after,
+
+div.topic::after,
+div.admonition::after,
+blockquote::after {
+    display: block;
+    content: '';
+    clear: both;
+}
+
+/* -- tables ---------------------------------------------------------------- */
+
+table.docutils {
+    margin-top: 10px;
+    margin-bottom: 10px;
+    border: 0;
+    border-collapse: collapse;
+}
+
+table.align-center {
+    margin-left: auto;
+    margin-right: auto;
+}
+
+table.align-default {
+    margin-left: auto;
+    margin-right: auto;
+}
+
+table caption span.caption-number {
+    font-style: italic;
+}
+
+table caption span.caption-text {
+}
+
+table.docutils td, table.docutils th {
+    padding: 1px 8px 1px 5px;
+    border-top: 0;
+    border-left: 0;
+    border-right: 0;
+    border-bottom: 1px solid #aaa;
+}
+
+th {
+    text-align: left;
+    padding-right: 5px;
+}
+
+table.citation {
+    border-left: solid 1px gray;
+    margin-left: 1px;
+}
+
+table.citation td {
+    border-bottom: none;
+}
+
+th > :first-child,
+td > :first-child {
+    margin-top: 0px;
+}
+
+th > :last-child,
+td > :last-child {
+    margin-bottom: 0px;
+}
+
+/* -- figures --------------------------------------------------------------- */
+
+div.figure, figure {
+    margin: 0.5em;
+    padding: 0.5em;
+}
+
+div.figure p.caption, figcaption {
+    padding: 0.3em;
+}
+
+div.figure p.caption span.caption-number,
+figcaption span.caption-number {
+    font-style: italic;
+}
+
+div.figure p.caption span.caption-text,
+figcaption span.caption-text {
+}
+
+/* -- field list styles ----------------------------------------------------- */
+
+table.field-list td, table.field-list th {
+    border: 0 !important;
+}
+
+.field-list ul {
+    margin: 0;
+    padding-left: 1em;
+}
+
+.field-list p {
+    margin: 0;
+}
+
+.field-name {
+    -moz-hyphens: manual;
+    -ms-hyphens: manual;
+    -webkit-hyphens: manual;
+    hyphens: manual;
+}
+
+/* -- hlist styles ---------------------------------------------------------- */
+
+table.hlist {
+    margin: 1em 0;
+}
+
+table.hlist td {
+    vertical-align: top;
+}
+
+/* -- object description styles --------------------------------------------- */
+
+.sig {
+	font-family: 'Consolas', 'Menlo', 'DejaVu Sans Mono', 'Bitstream Vera Sans Mono', monospace;
+}
+
+.sig-name, code.descname {
+    background-color: transparent;
+    font-weight: bold;
+}
+
+.sig-name {
+	font-size: 1.1em;
+}
+
+code.descname {
+    font-size: 1.2em;
+}
+
+.sig-prename, code.descclassname {
+    background-color: transparent;
+}
+
+.optional {
+    font-size: 1.3em;
+}
+
+.sig-paren {
+    font-size: larger;
+}
+
+.sig-param.n {
+	font-style: italic;
+}
+
+/* C++ specific styling */
+
+.sig-inline.c-texpr,
+.sig-inline.cpp-texpr {
+	font-family: unset;
+}
+
+.sig.c   .k, .sig.c   .kt,
+.sig.cpp .k, .sig.cpp .kt {
+	color: #0033B3;
+}
+
+.sig.c   .m,
+.sig.cpp .m {
+	color: #1750EB;
+}
+
+.sig.c   .s, .sig.c   .sc,
+.sig.cpp .s, .sig.cpp .sc {
+	color: #067D17;
+}
+
+
+/* -- other body styles ----------------------------------------------------- */
+
+ol.arabic {
+    list-style: decimal;
+}
+
+ol.loweralpha {
+    list-style: lower-alpha;
+}
+
+ol.upperalpha {
+    list-style: upper-alpha;
+}
+
+ol.lowerroman {
+    list-style: lower-roman;
+}
+
+ol.upperroman {
+    list-style: upper-roman;
+}
+
+:not(li) > ol > li:first-child > :first-child,
+:not(li) > ul > li:first-child > :first-child {
+    margin-top: 0px;
+}
+
+:not(li) > ol > li:last-child > :last-child,
+:not(li) > ul > li:last-child > :last-child {
+    margin-bottom: 0px;
+}
+
+ol.simple ol p,
+ol.simple ul p,
+ul.simple ol p,
+ul.simple ul p {
+    margin-top: 0;
+}
+
+ol.simple > li:not(:first-child) > p,
+ul.simple > li:not(:first-child) > p {
+    margin-top: 0;
+}
+
+ol.simple p,
+ul.simple p {
+    margin-bottom: 0;
+}
+
+/* Docutils 0.17 and older (footnotes & citations) */
+dl.footnote > dt,
+dl.citation > dt {
+    float: left;
+    margin-right: 0.5em;
+}
+
+dl.footnote > dd,
+dl.citation > dd {
+    margin-bottom: 0em;
+}
+
+dl.footnote > dd:after,
+dl.citation > dd:after {
+    content: "";
+    clear: both;
+}
+
+/* Docutils 0.18+ (footnotes & citations) */
+aside.footnote > span,
+div.citation > span {
+    float: left;
+}
+aside.footnote > span:last-of-type,
+div.citation > span:last-of-type {
+  padding-right: 0.5em;
+}
+aside.footnote > p {
+  margin-left: 2em;
+}
+div.citation > p {
+  margin-left: 4em;
+}
+aside.footnote > p:last-of-type,
+div.citation > p:last-of-type {
+    margin-bottom: 0em;
+}
+aside.footnote > p:last-of-type:after,
+div.citation > p:last-of-type:after {
+    content: "";
+    clear: both;
+}
+
+/* Footnotes & citations ends */
+
+dl.field-list {
+    display: grid;
+    grid-template-columns: fit-content(30%) auto;
+}
+
+dl.field-list > dt {
+    font-weight: bold;
+    word-break: break-word;
+    padding-left: 0.5em;
+    padding-right: 5px;
+}
+
+dl.field-list > dt:after {
+    content: ":";
+}
+
+dl.field-list > dd {
+    padding-left: 0.5em;
+    margin-top: 0em;
+    margin-left: 0em;
+    margin-bottom: 0em;
+}
+
+dl {
+    margin-bottom: 15px;
+}
+
+dd > :first-child {
+    margin-top: 0px;
+}
+
+dd ul, dd table {
+    margin-bottom: 10px;
+}
+
+dd {
+    margin-top: 3px;
+    margin-bottom: 10px;
+    margin-left: 30px;
+}
+
+dl > dd:last-child,
+dl > dd:last-child > :last-child {
+    margin-bottom: 0;
+}
+
+dt:target, span.highlighted {
+    background-color: #fbe54e;
+}
+
+rect.highlighted {
+    fill: #fbe54e;
+}
+
+dl.glossary dt {
+    font-weight: bold;
+    font-size: 1.1em;
+}
+
+.versionmodified {
+    font-style: italic;
+}
+
+.system-message {
+    background-color: #fda;
+    padding: 5px;
+    border: 3px solid red;
+}
+
+.footnote:target  {
+    background-color: #ffa;
+}
+
+.line-block {
+    display: block;
+    margin-top: 1em;
+    margin-bottom: 1em;
+}
+
+.line-block .line-block {
+    margin-top: 0;
+    margin-bottom: 0;
+    margin-left: 1.5em;
+}
+
+.guilabel, .menuselection {
+    font-family: sans-serif;
+}
+
+.accelerator {
+    text-decoration: underline;
+}
+
+.classifier {
+    font-style: oblique;
+}
+
+.classifier:before {
+    font-style: normal;
+    margin: 0 0.5em;
+    content: ":";
+    display: inline-block;
+}
+
+abbr, acronym {
+    border-bottom: dotted 1px;
+    cursor: help;
+}
+
+/* -- code displays --------------------------------------------------------- */
+
+pre {
+    overflow: auto;
+    overflow-y: hidden;  /* fixes display issues on Chrome browsers */
+}
+
+pre, div[class*="highlight-"] {
+    clear: both;
+}
+
+span.pre {
+    -moz-hyphens: none;
+    -ms-hyphens: none;
+    -webkit-hyphens: none;
+    hyphens: none;
+    white-space: nowrap;
+}
+
+div[class*="highlight-"] {
+    margin: 1em 0;
+}
+
+td.linenos pre {
+    border: 0;
+    background-color: transparent;
+    color: #aaa;
+}
+
+table.highlighttable {
+    display: block;
+}
+
+table.highlighttable tbody {
+    display: block;
+}
+
+table.highlighttable tr {
+    display: flex;
+}
+
+table.highlighttable td {
+    margin: 0;
+    padding: 0;
+}
+
+table.highlighttable td.linenos {
+    padding-right: 0.5em;
+}
+
+table.highlighttable td.code {
+    flex: 1;
+    overflow: hidden;
+}
+
+.highlight .hll {
+    display: block;
+}
+
+div.highlight pre,
+table.highlighttable pre {
+    margin: 0;
+}
+
+div.code-block-caption + div {
+    margin-top: 0;
+}
+
+div.code-block-caption {
+    margin-top: 1em;
+    padding: 2px 5px;
+    font-size: small;
+}
+
+div.code-block-caption code {
+    background-color: transparent;
+}
+
+table.highlighttable td.linenos,
+span.linenos,
+div.highlight span.gp {  /* gp: Generic.Prompt */
+  user-select: none;
+  -webkit-user-select: text; /* Safari fallback only */
+  -webkit-user-select: none; /* Chrome/Safari */
+  -moz-user-select: none; /* Firefox */
+  -ms-user-select: none; /* IE10+ */
+}
+
+div.code-block-caption span.caption-number {
+    padding: 0.1em 0.3em;
+    font-style: italic;
+}
+
+div.code-block-caption span.caption-text {
+}
+
+div.literal-block-wrapper {
+    margin: 1em 0;
+}
+
+code.xref, a code {
+    background-color: transparent;
+    font-weight: bold;
+}
+
+h1 code, h2 code, h3 code, h4 code, h5 code, h6 code {
+    background-color: transparent;
+}
+
+.viewcode-link {
+    float: right;
+}
+
+.viewcode-back {
+    float: right;
+    font-family: sans-serif;
+}
+
+div.viewcode-block:target {
+    margin: -1px -10px;
+    padding: 0 10px;
+}
+
+/* -- math display ---------------------------------------------------------- */
+
+img.math {
+    vertical-align: middle;
+}
+
+div.body div.math p {
+    text-align: center;
+}
+
+span.eqno {
+    float: right;
+}
+
+span.eqno a.headerlink {
+    position: absolute;
+    z-index: 1;
+}
+
+div.math:hover a.headerlink {
+    visibility: visible;
+}
+
+/* -- printout stylesheet --------------------------------------------------- */
+
+@media print {
+    div.document,
+    div.documentwrapper,
+    div.bodywrapper {
+        margin: 0 !important;
+        width: 100%;
+    }
+
+    div.sphinxsidebar,
+    div.related,
+    div.footer,
+    #top-link {
+        display: none;
+    }
+}
\ No newline at end of file
diff --git a/docs/build/html/_static/doctools.js b/docs/build/html/_static/doctools.js
new file mode 100644
index 0000000..c3db08d
--- /dev/null
+++ b/docs/build/html/_static/doctools.js
@@ -0,0 +1,264 @@
+/*
+ * doctools.js
+ * ~~~~~~~~~~~
+ *
+ * Base JavaScript utilities for all Sphinx HTML documentation.
+ *
+ * :copyright: Copyright 2007-2022 by the Sphinx team, see AUTHORS.
+ * :license: BSD, see LICENSE for details.
+ *
+ */
+"use strict";
+
+const _ready = (callback) => {
+  if (document.readyState !== "loading") {
+    callback();
+  } else {
+    document.addEventListener("DOMContentLoaded", callback);
+  }
+};
+
+/**
+ * highlight a given string on a node by wrapping it in
+ * span elements with the given class name.
+ */
+const _highlight = (node, addItems, text, className) => {
+  if (node.nodeType === Node.TEXT_NODE) {
+    const val = node.nodeValue;
+    const parent = node.parentNode;
+    const pos = val.toLowerCase().indexOf(text);
+    if (
+      pos >= 0 &&
+      !parent.classList.contains(className) &&
+      !parent.classList.contains("nohighlight")
+    ) {
+      let span;
+
+      const closestNode = parent.closest("body, svg, foreignObject");
+      const isInSVG = closestNode && closestNode.matches("svg");
+      if (isInSVG) {
+        span = document.createElementNS("http://www.w3.org/2000/svg", "tspan");
+      } else {
+        span = document.createElement("span");
+        span.classList.add(className);
+      }
+
+      span.appendChild(document.createTextNode(val.substr(pos, text.length)));
+      parent.insertBefore(
+        span,
+        parent.insertBefore(
+          document.createTextNode(val.substr(pos + text.length)),
+          node.nextSibling
+        )
+      );
+      node.nodeValue = val.substr(0, pos);
+
+      if (isInSVG) {
+        const rect = document.createElementNS(
+          "http://www.w3.org/2000/svg",
+          "rect"
+        );
+        const bbox = parent.getBBox();
+        rect.x.baseVal.value = bbox.x;
+        rect.y.baseVal.value = bbox.y;
+        rect.width.baseVal.value = bbox.width;
+        rect.height.baseVal.value = bbox.height;
+        rect.setAttribute("class", className);
+        addItems.push({ parent: parent, target: rect });
+      }
+    }
+  } else if (node.matches && !node.matches("button, select, textarea")) {
+    node.childNodes.forEach((el) => _highlight(el, addItems, text, className));
+  }
+};
+const _highlightText = (thisNode, text, className) => {
+  let addItems = [];
+  _highlight(thisNode, addItems, text, className);
+  addItems.forEach((obj) =>
+    obj.parent.insertAdjacentElement("beforebegin", obj.target)
+  );
+};
+
+/**
+ * Small JavaScript module for the documentation.
+ */
+const Documentation = {
+  init: () => {
+    Documentation.highlightSearchWords();
+    Documentation.initDomainIndexTable();
+    Documentation.initOnKeyListeners();
+  },
+
+  /**
+   * i18n support
+   */
+  TRANSLATIONS: {},
+  PLURAL_EXPR: (n) => (n === 1 ? 0 : 1),
+  LOCALE: "unknown",
+
+  // gettext and ngettext don't access this so that the functions
+  // can safely bound to a different name (_ = Documentation.gettext)
+  gettext: (string) => {
+    const translated = Documentation.TRANSLATIONS[string];
+    switch (typeof translated) {
+      case "undefined":
+        return string; // no translation
+      case "string":
+        return translated; // translation exists
+      default:
+        return translated[0]; // (singular, plural) translation tuple exists
+    }
+  },
+
+  ngettext: (singular, plural, n) => {
+    const translated = Documentation.TRANSLATIONS[singular];
+    if (typeof translated !== "undefined")
+      return translated[Documentation.PLURAL_EXPR(n)];
+    return n === 1 ? singular : plural;
+  },
+
+  addTranslations: (catalog) => {
+    Object.assign(Documentation.TRANSLATIONS, catalog.messages);
+    Documentation.PLURAL_EXPR = new Function(
+      "n",
+      `return (${catalog.plural_expr})`
+    );
+    Documentation.LOCALE = catalog.locale;
+  },
+
+  /**
+   * highlight the search words provided in the url in the text
+   */
+  highlightSearchWords: () => {
+    const highlight =
+      new URLSearchParams(window.location.search).get("highlight") || "";
+    const terms = highlight.toLowerCase().split(/\s+/).filter(x => x);
+    if (terms.length === 0) return; // nothing to do
+
+    // There should never be more than one element matching "div.body"
+    const divBody = document.querySelectorAll("div.body");
+    const body = divBody.length ? divBody[0] : document.querySelector("body");
+    window.setTimeout(() => {
+      terms.forEach((term) => _highlightText(body, term, "highlighted"));
+    }, 10);
+
+    const searchBox = document.getElementById("searchbox");
+    if (searchBox === null) return;
+    searchBox.appendChild(
+      document
+        .createRange()
+        .createContextualFragment(
+          '<p class="highlight-link">' +
+            '<a href="javascript:Documentation.hideSearchWords()">' +
+            Documentation.gettext("Hide Search Matches") +
+            "</a></p>"
+        )
+    );
+  },
+
+  /**
+   * helper function to hide the search marks again
+   */
+  hideSearchWords: () => {
+    document
+      .querySelectorAll("#searchbox .highlight-link")
+      .forEach((el) => el.remove());
+    document
+      .querySelectorAll("span.highlighted")
+      .forEach((el) => el.classList.remove("highlighted"));
+    const url = new URL(window.location);
+    url.searchParams.delete("highlight");
+    window.history.replaceState({}, "", url);
+  },
+
+  /**
+   * helper function to focus on search bar
+   */
+  focusSearchBar: () => {
+    document.querySelectorAll("input[name=q]")[0]?.focus();
+  },
+
+  /**
+   * Initialise the domain index toggle buttons
+   */
+  initDomainIndexTable: () => {
+    const toggler = (el) => {
+      const idNumber = el.id.substr(7);
+      const toggledRows = document.querySelectorAll(`tr.cg-${idNumber}`);
+      if (el.src.substr(-9) === "minus.png") {
+        el.src = `${el.src.substr(0, el.src.length - 9)}plus.png`;
+        toggledRows.forEach((el) => (el.style.display = "none"));
+      } else {
+        el.src = `${el.src.substr(0, el.src.length - 8)}minus.png`;
+        toggledRows.forEach((el) => (el.style.display = ""));
+      }
+    };
+
+    const togglerElements = document.querySelectorAll("img.toggler");
+    togglerElements.forEach((el) =>
+      el.addEventListener("click", (event) => toggler(event.currentTarget))
+    );
+    togglerElements.forEach((el) => (el.style.display = ""));
+    if (DOCUMENTATION_OPTIONS.COLLAPSE_INDEX) togglerElements.forEach(toggler);
+  },
+
+  initOnKeyListeners: () => {
+    // only install a listener if it is really needed
+    if (
+      !DOCUMENTATION_OPTIONS.NAVIGATION_WITH_KEYS &&
+      !DOCUMENTATION_OPTIONS.ENABLE_SEARCH_SHORTCUTS
+    )
+      return;
+
+    const blacklistedElements = new Set([
+      "TEXTAREA",
+      "INPUT",
+      "SELECT",
+      "BUTTON",
+    ]);
+    document.addEventListener("keydown", (event) => {
+      if (blacklistedElements.has(document.activeElement.tagName)) return; // bail for input elements
+      if (event.altKey || event.ctrlKey || event.metaKey) return; // bail with special keys
+
+      if (!event.shiftKey) {
+        switch (event.key) {
+          case "ArrowLeft":
+            if (!DOCUMENTATION_OPTIONS.NAVIGATION_WITH_KEYS) break;
+
+            const prevLink = document.querySelector('link[rel="prev"]');
+            if (prevLink && prevLink.href) {
+              window.location.href = prevLink.href;
+              event.preventDefault();
+            }
+            break;
+          case "ArrowRight":
+            if (!DOCUMENTATION_OPTIONS.NAVIGATION_WITH_KEYS) break;
+
+            const nextLink = document.querySelector('link[rel="next"]');
+            if (nextLink && nextLink.href) {
+              window.location.href = nextLink.href;
+              event.preventDefault();
+            }
+            break;
+          case "Escape":
+            if (!DOCUMENTATION_OPTIONS.ENABLE_SEARCH_SHORTCUTS) break;
+            Documentation.hideSearchWords();
+            event.preventDefault();
+        }
+      }
+
+      // some keyboard layouts may need Shift to get /
+      switch (event.key) {
+        case "/":
+          if (!DOCUMENTATION_OPTIONS.ENABLE_SEARCH_SHORTCUTS) break;
+          Documentation.focusSearchBar();
+          event.preventDefault();
+      }
+    });
+  },
+};
+
+// quick alias for translations
+const _ = Documentation.gettext;
+
+_ready(Documentation.init);
diff --git a/docs/build/html/_static/documentation_options.js b/docs/build/html/_static/documentation_options.js
new file mode 100644
index 0000000..00e2e11
--- /dev/null
+++ b/docs/build/html/_static/documentation_options.js
@@ -0,0 +1,14 @@
+var DOCUMENTATION_OPTIONS = {
+    URL_ROOT: document.getElementById("documentation_options").getAttribute('data-url_root'),
+    VERSION: '0.6.0',
+    LANGUAGE: 'en',
+    COLLAPSE_INDEX: false,
+    BUILDER: 'html',
+    FILE_SUFFIX: '.html',
+    LINK_SUFFIX: '.html',
+    HAS_SOURCE: true,
+    SOURCELINK_SUFFIX: '.txt',
+    NAVIGATION_WITH_KEYS: false,
+    SHOW_SEARCH_SUMMARY: true,
+    ENABLE_SEARCH_SHORTCUTS: false,
+};
\ No newline at end of file
diff --git a/docs/build/html/_static/file.png b/docs/build/html/_static/file.png
new file mode 100644
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diff --git a/docs/build/html/_static/jquery-3.6.0.js b/docs/build/html/_static/jquery-3.6.0.js
new file mode 100644
index 0000000..fc6c299
--- /dev/null
+++ b/docs/build/html/_static/jquery-3.6.0.js
@@ -0,0 +1,10881 @@
+/*!
+ * jQuery JavaScript Library v3.6.0
+ * https://jquery.com/
+ *
+ * Includes Sizzle.js
+ * https://sizzlejs.com/
+ *
+ * Copyright OpenJS Foundation and other contributors
+ * Released under the MIT license
+ * https://jquery.org/license
+ *
+ * Date: 2021-03-02T17:08Z
+ */
+( function( global, factory ) {
+
+	"use strict";
+
+	if ( typeof module === "object" && typeof module.exports === "object" ) {
+
+		// For CommonJS and CommonJS-like environments where a proper `window`
+		// is present, execute the factory and get jQuery.
+		// For environments that do not have a `window` with a `document`
+		// (such as Node.js), expose a factory as module.exports.
+		// This accentuates the need for the creation of a real `window`.
+		// e.g. var jQuery = require("jquery")(window);
+		// See ticket #14549 for more info.
+		module.exports = global.document ?
+			factory( global, true ) :
+			function( w ) {
+				if ( !w.document ) {
+					throw new Error( "jQuery requires a window with a document" );
+				}
+				return factory( w );
+			};
+	} else {
+		factory( global );
+	}
+
+// Pass this if window is not defined yet
+} )( typeof window !== "undefined" ? window : this, function( window, noGlobal ) {
+
+// Edge <= 12 - 13+, Firefox <=18 - 45+, IE 10 - 11, Safari 5.1 - 9+, iOS 6 - 9.1
+// throw exceptions when non-strict code (e.g., ASP.NET 4.5) accesses strict mode
+// arguments.callee.caller (trac-13335). But as of jQuery 3.0 (2016), strict mode should be common
+// enough that all such attempts are guarded in a try block.
+"use strict";
+
+var arr = [];
+
+var getProto = Object.getPrototypeOf;
+
+var slice = arr.slice;
+
+var flat = arr.flat ? function( array ) {
+	return arr.flat.call( array );
+} : function( array ) {
+	return arr.concat.apply( [], array );
+};
+
+
+var push = arr.push;
+
+var indexOf = arr.indexOf;
+
+var class2type = {};
+
+var toString = class2type.toString;
+
+var hasOwn = class2type.hasOwnProperty;
+
+var fnToString = hasOwn.toString;
+
+var ObjectFunctionString = fnToString.call( Object );
+
+var support = {};
+
+var isFunction = function isFunction( obj ) {
+
+		// Support: Chrome <=57, Firefox <=52
+		// In some browsers, typeof returns "function" for HTML <object> elements
+		// (i.e., `typeof document.createElement( "object" ) === "function"`).
+		// We don't want to classify *any* DOM node as a function.
+		// Support: QtWeb <=3.8.5, WebKit <=534.34, wkhtmltopdf tool <=0.12.5
+		// Plus for old WebKit, typeof returns "function" for HTML collections
+		// (e.g., `typeof document.getElementsByTagName("div") === "function"`). (gh-4756)
+		return typeof obj === "function" && typeof obj.nodeType !== "number" &&
+			typeof obj.item !== "function";
+	};
+
+
+var isWindow = function isWindow( obj ) {
+		return obj != null && obj === obj.window;
+	};
+
+
+var document = window.document;
+
+
+
+	var preservedScriptAttributes = {
+		type: true,
+		src: true,
+		nonce: true,
+		noModule: true
+	};
+
+	function DOMEval( code, node, doc ) {
+		doc = doc || document;
+
+		var i, val,
+			script = doc.createElement( "script" );
+
+		script.text = code;
+		if ( node ) {
+			for ( i in preservedScriptAttributes ) {
+
+				// Support: Firefox 64+, Edge 18+
+				// Some browsers don't support the "nonce" property on scripts.
+				// On the other hand, just using `getAttribute` is not enough as
+				// the `nonce` attribute is reset to an empty string whenever it
+				// becomes browsing-context connected.
+				// See https://github.com/whatwg/html/issues/2369
+				// See https://html.spec.whatwg.org/#nonce-attributes
+				// The `node.getAttribute` check was added for the sake of
+				// `jQuery.globalEval` so that it can fake a nonce-containing node
+				// via an object.
+				val = node[ i ] || node.getAttribute && node.getAttribute( i );
+				if ( val ) {
+					script.setAttribute( i, val );
+				}
+			}
+		}
+		doc.head.appendChild( script ).parentNode.removeChild( script );
+	}
+
+
+function toType( obj ) {
+	if ( obj == null ) {
+		return obj + "";
+	}
+
+	// Support: Android <=2.3 only (functionish RegExp)
+	return typeof obj === "object" || typeof obj === "function" ?
+		class2type[ toString.call( obj ) ] || "object" :
+		typeof obj;
+}
+/* global Symbol */
+// Defining this global in .eslintrc.json would create a danger of using the global
+// unguarded in another place, it seems safer to define global only for this module
+
+
+
+var
+	version = "3.6.0",
+
+	// Define a local copy of jQuery
+	jQuery = function( selector, context ) {
+
+		// The jQuery object is actually just the init constructor 'enhanced'
+		// Need init if jQuery is called (just allow error to be thrown if not included)
+		return new jQuery.fn.init( selector, context );
+	};
+
+jQuery.fn = jQuery.prototype = {
+
+	// The current version of jQuery being used
+	jquery: version,
+
+	constructor: jQuery,
+
+	// The default length of a jQuery object is 0
+	length: 0,
+
+	toArray: function() {
+		return slice.call( this );
+	},
+
+	// Get the Nth element in the matched element set OR
+	// Get the whole matched element set as a clean array
+	get: function( num ) {
+
+		// Return all the elements in a clean array
+		if ( num == null ) {
+			return slice.call( this );
+		}
+
+		// Return just the one element from the set
+		return num < 0 ? this[ num + this.length ] : this[ num ];
+	},
+
+	// Take an array of elements and push it onto the stack
+	// (returning the new matched element set)
+	pushStack: function( elems ) {
+
+		// Build a new jQuery matched element set
+		var ret = jQuery.merge( this.constructor(), elems );
+
+		// Add the old object onto the stack (as a reference)
+		ret.prevObject = this;
+
+		// Return the newly-formed element set
+		return ret;
+	},
+
+	// Execute a callback for every element in the matched set.
+	each: function( callback ) {
+		return jQuery.each( this, callback );
+	},
+
+	map: function( callback ) {
+		return this.pushStack( jQuery.map( this, function( elem, i ) {
+			return callback.call( elem, i, elem );
+		} ) );
+	},
+
+	slice: function() {
+		return this.pushStack( slice.apply( this, arguments ) );
+	},
+
+	first: function() {
+		return this.eq( 0 );
+	},
+
+	last: function() {
+		return this.eq( -1 );
+	},
+
+	even: function() {
+		return this.pushStack( jQuery.grep( this, function( _elem, i ) {
+			return ( i + 1 ) % 2;
+		} ) );
+	},
+
+	odd: function() {
+		return this.pushStack( jQuery.grep( this, function( _elem, i ) {
+			return i % 2;
+		} ) );
+	},
+
+	eq: function( i ) {
+		var len = this.length,
+			j = +i + ( i < 0 ? len : 0 );
+		return this.pushStack( j >= 0 && j < len ? [ this[ j ] ] : [] );
+	},
+
+	end: function() {
+		return this.prevObject || this.constructor();
+	},
+
+	// For internal use only.
+	// Behaves like an Array's method, not like a jQuery method.
+	push: push,
+	sort: arr.sort,
+	splice: arr.splice
+};
+
+jQuery.extend = jQuery.fn.extend = function() {
+	var options, name, src, copy, copyIsArray, clone,
+		target = arguments[ 0 ] || {},
+		i = 1,
+		length = arguments.length,
+		deep = false;
+
+	// Handle a deep copy situation
+	if ( typeof target === "boolean" ) {
+		deep = target;
+
+		// Skip the boolean and the target
+		target = arguments[ i ] || {};
+		i++;
+	}
+
+	// Handle case when target is a string or something (possible in deep copy)
+	if ( typeof target !== "object" && !isFunction( target ) ) {
+		target = {};
+	}
+
+	// Extend jQuery itself if only one argument is passed
+	if ( i === length ) {
+		target = this;
+		i--;
+	}
+
+	for ( ; i < length; i++ ) {
+
+		// Only deal with non-null/undefined values
+		if ( ( options = arguments[ i ] ) != null ) {
+
+			// Extend the base object
+			for ( name in options ) {
+				copy = options[ name ];
+
+				// Prevent Object.prototype pollution
+				// Prevent never-ending loop
+				if ( name === "__proto__" || target === copy ) {
+					continue;
+				}
+
+				// Recurse if we're merging plain objects or arrays
+				if ( deep && copy && ( jQuery.isPlainObject( copy ) ||
+					( copyIsArray = Array.isArray( copy ) ) ) ) {
+					src = target[ name ];
+
+					// Ensure proper type for the source value
+					if ( copyIsArray && !Array.isArray( src ) ) {
+						clone = [];
+					} else if ( !copyIsArray && !jQuery.isPlainObject( src ) ) {
+						clone = {};
+					} else {
+						clone = src;
+					}
+					copyIsArray = false;
+
+					// Never move original objects, clone them
+					target[ name ] = jQuery.extend( deep, clone, copy );
+
+				// Don't bring in undefined values
+				} else if ( copy !== undefined ) {
+					target[ name ] = copy;
+				}
+			}
+		}
+	}
+
+	// Return the modified object
+	return target;
+};
+
+jQuery.extend( {
+
+	// Unique for each copy of jQuery on the page
+	expando: "jQuery" + ( version + Math.random() ).replace( /\D/g, "" ),
+
+	// Assume jQuery is ready without the ready module
+	isReady: true,
+
+	error: function( msg ) {
+		throw new Error( msg );
+	},
+
+	noop: function() {},
+
+	isPlainObject: function( obj ) {
+		var proto, Ctor;
+
+		// Detect obvious negatives
+		// Use toString instead of jQuery.type to catch host objects
+		if ( !obj || toString.call( obj ) !== "[object Object]" ) {
+			return false;
+		}
+
+		proto = getProto( obj );
+
+		// Objects with no prototype (e.g., `Object.create( null )`) are plain
+		if ( !proto ) {
+			return true;
+		}
+
+		// Objects with prototype are plain iff they were constructed by a global Object function
+		Ctor = hasOwn.call( proto, "constructor" ) && proto.constructor;
+		return typeof Ctor === "function" && fnToString.call( Ctor ) === ObjectFunctionString;
+	},
+
+	isEmptyObject: function( obj ) {
+		var name;
+
+		for ( name in obj ) {
+			return false;
+		}
+		return true;
+	},
+
+	// Evaluates a script in a provided context; falls back to the global one
+	// if not specified.
+	globalEval: function( code, options, doc ) {
+		DOMEval( code, { nonce: options && options.nonce }, doc );
+	},
+
+	each: function( obj, callback ) {
+		var length, i = 0;
+
+		if ( isArrayLike( obj ) ) {
+			length = obj.length;
+			for ( ; i < length; i++ ) {
+				if ( callback.call( obj[ i ], i, obj[ i ] ) === false ) {
+					break;
+				}
+			}
+		} else {
+			for ( i in obj ) {
+				if ( callback.call( obj[ i ], i, obj[ i ] ) === false ) {
+					break;
+				}
+			}
+		}
+
+		return obj;
+	},
+
+	// results is for internal usage only
+	makeArray: function( arr, results ) {
+		var ret = results || [];
+
+		if ( arr != null ) {
+			if ( isArrayLike( Object( arr ) ) ) {
+				jQuery.merge( ret,
+					typeof arr === "string" ?
+						[ arr ] : arr
+				);
+			} else {
+				push.call( ret, arr );
+			}
+		}
+
+		return ret;
+	},
+
+	inArray: function( elem, arr, i ) {
+		return arr == null ? -1 : indexOf.call( arr, elem, i );
+	},
+
+	// Support: Android <=4.0 only, PhantomJS 1 only
+	// push.apply(_, arraylike) throws on ancient WebKit
+	merge: function( first, second ) {
+		var len = +second.length,
+			j = 0,
+			i = first.length;
+
+		for ( ; j < len; j++ ) {
+			first[ i++ ] = second[ j ];
+		}
+
+		first.length = i;
+
+		return first;
+	},
+
+	grep: function( elems, callback, invert ) {
+		var callbackInverse,
+			matches = [],
+			i = 0,
+			length = elems.length,
+			callbackExpect = !invert;
+
+		// Go through the array, only saving the items
+		// that pass the validator function
+		for ( ; i < length; i++ ) {
+			callbackInverse = !callback( elems[ i ], i );
+			if ( callbackInverse !== callbackExpect ) {
+				matches.push( elems[ i ] );
+			}
+		}
+
+		return matches;
+	},
+
+	// arg is for internal usage only
+	map: function( elems, callback, arg ) {
+		var length, value,
+			i = 0,
+			ret = [];
+
+		// Go through the array, translating each of the items to their new values
+		if ( isArrayLike( elems ) ) {
+			length = elems.length;
+			for ( ; i < length; i++ ) {
+				value = callback( elems[ i ], i, arg );
+
+				if ( value != null ) {
+					ret.push( value );
+				}
+			}
+
+		// Go through every key on the object,
+		} else {
+			for ( i in elems ) {
+				value = callback( elems[ i ], i, arg );
+
+				if ( value != null ) {
+					ret.push( value );
+				}
+			}
+		}
+
+		// Flatten any nested arrays
+		return flat( ret );
+	},
+
+	// A global GUID counter for objects
+	guid: 1,
+
+	// jQuery.support is not used in Core but other projects attach their
+	// properties to it so it needs to exist.
+	support: support
+} );
+
+if ( typeof Symbol === "function" ) {
+	jQuery.fn[ Symbol.iterator ] = arr[ Symbol.iterator ];
+}
+
+// Populate the class2type map
+jQuery.each( "Boolean Number String Function Array Date RegExp Object Error Symbol".split( " " ),
+	function( _i, name ) {
+		class2type[ "[object " + name + "]" ] = name.toLowerCase();
+	} );
+
+function isArrayLike( obj ) {
+
+	// Support: real iOS 8.2 only (not reproducible in simulator)
+	// `in` check used to prevent JIT error (gh-2145)
+	// hasOwn isn't used here due to false negatives
+	// regarding Nodelist length in IE
+	var length = !!obj && "length" in obj && obj.length,
+		type = toType( obj );
+
+	if ( isFunction( obj ) || isWindow( obj ) ) {
+		return false;
+	}
+
+	return type === "array" || length === 0 ||
+		typeof length === "number" && length > 0 && ( length - 1 ) in obj;
+}
+var Sizzle =
+/*!
+ * Sizzle CSS Selector Engine v2.3.6
+ * https://sizzlejs.com/
+ *
+ * Copyright JS Foundation and other contributors
+ * Released under the MIT license
+ * https://js.foundation/
+ *
+ * Date: 2021-02-16
+ */
+( function( window ) {
+var i,
+	support,
+	Expr,
+	getText,
+	isXML,
+	tokenize,
+	compile,
+	select,
+	outermostContext,
+	sortInput,
+	hasDuplicate,
+
+	// Local document vars
+	setDocument,
+	document,
+	docElem,
+	documentIsHTML,
+	rbuggyQSA,
+	rbuggyMatches,
+	matches,
+	contains,
+
+	// Instance-specific data
+	expando = "sizzle" + 1 * new Date(),
+	preferredDoc = window.document,
+	dirruns = 0,
+	done = 0,
+	classCache = createCache(),
+	tokenCache = createCache(),
+	compilerCache = createCache(),
+	nonnativeSelectorCache = createCache(),
+	sortOrder = function( a, b ) {
+		if ( a === b ) {
+			hasDuplicate = true;
+		}
+		return 0;
+	},
+
+	// Instance methods
+	hasOwn = ( {} ).hasOwnProperty,
+	arr = [],
+	pop = arr.pop,
+	pushNative = arr.push,
+	push = arr.push,
+	slice = arr.slice,
+
+	// Use a stripped-down indexOf as it's faster than native
+	// https://jsperf.com/thor-indexof-vs-for/5
+	indexOf = function( list, elem ) {
+		var i = 0,
+			len = list.length;
+		for ( ; i < len; i++ ) {
+			if ( list[ i ] === elem ) {
+				return i;
+			}
+		}
+		return -1;
+	},
+
+	booleans = "checked|selected|async|autofocus|autoplay|controls|defer|disabled|hidden|" +
+		"ismap|loop|multiple|open|readonly|required|scoped",
+
+	// Regular expressions
+
+	// http://www.w3.org/TR/css3-selectors/#whitespace
+	whitespace = "[\\x20\\t\\r\\n\\f]",
+
+	// https://www.w3.org/TR/css-syntax-3/#ident-token-diagram
+	identifier = "(?:\\\\[\\da-fA-F]{1,6}" + whitespace +
+		"?|\\\\[^\\r\\n\\f]|[\\w-]|[^\0-\\x7f])+",
+
+	// Attribute selectors: http://www.w3.org/TR/selectors/#attribute-selectors
+	attributes = "\\[" + whitespace + "*(" + identifier + ")(?:" + whitespace +
+
+		// Operator (capture 2)
+		"*([*^$|!~]?=)" + whitespace +
+
+		// "Attribute values must be CSS identifiers [capture 5]
+		// or strings [capture 3 or capture 4]"
+		"*(?:'((?:\\\\.|[^\\\\'])*)'|\"((?:\\\\.|[^\\\\\"])*)\"|(" + identifier + "))|)" +
+		whitespace + "*\\]",
+
+	pseudos = ":(" + identifier + ")(?:\\((" +
+
+		// To reduce the number of selectors needing tokenize in the preFilter, prefer arguments:
+		// 1. quoted (capture 3; capture 4 or capture 5)
+		"('((?:\\\\.|[^\\\\'])*)'|\"((?:\\\\.|[^\\\\\"])*)\")|" +
+
+		// 2. simple (capture 6)
+		"((?:\\\\.|[^\\\\()[\\]]|" + attributes + ")*)|" +
+
+		// 3. anything else (capture 2)
+		".*" +
+		")\\)|)",
+
+	// Leading and non-escaped trailing whitespace, capturing some non-whitespace characters preceding the latter
+	rwhitespace = new RegExp( whitespace + "+", "g" ),
+	rtrim = new RegExp( "^" + whitespace + "+|((?:^|[^\\\\])(?:\\\\.)*)" +
+		whitespace + "+$", "g" ),
+
+	rcomma = new RegExp( "^" + whitespace + "*," + whitespace + "*" ),
+	rcombinators = new RegExp( "^" + whitespace + "*([>+~]|" + whitespace + ")" + whitespace +
+		"*" ),
+	rdescend = new RegExp( whitespace + "|>" ),
+
+	rpseudo = new RegExp( pseudos ),
+	ridentifier = new RegExp( "^" + identifier + "$" ),
+
+	matchExpr = {
+		"ID": new RegExp( "^#(" + identifier + ")" ),
+		"CLASS": new RegExp( "^\\.(" + identifier + ")" ),
+		"TAG": new RegExp( "^(" + identifier + "|[*])" ),
+		"ATTR": new RegExp( "^" + attributes ),
+		"PSEUDO": new RegExp( "^" + pseudos ),
+		"CHILD": new RegExp( "^:(only|first|last|nth|nth-last)-(child|of-type)(?:\\(" +
+			whitespace + "*(even|odd|(([+-]|)(\\d*)n|)" + whitespace + "*(?:([+-]|)" +
+			whitespace + "*(\\d+)|))" + whitespace + "*\\)|)", "i" ),
+		"bool": new RegExp( "^(?:" + booleans + ")$", "i" ),
+
+		// For use in libraries implementing .is()
+		// We use this for POS matching in `select`
+		"needsContext": new RegExp( "^" + whitespace +
+			"*[>+~]|:(even|odd|eq|gt|lt|nth|first|last)(?:\\(" + whitespace +
+			"*((?:-\\d)?\\d*)" + whitespace + "*\\)|)(?=[^-]|$)", "i" )
+	},
+
+	rhtml = /HTML$/i,
+	rinputs = /^(?:input|select|textarea|button)$/i,
+	rheader = /^h\d$/i,
+
+	rnative = /^[^{]+\{\s*\[native \w/,
+
+	// Easily-parseable/retrievable ID or TAG or CLASS selectors
+	rquickExpr = /^(?:#([\w-]+)|(\w+)|\.([\w-]+))$/,
+
+	rsibling = /[+~]/,
+
+	// CSS escapes
+	// http://www.w3.org/TR/CSS21/syndata.html#escaped-characters
+	runescape = new RegExp( "\\\\[\\da-fA-F]{1,6}" + whitespace + "?|\\\\([^\\r\\n\\f])", "g" ),
+	funescape = function( escape, nonHex ) {
+		var high = "0x" + escape.slice( 1 ) - 0x10000;
+
+		return nonHex ?
+
+			// Strip the backslash prefix from a non-hex escape sequence
+			nonHex :
+
+			// Replace a hexadecimal escape sequence with the encoded Unicode code point
+			// Support: IE <=11+
+			// For values outside the Basic Multilingual Plane (BMP), manually construct a
+			// surrogate pair
+			high < 0 ?
+				String.fromCharCode( high + 0x10000 ) :
+				String.fromCharCode( high >> 10 | 0xD800, high & 0x3FF | 0xDC00 );
+	},
+
+	// CSS string/identifier serialization
+	// https://drafts.csswg.org/cssom/#common-serializing-idioms
+	rcssescape = /([\0-\x1f\x7f]|^-?\d)|^-$|[^\0-\x1f\x7f-\uFFFF\w-]/g,
+	fcssescape = function( ch, asCodePoint ) {
+		if ( asCodePoint ) {
+
+			// U+0000 NULL becomes U+FFFD REPLACEMENT CHARACTER
+			if ( ch === "\0" ) {
+				return "\uFFFD";
+			}
+
+			// Control characters and (dependent upon position) numbers get escaped as code points
+			return ch.slice( 0, -1 ) + "\\" +
+				ch.charCodeAt( ch.length - 1 ).toString( 16 ) + " ";
+		}
+
+		// Other potentially-special ASCII characters get backslash-escaped
+		return "\\" + ch;
+	},
+
+	// Used for iframes
+	// See setDocument()
+	// Removing the function wrapper causes a "Permission Denied"
+	// error in IE
+	unloadHandler = function() {
+		setDocument();
+	},
+
+	inDisabledFieldset = addCombinator(
+		function( elem ) {
+			return elem.disabled === true && elem.nodeName.toLowerCase() === "fieldset";
+		},
+		{ dir: "parentNode", next: "legend" }
+	);
+
+// Optimize for push.apply( _, NodeList )
+try {
+	push.apply(
+		( arr = slice.call( preferredDoc.childNodes ) ),
+		preferredDoc.childNodes
+	);
+
+	// Support: Android<4.0
+	// Detect silently failing push.apply
+	// eslint-disable-next-line no-unused-expressions
+	arr[ preferredDoc.childNodes.length ].nodeType;
+} catch ( e ) {
+	push = { apply: arr.length ?
+
+		// Leverage slice if possible
+		function( target, els ) {
+			pushNative.apply( target, slice.call( els ) );
+		} :
+
+		// Support: IE<9
+		// Otherwise append directly
+		function( target, els ) {
+			var j = target.length,
+				i = 0;
+
+			// Can't trust NodeList.length
+			while ( ( target[ j++ ] = els[ i++ ] ) ) {}
+			target.length = j - 1;
+		}
+	};
+}
+
+function Sizzle( selector, context, results, seed ) {
+	var m, i, elem, nid, match, groups, newSelector,
+		newContext = context && context.ownerDocument,
+
+		// nodeType defaults to 9, since context defaults to document
+		nodeType = context ? context.nodeType : 9;
+
+	results = results || [];
+
+	// Return early from calls with invalid selector or context
+	if ( typeof selector !== "string" || !selector ||
+		nodeType !== 1 && nodeType !== 9 && nodeType !== 11 ) {
+
+		return results;
+	}
+
+	// Try to shortcut find operations (as opposed to filters) in HTML documents
+	if ( !seed ) {
+		setDocument( context );
+		context = context || document;
+
+		if ( documentIsHTML ) {
+
+			// If the selector is sufficiently simple, try using a "get*By*" DOM method
+			// (excepting DocumentFragment context, where the methods don't exist)
+			if ( nodeType !== 11 && ( match = rquickExpr.exec( selector ) ) ) {
+
+				// ID selector
+				if ( ( m = match[ 1 ] ) ) {
+
+					// Document context
+					if ( nodeType === 9 ) {
+						if ( ( elem = context.getElementById( m ) ) ) {
+
+							// Support: IE, Opera, Webkit
+							// TODO: identify versions
+							// getElementById can match elements by name instead of ID
+							if ( elem.id === m ) {
+								results.push( elem );
+								return results;
+							}
+						} else {
+							return results;
+						}
+
+					// Element context
+					} else {
+
+						// Support: IE, Opera, Webkit
+						// TODO: identify versions
+						// getElementById can match elements by name instead of ID
+						if ( newContext && ( elem = newContext.getElementById( m ) ) &&
+							contains( context, elem ) &&
+							elem.id === m ) {
+
+							results.push( elem );
+							return results;
+						}
+					}
+
+				// Type selector
+				} else if ( match[ 2 ] ) {
+					push.apply( results, context.getElementsByTagName( selector ) );
+					return results;
+
+				// Class selector
+				} else if ( ( m = match[ 3 ] ) && support.getElementsByClassName &&
+					context.getElementsByClassName ) {
+
+					push.apply( results, context.getElementsByClassName( m ) );
+					return results;
+				}
+			}
+
+			// Take advantage of querySelectorAll
+			if ( support.qsa &&
+				!nonnativeSelectorCache[ selector + " " ] &&
+				( !rbuggyQSA || !rbuggyQSA.test( selector ) ) &&
+
+				// Support: IE 8 only
+				// Exclude object elements
+				( nodeType !== 1 || context.nodeName.toLowerCase() !== "object" ) ) {
+
+				newSelector = selector;
+				newContext = context;
+
+				// qSA considers elements outside a scoping root when evaluating child or
+				// descendant combinators, which is not what we want.
+				// In such cases, we work around the behavior by prefixing every selector in the
+				// list with an ID selector referencing the scope context.
+				// The technique has to be used as well when a leading combinator is used
+				// as such selectors are not recognized by querySelectorAll.
+				// Thanks to Andrew Dupont for this technique.
+				if ( nodeType === 1 &&
+					( rdescend.test( selector ) || rcombinators.test( selector ) ) ) {
+
+					// Expand context for sibling selectors
+					newContext = rsibling.test( selector ) && testContext( context.parentNode ) ||
+						context;
+
+					// We can use :scope instead of the ID hack if the browser
+					// supports it & if we're not changing the context.
+					if ( newContext !== context || !support.scope ) {
+
+						// Capture the context ID, setting it first if necessary
+						if ( ( nid = context.getAttribute( "id" ) ) ) {
+							nid = nid.replace( rcssescape, fcssescape );
+						} else {
+							context.setAttribute( "id", ( nid = expando ) );
+						}
+					}
+
+					// Prefix every selector in the list
+					groups = tokenize( selector );
+					i = groups.length;
+					while ( i-- ) {
+						groups[ i ] = ( nid ? "#" + nid : ":scope" ) + " " +
+							toSelector( groups[ i ] );
+					}
+					newSelector = groups.join( "," );
+				}
+
+				try {
+					push.apply( results,
+						newContext.querySelectorAll( newSelector )
+					);
+					return results;
+				} catch ( qsaError ) {
+					nonnativeSelectorCache( selector, true );
+				} finally {
+					if ( nid === expando ) {
+						context.removeAttribute( "id" );
+					}
+				}
+			}
+		}
+	}
+
+	// All others
+	return select( selector.replace( rtrim, "$1" ), context, results, seed );
+}
+
+/**
+ * Create key-value caches of limited size
+ * @returns {function(string, object)} Returns the Object data after storing it on itself with
+ *	property name the (space-suffixed) string and (if the cache is larger than Expr.cacheLength)
+ *	deleting the oldest entry
+ */
+function createCache() {
+	var keys = [];
+
+	function cache( key, value ) {
+
+		// Use (key + " ") to avoid collision with native prototype properties (see Issue #157)
+		if ( keys.push( key + " " ) > Expr.cacheLength ) {
+
+			// Only keep the most recent entries
+			delete cache[ keys.shift() ];
+		}
+		return ( cache[ key + " " ] = value );
+	}
+	return cache;
+}
+
+/**
+ * Mark a function for special use by Sizzle
+ * @param {Function} fn The function to mark
+ */
+function markFunction( fn ) {
+	fn[ expando ] = true;
+	return fn;
+}
+
+/**
+ * Support testing using an element
+ * @param {Function} fn Passed the created element and returns a boolean result
+ */
+function assert( fn ) {
+	var el = document.createElement( "fieldset" );
+
+	try {
+		return !!fn( el );
+	} catch ( e ) {
+		return false;
+	} finally {
+
+		// Remove from its parent by default
+		if ( el.parentNode ) {
+			el.parentNode.removeChild( el );
+		}
+
+		// release memory in IE
+		el = null;
+	}
+}
+
+/**
+ * Adds the same handler for all of the specified attrs
+ * @param {String} attrs Pipe-separated list of attributes
+ * @param {Function} handler The method that will be applied
+ */
+function addHandle( attrs, handler ) {
+	var arr = attrs.split( "|" ),
+		i = arr.length;
+
+	while ( i-- ) {
+		Expr.attrHandle[ arr[ i ] ] = handler;
+	}
+}
+
+/**
+ * Checks document order of two siblings
+ * @param {Element} a
+ * @param {Element} b
+ * @returns {Number} Returns less than 0 if a precedes b, greater than 0 if a follows b
+ */
+function siblingCheck( a, b ) {
+	var cur = b && a,
+		diff = cur && a.nodeType === 1 && b.nodeType === 1 &&
+			a.sourceIndex - b.sourceIndex;
+
+	// Use IE sourceIndex if available on both nodes
+	if ( diff ) {
+		return diff;
+	}
+
+	// Check if b follows a
+	if ( cur ) {
+		while ( ( cur = cur.nextSibling ) ) {
+			if ( cur === b ) {
+				return -1;
+			}
+		}
+	}
+
+	return a ? 1 : -1;
+}
+
+/**
+ * Returns a function to use in pseudos for input types
+ * @param {String} type
+ */
+function createInputPseudo( type ) {
+	return function( elem ) {
+		var name = elem.nodeName.toLowerCase();
+		return name === "input" && elem.type === type;
+	};
+}
+
+/**
+ * Returns a function to use in pseudos for buttons
+ * @param {String} type
+ */
+function createButtonPseudo( type ) {
+	return function( elem ) {
+		var name = elem.nodeName.toLowerCase();
+		return ( name === "input" || name === "button" ) && elem.type === type;
+	};
+}
+
+/**
+ * Returns a function to use in pseudos for :enabled/:disabled
+ * @param {Boolean} disabled true for :disabled; false for :enabled
+ */
+function createDisabledPseudo( disabled ) {
+
+	// Known :disabled false positives: fieldset[disabled] > legend:nth-of-type(n+2) :can-disable
+	return function( elem ) {
+
+		// Only certain elements can match :enabled or :disabled
+		// https://html.spec.whatwg.org/multipage/scripting.html#selector-enabled
+		// https://html.spec.whatwg.org/multipage/scripting.html#selector-disabled
+		if ( "form" in elem ) {
+
+			// Check for inherited disabledness on relevant non-disabled elements:
+			// * listed form-associated elements in a disabled fieldset
+			//   https://html.spec.whatwg.org/multipage/forms.html#category-listed
+			//   https://html.spec.whatwg.org/multipage/forms.html#concept-fe-disabled
+			// * option elements in a disabled optgroup
+			//   https://html.spec.whatwg.org/multipage/forms.html#concept-option-disabled
+			// All such elements have a "form" property.
+			if ( elem.parentNode && elem.disabled === false ) {
+
+				// Option elements defer to a parent optgroup if present
+				if ( "label" in elem ) {
+					if ( "label" in elem.parentNode ) {
+						return elem.parentNode.disabled === disabled;
+					} else {
+						return elem.disabled === disabled;
+					}
+				}
+
+				// Support: IE 6 - 11
+				// Use the isDisabled shortcut property to check for disabled fieldset ancestors
+				return elem.isDisabled === disabled ||
+
+					// Where there is no isDisabled, check manually
+					/* jshint -W018 */
+					elem.isDisabled !== !disabled &&
+					inDisabledFieldset( elem ) === disabled;
+			}
+
+			return elem.disabled === disabled;
+
+		// Try to winnow out elements that can't be disabled before trusting the disabled property.
+		// Some victims get caught in our net (label, legend, menu, track), but it shouldn't
+		// even exist on them, let alone have a boolean value.
+		} else if ( "label" in elem ) {
+			return elem.disabled === disabled;
+		}
+
+		// Remaining elements are neither :enabled nor :disabled
+		return false;
+	};
+}
+
+/**
+ * Returns a function to use in pseudos for positionals
+ * @param {Function} fn
+ */
+function createPositionalPseudo( fn ) {
+	return markFunction( function( argument ) {
+		argument = +argument;
+		return markFunction( function( seed, matches ) {
+			var j,
+				matchIndexes = fn( [], seed.length, argument ),
+				i = matchIndexes.length;
+
+			// Match elements found at the specified indexes
+			while ( i-- ) {
+				if ( seed[ ( j = matchIndexes[ i ] ) ] ) {
+					seed[ j ] = !( matches[ j ] = seed[ j ] );
+				}
+			}
+		} );
+	} );
+}
+
+/**
+ * Checks a node for validity as a Sizzle context
+ * @param {Element|Object=} context
+ * @returns {Element|Object|Boolean} The input node if acceptable, otherwise a falsy value
+ */
+function testContext( context ) {
+	return context && typeof context.getElementsByTagName !== "undefined" && context;
+}
+
+// Expose support vars for convenience
+support = Sizzle.support = {};
+
+/**
+ * Detects XML nodes
+ * @param {Element|Object} elem An element or a document
+ * @returns {Boolean} True iff elem is a non-HTML XML node
+ */
+isXML = Sizzle.isXML = function( elem ) {
+	var namespace = elem && elem.namespaceURI,
+		docElem = elem && ( elem.ownerDocument || elem ).documentElement;
+
+	// Support: IE <=8
+	// Assume HTML when documentElement doesn't yet exist, such as inside loading iframes
+	// https://bugs.jquery.com/ticket/4833
+	return !rhtml.test( namespace || docElem && docElem.nodeName || "HTML" );
+};
+
+/**
+ * Sets document-related variables once based on the current document
+ * @param {Element|Object} [doc] An element or document object to use to set the document
+ * @returns {Object} Returns the current document
+ */
+setDocument = Sizzle.setDocument = function( node ) {
+	var hasCompare, subWindow,
+		doc = node ? node.ownerDocument || node : preferredDoc;
+
+	// Return early if doc is invalid or already selected
+	// Support: IE 11+, Edge 17 - 18+
+	// IE/Edge sometimes throw a "Permission denied" error when strict-comparing
+	// two documents; shallow comparisons work.
+	// eslint-disable-next-line eqeqeq
+	if ( doc == document || doc.nodeType !== 9 || !doc.documentElement ) {
+		return document;
+	}
+
+	// Update global variables
+	document = doc;
+	docElem = document.documentElement;
+	documentIsHTML = !isXML( document );
+
+	// Support: IE 9 - 11+, Edge 12 - 18+
+	// Accessing iframe documents after unload throws "permission denied" errors (jQuery #13936)
+	// Support: IE 11+, Edge 17 - 18+
+	// IE/Edge sometimes throw a "Permission denied" error when strict-comparing
+	// two documents; shallow comparisons work.
+	// eslint-disable-next-line eqeqeq
+	if ( preferredDoc != document &&
+		( subWindow = document.defaultView ) && subWindow.top !== subWindow ) {
+
+		// Support: IE 11, Edge
+		if ( subWindow.addEventListener ) {
+			subWindow.addEventListener( "unload", unloadHandler, false );
+
+		// Support: IE 9 - 10 only
+		} else if ( subWindow.attachEvent ) {
+			subWindow.attachEvent( "onunload", unloadHandler );
+		}
+	}
+
+	// Support: IE 8 - 11+, Edge 12 - 18+, Chrome <=16 - 25 only, Firefox <=3.6 - 31 only,
+	// Safari 4 - 5 only, Opera <=11.6 - 12.x only
+	// IE/Edge & older browsers don't support the :scope pseudo-class.
+	// Support: Safari 6.0 only
+	// Safari 6.0 supports :scope but it's an alias of :root there.
+	support.scope = assert( function( el ) {
+		docElem.appendChild( el ).appendChild( document.createElement( "div" ) );
+		return typeof el.querySelectorAll !== "undefined" &&
+			!el.querySelectorAll( ":scope fieldset div" ).length;
+	} );
+
+	/* Attributes
+	---------------------------------------------------------------------- */
+
+	// Support: IE<8
+	// Verify that getAttribute really returns attributes and not properties
+	// (excepting IE8 booleans)
+	support.attributes = assert( function( el ) {
+		el.className = "i";
+		return !el.getAttribute( "className" );
+	} );
+
+	/* getElement(s)By*
+	---------------------------------------------------------------------- */
+
+	// Check if getElementsByTagName("*") returns only elements
+	support.getElementsByTagName = assert( function( el ) {
+		el.appendChild( document.createComment( "" ) );
+		return !el.getElementsByTagName( "*" ).length;
+	} );
+
+	// Support: IE<9
+	support.getElementsByClassName = rnative.test( document.getElementsByClassName );
+
+	// Support: IE<10
+	// Check if getElementById returns elements by name
+	// The broken getElementById methods don't pick up programmatically-set names,
+	// so use a roundabout getElementsByName test
+	support.getById = assert( function( el ) {
+		docElem.appendChild( el ).id = expando;
+		return !document.getElementsByName || !document.getElementsByName( expando ).length;
+	} );
+
+	// ID filter and find
+	if ( support.getById ) {
+		Expr.filter[ "ID" ] = function( id ) {
+			var attrId = id.replace( runescape, funescape );
+			return function( elem ) {
+				return elem.getAttribute( "id" ) === attrId;
+			};
+		};
+		Expr.find[ "ID" ] = function( id, context ) {
+			if ( typeof context.getElementById !== "undefined" && documentIsHTML ) {
+				var elem = context.getElementById( id );
+				return elem ? [ elem ] : [];
+			}
+		};
+	} else {
+		Expr.filter[ "ID" ] =  function( id ) {
+			var attrId = id.replace( runescape, funescape );
+			return function( elem ) {
+				var node = typeof elem.getAttributeNode !== "undefined" &&
+					elem.getAttributeNode( "id" );
+				return node && node.value === attrId;
+			};
+		};
+
+		// Support: IE 6 - 7 only
+		// getElementById is not reliable as a find shortcut
+		Expr.find[ "ID" ] = function( id, context ) {
+			if ( typeof context.getElementById !== "undefined" && documentIsHTML ) {
+				var node, i, elems,
+					elem = context.getElementById( id );
+
+				if ( elem ) {
+
+					// Verify the id attribute
+					node = elem.getAttributeNode( "id" );
+					if ( node && node.value === id ) {
+						return [ elem ];
+					}
+
+					// Fall back on getElementsByName
+					elems = context.getElementsByName( id );
+					i = 0;
+					while ( ( elem = elems[ i++ ] ) ) {
+						node = elem.getAttributeNode( "id" );
+						if ( node && node.value === id ) {
+							return [ elem ];
+						}
+					}
+				}
+
+				return [];
+			}
+		};
+	}
+
+	// Tag
+	Expr.find[ "TAG" ] = support.getElementsByTagName ?
+		function( tag, context ) {
+			if ( typeof context.getElementsByTagName !== "undefined" ) {
+				return context.getElementsByTagName( tag );
+
+			// DocumentFragment nodes don't have gEBTN
+			} else if ( support.qsa ) {
+				return context.querySelectorAll( tag );
+			}
+		} :
+
+		function( tag, context ) {
+			var elem,
+				tmp = [],
+				i = 0,
+
+				// By happy coincidence, a (broken) gEBTN appears on DocumentFragment nodes too
+				results = context.getElementsByTagName( tag );
+
+			// Filter out possible comments
+			if ( tag === "*" ) {
+				while ( ( elem = results[ i++ ] ) ) {
+					if ( elem.nodeType === 1 ) {
+						tmp.push( elem );
+					}
+				}
+
+				return tmp;
+			}
+			return results;
+		};
+
+	// Class
+	Expr.find[ "CLASS" ] = support.getElementsByClassName && function( className, context ) {
+		if ( typeof context.getElementsByClassName !== "undefined" && documentIsHTML ) {
+			return context.getElementsByClassName( className );
+		}
+	};
+
+	/* QSA/matchesSelector
+	---------------------------------------------------------------------- */
+
+	// QSA and matchesSelector support
+
+	// matchesSelector(:active) reports false when true (IE9/Opera 11.5)
+	rbuggyMatches = [];
+
+	// qSa(:focus) reports false when true (Chrome 21)
+	// We allow this because of a bug in IE8/9 that throws an error
+	// whenever `document.activeElement` is accessed on an iframe
+	// So, we allow :focus to pass through QSA all the time to avoid the IE error
+	// See https://bugs.jquery.com/ticket/13378
+	rbuggyQSA = [];
+
+	if ( ( support.qsa = rnative.test( document.querySelectorAll ) ) ) {
+
+		// Build QSA regex
+		// Regex strategy adopted from Diego Perini
+		assert( function( el ) {
+
+			var input;
+
+			// Select is set to empty string on purpose
+			// This is to test IE's treatment of not explicitly
+			// setting a boolean content attribute,
+			// since its presence should be enough
+			// https://bugs.jquery.com/ticket/12359
+			docElem.appendChild( el ).innerHTML = "<a id='" + expando + "'></a>" +
+				"<select id='" + expando + "-\r\\' msallowcapture=''>" +
+				"<option selected=''></option></select>";
+
+			// Support: IE8, Opera 11-12.16
+			// Nothing should be selected when empty strings follow ^= or $= or *=
+			// The test attribute must be unknown in Opera but "safe" for WinRT
+			// https://msdn.microsoft.com/en-us/library/ie/hh465388.aspx#attribute_section
+			if ( el.querySelectorAll( "[msallowcapture^='']" ).length ) {
+				rbuggyQSA.push( "[*^$]=" + whitespace + "*(?:''|\"\")" );
+			}
+
+			// Support: IE8
+			// Boolean attributes and "value" are not treated correctly
+			if ( !el.querySelectorAll( "[selected]" ).length ) {
+				rbuggyQSA.push( "\\[" + whitespace + "*(?:value|" + booleans + ")" );
+			}
+
+			// Support: Chrome<29, Android<4.4, Safari<7.0+, iOS<7.0+, PhantomJS<1.9.8+
+			if ( !el.querySelectorAll( "[id~=" + expando + "-]" ).length ) {
+				rbuggyQSA.push( "~=" );
+			}
+
+			// Support: IE 11+, Edge 15 - 18+
+			// IE 11/Edge don't find elements on a `[name='']` query in some cases.
+			// Adding a temporary attribute to the document before the selection works
+			// around the issue.
+			// Interestingly, IE 10 & older don't seem to have the issue.
+			input = document.createElement( "input" );
+			input.setAttribute( "name", "" );
+			el.appendChild( input );
+			if ( !el.querySelectorAll( "[name='']" ).length ) {
+				rbuggyQSA.push( "\\[" + whitespace + "*name" + whitespace + "*=" +
+					whitespace + "*(?:''|\"\")" );
+			}
+
+			// Webkit/Opera - :checked should return selected option elements
+			// http://www.w3.org/TR/2011/REC-css3-selectors-20110929/#checked
+			// IE8 throws error here and will not see later tests
+			if ( !el.querySelectorAll( ":checked" ).length ) {
+				rbuggyQSA.push( ":checked" );
+			}
+
+			// Support: Safari 8+, iOS 8+
+			// https://bugs.webkit.org/show_bug.cgi?id=136851
+			// In-page `selector#id sibling-combinator selector` fails
+			if ( !el.querySelectorAll( "a#" + expando + "+*" ).length ) {
+				rbuggyQSA.push( ".#.+[+~]" );
+			}
+
+			// Support: Firefox <=3.6 - 5 only
+			// Old Firefox doesn't throw on a badly-escaped identifier.
+			el.querySelectorAll( "\\\f" );
+			rbuggyQSA.push( "[\\r\\n\\f]" );
+		} );
+
+		assert( function( el ) {
+			el.innerHTML = "<a href='' disabled='disabled'></a>" +
+				"<select disabled='disabled'><option/></select>";
+
+			// Support: Windows 8 Native Apps
+			// The type and name attributes are restricted during .innerHTML assignment
+			var input = document.createElement( "input" );
+			input.setAttribute( "type", "hidden" );
+			el.appendChild( input ).setAttribute( "name", "D" );
+
+			// Support: IE8
+			// Enforce case-sensitivity of name attribute
+			if ( el.querySelectorAll( "[name=d]" ).length ) {
+				rbuggyQSA.push( "name" + whitespace + "*[*^$|!~]?=" );
+			}
+
+			// FF 3.5 - :enabled/:disabled and hidden elements (hidden elements are still enabled)
+			// IE8 throws error here and will not see later tests
+			if ( el.querySelectorAll( ":enabled" ).length !== 2 ) {
+				rbuggyQSA.push( ":enabled", ":disabled" );
+			}
+
+			// Support: IE9-11+
+			// IE's :disabled selector does not pick up the children of disabled fieldsets
+			docElem.appendChild( el ).disabled = true;
+			if ( el.querySelectorAll( ":disabled" ).length !== 2 ) {
+				rbuggyQSA.push( ":enabled", ":disabled" );
+			}
+
+			// Support: Opera 10 - 11 only
+			// Opera 10-11 does not throw on post-comma invalid pseudos
+			el.querySelectorAll( "*,:x" );
+			rbuggyQSA.push( ",.*:" );
+		} );
+	}
+
+	if ( ( support.matchesSelector = rnative.test( ( matches = docElem.matches ||
+		docElem.webkitMatchesSelector ||
+		docElem.mozMatchesSelector ||
+		docElem.oMatchesSelector ||
+		docElem.msMatchesSelector ) ) ) ) {
+
+		assert( function( el ) {
+
+			// Check to see if it's possible to do matchesSelector
+			// on a disconnected node (IE 9)
+			support.disconnectedMatch = matches.call( el, "*" );
+
+			// This should fail with an exception
+			// Gecko does not error, returns false instead
+			matches.call( el, "[s!='']:x" );
+			rbuggyMatches.push( "!=", pseudos );
+		} );
+	}
+
+	rbuggyQSA = rbuggyQSA.length && new RegExp( rbuggyQSA.join( "|" ) );
+	rbuggyMatches = rbuggyMatches.length && new RegExp( rbuggyMatches.join( "|" ) );
+
+	/* Contains
+	---------------------------------------------------------------------- */
+	hasCompare = rnative.test( docElem.compareDocumentPosition );
+
+	// Element contains another
+	// Purposefully self-exclusive
+	// As in, an element does not contain itself
+	contains = hasCompare || rnative.test( docElem.contains ) ?
+		function( a, b ) {
+			var adown = a.nodeType === 9 ? a.documentElement : a,
+				bup = b && b.parentNode;
+			return a === bup || !!( bup && bup.nodeType === 1 && (
+				adown.contains ?
+					adown.contains( bup ) :
+					a.compareDocumentPosition && a.compareDocumentPosition( bup ) & 16
+			) );
+		} :
+		function( a, b ) {
+			if ( b ) {
+				while ( ( b = b.parentNode ) ) {
+					if ( b === a ) {
+						return true;
+					}
+				}
+			}
+			return false;
+		};
+
+	/* Sorting
+	---------------------------------------------------------------------- */
+
+	// Document order sorting
+	sortOrder = hasCompare ?
+	function( a, b ) {
+
+		// Flag for duplicate removal
+		if ( a === b ) {
+			hasDuplicate = true;
+			return 0;
+		}
+
+		// Sort on method existence if only one input has compareDocumentPosition
+		var compare = !a.compareDocumentPosition - !b.compareDocumentPosition;
+		if ( compare ) {
+			return compare;
+		}
+
+		// Calculate position if both inputs belong to the same document
+		// Support: IE 11+, Edge 17 - 18+
+		// IE/Edge sometimes throw a "Permission denied" error when strict-comparing
+		// two documents; shallow comparisons work.
+		// eslint-disable-next-line eqeqeq
+		compare = ( a.ownerDocument || a ) == ( b.ownerDocument || b ) ?
+			a.compareDocumentPosition( b ) :
+
+			// Otherwise we know they are disconnected
+			1;
+
+		// Disconnected nodes
+		if ( compare & 1 ||
+			( !support.sortDetached && b.compareDocumentPosition( a ) === compare ) ) {
+
+			// Choose the first element that is related to our preferred document
+			// Support: IE 11+, Edge 17 - 18+
+			// IE/Edge sometimes throw a "Permission denied" error when strict-comparing
+			// two documents; shallow comparisons work.
+			// eslint-disable-next-line eqeqeq
+			if ( a == document || a.ownerDocument == preferredDoc &&
+				contains( preferredDoc, a ) ) {
+				return -1;
+			}
+
+			// Support: IE 11+, Edge 17 - 18+
+			// IE/Edge sometimes throw a "Permission denied" error when strict-comparing
+			// two documents; shallow comparisons work.
+			// eslint-disable-next-line eqeqeq
+			if ( b == document || b.ownerDocument == preferredDoc &&
+				contains( preferredDoc, b ) ) {
+				return 1;
+			}
+
+			// Maintain original order
+			return sortInput ?
+				( indexOf( sortInput, a ) - indexOf( sortInput, b ) ) :
+				0;
+		}
+
+		return compare & 4 ? -1 : 1;
+	} :
+	function( a, b ) {
+
+		// Exit early if the nodes are identical
+		if ( a === b ) {
+			hasDuplicate = true;
+			return 0;
+		}
+
+		var cur,
+			i = 0,
+			aup = a.parentNode,
+			bup = b.parentNode,
+			ap = [ a ],
+			bp = [ b ];
+
+		// Parentless nodes are either documents or disconnected
+		if ( !aup || !bup ) {
+
+			// Support: IE 11+, Edge 17 - 18+
+			// IE/Edge sometimes throw a "Permission denied" error when strict-comparing
+			// two documents; shallow comparisons work.
+			/* eslint-disable eqeqeq */
+			return a == document ? -1 :
+				b == document ? 1 :
+				/* eslint-enable eqeqeq */
+				aup ? -1 :
+				bup ? 1 :
+				sortInput ?
+				( indexOf( sortInput, a ) - indexOf( sortInput, b ) ) :
+				0;
+
+		// If the nodes are siblings, we can do a quick check
+		} else if ( aup === bup ) {
+			return siblingCheck( a, b );
+		}
+
+		// Otherwise we need full lists of their ancestors for comparison
+		cur = a;
+		while ( ( cur = cur.parentNode ) ) {
+			ap.unshift( cur );
+		}
+		cur = b;
+		while ( ( cur = cur.parentNode ) ) {
+			bp.unshift( cur );
+		}
+
+		// Walk down the tree looking for a discrepancy
+		while ( ap[ i ] === bp[ i ] ) {
+			i++;
+		}
+
+		return i ?
+
+			// Do a sibling check if the nodes have a common ancestor
+			siblingCheck( ap[ i ], bp[ i ] ) :
+
+			// Otherwise nodes in our document sort first
+			// Support: IE 11+, Edge 17 - 18+
+			// IE/Edge sometimes throw a "Permission denied" error when strict-comparing
+			// two documents; shallow comparisons work.
+			/* eslint-disable eqeqeq */
+			ap[ i ] == preferredDoc ? -1 :
+			bp[ i ] == preferredDoc ? 1 :
+			/* eslint-enable eqeqeq */
+			0;
+	};
+
+	return document;
+};
+
+Sizzle.matches = function( expr, elements ) {
+	return Sizzle( expr, null, null, elements );
+};
+
+Sizzle.matchesSelector = function( elem, expr ) {
+	setDocument( elem );
+
+	if ( support.matchesSelector && documentIsHTML &&
+		!nonnativeSelectorCache[ expr + " " ] &&
+		( !rbuggyMatches || !rbuggyMatches.test( expr ) ) &&
+		( !rbuggyQSA     || !rbuggyQSA.test( expr ) ) ) {
+
+		try {
+			var ret = matches.call( elem, expr );
+
+			// IE 9's matchesSelector returns false on disconnected nodes
+			if ( ret || support.disconnectedMatch ||
+
+				// As well, disconnected nodes are said to be in a document
+				// fragment in IE 9
+				elem.document && elem.document.nodeType !== 11 ) {
+				return ret;
+			}
+		} catch ( e ) {
+			nonnativeSelectorCache( expr, true );
+		}
+	}
+
+	return Sizzle( expr, document, null, [ elem ] ).length > 0;
+};
+
+Sizzle.contains = function( context, elem ) {
+
+	// Set document vars if needed
+	// Support: IE 11+, Edge 17 - 18+
+	// IE/Edge sometimes throw a "Permission denied" error when strict-comparing
+	// two documents; shallow comparisons work.
+	// eslint-disable-next-line eqeqeq
+	if ( ( context.ownerDocument || context ) != document ) {
+		setDocument( context );
+	}
+	return contains( context, elem );
+};
+
+Sizzle.attr = function( elem, name ) {
+
+	// Set document vars if needed
+	// Support: IE 11+, Edge 17 - 18+
+	// IE/Edge sometimes throw a "Permission denied" error when strict-comparing
+	// two documents; shallow comparisons work.
+	// eslint-disable-next-line eqeqeq
+	if ( ( elem.ownerDocument || elem ) != document ) {
+		setDocument( elem );
+	}
+
+	var fn = Expr.attrHandle[ name.toLowerCase() ],
+
+		// Don't get fooled by Object.prototype properties (jQuery #13807)
+		val = fn && hasOwn.call( Expr.attrHandle, name.toLowerCase() ) ?
+			fn( elem, name, !documentIsHTML ) :
+			undefined;
+
+	return val !== undefined ?
+		val :
+		support.attributes || !documentIsHTML ?
+			elem.getAttribute( name ) :
+			( val = elem.getAttributeNode( name ) ) && val.specified ?
+				val.value :
+				null;
+};
+
+Sizzle.escape = function( sel ) {
+	return ( sel + "" ).replace( rcssescape, fcssescape );
+};
+
+Sizzle.error = function( msg ) {
+	throw new Error( "Syntax error, unrecognized expression: " + msg );
+};
+
+/**
+ * Document sorting and removing duplicates
+ * @param {ArrayLike} results
+ */
+Sizzle.uniqueSort = function( results ) {
+	var elem,
+		duplicates = [],
+		j = 0,
+		i = 0;
+
+	// Unless we *know* we can detect duplicates, assume their presence
+	hasDuplicate = !support.detectDuplicates;
+	sortInput = !support.sortStable && results.slice( 0 );
+	results.sort( sortOrder );
+
+	if ( hasDuplicate ) {
+		while ( ( elem = results[ i++ ] ) ) {
+			if ( elem === results[ i ] ) {
+				j = duplicates.push( i );
+			}
+		}
+		while ( j-- ) {
+			results.splice( duplicates[ j ], 1 );
+		}
+	}
+
+	// Clear input after sorting to release objects
+	// See https://github.com/jquery/sizzle/pull/225
+	sortInput = null;
+
+	return results;
+};
+
+/**
+ * Utility function for retrieving the text value of an array of DOM nodes
+ * @param {Array|Element} elem
+ */
+getText = Sizzle.getText = function( elem ) {
+	var node,
+		ret = "",
+		i = 0,
+		nodeType = elem.nodeType;
+
+	if ( !nodeType ) {
+
+		// If no nodeType, this is expected to be an array
+		while ( ( node = elem[ i++ ] ) ) {
+
+			// Do not traverse comment nodes
+			ret += getText( node );
+		}
+	} else if ( nodeType === 1 || nodeType === 9 || nodeType === 11 ) {
+
+		// Use textContent for elements
+		// innerText usage removed for consistency of new lines (jQuery #11153)
+		if ( typeof elem.textContent === "string" ) {
+			return elem.textContent;
+		} else {
+
+			// Traverse its children
+			for ( elem = elem.firstChild; elem; elem = elem.nextSibling ) {
+				ret += getText( elem );
+			}
+		}
+	} else if ( nodeType === 3 || nodeType === 4 ) {
+		return elem.nodeValue;
+	}
+
+	// Do not include comment or processing instruction nodes
+
+	return ret;
+};
+
+Expr = Sizzle.selectors = {
+
+	// Can be adjusted by the user
+	cacheLength: 50,
+
+	createPseudo: markFunction,
+
+	match: matchExpr,
+
+	attrHandle: {},
+
+	find: {},
+
+	relative: {
+		">": { dir: "parentNode", first: true },
+		" ": { dir: "parentNode" },
+		"+": { dir: "previousSibling", first: true },
+		"~": { dir: "previousSibling" }
+	},
+
+	preFilter: {
+		"ATTR": function( match ) {
+			match[ 1 ] = match[ 1 ].replace( runescape, funescape );
+
+			// Move the given value to match[3] whether quoted or unquoted
+			match[ 3 ] = ( match[ 3 ] || match[ 4 ] ||
+				match[ 5 ] || "" ).replace( runescape, funescape );
+
+			if ( match[ 2 ] === "~=" ) {
+				match[ 3 ] = " " + match[ 3 ] + " ";
+			}
+
+			return match.slice( 0, 4 );
+		},
+
+		"CHILD": function( match ) {
+
+			/* matches from matchExpr["CHILD"]
+				1 type (only|nth|...)
+				2 what (child|of-type)
+				3 argument (even|odd|\d*|\d*n([+-]\d+)?|...)
+				4 xn-component of xn+y argument ([+-]?\d*n|)
+				5 sign of xn-component
+				6 x of xn-component
+				7 sign of y-component
+				8 y of y-component
+			*/
+			match[ 1 ] = match[ 1 ].toLowerCase();
+
+			if ( match[ 1 ].slice( 0, 3 ) === "nth" ) {
+
+				// nth-* requires argument
+				if ( !match[ 3 ] ) {
+					Sizzle.error( match[ 0 ] );
+				}
+
+				// numeric x and y parameters for Expr.filter.CHILD
+				// remember that false/true cast respectively to 0/1
+				match[ 4 ] = +( match[ 4 ] ?
+					match[ 5 ] + ( match[ 6 ] || 1 ) :
+					2 * ( match[ 3 ] === "even" || match[ 3 ] === "odd" ) );
+				match[ 5 ] = +( ( match[ 7 ] + match[ 8 ] ) || match[ 3 ] === "odd" );
+
+				// other types prohibit arguments
+			} else if ( match[ 3 ] ) {
+				Sizzle.error( match[ 0 ] );
+			}
+
+			return match;
+		},
+
+		"PSEUDO": function( match ) {
+			var excess,
+				unquoted = !match[ 6 ] && match[ 2 ];
+
+			if ( matchExpr[ "CHILD" ].test( match[ 0 ] ) ) {
+				return null;
+			}
+
+			// Accept quoted arguments as-is
+			if ( match[ 3 ] ) {
+				match[ 2 ] = match[ 4 ] || match[ 5 ] || "";
+
+			// Strip excess characters from unquoted arguments
+			} else if ( unquoted && rpseudo.test( unquoted ) &&
+
+				// Get excess from tokenize (recursively)
+				( excess = tokenize( unquoted, true ) ) &&
+
+				// advance to the next closing parenthesis
+				( excess = unquoted.indexOf( ")", unquoted.length - excess ) - unquoted.length ) ) {
+
+				// excess is a negative index
+				match[ 0 ] = match[ 0 ].slice( 0, excess );
+				match[ 2 ] = unquoted.slice( 0, excess );
+			}
+
+			// Return only captures needed by the pseudo filter method (type and argument)
+			return match.slice( 0, 3 );
+		}
+	},
+
+	filter: {
+
+		"TAG": function( nodeNameSelector ) {
+			var nodeName = nodeNameSelector.replace( runescape, funescape ).toLowerCase();
+			return nodeNameSelector === "*" ?
+				function() {
+					return true;
+				} :
+				function( elem ) {
+					return elem.nodeName && elem.nodeName.toLowerCase() === nodeName;
+				};
+		},
+
+		"CLASS": function( className ) {
+			var pattern = classCache[ className + " " ];
+
+			return pattern ||
+				( pattern = new RegExp( "(^|" + whitespace +
+					")" + className + "(" + whitespace + "|$)" ) ) && classCache(
+						className, function( elem ) {
+							return pattern.test(
+								typeof elem.className === "string" && elem.className ||
+								typeof elem.getAttribute !== "undefined" &&
+									elem.getAttribute( "class" ) ||
+								""
+							);
+				} );
+		},
+
+		"ATTR": function( name, operator, check ) {
+			return function( elem ) {
+				var result = Sizzle.attr( elem, name );
+
+				if ( result == null ) {
+					return operator === "!=";
+				}
+				if ( !operator ) {
+					return true;
+				}
+
+				result += "";
+
+				/* eslint-disable max-len */
+
+				return operator === "=" ? result === check :
+					operator === "!=" ? result !== check :
+					operator === "^=" ? check && result.indexOf( check ) === 0 :
+					operator === "*=" ? check && result.indexOf( check ) > -1 :
+					operator === "$=" ? check && result.slice( -check.length ) === check :
+					operator === "~=" ? ( " " + result.replace( rwhitespace, " " ) + " " ).indexOf( check ) > -1 :
+					operator === "|=" ? result === check || result.slice( 0, check.length + 1 ) === check + "-" :
+					false;
+				/* eslint-enable max-len */
+
+			};
+		},
+
+		"CHILD": function( type, what, _argument, first, last ) {
+			var simple = type.slice( 0, 3 ) !== "nth",
+				forward = type.slice( -4 ) !== "last",
+				ofType = what === "of-type";
+
+			return first === 1 && last === 0 ?
+
+				// Shortcut for :nth-*(n)
+				function( elem ) {
+					return !!elem.parentNode;
+				} :
+
+				function( elem, _context, xml ) {
+					var cache, uniqueCache, outerCache, node, nodeIndex, start,
+						dir = simple !== forward ? "nextSibling" : "previousSibling",
+						parent = elem.parentNode,
+						name = ofType && elem.nodeName.toLowerCase(),
+						useCache = !xml && !ofType,
+						diff = false;
+
+					if ( parent ) {
+
+						// :(first|last|only)-(child|of-type)
+						if ( simple ) {
+							while ( dir ) {
+								node = elem;
+								while ( ( node = node[ dir ] ) ) {
+									if ( ofType ?
+										node.nodeName.toLowerCase() === name :
+										node.nodeType === 1 ) {
+
+										return false;
+									}
+								}
+
+								// Reverse direction for :only-* (if we haven't yet done so)
+								start = dir = type === "only" && !start && "nextSibling";
+							}
+							return true;
+						}
+
+						start = [ forward ? parent.firstChild : parent.lastChild ];
+
+						// non-xml :nth-child(...) stores cache data on `parent`
+						if ( forward && useCache ) {
+
+							// Seek `elem` from a previously-cached index
+
+							// ...in a gzip-friendly way
+							node = parent;
+							outerCache = node[ expando ] || ( node[ expando ] = {} );
+
+							// Support: IE <9 only
+							// Defend against cloned attroperties (jQuery gh-1709)
+							uniqueCache = outerCache[ node.uniqueID ] ||
+								( outerCache[ node.uniqueID ] = {} );
+
+							cache = uniqueCache[ type ] || [];
+							nodeIndex = cache[ 0 ] === dirruns && cache[ 1 ];
+							diff = nodeIndex && cache[ 2 ];
+							node = nodeIndex && parent.childNodes[ nodeIndex ];
+
+							while ( ( node = ++nodeIndex && node && node[ dir ] ||
+
+								// Fallback to seeking `elem` from the start
+								( diff = nodeIndex = 0 ) || start.pop() ) ) {
+
+								// When found, cache indexes on `parent` and break
+								if ( node.nodeType === 1 && ++diff && node === elem ) {
+									uniqueCache[ type ] = [ dirruns, nodeIndex, diff ];
+									break;
+								}
+							}
+
+						} else {
+
+							// Use previously-cached element index if available
+							if ( useCache ) {
+
+								// ...in a gzip-friendly way
+								node = elem;
+								outerCache = node[ expando ] || ( node[ expando ] = {} );
+
+								// Support: IE <9 only
+								// Defend against cloned attroperties (jQuery gh-1709)
+								uniqueCache = outerCache[ node.uniqueID ] ||
+									( outerCache[ node.uniqueID ] = {} );
+
+								cache = uniqueCache[ type ] || [];
+								nodeIndex = cache[ 0 ] === dirruns && cache[ 1 ];
+								diff = nodeIndex;
+							}
+
+							// xml :nth-child(...)
+							// or :nth-last-child(...) or :nth(-last)?-of-type(...)
+							if ( diff === false ) {
+
+								// Use the same loop as above to seek `elem` from the start
+								while ( ( node = ++nodeIndex && node && node[ dir ] ||
+									( diff = nodeIndex = 0 ) || start.pop() ) ) {
+
+									if ( ( ofType ?
+										node.nodeName.toLowerCase() === name :
+										node.nodeType === 1 ) &&
+										++diff ) {
+
+										// Cache the index of each encountered element
+										if ( useCache ) {
+											outerCache = node[ expando ] ||
+												( node[ expando ] = {} );
+
+											// Support: IE <9 only
+											// Defend against cloned attroperties (jQuery gh-1709)
+											uniqueCache = outerCache[ node.uniqueID ] ||
+												( outerCache[ node.uniqueID ] = {} );
+
+											uniqueCache[ type ] = [ dirruns, diff ];
+										}
+
+										if ( node === elem ) {
+											break;
+										}
+									}
+								}
+							}
+						}
+
+						// Incorporate the offset, then check against cycle size
+						diff -= last;
+						return diff === first || ( diff % first === 0 && diff / first >= 0 );
+					}
+				};
+		},
+
+		"PSEUDO": function( pseudo, argument ) {
+
+			// pseudo-class names are case-insensitive
+			// http://www.w3.org/TR/selectors/#pseudo-classes
+			// Prioritize by case sensitivity in case custom pseudos are added with uppercase letters
+			// Remember that setFilters inherits from pseudos
+			var args,
+				fn = Expr.pseudos[ pseudo ] || Expr.setFilters[ pseudo.toLowerCase() ] ||
+					Sizzle.error( "unsupported pseudo: " + pseudo );
+
+			// The user may use createPseudo to indicate that
+			// arguments are needed to create the filter function
+			// just as Sizzle does
+			if ( fn[ expando ] ) {
+				return fn( argument );
+			}
+
+			// But maintain support for old signatures
+			if ( fn.length > 1 ) {
+				args = [ pseudo, pseudo, "", argument ];
+				return Expr.setFilters.hasOwnProperty( pseudo.toLowerCase() ) ?
+					markFunction( function( seed, matches ) {
+						var idx,
+							matched = fn( seed, argument ),
+							i = matched.length;
+						while ( i-- ) {
+							idx = indexOf( seed, matched[ i ] );
+							seed[ idx ] = !( matches[ idx ] = matched[ i ] );
+						}
+					} ) :
+					function( elem ) {
+						return fn( elem, 0, args );
+					};
+			}
+
+			return fn;
+		}
+	},
+
+	pseudos: {
+
+		// Potentially complex pseudos
+		"not": markFunction( function( selector ) {
+
+			// Trim the selector passed to compile
+			// to avoid treating leading and trailing
+			// spaces as combinators
+			var input = [],
+				results = [],
+				matcher = compile( selector.replace( rtrim, "$1" ) );
+
+			return matcher[ expando ] ?
+				markFunction( function( seed, matches, _context, xml ) {
+					var elem,
+						unmatched = matcher( seed, null, xml, [] ),
+						i = seed.length;
+
+					// Match elements unmatched by `matcher`
+					while ( i-- ) {
+						if ( ( elem = unmatched[ i ] ) ) {
+							seed[ i ] = !( matches[ i ] = elem );
+						}
+					}
+				} ) :
+				function( elem, _context, xml ) {
+					input[ 0 ] = elem;
+					matcher( input, null, xml, results );
+
+					// Don't keep the element (issue #299)
+					input[ 0 ] = null;
+					return !results.pop();
+				};
+		} ),
+
+		"has": markFunction( function( selector ) {
+			return function( elem ) {
+				return Sizzle( selector, elem ).length > 0;
+			};
+		} ),
+
+		"contains": markFunction( function( text ) {
+			text = text.replace( runescape, funescape );
+			return function( elem ) {
+				return ( elem.textContent || getText( elem ) ).indexOf( text ) > -1;
+			};
+		} ),
+
+		// "Whether an element is represented by a :lang() selector
+		// is based solely on the element's language value
+		// being equal to the identifier C,
+		// or beginning with the identifier C immediately followed by "-".
+		// The matching of C against the element's language value is performed case-insensitively.
+		// The identifier C does not have to be a valid language name."
+		// http://www.w3.org/TR/selectors/#lang-pseudo
+		"lang": markFunction( function( lang ) {
+
+			// lang value must be a valid identifier
+			if ( !ridentifier.test( lang || "" ) ) {
+				Sizzle.error( "unsupported lang: " + lang );
+			}
+			lang = lang.replace( runescape, funescape ).toLowerCase();
+			return function( elem ) {
+				var elemLang;
+				do {
+					if ( ( elemLang = documentIsHTML ?
+						elem.lang :
+						elem.getAttribute( "xml:lang" ) || elem.getAttribute( "lang" ) ) ) {
+
+						elemLang = elemLang.toLowerCase();
+						return elemLang === lang || elemLang.indexOf( lang + "-" ) === 0;
+					}
+				} while ( ( elem = elem.parentNode ) && elem.nodeType === 1 );
+				return false;
+			};
+		} ),
+
+		// Miscellaneous
+		"target": function( elem ) {
+			var hash = window.location && window.location.hash;
+			return hash && hash.slice( 1 ) === elem.id;
+		},
+
+		"root": function( elem ) {
+			return elem === docElem;
+		},
+
+		"focus": function( elem ) {
+			return elem === document.activeElement &&
+				( !document.hasFocus || document.hasFocus() ) &&
+				!!( elem.type || elem.href || ~elem.tabIndex );
+		},
+
+		// Boolean properties
+		"enabled": createDisabledPseudo( false ),
+		"disabled": createDisabledPseudo( true ),
+
+		"checked": function( elem ) {
+
+			// In CSS3, :checked should return both checked and selected elements
+			// http://www.w3.org/TR/2011/REC-css3-selectors-20110929/#checked
+			var nodeName = elem.nodeName.toLowerCase();
+			return ( nodeName === "input" && !!elem.checked ) ||
+				( nodeName === "option" && !!elem.selected );
+		},
+
+		"selected": function( elem ) {
+
+			// Accessing this property makes selected-by-default
+			// options in Safari work properly
+			if ( elem.parentNode ) {
+				// eslint-disable-next-line no-unused-expressions
+				elem.parentNode.selectedIndex;
+			}
+
+			return elem.selected === true;
+		},
+
+		// Contents
+		"empty": function( elem ) {
+
+			// http://www.w3.org/TR/selectors/#empty-pseudo
+			// :empty is negated by element (1) or content nodes (text: 3; cdata: 4; entity ref: 5),
+			//   but not by others (comment: 8; processing instruction: 7; etc.)
+			// nodeType < 6 works because attributes (2) do not appear as children
+			for ( elem = elem.firstChild; elem; elem = elem.nextSibling ) {
+				if ( elem.nodeType < 6 ) {
+					return false;
+				}
+			}
+			return true;
+		},
+
+		"parent": function( elem ) {
+			return !Expr.pseudos[ "empty" ]( elem );
+		},
+
+		// Element/input types
+		"header": function( elem ) {
+			return rheader.test( elem.nodeName );
+		},
+
+		"input": function( elem ) {
+			return rinputs.test( elem.nodeName );
+		},
+
+		"button": function( elem ) {
+			var name = elem.nodeName.toLowerCase();
+			return name === "input" && elem.type === "button" || name === "button";
+		},
+
+		"text": function( elem ) {
+			var attr;
+			return elem.nodeName.toLowerCase() === "input" &&
+				elem.type === "text" &&
+
+				// Support: IE<8
+				// New HTML5 attribute values (e.g., "search") appear with elem.type === "text"
+				( ( attr = elem.getAttribute( "type" ) ) == null ||
+					attr.toLowerCase() === "text" );
+		},
+
+		// Position-in-collection
+		"first": createPositionalPseudo( function() {
+			return [ 0 ];
+		} ),
+
+		"last": createPositionalPseudo( function( _matchIndexes, length ) {
+			return [ length - 1 ];
+		} ),
+
+		"eq": createPositionalPseudo( function( _matchIndexes, length, argument ) {
+			return [ argument < 0 ? argument + length : argument ];
+		} ),
+
+		"even": createPositionalPseudo( function( matchIndexes, length ) {
+			var i = 0;
+			for ( ; i < length; i += 2 ) {
+				matchIndexes.push( i );
+			}
+			return matchIndexes;
+		} ),
+
+		"odd": createPositionalPseudo( function( matchIndexes, length ) {
+			var i = 1;
+			for ( ; i < length; i += 2 ) {
+				matchIndexes.push( i );
+			}
+			return matchIndexes;
+		} ),
+
+		"lt": createPositionalPseudo( function( matchIndexes, length, argument ) {
+			var i = argument < 0 ?
+				argument + length :
+				argument > length ?
+					length :
+					argument;
+			for ( ; --i >= 0; ) {
+				matchIndexes.push( i );
+			}
+			return matchIndexes;
+		} ),
+
+		"gt": createPositionalPseudo( function( matchIndexes, length, argument ) {
+			var i = argument < 0 ? argument + length : argument;
+			for ( ; ++i < length; ) {
+				matchIndexes.push( i );
+			}
+			return matchIndexes;
+		} )
+	}
+};
+
+Expr.pseudos[ "nth" ] = Expr.pseudos[ "eq" ];
+
+// Add button/input type pseudos
+for ( i in { radio: true, checkbox: true, file: true, password: true, image: true } ) {
+	Expr.pseudos[ i ] = createInputPseudo( i );
+}
+for ( i in { submit: true, reset: true } ) {
+	Expr.pseudos[ i ] = createButtonPseudo( i );
+}
+
+// Easy API for creating new setFilters
+function setFilters() {}
+setFilters.prototype = Expr.filters = Expr.pseudos;
+Expr.setFilters = new setFilters();
+
+tokenize = Sizzle.tokenize = function( selector, parseOnly ) {
+	var matched, match, tokens, type,
+		soFar, groups, preFilters,
+		cached = tokenCache[ selector + " " ];
+
+	if ( cached ) {
+		return parseOnly ? 0 : cached.slice( 0 );
+	}
+
+	soFar = selector;
+	groups = [];
+	preFilters = Expr.preFilter;
+
+	while ( soFar ) {
+
+		// Comma and first run
+		if ( !matched || ( match = rcomma.exec( soFar ) ) ) {
+			if ( match ) {
+
+				// Don't consume trailing commas as valid
+				soFar = soFar.slice( match[ 0 ].length ) || soFar;
+			}
+			groups.push( ( tokens = [] ) );
+		}
+
+		matched = false;
+
+		// Combinators
+		if ( ( match = rcombinators.exec( soFar ) ) ) {
+			matched = match.shift();
+			tokens.push( {
+				value: matched,
+
+				// Cast descendant combinators to space
+				type: match[ 0 ].replace( rtrim, " " )
+			} );
+			soFar = soFar.slice( matched.length );
+		}
+
+		// Filters
+		for ( type in Expr.filter ) {
+			if ( ( match = matchExpr[ type ].exec( soFar ) ) && ( !preFilters[ type ] ||
+				( match = preFilters[ type ]( match ) ) ) ) {
+				matched = match.shift();
+				tokens.push( {
+					value: matched,
+					type: type,
+					matches: match
+				} );
+				soFar = soFar.slice( matched.length );
+			}
+		}
+
+		if ( !matched ) {
+			break;
+		}
+	}
+
+	// Return the length of the invalid excess
+	// if we're just parsing
+	// Otherwise, throw an error or return tokens
+	return parseOnly ?
+		soFar.length :
+		soFar ?
+			Sizzle.error( selector ) :
+
+			// Cache the tokens
+			tokenCache( selector, groups ).slice( 0 );
+};
+
+function toSelector( tokens ) {
+	var i = 0,
+		len = tokens.length,
+		selector = "";
+	for ( ; i < len; i++ ) {
+		selector += tokens[ i ].value;
+	}
+	return selector;
+}
+
+function addCombinator( matcher, combinator, base ) {
+	var dir = combinator.dir,
+		skip = combinator.next,
+		key = skip || dir,
+		checkNonElements = base && key === "parentNode",
+		doneName = done++;
+
+	return combinator.first ?
+
+		// Check against closest ancestor/preceding element
+		function( elem, context, xml ) {
+			while ( ( elem = elem[ dir ] ) ) {
+				if ( elem.nodeType === 1 || checkNonElements ) {
+					return matcher( elem, context, xml );
+				}
+			}
+			return false;
+		} :
+
+		// Check against all ancestor/preceding elements
+		function( elem, context, xml ) {
+			var oldCache, uniqueCache, outerCache,
+				newCache = [ dirruns, doneName ];
+
+			// We can't set arbitrary data on XML nodes, so they don't benefit from combinator caching
+			if ( xml ) {
+				while ( ( elem = elem[ dir ] ) ) {
+					if ( elem.nodeType === 1 || checkNonElements ) {
+						if ( matcher( elem, context, xml ) ) {
+							return true;
+						}
+					}
+				}
+			} else {
+				while ( ( elem = elem[ dir ] ) ) {
+					if ( elem.nodeType === 1 || checkNonElements ) {
+						outerCache = elem[ expando ] || ( elem[ expando ] = {} );
+
+						// Support: IE <9 only
+						// Defend against cloned attroperties (jQuery gh-1709)
+						uniqueCache = outerCache[ elem.uniqueID ] ||
+							( outerCache[ elem.uniqueID ] = {} );
+
+						if ( skip && skip === elem.nodeName.toLowerCase() ) {
+							elem = elem[ dir ] || elem;
+						} else if ( ( oldCache = uniqueCache[ key ] ) &&
+							oldCache[ 0 ] === dirruns && oldCache[ 1 ] === doneName ) {
+
+							// Assign to newCache so results back-propagate to previous elements
+							return ( newCache[ 2 ] = oldCache[ 2 ] );
+						} else {
+
+							// Reuse newcache so results back-propagate to previous elements
+							uniqueCache[ key ] = newCache;
+
+							// A match means we're done; a fail means we have to keep checking
+							if ( ( newCache[ 2 ] = matcher( elem, context, xml ) ) ) {
+								return true;
+							}
+						}
+					}
+				}
+			}
+			return false;
+		};
+}
+
+function elementMatcher( matchers ) {
+	return matchers.length > 1 ?
+		function( elem, context, xml ) {
+			var i = matchers.length;
+			while ( i-- ) {
+				if ( !matchers[ i ]( elem, context, xml ) ) {
+					return false;
+				}
+			}
+			return true;
+		} :
+		matchers[ 0 ];
+}
+
+function multipleContexts( selector, contexts, results ) {
+	var i = 0,
+		len = contexts.length;
+	for ( ; i < len; i++ ) {
+		Sizzle( selector, contexts[ i ], results );
+	}
+	return results;
+}
+
+function condense( unmatched, map, filter, context, xml ) {
+	var elem,
+		newUnmatched = [],
+		i = 0,
+		len = unmatched.length,
+		mapped = map != null;
+
+	for ( ; i < len; i++ ) {
+		if ( ( elem = unmatched[ i ] ) ) {
+			if ( !filter || filter( elem, context, xml ) ) {
+				newUnmatched.push( elem );
+				if ( mapped ) {
+					map.push( i );
+				}
+			}
+		}
+	}
+
+	return newUnmatched;
+}
+
+function setMatcher( preFilter, selector, matcher, postFilter, postFinder, postSelector ) {
+	if ( postFilter && !postFilter[ expando ] ) {
+		postFilter = setMatcher( postFilter );
+	}
+	if ( postFinder && !postFinder[ expando ] ) {
+		postFinder = setMatcher( postFinder, postSelector );
+	}
+	return markFunction( function( seed, results, context, xml ) {
+		var temp, i, elem,
+			preMap = [],
+			postMap = [],
+			preexisting = results.length,
+
+			// Get initial elements from seed or context
+			elems = seed || multipleContexts(
+				selector || "*",
+				context.nodeType ? [ context ] : context,
+				[]
+			),
+
+			// Prefilter to get matcher input, preserving a map for seed-results synchronization
+			matcherIn = preFilter && ( seed || !selector ) ?
+				condense( elems, preMap, preFilter, context, xml ) :
+				elems,
+
+			matcherOut = matcher ?
+
+				// If we have a postFinder, or filtered seed, or non-seed postFilter or preexisting results,
+				postFinder || ( seed ? preFilter : preexisting || postFilter ) ?
+
+					// ...intermediate processing is necessary
+					[] :
+
+					// ...otherwise use results directly
+					results :
+				matcherIn;
+
+		// Find primary matches
+		if ( matcher ) {
+			matcher( matcherIn, matcherOut, context, xml );
+		}
+
+		// Apply postFilter
+		if ( postFilter ) {
+			temp = condense( matcherOut, postMap );
+			postFilter( temp, [], context, xml );
+
+			// Un-match failing elements by moving them back to matcherIn
+			i = temp.length;
+			while ( i-- ) {
+				if ( ( elem = temp[ i ] ) ) {
+					matcherOut[ postMap[ i ] ] = !( matcherIn[ postMap[ i ] ] = elem );
+				}
+			}
+		}
+
+		if ( seed ) {
+			if ( postFinder || preFilter ) {
+				if ( postFinder ) {
+
+					// Get the final matcherOut by condensing this intermediate into postFinder contexts
+					temp = [];
+					i = matcherOut.length;
+					while ( i-- ) {
+						if ( ( elem = matcherOut[ i ] ) ) {
+
+							// Restore matcherIn since elem is not yet a final match
+							temp.push( ( matcherIn[ i ] = elem ) );
+						}
+					}
+					postFinder( null, ( matcherOut = [] ), temp, xml );
+				}
+
+				// Move matched elements from seed to results to keep them synchronized
+				i = matcherOut.length;
+				while ( i-- ) {
+					if ( ( elem = matcherOut[ i ] ) &&
+						( temp = postFinder ? indexOf( seed, elem ) : preMap[ i ] ) > -1 ) {
+
+						seed[ temp ] = !( results[ temp ] = elem );
+					}
+				}
+			}
+
+		// Add elements to results, through postFinder if defined
+		} else {
+			matcherOut = condense(
+				matcherOut === results ?
+					matcherOut.splice( preexisting, matcherOut.length ) :
+					matcherOut
+			);
+			if ( postFinder ) {
+				postFinder( null, results, matcherOut, xml );
+			} else {
+				push.apply( results, matcherOut );
+			}
+		}
+	} );
+}
+
+function matcherFromTokens( tokens ) {
+	var checkContext, matcher, j,
+		len = tokens.length,
+		leadingRelative = Expr.relative[ tokens[ 0 ].type ],
+		implicitRelative = leadingRelative || Expr.relative[ " " ],
+		i = leadingRelative ? 1 : 0,
+
+		// The foundational matcher ensures that elements are reachable from top-level context(s)
+		matchContext = addCombinator( function( elem ) {
+			return elem === checkContext;
+		}, implicitRelative, true ),
+		matchAnyContext = addCombinator( function( elem ) {
+			return indexOf( checkContext, elem ) > -1;
+		}, implicitRelative, true ),
+		matchers = [ function( elem, context, xml ) {
+			var ret = ( !leadingRelative && ( xml || context !== outermostContext ) ) || (
+				( checkContext = context ).nodeType ?
+					matchContext( elem, context, xml ) :
+					matchAnyContext( elem, context, xml ) );
+
+			// Avoid hanging onto element (issue #299)
+			checkContext = null;
+			return ret;
+		} ];
+
+	for ( ; i < len; i++ ) {
+		if ( ( matcher = Expr.relative[ tokens[ i ].type ] ) ) {
+			matchers = [ addCombinator( elementMatcher( matchers ), matcher ) ];
+		} else {
+			matcher = Expr.filter[ tokens[ i ].type ].apply( null, tokens[ i ].matches );
+
+			// Return special upon seeing a positional matcher
+			if ( matcher[ expando ] ) {
+
+				// Find the next relative operator (if any) for proper handling
+				j = ++i;
+				for ( ; j < len; j++ ) {
+					if ( Expr.relative[ tokens[ j ].type ] ) {
+						break;
+					}
+				}
+				return setMatcher(
+					i > 1 && elementMatcher( matchers ),
+					i > 1 && toSelector(
+
+					// If the preceding token was a descendant combinator, insert an implicit any-element `*`
+					tokens
+						.slice( 0, i - 1 )
+						.concat( { value: tokens[ i - 2 ].type === " " ? "*" : "" } )
+					).replace( rtrim, "$1" ),
+					matcher,
+					i < j && matcherFromTokens( tokens.slice( i, j ) ),
+					j < len && matcherFromTokens( ( tokens = tokens.slice( j ) ) ),
+					j < len && toSelector( tokens )
+				);
+			}
+			matchers.push( matcher );
+		}
+	}
+
+	return elementMatcher( matchers );
+}
+
+function matcherFromGroupMatchers( elementMatchers, setMatchers ) {
+	var bySet = setMatchers.length > 0,
+		byElement = elementMatchers.length > 0,
+		superMatcher = function( seed, context, xml, results, outermost ) {
+			var elem, j, matcher,
+				matchedCount = 0,
+				i = "0",
+				unmatched = seed && [],
+				setMatched = [],
+				contextBackup = outermostContext,
+
+				// We must always have either seed elements or outermost context
+				elems = seed || byElement && Expr.find[ "TAG" ]( "*", outermost ),
+
+				// Use integer dirruns iff this is the outermost matcher
+				dirrunsUnique = ( dirruns += contextBackup == null ? 1 : Math.random() || 0.1 ),
+				len = elems.length;
+
+			if ( outermost ) {
+
+				// Support: IE 11+, Edge 17 - 18+
+				// IE/Edge sometimes throw a "Permission denied" error when strict-comparing
+				// two documents; shallow comparisons work.
+				// eslint-disable-next-line eqeqeq
+				outermostContext = context == document || context || outermost;
+			}
+
+			// Add elements passing elementMatchers directly to results
+			// Support: IE<9, Safari
+			// Tolerate NodeList properties (IE: "length"; Safari: <number>) matching elements by id
+			for ( ; i !== len && ( elem = elems[ i ] ) != null; i++ ) {
+				if ( byElement && elem ) {
+					j = 0;
+
+					// Support: IE 11+, Edge 17 - 18+
+					// IE/Edge sometimes throw a "Permission denied" error when strict-comparing
+					// two documents; shallow comparisons work.
+					// eslint-disable-next-line eqeqeq
+					if ( !context && elem.ownerDocument != document ) {
+						setDocument( elem );
+						xml = !documentIsHTML;
+					}
+					while ( ( matcher = elementMatchers[ j++ ] ) ) {
+						if ( matcher( elem, context || document, xml ) ) {
+							results.push( elem );
+							break;
+						}
+					}
+					if ( outermost ) {
+						dirruns = dirrunsUnique;
+					}
+				}
+
+				// Track unmatched elements for set filters
+				if ( bySet ) {
+
+					// They will have gone through all possible matchers
+					if ( ( elem = !matcher && elem ) ) {
+						matchedCount--;
+					}
+
+					// Lengthen the array for every element, matched or not
+					if ( seed ) {
+						unmatched.push( elem );
+					}
+				}
+			}
+
+			// `i` is now the count of elements visited above, and adding it to `matchedCount`
+			// makes the latter nonnegative.
+			matchedCount += i;
+
+			// Apply set filters to unmatched elements
+			// NOTE: This can be skipped if there are no unmatched elements (i.e., `matchedCount`
+			// equals `i`), unless we didn't visit _any_ elements in the above loop because we have
+			// no element matchers and no seed.
+			// Incrementing an initially-string "0" `i` allows `i` to remain a string only in that
+			// case, which will result in a "00" `matchedCount` that differs from `i` but is also
+			// numerically zero.
+			if ( bySet && i !== matchedCount ) {
+				j = 0;
+				while ( ( matcher = setMatchers[ j++ ] ) ) {
+					matcher( unmatched, setMatched, context, xml );
+				}
+
+				if ( seed ) {
+
+					// Reintegrate element matches to eliminate the need for sorting
+					if ( matchedCount > 0 ) {
+						while ( i-- ) {
+							if ( !( unmatched[ i ] || setMatched[ i ] ) ) {
+								setMatched[ i ] = pop.call( results );
+							}
+						}
+					}
+
+					// Discard index placeholder values to get only actual matches
+					setMatched = condense( setMatched );
+				}
+
+				// Add matches to results
+				push.apply( results, setMatched );
+
+				// Seedless set matches succeeding multiple successful matchers stipulate sorting
+				if ( outermost && !seed && setMatched.length > 0 &&
+					( matchedCount + setMatchers.length ) > 1 ) {
+
+					Sizzle.uniqueSort( results );
+				}
+			}
+
+			// Override manipulation of globals by nested matchers
+			if ( outermost ) {
+				dirruns = dirrunsUnique;
+				outermostContext = contextBackup;
+			}
+
+			return unmatched;
+		};
+
+	return bySet ?
+		markFunction( superMatcher ) :
+		superMatcher;
+}
+
+compile = Sizzle.compile = function( selector, match /* Internal Use Only */ ) {
+	var i,
+		setMatchers = [],
+		elementMatchers = [],
+		cached = compilerCache[ selector + " " ];
+
+	if ( !cached ) {
+
+		// Generate a function of recursive functions that can be used to check each element
+		if ( !match ) {
+			match = tokenize( selector );
+		}
+		i = match.length;
+		while ( i-- ) {
+			cached = matcherFromTokens( match[ i ] );
+			if ( cached[ expando ] ) {
+				setMatchers.push( cached );
+			} else {
+				elementMatchers.push( cached );
+			}
+		}
+
+		// Cache the compiled function
+		cached = compilerCache(
+			selector,
+			matcherFromGroupMatchers( elementMatchers, setMatchers )
+		);
+
+		// Save selector and tokenization
+		cached.selector = selector;
+	}
+	return cached;
+};
+
+/**
+ * A low-level selection function that works with Sizzle's compiled
+ *  selector functions
+ * @param {String|Function} selector A selector or a pre-compiled
+ *  selector function built with Sizzle.compile
+ * @param {Element} context
+ * @param {Array} [results]
+ * @param {Array} [seed] A set of elements to match against
+ */
+select = Sizzle.select = function( selector, context, results, seed ) {
+	var i, tokens, token, type, find,
+		compiled = typeof selector === "function" && selector,
+		match = !seed && tokenize( ( selector = compiled.selector || selector ) );
+
+	results = results || [];
+
+	// Try to minimize operations if there is only one selector in the list and no seed
+	// (the latter of which guarantees us context)
+	if ( match.length === 1 ) {
+
+		// Reduce context if the leading compound selector is an ID
+		tokens = match[ 0 ] = match[ 0 ].slice( 0 );
+		if ( tokens.length > 2 && ( token = tokens[ 0 ] ).type === "ID" &&
+			context.nodeType === 9 && documentIsHTML && Expr.relative[ tokens[ 1 ].type ] ) {
+
+			context = ( Expr.find[ "ID" ]( token.matches[ 0 ]
+				.replace( runescape, funescape ), context ) || [] )[ 0 ];
+			if ( !context ) {
+				return results;
+
+			// Precompiled matchers will still verify ancestry, so step up a level
+			} else if ( compiled ) {
+				context = context.parentNode;
+			}
+
+			selector = selector.slice( tokens.shift().value.length );
+		}
+
+		// Fetch a seed set for right-to-left matching
+		i = matchExpr[ "needsContext" ].test( selector ) ? 0 : tokens.length;
+		while ( i-- ) {
+			token = tokens[ i ];
+
+			// Abort if we hit a combinator
+			if ( Expr.relative[ ( type = token.type ) ] ) {
+				break;
+			}
+			if ( ( find = Expr.find[ type ] ) ) {
+
+				// Search, expanding context for leading sibling combinators
+				if ( ( seed = find(
+					token.matches[ 0 ].replace( runescape, funescape ),
+					rsibling.test( tokens[ 0 ].type ) && testContext( context.parentNode ) ||
+						context
+				) ) ) {
+
+					// If seed is empty or no tokens remain, we can return early
+					tokens.splice( i, 1 );
+					selector = seed.length && toSelector( tokens );
+					if ( !selector ) {
+						push.apply( results, seed );
+						return results;
+					}
+
+					break;
+				}
+			}
+		}
+	}
+
+	// Compile and execute a filtering function if one is not provided
+	// Provide `match` to avoid retokenization if we modified the selector above
+	( compiled || compile( selector, match ) )(
+		seed,
+		context,
+		!documentIsHTML,
+		results,
+		!context || rsibling.test( selector ) && testContext( context.parentNode ) || context
+	);
+	return results;
+};
+
+// One-time assignments
+
+// Sort stability
+support.sortStable = expando.split( "" ).sort( sortOrder ).join( "" ) === expando;
+
+// Support: Chrome 14-35+
+// Always assume duplicates if they aren't passed to the comparison function
+support.detectDuplicates = !!hasDuplicate;
+
+// Initialize against the default document
+setDocument();
+
+// Support: Webkit<537.32 - Safari 6.0.3/Chrome 25 (fixed in Chrome 27)
+// Detached nodes confoundingly follow *each other*
+support.sortDetached = assert( function( el ) {
+
+	// Should return 1, but returns 4 (following)
+	return el.compareDocumentPosition( document.createElement( "fieldset" ) ) & 1;
+} );
+
+// Support: IE<8
+// Prevent attribute/property "interpolation"
+// https://msdn.microsoft.com/en-us/library/ms536429%28VS.85%29.aspx
+if ( !assert( function( el ) {
+	el.innerHTML = "<a href='#'></a>";
+	return el.firstChild.getAttribute( "href" ) === "#";
+} ) ) {
+	addHandle( "type|href|height|width", function( elem, name, isXML ) {
+		if ( !isXML ) {
+			return elem.getAttribute( name, name.toLowerCase() === "type" ? 1 : 2 );
+		}
+	} );
+}
+
+// Support: IE<9
+// Use defaultValue in place of getAttribute("value")
+if ( !support.attributes || !assert( function( el ) {
+	el.innerHTML = "<input/>";
+	el.firstChild.setAttribute( "value", "" );
+	return el.firstChild.getAttribute( "value" ) === "";
+} ) ) {
+	addHandle( "value", function( elem, _name, isXML ) {
+		if ( !isXML && elem.nodeName.toLowerCase() === "input" ) {
+			return elem.defaultValue;
+		}
+	} );
+}
+
+// Support: IE<9
+// Use getAttributeNode to fetch booleans when getAttribute lies
+if ( !assert( function( el ) {
+	return el.getAttribute( "disabled" ) == null;
+} ) ) {
+	addHandle( booleans, function( elem, name, isXML ) {
+		var val;
+		if ( !isXML ) {
+			return elem[ name ] === true ? name.toLowerCase() :
+				( val = elem.getAttributeNode( name ) ) && val.specified ?
+					val.value :
+					null;
+		}
+	} );
+}
+
+return Sizzle;
+
+} )( window );
+
+
+
+jQuery.find = Sizzle;
+jQuery.expr = Sizzle.selectors;
+
+// Deprecated
+jQuery.expr[ ":" ] = jQuery.expr.pseudos;
+jQuery.uniqueSort = jQuery.unique = Sizzle.uniqueSort;
+jQuery.text = Sizzle.getText;
+jQuery.isXMLDoc = Sizzle.isXML;
+jQuery.contains = Sizzle.contains;
+jQuery.escapeSelector = Sizzle.escape;
+
+
+
+
+var dir = function( elem, dir, until ) {
+	var matched = [],
+		truncate = until !== undefined;
+
+	while ( ( elem = elem[ dir ] ) && elem.nodeType !== 9 ) {
+		if ( elem.nodeType === 1 ) {
+			if ( truncate && jQuery( elem ).is( until ) ) {
+				break;
+			}
+			matched.push( elem );
+		}
+	}
+	return matched;
+};
+
+
+var siblings = function( n, elem ) {
+	var matched = [];
+
+	for ( ; n; n = n.nextSibling ) {
+		if ( n.nodeType === 1 && n !== elem ) {
+			matched.push( n );
+		}
+	}
+
+	return matched;
+};
+
+
+var rneedsContext = jQuery.expr.match.needsContext;
+
+
+
+function nodeName( elem, name ) {
+
+	return elem.nodeName && elem.nodeName.toLowerCase() === name.toLowerCase();
+
+}
+var rsingleTag = ( /^<([a-z][^\/\0>:\x20\t\r\n\f]*)[\x20\t\r\n\f]*\/?>(?:<\/\1>|)$/i );
+
+
+
+// Implement the identical functionality for filter and not
+function winnow( elements, qualifier, not ) {
+	if ( isFunction( qualifier ) ) {
+		return jQuery.grep( elements, function( elem, i ) {
+			return !!qualifier.call( elem, i, elem ) !== not;
+		} );
+	}
+
+	// Single element
+	if ( qualifier.nodeType ) {
+		return jQuery.grep( elements, function( elem ) {
+			return ( elem === qualifier ) !== not;
+		} );
+	}
+
+	// Arraylike of elements (jQuery, arguments, Array)
+	if ( typeof qualifier !== "string" ) {
+		return jQuery.grep( elements, function( elem ) {
+			return ( indexOf.call( qualifier, elem ) > -1 ) !== not;
+		} );
+	}
+
+	// Filtered directly for both simple and complex selectors
+	return jQuery.filter( qualifier, elements, not );
+}
+
+jQuery.filter = function( expr, elems, not ) {
+	var elem = elems[ 0 ];
+
+	if ( not ) {
+		expr = ":not(" + expr + ")";
+	}
+
+	if ( elems.length === 1 && elem.nodeType === 1 ) {
+		return jQuery.find.matchesSelector( elem, expr ) ? [ elem ] : [];
+	}
+
+	return jQuery.find.matches( expr, jQuery.grep( elems, function( elem ) {
+		return elem.nodeType === 1;
+	} ) );
+};
+
+jQuery.fn.extend( {
+	find: function( selector ) {
+		var i, ret,
+			len = this.length,
+			self = this;
+
+		if ( typeof selector !== "string" ) {
+			return this.pushStack( jQuery( selector ).filter( function() {
+				for ( i = 0; i < len; i++ ) {
+					if ( jQuery.contains( self[ i ], this ) ) {
+						return true;
+					}
+				}
+			} ) );
+		}
+
+		ret = this.pushStack( [] );
+
+		for ( i = 0; i < len; i++ ) {
+			jQuery.find( selector, self[ i ], ret );
+		}
+
+		return len > 1 ? jQuery.uniqueSort( ret ) : ret;
+	},
+	filter: function( selector ) {
+		return this.pushStack( winnow( this, selector || [], false ) );
+	},
+	not: function( selector ) {
+		return this.pushStack( winnow( this, selector || [], true ) );
+	},
+	is: function( selector ) {
+		return !!winnow(
+			this,
+
+			// If this is a positional/relative selector, check membership in the returned set
+			// so $("p:first").is("p:last") won't return true for a doc with two "p".
+			typeof selector === "string" && rneedsContext.test( selector ) ?
+				jQuery( selector ) :
+				selector || [],
+			false
+		).length;
+	}
+} );
+
+
+// Initialize a jQuery object
+
+
+// A central reference to the root jQuery(document)
+var rootjQuery,
+
+	// A simple way to check for HTML strings
+	// Prioritize #id over <tag> to avoid XSS via location.hash (#9521)
+	// Strict HTML recognition (#11290: must start with <)
+	// Shortcut simple #id case for speed
+	rquickExpr = /^(?:\s*(<[\w\W]+>)[^>]*|#([\w-]+))$/,
+
+	init = jQuery.fn.init = function( selector, context, root ) {
+		var match, elem;
+
+		// HANDLE: $(""), $(null), $(undefined), $(false)
+		if ( !selector ) {
+			return this;
+		}
+
+		// Method init() accepts an alternate rootjQuery
+		// so migrate can support jQuery.sub (gh-2101)
+		root = root || rootjQuery;
+
+		// Handle HTML strings
+		if ( typeof selector === "string" ) {
+			if ( selector[ 0 ] === "<" &&
+				selector[ selector.length - 1 ] === ">" &&
+				selector.length >= 3 ) {
+
+				// Assume that strings that start and end with <> are HTML and skip the regex check
+				match = [ null, selector, null ];
+
+			} else {
+				match = rquickExpr.exec( selector );
+			}
+
+			// Match html or make sure no context is specified for #id
+			if ( match && ( match[ 1 ] || !context ) ) {
+
+				// HANDLE: $(html) -> $(array)
+				if ( match[ 1 ] ) {
+					context = context instanceof jQuery ? context[ 0 ] : context;
+
+					// Option to run scripts is true for back-compat
+					// Intentionally let the error be thrown if parseHTML is not present
+					jQuery.merge( this, jQuery.parseHTML(
+						match[ 1 ],
+						context && context.nodeType ? context.ownerDocument || context : document,
+						true
+					) );
+
+					// HANDLE: $(html, props)
+					if ( rsingleTag.test( match[ 1 ] ) && jQuery.isPlainObject( context ) ) {
+						for ( match in context ) {
+
+							// Properties of context are called as methods if possible
+							if ( isFunction( this[ match ] ) ) {
+								this[ match ]( context[ match ] );
+
+							// ...and otherwise set as attributes
+							} else {
+								this.attr( match, context[ match ] );
+							}
+						}
+					}
+
+					return this;
+
+				// HANDLE: $(#id)
+				} else {
+					elem = document.getElementById( match[ 2 ] );
+
+					if ( elem ) {
+
+						// Inject the element directly into the jQuery object
+						this[ 0 ] = elem;
+						this.length = 1;
+					}
+					return this;
+				}
+
+			// HANDLE: $(expr, $(...))
+			} else if ( !context || context.jquery ) {
+				return ( context || root ).find( selector );
+
+			// HANDLE: $(expr, context)
+			// (which is just equivalent to: $(context).find(expr)
+			} else {
+				return this.constructor( context ).find( selector );
+			}
+
+		// HANDLE: $(DOMElement)
+		} else if ( selector.nodeType ) {
+			this[ 0 ] = selector;
+			this.length = 1;
+			return this;
+
+		// HANDLE: $(function)
+		// Shortcut for document ready
+		} else if ( isFunction( selector ) ) {
+			return root.ready !== undefined ?
+				root.ready( selector ) :
+
+				// Execute immediately if ready is not present
+				selector( jQuery );
+		}
+
+		return jQuery.makeArray( selector, this );
+	};
+
+// Give the init function the jQuery prototype for later instantiation
+init.prototype = jQuery.fn;
+
+// Initialize central reference
+rootjQuery = jQuery( document );
+
+
+var rparentsprev = /^(?:parents|prev(?:Until|All))/,
+
+	// Methods guaranteed to produce a unique set when starting from a unique set
+	guaranteedUnique = {
+		children: true,
+		contents: true,
+		next: true,
+		prev: true
+	};
+
+jQuery.fn.extend( {
+	has: function( target ) {
+		var targets = jQuery( target, this ),
+			l = targets.length;
+
+		return this.filter( function() {
+			var i = 0;
+			for ( ; i < l; i++ ) {
+				if ( jQuery.contains( this, targets[ i ] ) ) {
+					return true;
+				}
+			}
+		} );
+	},
+
+	closest: function( selectors, context ) {
+		var cur,
+			i = 0,
+			l = this.length,
+			matched = [],
+			targets = typeof selectors !== "string" && jQuery( selectors );
+
+		// Positional selectors never match, since there's no _selection_ context
+		if ( !rneedsContext.test( selectors ) ) {
+			for ( ; i < l; i++ ) {
+				for ( cur = this[ i ]; cur && cur !== context; cur = cur.parentNode ) {
+
+					// Always skip document fragments
+					if ( cur.nodeType < 11 && ( targets ?
+						targets.index( cur ) > -1 :
+
+						// Don't pass non-elements to Sizzle
+						cur.nodeType === 1 &&
+							jQuery.find.matchesSelector( cur, selectors ) ) ) {
+
+						matched.push( cur );
+						break;
+					}
+				}
+			}
+		}
+
+		return this.pushStack( matched.length > 1 ? jQuery.uniqueSort( matched ) : matched );
+	},
+
+	// Determine the position of an element within the set
+	index: function( elem ) {
+
+		// No argument, return index in parent
+		if ( !elem ) {
+			return ( this[ 0 ] && this[ 0 ].parentNode ) ? this.first().prevAll().length : -1;
+		}
+
+		// Index in selector
+		if ( typeof elem === "string" ) {
+			return indexOf.call( jQuery( elem ), this[ 0 ] );
+		}
+
+		// Locate the position of the desired element
+		return indexOf.call( this,
+
+			// If it receives a jQuery object, the first element is used
+			elem.jquery ? elem[ 0 ] : elem
+		);
+	},
+
+	add: function( selector, context ) {
+		return this.pushStack(
+			jQuery.uniqueSort(
+				jQuery.merge( this.get(), jQuery( selector, context ) )
+			)
+		);
+	},
+
+	addBack: function( selector ) {
+		return this.add( selector == null ?
+			this.prevObject : this.prevObject.filter( selector )
+		);
+	}
+} );
+
+function sibling( cur, dir ) {
+	while ( ( cur = cur[ dir ] ) && cur.nodeType !== 1 ) {}
+	return cur;
+}
+
+jQuery.each( {
+	parent: function( elem ) {
+		var parent = elem.parentNode;
+		return parent && parent.nodeType !== 11 ? parent : null;
+	},
+	parents: function( elem ) {
+		return dir( elem, "parentNode" );
+	},
+	parentsUntil: function( elem, _i, until ) {
+		return dir( elem, "parentNode", until );
+	},
+	next: function( elem ) {
+		return sibling( elem, "nextSibling" );
+	},
+	prev: function( elem ) {
+		return sibling( elem, "previousSibling" );
+	},
+	nextAll: function( elem ) {
+		return dir( elem, "nextSibling" );
+	},
+	prevAll: function( elem ) {
+		return dir( elem, "previousSibling" );
+	},
+	nextUntil: function( elem, _i, until ) {
+		return dir( elem, "nextSibling", until );
+	},
+	prevUntil: function( elem, _i, until ) {
+		return dir( elem, "previousSibling", until );
+	},
+	siblings: function( elem ) {
+		return siblings( ( elem.parentNode || {} ).firstChild, elem );
+	},
+	children: function( elem ) {
+		return siblings( elem.firstChild );
+	},
+	contents: function( elem ) {
+		if ( elem.contentDocument != null &&
+
+			// Support: IE 11+
+			// <object> elements with no `data` attribute has an object
+			// `contentDocument` with a `null` prototype.
+			getProto( elem.contentDocument ) ) {
+
+			return elem.contentDocument;
+		}
+
+		// Support: IE 9 - 11 only, iOS 7 only, Android Browser <=4.3 only
+		// Treat the template element as a regular one in browsers that
+		// don't support it.
+		if ( nodeName( elem, "template" ) ) {
+			elem = elem.content || elem;
+		}
+
+		return jQuery.merge( [], elem.childNodes );
+	}
+}, function( name, fn ) {
+	jQuery.fn[ name ] = function( until, selector ) {
+		var matched = jQuery.map( this, fn, until );
+
+		if ( name.slice( -5 ) !== "Until" ) {
+			selector = until;
+		}
+
+		if ( selector && typeof selector === "string" ) {
+			matched = jQuery.filter( selector, matched );
+		}
+
+		if ( this.length > 1 ) {
+
+			// Remove duplicates
+			if ( !guaranteedUnique[ name ] ) {
+				jQuery.uniqueSort( matched );
+			}
+
+			// Reverse order for parents* and prev-derivatives
+			if ( rparentsprev.test( name ) ) {
+				matched.reverse();
+			}
+		}
+
+		return this.pushStack( matched );
+	};
+} );
+var rnothtmlwhite = ( /[^\x20\t\r\n\f]+/g );
+
+
+
+// Convert String-formatted options into Object-formatted ones
+function createOptions( options ) {
+	var object = {};
+	jQuery.each( options.match( rnothtmlwhite ) || [], function( _, flag ) {
+		object[ flag ] = true;
+	} );
+	return object;
+}
+
+/*
+ * Create a callback list using the following parameters:
+ *
+ *	options: an optional list of space-separated options that will change how
+ *			the callback list behaves or a more traditional option object
+ *
+ * By default a callback list will act like an event callback list and can be
+ * "fired" multiple times.
+ *
+ * Possible options:
+ *
+ *	once:			will ensure the callback list can only be fired once (like a Deferred)
+ *
+ *	memory:			will keep track of previous values and will call any callback added
+ *					after the list has been fired right away with the latest "memorized"
+ *					values (like a Deferred)
+ *
+ *	unique:			will ensure a callback can only be added once (no duplicate in the list)
+ *
+ *	stopOnFalse:	interrupt callings when a callback returns false
+ *
+ */
+jQuery.Callbacks = function( options ) {
+
+	// Convert options from String-formatted to Object-formatted if needed
+	// (we check in cache first)
+	options = typeof options === "string" ?
+		createOptions( options ) :
+		jQuery.extend( {}, options );
+
+	var // Flag to know if list is currently firing
+		firing,
+
+		// Last fire value for non-forgettable lists
+		memory,
+
+		// Flag to know if list was already fired
+		fired,
+
+		// Flag to prevent firing
+		locked,
+
+		// Actual callback list
+		list = [],
+
+		// Queue of execution data for repeatable lists
+		queue = [],
+
+		// Index of currently firing callback (modified by add/remove as needed)
+		firingIndex = -1,
+
+		// Fire callbacks
+		fire = function() {
+
+			// Enforce single-firing
+			locked = locked || options.once;
+
+			// Execute callbacks for all pending executions,
+			// respecting firingIndex overrides and runtime changes
+			fired = firing = true;
+			for ( ; queue.length; firingIndex = -1 ) {
+				memory = queue.shift();
+				while ( ++firingIndex < list.length ) {
+
+					// Run callback and check for early termination
+					if ( list[ firingIndex ].apply( memory[ 0 ], memory[ 1 ] ) === false &&
+						options.stopOnFalse ) {
+
+						// Jump to end and forget the data so .add doesn't re-fire
+						firingIndex = list.length;
+						memory = false;
+					}
+				}
+			}
+
+			// Forget the data if we're done with it
+			if ( !options.memory ) {
+				memory = false;
+			}
+
+			firing = false;
+
+			// Clean up if we're done firing for good
+			if ( locked ) {
+
+				// Keep an empty list if we have data for future add calls
+				if ( memory ) {
+					list = [];
+
+				// Otherwise, this object is spent
+				} else {
+					list = "";
+				}
+			}
+		},
+
+		// Actual Callbacks object
+		self = {
+
+			// Add a callback or a collection of callbacks to the list
+			add: function() {
+				if ( list ) {
+
+					// If we have memory from a past run, we should fire after adding
+					if ( memory && !firing ) {
+						firingIndex = list.length - 1;
+						queue.push( memory );
+					}
+
+					( function add( args ) {
+						jQuery.each( args, function( _, arg ) {
+							if ( isFunction( arg ) ) {
+								if ( !options.unique || !self.has( arg ) ) {
+									list.push( arg );
+								}
+							} else if ( arg && arg.length && toType( arg ) !== "string" ) {
+
+								// Inspect recursively
+								add( arg );
+							}
+						} );
+					} )( arguments );
+
+					if ( memory && !firing ) {
+						fire();
+					}
+				}
+				return this;
+			},
+
+			// Remove a callback from the list
+			remove: function() {
+				jQuery.each( arguments, function( _, arg ) {
+					var index;
+					while ( ( index = jQuery.inArray( arg, list, index ) ) > -1 ) {
+						list.splice( index, 1 );
+
+						// Handle firing indexes
+						if ( index <= firingIndex ) {
+							firingIndex--;
+						}
+					}
+				} );
+				return this;
+			},
+
+			// Check if a given callback is in the list.
+			// If no argument is given, return whether or not list has callbacks attached.
+			has: function( fn ) {
+				return fn ?
+					jQuery.inArray( fn, list ) > -1 :
+					list.length > 0;
+			},
+
+			// Remove all callbacks from the list
+			empty: function() {
+				if ( list ) {
+					list = [];
+				}
+				return this;
+			},
+
+			// Disable .fire and .add
+			// Abort any current/pending executions
+			// Clear all callbacks and values
+			disable: function() {
+				locked = queue = [];
+				list = memory = "";
+				return this;
+			},
+			disabled: function() {
+				return !list;
+			},
+
+			// Disable .fire
+			// Also disable .add unless we have memory (since it would have no effect)
+			// Abort any pending executions
+			lock: function() {
+				locked = queue = [];
+				if ( !memory && !firing ) {
+					list = memory = "";
+				}
+				return this;
+			},
+			locked: function() {
+				return !!locked;
+			},
+
+			// Call all callbacks with the given context and arguments
+			fireWith: function( context, args ) {
+				if ( !locked ) {
+					args = args || [];
+					args = [ context, args.slice ? args.slice() : args ];
+					queue.push( args );
+					if ( !firing ) {
+						fire();
+					}
+				}
+				return this;
+			},
+
+			// Call all the callbacks with the given arguments
+			fire: function() {
+				self.fireWith( this, arguments );
+				return this;
+			},
+
+			// To know if the callbacks have already been called at least once
+			fired: function() {
+				return !!fired;
+			}
+		};
+
+	return self;
+};
+
+
+function Identity( v ) {
+	return v;
+}
+function Thrower( ex ) {
+	throw ex;
+}
+
+function adoptValue( value, resolve, reject, noValue ) {
+	var method;
+
+	try {
+
+		// Check for promise aspect first to privilege synchronous behavior
+		if ( value && isFunction( ( method = value.promise ) ) ) {
+			method.call( value ).done( resolve ).fail( reject );
+
+		// Other thenables
+		} else if ( value && isFunction( ( method = value.then ) ) ) {
+			method.call( value, resolve, reject );
+
+		// Other non-thenables
+		} else {
+
+			// Control `resolve` arguments by letting Array#slice cast boolean `noValue` to integer:
+			// * false: [ value ].slice( 0 ) => resolve( value )
+			// * true: [ value ].slice( 1 ) => resolve()
+			resolve.apply( undefined, [ value ].slice( noValue ) );
+		}
+
+	// For Promises/A+, convert exceptions into rejections
+	// Since jQuery.when doesn't unwrap thenables, we can skip the extra checks appearing in
+	// Deferred#then to conditionally suppress rejection.
+	} catch ( value ) {
+
+		// Support: Android 4.0 only
+		// Strict mode functions invoked without .call/.apply get global-object context
+		reject.apply( undefined, [ value ] );
+	}
+}
+
+jQuery.extend( {
+
+	Deferred: function( func ) {
+		var tuples = [
+
+				// action, add listener, callbacks,
+				// ... .then handlers, argument index, [final state]
+				[ "notify", "progress", jQuery.Callbacks( "memory" ),
+					jQuery.Callbacks( "memory" ), 2 ],
+				[ "resolve", "done", jQuery.Callbacks( "once memory" ),
+					jQuery.Callbacks( "once memory" ), 0, "resolved" ],
+				[ "reject", "fail", jQuery.Callbacks( "once memory" ),
+					jQuery.Callbacks( "once memory" ), 1, "rejected" ]
+			],
+			state = "pending",
+			promise = {
+				state: function() {
+					return state;
+				},
+				always: function() {
+					deferred.done( arguments ).fail( arguments );
+					return this;
+				},
+				"catch": function( fn ) {
+					return promise.then( null, fn );
+				},
+
+				// Keep pipe for back-compat
+				pipe: function( /* fnDone, fnFail, fnProgress */ ) {
+					var fns = arguments;
+
+					return jQuery.Deferred( function( newDefer ) {
+						jQuery.each( tuples, function( _i, tuple ) {
+
+							// Map tuples (progress, done, fail) to arguments (done, fail, progress)
+							var fn = isFunction( fns[ tuple[ 4 ] ] ) && fns[ tuple[ 4 ] ];
+
+							// deferred.progress(function() { bind to newDefer or newDefer.notify })
+							// deferred.done(function() { bind to newDefer or newDefer.resolve })
+							// deferred.fail(function() { bind to newDefer or newDefer.reject })
+							deferred[ tuple[ 1 ] ]( function() {
+								var returned = fn && fn.apply( this, arguments );
+								if ( returned && isFunction( returned.promise ) ) {
+									returned.promise()
+										.progress( newDefer.notify )
+										.done( newDefer.resolve )
+										.fail( newDefer.reject );
+								} else {
+									newDefer[ tuple[ 0 ] + "With" ](
+										this,
+										fn ? [ returned ] : arguments
+									);
+								}
+							} );
+						} );
+						fns = null;
+					} ).promise();
+				},
+				then: function( onFulfilled, onRejected, onProgress ) {
+					var maxDepth = 0;
+					function resolve( depth, deferred, handler, special ) {
+						return function() {
+							var that = this,
+								args = arguments,
+								mightThrow = function() {
+									var returned, then;
+
+									// Support: Promises/A+ section 2.3.3.3.3
+									// https://promisesaplus.com/#point-59
+									// Ignore double-resolution attempts
+									if ( depth < maxDepth ) {
+										return;
+									}
+
+									returned = handler.apply( that, args );
+
+									// Support: Promises/A+ section 2.3.1
+									// https://promisesaplus.com/#point-48
+									if ( returned === deferred.promise() ) {
+										throw new TypeError( "Thenable self-resolution" );
+									}
+
+									// Support: Promises/A+ sections 2.3.3.1, 3.5
+									// https://promisesaplus.com/#point-54
+									// https://promisesaplus.com/#point-75
+									// Retrieve `then` only once
+									then = returned &&
+
+										// Support: Promises/A+ section 2.3.4
+										// https://promisesaplus.com/#point-64
+										// Only check objects and functions for thenability
+										( typeof returned === "object" ||
+											typeof returned === "function" ) &&
+										returned.then;
+
+									// Handle a returned thenable
+									if ( isFunction( then ) ) {
+
+										// Special processors (notify) just wait for resolution
+										if ( special ) {
+											then.call(
+												returned,
+												resolve( maxDepth, deferred, Identity, special ),
+												resolve( maxDepth, deferred, Thrower, special )
+											);
+
+										// Normal processors (resolve) also hook into progress
+										} else {
+
+											// ...and disregard older resolution values
+											maxDepth++;
+
+											then.call(
+												returned,
+												resolve( maxDepth, deferred, Identity, special ),
+												resolve( maxDepth, deferred, Thrower, special ),
+												resolve( maxDepth, deferred, Identity,
+													deferred.notifyWith )
+											);
+										}
+
+									// Handle all other returned values
+									} else {
+
+										// Only substitute handlers pass on context
+										// and multiple values (non-spec behavior)
+										if ( handler !== Identity ) {
+											that = undefined;
+											args = [ returned ];
+										}
+
+										// Process the value(s)
+										// Default process is resolve
+										( special || deferred.resolveWith )( that, args );
+									}
+								},
+
+								// Only normal processors (resolve) catch and reject exceptions
+								process = special ?
+									mightThrow :
+									function() {
+										try {
+											mightThrow();
+										} catch ( e ) {
+
+											if ( jQuery.Deferred.exceptionHook ) {
+												jQuery.Deferred.exceptionHook( e,
+													process.stackTrace );
+											}
+
+											// Support: Promises/A+ section 2.3.3.3.4.1
+											// https://promisesaplus.com/#point-61
+											// Ignore post-resolution exceptions
+											if ( depth + 1 >= maxDepth ) {
+
+												// Only substitute handlers pass on context
+												// and multiple values (non-spec behavior)
+												if ( handler !== Thrower ) {
+													that = undefined;
+													args = [ e ];
+												}
+
+												deferred.rejectWith( that, args );
+											}
+										}
+									};
+
+							// Support: Promises/A+ section 2.3.3.3.1
+							// https://promisesaplus.com/#point-57
+							// Re-resolve promises immediately to dodge false rejection from
+							// subsequent errors
+							if ( depth ) {
+								process();
+							} else {
+
+								// Call an optional hook to record the stack, in case of exception
+								// since it's otherwise lost when execution goes async
+								if ( jQuery.Deferred.getStackHook ) {
+									process.stackTrace = jQuery.Deferred.getStackHook();
+								}
+								window.setTimeout( process );
+							}
+						};
+					}
+
+					return jQuery.Deferred( function( newDefer ) {
+
+						// progress_handlers.add( ... )
+						tuples[ 0 ][ 3 ].add(
+							resolve(
+								0,
+								newDefer,
+								isFunction( onProgress ) ?
+									onProgress :
+									Identity,
+								newDefer.notifyWith
+							)
+						);
+
+						// fulfilled_handlers.add( ... )
+						tuples[ 1 ][ 3 ].add(
+							resolve(
+								0,
+								newDefer,
+								isFunction( onFulfilled ) ?
+									onFulfilled :
+									Identity
+							)
+						);
+
+						// rejected_handlers.add( ... )
+						tuples[ 2 ][ 3 ].add(
+							resolve(
+								0,
+								newDefer,
+								isFunction( onRejected ) ?
+									onRejected :
+									Thrower
+							)
+						);
+					} ).promise();
+				},
+
+				// Get a promise for this deferred
+				// If obj is provided, the promise aspect is added to the object
+				promise: function( obj ) {
+					return obj != null ? jQuery.extend( obj, promise ) : promise;
+				}
+			},
+			deferred = {};
+
+		// Add list-specific methods
+		jQuery.each( tuples, function( i, tuple ) {
+			var list = tuple[ 2 ],
+				stateString = tuple[ 5 ];
+
+			// promise.progress = list.add
+			// promise.done = list.add
+			// promise.fail = list.add
+			promise[ tuple[ 1 ] ] = list.add;
+
+			// Handle state
+			if ( stateString ) {
+				list.add(
+					function() {
+
+						// state = "resolved" (i.e., fulfilled)
+						// state = "rejected"
+						state = stateString;
+					},
+
+					// rejected_callbacks.disable
+					// fulfilled_callbacks.disable
+					tuples[ 3 - i ][ 2 ].disable,
+
+					// rejected_handlers.disable
+					// fulfilled_handlers.disable
+					tuples[ 3 - i ][ 3 ].disable,
+
+					// progress_callbacks.lock
+					tuples[ 0 ][ 2 ].lock,
+
+					// progress_handlers.lock
+					tuples[ 0 ][ 3 ].lock
+				);
+			}
+
+			// progress_handlers.fire
+			// fulfilled_handlers.fire
+			// rejected_handlers.fire
+			list.add( tuple[ 3 ].fire );
+
+			// deferred.notify = function() { deferred.notifyWith(...) }
+			// deferred.resolve = function() { deferred.resolveWith(...) }
+			// deferred.reject = function() { deferred.rejectWith(...) }
+			deferred[ tuple[ 0 ] ] = function() {
+				deferred[ tuple[ 0 ] + "With" ]( this === deferred ? undefined : this, arguments );
+				return this;
+			};
+
+			// deferred.notifyWith = list.fireWith
+			// deferred.resolveWith = list.fireWith
+			// deferred.rejectWith = list.fireWith
+			deferred[ tuple[ 0 ] + "With" ] = list.fireWith;
+		} );
+
+		// Make the deferred a promise
+		promise.promise( deferred );
+
+		// Call given func if any
+		if ( func ) {
+			func.call( deferred, deferred );
+		}
+
+		// All done!
+		return deferred;
+	},
+
+	// Deferred helper
+	when: function( singleValue ) {
+		var
+
+			// count of uncompleted subordinates
+			remaining = arguments.length,
+
+			// count of unprocessed arguments
+			i = remaining,
+
+			// subordinate fulfillment data
+			resolveContexts = Array( i ),
+			resolveValues = slice.call( arguments ),
+
+			// the primary Deferred
+			primary = jQuery.Deferred(),
+
+			// subordinate callback factory
+			updateFunc = function( i ) {
+				return function( value ) {
+					resolveContexts[ i ] = this;
+					resolveValues[ i ] = arguments.length > 1 ? slice.call( arguments ) : value;
+					if ( !( --remaining ) ) {
+						primary.resolveWith( resolveContexts, resolveValues );
+					}
+				};
+			};
+
+		// Single- and empty arguments are adopted like Promise.resolve
+		if ( remaining <= 1 ) {
+			adoptValue( singleValue, primary.done( updateFunc( i ) ).resolve, primary.reject,
+				!remaining );
+
+			// Use .then() to unwrap secondary thenables (cf. gh-3000)
+			if ( primary.state() === "pending" ||
+				isFunction( resolveValues[ i ] && resolveValues[ i ].then ) ) {
+
+				return primary.then();
+			}
+		}
+
+		// Multiple arguments are aggregated like Promise.all array elements
+		while ( i-- ) {
+			adoptValue( resolveValues[ i ], updateFunc( i ), primary.reject );
+		}
+
+		return primary.promise();
+	}
+} );
+
+
+// These usually indicate a programmer mistake during development,
+// warn about them ASAP rather than swallowing them by default.
+var rerrorNames = /^(Eval|Internal|Range|Reference|Syntax|Type|URI)Error$/;
+
+jQuery.Deferred.exceptionHook = function( error, stack ) {
+
+	// Support: IE 8 - 9 only
+	// Console exists when dev tools are open, which can happen at any time
+	if ( window.console && window.console.warn && error && rerrorNames.test( error.name ) ) {
+		window.console.warn( "jQuery.Deferred exception: " + error.message, error.stack, stack );
+	}
+};
+
+
+
+
+jQuery.readyException = function( error ) {
+	window.setTimeout( function() {
+		throw error;
+	} );
+};
+
+
+
+
+// The deferred used on DOM ready
+var readyList = jQuery.Deferred();
+
+jQuery.fn.ready = function( fn ) {
+
+	readyList
+		.then( fn )
+
+		// Wrap jQuery.readyException in a function so that the lookup
+		// happens at the time of error handling instead of callback
+		// registration.
+		.catch( function( error ) {
+			jQuery.readyException( error );
+		} );
+
+	return this;
+};
+
+jQuery.extend( {
+
+	// Is the DOM ready to be used? Set to true once it occurs.
+	isReady: false,
+
+	// A counter to track how many items to wait for before
+	// the ready event fires. See #6781
+	readyWait: 1,
+
+	// Handle when the DOM is ready
+	ready: function( wait ) {
+
+		// Abort if there are pending holds or we're already ready
+		if ( wait === true ? --jQuery.readyWait : jQuery.isReady ) {
+			return;
+		}
+
+		// Remember that the DOM is ready
+		jQuery.isReady = true;
+
+		// If a normal DOM Ready event fired, decrement, and wait if need be
+		if ( wait !== true && --jQuery.readyWait > 0 ) {
+			return;
+		}
+
+		// If there are functions bound, to execute
+		readyList.resolveWith( document, [ jQuery ] );
+	}
+} );
+
+jQuery.ready.then = readyList.then;
+
+// The ready event handler and self cleanup method
+function completed() {
+	document.removeEventListener( "DOMContentLoaded", completed );
+	window.removeEventListener( "load", completed );
+	jQuery.ready();
+}
+
+// Catch cases where $(document).ready() is called
+// after the browser event has already occurred.
+// Support: IE <=9 - 10 only
+// Older IE sometimes signals "interactive" too soon
+if ( document.readyState === "complete" ||
+	( document.readyState !== "loading" && !document.documentElement.doScroll ) ) {
+
+	// Handle it asynchronously to allow scripts the opportunity to delay ready
+	window.setTimeout( jQuery.ready );
+
+} else {
+
+	// Use the handy event callback
+	document.addEventListener( "DOMContentLoaded", completed );
+
+	// A fallback to window.onload, that will always work
+	window.addEventListener( "load", completed );
+}
+
+
+
+
+// Multifunctional method to get and set values of a collection
+// The value/s can optionally be executed if it's a function
+var access = function( elems, fn, key, value, chainable, emptyGet, raw ) {
+	var i = 0,
+		len = elems.length,
+		bulk = key == null;
+
+	// Sets many values
+	if ( toType( key ) === "object" ) {
+		chainable = true;
+		for ( i in key ) {
+			access( elems, fn, i, key[ i ], true, emptyGet, raw );
+		}
+
+	// Sets one value
+	} else if ( value !== undefined ) {
+		chainable = true;
+
+		if ( !isFunction( value ) ) {
+			raw = true;
+		}
+
+		if ( bulk ) {
+
+			// Bulk operations run against the entire set
+			if ( raw ) {
+				fn.call( elems, value );
+				fn = null;
+
+			// ...except when executing function values
+			} else {
+				bulk = fn;
+				fn = function( elem, _key, value ) {
+					return bulk.call( jQuery( elem ), value );
+				};
+			}
+		}
+
+		if ( fn ) {
+			for ( ; i < len; i++ ) {
+				fn(
+					elems[ i ], key, raw ?
+						value :
+						value.call( elems[ i ], i, fn( elems[ i ], key ) )
+				);
+			}
+		}
+	}
+
+	if ( chainable ) {
+		return elems;
+	}
+
+	// Gets
+	if ( bulk ) {
+		return fn.call( elems );
+	}
+
+	return len ? fn( elems[ 0 ], key ) : emptyGet;
+};
+
+
+// Matches dashed string for camelizing
+var rmsPrefix = /^-ms-/,
+	rdashAlpha = /-([a-z])/g;
+
+// Used by camelCase as callback to replace()
+function fcamelCase( _all, letter ) {
+	return letter.toUpperCase();
+}
+
+// Convert dashed to camelCase; used by the css and data modules
+// Support: IE <=9 - 11, Edge 12 - 15
+// Microsoft forgot to hump their vendor prefix (#9572)
+function camelCase( string ) {
+	return string.replace( rmsPrefix, "ms-" ).replace( rdashAlpha, fcamelCase );
+}
+var acceptData = function( owner ) {
+
+	// Accepts only:
+	//  - Node
+	//    - Node.ELEMENT_NODE
+	//    - Node.DOCUMENT_NODE
+	//  - Object
+	//    - Any
+	return owner.nodeType === 1 || owner.nodeType === 9 || !( +owner.nodeType );
+};
+
+
+
+
+function Data() {
+	this.expando = jQuery.expando + Data.uid++;
+}
+
+Data.uid = 1;
+
+Data.prototype = {
+
+	cache: function( owner ) {
+
+		// Check if the owner object already has a cache
+		var value = owner[ this.expando ];
+
+		// If not, create one
+		if ( !value ) {
+			value = {};
+
+			// We can accept data for non-element nodes in modern browsers,
+			// but we should not, see #8335.
+			// Always return an empty object.
+			if ( acceptData( owner ) ) {
+
+				// If it is a node unlikely to be stringify-ed or looped over
+				// use plain assignment
+				if ( owner.nodeType ) {
+					owner[ this.expando ] = value;
+
+				// Otherwise secure it in a non-enumerable property
+				// configurable must be true to allow the property to be
+				// deleted when data is removed
+				} else {
+					Object.defineProperty( owner, this.expando, {
+						value: value,
+						configurable: true
+					} );
+				}
+			}
+		}
+
+		return value;
+	},
+	set: function( owner, data, value ) {
+		var prop,
+			cache = this.cache( owner );
+
+		// Handle: [ owner, key, value ] args
+		// Always use camelCase key (gh-2257)
+		if ( typeof data === "string" ) {
+			cache[ camelCase( data ) ] = value;
+
+		// Handle: [ owner, { properties } ] args
+		} else {
+
+			// Copy the properties one-by-one to the cache object
+			for ( prop in data ) {
+				cache[ camelCase( prop ) ] = data[ prop ];
+			}
+		}
+		return cache;
+	},
+	get: function( owner, key ) {
+		return key === undefined ?
+			this.cache( owner ) :
+
+			// Always use camelCase key (gh-2257)
+			owner[ this.expando ] && owner[ this.expando ][ camelCase( key ) ];
+	},
+	access: function( owner, key, value ) {
+
+		// In cases where either:
+		//
+		//   1. No key was specified
+		//   2. A string key was specified, but no value provided
+		//
+		// Take the "read" path and allow the get method to determine
+		// which value to return, respectively either:
+		//
+		//   1. The entire cache object
+		//   2. The data stored at the key
+		//
+		if ( key === undefined ||
+				( ( key && typeof key === "string" ) && value === undefined ) ) {
+
+			return this.get( owner, key );
+		}
+
+		// When the key is not a string, or both a key and value
+		// are specified, set or extend (existing objects) with either:
+		//
+		//   1. An object of properties
+		//   2. A key and value
+		//
+		this.set( owner, key, value );
+
+		// Since the "set" path can have two possible entry points
+		// return the expected data based on which path was taken[*]
+		return value !== undefined ? value : key;
+	},
+	remove: function( owner, key ) {
+		var i,
+			cache = owner[ this.expando ];
+
+		if ( cache === undefined ) {
+			return;
+		}
+
+		if ( key !== undefined ) {
+
+			// Support array or space separated string of keys
+			if ( Array.isArray( key ) ) {
+
+				// If key is an array of keys...
+				// We always set camelCase keys, so remove that.
+				key = key.map( camelCase );
+			} else {
+				key = camelCase( key );
+
+				// If a key with the spaces exists, use it.
+				// Otherwise, create an array by matching non-whitespace
+				key = key in cache ?
+					[ key ] :
+					( key.match( rnothtmlwhite ) || [] );
+			}
+
+			i = key.length;
+
+			while ( i-- ) {
+				delete cache[ key[ i ] ];
+			}
+		}
+
+		// Remove the expando if there's no more data
+		if ( key === undefined || jQuery.isEmptyObject( cache ) ) {
+
+			// Support: Chrome <=35 - 45
+			// Webkit & Blink performance suffers when deleting properties
+			// from DOM nodes, so set to undefined instead
+			// https://bugs.chromium.org/p/chromium/issues/detail?id=378607 (bug restricted)
+			if ( owner.nodeType ) {
+				owner[ this.expando ] = undefined;
+			} else {
+				delete owner[ this.expando ];
+			}
+		}
+	},
+	hasData: function( owner ) {
+		var cache = owner[ this.expando ];
+		return cache !== undefined && !jQuery.isEmptyObject( cache );
+	}
+};
+var dataPriv = new Data();
+
+var dataUser = new Data();
+
+
+
+//	Implementation Summary
+//
+//	1. Enforce API surface and semantic compatibility with 1.9.x branch
+//	2. Improve the module's maintainability by reducing the storage
+//		paths to a single mechanism.
+//	3. Use the same single mechanism to support "private" and "user" data.
+//	4. _Never_ expose "private" data to user code (TODO: Drop _data, _removeData)
+//	5. Avoid exposing implementation details on user objects (eg. expando properties)
+//	6. Provide a clear path for implementation upgrade to WeakMap in 2014
+
+var rbrace = /^(?:\{[\w\W]*\}|\[[\w\W]*\])$/,
+	rmultiDash = /[A-Z]/g;
+
+function getData( data ) {
+	if ( data === "true" ) {
+		return true;
+	}
+
+	if ( data === "false" ) {
+		return false;
+	}
+
+	if ( data === "null" ) {
+		return null;
+	}
+
+	// Only convert to a number if it doesn't change the string
+	if ( data === +data + "" ) {
+		return +data;
+	}
+
+	if ( rbrace.test( data ) ) {
+		return JSON.parse( data );
+	}
+
+	return data;
+}
+
+function dataAttr( elem, key, data ) {
+	var name;
+
+	// If nothing was found internally, try to fetch any
+	// data from the HTML5 data-* attribute
+	if ( data === undefined && elem.nodeType === 1 ) {
+		name = "data-" + key.replace( rmultiDash, "-$&" ).toLowerCase();
+		data = elem.getAttribute( name );
+
+		if ( typeof data === "string" ) {
+			try {
+				data = getData( data );
+			} catch ( e ) {}
+
+			// Make sure we set the data so it isn't changed later
+			dataUser.set( elem, key, data );
+		} else {
+			data = undefined;
+		}
+	}
+	return data;
+}
+
+jQuery.extend( {
+	hasData: function( elem ) {
+		return dataUser.hasData( elem ) || dataPriv.hasData( elem );
+	},
+
+	data: function( elem, name, data ) {
+		return dataUser.access( elem, name, data );
+	},
+
+	removeData: function( elem, name ) {
+		dataUser.remove( elem, name );
+	},
+
+	// TODO: Now that all calls to _data and _removeData have been replaced
+	// with direct calls to dataPriv methods, these can be deprecated.
+	_data: function( elem, name, data ) {
+		return dataPriv.access( elem, name, data );
+	},
+
+	_removeData: function( elem, name ) {
+		dataPriv.remove( elem, name );
+	}
+} );
+
+jQuery.fn.extend( {
+	data: function( key, value ) {
+		var i, name, data,
+			elem = this[ 0 ],
+			attrs = elem && elem.attributes;
+
+		// Gets all values
+		if ( key === undefined ) {
+			if ( this.length ) {
+				data = dataUser.get( elem );
+
+				if ( elem.nodeType === 1 && !dataPriv.get( elem, "hasDataAttrs" ) ) {
+					i = attrs.length;
+					while ( i-- ) {
+
+						// Support: IE 11 only
+						// The attrs elements can be null (#14894)
+						if ( attrs[ i ] ) {
+							name = attrs[ i ].name;
+							if ( name.indexOf( "data-" ) === 0 ) {
+								name = camelCase( name.slice( 5 ) );
+								dataAttr( elem, name, data[ name ] );
+							}
+						}
+					}
+					dataPriv.set( elem, "hasDataAttrs", true );
+				}
+			}
+
+			return data;
+		}
+
+		// Sets multiple values
+		if ( typeof key === "object" ) {
+			return this.each( function() {
+				dataUser.set( this, key );
+			} );
+		}
+
+		return access( this, function( value ) {
+			var data;
+
+			// The calling jQuery object (element matches) is not empty
+			// (and therefore has an element appears at this[ 0 ]) and the
+			// `value` parameter was not undefined. An empty jQuery object
+			// will result in `undefined` for elem = this[ 0 ] which will
+			// throw an exception if an attempt to read a data cache is made.
+			if ( elem && value === undefined ) {
+
+				// Attempt to get data from the cache
+				// The key will always be camelCased in Data
+				data = dataUser.get( elem, key );
+				if ( data !== undefined ) {
+					return data;
+				}
+
+				// Attempt to "discover" the data in
+				// HTML5 custom data-* attrs
+				data = dataAttr( elem, key );
+				if ( data !== undefined ) {
+					return data;
+				}
+
+				// We tried really hard, but the data doesn't exist.
+				return;
+			}
+
+			// Set the data...
+			this.each( function() {
+
+				// We always store the camelCased key
+				dataUser.set( this, key, value );
+			} );
+		}, null, value, arguments.length > 1, null, true );
+	},
+
+	removeData: function( key ) {
+		return this.each( function() {
+			dataUser.remove( this, key );
+		} );
+	}
+} );
+
+
+jQuery.extend( {
+	queue: function( elem, type, data ) {
+		var queue;
+
+		if ( elem ) {
+			type = ( type || "fx" ) + "queue";
+			queue = dataPriv.get( elem, type );
+
+			// Speed up dequeue by getting out quickly if this is just a lookup
+			if ( data ) {
+				if ( !queue || Array.isArray( data ) ) {
+					queue = dataPriv.access( elem, type, jQuery.makeArray( data ) );
+				} else {
+					queue.push( data );
+				}
+			}
+			return queue || [];
+		}
+	},
+
+	dequeue: function( elem, type ) {
+		type = type || "fx";
+
+		var queue = jQuery.queue( elem, type ),
+			startLength = queue.length,
+			fn = queue.shift(),
+			hooks = jQuery._queueHooks( elem, type ),
+			next = function() {
+				jQuery.dequeue( elem, type );
+			};
+
+		// If the fx queue is dequeued, always remove the progress sentinel
+		if ( fn === "inprogress" ) {
+			fn = queue.shift();
+			startLength--;
+		}
+
+		if ( fn ) {
+
+			// Add a progress sentinel to prevent the fx queue from being
+			// automatically dequeued
+			if ( type === "fx" ) {
+				queue.unshift( "inprogress" );
+			}
+
+			// Clear up the last queue stop function
+			delete hooks.stop;
+			fn.call( elem, next, hooks );
+		}
+
+		if ( !startLength && hooks ) {
+			hooks.empty.fire();
+		}
+	},
+
+	// Not public - generate a queueHooks object, or return the current one
+	_queueHooks: function( elem, type ) {
+		var key = type + "queueHooks";
+		return dataPriv.get( elem, key ) || dataPriv.access( elem, key, {
+			empty: jQuery.Callbacks( "once memory" ).add( function() {
+				dataPriv.remove( elem, [ type + "queue", key ] );
+			} )
+		} );
+	}
+} );
+
+jQuery.fn.extend( {
+	queue: function( type, data ) {
+		var setter = 2;
+
+		if ( typeof type !== "string" ) {
+			data = type;
+			type = "fx";
+			setter--;
+		}
+
+		if ( arguments.length < setter ) {
+			return jQuery.queue( this[ 0 ], type );
+		}
+
+		return data === undefined ?
+			this :
+			this.each( function() {
+				var queue = jQuery.queue( this, type, data );
+
+				// Ensure a hooks for this queue
+				jQuery._queueHooks( this, type );
+
+				if ( type === "fx" && queue[ 0 ] !== "inprogress" ) {
+					jQuery.dequeue( this, type );
+				}
+			} );
+	},
+	dequeue: function( type ) {
+		return this.each( function() {
+			jQuery.dequeue( this, type );
+		} );
+	},
+	clearQueue: function( type ) {
+		return this.queue( type || "fx", [] );
+	},
+
+	// Get a promise resolved when queues of a certain type
+	// are emptied (fx is the type by default)
+	promise: function( type, obj ) {
+		var tmp,
+			count = 1,
+			defer = jQuery.Deferred(),
+			elements = this,
+			i = this.length,
+			resolve = function() {
+				if ( !( --count ) ) {
+					defer.resolveWith( elements, [ elements ] );
+				}
+			};
+
+		if ( typeof type !== "string" ) {
+			obj = type;
+			type = undefined;
+		}
+		type = type || "fx";
+
+		while ( i-- ) {
+			tmp = dataPriv.get( elements[ i ], type + "queueHooks" );
+			if ( tmp && tmp.empty ) {
+				count++;
+				tmp.empty.add( resolve );
+			}
+		}
+		resolve();
+		return defer.promise( obj );
+	}
+} );
+var pnum = ( /[+-]?(?:\d*\.|)\d+(?:[eE][+-]?\d+|)/ ).source;
+
+var rcssNum = new RegExp( "^(?:([+-])=|)(" + pnum + ")([a-z%]*)$", "i" );
+
+
+var cssExpand = [ "Top", "Right", "Bottom", "Left" ];
+
+var documentElement = document.documentElement;
+
+
+
+	var isAttached = function( elem ) {
+			return jQuery.contains( elem.ownerDocument, elem );
+		},
+		composed = { composed: true };
+
+	// Support: IE 9 - 11+, Edge 12 - 18+, iOS 10.0 - 10.2 only
+	// Check attachment across shadow DOM boundaries when possible (gh-3504)
+	// Support: iOS 10.0-10.2 only
+	// Early iOS 10 versions support `attachShadow` but not `getRootNode`,
+	// leading to errors. We need to check for `getRootNode`.
+	if ( documentElement.getRootNode ) {
+		isAttached = function( elem ) {
+			return jQuery.contains( elem.ownerDocument, elem ) ||
+				elem.getRootNode( composed ) === elem.ownerDocument;
+		};
+	}
+var isHiddenWithinTree = function( elem, el ) {
+
+		// isHiddenWithinTree might be called from jQuery#filter function;
+		// in that case, element will be second argument
+		elem = el || elem;
+
+		// Inline style trumps all
+		return elem.style.display === "none" ||
+			elem.style.display === "" &&
+
+			// Otherwise, check computed style
+			// Support: Firefox <=43 - 45
+			// Disconnected elements can have computed display: none, so first confirm that elem is
+			// in the document.
+			isAttached( elem ) &&
+
+			jQuery.css( elem, "display" ) === "none";
+	};
+
+
+
+function adjustCSS( elem, prop, valueParts, tween ) {
+	var adjusted, scale,
+		maxIterations = 20,
+		currentValue = tween ?
+			function() {
+				return tween.cur();
+			} :
+			function() {
+				return jQuery.css( elem, prop, "" );
+			},
+		initial = currentValue(),
+		unit = valueParts && valueParts[ 3 ] || ( jQuery.cssNumber[ prop ] ? "" : "px" ),
+
+		// Starting value computation is required for potential unit mismatches
+		initialInUnit = elem.nodeType &&
+			( jQuery.cssNumber[ prop ] || unit !== "px" && +initial ) &&
+			rcssNum.exec( jQuery.css( elem, prop ) );
+
+	if ( initialInUnit && initialInUnit[ 3 ] !== unit ) {
+
+		// Support: Firefox <=54
+		// Halve the iteration target value to prevent interference from CSS upper bounds (gh-2144)
+		initial = initial / 2;
+
+		// Trust units reported by jQuery.css
+		unit = unit || initialInUnit[ 3 ];
+
+		// Iteratively approximate from a nonzero starting point
+		initialInUnit = +initial || 1;
+
+		while ( maxIterations-- ) {
+
+			// Evaluate and update our best guess (doubling guesses that zero out).
+			// Finish if the scale equals or crosses 1 (making the old*new product non-positive).
+			jQuery.style( elem, prop, initialInUnit + unit );
+			if ( ( 1 - scale ) * ( 1 - ( scale = currentValue() / initial || 0.5 ) ) <= 0 ) {
+				maxIterations = 0;
+			}
+			initialInUnit = initialInUnit / scale;
+
+		}
+
+		initialInUnit = initialInUnit * 2;
+		jQuery.style( elem, prop, initialInUnit + unit );
+
+		// Make sure we update the tween properties later on
+		valueParts = valueParts || [];
+	}
+
+	if ( valueParts ) {
+		initialInUnit = +initialInUnit || +initial || 0;
+
+		// Apply relative offset (+=/-=) if specified
+		adjusted = valueParts[ 1 ] ?
+			initialInUnit + ( valueParts[ 1 ] + 1 ) * valueParts[ 2 ] :
+			+valueParts[ 2 ];
+		if ( tween ) {
+			tween.unit = unit;
+			tween.start = initialInUnit;
+			tween.end = adjusted;
+		}
+	}
+	return adjusted;
+}
+
+
+var defaultDisplayMap = {};
+
+function getDefaultDisplay( elem ) {
+	var temp,
+		doc = elem.ownerDocument,
+		nodeName = elem.nodeName,
+		display = defaultDisplayMap[ nodeName ];
+
+	if ( display ) {
+		return display;
+	}
+
+	temp = doc.body.appendChild( doc.createElement( nodeName ) );
+	display = jQuery.css( temp, "display" );
+
+	temp.parentNode.removeChild( temp );
+
+	if ( display === "none" ) {
+		display = "block";
+	}
+	defaultDisplayMap[ nodeName ] = display;
+
+	return display;
+}
+
+function showHide( elements, show ) {
+	var display, elem,
+		values = [],
+		index = 0,
+		length = elements.length;
+
+	// Determine new display value for elements that need to change
+	for ( ; index < length; index++ ) {
+		elem = elements[ index ];
+		if ( !elem.style ) {
+			continue;
+		}
+
+		display = elem.style.display;
+		if ( show ) {
+
+			// Since we force visibility upon cascade-hidden elements, an immediate (and slow)
+			// check is required in this first loop unless we have a nonempty display value (either
+			// inline or about-to-be-restored)
+			if ( display === "none" ) {
+				values[ index ] = dataPriv.get( elem, "display" ) || null;
+				if ( !values[ index ] ) {
+					elem.style.display = "";
+				}
+			}
+			if ( elem.style.display === "" && isHiddenWithinTree( elem ) ) {
+				values[ index ] = getDefaultDisplay( elem );
+			}
+		} else {
+			if ( display !== "none" ) {
+				values[ index ] = "none";
+
+				// Remember what we're overwriting
+				dataPriv.set( elem, "display", display );
+			}
+		}
+	}
+
+	// Set the display of the elements in a second loop to avoid constant reflow
+	for ( index = 0; index < length; index++ ) {
+		if ( values[ index ] != null ) {
+			elements[ index ].style.display = values[ index ];
+		}
+	}
+
+	return elements;
+}
+
+jQuery.fn.extend( {
+	show: function() {
+		return showHide( this, true );
+	},
+	hide: function() {
+		return showHide( this );
+	},
+	toggle: function( state ) {
+		if ( typeof state === "boolean" ) {
+			return state ? this.show() : this.hide();
+		}
+
+		return this.each( function() {
+			if ( isHiddenWithinTree( this ) ) {
+				jQuery( this ).show();
+			} else {
+				jQuery( this ).hide();
+			}
+		} );
+	}
+} );
+var rcheckableType = ( /^(?:checkbox|radio)$/i );
+
+var rtagName = ( /<([a-z][^\/\0>\x20\t\r\n\f]*)/i );
+
+var rscriptType = ( /^$|^module$|\/(?:java|ecma)script/i );
+
+
+
+( function() {
+	var fragment = document.createDocumentFragment(),
+		div = fragment.appendChild( document.createElement( "div" ) ),
+		input = document.createElement( "input" );
+
+	// Support: Android 4.0 - 4.3 only
+	// Check state lost if the name is set (#11217)
+	// Support: Windows Web Apps (WWA)
+	// `name` and `type` must use .setAttribute for WWA (#14901)
+	input.setAttribute( "type", "radio" );
+	input.setAttribute( "checked", "checked" );
+	input.setAttribute( "name", "t" );
+
+	div.appendChild( input );
+
+	// Support: Android <=4.1 only
+	// Older WebKit doesn't clone checked state correctly in fragments
+	support.checkClone = div.cloneNode( true ).cloneNode( true ).lastChild.checked;
+
+	// Support: IE <=11 only
+	// Make sure textarea (and checkbox) defaultValue is properly cloned
+	div.innerHTML = "<textarea>x</textarea>";
+	support.noCloneChecked = !!div.cloneNode( true ).lastChild.defaultValue;
+
+	// Support: IE <=9 only
+	// IE <=9 replaces <option> tags with their contents when inserted outside of
+	// the select element.
+	div.innerHTML = "<option></option>";
+	support.option = !!div.lastChild;
+} )();
+
+
+// We have to close these tags to support XHTML (#13200)
+var wrapMap = {
+
+	// XHTML parsers do not magically insert elements in the
+	// same way that tag soup parsers do. So we cannot shorten
+	// this by omitting <tbody> or other required elements.
+	thead: [ 1, "<table>", "</table>" ],
+	col: [ 2, "<table><colgroup>", "</colgroup></table>" ],
+	tr: [ 2, "<table><tbody>", "</tbody></table>" ],
+	td: [ 3, "<table><tbody><tr>", "</tr></tbody></table>" ],
+
+	_default: [ 0, "", "" ]
+};
+
+wrapMap.tbody = wrapMap.tfoot = wrapMap.colgroup = wrapMap.caption = wrapMap.thead;
+wrapMap.th = wrapMap.td;
+
+// Support: IE <=9 only
+if ( !support.option ) {
+	wrapMap.optgroup = wrapMap.option = [ 1, "<select multiple='multiple'>", "</select>" ];
+}
+
+
+function getAll( context, tag ) {
+
+	// Support: IE <=9 - 11 only
+	// Use typeof to avoid zero-argument method invocation on host objects (#15151)
+	var ret;
+
+	if ( typeof context.getElementsByTagName !== "undefined" ) {
+		ret = context.getElementsByTagName( tag || "*" );
+
+	} else if ( typeof context.querySelectorAll !== "undefined" ) {
+		ret = context.querySelectorAll( tag || "*" );
+
+	} else {
+		ret = [];
+	}
+
+	if ( tag === undefined || tag && nodeName( context, tag ) ) {
+		return jQuery.merge( [ context ], ret );
+	}
+
+	return ret;
+}
+
+
+// Mark scripts as having already been evaluated
+function setGlobalEval( elems, refElements ) {
+	var i = 0,
+		l = elems.length;
+
+	for ( ; i < l; i++ ) {
+		dataPriv.set(
+			elems[ i ],
+			"globalEval",
+			!refElements || dataPriv.get( refElements[ i ], "globalEval" )
+		);
+	}
+}
+
+
+var rhtml = /<|&#?\w+;/;
+
+function buildFragment( elems, context, scripts, selection, ignored ) {
+	var elem, tmp, tag, wrap, attached, j,
+		fragment = context.createDocumentFragment(),
+		nodes = [],
+		i = 0,
+		l = elems.length;
+
+	for ( ; i < l; i++ ) {
+		elem = elems[ i ];
+
+		if ( elem || elem === 0 ) {
+
+			// Add nodes directly
+			if ( toType( elem ) === "object" ) {
+
+				// Support: Android <=4.0 only, PhantomJS 1 only
+				// push.apply(_, arraylike) throws on ancient WebKit
+				jQuery.merge( nodes, elem.nodeType ? [ elem ] : elem );
+
+			// Convert non-html into a text node
+			} else if ( !rhtml.test( elem ) ) {
+				nodes.push( context.createTextNode( elem ) );
+
+			// Convert html into DOM nodes
+			} else {
+				tmp = tmp || fragment.appendChild( context.createElement( "div" ) );
+
+				// Deserialize a standard representation
+				tag = ( rtagName.exec( elem ) || [ "", "" ] )[ 1 ].toLowerCase();
+				wrap = wrapMap[ tag ] || wrapMap._default;
+				tmp.innerHTML = wrap[ 1 ] + jQuery.htmlPrefilter( elem ) + wrap[ 2 ];
+
+				// Descend through wrappers to the right content
+				j = wrap[ 0 ];
+				while ( j-- ) {
+					tmp = tmp.lastChild;
+				}
+
+				// Support: Android <=4.0 only, PhantomJS 1 only
+				// push.apply(_, arraylike) throws on ancient WebKit
+				jQuery.merge( nodes, tmp.childNodes );
+
+				// Remember the top-level container
+				tmp = fragment.firstChild;
+
+				// Ensure the created nodes are orphaned (#12392)
+				tmp.textContent = "";
+			}
+		}
+	}
+
+	// Remove wrapper from fragment
+	fragment.textContent = "";
+
+	i = 0;
+	while ( ( elem = nodes[ i++ ] ) ) {
+
+		// Skip elements already in the context collection (trac-4087)
+		if ( selection && jQuery.inArray( elem, selection ) > -1 ) {
+			if ( ignored ) {
+				ignored.push( elem );
+			}
+			continue;
+		}
+
+		attached = isAttached( elem );
+
+		// Append to fragment
+		tmp = getAll( fragment.appendChild( elem ), "script" );
+
+		// Preserve script evaluation history
+		if ( attached ) {
+			setGlobalEval( tmp );
+		}
+
+		// Capture executables
+		if ( scripts ) {
+			j = 0;
+			while ( ( elem = tmp[ j++ ] ) ) {
+				if ( rscriptType.test( elem.type || "" ) ) {
+					scripts.push( elem );
+				}
+			}
+		}
+	}
+
+	return fragment;
+}
+
+
+var rtypenamespace = /^([^.]*)(?:\.(.+)|)/;
+
+function returnTrue() {
+	return true;
+}
+
+function returnFalse() {
+	return false;
+}
+
+// Support: IE <=9 - 11+
+// focus() and blur() are asynchronous, except when they are no-op.
+// So expect focus to be synchronous when the element is already active,
+// and blur to be synchronous when the element is not already active.
+// (focus and blur are always synchronous in other supported browsers,
+// this just defines when we can count on it).
+function expectSync( elem, type ) {
+	return ( elem === safeActiveElement() ) === ( type === "focus" );
+}
+
+// Support: IE <=9 only
+// Accessing document.activeElement can throw unexpectedly
+// https://bugs.jquery.com/ticket/13393
+function safeActiveElement() {
+	try {
+		return document.activeElement;
+	} catch ( err ) { }
+}
+
+function on( elem, types, selector, data, fn, one ) {
+	var origFn, type;
+
+	// Types can be a map of types/handlers
+	if ( typeof types === "object" ) {
+
+		// ( types-Object, selector, data )
+		if ( typeof selector !== "string" ) {
+
+			// ( types-Object, data )
+			data = data || selector;
+			selector = undefined;
+		}
+		for ( type in types ) {
+			on( elem, type, selector, data, types[ type ], one );
+		}
+		return elem;
+	}
+
+	if ( data == null && fn == null ) {
+
+		// ( types, fn )
+		fn = selector;
+		data = selector = undefined;
+	} else if ( fn == null ) {
+		if ( typeof selector === "string" ) {
+
+			// ( types, selector, fn )
+			fn = data;
+			data = undefined;
+		} else {
+
+			// ( types, data, fn )
+			fn = data;
+			data = selector;
+			selector = undefined;
+		}
+	}
+	if ( fn === false ) {
+		fn = returnFalse;
+	} else if ( !fn ) {
+		return elem;
+	}
+
+	if ( one === 1 ) {
+		origFn = fn;
+		fn = function( event ) {
+
+			// Can use an empty set, since event contains the info
+			jQuery().off( event );
+			return origFn.apply( this, arguments );
+		};
+
+		// Use same guid so caller can remove using origFn
+		fn.guid = origFn.guid || ( origFn.guid = jQuery.guid++ );
+	}
+	return elem.each( function() {
+		jQuery.event.add( this, types, fn, data, selector );
+	} );
+}
+
+/*
+ * Helper functions for managing events -- not part of the public interface.
+ * Props to Dean Edwards' addEvent library for many of the ideas.
+ */
+jQuery.event = {
+
+	global: {},
+
+	add: function( elem, types, handler, data, selector ) {
+
+		var handleObjIn, eventHandle, tmp,
+			events, t, handleObj,
+			special, handlers, type, namespaces, origType,
+			elemData = dataPriv.get( elem );
+
+		// Only attach events to objects that accept data
+		if ( !acceptData( elem ) ) {
+			return;
+		}
+
+		// Caller can pass in an object of custom data in lieu of the handler
+		if ( handler.handler ) {
+			handleObjIn = handler;
+			handler = handleObjIn.handler;
+			selector = handleObjIn.selector;
+		}
+
+		// Ensure that invalid selectors throw exceptions at attach time
+		// Evaluate against documentElement in case elem is a non-element node (e.g., document)
+		if ( selector ) {
+			jQuery.find.matchesSelector( documentElement, selector );
+		}
+
+		// Make sure that the handler has a unique ID, used to find/remove it later
+		if ( !handler.guid ) {
+			handler.guid = jQuery.guid++;
+		}
+
+		// Init the element's event structure and main handler, if this is the first
+		if ( !( events = elemData.events ) ) {
+			events = elemData.events = Object.create( null );
+		}
+		if ( !( eventHandle = elemData.handle ) ) {
+			eventHandle = elemData.handle = function( e ) {
+
+				// Discard the second event of a jQuery.event.trigger() and
+				// when an event is called after a page has unloaded
+				return typeof jQuery !== "undefined" && jQuery.event.triggered !== e.type ?
+					jQuery.event.dispatch.apply( elem, arguments ) : undefined;
+			};
+		}
+
+		// Handle multiple events separated by a space
+		types = ( types || "" ).match( rnothtmlwhite ) || [ "" ];
+		t = types.length;
+		while ( t-- ) {
+			tmp = rtypenamespace.exec( types[ t ] ) || [];
+			type = origType = tmp[ 1 ];
+			namespaces = ( tmp[ 2 ] || "" ).split( "." ).sort();
+
+			// There *must* be a type, no attaching namespace-only handlers
+			if ( !type ) {
+				continue;
+			}
+
+			// If event changes its type, use the special event handlers for the changed type
+			special = jQuery.event.special[ type ] || {};
+
+			// If selector defined, determine special event api type, otherwise given type
+			type = ( selector ? special.delegateType : special.bindType ) || type;
+
+			// Update special based on newly reset type
+			special = jQuery.event.special[ type ] || {};
+
+			// handleObj is passed to all event handlers
+			handleObj = jQuery.extend( {
+				type: type,
+				origType: origType,
+				data: data,
+				handler: handler,
+				guid: handler.guid,
+				selector: selector,
+				needsContext: selector && jQuery.expr.match.needsContext.test( selector ),
+				namespace: namespaces.join( "." )
+			}, handleObjIn );
+
+			// Init the event handler queue if we're the first
+			if ( !( handlers = events[ type ] ) ) {
+				handlers = events[ type ] = [];
+				handlers.delegateCount = 0;
+
+				// Only use addEventListener if the special events handler returns false
+				if ( !special.setup ||
+					special.setup.call( elem, data, namespaces, eventHandle ) === false ) {
+
+					if ( elem.addEventListener ) {
+						elem.addEventListener( type, eventHandle );
+					}
+				}
+			}
+
+			if ( special.add ) {
+				special.add.call( elem, handleObj );
+
+				if ( !handleObj.handler.guid ) {
+					handleObj.handler.guid = handler.guid;
+				}
+			}
+
+			// Add to the element's handler list, delegates in front
+			if ( selector ) {
+				handlers.splice( handlers.delegateCount++, 0, handleObj );
+			} else {
+				handlers.push( handleObj );
+			}
+
+			// Keep track of which events have ever been used, for event optimization
+			jQuery.event.global[ type ] = true;
+		}
+
+	},
+
+	// Detach an event or set of events from an element
+	remove: function( elem, types, handler, selector, mappedTypes ) {
+
+		var j, origCount, tmp,
+			events, t, handleObj,
+			special, handlers, type, namespaces, origType,
+			elemData = dataPriv.hasData( elem ) && dataPriv.get( elem );
+
+		if ( !elemData || !( events = elemData.events ) ) {
+			return;
+		}
+
+		// Once for each type.namespace in types; type may be omitted
+		types = ( types || "" ).match( rnothtmlwhite ) || [ "" ];
+		t = types.length;
+		while ( t-- ) {
+			tmp = rtypenamespace.exec( types[ t ] ) || [];
+			type = origType = tmp[ 1 ];
+			namespaces = ( tmp[ 2 ] || "" ).split( "." ).sort();
+
+			// Unbind all events (on this namespace, if provided) for the element
+			if ( !type ) {
+				for ( type in events ) {
+					jQuery.event.remove( elem, type + types[ t ], handler, selector, true );
+				}
+				continue;
+			}
+
+			special = jQuery.event.special[ type ] || {};
+			type = ( selector ? special.delegateType : special.bindType ) || type;
+			handlers = events[ type ] || [];
+			tmp = tmp[ 2 ] &&
+				new RegExp( "(^|\\.)" + namespaces.join( "\\.(?:.*\\.|)" ) + "(\\.|$)" );
+
+			// Remove matching events
+			origCount = j = handlers.length;
+			while ( j-- ) {
+				handleObj = handlers[ j ];
+
+				if ( ( mappedTypes || origType === handleObj.origType ) &&
+					( !handler || handler.guid === handleObj.guid ) &&
+					( !tmp || tmp.test( handleObj.namespace ) ) &&
+					( !selector || selector === handleObj.selector ||
+						selector === "**" && handleObj.selector ) ) {
+					handlers.splice( j, 1 );
+
+					if ( handleObj.selector ) {
+						handlers.delegateCount--;
+					}
+					if ( special.remove ) {
+						special.remove.call( elem, handleObj );
+					}
+				}
+			}
+
+			// Remove generic event handler if we removed something and no more handlers exist
+			// (avoids potential for endless recursion during removal of special event handlers)
+			if ( origCount && !handlers.length ) {
+				if ( !special.teardown ||
+					special.teardown.call( elem, namespaces, elemData.handle ) === false ) {
+
+					jQuery.removeEvent( elem, type, elemData.handle );
+				}
+
+				delete events[ type ];
+			}
+		}
+
+		// Remove data and the expando if it's no longer used
+		if ( jQuery.isEmptyObject( events ) ) {
+			dataPriv.remove( elem, "handle events" );
+		}
+	},
+
+	dispatch: function( nativeEvent ) {
+
+		var i, j, ret, matched, handleObj, handlerQueue,
+			args = new Array( arguments.length ),
+
+			// Make a writable jQuery.Event from the native event object
+			event = jQuery.event.fix( nativeEvent ),
+
+			handlers = (
+				dataPriv.get( this, "events" ) || Object.create( null )
+			)[ event.type ] || [],
+			special = jQuery.event.special[ event.type ] || {};
+
+		// Use the fix-ed jQuery.Event rather than the (read-only) native event
+		args[ 0 ] = event;
+
+		for ( i = 1; i < arguments.length; i++ ) {
+			args[ i ] = arguments[ i ];
+		}
+
+		event.delegateTarget = this;
+
+		// Call the preDispatch hook for the mapped type, and let it bail if desired
+		if ( special.preDispatch && special.preDispatch.call( this, event ) === false ) {
+			return;
+		}
+
+		// Determine handlers
+		handlerQueue = jQuery.event.handlers.call( this, event, handlers );
+
+		// Run delegates first; they may want to stop propagation beneath us
+		i = 0;
+		while ( ( matched = handlerQueue[ i++ ] ) && !event.isPropagationStopped() ) {
+			event.currentTarget = matched.elem;
+
+			j = 0;
+			while ( ( handleObj = matched.handlers[ j++ ] ) &&
+				!event.isImmediatePropagationStopped() ) {
+
+				// If the event is namespaced, then each handler is only invoked if it is
+				// specially universal or its namespaces are a superset of the event's.
+				if ( !event.rnamespace || handleObj.namespace === false ||
+					event.rnamespace.test( handleObj.namespace ) ) {
+
+					event.handleObj = handleObj;
+					event.data = handleObj.data;
+
+					ret = ( ( jQuery.event.special[ handleObj.origType ] || {} ).handle ||
+						handleObj.handler ).apply( matched.elem, args );
+
+					if ( ret !== undefined ) {
+						if ( ( event.result = ret ) === false ) {
+							event.preventDefault();
+							event.stopPropagation();
+						}
+					}
+				}
+			}
+		}
+
+		// Call the postDispatch hook for the mapped type
+		if ( special.postDispatch ) {
+			special.postDispatch.call( this, event );
+		}
+
+		return event.result;
+	},
+
+	handlers: function( event, handlers ) {
+		var i, handleObj, sel, matchedHandlers, matchedSelectors,
+			handlerQueue = [],
+			delegateCount = handlers.delegateCount,
+			cur = event.target;
+
+		// Find delegate handlers
+		if ( delegateCount &&
+
+			// Support: IE <=9
+			// Black-hole SVG <use> instance trees (trac-13180)
+			cur.nodeType &&
+
+			// Support: Firefox <=42
+			// Suppress spec-violating clicks indicating a non-primary pointer button (trac-3861)
+			// https://www.w3.org/TR/DOM-Level-3-Events/#event-type-click
+			// Support: IE 11 only
+			// ...but not arrow key "clicks" of radio inputs, which can have `button` -1 (gh-2343)
+			!( event.type === "click" && event.button >= 1 ) ) {
+
+			for ( ; cur !== this; cur = cur.parentNode || this ) {
+
+				// Don't check non-elements (#13208)
+				// Don't process clicks on disabled elements (#6911, #8165, #11382, #11764)
+				if ( cur.nodeType === 1 && !( event.type === "click" && cur.disabled === true ) ) {
+					matchedHandlers = [];
+					matchedSelectors = {};
+					for ( i = 0; i < delegateCount; i++ ) {
+						handleObj = handlers[ i ];
+
+						// Don't conflict with Object.prototype properties (#13203)
+						sel = handleObj.selector + " ";
+
+						if ( matchedSelectors[ sel ] === undefined ) {
+							matchedSelectors[ sel ] = handleObj.needsContext ?
+								jQuery( sel, this ).index( cur ) > -1 :
+								jQuery.find( sel, this, null, [ cur ] ).length;
+						}
+						if ( matchedSelectors[ sel ] ) {
+							matchedHandlers.push( handleObj );
+						}
+					}
+					if ( matchedHandlers.length ) {
+						handlerQueue.push( { elem: cur, handlers: matchedHandlers } );
+					}
+				}
+			}
+		}
+
+		// Add the remaining (directly-bound) handlers
+		cur = this;
+		if ( delegateCount < handlers.length ) {
+			handlerQueue.push( { elem: cur, handlers: handlers.slice( delegateCount ) } );
+		}
+
+		return handlerQueue;
+	},
+
+	addProp: function( name, hook ) {
+		Object.defineProperty( jQuery.Event.prototype, name, {
+			enumerable: true,
+			configurable: true,
+
+			get: isFunction( hook ) ?
+				function() {
+					if ( this.originalEvent ) {
+						return hook( this.originalEvent );
+					}
+				} :
+				function() {
+					if ( this.originalEvent ) {
+						return this.originalEvent[ name ];
+					}
+				},
+
+			set: function( value ) {
+				Object.defineProperty( this, name, {
+					enumerable: true,
+					configurable: true,
+					writable: true,
+					value: value
+				} );
+			}
+		} );
+	},
+
+	fix: function( originalEvent ) {
+		return originalEvent[ jQuery.expando ] ?
+			originalEvent :
+			new jQuery.Event( originalEvent );
+	},
+
+	special: {
+		load: {
+
+			// Prevent triggered image.load events from bubbling to window.load
+			noBubble: true
+		},
+		click: {
+
+			// Utilize native event to ensure correct state for checkable inputs
+			setup: function( data ) {
+
+				// For mutual compressibility with _default, replace `this` access with a local var.
+				// `|| data` is dead code meant only to preserve the variable through minification.
+				var el = this || data;
+
+				// Claim the first handler
+				if ( rcheckableType.test( el.type ) &&
+					el.click && nodeName( el, "input" ) ) {
+
+					// dataPriv.set( el, "click", ... )
+					leverageNative( el, "click", returnTrue );
+				}
+
+				// Return false to allow normal processing in the caller
+				return false;
+			},
+			trigger: function( data ) {
+
+				// For mutual compressibility with _default, replace `this` access with a local var.
+				// `|| data` is dead code meant only to preserve the variable through minification.
+				var el = this || data;
+
+				// Force setup before triggering a click
+				if ( rcheckableType.test( el.type ) &&
+					el.click && nodeName( el, "input" ) ) {
+
+					leverageNative( el, "click" );
+				}
+
+				// Return non-false to allow normal event-path propagation
+				return true;
+			},
+
+			// For cross-browser consistency, suppress native .click() on links
+			// Also prevent it if we're currently inside a leveraged native-event stack
+			_default: function( event ) {
+				var target = event.target;
+				return rcheckableType.test( target.type ) &&
+					target.click && nodeName( target, "input" ) &&
+					dataPriv.get( target, "click" ) ||
+					nodeName( target, "a" );
+			}
+		},
+
+		beforeunload: {
+			postDispatch: function( event ) {
+
+				// Support: Firefox 20+
+				// Firefox doesn't alert if the returnValue field is not set.
+				if ( event.result !== undefined && event.originalEvent ) {
+					event.originalEvent.returnValue = event.result;
+				}
+			}
+		}
+	}
+};
+
+// Ensure the presence of an event listener that handles manually-triggered
+// synthetic events by interrupting progress until reinvoked in response to
+// *native* events that it fires directly, ensuring that state changes have
+// already occurred before other listeners are invoked.
+function leverageNative( el, type, expectSync ) {
+
+	// Missing expectSync indicates a trigger call, which must force setup through jQuery.event.add
+	if ( !expectSync ) {
+		if ( dataPriv.get( el, type ) === undefined ) {
+			jQuery.event.add( el, type, returnTrue );
+		}
+		return;
+	}
+
+	// Register the controller as a special universal handler for all event namespaces
+	dataPriv.set( el, type, false );
+	jQuery.event.add( el, type, {
+		namespace: false,
+		handler: function( event ) {
+			var notAsync, result,
+				saved = dataPriv.get( this, type );
+
+			if ( ( event.isTrigger & 1 ) && this[ type ] ) {
+
+				// Interrupt processing of the outer synthetic .trigger()ed event
+				// Saved data should be false in such cases, but might be a leftover capture object
+				// from an async native handler (gh-4350)
+				if ( !saved.length ) {
+
+					// Store arguments for use when handling the inner native event
+					// There will always be at least one argument (an event object), so this array
+					// will not be confused with a leftover capture object.
+					saved = slice.call( arguments );
+					dataPriv.set( this, type, saved );
+
+					// Trigger the native event and capture its result
+					// Support: IE <=9 - 11+
+					// focus() and blur() are asynchronous
+					notAsync = expectSync( this, type );
+					this[ type ]();
+					result = dataPriv.get( this, type );
+					if ( saved !== result || notAsync ) {
+						dataPriv.set( this, type, false );
+					} else {
+						result = {};
+					}
+					if ( saved !== result ) {
+
+						// Cancel the outer synthetic event
+						event.stopImmediatePropagation();
+						event.preventDefault();
+
+						// Support: Chrome 86+
+						// In Chrome, if an element having a focusout handler is blurred by
+						// clicking outside of it, it invokes the handler synchronously. If
+						// that handler calls `.remove()` on the element, the data is cleared,
+						// leaving `result` undefined. We need to guard against this.
+						return result && result.value;
+					}
+
+				// If this is an inner synthetic event for an event with a bubbling surrogate
+				// (focus or blur), assume that the surrogate already propagated from triggering the
+				// native event and prevent that from happening again here.
+				// This technically gets the ordering wrong w.r.t. to `.trigger()` (in which the
+				// bubbling surrogate propagates *after* the non-bubbling base), but that seems
+				// less bad than duplication.
+				} else if ( ( jQuery.event.special[ type ] || {} ).delegateType ) {
+					event.stopPropagation();
+				}
+
+			// If this is a native event triggered above, everything is now in order
+			// Fire an inner synthetic event with the original arguments
+			} else if ( saved.length ) {
+
+				// ...and capture the result
+				dataPriv.set( this, type, {
+					value: jQuery.event.trigger(
+
+						// Support: IE <=9 - 11+
+						// Extend with the prototype to reset the above stopImmediatePropagation()
+						jQuery.extend( saved[ 0 ], jQuery.Event.prototype ),
+						saved.slice( 1 ),
+						this
+					)
+				} );
+
+				// Abort handling of the native event
+				event.stopImmediatePropagation();
+			}
+		}
+	} );
+}
+
+jQuery.removeEvent = function( elem, type, handle ) {
+
+	// This "if" is needed for plain objects
+	if ( elem.removeEventListener ) {
+		elem.removeEventListener( type, handle );
+	}
+};
+
+jQuery.Event = function( src, props ) {
+
+	// Allow instantiation without the 'new' keyword
+	if ( !( this instanceof jQuery.Event ) ) {
+		return new jQuery.Event( src, props );
+	}
+
+	// Event object
+	if ( src && src.type ) {
+		this.originalEvent = src;
+		this.type = src.type;
+
+		// Events bubbling up the document may have been marked as prevented
+		// by a handler lower down the tree; reflect the correct value.
+		this.isDefaultPrevented = src.defaultPrevented ||
+				src.defaultPrevented === undefined &&
+
+				// Support: Android <=2.3 only
+				src.returnValue === false ?
+			returnTrue :
+			returnFalse;
+
+		// Create target properties
+		// Support: Safari <=6 - 7 only
+		// Target should not be a text node (#504, #13143)
+		this.target = ( src.target && src.target.nodeType === 3 ) ?
+			src.target.parentNode :
+			src.target;
+
+		this.currentTarget = src.currentTarget;
+		this.relatedTarget = src.relatedTarget;
+
+	// Event type
+	} else {
+		this.type = src;
+	}
+
+	// Put explicitly provided properties onto the event object
+	if ( props ) {
+		jQuery.extend( this, props );
+	}
+
+	// Create a timestamp if incoming event doesn't have one
+	this.timeStamp = src && src.timeStamp || Date.now();
+
+	// Mark it as fixed
+	this[ jQuery.expando ] = true;
+};
+
+// jQuery.Event is based on DOM3 Events as specified by the ECMAScript Language Binding
+// https://www.w3.org/TR/2003/WD-DOM-Level-3-Events-20030331/ecma-script-binding.html
+jQuery.Event.prototype = {
+	constructor: jQuery.Event,
+	isDefaultPrevented: returnFalse,
+	isPropagationStopped: returnFalse,
+	isImmediatePropagationStopped: returnFalse,
+	isSimulated: false,
+
+	preventDefault: function() {
+		var e = this.originalEvent;
+
+		this.isDefaultPrevented = returnTrue;
+
+		if ( e && !this.isSimulated ) {
+			e.preventDefault();
+		}
+	},
+	stopPropagation: function() {
+		var e = this.originalEvent;
+
+		this.isPropagationStopped = returnTrue;
+
+		if ( e && !this.isSimulated ) {
+			e.stopPropagation();
+		}
+	},
+	stopImmediatePropagation: function() {
+		var e = this.originalEvent;
+
+		this.isImmediatePropagationStopped = returnTrue;
+
+		if ( e && !this.isSimulated ) {
+			e.stopImmediatePropagation();
+		}
+
+		this.stopPropagation();
+	}
+};
+
+// Includes all common event props including KeyEvent and MouseEvent specific props
+jQuery.each( {
+	altKey: true,
+	bubbles: true,
+	cancelable: true,
+	changedTouches: true,
+	ctrlKey: true,
+	detail: true,
+	eventPhase: true,
+	metaKey: true,
+	pageX: true,
+	pageY: true,
+	shiftKey: true,
+	view: true,
+	"char": true,
+	code: true,
+	charCode: true,
+	key: true,
+	keyCode: true,
+	button: true,
+	buttons: true,
+	clientX: true,
+	clientY: true,
+	offsetX: true,
+	offsetY: true,
+	pointerId: true,
+	pointerType: true,
+	screenX: true,
+	screenY: true,
+	targetTouches: true,
+	toElement: true,
+	touches: true,
+	which: true
+}, jQuery.event.addProp );
+
+jQuery.each( { focus: "focusin", blur: "focusout" }, function( type, delegateType ) {
+	jQuery.event.special[ type ] = {
+
+		// Utilize native event if possible so blur/focus sequence is correct
+		setup: function() {
+
+			// Claim the first handler
+			// dataPriv.set( this, "focus", ... )
+			// dataPriv.set( this, "blur", ... )
+			leverageNative( this, type, expectSync );
+
+			// Return false to allow normal processing in the caller
+			return false;
+		},
+		trigger: function() {
+
+			// Force setup before trigger
+			leverageNative( this, type );
+
+			// Return non-false to allow normal event-path propagation
+			return true;
+		},
+
+		// Suppress native focus or blur as it's already being fired
+		// in leverageNative.
+		_default: function() {
+			return true;
+		},
+
+		delegateType: delegateType
+	};
+} );
+
+// Create mouseenter/leave events using mouseover/out and event-time checks
+// so that event delegation works in jQuery.
+// Do the same for pointerenter/pointerleave and pointerover/pointerout
+//
+// Support: Safari 7 only
+// Safari sends mouseenter too often; see:
+// https://bugs.chromium.org/p/chromium/issues/detail?id=470258
+// for the description of the bug (it existed in older Chrome versions as well).
+jQuery.each( {
+	mouseenter: "mouseover",
+	mouseleave: "mouseout",
+	pointerenter: "pointerover",
+	pointerleave: "pointerout"
+}, function( orig, fix ) {
+	jQuery.event.special[ orig ] = {
+		delegateType: fix,
+		bindType: fix,
+
+		handle: function( event ) {
+			var ret,
+				target = this,
+				related = event.relatedTarget,
+				handleObj = event.handleObj;
+
+			// For mouseenter/leave call the handler if related is outside the target.
+			// NB: No relatedTarget if the mouse left/entered the browser window
+			if ( !related || ( related !== target && !jQuery.contains( target, related ) ) ) {
+				event.type = handleObj.origType;
+				ret = handleObj.handler.apply( this, arguments );
+				event.type = fix;
+			}
+			return ret;
+		}
+	};
+} );
+
+jQuery.fn.extend( {
+
+	on: function( types, selector, data, fn ) {
+		return on( this, types, selector, data, fn );
+	},
+	one: function( types, selector, data, fn ) {
+		return on( this, types, selector, data, fn, 1 );
+	},
+	off: function( types, selector, fn ) {
+		var handleObj, type;
+		if ( types && types.preventDefault && types.handleObj ) {
+
+			// ( event )  dispatched jQuery.Event
+			handleObj = types.handleObj;
+			jQuery( types.delegateTarget ).off(
+				handleObj.namespace ?
+					handleObj.origType + "." + handleObj.namespace :
+					handleObj.origType,
+				handleObj.selector,
+				handleObj.handler
+			);
+			return this;
+		}
+		if ( typeof types === "object" ) {
+
+			// ( types-object [, selector] )
+			for ( type in types ) {
+				this.off( type, selector, types[ type ] );
+			}
+			return this;
+		}
+		if ( selector === false || typeof selector === "function" ) {
+
+			// ( types [, fn] )
+			fn = selector;
+			selector = undefined;
+		}
+		if ( fn === false ) {
+			fn = returnFalse;
+		}
+		return this.each( function() {
+			jQuery.event.remove( this, types, fn, selector );
+		} );
+	}
+} );
+
+
+var
+
+	// Support: IE <=10 - 11, Edge 12 - 13 only
+	// In IE/Edge using regex groups here causes severe slowdowns.
+	// See https://connect.microsoft.com/IE/feedback/details/1736512/
+	rnoInnerhtml = /<script|<style|<link/i,
+
+	// checked="checked" or checked
+	rchecked = /checked\s*(?:[^=]|=\s*.checked.)/i,
+	rcleanScript = /^\s*<!(?:\[CDATA\[|--)|(?:\]\]|--)>\s*$/g;
+
+// Prefer a tbody over its parent table for containing new rows
+function manipulationTarget( elem, content ) {
+	if ( nodeName( elem, "table" ) &&
+		nodeName( content.nodeType !== 11 ? content : content.firstChild, "tr" ) ) {
+
+		return jQuery( elem ).children( "tbody" )[ 0 ] || elem;
+	}
+
+	return elem;
+}
+
+// Replace/restore the type attribute of script elements for safe DOM manipulation
+function disableScript( elem ) {
+	elem.type = ( elem.getAttribute( "type" ) !== null ) + "/" + elem.type;
+	return elem;
+}
+function restoreScript( elem ) {
+	if ( ( elem.type || "" ).slice( 0, 5 ) === "true/" ) {
+		elem.type = elem.type.slice( 5 );
+	} else {
+		elem.removeAttribute( "type" );
+	}
+
+	return elem;
+}
+
+function cloneCopyEvent( src, dest ) {
+	var i, l, type, pdataOld, udataOld, udataCur, events;
+
+	if ( dest.nodeType !== 1 ) {
+		return;
+	}
+
+	// 1. Copy private data: events, handlers, etc.
+	if ( dataPriv.hasData( src ) ) {
+		pdataOld = dataPriv.get( src );
+		events = pdataOld.events;
+
+		if ( events ) {
+			dataPriv.remove( dest, "handle events" );
+
+			for ( type in events ) {
+				for ( i = 0, l = events[ type ].length; i < l; i++ ) {
+					jQuery.event.add( dest, type, events[ type ][ i ] );
+				}
+			}
+		}
+	}
+
+	// 2. Copy user data
+	if ( dataUser.hasData( src ) ) {
+		udataOld = dataUser.access( src );
+		udataCur = jQuery.extend( {}, udataOld );
+
+		dataUser.set( dest, udataCur );
+	}
+}
+
+// Fix IE bugs, see support tests
+function fixInput( src, dest ) {
+	var nodeName = dest.nodeName.toLowerCase();
+
+	// Fails to persist the checked state of a cloned checkbox or radio button.
+	if ( nodeName === "input" && rcheckableType.test( src.type ) ) {
+		dest.checked = src.checked;
+
+	// Fails to return the selected option to the default selected state when cloning options
+	} else if ( nodeName === "input" || nodeName === "textarea" ) {
+		dest.defaultValue = src.defaultValue;
+	}
+}
+
+function domManip( collection, args, callback, ignored ) {
+
+	// Flatten any nested arrays
+	args = flat( args );
+
+	var fragment, first, scripts, hasScripts, node, doc,
+		i = 0,
+		l = collection.length,
+		iNoClone = l - 1,
+		value = args[ 0 ],
+		valueIsFunction = isFunction( value );
+
+	// We can't cloneNode fragments that contain checked, in WebKit
+	if ( valueIsFunction ||
+			( l > 1 && typeof value === "string" &&
+				!support.checkClone && rchecked.test( value ) ) ) {
+		return collection.each( function( index ) {
+			var self = collection.eq( index );
+			if ( valueIsFunction ) {
+				args[ 0 ] = value.call( this, index, self.html() );
+			}
+			domManip( self, args, callback, ignored );
+		} );
+	}
+
+	if ( l ) {
+		fragment = buildFragment( args, collection[ 0 ].ownerDocument, false, collection, ignored );
+		first = fragment.firstChild;
+
+		if ( fragment.childNodes.length === 1 ) {
+			fragment = first;
+		}
+
+		// Require either new content or an interest in ignored elements to invoke the callback
+		if ( first || ignored ) {
+			scripts = jQuery.map( getAll( fragment, "script" ), disableScript );
+			hasScripts = scripts.length;
+
+			// Use the original fragment for the last item
+			// instead of the first because it can end up
+			// being emptied incorrectly in certain situations (#8070).
+			for ( ; i < l; i++ ) {
+				node = fragment;
+
+				if ( i !== iNoClone ) {
+					node = jQuery.clone( node, true, true );
+
+					// Keep references to cloned scripts for later restoration
+					if ( hasScripts ) {
+
+						// Support: Android <=4.0 only, PhantomJS 1 only
+						// push.apply(_, arraylike) throws on ancient WebKit
+						jQuery.merge( scripts, getAll( node, "script" ) );
+					}
+				}
+
+				callback.call( collection[ i ], node, i );
+			}
+
+			if ( hasScripts ) {
+				doc = scripts[ scripts.length - 1 ].ownerDocument;
+
+				// Reenable scripts
+				jQuery.map( scripts, restoreScript );
+
+				// Evaluate executable scripts on first document insertion
+				for ( i = 0; i < hasScripts; i++ ) {
+					node = scripts[ i ];
+					if ( rscriptType.test( node.type || "" ) &&
+						!dataPriv.access( node, "globalEval" ) &&
+						jQuery.contains( doc, node ) ) {
+
+						if ( node.src && ( node.type || "" ).toLowerCase()  !== "module" ) {
+
+							// Optional AJAX dependency, but won't run scripts if not present
+							if ( jQuery._evalUrl && !node.noModule ) {
+								jQuery._evalUrl( node.src, {
+									nonce: node.nonce || node.getAttribute( "nonce" )
+								}, doc );
+							}
+						} else {
+							DOMEval( node.textContent.replace( rcleanScript, "" ), node, doc );
+						}
+					}
+				}
+			}
+		}
+	}
+
+	return collection;
+}
+
+function remove( elem, selector, keepData ) {
+	var node,
+		nodes = selector ? jQuery.filter( selector, elem ) : elem,
+		i = 0;
+
+	for ( ; ( node = nodes[ i ] ) != null; i++ ) {
+		if ( !keepData && node.nodeType === 1 ) {
+			jQuery.cleanData( getAll( node ) );
+		}
+
+		if ( node.parentNode ) {
+			if ( keepData && isAttached( node ) ) {
+				setGlobalEval( getAll( node, "script" ) );
+			}
+			node.parentNode.removeChild( node );
+		}
+	}
+
+	return elem;
+}
+
+jQuery.extend( {
+	htmlPrefilter: function( html ) {
+		return html;
+	},
+
+	clone: function( elem, dataAndEvents, deepDataAndEvents ) {
+		var i, l, srcElements, destElements,
+			clone = elem.cloneNode( true ),
+			inPage = isAttached( elem );
+
+		// Fix IE cloning issues
+		if ( !support.noCloneChecked && ( elem.nodeType === 1 || elem.nodeType === 11 ) &&
+				!jQuery.isXMLDoc( elem ) ) {
+
+			// We eschew Sizzle here for performance reasons: https://jsperf.com/getall-vs-sizzle/2
+			destElements = getAll( clone );
+			srcElements = getAll( elem );
+
+			for ( i = 0, l = srcElements.length; i < l; i++ ) {
+				fixInput( srcElements[ i ], destElements[ i ] );
+			}
+		}
+
+		// Copy the events from the original to the clone
+		if ( dataAndEvents ) {
+			if ( deepDataAndEvents ) {
+				srcElements = srcElements || getAll( elem );
+				destElements = destElements || getAll( clone );
+
+				for ( i = 0, l = srcElements.length; i < l; i++ ) {
+					cloneCopyEvent( srcElements[ i ], destElements[ i ] );
+				}
+			} else {
+				cloneCopyEvent( elem, clone );
+			}
+		}
+
+		// Preserve script evaluation history
+		destElements = getAll( clone, "script" );
+		if ( destElements.length > 0 ) {
+			setGlobalEval( destElements, !inPage && getAll( elem, "script" ) );
+		}
+
+		// Return the cloned set
+		return clone;
+	},
+
+	cleanData: function( elems ) {
+		var data, elem, type,
+			special = jQuery.event.special,
+			i = 0;
+
+		for ( ; ( elem = elems[ i ] ) !== undefined; i++ ) {
+			if ( acceptData( elem ) ) {
+				if ( ( data = elem[ dataPriv.expando ] ) ) {
+					if ( data.events ) {
+						for ( type in data.events ) {
+							if ( special[ type ] ) {
+								jQuery.event.remove( elem, type );
+
+							// This is a shortcut to avoid jQuery.event.remove's overhead
+							} else {
+								jQuery.removeEvent( elem, type, data.handle );
+							}
+						}
+					}
+
+					// Support: Chrome <=35 - 45+
+					// Assign undefined instead of using delete, see Data#remove
+					elem[ dataPriv.expando ] = undefined;
+				}
+				if ( elem[ dataUser.expando ] ) {
+
+					// Support: Chrome <=35 - 45+
+					// Assign undefined instead of using delete, see Data#remove
+					elem[ dataUser.expando ] = undefined;
+				}
+			}
+		}
+	}
+} );
+
+jQuery.fn.extend( {
+	detach: function( selector ) {
+		return remove( this, selector, true );
+	},
+
+	remove: function( selector ) {
+		return remove( this, selector );
+	},
+
+	text: function( value ) {
+		return access( this, function( value ) {
+			return value === undefined ?
+				jQuery.text( this ) :
+				this.empty().each( function() {
+					if ( this.nodeType === 1 || this.nodeType === 11 || this.nodeType === 9 ) {
+						this.textContent = value;
+					}
+				} );
+		}, null, value, arguments.length );
+	},
+
+	append: function() {
+		return domManip( this, arguments, function( elem ) {
+			if ( this.nodeType === 1 || this.nodeType === 11 || this.nodeType === 9 ) {
+				var target = manipulationTarget( this, elem );
+				target.appendChild( elem );
+			}
+		} );
+	},
+
+	prepend: function() {
+		return domManip( this, arguments, function( elem ) {
+			if ( this.nodeType === 1 || this.nodeType === 11 || this.nodeType === 9 ) {
+				var target = manipulationTarget( this, elem );
+				target.insertBefore( elem, target.firstChild );
+			}
+		} );
+	},
+
+	before: function() {
+		return domManip( this, arguments, function( elem ) {
+			if ( this.parentNode ) {
+				this.parentNode.insertBefore( elem, this );
+			}
+		} );
+	},
+
+	after: function() {
+		return domManip( this, arguments, function( elem ) {
+			if ( this.parentNode ) {
+				this.parentNode.insertBefore( elem, this.nextSibling );
+			}
+		} );
+	},
+
+	empty: function() {
+		var elem,
+			i = 0;
+
+		for ( ; ( elem = this[ i ] ) != null; i++ ) {
+			if ( elem.nodeType === 1 ) {
+
+				// Prevent memory leaks
+				jQuery.cleanData( getAll( elem, false ) );
+
+				// Remove any remaining nodes
+				elem.textContent = "";
+			}
+		}
+
+		return this;
+	},
+
+	clone: function( dataAndEvents, deepDataAndEvents ) {
+		dataAndEvents = dataAndEvents == null ? false : dataAndEvents;
+		deepDataAndEvents = deepDataAndEvents == null ? dataAndEvents : deepDataAndEvents;
+
+		return this.map( function() {
+			return jQuery.clone( this, dataAndEvents, deepDataAndEvents );
+		} );
+	},
+
+	html: function( value ) {
+		return access( this, function( value ) {
+			var elem = this[ 0 ] || {},
+				i = 0,
+				l = this.length;
+
+			if ( value === undefined && elem.nodeType === 1 ) {
+				return elem.innerHTML;
+			}
+
+			// See if we can take a shortcut and just use innerHTML
+			if ( typeof value === "string" && !rnoInnerhtml.test( value ) &&
+				!wrapMap[ ( rtagName.exec( value ) || [ "", "" ] )[ 1 ].toLowerCase() ] ) {
+
+				value = jQuery.htmlPrefilter( value );
+
+				try {
+					for ( ; i < l; i++ ) {
+						elem = this[ i ] || {};
+
+						// Remove element nodes and prevent memory leaks
+						if ( elem.nodeType === 1 ) {
+							jQuery.cleanData( getAll( elem, false ) );
+							elem.innerHTML = value;
+						}
+					}
+
+					elem = 0;
+
+				// If using innerHTML throws an exception, use the fallback method
+				} catch ( e ) {}
+			}
+
+			if ( elem ) {
+				this.empty().append( value );
+			}
+		}, null, value, arguments.length );
+	},
+
+	replaceWith: function() {
+		var ignored = [];
+
+		// Make the changes, replacing each non-ignored context element with the new content
+		return domManip( this, arguments, function( elem ) {
+			var parent = this.parentNode;
+
+			if ( jQuery.inArray( this, ignored ) < 0 ) {
+				jQuery.cleanData( getAll( this ) );
+				if ( parent ) {
+					parent.replaceChild( elem, this );
+				}
+			}
+
+		// Force callback invocation
+		}, ignored );
+	}
+} );
+
+jQuery.each( {
+	appendTo: "append",
+	prependTo: "prepend",
+	insertBefore: "before",
+	insertAfter: "after",
+	replaceAll: "replaceWith"
+}, function( name, original ) {
+	jQuery.fn[ name ] = function( selector ) {
+		var elems,
+			ret = [],
+			insert = jQuery( selector ),
+			last = insert.length - 1,
+			i = 0;
+
+		for ( ; i <= last; i++ ) {
+			elems = i === last ? this : this.clone( true );
+			jQuery( insert[ i ] )[ original ]( elems );
+
+			// Support: Android <=4.0 only, PhantomJS 1 only
+			// .get() because push.apply(_, arraylike) throws on ancient WebKit
+			push.apply( ret, elems.get() );
+		}
+
+		return this.pushStack( ret );
+	};
+} );
+var rnumnonpx = new RegExp( "^(" + pnum + ")(?!px)[a-z%]+$", "i" );
+
+var getStyles = function( elem ) {
+
+		// Support: IE <=11 only, Firefox <=30 (#15098, #14150)
+		// IE throws on elements created in popups
+		// FF meanwhile throws on frame elements through "defaultView.getComputedStyle"
+		var view = elem.ownerDocument.defaultView;
+
+		if ( !view || !view.opener ) {
+			view = window;
+		}
+
+		return view.getComputedStyle( elem );
+	};
+
+var swap = function( elem, options, callback ) {
+	var ret, name,
+		old = {};
+
+	// Remember the old values, and insert the new ones
+	for ( name in options ) {
+		old[ name ] = elem.style[ name ];
+		elem.style[ name ] = options[ name ];
+	}
+
+	ret = callback.call( elem );
+
+	// Revert the old values
+	for ( name in options ) {
+		elem.style[ name ] = old[ name ];
+	}
+
+	return ret;
+};
+
+
+var rboxStyle = new RegExp( cssExpand.join( "|" ), "i" );
+
+
+
+( function() {
+
+	// Executing both pixelPosition & boxSizingReliable tests require only one layout
+	// so they're executed at the same time to save the second computation.
+	function computeStyleTests() {
+
+		// This is a singleton, we need to execute it only once
+		if ( !div ) {
+			return;
+		}
+
+		container.style.cssText = "position:absolute;left:-11111px;width:60px;" +
+			"margin-top:1px;padding:0;border:0";
+		div.style.cssText =
+			"position:relative;display:block;box-sizing:border-box;overflow:scroll;" +
+			"margin:auto;border:1px;padding:1px;" +
+			"width:60%;top:1%";
+		documentElement.appendChild( container ).appendChild( div );
+
+		var divStyle = window.getComputedStyle( div );
+		pixelPositionVal = divStyle.top !== "1%";
+
+		// Support: Android 4.0 - 4.3 only, Firefox <=3 - 44
+		reliableMarginLeftVal = roundPixelMeasures( divStyle.marginLeft ) === 12;
+
+		// Support: Android 4.0 - 4.3 only, Safari <=9.1 - 10.1, iOS <=7.0 - 9.3
+		// Some styles come back with percentage values, even though they shouldn't
+		div.style.right = "60%";
+		pixelBoxStylesVal = roundPixelMeasures( divStyle.right ) === 36;
+
+		// Support: IE 9 - 11 only
+		// Detect misreporting of content dimensions for box-sizing:border-box elements
+		boxSizingReliableVal = roundPixelMeasures( divStyle.width ) === 36;
+
+		// Support: IE 9 only
+		// Detect overflow:scroll screwiness (gh-3699)
+		// Support: Chrome <=64
+		// Don't get tricked when zoom affects offsetWidth (gh-4029)
+		div.style.position = "absolute";
+		scrollboxSizeVal = roundPixelMeasures( div.offsetWidth / 3 ) === 12;
+
+		documentElement.removeChild( container );
+
+		// Nullify the div so it wouldn't be stored in the memory and
+		// it will also be a sign that checks already performed
+		div = null;
+	}
+
+	function roundPixelMeasures( measure ) {
+		return Math.round( parseFloat( measure ) );
+	}
+
+	var pixelPositionVal, boxSizingReliableVal, scrollboxSizeVal, pixelBoxStylesVal,
+		reliableTrDimensionsVal, reliableMarginLeftVal,
+		container = document.createElement( "div" ),
+		div = document.createElement( "div" );
+
+	// Finish early in limited (non-browser) environments
+	if ( !div.style ) {
+		return;
+	}
+
+	// Support: IE <=9 - 11 only
+	// Style of cloned element affects source element cloned (#8908)
+	div.style.backgroundClip = "content-box";
+	div.cloneNode( true ).style.backgroundClip = "";
+	support.clearCloneStyle = div.style.backgroundClip === "content-box";
+
+	jQuery.extend( support, {
+		boxSizingReliable: function() {
+			computeStyleTests();
+			return boxSizingReliableVal;
+		},
+		pixelBoxStyles: function() {
+			computeStyleTests();
+			return pixelBoxStylesVal;
+		},
+		pixelPosition: function() {
+			computeStyleTests();
+			return pixelPositionVal;
+		},
+		reliableMarginLeft: function() {
+			computeStyleTests();
+			return reliableMarginLeftVal;
+		},
+		scrollboxSize: function() {
+			computeStyleTests();
+			return scrollboxSizeVal;
+		},
+
+		// Support: IE 9 - 11+, Edge 15 - 18+
+		// IE/Edge misreport `getComputedStyle` of table rows with width/height
+		// set in CSS while `offset*` properties report correct values.
+		// Behavior in IE 9 is more subtle than in newer versions & it passes
+		// some versions of this test; make sure not to make it pass there!
+		//
+		// Support: Firefox 70+
+		// Only Firefox includes border widths
+		// in computed dimensions. (gh-4529)
+		reliableTrDimensions: function() {
+			var table, tr, trChild, trStyle;
+			if ( reliableTrDimensionsVal == null ) {
+				table = document.createElement( "table" );
+				tr = document.createElement( "tr" );
+				trChild = document.createElement( "div" );
+
+				table.style.cssText = "position:absolute;left:-11111px;border-collapse:separate";
+				tr.style.cssText = "border:1px solid";
+
+				// Support: Chrome 86+
+				// Height set through cssText does not get applied.
+				// Computed height then comes back as 0.
+				tr.style.height = "1px";
+				trChild.style.height = "9px";
+
+				// Support: Android 8 Chrome 86+
+				// In our bodyBackground.html iframe,
+				// display for all div elements is set to "inline",
+				// which causes a problem only in Android 8 Chrome 86.
+				// Ensuring the div is display: block
+				// gets around this issue.
+				trChild.style.display = "block";
+
+				documentElement
+					.appendChild( table )
+					.appendChild( tr )
+					.appendChild( trChild );
+
+				trStyle = window.getComputedStyle( tr );
+				reliableTrDimensionsVal = ( parseInt( trStyle.height, 10 ) +
+					parseInt( trStyle.borderTopWidth, 10 ) +
+					parseInt( trStyle.borderBottomWidth, 10 ) ) === tr.offsetHeight;
+
+				documentElement.removeChild( table );
+			}
+			return reliableTrDimensionsVal;
+		}
+	} );
+} )();
+
+
+function curCSS( elem, name, computed ) {
+	var width, minWidth, maxWidth, ret,
+
+		// Support: Firefox 51+
+		// Retrieving style before computed somehow
+		// fixes an issue with getting wrong values
+		// on detached elements
+		style = elem.style;
+
+	computed = computed || getStyles( elem );
+
+	// getPropertyValue is needed for:
+	//   .css('filter') (IE 9 only, #12537)
+	//   .css('--customProperty) (#3144)
+	if ( computed ) {
+		ret = computed.getPropertyValue( name ) || computed[ name ];
+
+		if ( ret === "" && !isAttached( elem ) ) {
+			ret = jQuery.style( elem, name );
+		}
+
+		// A tribute to the "awesome hack by Dean Edwards"
+		// Android Browser returns percentage for some values,
+		// but width seems to be reliably pixels.
+		// This is against the CSSOM draft spec:
+		// https://drafts.csswg.org/cssom/#resolved-values
+		if ( !support.pixelBoxStyles() && rnumnonpx.test( ret ) && rboxStyle.test( name ) ) {
+
+			// Remember the original values
+			width = style.width;
+			minWidth = style.minWidth;
+			maxWidth = style.maxWidth;
+
+			// Put in the new values to get a computed value out
+			style.minWidth = style.maxWidth = style.width = ret;
+			ret = computed.width;
+
+			// Revert the changed values
+			style.width = width;
+			style.minWidth = minWidth;
+			style.maxWidth = maxWidth;
+		}
+	}
+
+	return ret !== undefined ?
+
+		// Support: IE <=9 - 11 only
+		// IE returns zIndex value as an integer.
+		ret + "" :
+		ret;
+}
+
+
+function addGetHookIf( conditionFn, hookFn ) {
+
+	// Define the hook, we'll check on the first run if it's really needed.
+	return {
+		get: function() {
+			if ( conditionFn() ) {
+
+				// Hook not needed (or it's not possible to use it due
+				// to missing dependency), remove it.
+				delete this.get;
+				return;
+			}
+
+			// Hook needed; redefine it so that the support test is not executed again.
+			return ( this.get = hookFn ).apply( this, arguments );
+		}
+	};
+}
+
+
+var cssPrefixes = [ "Webkit", "Moz", "ms" ],
+	emptyStyle = document.createElement( "div" ).style,
+	vendorProps = {};
+
+// Return a vendor-prefixed property or undefined
+function vendorPropName( name ) {
+
+	// Check for vendor prefixed names
+	var capName = name[ 0 ].toUpperCase() + name.slice( 1 ),
+		i = cssPrefixes.length;
+
+	while ( i-- ) {
+		name = cssPrefixes[ i ] + capName;
+		if ( name in emptyStyle ) {
+			return name;
+		}
+	}
+}
+
+// Return a potentially-mapped jQuery.cssProps or vendor prefixed property
+function finalPropName( name ) {
+	var final = jQuery.cssProps[ name ] || vendorProps[ name ];
+
+	if ( final ) {
+		return final;
+	}
+	if ( name in emptyStyle ) {
+		return name;
+	}
+	return vendorProps[ name ] = vendorPropName( name ) || name;
+}
+
+
+var
+
+	// Swappable if display is none or starts with table
+	// except "table", "table-cell", or "table-caption"
+	// See here for display values: https://developer.mozilla.org/en-US/docs/CSS/display
+	rdisplayswap = /^(none|table(?!-c[ea]).+)/,
+	rcustomProp = /^--/,
+	cssShow = { position: "absolute", visibility: "hidden", display: "block" },
+	cssNormalTransform = {
+		letterSpacing: "0",
+		fontWeight: "400"
+	};
+
+function setPositiveNumber( _elem, value, subtract ) {
+
+	// Any relative (+/-) values have already been
+	// normalized at this point
+	var matches = rcssNum.exec( value );
+	return matches ?
+
+		// Guard against undefined "subtract", e.g., when used as in cssHooks
+		Math.max( 0, matches[ 2 ] - ( subtract || 0 ) ) + ( matches[ 3 ] || "px" ) :
+		value;
+}
+
+function boxModelAdjustment( elem, dimension, box, isBorderBox, styles, computedVal ) {
+	var i = dimension === "width" ? 1 : 0,
+		extra = 0,
+		delta = 0;
+
+	// Adjustment may not be necessary
+	if ( box === ( isBorderBox ? "border" : "content" ) ) {
+		return 0;
+	}
+
+	for ( ; i < 4; i += 2 ) {
+
+		// Both box models exclude margin
+		if ( box === "margin" ) {
+			delta += jQuery.css( elem, box + cssExpand[ i ], true, styles );
+		}
+
+		// If we get here with a content-box, we're seeking "padding" or "border" or "margin"
+		if ( !isBorderBox ) {
+
+			// Add padding
+			delta += jQuery.css( elem, "padding" + cssExpand[ i ], true, styles );
+
+			// For "border" or "margin", add border
+			if ( box !== "padding" ) {
+				delta += jQuery.css( elem, "border" + cssExpand[ i ] + "Width", true, styles );
+
+			// But still keep track of it otherwise
+			} else {
+				extra += jQuery.css( elem, "border" + cssExpand[ i ] + "Width", true, styles );
+			}
+
+		// If we get here with a border-box (content + padding + border), we're seeking "content" or
+		// "padding" or "margin"
+		} else {
+
+			// For "content", subtract padding
+			if ( box === "content" ) {
+				delta -= jQuery.css( elem, "padding" + cssExpand[ i ], true, styles );
+			}
+
+			// For "content" or "padding", subtract border
+			if ( box !== "margin" ) {
+				delta -= jQuery.css( elem, "border" + cssExpand[ i ] + "Width", true, styles );
+			}
+		}
+	}
+
+	// Account for positive content-box scroll gutter when requested by providing computedVal
+	if ( !isBorderBox && computedVal >= 0 ) {
+
+		// offsetWidth/offsetHeight is a rounded sum of content, padding, scroll gutter, and border
+		// Assuming integer scroll gutter, subtract the rest and round down
+		delta += Math.max( 0, Math.ceil(
+			elem[ "offset" + dimension[ 0 ].toUpperCase() + dimension.slice( 1 ) ] -
+			computedVal -
+			delta -
+			extra -
+			0.5
+
+		// If offsetWidth/offsetHeight is unknown, then we can't determine content-box scroll gutter
+		// Use an explicit zero to avoid NaN (gh-3964)
+		) ) || 0;
+	}
+
+	return delta;
+}
+
+function getWidthOrHeight( elem, dimension, extra ) {
+
+	// Start with computed style
+	var styles = getStyles( elem ),
+
+		// To avoid forcing a reflow, only fetch boxSizing if we need it (gh-4322).
+		// Fake content-box until we know it's needed to know the true value.
+		boxSizingNeeded = !support.boxSizingReliable() || extra,
+		isBorderBox = boxSizingNeeded &&
+			jQuery.css( elem, "boxSizing", false, styles ) === "border-box",
+		valueIsBorderBox = isBorderBox,
+
+		val = curCSS( elem, dimension, styles ),
+		offsetProp = "offset" + dimension[ 0 ].toUpperCase() + dimension.slice( 1 );
+
+	// Support: Firefox <=54
+	// Return a confounding non-pixel value or feign ignorance, as appropriate.
+	if ( rnumnonpx.test( val ) ) {
+		if ( !extra ) {
+			return val;
+		}
+		val = "auto";
+	}
+
+
+	// Support: IE 9 - 11 only
+	// Use offsetWidth/offsetHeight for when box sizing is unreliable.
+	// In those cases, the computed value can be trusted to be border-box.
+	if ( ( !support.boxSizingReliable() && isBorderBox ||
+
+		// Support: IE 10 - 11+, Edge 15 - 18+
+		// IE/Edge misreport `getComputedStyle` of table rows with width/height
+		// set in CSS while `offset*` properties report correct values.
+		// Interestingly, in some cases IE 9 doesn't suffer from this issue.
+		!support.reliableTrDimensions() && nodeName( elem, "tr" ) ||
+
+		// Fall back to offsetWidth/offsetHeight when value is "auto"
+		// This happens for inline elements with no explicit setting (gh-3571)
+		val === "auto" ||
+
+		// Support: Android <=4.1 - 4.3 only
+		// Also use offsetWidth/offsetHeight for misreported inline dimensions (gh-3602)
+		!parseFloat( val ) && jQuery.css( elem, "display", false, styles ) === "inline" ) &&
+
+		// Make sure the element is visible & connected
+		elem.getClientRects().length ) {
+
+		isBorderBox = jQuery.css( elem, "boxSizing", false, styles ) === "border-box";
+
+		// Where available, offsetWidth/offsetHeight approximate border box dimensions.
+		// Where not available (e.g., SVG), assume unreliable box-sizing and interpret the
+		// retrieved value as a content box dimension.
+		valueIsBorderBox = offsetProp in elem;
+		if ( valueIsBorderBox ) {
+			val = elem[ offsetProp ];
+		}
+	}
+
+	// Normalize "" and auto
+	val = parseFloat( val ) || 0;
+
+	// Adjust for the element's box model
+	return ( val +
+		boxModelAdjustment(
+			elem,
+			dimension,
+			extra || ( isBorderBox ? "border" : "content" ),
+			valueIsBorderBox,
+			styles,
+
+			// Provide the current computed size to request scroll gutter calculation (gh-3589)
+			val
+		)
+	) + "px";
+}
+
+jQuery.extend( {
+
+	// Add in style property hooks for overriding the default
+	// behavior of getting and setting a style property
+	cssHooks: {
+		opacity: {
+			get: function( elem, computed ) {
+				if ( computed ) {
+
+					// We should always get a number back from opacity
+					var ret = curCSS( elem, "opacity" );
+					return ret === "" ? "1" : ret;
+				}
+			}
+		}
+	},
+
+	// Don't automatically add "px" to these possibly-unitless properties
+	cssNumber: {
+		"animationIterationCount": true,
+		"columnCount": true,
+		"fillOpacity": true,
+		"flexGrow": true,
+		"flexShrink": true,
+		"fontWeight": true,
+		"gridArea": true,
+		"gridColumn": true,
+		"gridColumnEnd": true,
+		"gridColumnStart": true,
+		"gridRow": true,
+		"gridRowEnd": true,
+		"gridRowStart": true,
+		"lineHeight": true,
+		"opacity": true,
+		"order": true,
+		"orphans": true,
+		"widows": true,
+		"zIndex": true,
+		"zoom": true
+	},
+
+	// Add in properties whose names you wish to fix before
+	// setting or getting the value
+	cssProps: {},
+
+	// Get and set the style property on a DOM Node
+	style: function( elem, name, value, extra ) {
+
+		// Don't set styles on text and comment nodes
+		if ( !elem || elem.nodeType === 3 || elem.nodeType === 8 || !elem.style ) {
+			return;
+		}
+
+		// Make sure that we're working with the right name
+		var ret, type, hooks,
+			origName = camelCase( name ),
+			isCustomProp = rcustomProp.test( name ),
+			style = elem.style;
+
+		// Make sure that we're working with the right name. We don't
+		// want to query the value if it is a CSS custom property
+		// since they are user-defined.
+		if ( !isCustomProp ) {
+			name = finalPropName( origName );
+		}
+
+		// Gets hook for the prefixed version, then unprefixed version
+		hooks = jQuery.cssHooks[ name ] || jQuery.cssHooks[ origName ];
+
+		// Check if we're setting a value
+		if ( value !== undefined ) {
+			type = typeof value;
+
+			// Convert "+=" or "-=" to relative numbers (#7345)
+			if ( type === "string" && ( ret = rcssNum.exec( value ) ) && ret[ 1 ] ) {
+				value = adjustCSS( elem, name, ret );
+
+				// Fixes bug #9237
+				type = "number";
+			}
+
+			// Make sure that null and NaN values aren't set (#7116)
+			if ( value == null || value !== value ) {
+				return;
+			}
+
+			// If a number was passed in, add the unit (except for certain CSS properties)
+			// The isCustomProp check can be removed in jQuery 4.0 when we only auto-append
+			// "px" to a few hardcoded values.
+			if ( type === "number" && !isCustomProp ) {
+				value += ret && ret[ 3 ] || ( jQuery.cssNumber[ origName ] ? "" : "px" );
+			}
+
+			// background-* props affect original clone's values
+			if ( !support.clearCloneStyle && value === "" && name.indexOf( "background" ) === 0 ) {
+				style[ name ] = "inherit";
+			}
+
+			// If a hook was provided, use that value, otherwise just set the specified value
+			if ( !hooks || !( "set" in hooks ) ||
+				( value = hooks.set( elem, value, extra ) ) !== undefined ) {
+
+				if ( isCustomProp ) {
+					style.setProperty( name, value );
+				} else {
+					style[ name ] = value;
+				}
+			}
+
+		} else {
+
+			// If a hook was provided get the non-computed value from there
+			if ( hooks && "get" in hooks &&
+				( ret = hooks.get( elem, false, extra ) ) !== undefined ) {
+
+				return ret;
+			}
+
+			// Otherwise just get the value from the style object
+			return style[ name ];
+		}
+	},
+
+	css: function( elem, name, extra, styles ) {
+		var val, num, hooks,
+			origName = camelCase( name ),
+			isCustomProp = rcustomProp.test( name );
+
+		// Make sure that we're working with the right name. We don't
+		// want to modify the value if it is a CSS custom property
+		// since they are user-defined.
+		if ( !isCustomProp ) {
+			name = finalPropName( origName );
+		}
+
+		// Try prefixed name followed by the unprefixed name
+		hooks = jQuery.cssHooks[ name ] || jQuery.cssHooks[ origName ];
+
+		// If a hook was provided get the computed value from there
+		if ( hooks && "get" in hooks ) {
+			val = hooks.get( elem, true, extra );
+		}
+
+		// Otherwise, if a way to get the computed value exists, use that
+		if ( val === undefined ) {
+			val = curCSS( elem, name, styles );
+		}
+
+		// Convert "normal" to computed value
+		if ( val === "normal" && name in cssNormalTransform ) {
+			val = cssNormalTransform[ name ];
+		}
+
+		// Make numeric if forced or a qualifier was provided and val looks numeric
+		if ( extra === "" || extra ) {
+			num = parseFloat( val );
+			return extra === true || isFinite( num ) ? num || 0 : val;
+		}
+
+		return val;
+	}
+} );
+
+jQuery.each( [ "height", "width" ], function( _i, dimension ) {
+	jQuery.cssHooks[ dimension ] = {
+		get: function( elem, computed, extra ) {
+			if ( computed ) {
+
+				// Certain elements can have dimension info if we invisibly show them
+				// but it must have a current display style that would benefit
+				return rdisplayswap.test( jQuery.css( elem, "display" ) ) &&
+
+					// Support: Safari 8+
+					// Table columns in Safari have non-zero offsetWidth & zero
+					// getBoundingClientRect().width unless display is changed.
+					// Support: IE <=11 only
+					// Running getBoundingClientRect on a disconnected node
+					// in IE throws an error.
+					( !elem.getClientRects().length || !elem.getBoundingClientRect().width ) ?
+					swap( elem, cssShow, function() {
+						return getWidthOrHeight( elem, dimension, extra );
+					} ) :
+					getWidthOrHeight( elem, dimension, extra );
+			}
+		},
+
+		set: function( elem, value, extra ) {
+			var matches,
+				styles = getStyles( elem ),
+
+				// Only read styles.position if the test has a chance to fail
+				// to avoid forcing a reflow.
+				scrollboxSizeBuggy = !support.scrollboxSize() &&
+					styles.position === "absolute",
+
+				// To avoid forcing a reflow, only fetch boxSizing if we need it (gh-3991)
+				boxSizingNeeded = scrollboxSizeBuggy || extra,
+				isBorderBox = boxSizingNeeded &&
+					jQuery.css( elem, "boxSizing", false, styles ) === "border-box",
+				subtract = extra ?
+					boxModelAdjustment(
+						elem,
+						dimension,
+						extra,
+						isBorderBox,
+						styles
+					) :
+					0;
+
+			// Account for unreliable border-box dimensions by comparing offset* to computed and
+			// faking a content-box to get border and padding (gh-3699)
+			if ( isBorderBox && scrollboxSizeBuggy ) {
+				subtract -= Math.ceil(
+					elem[ "offset" + dimension[ 0 ].toUpperCase() + dimension.slice( 1 ) ] -
+					parseFloat( styles[ dimension ] ) -
+					boxModelAdjustment( elem, dimension, "border", false, styles ) -
+					0.5
+				);
+			}
+
+			// Convert to pixels if value adjustment is needed
+			if ( subtract && ( matches = rcssNum.exec( value ) ) &&
+				( matches[ 3 ] || "px" ) !== "px" ) {
+
+				elem.style[ dimension ] = value;
+				value = jQuery.css( elem, dimension );
+			}
+
+			return setPositiveNumber( elem, value, subtract );
+		}
+	};
+} );
+
+jQuery.cssHooks.marginLeft = addGetHookIf( support.reliableMarginLeft,
+	function( elem, computed ) {
+		if ( computed ) {
+			return ( parseFloat( curCSS( elem, "marginLeft" ) ) ||
+				elem.getBoundingClientRect().left -
+					swap( elem, { marginLeft: 0 }, function() {
+						return elem.getBoundingClientRect().left;
+					} )
+			) + "px";
+		}
+	}
+);
+
+// These hooks are used by animate to expand properties
+jQuery.each( {
+	margin: "",
+	padding: "",
+	border: "Width"
+}, function( prefix, suffix ) {
+	jQuery.cssHooks[ prefix + suffix ] = {
+		expand: function( value ) {
+			var i = 0,
+				expanded = {},
+
+				// Assumes a single number if not a string
+				parts = typeof value === "string" ? value.split( " " ) : [ value ];
+
+			for ( ; i < 4; i++ ) {
+				expanded[ prefix + cssExpand[ i ] + suffix ] =
+					parts[ i ] || parts[ i - 2 ] || parts[ 0 ];
+			}
+
+			return expanded;
+		}
+	};
+
+	if ( prefix !== "margin" ) {
+		jQuery.cssHooks[ prefix + suffix ].set = setPositiveNumber;
+	}
+} );
+
+jQuery.fn.extend( {
+	css: function( name, value ) {
+		return access( this, function( elem, name, value ) {
+			var styles, len,
+				map = {},
+				i = 0;
+
+			if ( Array.isArray( name ) ) {
+				styles = getStyles( elem );
+				len = name.length;
+
+				for ( ; i < len; i++ ) {
+					map[ name[ i ] ] = jQuery.css( elem, name[ i ], false, styles );
+				}
+
+				return map;
+			}
+
+			return value !== undefined ?
+				jQuery.style( elem, name, value ) :
+				jQuery.css( elem, name );
+		}, name, value, arguments.length > 1 );
+	}
+} );
+
+
+function Tween( elem, options, prop, end, easing ) {
+	return new Tween.prototype.init( elem, options, prop, end, easing );
+}
+jQuery.Tween = Tween;
+
+Tween.prototype = {
+	constructor: Tween,
+	init: function( elem, options, prop, end, easing, unit ) {
+		this.elem = elem;
+		this.prop = prop;
+		this.easing = easing || jQuery.easing._default;
+		this.options = options;
+		this.start = this.now = this.cur();
+		this.end = end;
+		this.unit = unit || ( jQuery.cssNumber[ prop ] ? "" : "px" );
+	},
+	cur: function() {
+		var hooks = Tween.propHooks[ this.prop ];
+
+		return hooks && hooks.get ?
+			hooks.get( this ) :
+			Tween.propHooks._default.get( this );
+	},
+	run: function( percent ) {
+		var eased,
+			hooks = Tween.propHooks[ this.prop ];
+
+		if ( this.options.duration ) {
+			this.pos = eased = jQuery.easing[ this.easing ](
+				percent, this.options.duration * percent, 0, 1, this.options.duration
+			);
+		} else {
+			this.pos = eased = percent;
+		}
+		this.now = ( this.end - this.start ) * eased + this.start;
+
+		if ( this.options.step ) {
+			this.options.step.call( this.elem, this.now, this );
+		}
+
+		if ( hooks && hooks.set ) {
+			hooks.set( this );
+		} else {
+			Tween.propHooks._default.set( this );
+		}
+		return this;
+	}
+};
+
+Tween.prototype.init.prototype = Tween.prototype;
+
+Tween.propHooks = {
+	_default: {
+		get: function( tween ) {
+			var result;
+
+			// Use a property on the element directly when it is not a DOM element,
+			// or when there is no matching style property that exists.
+			if ( tween.elem.nodeType !== 1 ||
+				tween.elem[ tween.prop ] != null && tween.elem.style[ tween.prop ] == null ) {
+				return tween.elem[ tween.prop ];
+			}
+
+			// Passing an empty string as a 3rd parameter to .css will automatically
+			// attempt a parseFloat and fallback to a string if the parse fails.
+			// Simple values such as "10px" are parsed to Float;
+			// complex values such as "rotate(1rad)" are returned as-is.
+			result = jQuery.css( tween.elem, tween.prop, "" );
+
+			// Empty strings, null, undefined and "auto" are converted to 0.
+			return !result || result === "auto" ? 0 : result;
+		},
+		set: function( tween ) {
+
+			// Use step hook for back compat.
+			// Use cssHook if its there.
+			// Use .style if available and use plain properties where available.
+			if ( jQuery.fx.step[ tween.prop ] ) {
+				jQuery.fx.step[ tween.prop ]( tween );
+			} else if ( tween.elem.nodeType === 1 && (
+				jQuery.cssHooks[ tween.prop ] ||
+					tween.elem.style[ finalPropName( tween.prop ) ] != null ) ) {
+				jQuery.style( tween.elem, tween.prop, tween.now + tween.unit );
+			} else {
+				tween.elem[ tween.prop ] = tween.now;
+			}
+		}
+	}
+};
+
+// Support: IE <=9 only
+// Panic based approach to setting things on disconnected nodes
+Tween.propHooks.scrollTop = Tween.propHooks.scrollLeft = {
+	set: function( tween ) {
+		if ( tween.elem.nodeType && tween.elem.parentNode ) {
+			tween.elem[ tween.prop ] = tween.now;
+		}
+	}
+};
+
+jQuery.easing = {
+	linear: function( p ) {
+		return p;
+	},
+	swing: function( p ) {
+		return 0.5 - Math.cos( p * Math.PI ) / 2;
+	},
+	_default: "swing"
+};
+
+jQuery.fx = Tween.prototype.init;
+
+// Back compat <1.8 extension point
+jQuery.fx.step = {};
+
+
+
+
+var
+	fxNow, inProgress,
+	rfxtypes = /^(?:toggle|show|hide)$/,
+	rrun = /queueHooks$/;
+
+function schedule() {
+	if ( inProgress ) {
+		if ( document.hidden === false && window.requestAnimationFrame ) {
+			window.requestAnimationFrame( schedule );
+		} else {
+			window.setTimeout( schedule, jQuery.fx.interval );
+		}
+
+		jQuery.fx.tick();
+	}
+}
+
+// Animations created synchronously will run synchronously
+function createFxNow() {
+	window.setTimeout( function() {
+		fxNow = undefined;
+	} );
+	return ( fxNow = Date.now() );
+}
+
+// Generate parameters to create a standard animation
+function genFx( type, includeWidth ) {
+	var which,
+		i = 0,
+		attrs = { height: type };
+
+	// If we include width, step value is 1 to do all cssExpand values,
+	// otherwise step value is 2 to skip over Left and Right
+	includeWidth = includeWidth ? 1 : 0;
+	for ( ; i < 4; i += 2 - includeWidth ) {
+		which = cssExpand[ i ];
+		attrs[ "margin" + which ] = attrs[ "padding" + which ] = type;
+	}
+
+	if ( includeWidth ) {
+		attrs.opacity = attrs.width = type;
+	}
+
+	return attrs;
+}
+
+function createTween( value, prop, animation ) {
+	var tween,
+		collection = ( Animation.tweeners[ prop ] || [] ).concat( Animation.tweeners[ "*" ] ),
+		index = 0,
+		length = collection.length;
+	for ( ; index < length; index++ ) {
+		if ( ( tween = collection[ index ].call( animation, prop, value ) ) ) {
+
+			// We're done with this property
+			return tween;
+		}
+	}
+}
+
+function defaultPrefilter( elem, props, opts ) {
+	var prop, value, toggle, hooks, oldfire, propTween, restoreDisplay, display,
+		isBox = "width" in props || "height" in props,
+		anim = this,
+		orig = {},
+		style = elem.style,
+		hidden = elem.nodeType && isHiddenWithinTree( elem ),
+		dataShow = dataPriv.get( elem, "fxshow" );
+
+	// Queue-skipping animations hijack the fx hooks
+	if ( !opts.queue ) {
+		hooks = jQuery._queueHooks( elem, "fx" );
+		if ( hooks.unqueued == null ) {
+			hooks.unqueued = 0;
+			oldfire = hooks.empty.fire;
+			hooks.empty.fire = function() {
+				if ( !hooks.unqueued ) {
+					oldfire();
+				}
+			};
+		}
+		hooks.unqueued++;
+
+		anim.always( function() {
+
+			// Ensure the complete handler is called before this completes
+			anim.always( function() {
+				hooks.unqueued--;
+				if ( !jQuery.queue( elem, "fx" ).length ) {
+					hooks.empty.fire();
+				}
+			} );
+		} );
+	}
+
+	// Detect show/hide animations
+	for ( prop in props ) {
+		value = props[ prop ];
+		if ( rfxtypes.test( value ) ) {
+			delete props[ prop ];
+			toggle = toggle || value === "toggle";
+			if ( value === ( hidden ? "hide" : "show" ) ) {
+
+				// Pretend to be hidden if this is a "show" and
+				// there is still data from a stopped show/hide
+				if ( value === "show" && dataShow && dataShow[ prop ] !== undefined ) {
+					hidden = true;
+
+				// Ignore all other no-op show/hide data
+				} else {
+					continue;
+				}
+			}
+			orig[ prop ] = dataShow && dataShow[ prop ] || jQuery.style( elem, prop );
+		}
+	}
+
+	// Bail out if this is a no-op like .hide().hide()
+	propTween = !jQuery.isEmptyObject( props );
+	if ( !propTween && jQuery.isEmptyObject( orig ) ) {
+		return;
+	}
+
+	// Restrict "overflow" and "display" styles during box animations
+	if ( isBox && elem.nodeType === 1 ) {
+
+		// Support: IE <=9 - 11, Edge 12 - 15
+		// Record all 3 overflow attributes because IE does not infer the shorthand
+		// from identically-valued overflowX and overflowY and Edge just mirrors
+		// the overflowX value there.
+		opts.overflow = [ style.overflow, style.overflowX, style.overflowY ];
+
+		// Identify a display type, preferring old show/hide data over the CSS cascade
+		restoreDisplay = dataShow && dataShow.display;
+		if ( restoreDisplay == null ) {
+			restoreDisplay = dataPriv.get( elem, "display" );
+		}
+		display = jQuery.css( elem, "display" );
+		if ( display === "none" ) {
+			if ( restoreDisplay ) {
+				display = restoreDisplay;
+			} else {
+
+				// Get nonempty value(s) by temporarily forcing visibility
+				showHide( [ elem ], true );
+				restoreDisplay = elem.style.display || restoreDisplay;
+				display = jQuery.css( elem, "display" );
+				showHide( [ elem ] );
+			}
+		}
+
+		// Animate inline elements as inline-block
+		if ( display === "inline" || display === "inline-block" && restoreDisplay != null ) {
+			if ( jQuery.css( elem, "float" ) === "none" ) {
+
+				// Restore the original display value at the end of pure show/hide animations
+				if ( !propTween ) {
+					anim.done( function() {
+						style.display = restoreDisplay;
+					} );
+					if ( restoreDisplay == null ) {
+						display = style.display;
+						restoreDisplay = display === "none" ? "" : display;
+					}
+				}
+				style.display = "inline-block";
+			}
+		}
+	}
+
+	if ( opts.overflow ) {
+		style.overflow = "hidden";
+		anim.always( function() {
+			style.overflow = opts.overflow[ 0 ];
+			style.overflowX = opts.overflow[ 1 ];
+			style.overflowY = opts.overflow[ 2 ];
+		} );
+	}
+
+	// Implement show/hide animations
+	propTween = false;
+	for ( prop in orig ) {
+
+		// General show/hide setup for this element animation
+		if ( !propTween ) {
+			if ( dataShow ) {
+				if ( "hidden" in dataShow ) {
+					hidden = dataShow.hidden;
+				}
+			} else {
+				dataShow = dataPriv.access( elem, "fxshow", { display: restoreDisplay } );
+			}
+
+			// Store hidden/visible for toggle so `.stop().toggle()` "reverses"
+			if ( toggle ) {
+				dataShow.hidden = !hidden;
+			}
+
+			// Show elements before animating them
+			if ( hidden ) {
+				showHide( [ elem ], true );
+			}
+
+			/* eslint-disable no-loop-func */
+
+			anim.done( function() {
+
+				/* eslint-enable no-loop-func */
+
+				// The final step of a "hide" animation is actually hiding the element
+				if ( !hidden ) {
+					showHide( [ elem ] );
+				}
+				dataPriv.remove( elem, "fxshow" );
+				for ( prop in orig ) {
+					jQuery.style( elem, prop, orig[ prop ] );
+				}
+			} );
+		}
+
+		// Per-property setup
+		propTween = createTween( hidden ? dataShow[ prop ] : 0, prop, anim );
+		if ( !( prop in dataShow ) ) {
+			dataShow[ prop ] = propTween.start;
+			if ( hidden ) {
+				propTween.end = propTween.start;
+				propTween.start = 0;
+			}
+		}
+	}
+}
+
+function propFilter( props, specialEasing ) {
+	var index, name, easing, value, hooks;
+
+	// camelCase, specialEasing and expand cssHook pass
+	for ( index in props ) {
+		name = camelCase( index );
+		easing = specialEasing[ name ];
+		value = props[ index ];
+		if ( Array.isArray( value ) ) {
+			easing = value[ 1 ];
+			value = props[ index ] = value[ 0 ];
+		}
+
+		if ( index !== name ) {
+			props[ name ] = value;
+			delete props[ index ];
+		}
+
+		hooks = jQuery.cssHooks[ name ];
+		if ( hooks && "expand" in hooks ) {
+			value = hooks.expand( value );
+			delete props[ name ];
+
+			// Not quite $.extend, this won't overwrite existing keys.
+			// Reusing 'index' because we have the correct "name"
+			for ( index in value ) {
+				if ( !( index in props ) ) {
+					props[ index ] = value[ index ];
+					specialEasing[ index ] = easing;
+				}
+			}
+		} else {
+			specialEasing[ name ] = easing;
+		}
+	}
+}
+
+function Animation( elem, properties, options ) {
+	var result,
+		stopped,
+		index = 0,
+		length = Animation.prefilters.length,
+		deferred = jQuery.Deferred().always( function() {
+
+			// Don't match elem in the :animated selector
+			delete tick.elem;
+		} ),
+		tick = function() {
+			if ( stopped ) {
+				return false;
+			}
+			var currentTime = fxNow || createFxNow(),
+				remaining = Math.max( 0, animation.startTime + animation.duration - currentTime ),
+
+				// Support: Android 2.3 only
+				// Archaic crash bug won't allow us to use `1 - ( 0.5 || 0 )` (#12497)
+				temp = remaining / animation.duration || 0,
+				percent = 1 - temp,
+				index = 0,
+				length = animation.tweens.length;
+
+			for ( ; index < length; index++ ) {
+				animation.tweens[ index ].run( percent );
+			}
+
+			deferred.notifyWith( elem, [ animation, percent, remaining ] );
+
+			// If there's more to do, yield
+			if ( percent < 1 && length ) {
+				return remaining;
+			}
+
+			// If this was an empty animation, synthesize a final progress notification
+			if ( !length ) {
+				deferred.notifyWith( elem, [ animation, 1, 0 ] );
+			}
+
+			// Resolve the animation and report its conclusion
+			deferred.resolveWith( elem, [ animation ] );
+			return false;
+		},
+		animation = deferred.promise( {
+			elem: elem,
+			props: jQuery.extend( {}, properties ),
+			opts: jQuery.extend( true, {
+				specialEasing: {},
+				easing: jQuery.easing._default
+			}, options ),
+			originalProperties: properties,
+			originalOptions: options,
+			startTime: fxNow || createFxNow(),
+			duration: options.duration,
+			tweens: [],
+			createTween: function( prop, end ) {
+				var tween = jQuery.Tween( elem, animation.opts, prop, end,
+					animation.opts.specialEasing[ prop ] || animation.opts.easing );
+				animation.tweens.push( tween );
+				return tween;
+			},
+			stop: function( gotoEnd ) {
+				var index = 0,
+
+					// If we are going to the end, we want to run all the tweens
+					// otherwise we skip this part
+					length = gotoEnd ? animation.tweens.length : 0;
+				if ( stopped ) {
+					return this;
+				}
+				stopped = true;
+				for ( ; index < length; index++ ) {
+					animation.tweens[ index ].run( 1 );
+				}
+
+				// Resolve when we played the last frame; otherwise, reject
+				if ( gotoEnd ) {
+					deferred.notifyWith( elem, [ animation, 1, 0 ] );
+					deferred.resolveWith( elem, [ animation, gotoEnd ] );
+				} else {
+					deferred.rejectWith( elem, [ animation, gotoEnd ] );
+				}
+				return this;
+			}
+		} ),
+		props = animation.props;
+
+	propFilter( props, animation.opts.specialEasing );
+
+	for ( ; index < length; index++ ) {
+		result = Animation.prefilters[ index ].call( animation, elem, props, animation.opts );
+		if ( result ) {
+			if ( isFunction( result.stop ) ) {
+				jQuery._queueHooks( animation.elem, animation.opts.queue ).stop =
+					result.stop.bind( result );
+			}
+			return result;
+		}
+	}
+
+	jQuery.map( props, createTween, animation );
+
+	if ( isFunction( animation.opts.start ) ) {
+		animation.opts.start.call( elem, animation );
+	}
+
+	// Attach callbacks from options
+	animation
+		.progress( animation.opts.progress )
+		.done( animation.opts.done, animation.opts.complete )
+		.fail( animation.opts.fail )
+		.always( animation.opts.always );
+
+	jQuery.fx.timer(
+		jQuery.extend( tick, {
+			elem: elem,
+			anim: animation,
+			queue: animation.opts.queue
+		} )
+	);
+
+	return animation;
+}
+
+jQuery.Animation = jQuery.extend( Animation, {
+
+	tweeners: {
+		"*": [ function( prop, value ) {
+			var tween = this.createTween( prop, value );
+			adjustCSS( tween.elem, prop, rcssNum.exec( value ), tween );
+			return tween;
+		} ]
+	},
+
+	tweener: function( props, callback ) {
+		if ( isFunction( props ) ) {
+			callback = props;
+			props = [ "*" ];
+		} else {
+			props = props.match( rnothtmlwhite );
+		}
+
+		var prop,
+			index = 0,
+			length = props.length;
+
+		for ( ; index < length; index++ ) {
+			prop = props[ index ];
+			Animation.tweeners[ prop ] = Animation.tweeners[ prop ] || [];
+			Animation.tweeners[ prop ].unshift( callback );
+		}
+	},
+
+	prefilters: [ defaultPrefilter ],
+
+	prefilter: function( callback, prepend ) {
+		if ( prepend ) {
+			Animation.prefilters.unshift( callback );
+		} else {
+			Animation.prefilters.push( callback );
+		}
+	}
+} );
+
+jQuery.speed = function( speed, easing, fn ) {
+	var opt = speed && typeof speed === "object" ? jQuery.extend( {}, speed ) : {
+		complete: fn || !fn && easing ||
+			isFunction( speed ) && speed,
+		duration: speed,
+		easing: fn && easing || easing && !isFunction( easing ) && easing
+	};
+
+	// Go to the end state if fx are off
+	if ( jQuery.fx.off ) {
+		opt.duration = 0;
+
+	} else {
+		if ( typeof opt.duration !== "number" ) {
+			if ( opt.duration in jQuery.fx.speeds ) {
+				opt.duration = jQuery.fx.speeds[ opt.duration ];
+
+			} else {
+				opt.duration = jQuery.fx.speeds._default;
+			}
+		}
+	}
+
+	// Normalize opt.queue - true/undefined/null -> "fx"
+	if ( opt.queue == null || opt.queue === true ) {
+		opt.queue = "fx";
+	}
+
+	// Queueing
+	opt.old = opt.complete;
+
+	opt.complete = function() {
+		if ( isFunction( opt.old ) ) {
+			opt.old.call( this );
+		}
+
+		if ( opt.queue ) {
+			jQuery.dequeue( this, opt.queue );
+		}
+	};
+
+	return opt;
+};
+
+jQuery.fn.extend( {
+	fadeTo: function( speed, to, easing, callback ) {
+
+		// Show any hidden elements after setting opacity to 0
+		return this.filter( isHiddenWithinTree ).css( "opacity", 0 ).show()
+
+			// Animate to the value specified
+			.end().animate( { opacity: to }, speed, easing, callback );
+	},
+	animate: function( prop, speed, easing, callback ) {
+		var empty = jQuery.isEmptyObject( prop ),
+			optall = jQuery.speed( speed, easing, callback ),
+			doAnimation = function() {
+
+				// Operate on a copy of prop so per-property easing won't be lost
+				var anim = Animation( this, jQuery.extend( {}, prop ), optall );
+
+				// Empty animations, or finishing resolves immediately
+				if ( empty || dataPriv.get( this, "finish" ) ) {
+					anim.stop( true );
+				}
+			};
+
+		doAnimation.finish = doAnimation;
+
+		return empty || optall.queue === false ?
+			this.each( doAnimation ) :
+			this.queue( optall.queue, doAnimation );
+	},
+	stop: function( type, clearQueue, gotoEnd ) {
+		var stopQueue = function( hooks ) {
+			var stop = hooks.stop;
+			delete hooks.stop;
+			stop( gotoEnd );
+		};
+
+		if ( typeof type !== "string" ) {
+			gotoEnd = clearQueue;
+			clearQueue = type;
+			type = undefined;
+		}
+		if ( clearQueue ) {
+			this.queue( type || "fx", [] );
+		}
+
+		return this.each( function() {
+			var dequeue = true,
+				index = type != null && type + "queueHooks",
+				timers = jQuery.timers,
+				data = dataPriv.get( this );
+
+			if ( index ) {
+				if ( data[ index ] && data[ index ].stop ) {
+					stopQueue( data[ index ] );
+				}
+			} else {
+				for ( index in data ) {
+					if ( data[ index ] && data[ index ].stop && rrun.test( index ) ) {
+						stopQueue( data[ index ] );
+					}
+				}
+			}
+
+			for ( index = timers.length; index--; ) {
+				if ( timers[ index ].elem === this &&
+					( type == null || timers[ index ].queue === type ) ) {
+
+					timers[ index ].anim.stop( gotoEnd );
+					dequeue = false;
+					timers.splice( index, 1 );
+				}
+			}
+
+			// Start the next in the queue if the last step wasn't forced.
+			// Timers currently will call their complete callbacks, which
+			// will dequeue but only if they were gotoEnd.
+			if ( dequeue || !gotoEnd ) {
+				jQuery.dequeue( this, type );
+			}
+		} );
+	},
+	finish: function( type ) {
+		if ( type !== false ) {
+			type = type || "fx";
+		}
+		return this.each( function() {
+			var index,
+				data = dataPriv.get( this ),
+				queue = data[ type + "queue" ],
+				hooks = data[ type + "queueHooks" ],
+				timers = jQuery.timers,
+				length = queue ? queue.length : 0;
+
+			// Enable finishing flag on private data
+			data.finish = true;
+
+			// Empty the queue first
+			jQuery.queue( this, type, [] );
+
+			if ( hooks && hooks.stop ) {
+				hooks.stop.call( this, true );
+			}
+
+			// Look for any active animations, and finish them
+			for ( index = timers.length; index--; ) {
+				if ( timers[ index ].elem === this && timers[ index ].queue === type ) {
+					timers[ index ].anim.stop( true );
+					timers.splice( index, 1 );
+				}
+			}
+
+			// Look for any animations in the old queue and finish them
+			for ( index = 0; index < length; index++ ) {
+				if ( queue[ index ] && queue[ index ].finish ) {
+					queue[ index ].finish.call( this );
+				}
+			}
+
+			// Turn off finishing flag
+			delete data.finish;
+		} );
+	}
+} );
+
+jQuery.each( [ "toggle", "show", "hide" ], function( _i, name ) {
+	var cssFn = jQuery.fn[ name ];
+	jQuery.fn[ name ] = function( speed, easing, callback ) {
+		return speed == null || typeof speed === "boolean" ?
+			cssFn.apply( this, arguments ) :
+			this.animate( genFx( name, true ), speed, easing, callback );
+	};
+} );
+
+// Generate shortcuts for custom animations
+jQuery.each( {
+	slideDown: genFx( "show" ),
+	slideUp: genFx( "hide" ),
+	slideToggle: genFx( "toggle" ),
+	fadeIn: { opacity: "show" },
+	fadeOut: { opacity: "hide" },
+	fadeToggle: { opacity: "toggle" }
+}, function( name, props ) {
+	jQuery.fn[ name ] = function( speed, easing, callback ) {
+		return this.animate( props, speed, easing, callback );
+	};
+} );
+
+jQuery.timers = [];
+jQuery.fx.tick = function() {
+	var timer,
+		i = 0,
+		timers = jQuery.timers;
+
+	fxNow = Date.now();
+
+	for ( ; i < timers.length; i++ ) {
+		timer = timers[ i ];
+
+		// Run the timer and safely remove it when done (allowing for external removal)
+		if ( !timer() && timers[ i ] === timer ) {
+			timers.splice( i--, 1 );
+		}
+	}
+
+	if ( !timers.length ) {
+		jQuery.fx.stop();
+	}
+	fxNow = undefined;
+};
+
+jQuery.fx.timer = function( timer ) {
+	jQuery.timers.push( timer );
+	jQuery.fx.start();
+};
+
+jQuery.fx.interval = 13;
+jQuery.fx.start = function() {
+	if ( inProgress ) {
+		return;
+	}
+
+	inProgress = true;
+	schedule();
+};
+
+jQuery.fx.stop = function() {
+	inProgress = null;
+};
+
+jQuery.fx.speeds = {
+	slow: 600,
+	fast: 200,
+
+	// Default speed
+	_default: 400
+};
+
+
+// Based off of the plugin by Clint Helfers, with permission.
+// https://web.archive.org/web/20100324014747/http://blindsignals.com/index.php/2009/07/jquery-delay/
+jQuery.fn.delay = function( time, type ) {
+	time = jQuery.fx ? jQuery.fx.speeds[ time ] || time : time;
+	type = type || "fx";
+
+	return this.queue( type, function( next, hooks ) {
+		var timeout = window.setTimeout( next, time );
+		hooks.stop = function() {
+			window.clearTimeout( timeout );
+		};
+	} );
+};
+
+
+( function() {
+	var input = document.createElement( "input" ),
+		select = document.createElement( "select" ),
+		opt = select.appendChild( document.createElement( "option" ) );
+
+	input.type = "checkbox";
+
+	// Support: Android <=4.3 only
+	// Default value for a checkbox should be "on"
+	support.checkOn = input.value !== "";
+
+	// Support: IE <=11 only
+	// Must access selectedIndex to make default options select
+	support.optSelected = opt.selected;
+
+	// Support: IE <=11 only
+	// An input loses its value after becoming a radio
+	input = document.createElement( "input" );
+	input.value = "t";
+	input.type = "radio";
+	support.radioValue = input.value === "t";
+} )();
+
+
+var boolHook,
+	attrHandle = jQuery.expr.attrHandle;
+
+jQuery.fn.extend( {
+	attr: function( name, value ) {
+		return access( this, jQuery.attr, name, value, arguments.length > 1 );
+	},
+
+	removeAttr: function( name ) {
+		return this.each( function() {
+			jQuery.removeAttr( this, name );
+		} );
+	}
+} );
+
+jQuery.extend( {
+	attr: function( elem, name, value ) {
+		var ret, hooks,
+			nType = elem.nodeType;
+
+		// Don't get/set attributes on text, comment and attribute nodes
+		if ( nType === 3 || nType === 8 || nType === 2 ) {
+			return;
+		}
+
+		// Fallback to prop when attributes are not supported
+		if ( typeof elem.getAttribute === "undefined" ) {
+			return jQuery.prop( elem, name, value );
+		}
+
+		// Attribute hooks are determined by the lowercase version
+		// Grab necessary hook if one is defined
+		if ( nType !== 1 || !jQuery.isXMLDoc( elem ) ) {
+			hooks = jQuery.attrHooks[ name.toLowerCase() ] ||
+				( jQuery.expr.match.bool.test( name ) ? boolHook : undefined );
+		}
+
+		if ( value !== undefined ) {
+			if ( value === null ) {
+				jQuery.removeAttr( elem, name );
+				return;
+			}
+
+			if ( hooks && "set" in hooks &&
+				( ret = hooks.set( elem, value, name ) ) !== undefined ) {
+				return ret;
+			}
+
+			elem.setAttribute( name, value + "" );
+			return value;
+		}
+
+		if ( hooks && "get" in hooks && ( ret = hooks.get( elem, name ) ) !== null ) {
+			return ret;
+		}
+
+		ret = jQuery.find.attr( elem, name );
+
+		// Non-existent attributes return null, we normalize to undefined
+		return ret == null ? undefined : ret;
+	},
+
+	attrHooks: {
+		type: {
+			set: function( elem, value ) {
+				if ( !support.radioValue && value === "radio" &&
+					nodeName( elem, "input" ) ) {
+					var val = elem.value;
+					elem.setAttribute( "type", value );
+					if ( val ) {
+						elem.value = val;
+					}
+					return value;
+				}
+			}
+		}
+	},
+
+	removeAttr: function( elem, value ) {
+		var name,
+			i = 0,
+
+			// Attribute names can contain non-HTML whitespace characters
+			// https://html.spec.whatwg.org/multipage/syntax.html#attributes-2
+			attrNames = value && value.match( rnothtmlwhite );
+
+		if ( attrNames && elem.nodeType === 1 ) {
+			while ( ( name = attrNames[ i++ ] ) ) {
+				elem.removeAttribute( name );
+			}
+		}
+	}
+} );
+
+// Hooks for boolean attributes
+boolHook = {
+	set: function( elem, value, name ) {
+		if ( value === false ) {
+
+			// Remove boolean attributes when set to false
+			jQuery.removeAttr( elem, name );
+		} else {
+			elem.setAttribute( name, name );
+		}
+		return name;
+	}
+};
+
+jQuery.each( jQuery.expr.match.bool.source.match( /\w+/g ), function( _i, name ) {
+	var getter = attrHandle[ name ] || jQuery.find.attr;
+
+	attrHandle[ name ] = function( elem, name, isXML ) {
+		var ret, handle,
+			lowercaseName = name.toLowerCase();
+
+		if ( !isXML ) {
+
+			// Avoid an infinite loop by temporarily removing this function from the getter
+			handle = attrHandle[ lowercaseName ];
+			attrHandle[ lowercaseName ] = ret;
+			ret = getter( elem, name, isXML ) != null ?
+				lowercaseName :
+				null;
+			attrHandle[ lowercaseName ] = handle;
+		}
+		return ret;
+	};
+} );
+
+
+
+
+var rfocusable = /^(?:input|select|textarea|button)$/i,
+	rclickable = /^(?:a|area)$/i;
+
+jQuery.fn.extend( {
+	prop: function( name, value ) {
+		return access( this, jQuery.prop, name, value, arguments.length > 1 );
+	},
+
+	removeProp: function( name ) {
+		return this.each( function() {
+			delete this[ jQuery.propFix[ name ] || name ];
+		} );
+	}
+} );
+
+jQuery.extend( {
+	prop: function( elem, name, value ) {
+		var ret, hooks,
+			nType = elem.nodeType;
+
+		// Don't get/set properties on text, comment and attribute nodes
+		if ( nType === 3 || nType === 8 || nType === 2 ) {
+			return;
+		}
+
+		if ( nType !== 1 || !jQuery.isXMLDoc( elem ) ) {
+
+			// Fix name and attach hooks
+			name = jQuery.propFix[ name ] || name;
+			hooks = jQuery.propHooks[ name ];
+		}
+
+		if ( value !== undefined ) {
+			if ( hooks && "set" in hooks &&
+				( ret = hooks.set( elem, value, name ) ) !== undefined ) {
+				return ret;
+			}
+
+			return ( elem[ name ] = value );
+		}
+
+		if ( hooks && "get" in hooks && ( ret = hooks.get( elem, name ) ) !== null ) {
+			return ret;
+		}
+
+		return elem[ name ];
+	},
+
+	propHooks: {
+		tabIndex: {
+			get: function( elem ) {
+
+				// Support: IE <=9 - 11 only
+				// elem.tabIndex doesn't always return the
+				// correct value when it hasn't been explicitly set
+				// https://web.archive.org/web/20141116233347/http://fluidproject.org/blog/2008/01/09/getting-setting-and-removing-tabindex-values-with-javascript/
+				// Use proper attribute retrieval(#12072)
+				var tabindex = jQuery.find.attr( elem, "tabindex" );
+
+				if ( tabindex ) {
+					return parseInt( tabindex, 10 );
+				}
+
+				if (
+					rfocusable.test( elem.nodeName ) ||
+					rclickable.test( elem.nodeName ) &&
+					elem.href
+				) {
+					return 0;
+				}
+
+				return -1;
+			}
+		}
+	},
+
+	propFix: {
+		"for": "htmlFor",
+		"class": "className"
+	}
+} );
+
+// Support: IE <=11 only
+// Accessing the selectedIndex property
+// forces the browser to respect setting selected
+// on the option
+// The getter ensures a default option is selected
+// when in an optgroup
+// eslint rule "no-unused-expressions" is disabled for this code
+// since it considers such accessions noop
+if ( !support.optSelected ) {
+	jQuery.propHooks.selected = {
+		get: function( elem ) {
+
+			/* eslint no-unused-expressions: "off" */
+
+			var parent = elem.parentNode;
+			if ( parent && parent.parentNode ) {
+				parent.parentNode.selectedIndex;
+			}
+			return null;
+		},
+		set: function( elem ) {
+
+			/* eslint no-unused-expressions: "off" */
+
+			var parent = elem.parentNode;
+			if ( parent ) {
+				parent.selectedIndex;
+
+				if ( parent.parentNode ) {
+					parent.parentNode.selectedIndex;
+				}
+			}
+		}
+	};
+}
+
+jQuery.each( [
+	"tabIndex",
+	"readOnly",
+	"maxLength",
+	"cellSpacing",
+	"cellPadding",
+	"rowSpan",
+	"colSpan",
+	"useMap",
+	"frameBorder",
+	"contentEditable"
+], function() {
+	jQuery.propFix[ this.toLowerCase() ] = this;
+} );
+
+
+
+
+	// Strip and collapse whitespace according to HTML spec
+	// https://infra.spec.whatwg.org/#strip-and-collapse-ascii-whitespace
+	function stripAndCollapse( value ) {
+		var tokens = value.match( rnothtmlwhite ) || [];
+		return tokens.join( " " );
+	}
+
+
+function getClass( elem ) {
+	return elem.getAttribute && elem.getAttribute( "class" ) || "";
+}
+
+function classesToArray( value ) {
+	if ( Array.isArray( value ) ) {
+		return value;
+	}
+	if ( typeof value === "string" ) {
+		return value.match( rnothtmlwhite ) || [];
+	}
+	return [];
+}
+
+jQuery.fn.extend( {
+	addClass: function( value ) {
+		var classes, elem, cur, curValue, clazz, j, finalValue,
+			i = 0;
+
+		if ( isFunction( value ) ) {
+			return this.each( function( j ) {
+				jQuery( this ).addClass( value.call( this, j, getClass( this ) ) );
+			} );
+		}
+
+		classes = classesToArray( value );
+
+		if ( classes.length ) {
+			while ( ( elem = this[ i++ ] ) ) {
+				curValue = getClass( elem );
+				cur = elem.nodeType === 1 && ( " " + stripAndCollapse( curValue ) + " " );
+
+				if ( cur ) {
+					j = 0;
+					while ( ( clazz = classes[ j++ ] ) ) {
+						if ( cur.indexOf( " " + clazz + " " ) < 0 ) {
+							cur += clazz + " ";
+						}
+					}
+
+					// Only assign if different to avoid unneeded rendering.
+					finalValue = stripAndCollapse( cur );
+					if ( curValue !== finalValue ) {
+						elem.setAttribute( "class", finalValue );
+					}
+				}
+			}
+		}
+
+		return this;
+	},
+
+	removeClass: function( value ) {
+		var classes, elem, cur, curValue, clazz, j, finalValue,
+			i = 0;
+
+		if ( isFunction( value ) ) {
+			return this.each( function( j ) {
+				jQuery( this ).removeClass( value.call( this, j, getClass( this ) ) );
+			} );
+		}
+
+		if ( !arguments.length ) {
+			return this.attr( "class", "" );
+		}
+
+		classes = classesToArray( value );
+
+		if ( classes.length ) {
+			while ( ( elem = this[ i++ ] ) ) {
+				curValue = getClass( elem );
+
+				// This expression is here for better compressibility (see addClass)
+				cur = elem.nodeType === 1 && ( " " + stripAndCollapse( curValue ) + " " );
+
+				if ( cur ) {
+					j = 0;
+					while ( ( clazz = classes[ j++ ] ) ) {
+
+						// Remove *all* instances
+						while ( cur.indexOf( " " + clazz + " " ) > -1 ) {
+							cur = cur.replace( " " + clazz + " ", " " );
+						}
+					}
+
+					// Only assign if different to avoid unneeded rendering.
+					finalValue = stripAndCollapse( cur );
+					if ( curValue !== finalValue ) {
+						elem.setAttribute( "class", finalValue );
+					}
+				}
+			}
+		}
+
+		return this;
+	},
+
+	toggleClass: function( value, stateVal ) {
+		var type = typeof value,
+			isValidValue = type === "string" || Array.isArray( value );
+
+		if ( typeof stateVal === "boolean" && isValidValue ) {
+			return stateVal ? this.addClass( value ) : this.removeClass( value );
+		}
+
+		if ( isFunction( value ) ) {
+			return this.each( function( i ) {
+				jQuery( this ).toggleClass(
+					value.call( this, i, getClass( this ), stateVal ),
+					stateVal
+				);
+			} );
+		}
+
+		return this.each( function() {
+			var className, i, self, classNames;
+
+			if ( isValidValue ) {
+
+				// Toggle individual class names
+				i = 0;
+				self = jQuery( this );
+				classNames = classesToArray( value );
+
+				while ( ( className = classNames[ i++ ] ) ) {
+
+					// Check each className given, space separated list
+					if ( self.hasClass( className ) ) {
+						self.removeClass( className );
+					} else {
+						self.addClass( className );
+					}
+				}
+
+			// Toggle whole class name
+			} else if ( value === undefined || type === "boolean" ) {
+				className = getClass( this );
+				if ( className ) {
+
+					// Store className if set
+					dataPriv.set( this, "__className__", className );
+				}
+
+				// If the element has a class name or if we're passed `false`,
+				// then remove the whole classname (if there was one, the above saved it).
+				// Otherwise bring back whatever was previously saved (if anything),
+				// falling back to the empty string if nothing was stored.
+				if ( this.setAttribute ) {
+					this.setAttribute( "class",
+						className || value === false ?
+							"" :
+							dataPriv.get( this, "__className__" ) || ""
+					);
+				}
+			}
+		} );
+	},
+
+	hasClass: function( selector ) {
+		var className, elem,
+			i = 0;
+
+		className = " " + selector + " ";
+		while ( ( elem = this[ i++ ] ) ) {
+			if ( elem.nodeType === 1 &&
+				( " " + stripAndCollapse( getClass( elem ) ) + " " ).indexOf( className ) > -1 ) {
+				return true;
+			}
+		}
+
+		return false;
+	}
+} );
+
+
+
+
+var rreturn = /\r/g;
+
+jQuery.fn.extend( {
+	val: function( value ) {
+		var hooks, ret, valueIsFunction,
+			elem = this[ 0 ];
+
+		if ( !arguments.length ) {
+			if ( elem ) {
+				hooks = jQuery.valHooks[ elem.type ] ||
+					jQuery.valHooks[ elem.nodeName.toLowerCase() ];
+
+				if ( hooks &&
+					"get" in hooks &&
+					( ret = hooks.get( elem, "value" ) ) !== undefined
+				) {
+					return ret;
+				}
+
+				ret = elem.value;
+
+				// Handle most common string cases
+				if ( typeof ret === "string" ) {
+					return ret.replace( rreturn, "" );
+				}
+
+				// Handle cases where value is null/undef or number
+				return ret == null ? "" : ret;
+			}
+
+			return;
+		}
+
+		valueIsFunction = isFunction( value );
+
+		return this.each( function( i ) {
+			var val;
+
+			if ( this.nodeType !== 1 ) {
+				return;
+			}
+
+			if ( valueIsFunction ) {
+				val = value.call( this, i, jQuery( this ).val() );
+			} else {
+				val = value;
+			}
+
+			// Treat null/undefined as ""; convert numbers to string
+			if ( val == null ) {
+				val = "";
+
+			} else if ( typeof val === "number" ) {
+				val += "";
+
+			} else if ( Array.isArray( val ) ) {
+				val = jQuery.map( val, function( value ) {
+					return value == null ? "" : value + "";
+				} );
+			}
+
+			hooks = jQuery.valHooks[ this.type ] || jQuery.valHooks[ this.nodeName.toLowerCase() ];
+
+			// If set returns undefined, fall back to normal setting
+			if ( !hooks || !( "set" in hooks ) || hooks.set( this, val, "value" ) === undefined ) {
+				this.value = val;
+			}
+		} );
+	}
+} );
+
+jQuery.extend( {
+	valHooks: {
+		option: {
+			get: function( elem ) {
+
+				var val = jQuery.find.attr( elem, "value" );
+				return val != null ?
+					val :
+
+					// Support: IE <=10 - 11 only
+					// option.text throws exceptions (#14686, #14858)
+					// Strip and collapse whitespace
+					// https://html.spec.whatwg.org/#strip-and-collapse-whitespace
+					stripAndCollapse( jQuery.text( elem ) );
+			}
+		},
+		select: {
+			get: function( elem ) {
+				var value, option, i,
+					options = elem.options,
+					index = elem.selectedIndex,
+					one = elem.type === "select-one",
+					values = one ? null : [],
+					max = one ? index + 1 : options.length;
+
+				if ( index < 0 ) {
+					i = max;
+
+				} else {
+					i = one ? index : 0;
+				}
+
+				// Loop through all the selected options
+				for ( ; i < max; i++ ) {
+					option = options[ i ];
+
+					// Support: IE <=9 only
+					// IE8-9 doesn't update selected after form reset (#2551)
+					if ( ( option.selected || i === index ) &&
+
+							// Don't return options that are disabled or in a disabled optgroup
+							!option.disabled &&
+							( !option.parentNode.disabled ||
+								!nodeName( option.parentNode, "optgroup" ) ) ) {
+
+						// Get the specific value for the option
+						value = jQuery( option ).val();
+
+						// We don't need an array for one selects
+						if ( one ) {
+							return value;
+						}
+
+						// Multi-Selects return an array
+						values.push( value );
+					}
+				}
+
+				return values;
+			},
+
+			set: function( elem, value ) {
+				var optionSet, option,
+					options = elem.options,
+					values = jQuery.makeArray( value ),
+					i = options.length;
+
+				while ( i-- ) {
+					option = options[ i ];
+
+					/* eslint-disable no-cond-assign */
+
+					if ( option.selected =
+						jQuery.inArray( jQuery.valHooks.option.get( option ), values ) > -1
+					) {
+						optionSet = true;
+					}
+
+					/* eslint-enable no-cond-assign */
+				}
+
+				// Force browsers to behave consistently when non-matching value is set
+				if ( !optionSet ) {
+					elem.selectedIndex = -1;
+				}
+				return values;
+			}
+		}
+	}
+} );
+
+// Radios and checkboxes getter/setter
+jQuery.each( [ "radio", "checkbox" ], function() {
+	jQuery.valHooks[ this ] = {
+		set: function( elem, value ) {
+			if ( Array.isArray( value ) ) {
+				return ( elem.checked = jQuery.inArray( jQuery( elem ).val(), value ) > -1 );
+			}
+		}
+	};
+	if ( !support.checkOn ) {
+		jQuery.valHooks[ this ].get = function( elem ) {
+			return elem.getAttribute( "value" ) === null ? "on" : elem.value;
+		};
+	}
+} );
+
+
+
+
+// Return jQuery for attributes-only inclusion
+
+
+support.focusin = "onfocusin" in window;
+
+
+var rfocusMorph = /^(?:focusinfocus|focusoutblur)$/,
+	stopPropagationCallback = function( e ) {
+		e.stopPropagation();
+	};
+
+jQuery.extend( jQuery.event, {
+
+	trigger: function( event, data, elem, onlyHandlers ) {
+
+		var i, cur, tmp, bubbleType, ontype, handle, special, lastElement,
+			eventPath = [ elem || document ],
+			type = hasOwn.call( event, "type" ) ? event.type : event,
+			namespaces = hasOwn.call( event, "namespace" ) ? event.namespace.split( "." ) : [];
+
+		cur = lastElement = tmp = elem = elem || document;
+
+		// Don't do events on text and comment nodes
+		if ( elem.nodeType === 3 || elem.nodeType === 8 ) {
+			return;
+		}
+
+		// focus/blur morphs to focusin/out; ensure we're not firing them right now
+		if ( rfocusMorph.test( type + jQuery.event.triggered ) ) {
+			return;
+		}
+
+		if ( type.indexOf( "." ) > -1 ) {
+
+			// Namespaced trigger; create a regexp to match event type in handle()
+			namespaces = type.split( "." );
+			type = namespaces.shift();
+			namespaces.sort();
+		}
+		ontype = type.indexOf( ":" ) < 0 && "on" + type;
+
+		// Caller can pass in a jQuery.Event object, Object, or just an event type string
+		event = event[ jQuery.expando ] ?
+			event :
+			new jQuery.Event( type, typeof event === "object" && event );
+
+		// Trigger bitmask: & 1 for native handlers; & 2 for jQuery (always true)
+		event.isTrigger = onlyHandlers ? 2 : 3;
+		event.namespace = namespaces.join( "." );
+		event.rnamespace = event.namespace ?
+			new RegExp( "(^|\\.)" + namespaces.join( "\\.(?:.*\\.|)" ) + "(\\.|$)" ) :
+			null;
+
+		// Clean up the event in case it is being reused
+		event.result = undefined;
+		if ( !event.target ) {
+			event.target = elem;
+		}
+
+		// Clone any incoming data and prepend the event, creating the handler arg list
+		data = data == null ?
+			[ event ] :
+			jQuery.makeArray( data, [ event ] );
+
+		// Allow special events to draw outside the lines
+		special = jQuery.event.special[ type ] || {};
+		if ( !onlyHandlers && special.trigger && special.trigger.apply( elem, data ) === false ) {
+			return;
+		}
+
+		// Determine event propagation path in advance, per W3C events spec (#9951)
+		// Bubble up to document, then to window; watch for a global ownerDocument var (#9724)
+		if ( !onlyHandlers && !special.noBubble && !isWindow( elem ) ) {
+
+			bubbleType = special.delegateType || type;
+			if ( !rfocusMorph.test( bubbleType + type ) ) {
+				cur = cur.parentNode;
+			}
+			for ( ; cur; cur = cur.parentNode ) {
+				eventPath.push( cur );
+				tmp = cur;
+			}
+
+			// Only add window if we got to document (e.g., not plain obj or detached DOM)
+			if ( tmp === ( elem.ownerDocument || document ) ) {
+				eventPath.push( tmp.defaultView || tmp.parentWindow || window );
+			}
+		}
+
+		// Fire handlers on the event path
+		i = 0;
+		while ( ( cur = eventPath[ i++ ] ) && !event.isPropagationStopped() ) {
+			lastElement = cur;
+			event.type = i > 1 ?
+				bubbleType :
+				special.bindType || type;
+
+			// jQuery handler
+			handle = ( dataPriv.get( cur, "events" ) || Object.create( null ) )[ event.type ] &&
+				dataPriv.get( cur, "handle" );
+			if ( handle ) {
+				handle.apply( cur, data );
+			}
+
+			// Native handler
+			handle = ontype && cur[ ontype ];
+			if ( handle && handle.apply && acceptData( cur ) ) {
+				event.result = handle.apply( cur, data );
+				if ( event.result === false ) {
+					event.preventDefault();
+				}
+			}
+		}
+		event.type = type;
+
+		// If nobody prevented the default action, do it now
+		if ( !onlyHandlers && !event.isDefaultPrevented() ) {
+
+			if ( ( !special._default ||
+				special._default.apply( eventPath.pop(), data ) === false ) &&
+				acceptData( elem ) ) {
+
+				// Call a native DOM method on the target with the same name as the event.
+				// Don't do default actions on window, that's where global variables be (#6170)
+				if ( ontype && isFunction( elem[ type ] ) && !isWindow( elem ) ) {
+
+					// Don't re-trigger an onFOO event when we call its FOO() method
+					tmp = elem[ ontype ];
+
+					if ( tmp ) {
+						elem[ ontype ] = null;
+					}
+
+					// Prevent re-triggering of the same event, since we already bubbled it above
+					jQuery.event.triggered = type;
+
+					if ( event.isPropagationStopped() ) {
+						lastElement.addEventListener( type, stopPropagationCallback );
+					}
+
+					elem[ type ]();
+
+					if ( event.isPropagationStopped() ) {
+						lastElement.removeEventListener( type, stopPropagationCallback );
+					}
+
+					jQuery.event.triggered = undefined;
+
+					if ( tmp ) {
+						elem[ ontype ] = tmp;
+					}
+				}
+			}
+		}
+
+		return event.result;
+	},
+
+	// Piggyback on a donor event to simulate a different one
+	// Used only for `focus(in | out)` events
+	simulate: function( type, elem, event ) {
+		var e = jQuery.extend(
+			new jQuery.Event(),
+			event,
+			{
+				type: type,
+				isSimulated: true
+			}
+		);
+
+		jQuery.event.trigger( e, null, elem );
+	}
+
+} );
+
+jQuery.fn.extend( {
+
+	trigger: function( type, data ) {
+		return this.each( function() {
+			jQuery.event.trigger( type, data, this );
+		} );
+	},
+	triggerHandler: function( type, data ) {
+		var elem = this[ 0 ];
+		if ( elem ) {
+			return jQuery.event.trigger( type, data, elem, true );
+		}
+	}
+} );
+
+
+// Support: Firefox <=44
+// Firefox doesn't have focus(in | out) events
+// Related ticket - https://bugzilla.mozilla.org/show_bug.cgi?id=687787
+//
+// Support: Chrome <=48 - 49, Safari <=9.0 - 9.1
+// focus(in | out) events fire after focus & blur events,
+// which is spec violation - http://www.w3.org/TR/DOM-Level-3-Events/#events-focusevent-event-order
+// Related ticket - https://bugs.chromium.org/p/chromium/issues/detail?id=449857
+if ( !support.focusin ) {
+	jQuery.each( { focus: "focusin", blur: "focusout" }, function( orig, fix ) {
+
+		// Attach a single capturing handler on the document while someone wants focusin/focusout
+		var handler = function( event ) {
+			jQuery.event.simulate( fix, event.target, jQuery.event.fix( event ) );
+		};
+
+		jQuery.event.special[ fix ] = {
+			setup: function() {
+
+				// Handle: regular nodes (via `this.ownerDocument`), window
+				// (via `this.document`) & document (via `this`).
+				var doc = this.ownerDocument || this.document || this,
+					attaches = dataPriv.access( doc, fix );
+
+				if ( !attaches ) {
+					doc.addEventListener( orig, handler, true );
+				}
+				dataPriv.access( doc, fix, ( attaches || 0 ) + 1 );
+			},
+			teardown: function() {
+				var doc = this.ownerDocument || this.document || this,
+					attaches = dataPriv.access( doc, fix ) - 1;
+
+				if ( !attaches ) {
+					doc.removeEventListener( orig, handler, true );
+					dataPriv.remove( doc, fix );
+
+				} else {
+					dataPriv.access( doc, fix, attaches );
+				}
+			}
+		};
+	} );
+}
+var location = window.location;
+
+var nonce = { guid: Date.now() };
+
+var rquery = ( /\?/ );
+
+
+
+// Cross-browser xml parsing
+jQuery.parseXML = function( data ) {
+	var xml, parserErrorElem;
+	if ( !data || typeof data !== "string" ) {
+		return null;
+	}
+
+	// Support: IE 9 - 11 only
+	// IE throws on parseFromString with invalid input.
+	try {
+		xml = ( new window.DOMParser() ).parseFromString( data, "text/xml" );
+	} catch ( e ) {}
+
+	parserErrorElem = xml && xml.getElementsByTagName( "parsererror" )[ 0 ];
+	if ( !xml || parserErrorElem ) {
+		jQuery.error( "Invalid XML: " + (
+			parserErrorElem ?
+				jQuery.map( parserErrorElem.childNodes, function( el ) {
+					return el.textContent;
+				} ).join( "\n" ) :
+				data
+		) );
+	}
+	return xml;
+};
+
+
+var
+	rbracket = /\[\]$/,
+	rCRLF = /\r?\n/g,
+	rsubmitterTypes = /^(?:submit|button|image|reset|file)$/i,
+	rsubmittable = /^(?:input|select|textarea|keygen)/i;
+
+function buildParams( prefix, obj, traditional, add ) {
+	var name;
+
+	if ( Array.isArray( obj ) ) {
+
+		// Serialize array item.
+		jQuery.each( obj, function( i, v ) {
+			if ( traditional || rbracket.test( prefix ) ) {
+
+				// Treat each array item as a scalar.
+				add( prefix, v );
+
+			} else {
+
+				// Item is non-scalar (array or object), encode its numeric index.
+				buildParams(
+					prefix + "[" + ( typeof v === "object" && v != null ? i : "" ) + "]",
+					v,
+					traditional,
+					add
+				);
+			}
+		} );
+
+	} else if ( !traditional && toType( obj ) === "object" ) {
+
+		// Serialize object item.
+		for ( name in obj ) {
+			buildParams( prefix + "[" + name + "]", obj[ name ], traditional, add );
+		}
+
+	} else {
+
+		// Serialize scalar item.
+		add( prefix, obj );
+	}
+}
+
+// Serialize an array of form elements or a set of
+// key/values into a query string
+jQuery.param = function( a, traditional ) {
+	var prefix,
+		s = [],
+		add = function( key, valueOrFunction ) {
+
+			// If value is a function, invoke it and use its return value
+			var value = isFunction( valueOrFunction ) ?
+				valueOrFunction() :
+				valueOrFunction;
+
+			s[ s.length ] = encodeURIComponent( key ) + "=" +
+				encodeURIComponent( value == null ? "" : value );
+		};
+
+	if ( a == null ) {
+		return "";
+	}
+
+	// If an array was passed in, assume that it is an array of form elements.
+	if ( Array.isArray( a ) || ( a.jquery && !jQuery.isPlainObject( a ) ) ) {
+
+		// Serialize the form elements
+		jQuery.each( a, function() {
+			add( this.name, this.value );
+		} );
+
+	} else {
+
+		// If traditional, encode the "old" way (the way 1.3.2 or older
+		// did it), otherwise encode params recursively.
+		for ( prefix in a ) {
+			buildParams( prefix, a[ prefix ], traditional, add );
+		}
+	}
+
+	// Return the resulting serialization
+	return s.join( "&" );
+};
+
+jQuery.fn.extend( {
+	serialize: function() {
+		return jQuery.param( this.serializeArray() );
+	},
+	serializeArray: function() {
+		return this.map( function() {
+
+			// Can add propHook for "elements" to filter or add form elements
+			var elements = jQuery.prop( this, "elements" );
+			return elements ? jQuery.makeArray( elements ) : this;
+		} ).filter( function() {
+			var type = this.type;
+
+			// Use .is( ":disabled" ) so that fieldset[disabled] works
+			return this.name && !jQuery( this ).is( ":disabled" ) &&
+				rsubmittable.test( this.nodeName ) && !rsubmitterTypes.test( type ) &&
+				( this.checked || !rcheckableType.test( type ) );
+		} ).map( function( _i, elem ) {
+			var val = jQuery( this ).val();
+
+			if ( val == null ) {
+				return null;
+			}
+
+			if ( Array.isArray( val ) ) {
+				return jQuery.map( val, function( val ) {
+					return { name: elem.name, value: val.replace( rCRLF, "\r\n" ) };
+				} );
+			}
+
+			return { name: elem.name, value: val.replace( rCRLF, "\r\n" ) };
+		} ).get();
+	}
+} );
+
+
+var
+	r20 = /%20/g,
+	rhash = /#.*$/,
+	rantiCache = /([?&])_=[^&]*/,
+	rheaders = /^(.*?):[ \t]*([^\r\n]*)$/mg,
+
+	// #7653, #8125, #8152: local protocol detection
+	rlocalProtocol = /^(?:about|app|app-storage|.+-extension|file|res|widget):$/,
+	rnoContent = /^(?:GET|HEAD)$/,
+	rprotocol = /^\/\//,
+
+	/* Prefilters
+	 * 1) They are useful to introduce custom dataTypes (see ajax/jsonp.js for an example)
+	 * 2) These are called:
+	 *    - BEFORE asking for a transport
+	 *    - AFTER param serialization (s.data is a string if s.processData is true)
+	 * 3) key is the dataType
+	 * 4) the catchall symbol "*" can be used
+	 * 5) execution will start with transport dataType and THEN continue down to "*" if needed
+	 */
+	prefilters = {},
+
+	/* Transports bindings
+	 * 1) key is the dataType
+	 * 2) the catchall symbol "*" can be used
+	 * 3) selection will start with transport dataType and THEN go to "*" if needed
+	 */
+	transports = {},
+
+	// Avoid comment-prolog char sequence (#10098); must appease lint and evade compression
+	allTypes = "*/".concat( "*" ),
+
+	// Anchor tag for parsing the document origin
+	originAnchor = document.createElement( "a" );
+
+originAnchor.href = location.href;
+
+// Base "constructor" for jQuery.ajaxPrefilter and jQuery.ajaxTransport
+function addToPrefiltersOrTransports( structure ) {
+
+	// dataTypeExpression is optional and defaults to "*"
+	return function( dataTypeExpression, func ) {
+
+		if ( typeof dataTypeExpression !== "string" ) {
+			func = dataTypeExpression;
+			dataTypeExpression = "*";
+		}
+
+		var dataType,
+			i = 0,
+			dataTypes = dataTypeExpression.toLowerCase().match( rnothtmlwhite ) || [];
+
+		if ( isFunction( func ) ) {
+
+			// For each dataType in the dataTypeExpression
+			while ( ( dataType = dataTypes[ i++ ] ) ) {
+
+				// Prepend if requested
+				if ( dataType[ 0 ] === "+" ) {
+					dataType = dataType.slice( 1 ) || "*";
+					( structure[ dataType ] = structure[ dataType ] || [] ).unshift( func );
+
+				// Otherwise append
+				} else {
+					( structure[ dataType ] = structure[ dataType ] || [] ).push( func );
+				}
+			}
+		}
+	};
+}
+
+// Base inspection function for prefilters and transports
+function inspectPrefiltersOrTransports( structure, options, originalOptions, jqXHR ) {
+
+	var inspected = {},
+		seekingTransport = ( structure === transports );
+
+	function inspect( dataType ) {
+		var selected;
+		inspected[ dataType ] = true;
+		jQuery.each( structure[ dataType ] || [], function( _, prefilterOrFactory ) {
+			var dataTypeOrTransport = prefilterOrFactory( options, originalOptions, jqXHR );
+			if ( typeof dataTypeOrTransport === "string" &&
+				!seekingTransport && !inspected[ dataTypeOrTransport ] ) {
+
+				options.dataTypes.unshift( dataTypeOrTransport );
+				inspect( dataTypeOrTransport );
+				return false;
+			} else if ( seekingTransport ) {
+				return !( selected = dataTypeOrTransport );
+			}
+		} );
+		return selected;
+	}
+
+	return inspect( options.dataTypes[ 0 ] ) || !inspected[ "*" ] && inspect( "*" );
+}
+
+// A special extend for ajax options
+// that takes "flat" options (not to be deep extended)
+// Fixes #9887
+function ajaxExtend( target, src ) {
+	var key, deep,
+		flatOptions = jQuery.ajaxSettings.flatOptions || {};
+
+	for ( key in src ) {
+		if ( src[ key ] !== undefined ) {
+			( flatOptions[ key ] ? target : ( deep || ( deep = {} ) ) )[ key ] = src[ key ];
+		}
+	}
+	if ( deep ) {
+		jQuery.extend( true, target, deep );
+	}
+
+	return target;
+}
+
+/* Handles responses to an ajax request:
+ * - finds the right dataType (mediates between content-type and expected dataType)
+ * - returns the corresponding response
+ */
+function ajaxHandleResponses( s, jqXHR, responses ) {
+
+	var ct, type, finalDataType, firstDataType,
+		contents = s.contents,
+		dataTypes = s.dataTypes;
+
+	// Remove auto dataType and get content-type in the process
+	while ( dataTypes[ 0 ] === "*" ) {
+		dataTypes.shift();
+		if ( ct === undefined ) {
+			ct = s.mimeType || jqXHR.getResponseHeader( "Content-Type" );
+		}
+	}
+
+	// Check if we're dealing with a known content-type
+	if ( ct ) {
+		for ( type in contents ) {
+			if ( contents[ type ] && contents[ type ].test( ct ) ) {
+				dataTypes.unshift( type );
+				break;
+			}
+		}
+	}
+
+	// Check to see if we have a response for the expected dataType
+	if ( dataTypes[ 0 ] in responses ) {
+		finalDataType = dataTypes[ 0 ];
+	} else {
+
+		// Try convertible dataTypes
+		for ( type in responses ) {
+			if ( !dataTypes[ 0 ] || s.converters[ type + " " + dataTypes[ 0 ] ] ) {
+				finalDataType = type;
+				break;
+			}
+			if ( !firstDataType ) {
+				firstDataType = type;
+			}
+		}
+
+		// Or just use first one
+		finalDataType = finalDataType || firstDataType;
+	}
+
+	// If we found a dataType
+	// We add the dataType to the list if needed
+	// and return the corresponding response
+	if ( finalDataType ) {
+		if ( finalDataType !== dataTypes[ 0 ] ) {
+			dataTypes.unshift( finalDataType );
+		}
+		return responses[ finalDataType ];
+	}
+}
+
+/* Chain conversions given the request and the original response
+ * Also sets the responseXXX fields on the jqXHR instance
+ */
+function ajaxConvert( s, response, jqXHR, isSuccess ) {
+	var conv2, current, conv, tmp, prev,
+		converters = {},
+
+		// Work with a copy of dataTypes in case we need to modify it for conversion
+		dataTypes = s.dataTypes.slice();
+
+	// Create converters map with lowercased keys
+	if ( dataTypes[ 1 ] ) {
+		for ( conv in s.converters ) {
+			converters[ conv.toLowerCase() ] = s.converters[ conv ];
+		}
+	}
+
+	current = dataTypes.shift();
+
+	// Convert to each sequential dataType
+	while ( current ) {
+
+		if ( s.responseFields[ current ] ) {
+			jqXHR[ s.responseFields[ current ] ] = response;
+		}
+
+		// Apply the dataFilter if provided
+		if ( !prev && isSuccess && s.dataFilter ) {
+			response = s.dataFilter( response, s.dataType );
+		}
+
+		prev = current;
+		current = dataTypes.shift();
+
+		if ( current ) {
+
+			// There's only work to do if current dataType is non-auto
+			if ( current === "*" ) {
+
+				current = prev;
+
+			// Convert response if prev dataType is non-auto and differs from current
+			} else if ( prev !== "*" && prev !== current ) {
+
+				// Seek a direct converter
+				conv = converters[ prev + " " + current ] || converters[ "* " + current ];
+
+				// If none found, seek a pair
+				if ( !conv ) {
+					for ( conv2 in converters ) {
+
+						// If conv2 outputs current
+						tmp = conv2.split( " " );
+						if ( tmp[ 1 ] === current ) {
+
+							// If prev can be converted to accepted input
+							conv = converters[ prev + " " + tmp[ 0 ] ] ||
+								converters[ "* " + tmp[ 0 ] ];
+							if ( conv ) {
+
+								// Condense equivalence converters
+								if ( conv === true ) {
+									conv = converters[ conv2 ];
+
+								// Otherwise, insert the intermediate dataType
+								} else if ( converters[ conv2 ] !== true ) {
+									current = tmp[ 0 ];
+									dataTypes.unshift( tmp[ 1 ] );
+								}
+								break;
+							}
+						}
+					}
+				}
+
+				// Apply converter (if not an equivalence)
+				if ( conv !== true ) {
+
+					// Unless errors are allowed to bubble, catch and return them
+					if ( conv && s.throws ) {
+						response = conv( response );
+					} else {
+						try {
+							response = conv( response );
+						} catch ( e ) {
+							return {
+								state: "parsererror",
+								error: conv ? e : "No conversion from " + prev + " to " + current
+							};
+						}
+					}
+				}
+			}
+		}
+	}
+
+	return { state: "success", data: response };
+}
+
+jQuery.extend( {
+
+	// Counter for holding the number of active queries
+	active: 0,
+
+	// Last-Modified header cache for next request
+	lastModified: {},
+	etag: {},
+
+	ajaxSettings: {
+		url: location.href,
+		type: "GET",
+		isLocal: rlocalProtocol.test( location.protocol ),
+		global: true,
+		processData: true,
+		async: true,
+		contentType: "application/x-www-form-urlencoded; charset=UTF-8",
+
+		/*
+		timeout: 0,
+		data: null,
+		dataType: null,
+		username: null,
+		password: null,
+		cache: null,
+		throws: false,
+		traditional: false,
+		headers: {},
+		*/
+
+		accepts: {
+			"*": allTypes,
+			text: "text/plain",
+			html: "text/html",
+			xml: "application/xml, text/xml",
+			json: "application/json, text/javascript"
+		},
+
+		contents: {
+			xml: /\bxml\b/,
+			html: /\bhtml/,
+			json: /\bjson\b/
+		},
+
+		responseFields: {
+			xml: "responseXML",
+			text: "responseText",
+			json: "responseJSON"
+		},
+
+		// Data converters
+		// Keys separate source (or catchall "*") and destination types with a single space
+		converters: {
+
+			// Convert anything to text
+			"* text": String,
+
+			// Text to html (true = no transformation)
+			"text html": true,
+
+			// Evaluate text as a json expression
+			"text json": JSON.parse,
+
+			// Parse text as xml
+			"text xml": jQuery.parseXML
+		},
+
+		// For options that shouldn't be deep extended:
+		// you can add your own custom options here if
+		// and when you create one that shouldn't be
+		// deep extended (see ajaxExtend)
+		flatOptions: {
+			url: true,
+			context: true
+		}
+	},
+
+	// Creates a full fledged settings object into target
+	// with both ajaxSettings and settings fields.
+	// If target is omitted, writes into ajaxSettings.
+	ajaxSetup: function( target, settings ) {
+		return settings ?
+
+			// Building a settings object
+			ajaxExtend( ajaxExtend( target, jQuery.ajaxSettings ), settings ) :
+
+			// Extending ajaxSettings
+			ajaxExtend( jQuery.ajaxSettings, target );
+	},
+
+	ajaxPrefilter: addToPrefiltersOrTransports( prefilters ),
+	ajaxTransport: addToPrefiltersOrTransports( transports ),
+
+	// Main method
+	ajax: function( url, options ) {
+
+		// If url is an object, simulate pre-1.5 signature
+		if ( typeof url === "object" ) {
+			options = url;
+			url = undefined;
+		}
+
+		// Force options to be an object
+		options = options || {};
+
+		var transport,
+
+			// URL without anti-cache param
+			cacheURL,
+
+			// Response headers
+			responseHeadersString,
+			responseHeaders,
+
+			// timeout handle
+			timeoutTimer,
+
+			// Url cleanup var
+			urlAnchor,
+
+			// Request state (becomes false upon send and true upon completion)
+			completed,
+
+			// To know if global events are to be dispatched
+			fireGlobals,
+
+			// Loop variable
+			i,
+
+			// uncached part of the url
+			uncached,
+
+			// Create the final options object
+			s = jQuery.ajaxSetup( {}, options ),
+
+			// Callbacks context
+			callbackContext = s.context || s,
+
+			// Context for global events is callbackContext if it is a DOM node or jQuery collection
+			globalEventContext = s.context &&
+				( callbackContext.nodeType || callbackContext.jquery ) ?
+				jQuery( callbackContext ) :
+				jQuery.event,
+
+			// Deferreds
+			deferred = jQuery.Deferred(),
+			completeDeferred = jQuery.Callbacks( "once memory" ),
+
+			// Status-dependent callbacks
+			statusCode = s.statusCode || {},
+
+			// Headers (they are sent all at once)
+			requestHeaders = {},
+			requestHeadersNames = {},
+
+			// Default abort message
+			strAbort = "canceled",
+
+			// Fake xhr
+			jqXHR = {
+				readyState: 0,
+
+				// Builds headers hashtable if needed
+				getResponseHeader: function( key ) {
+					var match;
+					if ( completed ) {
+						if ( !responseHeaders ) {
+							responseHeaders = {};
+							while ( ( match = rheaders.exec( responseHeadersString ) ) ) {
+								responseHeaders[ match[ 1 ].toLowerCase() + " " ] =
+									( responseHeaders[ match[ 1 ].toLowerCase() + " " ] || [] )
+										.concat( match[ 2 ] );
+							}
+						}
+						match = responseHeaders[ key.toLowerCase() + " " ];
+					}
+					return match == null ? null : match.join( ", " );
+				},
+
+				// Raw string
+				getAllResponseHeaders: function() {
+					return completed ? responseHeadersString : null;
+				},
+
+				// Caches the header
+				setRequestHeader: function( name, value ) {
+					if ( completed == null ) {
+						name = requestHeadersNames[ name.toLowerCase() ] =
+							requestHeadersNames[ name.toLowerCase() ] || name;
+						requestHeaders[ name ] = value;
+					}
+					return this;
+				},
+
+				// Overrides response content-type header
+				overrideMimeType: function( type ) {
+					if ( completed == null ) {
+						s.mimeType = type;
+					}
+					return this;
+				},
+
+				// Status-dependent callbacks
+				statusCode: function( map ) {
+					var code;
+					if ( map ) {
+						if ( completed ) {
+
+							// Execute the appropriate callbacks
+							jqXHR.always( map[ jqXHR.status ] );
+						} else {
+
+							// Lazy-add the new callbacks in a way that preserves old ones
+							for ( code in map ) {
+								statusCode[ code ] = [ statusCode[ code ], map[ code ] ];
+							}
+						}
+					}
+					return this;
+				},
+
+				// Cancel the request
+				abort: function( statusText ) {
+					var finalText = statusText || strAbort;
+					if ( transport ) {
+						transport.abort( finalText );
+					}
+					done( 0, finalText );
+					return this;
+				}
+			};
+
+		// Attach deferreds
+		deferred.promise( jqXHR );
+
+		// Add protocol if not provided (prefilters might expect it)
+		// Handle falsy url in the settings object (#10093: consistency with old signature)
+		// We also use the url parameter if available
+		s.url = ( ( url || s.url || location.href ) + "" )
+			.replace( rprotocol, location.protocol + "//" );
+
+		// Alias method option to type as per ticket #12004
+		s.type = options.method || options.type || s.method || s.type;
+
+		// Extract dataTypes list
+		s.dataTypes = ( s.dataType || "*" ).toLowerCase().match( rnothtmlwhite ) || [ "" ];
+
+		// A cross-domain request is in order when the origin doesn't match the current origin.
+		if ( s.crossDomain == null ) {
+			urlAnchor = document.createElement( "a" );
+
+			// Support: IE <=8 - 11, Edge 12 - 15
+			// IE throws exception on accessing the href property if url is malformed,
+			// e.g. http://example.com:80x/
+			try {
+				urlAnchor.href = s.url;
+
+				// Support: IE <=8 - 11 only
+				// Anchor's host property isn't correctly set when s.url is relative
+				urlAnchor.href = urlAnchor.href;
+				s.crossDomain = originAnchor.protocol + "//" + originAnchor.host !==
+					urlAnchor.protocol + "//" + urlAnchor.host;
+			} catch ( e ) {
+
+				// If there is an error parsing the URL, assume it is crossDomain,
+				// it can be rejected by the transport if it is invalid
+				s.crossDomain = true;
+			}
+		}
+
+		// Convert data if not already a string
+		if ( s.data && s.processData && typeof s.data !== "string" ) {
+			s.data = jQuery.param( s.data, s.traditional );
+		}
+
+		// Apply prefilters
+		inspectPrefiltersOrTransports( prefilters, s, options, jqXHR );
+
+		// If request was aborted inside a prefilter, stop there
+		if ( completed ) {
+			return jqXHR;
+		}
+
+		// We can fire global events as of now if asked to
+		// Don't fire events if jQuery.event is undefined in an AMD-usage scenario (#15118)
+		fireGlobals = jQuery.event && s.global;
+
+		// Watch for a new set of requests
+		if ( fireGlobals && jQuery.active++ === 0 ) {
+			jQuery.event.trigger( "ajaxStart" );
+		}
+
+		// Uppercase the type
+		s.type = s.type.toUpperCase();
+
+		// Determine if request has content
+		s.hasContent = !rnoContent.test( s.type );
+
+		// Save the URL in case we're toying with the If-Modified-Since
+		// and/or If-None-Match header later on
+		// Remove hash to simplify url manipulation
+		cacheURL = s.url.replace( rhash, "" );
+
+		// More options handling for requests with no content
+		if ( !s.hasContent ) {
+
+			// Remember the hash so we can put it back
+			uncached = s.url.slice( cacheURL.length );
+
+			// If data is available and should be processed, append data to url
+			if ( s.data && ( s.processData || typeof s.data === "string" ) ) {
+				cacheURL += ( rquery.test( cacheURL ) ? "&" : "?" ) + s.data;
+
+				// #9682: remove data so that it's not used in an eventual retry
+				delete s.data;
+			}
+
+			// Add or update anti-cache param if needed
+			if ( s.cache === false ) {
+				cacheURL = cacheURL.replace( rantiCache, "$1" );
+				uncached = ( rquery.test( cacheURL ) ? "&" : "?" ) + "_=" + ( nonce.guid++ ) +
+					uncached;
+			}
+
+			// Put hash and anti-cache on the URL that will be requested (gh-1732)
+			s.url = cacheURL + uncached;
+
+		// Change '%20' to '+' if this is encoded form body content (gh-2658)
+		} else if ( s.data && s.processData &&
+			( s.contentType || "" ).indexOf( "application/x-www-form-urlencoded" ) === 0 ) {
+			s.data = s.data.replace( r20, "+" );
+		}
+
+		// Set the If-Modified-Since and/or If-None-Match header, if in ifModified mode.
+		if ( s.ifModified ) {
+			if ( jQuery.lastModified[ cacheURL ] ) {
+				jqXHR.setRequestHeader( "If-Modified-Since", jQuery.lastModified[ cacheURL ] );
+			}
+			if ( jQuery.etag[ cacheURL ] ) {
+				jqXHR.setRequestHeader( "If-None-Match", jQuery.etag[ cacheURL ] );
+			}
+		}
+
+		// Set the correct header, if data is being sent
+		if ( s.data && s.hasContent && s.contentType !== false || options.contentType ) {
+			jqXHR.setRequestHeader( "Content-Type", s.contentType );
+		}
+
+		// Set the Accepts header for the server, depending on the dataType
+		jqXHR.setRequestHeader(
+			"Accept",
+			s.dataTypes[ 0 ] && s.accepts[ s.dataTypes[ 0 ] ] ?
+				s.accepts[ s.dataTypes[ 0 ] ] +
+					( s.dataTypes[ 0 ] !== "*" ? ", " + allTypes + "; q=0.01" : "" ) :
+				s.accepts[ "*" ]
+		);
+
+		// Check for headers option
+		for ( i in s.headers ) {
+			jqXHR.setRequestHeader( i, s.headers[ i ] );
+		}
+
+		// Allow custom headers/mimetypes and early abort
+		if ( s.beforeSend &&
+			( s.beforeSend.call( callbackContext, jqXHR, s ) === false || completed ) ) {
+
+			// Abort if not done already and return
+			return jqXHR.abort();
+		}
+
+		// Aborting is no longer a cancellation
+		strAbort = "abort";
+
+		// Install callbacks on deferreds
+		completeDeferred.add( s.complete );
+		jqXHR.done( s.success );
+		jqXHR.fail( s.error );
+
+		// Get transport
+		transport = inspectPrefiltersOrTransports( transports, s, options, jqXHR );
+
+		// If no transport, we auto-abort
+		if ( !transport ) {
+			done( -1, "No Transport" );
+		} else {
+			jqXHR.readyState = 1;
+
+			// Send global event
+			if ( fireGlobals ) {
+				globalEventContext.trigger( "ajaxSend", [ jqXHR, s ] );
+			}
+
+			// If request was aborted inside ajaxSend, stop there
+			if ( completed ) {
+				return jqXHR;
+			}
+
+			// Timeout
+			if ( s.async && s.timeout > 0 ) {
+				timeoutTimer = window.setTimeout( function() {
+					jqXHR.abort( "timeout" );
+				}, s.timeout );
+			}
+
+			try {
+				completed = false;
+				transport.send( requestHeaders, done );
+			} catch ( e ) {
+
+				// Rethrow post-completion exceptions
+				if ( completed ) {
+					throw e;
+				}
+
+				// Propagate others as results
+				done( -1, e );
+			}
+		}
+
+		// Callback for when everything is done
+		function done( status, nativeStatusText, responses, headers ) {
+			var isSuccess, success, error, response, modified,
+				statusText = nativeStatusText;
+
+			// Ignore repeat invocations
+			if ( completed ) {
+				return;
+			}
+
+			completed = true;
+
+			// Clear timeout if it exists
+			if ( timeoutTimer ) {
+				window.clearTimeout( timeoutTimer );
+			}
+
+			// Dereference transport for early garbage collection
+			// (no matter how long the jqXHR object will be used)
+			transport = undefined;
+
+			// Cache response headers
+			responseHeadersString = headers || "";
+
+			// Set readyState
+			jqXHR.readyState = status > 0 ? 4 : 0;
+
+			// Determine if successful
+			isSuccess = status >= 200 && status < 300 || status === 304;
+
+			// Get response data
+			if ( responses ) {
+				response = ajaxHandleResponses( s, jqXHR, responses );
+			}
+
+			// Use a noop converter for missing script but not if jsonp
+			if ( !isSuccess &&
+				jQuery.inArray( "script", s.dataTypes ) > -1 &&
+				jQuery.inArray( "json", s.dataTypes ) < 0 ) {
+				s.converters[ "text script" ] = function() {};
+			}
+
+			// Convert no matter what (that way responseXXX fields are always set)
+			response = ajaxConvert( s, response, jqXHR, isSuccess );
+
+			// If successful, handle type chaining
+			if ( isSuccess ) {
+
+				// Set the If-Modified-Since and/or If-None-Match header, if in ifModified mode.
+				if ( s.ifModified ) {
+					modified = jqXHR.getResponseHeader( "Last-Modified" );
+					if ( modified ) {
+						jQuery.lastModified[ cacheURL ] = modified;
+					}
+					modified = jqXHR.getResponseHeader( "etag" );
+					if ( modified ) {
+						jQuery.etag[ cacheURL ] = modified;
+					}
+				}
+
+				// if no content
+				if ( status === 204 || s.type === "HEAD" ) {
+					statusText = "nocontent";
+
+				// if not modified
+				} else if ( status === 304 ) {
+					statusText = "notmodified";
+
+				// If we have data, let's convert it
+				} else {
+					statusText = response.state;
+					success = response.data;
+					error = response.error;
+					isSuccess = !error;
+				}
+			} else {
+
+				// Extract error from statusText and normalize for non-aborts
+				error = statusText;
+				if ( status || !statusText ) {
+					statusText = "error";
+					if ( status < 0 ) {
+						status = 0;
+					}
+				}
+			}
+
+			// Set data for the fake xhr object
+			jqXHR.status = status;
+			jqXHR.statusText = ( nativeStatusText || statusText ) + "";
+
+			// Success/Error
+			if ( isSuccess ) {
+				deferred.resolveWith( callbackContext, [ success, statusText, jqXHR ] );
+			} else {
+				deferred.rejectWith( callbackContext, [ jqXHR, statusText, error ] );
+			}
+
+			// Status-dependent callbacks
+			jqXHR.statusCode( statusCode );
+			statusCode = undefined;
+
+			if ( fireGlobals ) {
+				globalEventContext.trigger( isSuccess ? "ajaxSuccess" : "ajaxError",
+					[ jqXHR, s, isSuccess ? success : error ] );
+			}
+
+			// Complete
+			completeDeferred.fireWith( callbackContext, [ jqXHR, statusText ] );
+
+			if ( fireGlobals ) {
+				globalEventContext.trigger( "ajaxComplete", [ jqXHR, s ] );
+
+				// Handle the global AJAX counter
+				if ( !( --jQuery.active ) ) {
+					jQuery.event.trigger( "ajaxStop" );
+				}
+			}
+		}
+
+		return jqXHR;
+	},
+
+	getJSON: function( url, data, callback ) {
+		return jQuery.get( url, data, callback, "json" );
+	},
+
+	getScript: function( url, callback ) {
+		return jQuery.get( url, undefined, callback, "script" );
+	}
+} );
+
+jQuery.each( [ "get", "post" ], function( _i, method ) {
+	jQuery[ method ] = function( url, data, callback, type ) {
+
+		// Shift arguments if data argument was omitted
+		if ( isFunction( data ) ) {
+			type = type || callback;
+			callback = data;
+			data = undefined;
+		}
+
+		// The url can be an options object (which then must have .url)
+		return jQuery.ajax( jQuery.extend( {
+			url: url,
+			type: method,
+			dataType: type,
+			data: data,
+			success: callback
+		}, jQuery.isPlainObject( url ) && url ) );
+	};
+} );
+
+jQuery.ajaxPrefilter( function( s ) {
+	var i;
+	for ( i in s.headers ) {
+		if ( i.toLowerCase() === "content-type" ) {
+			s.contentType = s.headers[ i ] || "";
+		}
+	}
+} );
+
+
+jQuery._evalUrl = function( url, options, doc ) {
+	return jQuery.ajax( {
+		url: url,
+
+		// Make this explicit, since user can override this through ajaxSetup (#11264)
+		type: "GET",
+		dataType: "script",
+		cache: true,
+		async: false,
+		global: false,
+
+		// Only evaluate the response if it is successful (gh-4126)
+		// dataFilter is not invoked for failure responses, so using it instead
+		// of the default converter is kludgy but it works.
+		converters: {
+			"text script": function() {}
+		},
+		dataFilter: function( response ) {
+			jQuery.globalEval( response, options, doc );
+		}
+	} );
+};
+
+
+jQuery.fn.extend( {
+	wrapAll: function( html ) {
+		var wrap;
+
+		if ( this[ 0 ] ) {
+			if ( isFunction( html ) ) {
+				html = html.call( this[ 0 ] );
+			}
+
+			// The elements to wrap the target around
+			wrap = jQuery( html, this[ 0 ].ownerDocument ).eq( 0 ).clone( true );
+
+			if ( this[ 0 ].parentNode ) {
+				wrap.insertBefore( this[ 0 ] );
+			}
+
+			wrap.map( function() {
+				var elem = this;
+
+				while ( elem.firstElementChild ) {
+					elem = elem.firstElementChild;
+				}
+
+				return elem;
+			} ).append( this );
+		}
+
+		return this;
+	},
+
+	wrapInner: function( html ) {
+		if ( isFunction( html ) ) {
+			return this.each( function( i ) {
+				jQuery( this ).wrapInner( html.call( this, i ) );
+			} );
+		}
+
+		return this.each( function() {
+			var self = jQuery( this ),
+				contents = self.contents();
+
+			if ( contents.length ) {
+				contents.wrapAll( html );
+
+			} else {
+				self.append( html );
+			}
+		} );
+	},
+
+	wrap: function( html ) {
+		var htmlIsFunction = isFunction( html );
+
+		return this.each( function( i ) {
+			jQuery( this ).wrapAll( htmlIsFunction ? html.call( this, i ) : html );
+		} );
+	},
+
+	unwrap: function( selector ) {
+		this.parent( selector ).not( "body" ).each( function() {
+			jQuery( this ).replaceWith( this.childNodes );
+		} );
+		return this;
+	}
+} );
+
+
+jQuery.expr.pseudos.hidden = function( elem ) {
+	return !jQuery.expr.pseudos.visible( elem );
+};
+jQuery.expr.pseudos.visible = function( elem ) {
+	return !!( elem.offsetWidth || elem.offsetHeight || elem.getClientRects().length );
+};
+
+
+
+
+jQuery.ajaxSettings.xhr = function() {
+	try {
+		return new window.XMLHttpRequest();
+	} catch ( e ) {}
+};
+
+var xhrSuccessStatus = {
+
+		// File protocol always yields status code 0, assume 200
+		0: 200,
+
+		// Support: IE <=9 only
+		// #1450: sometimes IE returns 1223 when it should be 204
+		1223: 204
+	},
+	xhrSupported = jQuery.ajaxSettings.xhr();
+
+support.cors = !!xhrSupported && ( "withCredentials" in xhrSupported );
+support.ajax = xhrSupported = !!xhrSupported;
+
+jQuery.ajaxTransport( function( options ) {
+	var callback, errorCallback;
+
+	// Cross domain only allowed if supported through XMLHttpRequest
+	if ( support.cors || xhrSupported && !options.crossDomain ) {
+		return {
+			send: function( headers, complete ) {
+				var i,
+					xhr = options.xhr();
+
+				xhr.open(
+					options.type,
+					options.url,
+					options.async,
+					options.username,
+					options.password
+				);
+
+				// Apply custom fields if provided
+				if ( options.xhrFields ) {
+					for ( i in options.xhrFields ) {
+						xhr[ i ] = options.xhrFields[ i ];
+					}
+				}
+
+				// Override mime type if needed
+				if ( options.mimeType && xhr.overrideMimeType ) {
+					xhr.overrideMimeType( options.mimeType );
+				}
+
+				// X-Requested-With header
+				// For cross-domain requests, seeing as conditions for a preflight are
+				// akin to a jigsaw puzzle, we simply never set it to be sure.
+				// (it can always be set on a per-request basis or even using ajaxSetup)
+				// For same-domain requests, won't change header if already provided.
+				if ( !options.crossDomain && !headers[ "X-Requested-With" ] ) {
+					headers[ "X-Requested-With" ] = "XMLHttpRequest";
+				}
+
+				// Set headers
+				for ( i in headers ) {
+					xhr.setRequestHeader( i, headers[ i ] );
+				}
+
+				// Callback
+				callback = function( type ) {
+					return function() {
+						if ( callback ) {
+							callback = errorCallback = xhr.onload =
+								xhr.onerror = xhr.onabort = xhr.ontimeout =
+									xhr.onreadystatechange = null;
+
+							if ( type === "abort" ) {
+								xhr.abort();
+							} else if ( type === "error" ) {
+
+								// Support: IE <=9 only
+								// On a manual native abort, IE9 throws
+								// errors on any property access that is not readyState
+								if ( typeof xhr.status !== "number" ) {
+									complete( 0, "error" );
+								} else {
+									complete(
+
+										// File: protocol always yields status 0; see #8605, #14207
+										xhr.status,
+										xhr.statusText
+									);
+								}
+							} else {
+								complete(
+									xhrSuccessStatus[ xhr.status ] || xhr.status,
+									xhr.statusText,
+
+									// Support: IE <=9 only
+									// IE9 has no XHR2 but throws on binary (trac-11426)
+									// For XHR2 non-text, let the caller handle it (gh-2498)
+									( xhr.responseType || "text" ) !== "text"  ||
+									typeof xhr.responseText !== "string" ?
+										{ binary: xhr.response } :
+										{ text: xhr.responseText },
+									xhr.getAllResponseHeaders()
+								);
+							}
+						}
+					};
+				};
+
+				// Listen to events
+				xhr.onload = callback();
+				errorCallback = xhr.onerror = xhr.ontimeout = callback( "error" );
+
+				// Support: IE 9 only
+				// Use onreadystatechange to replace onabort
+				// to handle uncaught aborts
+				if ( xhr.onabort !== undefined ) {
+					xhr.onabort = errorCallback;
+				} else {
+					xhr.onreadystatechange = function() {
+
+						// Check readyState before timeout as it changes
+						if ( xhr.readyState === 4 ) {
+
+							// Allow onerror to be called first,
+							// but that will not handle a native abort
+							// Also, save errorCallback to a variable
+							// as xhr.onerror cannot be accessed
+							window.setTimeout( function() {
+								if ( callback ) {
+									errorCallback();
+								}
+							} );
+						}
+					};
+				}
+
+				// Create the abort callback
+				callback = callback( "abort" );
+
+				try {
+
+					// Do send the request (this may raise an exception)
+					xhr.send( options.hasContent && options.data || null );
+				} catch ( e ) {
+
+					// #14683: Only rethrow if this hasn't been notified as an error yet
+					if ( callback ) {
+						throw e;
+					}
+				}
+			},
+
+			abort: function() {
+				if ( callback ) {
+					callback();
+				}
+			}
+		};
+	}
+} );
+
+
+
+
+// Prevent auto-execution of scripts when no explicit dataType was provided (See gh-2432)
+jQuery.ajaxPrefilter( function( s ) {
+	if ( s.crossDomain ) {
+		s.contents.script = false;
+	}
+} );
+
+// Install script dataType
+jQuery.ajaxSetup( {
+	accepts: {
+		script: "text/javascript, application/javascript, " +
+			"application/ecmascript, application/x-ecmascript"
+	},
+	contents: {
+		script: /\b(?:java|ecma)script\b/
+	},
+	converters: {
+		"text script": function( text ) {
+			jQuery.globalEval( text );
+			return text;
+		}
+	}
+} );
+
+// Handle cache's special case and crossDomain
+jQuery.ajaxPrefilter( "script", function( s ) {
+	if ( s.cache === undefined ) {
+		s.cache = false;
+	}
+	if ( s.crossDomain ) {
+		s.type = "GET";
+	}
+} );
+
+// Bind script tag hack transport
+jQuery.ajaxTransport( "script", function( s ) {
+
+	// This transport only deals with cross domain or forced-by-attrs requests
+	if ( s.crossDomain || s.scriptAttrs ) {
+		var script, callback;
+		return {
+			send: function( _, complete ) {
+				script = jQuery( "<script>" )
+					.attr( s.scriptAttrs || {} )
+					.prop( { charset: s.scriptCharset, src: s.url } )
+					.on( "load error", callback = function( evt ) {
+						script.remove();
+						callback = null;
+						if ( evt ) {
+							complete( evt.type === "error" ? 404 : 200, evt.type );
+						}
+					} );
+
+				// Use native DOM manipulation to avoid our domManip AJAX trickery
+				document.head.appendChild( script[ 0 ] );
+			},
+			abort: function() {
+				if ( callback ) {
+					callback();
+				}
+			}
+		};
+	}
+} );
+
+
+
+
+var oldCallbacks = [],
+	rjsonp = /(=)\?(?=&|$)|\?\?/;
+
+// Default jsonp settings
+jQuery.ajaxSetup( {
+	jsonp: "callback",
+	jsonpCallback: function() {
+		var callback = oldCallbacks.pop() || ( jQuery.expando + "_" + ( nonce.guid++ ) );
+		this[ callback ] = true;
+		return callback;
+	}
+} );
+
+// Detect, normalize options and install callbacks for jsonp requests
+jQuery.ajaxPrefilter( "json jsonp", function( s, originalSettings, jqXHR ) {
+
+	var callbackName, overwritten, responseContainer,
+		jsonProp = s.jsonp !== false && ( rjsonp.test( s.url ) ?
+			"url" :
+			typeof s.data === "string" &&
+				( s.contentType || "" )
+					.indexOf( "application/x-www-form-urlencoded" ) === 0 &&
+				rjsonp.test( s.data ) && "data"
+		);
+
+	// Handle iff the expected data type is "jsonp" or we have a parameter to set
+	if ( jsonProp || s.dataTypes[ 0 ] === "jsonp" ) {
+
+		// Get callback name, remembering preexisting value associated with it
+		callbackName = s.jsonpCallback = isFunction( s.jsonpCallback ) ?
+			s.jsonpCallback() :
+			s.jsonpCallback;
+
+		// Insert callback into url or form data
+		if ( jsonProp ) {
+			s[ jsonProp ] = s[ jsonProp ].replace( rjsonp, "$1" + callbackName );
+		} else if ( s.jsonp !== false ) {
+			s.url += ( rquery.test( s.url ) ? "&" : "?" ) + s.jsonp + "=" + callbackName;
+		}
+
+		// Use data converter to retrieve json after script execution
+		s.converters[ "script json" ] = function() {
+			if ( !responseContainer ) {
+				jQuery.error( callbackName + " was not called" );
+			}
+			return responseContainer[ 0 ];
+		};
+
+		// Force json dataType
+		s.dataTypes[ 0 ] = "json";
+
+		// Install callback
+		overwritten = window[ callbackName ];
+		window[ callbackName ] = function() {
+			responseContainer = arguments;
+		};
+
+		// Clean-up function (fires after converters)
+		jqXHR.always( function() {
+
+			// If previous value didn't exist - remove it
+			if ( overwritten === undefined ) {
+				jQuery( window ).removeProp( callbackName );
+
+			// Otherwise restore preexisting value
+			} else {
+				window[ callbackName ] = overwritten;
+			}
+
+			// Save back as free
+			if ( s[ callbackName ] ) {
+
+				// Make sure that re-using the options doesn't screw things around
+				s.jsonpCallback = originalSettings.jsonpCallback;
+
+				// Save the callback name for future use
+				oldCallbacks.push( callbackName );
+			}
+
+			// Call if it was a function and we have a response
+			if ( responseContainer && isFunction( overwritten ) ) {
+				overwritten( responseContainer[ 0 ] );
+			}
+
+			responseContainer = overwritten = undefined;
+		} );
+
+		// Delegate to script
+		return "script";
+	}
+} );
+
+
+
+
+// Support: Safari 8 only
+// In Safari 8 documents created via document.implementation.createHTMLDocument
+// collapse sibling forms: the second one becomes a child of the first one.
+// Because of that, this security measure has to be disabled in Safari 8.
+// https://bugs.webkit.org/show_bug.cgi?id=137337
+support.createHTMLDocument = ( function() {
+	var body = document.implementation.createHTMLDocument( "" ).body;
+	body.innerHTML = "<form></form><form></form>";
+	return body.childNodes.length === 2;
+} )();
+
+
+// Argument "data" should be string of html
+// context (optional): If specified, the fragment will be created in this context,
+// defaults to document
+// keepScripts (optional): If true, will include scripts passed in the html string
+jQuery.parseHTML = function( data, context, keepScripts ) {
+	if ( typeof data !== "string" ) {
+		return [];
+	}
+	if ( typeof context === "boolean" ) {
+		keepScripts = context;
+		context = false;
+	}
+
+	var base, parsed, scripts;
+
+	if ( !context ) {
+
+		// Stop scripts or inline event handlers from being executed immediately
+		// by using document.implementation
+		if ( support.createHTMLDocument ) {
+			context = document.implementation.createHTMLDocument( "" );
+
+			// Set the base href for the created document
+			// so any parsed elements with URLs
+			// are based on the document's URL (gh-2965)
+			base = context.createElement( "base" );
+			base.href = document.location.href;
+			context.head.appendChild( base );
+		} else {
+			context = document;
+		}
+	}
+
+	parsed = rsingleTag.exec( data );
+	scripts = !keepScripts && [];
+
+	// Single tag
+	if ( parsed ) {
+		return [ context.createElement( parsed[ 1 ] ) ];
+	}
+
+	parsed = buildFragment( [ data ], context, scripts );
+
+	if ( scripts && scripts.length ) {
+		jQuery( scripts ).remove();
+	}
+
+	return jQuery.merge( [], parsed.childNodes );
+};
+
+
+/**
+ * Load a url into a page
+ */
+jQuery.fn.load = function( url, params, callback ) {
+	var selector, type, response,
+		self = this,
+		off = url.indexOf( " " );
+
+	if ( off > -1 ) {
+		selector = stripAndCollapse( url.slice( off ) );
+		url = url.slice( 0, off );
+	}
+
+	// If it's a function
+	if ( isFunction( params ) ) {
+
+		// We assume that it's the callback
+		callback = params;
+		params = undefined;
+
+	// Otherwise, build a param string
+	} else if ( params && typeof params === "object" ) {
+		type = "POST";
+	}
+
+	// If we have elements to modify, make the request
+	if ( self.length > 0 ) {
+		jQuery.ajax( {
+			url: url,
+
+			// If "type" variable is undefined, then "GET" method will be used.
+			// Make value of this field explicit since
+			// user can override it through ajaxSetup method
+			type: type || "GET",
+			dataType: "html",
+			data: params
+		} ).done( function( responseText ) {
+
+			// Save response for use in complete callback
+			response = arguments;
+
+			self.html( selector ?
+
+				// If a selector was specified, locate the right elements in a dummy div
+				// Exclude scripts to avoid IE 'Permission Denied' errors
+				jQuery( "<div>" ).append( jQuery.parseHTML( responseText ) ).find( selector ) :
+
+				// Otherwise use the full result
+				responseText );
+
+		// If the request succeeds, this function gets "data", "status", "jqXHR"
+		// but they are ignored because response was set above.
+		// If it fails, this function gets "jqXHR", "status", "error"
+		} ).always( callback && function( jqXHR, status ) {
+			self.each( function() {
+				callback.apply( this, response || [ jqXHR.responseText, status, jqXHR ] );
+			} );
+		} );
+	}
+
+	return this;
+};
+
+
+
+
+jQuery.expr.pseudos.animated = function( elem ) {
+	return jQuery.grep( jQuery.timers, function( fn ) {
+		return elem === fn.elem;
+	} ).length;
+};
+
+
+
+
+jQuery.offset = {
+	setOffset: function( elem, options, i ) {
+		var curPosition, curLeft, curCSSTop, curTop, curOffset, curCSSLeft, calculatePosition,
+			position = jQuery.css( elem, "position" ),
+			curElem = jQuery( elem ),
+			props = {};
+
+		// Set position first, in-case top/left are set even on static elem
+		if ( position === "static" ) {
+			elem.style.position = "relative";
+		}
+
+		curOffset = curElem.offset();
+		curCSSTop = jQuery.css( elem, "top" );
+		curCSSLeft = jQuery.css( elem, "left" );
+		calculatePosition = ( position === "absolute" || position === "fixed" ) &&
+			( curCSSTop + curCSSLeft ).indexOf( "auto" ) > -1;
+
+		// Need to be able to calculate position if either
+		// top or left is auto and position is either absolute or fixed
+		if ( calculatePosition ) {
+			curPosition = curElem.position();
+			curTop = curPosition.top;
+			curLeft = curPosition.left;
+
+		} else {
+			curTop = parseFloat( curCSSTop ) || 0;
+			curLeft = parseFloat( curCSSLeft ) || 0;
+		}
+
+		if ( isFunction( options ) ) {
+
+			// Use jQuery.extend here to allow modification of coordinates argument (gh-1848)
+			options = options.call( elem, i, jQuery.extend( {}, curOffset ) );
+		}
+
+		if ( options.top != null ) {
+			props.top = ( options.top - curOffset.top ) + curTop;
+		}
+		if ( options.left != null ) {
+			props.left = ( options.left - curOffset.left ) + curLeft;
+		}
+
+		if ( "using" in options ) {
+			options.using.call( elem, props );
+
+		} else {
+			curElem.css( props );
+		}
+	}
+};
+
+jQuery.fn.extend( {
+
+	// offset() relates an element's border box to the document origin
+	offset: function( options ) {
+
+		// Preserve chaining for setter
+		if ( arguments.length ) {
+			return options === undefined ?
+				this :
+				this.each( function( i ) {
+					jQuery.offset.setOffset( this, options, i );
+				} );
+		}
+
+		var rect, win,
+			elem = this[ 0 ];
+
+		if ( !elem ) {
+			return;
+		}
+
+		// Return zeros for disconnected and hidden (display: none) elements (gh-2310)
+		// Support: IE <=11 only
+		// Running getBoundingClientRect on a
+		// disconnected node in IE throws an error
+		if ( !elem.getClientRects().length ) {
+			return { top: 0, left: 0 };
+		}
+
+		// Get document-relative position by adding viewport scroll to viewport-relative gBCR
+		rect = elem.getBoundingClientRect();
+		win = elem.ownerDocument.defaultView;
+		return {
+			top: rect.top + win.pageYOffset,
+			left: rect.left + win.pageXOffset
+		};
+	},
+
+	// position() relates an element's margin box to its offset parent's padding box
+	// This corresponds to the behavior of CSS absolute positioning
+	position: function() {
+		if ( !this[ 0 ] ) {
+			return;
+		}
+
+		var offsetParent, offset, doc,
+			elem = this[ 0 ],
+			parentOffset = { top: 0, left: 0 };
+
+		// position:fixed elements are offset from the viewport, which itself always has zero offset
+		if ( jQuery.css( elem, "position" ) === "fixed" ) {
+
+			// Assume position:fixed implies availability of getBoundingClientRect
+			offset = elem.getBoundingClientRect();
+
+		} else {
+			offset = this.offset();
+
+			// Account for the *real* offset parent, which can be the document or its root element
+			// when a statically positioned element is identified
+			doc = elem.ownerDocument;
+			offsetParent = elem.offsetParent || doc.documentElement;
+			while ( offsetParent &&
+				( offsetParent === doc.body || offsetParent === doc.documentElement ) &&
+				jQuery.css( offsetParent, "position" ) === "static" ) {
+
+				offsetParent = offsetParent.parentNode;
+			}
+			if ( offsetParent && offsetParent !== elem && offsetParent.nodeType === 1 ) {
+
+				// Incorporate borders into its offset, since they are outside its content origin
+				parentOffset = jQuery( offsetParent ).offset();
+				parentOffset.top += jQuery.css( offsetParent, "borderTopWidth", true );
+				parentOffset.left += jQuery.css( offsetParent, "borderLeftWidth", true );
+			}
+		}
+
+		// Subtract parent offsets and element margins
+		return {
+			top: offset.top - parentOffset.top - jQuery.css( elem, "marginTop", true ),
+			left: offset.left - parentOffset.left - jQuery.css( elem, "marginLeft", true )
+		};
+	},
+
+	// This method will return documentElement in the following cases:
+	// 1) For the element inside the iframe without offsetParent, this method will return
+	//    documentElement of the parent window
+	// 2) For the hidden or detached element
+	// 3) For body or html element, i.e. in case of the html node - it will return itself
+	//
+	// but those exceptions were never presented as a real life use-cases
+	// and might be considered as more preferable results.
+	//
+	// This logic, however, is not guaranteed and can change at any point in the future
+	offsetParent: function() {
+		return this.map( function() {
+			var offsetParent = this.offsetParent;
+
+			while ( offsetParent && jQuery.css( offsetParent, "position" ) === "static" ) {
+				offsetParent = offsetParent.offsetParent;
+			}
+
+			return offsetParent || documentElement;
+		} );
+	}
+} );
+
+// Create scrollLeft and scrollTop methods
+jQuery.each( { scrollLeft: "pageXOffset", scrollTop: "pageYOffset" }, function( method, prop ) {
+	var top = "pageYOffset" === prop;
+
+	jQuery.fn[ method ] = function( val ) {
+		return access( this, function( elem, method, val ) {
+
+			// Coalesce documents and windows
+			var win;
+			if ( isWindow( elem ) ) {
+				win = elem;
+			} else if ( elem.nodeType === 9 ) {
+				win = elem.defaultView;
+			}
+
+			if ( val === undefined ) {
+				return win ? win[ prop ] : elem[ method ];
+			}
+
+			if ( win ) {
+				win.scrollTo(
+					!top ? val : win.pageXOffset,
+					top ? val : win.pageYOffset
+				);
+
+			} else {
+				elem[ method ] = val;
+			}
+		}, method, val, arguments.length );
+	};
+} );
+
+// Support: Safari <=7 - 9.1, Chrome <=37 - 49
+// Add the top/left cssHooks using jQuery.fn.position
+// Webkit bug: https://bugs.webkit.org/show_bug.cgi?id=29084
+// Blink bug: https://bugs.chromium.org/p/chromium/issues/detail?id=589347
+// getComputedStyle returns percent when specified for top/left/bottom/right;
+// rather than make the css module depend on the offset module, just check for it here
+jQuery.each( [ "top", "left" ], function( _i, prop ) {
+	jQuery.cssHooks[ prop ] = addGetHookIf( support.pixelPosition,
+		function( elem, computed ) {
+			if ( computed ) {
+				computed = curCSS( elem, prop );
+
+				// If curCSS returns percentage, fallback to offset
+				return rnumnonpx.test( computed ) ?
+					jQuery( elem ).position()[ prop ] + "px" :
+					computed;
+			}
+		}
+	);
+} );
+
+
+// Create innerHeight, innerWidth, height, width, outerHeight and outerWidth methods
+jQuery.each( { Height: "height", Width: "width" }, function( name, type ) {
+	jQuery.each( {
+		padding: "inner" + name,
+		content: type,
+		"": "outer" + name
+	}, function( defaultExtra, funcName ) {
+
+		// Margin is only for outerHeight, outerWidth
+		jQuery.fn[ funcName ] = function( margin, value ) {
+			var chainable = arguments.length && ( defaultExtra || typeof margin !== "boolean" ),
+				extra = defaultExtra || ( margin === true || value === true ? "margin" : "border" );
+
+			return access( this, function( elem, type, value ) {
+				var doc;
+
+				if ( isWindow( elem ) ) {
+
+					// $( window ).outerWidth/Height return w/h including scrollbars (gh-1729)
+					return funcName.indexOf( "outer" ) === 0 ?
+						elem[ "inner" + name ] :
+						elem.document.documentElement[ "client" + name ];
+				}
+
+				// Get document width or height
+				if ( elem.nodeType === 9 ) {
+					doc = elem.documentElement;
+
+					// Either scroll[Width/Height] or offset[Width/Height] or client[Width/Height],
+					// whichever is greatest
+					return Math.max(
+						elem.body[ "scroll" + name ], doc[ "scroll" + name ],
+						elem.body[ "offset" + name ], doc[ "offset" + name ],
+						doc[ "client" + name ]
+					);
+				}
+
+				return value === undefined ?
+
+					// Get width or height on the element, requesting but not forcing parseFloat
+					jQuery.css( elem, type, extra ) :
+
+					// Set width or height on the element
+					jQuery.style( elem, type, value, extra );
+			}, type, chainable ? margin : undefined, chainable );
+		};
+	} );
+} );
+
+
+jQuery.each( [
+	"ajaxStart",
+	"ajaxStop",
+	"ajaxComplete",
+	"ajaxError",
+	"ajaxSuccess",
+	"ajaxSend"
+], function( _i, type ) {
+	jQuery.fn[ type ] = function( fn ) {
+		return this.on( type, fn );
+	};
+} );
+
+
+
+
+jQuery.fn.extend( {
+
+	bind: function( types, data, fn ) {
+		return this.on( types, null, data, fn );
+	},
+	unbind: function( types, fn ) {
+		return this.off( types, null, fn );
+	},
+
+	delegate: function( selector, types, data, fn ) {
+		return this.on( types, selector, data, fn );
+	},
+	undelegate: function( selector, types, fn ) {
+
+		// ( namespace ) or ( selector, types [, fn] )
+		return arguments.length === 1 ?
+			this.off( selector, "**" ) :
+			this.off( types, selector || "**", fn );
+	},
+
+	hover: function( fnOver, fnOut ) {
+		return this.mouseenter( fnOver ).mouseleave( fnOut || fnOver );
+	}
+} );
+
+jQuery.each(
+	( "blur focus focusin focusout resize scroll click dblclick " +
+	"mousedown mouseup mousemove mouseover mouseout mouseenter mouseleave " +
+	"change select submit keydown keypress keyup contextmenu" ).split( " " ),
+	function( _i, name ) {
+
+		// Handle event binding
+		jQuery.fn[ name ] = function( data, fn ) {
+			return arguments.length > 0 ?
+				this.on( name, null, data, fn ) :
+				this.trigger( name );
+		};
+	}
+);
+
+
+
+
+// Support: Android <=4.0 only
+// Make sure we trim BOM and NBSP
+var rtrim = /^[\s\uFEFF\xA0]+|[\s\uFEFF\xA0]+$/g;
+
+// Bind a function to a context, optionally partially applying any
+// arguments.
+// jQuery.proxy is deprecated to promote standards (specifically Function#bind)
+// However, it is not slated for removal any time soon
+jQuery.proxy = function( fn, context ) {
+	var tmp, args, proxy;
+
+	if ( typeof context === "string" ) {
+		tmp = fn[ context ];
+		context = fn;
+		fn = tmp;
+	}
+
+	// Quick check to determine if target is callable, in the spec
+	// this throws a TypeError, but we will just return undefined.
+	if ( !isFunction( fn ) ) {
+		return undefined;
+	}
+
+	// Simulated bind
+	args = slice.call( arguments, 2 );
+	proxy = function() {
+		return fn.apply( context || this, args.concat( slice.call( arguments ) ) );
+	};
+
+	// Set the guid of unique handler to the same of original handler, so it can be removed
+	proxy.guid = fn.guid = fn.guid || jQuery.guid++;
+
+	return proxy;
+};
+
+jQuery.holdReady = function( hold ) {
+	if ( hold ) {
+		jQuery.readyWait++;
+	} else {
+		jQuery.ready( true );
+	}
+};
+jQuery.isArray = Array.isArray;
+jQuery.parseJSON = JSON.parse;
+jQuery.nodeName = nodeName;
+jQuery.isFunction = isFunction;
+jQuery.isWindow = isWindow;
+jQuery.camelCase = camelCase;
+jQuery.type = toType;
+
+jQuery.now = Date.now;
+
+jQuery.isNumeric = function( obj ) {
+
+	// As of jQuery 3.0, isNumeric is limited to
+	// strings and numbers (primitives or objects)
+	// that can be coerced to finite numbers (gh-2662)
+	var type = jQuery.type( obj );
+	return ( type === "number" || type === "string" ) &&
+
+		// parseFloat NaNs numeric-cast false positives ("")
+		// ...but misinterprets leading-number strings, particularly hex literals ("0x...")
+		// subtraction forces infinities to NaN
+		!isNaN( obj - parseFloat( obj ) );
+};
+
+jQuery.trim = function( text ) {
+	return text == null ?
+		"" :
+		( text + "" ).replace( rtrim, "" );
+};
+
+
+
+// Register as a named AMD module, since jQuery can be concatenated with other
+// files that may use define, but not via a proper concatenation script that
+// understands anonymous AMD modules. A named AMD is safest and most robust
+// way to register. Lowercase jquery is used because AMD module names are
+// derived from file names, and jQuery is normally delivered in a lowercase
+// file name. Do this after creating the global so that if an AMD module wants
+// to call noConflict to hide this version of jQuery, it will work.
+
+// Note that for maximum portability, libraries that are not jQuery should
+// declare themselves as anonymous modules, and avoid setting a global if an
+// AMD loader is present. jQuery is a special case. For more information, see
+// https://github.com/jrburke/requirejs/wiki/Updating-existing-libraries#wiki-anon
+
+if ( typeof define === "function" && define.amd ) {
+	define( "jquery", [], function() {
+		return jQuery;
+	} );
+}
+
+
+
+
+var
+
+	// Map over jQuery in case of overwrite
+	_jQuery = window.jQuery,
+
+	// Map over the $ in case of overwrite
+	_$ = window.$;
+
+jQuery.noConflict = function( deep ) {
+	if ( window.$ === jQuery ) {
+		window.$ = _$;
+	}
+
+	if ( deep && window.jQuery === jQuery ) {
+		window.jQuery = _jQuery;
+	}
+
+	return jQuery;
+};
+
+// Expose jQuery and $ identifiers, even in AMD
+// (#7102#comment:10, https://github.com/jquery/jquery/pull/557)
+// and CommonJS for browser emulators (#13566)
+if ( typeof noGlobal === "undefined" ) {
+	window.jQuery = window.$ = jQuery;
+}
+
+
+
+
+return jQuery;
+} );
diff --git a/docs/build/html/_static/jquery.js b/docs/build/html/_static/jquery.js
new file mode 100644
index 0000000..c4c6022
--- /dev/null
+++ b/docs/build/html/_static/jquery.js
@@ -0,0 +1,2 @@
+/*! jQuery v3.6.0 | (c) OpenJS Foundation and other contributors | jquery.org/license */
+!function(e,t){"use strict";"object"==typeof module&&"object"==typeof module.exports?module.exports=e.document?t(e,!0):function(e){if(!e.document)throw new Error("jQuery requires a window with a document");return t(e)}:t(e)}("undefined"!=typeof window?window:this,function(C,e){"use strict";var t=[],r=Object.getPrototypeOf,s=t.slice,g=t.flat?function(e){return t.flat.call(e)}:function(e){return t.concat.apply([],e)},u=t.push,i=t.indexOf,n={},o=n.toString,v=n.hasOwnProperty,a=v.toString,l=a.call(Object),y={},m=function(e){return"function"==typeof e&&"number"!=typeof e.nodeType&&"function"!=typeof e.item},x=function(e){return null!=e&&e===e.window},E=C.document,c={type:!0,src:!0,nonce:!0,noModule:!0};function b(e,t,n){var r,i,o=(n=n||E).createElement("script");if(o.text=e,t)for(r in c)(i=t[r]||t.getAttribute&&t.getAttribute(r))&&o.setAttribute(r,i);n.head.appendChild(o).parentNode.removeChild(o)}function w(e){return null==e?e+"":"object"==typeof e||"function"==typeof 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diff --git a/docs/build/html/_static/language_data.js b/docs/build/html/_static/language_data.js
new file mode 100644
index 0000000..2e22b06
--- /dev/null
+++ b/docs/build/html/_static/language_data.js
@@ -0,0 +1,199 @@
+/*
+ * language_data.js
+ * ~~~~~~~~~~~~~~~~
+ *
+ * This script contains the language-specific data used by searchtools.js,
+ * namely the list of stopwords, stemmer, scorer and splitter.
+ *
+ * :copyright: Copyright 2007-2022 by the Sphinx team, see AUTHORS.
+ * :license: BSD, see LICENSE for details.
+ *
+ */
+
+var stopwords = ["a", "and", "are", "as", "at", "be", "but", "by", "for", "if", "in", "into", "is", "it", "near", "no", "not", "of", "on", "or", "such", "that", "the", "their", "then", "there", "these", "they", "this", "to", "was", "will", "with"];
+
+
+/* Non-minified version is copied as a separate JS file, is available */
+
+/**
+ * Porter Stemmer
+ */
+var Stemmer = function() {
+
+  var step2list = {
+    ational: 'ate',
+    tional: 'tion',
+    enci: 'ence',
+    anci: 'ance',
+    izer: 'ize',
+    bli: 'ble',
+    alli: 'al',
+    entli: 'ent',
+    eli: 'e',
+    ousli: 'ous',
+    ization: 'ize',
+    ation: 'ate',
+    ator: 'ate',
+    alism: 'al',
+    iveness: 'ive',
+    fulness: 'ful',
+    ousness: 'ous',
+    aliti: 'al',
+    iviti: 'ive',
+    biliti: 'ble',
+    logi: 'log'
+  };
+
+  var step3list = {
+    icate: 'ic',
+    ative: '',
+    alize: 'al',
+    iciti: 'ic',
+    ical: 'ic',
+    ful: '',
+    ness: ''
+  };
+
+  var c = "[^aeiou]";          // consonant
+  var v = "[aeiouy]";          // vowel
+  var C = c + "[^aeiouy]*";    // consonant sequence
+  var V = v + "[aeiou]*";      // vowel sequence
+
+  var mgr0 = "^(" + C + ")?" + V + C;                      // [C]VC... is m>0
+  var meq1 = "^(" + C + ")?" + V + C + "(" + V + ")?$";    // [C]VC[V] is m=1
+  var mgr1 = "^(" + C + ")?" + V + C + V + C;              // [C]VCVC... is m>1
+  var s_v   = "^(" + C + ")?" + v;                         // vowel in stem
+
+  this.stemWord = function (w) {
+    var stem;
+    var suffix;
+    var firstch;
+    var origword = w;
+
+    if (w.length < 3)
+      return w;
+
+    var re;
+    var re2;
+    var re3;
+    var re4;
+
+    firstch = w.substr(0,1);
+    if (firstch == "y")
+      w = firstch.toUpperCase() + w.substr(1);
+
+    // Step 1a
+    re = /^(.+?)(ss|i)es$/;
+    re2 = /^(.+?)([^s])s$/;
+
+    if (re.test(w))
+      w = w.replace(re,"$1$2");
+    else if (re2.test(w))
+      w = w.replace(re2,"$1$2");
+
+    // Step 1b
+    re = /^(.+?)eed$/;
+    re2 = /^(.+?)(ed|ing)$/;
+    if (re.test(w)) {
+      var fp = re.exec(w);
+      re = new RegExp(mgr0);
+      if (re.test(fp[1])) {
+        re = /.$/;
+        w = w.replace(re,"");
+      }
+    }
+    else if (re2.test(w)) {
+      var fp = re2.exec(w);
+      stem = fp[1];
+      re2 = new RegExp(s_v);
+      if (re2.test(stem)) {
+        w = stem;
+        re2 = /(at|bl|iz)$/;
+        re3 = new RegExp("([^aeiouylsz])\\1$");
+        re4 = new RegExp("^" + C + v + "[^aeiouwxy]$");
+        if (re2.test(w))
+          w = w + "e";
+        else if (re3.test(w)) {
+          re = /.$/;
+          w = w.replace(re,"");
+        }
+        else if (re4.test(w))
+          w = w + "e";
+      }
+    }
+
+    // Step 1c
+    re = /^(.+?)y$/;
+    if (re.test(w)) {
+      var fp = re.exec(w);
+      stem = fp[1];
+      re = new RegExp(s_v);
+      if (re.test(stem))
+        w = stem + "i";
+    }
+
+    // Step 2
+    re = /^(.+?)(ational|tional|enci|anci|izer|bli|alli|entli|eli|ousli|ization|ation|ator|alism|iveness|fulness|ousness|aliti|iviti|biliti|logi)$/;
+    if (re.test(w)) {
+      var fp = re.exec(w);
+      stem = fp[1];
+      suffix = fp[2];
+      re = new RegExp(mgr0);
+      if (re.test(stem))
+        w = stem + step2list[suffix];
+    }
+
+    // Step 3
+    re = /^(.+?)(icate|ative|alize|iciti|ical|ful|ness)$/;
+    if (re.test(w)) {
+      var fp = re.exec(w);
+      stem = fp[1];
+      suffix = fp[2];
+      re = new RegExp(mgr0);
+      if (re.test(stem))
+        w = stem + step3list[suffix];
+    }
+
+    // Step 4
+    re = /^(.+?)(al|ance|ence|er|ic|able|ible|ant|ement|ment|ent|ou|ism|ate|iti|ous|ive|ize)$/;
+    re2 = /^(.+?)(s|t)(ion)$/;
+    if (re.test(w)) {
+      var fp = re.exec(w);
+      stem = fp[1];
+      re = new RegExp(mgr1);
+      if (re.test(stem))
+        w = stem;
+    }
+    else if (re2.test(w)) {
+      var fp = re2.exec(w);
+      stem = fp[1] + fp[2];
+      re2 = new RegExp(mgr1);
+      if (re2.test(stem))
+        w = stem;
+    }
+
+    // Step 5
+    re = /^(.+?)e$/;
+    if (re.test(w)) {
+      var fp = re.exec(w);
+      stem = fp[1];
+      re = new RegExp(mgr1);
+      re2 = new RegExp(meq1);
+      re3 = new RegExp("^" + C + v + "[^aeiouwxy]$");
+      if (re.test(stem) || (re2.test(stem) && !(re3.test(stem))))
+        w = stem;
+    }
+    re = /ll$/;
+    re2 = new RegExp(mgr1);
+    if (re.test(w) && re2.test(w)) {
+      re = /.$/;
+      w = w.replace(re,"");
+    }
+
+    // and turn initial Y back to y
+    if (firstch == "y")
+      w = firstch.toLowerCase() + w.substr(1);
+    return w;
+  }
+}
+
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diff --git a/docs/build/html/_static/nature.css b/docs/build/html/_static/nature.css
new file mode 100644
index 0000000..5e981bf
--- /dev/null
+++ b/docs/build/html/_static/nature.css
@@ -0,0 +1,248 @@
+/*
+ * nature.css_t
+ * ~~~~~~~~~~~~
+ *
+ * Sphinx stylesheet -- nature theme.
+ *
+ * :copyright: Copyright 2007-2022 by the Sphinx team, see AUTHORS.
+ * :license: BSD, see LICENSE for details.
+ *
+ */
+
+@import url("basic.css");
+
+/* -- page layout ----------------------------------------------------------- */
+
+body {
+    font-family: Arial, sans-serif;
+    font-size: 100%;
+    background-color: #fff;
+    color: #555;
+    margin: 0;
+    padding: 0;
+}
+
+div.documentwrapper {
+    float: left;
+    width: 100%;
+}
+
+div.bodywrapper {
+    margin: 0 0 0 230px;
+}
+
+hr {
+    border: 1px solid #B1B4B6;
+}
+
+div.document {
+    background-color: #eee;
+}
+
+div.body {
+    background-color: #ffffff;
+    color: #3E4349;
+    padding: 0 30px 30px 30px;
+    font-size: 0.9em;
+}
+
+div.footer {
+    color: #555;
+    width: 100%;
+    padding: 13px 0;
+    text-align: center;
+    font-size: 75%;
+}
+
+div.footer a {
+    color: #444;
+    text-decoration: underline;
+}
+
+div.related {
+    background-color: #6BA81E;
+    line-height: 32px;
+    color: #fff;
+    text-shadow: 0px 1px 0 #444;
+    font-size: 0.9em;
+}
+
+div.related a {
+    color: #E2F3CC;
+}
+
+div.sphinxsidebar {
+    font-size: 0.75em;
+    line-height: 1.5em;
+}
+
+div.sphinxsidebarwrapper{
+    padding: 20px 0;
+}
+
+div.sphinxsidebar h3,
+div.sphinxsidebar h4 {
+    font-family: Arial, sans-serif;
+    color: #222;
+    font-size: 1.2em;
+    font-weight: normal;
+    margin: 0;
+    padding: 5px 10px;
+    background-color: #ddd;
+    text-shadow: 1px 1px 0 white
+}
+
+div.sphinxsidebar h4{
+    font-size: 1.1em;
+}
+
+div.sphinxsidebar h3 a {
+    color: #444;
+}
+
+
+div.sphinxsidebar p {
+    color: #888;
+    padding: 5px 20px;
+}
+
+div.sphinxsidebar p.topless {
+}
+
+div.sphinxsidebar ul {
+    margin: 10px 20px;
+    padding: 0;
+    color: #000;
+}
+
+div.sphinxsidebar a {
+    color: #444;
+}
+
+div.sphinxsidebar input {
+    border: 1px solid #ccc;
+    font-family: sans-serif;
+    font-size: 1em;
+}
+
+div.sphinxsidebar .searchformwrapper {
+    margin-left: 20px;
+    margin-right: 20px;
+}
+
+/* -- body styles ----------------------------------------------------------- */
+
+a {
+    color: #005B81;
+    text-decoration: none;
+}
+
+a:hover {
+    color: #E32E00;
+    text-decoration: underline;
+}
+
+div.body h1,
+div.body h2,
+div.body h3,
+div.body h4,
+div.body h5,
+div.body h6 {
+    font-family: Arial, sans-serif;
+    background-color: #BED4EB;
+    font-weight: normal;
+    color: #212224;
+    margin: 30px 0px 10px 0px;
+    padding: 5px 0 5px 10px;
+    text-shadow: 0px 1px 0 white
+}
+
+div.body h1 { border-top: 20px solid white; margin-top: 0; font-size: 200%; }
+div.body h2 { font-size: 150%; background-color: #C8D5E3; }
+div.body h3 { font-size: 120%; background-color: #D8DEE3; }
+div.body h4 { font-size: 110%; background-color: #D8DEE3; }
+div.body h5 { font-size: 100%; background-color: #D8DEE3; }
+div.body h6 { font-size: 100%; background-color: #D8DEE3; }
+
+a.headerlink {
+    color: #c60f0f;
+    font-size: 0.8em;
+    padding: 0 4px 0 4px;
+    text-decoration: none;
+}
+
+a.headerlink:hover {
+    background-color: #c60f0f;
+    color: white;
+}
+
+div.body p, div.body dd, div.body li {
+    line-height: 1.5em;
+}
+
+div.admonition p.admonition-title + p {
+    display: inline;
+}
+
+div.note {
+    background-color: #eee;
+    border: 1px solid #ccc;
+}
+
+div.seealso {
+    background-color: #ffc;
+    border: 1px solid #ff6;
+}
+nav.contents,
+aside.topic,
+
+div.topic {
+    background-color: #eee;
+}
+
+div.warning {
+    background-color: #ffe4e4;
+    border: 1px solid #f66;
+}
+
+p.admonition-title {
+    display: inline;
+}
+
+p.admonition-title:after {
+    content: ":";
+}
+
+pre {
+    padding: 10px;
+    line-height: 1.2em;
+    border: 1px solid #C6C9CB;
+    font-size: 1.1em;
+    margin: 1.5em 0 1.5em 0;
+    -webkit-box-shadow: 1px 1px 1px #d8d8d8;
+    -moz-box-shadow: 1px 1px 1px #d8d8d8;
+}
+
+code {
+    background-color: #ecf0f3;
+    color: #222;
+    /* padding: 1px 2px; */
+    font-size: 1.1em;
+    font-family: monospace;
+}
+
+.viewcode-back {
+    font-family: Arial, sans-serif;
+}
+
+div.viewcode-block:target {
+    background-color: #f4debf;
+    border-top: 1px solid #ac9;
+    border-bottom: 1px solid #ac9;
+}
+
+div.code-block-caption {
+    background-color: #ddd;
+    color: #222;
+    border: 1px solid #C6C9CB;
+}
\ No newline at end of file
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+pre { line-height: 125%; }
+td.linenos .normal { color: inherit; background-color: transparent; padding-left: 5px; padding-right: 5px; }
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+td.linenos .special { color: #000000; background-color: #ffffc0; padding-left: 5px; padding-right: 5px; }
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+.highlight { background: #f8f8f8; }
+.highlight .c { color: #8f5902; font-style: italic } /* Comment */
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+.highlight .vi { color: #000000 } /* Name.Variable.Instance */
+.highlight .vm { color: #000000 } /* Name.Variable.Magic */
+.highlight .il { color: #0000cf; font-weight: bold } /* Literal.Number.Integer.Long */
\ No newline at end of file
diff --git a/docs/build/html/_static/searchtools.js b/docs/build/html/_static/searchtools.js
new file mode 100644
index 0000000..ac4d586
--- /dev/null
+++ b/docs/build/html/_static/searchtools.js
@@ -0,0 +1,531 @@
+/*
+ * searchtools.js
+ * ~~~~~~~~~~~~~~~~
+ *
+ * Sphinx JavaScript utilities for the full-text search.
+ *
+ * :copyright: Copyright 2007-2022 by the Sphinx team, see AUTHORS.
+ * :license: BSD, see LICENSE for details.
+ *
+ */
+"use strict";
+
+/**
+ * Simple result scoring code.
+ */
+if (typeof Scorer === "undefined") {
+  var Scorer = {
+    // Implement the following function to further tweak the score for each result
+    // The function takes a result array [docname, title, anchor, descr, score, filename]
+    // and returns the new score.
+    /*
+    score: result => {
+      const [docname, title, anchor, descr, score, filename] = result
+      return score
+    },
+    */
+
+    // query matches the full name of an object
+    objNameMatch: 11,
+    // or matches in the last dotted part of the object name
+    objPartialMatch: 6,
+    // Additive scores depending on the priority of the object
+    objPrio: {
+      0: 15, // used to be importantResults
+      1: 5, // used to be objectResults
+      2: -5, // used to be unimportantResults
+    },
+    //  Used when the priority is not in the mapping.
+    objPrioDefault: 0,
+
+    // query found in title
+    title: 15,
+    partialTitle: 7,
+    // query found in terms
+    term: 5,
+    partialTerm: 2,
+  };
+}
+
+const _removeChildren = (element) => {
+  while (element && element.lastChild) element.removeChild(element.lastChild);
+};
+
+/**
+ * See https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Regular_Expressions#escaping
+ */
+const _escapeRegExp = (string) =>
+  string.replace(/[.*+\-?^${}()|[\]\\]/g, "\\$&"); // $& means the whole matched string
+
+const _displayItem = (item, highlightTerms, searchTerms) => {
+  const docBuilder = DOCUMENTATION_OPTIONS.BUILDER;
+  const docUrlRoot = DOCUMENTATION_OPTIONS.URL_ROOT;
+  const docFileSuffix = DOCUMENTATION_OPTIONS.FILE_SUFFIX;
+  const docLinkSuffix = DOCUMENTATION_OPTIONS.LINK_SUFFIX;
+  const showSearchSummary = DOCUMENTATION_OPTIONS.SHOW_SEARCH_SUMMARY;
+
+  const [docName, title, anchor, descr] = item;
+
+  let listItem = document.createElement("li");
+  let requestUrl;
+  let linkUrl;
+  if (docBuilder === "dirhtml") {
+    // dirhtml builder
+    let dirname = docName + "/";
+    if (dirname.match(/\/index\/$/))
+      dirname = dirname.substring(0, dirname.length - 6);
+    else if (dirname === "index/") dirname = "";
+    requestUrl = docUrlRoot + dirname;
+    linkUrl = requestUrl;
+  } else {
+    // normal html builders
+    requestUrl = docUrlRoot + docName + docFileSuffix;
+    linkUrl = docName + docLinkSuffix;
+  }
+  const params = new URLSearchParams();
+  params.set("highlight", [...highlightTerms].join(" "));
+  let linkEl = listItem.appendChild(document.createElement("a"));
+  linkEl.href = linkUrl + "?" + params.toString() + anchor;
+  linkEl.innerHTML = title;
+  if (descr)
+    listItem.appendChild(document.createElement("span")).innerText =
+      " (" + descr + ")";
+  else if (showSearchSummary)
+    fetch(requestUrl)
+      .then((responseData) => responseData.text())
+      .then((data) => {
+        if (data)
+          listItem.appendChild(
+            Search.makeSearchSummary(data, searchTerms, highlightTerms)
+          );
+      });
+  Search.output.appendChild(listItem);
+};
+const _finishSearch = (resultCount) => {
+  Search.stopPulse();
+  Search.title.innerText = _("Search Results");
+  if (!resultCount)
+    Search.status.innerText = Documentation.gettext(
+      "Your search did not match any documents. Please make sure that all words are spelled correctly and that you've selected enough categories."
+    );
+  else
+    Search.status.innerText = _(
+      `Search finished, found ${resultCount} page(s) matching the search query.`
+    );
+};
+const _displayNextItem = (
+  results,
+  resultCount,
+  highlightTerms,
+  searchTerms
+) => {
+  // results left, load the summary and display it
+  // this is intended to be dynamic (don't sub resultsCount)
+  if (results.length) {
+    _displayItem(results.pop(), highlightTerms, searchTerms);
+    setTimeout(
+      () => _displayNextItem(results, resultCount, highlightTerms, searchTerms),
+      5
+    );
+  }
+  // search finished, update title and status message
+  else _finishSearch(resultCount);
+};
+
+/**
+ * Default splitQuery function. Can be overridden in ``sphinx.search`` with a
+ * custom function per language.
+ *
+ * The regular expression works by splitting the string on consecutive characters
+ * that are not Unicode letters, numbers, underscores, or emoji characters.
+ * This is the same as ``\W+`` in Python, preserving the surrogate pair area.
+ */
+if (typeof splitQuery === "undefined") {
+  var splitQuery = (query) => query
+      .split(/[^\p{Letter}\p{Number}_\p{Emoji_Presentation}]+/gu)
+      .filter(term => term)  // remove remaining empty strings
+}
+
+/**
+ * Search Module
+ */
+const Search = {
+  _index: null,
+  _queued_query: null,
+  _pulse_status: -1,
+
+  htmlToText: (htmlString) => {
+    const htmlElement = document
+      .createRange()
+      .createContextualFragment(htmlString);
+    _removeChildren(htmlElement.querySelectorAll(".headerlink"));
+    const docContent = htmlElement.querySelector('[role="main"]');
+    if (docContent !== undefined) return docContent.textContent;
+    console.warn(
+      "Content block not found. Sphinx search tries to obtain it via '[role=main]'. Could you check your theme or template."
+    );
+    return "";
+  },
+
+  init: () => {
+    const query = new URLSearchParams(window.location.search).get("q");
+    document
+      .querySelectorAll('input[name="q"]')
+      .forEach((el) => (el.value = query));
+    if (query) Search.performSearch(query);
+  },
+
+  loadIndex: (url) =>
+    (document.body.appendChild(document.createElement("script")).src = url),
+
+  setIndex: (index) => {
+    Search._index = index;
+    if (Search._queued_query !== null) {
+      const query = Search._queued_query;
+      Search._queued_query = null;
+      Search.query(query);
+    }
+  },
+
+  hasIndex: () => Search._index !== null,
+
+  deferQuery: (query) => (Search._queued_query = query),
+
+  stopPulse: () => (Search._pulse_status = -1),
+
+  startPulse: () => {
+    if (Search._pulse_status >= 0) return;
+
+    const pulse = () => {
+      Search._pulse_status = (Search._pulse_status + 1) % 4;
+      Search.dots.innerText = ".".repeat(Search._pulse_status);
+      if (Search._pulse_status >= 0) window.setTimeout(pulse, 500);
+    };
+    pulse();
+  },
+
+  /**
+   * perform a search for something (or wait until index is loaded)
+   */
+  performSearch: (query) => {
+    // create the required interface elements
+    const searchText = document.createElement("h2");
+    searchText.textContent = _("Searching");
+    const searchSummary = document.createElement("p");
+    searchSummary.classList.add("search-summary");
+    searchSummary.innerText = "";
+    const searchList = document.createElement("ul");
+    searchList.classList.add("search");
+
+    const out = document.getElementById("search-results");
+    Search.title = out.appendChild(searchText);
+    Search.dots = Search.title.appendChild(document.createElement("span"));
+    Search.status = out.appendChild(searchSummary);
+    Search.output = out.appendChild(searchList);
+
+    const searchProgress = document.getElementById("search-progress");
+    // Some themes don't use the search progress node
+    if (searchProgress) {
+      searchProgress.innerText = _("Preparing search...");
+    }
+    Search.startPulse();
+
+    // index already loaded, the browser was quick!
+    if (Search.hasIndex()) Search.query(query);
+    else Search.deferQuery(query);
+  },
+
+  /**
+   * execute search (requires search index to be loaded)
+   */
+  query: (query) => {
+    // stem the search terms and add them to the correct list
+    const stemmer = new Stemmer();
+    const searchTerms = new Set();
+    const excludedTerms = new Set();
+    const highlightTerms = new Set();
+    const objectTerms = new Set(splitQuery(query.toLowerCase().trim()));
+    splitQuery(query.trim()).forEach((queryTerm) => {
+      const queryTermLower = queryTerm.toLowerCase();
+
+      // maybe skip this "word"
+      // stopwords array is from language_data.js
+      if (
+        stopwords.indexOf(queryTermLower) !== -1 ||
+        queryTerm.match(/^\d+$/)
+      )
+        return;
+
+      // stem the word
+      let word = stemmer.stemWord(queryTermLower);
+      // select the correct list
+      if (word[0] === "-") excludedTerms.add(word.substr(1));
+      else {
+        searchTerms.add(word);
+        highlightTerms.add(queryTermLower);
+      }
+    });
+
+    // console.debug("SEARCH: searching for:");
+    // console.info("required: ", [...searchTerms]);
+    // console.info("excluded: ", [...excludedTerms]);
+
+    // array of [docname, title, anchor, descr, score, filename]
+    let results = [];
+    _removeChildren(document.getElementById("search-progress"));
+
+    // lookup as object
+    objectTerms.forEach((term) =>
+      results.push(...Search.performObjectSearch(term, objectTerms))
+    );
+
+    // lookup as search terms in fulltext
+    results.push(...Search.performTermsSearch(searchTerms, excludedTerms));
+
+    // let the scorer override scores with a custom scoring function
+    if (Scorer.score) results.forEach((item) => (item[4] = Scorer.score(item)));
+
+    // now sort the results by score (in opposite order of appearance, since the
+    // display function below uses pop() to retrieve items) and then
+    // alphabetically
+    results.sort((a, b) => {
+      const leftScore = a[4];
+      const rightScore = b[4];
+      if (leftScore === rightScore) {
+        // same score: sort alphabetically
+        const leftTitle = a[1].toLowerCase();
+        const rightTitle = b[1].toLowerCase();
+        if (leftTitle === rightTitle) return 0;
+        return leftTitle > rightTitle ? -1 : 1; // inverted is intentional
+      }
+      return leftScore > rightScore ? 1 : -1;
+    });
+
+    // remove duplicate search results
+    // note the reversing of results, so that in the case of duplicates, the highest-scoring entry is kept
+    let seen = new Set();
+    results = results.reverse().reduce((acc, result) => {
+      let resultStr = result.slice(0, 4).concat([result[5]]).map(v => String(v)).join(',');
+      if (!seen.has(resultStr)) {
+        acc.push(result);
+        seen.add(resultStr);
+      }
+      return acc;
+    }, []);
+
+    results = results.reverse();
+
+    // for debugging
+    //Search.lastresults = results.slice();  // a copy
+    // console.info("search results:", Search.lastresults);
+
+    // print the results
+    _displayNextItem(results, results.length, highlightTerms, searchTerms);
+  },
+
+  /**
+   * search for object names
+   */
+  performObjectSearch: (object, objectTerms) => {
+    const filenames = Search._index.filenames;
+    const docNames = Search._index.docnames;
+    const objects = Search._index.objects;
+    const objNames = Search._index.objnames;
+    const titles = Search._index.titles;
+
+    const results = [];
+
+    const objectSearchCallback = (prefix, match) => {
+      const name = match[4]
+      const fullname = (prefix ? prefix + "." : "") + name;
+      const fullnameLower = fullname.toLowerCase();
+      if (fullnameLower.indexOf(object) < 0) return;
+
+      let score = 0;
+      const parts = fullnameLower.split(".");
+
+      // check for different match types: exact matches of full name or
+      // "last name" (i.e. last dotted part)
+      if (fullnameLower === object || parts.slice(-1)[0] === object)
+        score += Scorer.objNameMatch;
+      else if (parts.slice(-1)[0].indexOf(object) > -1)
+        score += Scorer.objPartialMatch; // matches in last name
+
+      const objName = objNames[match[1]][2];
+      const title = titles[match[0]];
+
+      // If more than one term searched for, we require other words to be
+      // found in the name/title/description
+      const otherTerms = new Set(objectTerms);
+      otherTerms.delete(object);
+      if (otherTerms.size > 0) {
+        const haystack = `${prefix} ${name} ${objName} ${title}`.toLowerCase();
+        if (
+          [...otherTerms].some((otherTerm) => haystack.indexOf(otherTerm) < 0)
+        )
+          return;
+      }
+
+      let anchor = match[3];
+      if (anchor === "") anchor = fullname;
+      else if (anchor === "-") anchor = objNames[match[1]][1] + "-" + fullname;
+
+      const descr = objName + _(", in ") + title;
+
+      // add custom score for some objects according to scorer
+      if (Scorer.objPrio.hasOwnProperty(match[2]))
+        score += Scorer.objPrio[match[2]];
+      else score += Scorer.objPrioDefault;
+
+      results.push([
+        docNames[match[0]],
+        fullname,
+        "#" + anchor,
+        descr,
+        score,
+        filenames[match[0]],
+      ]);
+    };
+    Object.keys(objects).forEach((prefix) =>
+      objects[prefix].forEach((array) =>
+        objectSearchCallback(prefix, array)
+      )
+    );
+    return results;
+  },
+
+  /**
+   * search for full-text terms in the index
+   */
+  performTermsSearch: (searchTerms, excludedTerms) => {
+    // prepare search
+    const terms = Search._index.terms;
+    const titleTerms = Search._index.titleterms;
+    const docNames = Search._index.docnames;
+    const filenames = Search._index.filenames;
+    const titles = Search._index.titles;
+
+    const scoreMap = new Map();
+    const fileMap = new Map();
+
+    // perform the search on the required terms
+    searchTerms.forEach((word) => {
+      const files = [];
+      const arr = [
+        { files: terms[word], score: Scorer.term },
+        { files: titleTerms[word], score: Scorer.title },
+      ];
+      // add support for partial matches
+      if (word.length > 2) {
+        const escapedWord = _escapeRegExp(word);
+        Object.keys(terms).forEach((term) => {
+          if (term.match(escapedWord) && !terms[word])
+            arr.push({ files: terms[term], score: Scorer.partialTerm });
+        });
+        Object.keys(titleTerms).forEach((term) => {
+          if (term.match(escapedWord) && !titleTerms[word])
+            arr.push({ files: titleTerms[word], score: Scorer.partialTitle });
+        });
+      }
+
+      // no match but word was a required one
+      if (arr.every((record) => record.files === undefined)) return;
+
+      // found search word in contents
+      arr.forEach((record) => {
+        if (record.files === undefined) return;
+
+        let recordFiles = record.files;
+        if (recordFiles.length === undefined) recordFiles = [recordFiles];
+        files.push(...recordFiles);
+
+        // set score for the word in each file
+        recordFiles.forEach((file) => {
+          if (!scoreMap.has(file)) scoreMap.set(file, {});
+          scoreMap.get(file)[word] = record.score;
+        });
+      });
+
+      // create the mapping
+      files.forEach((file) => {
+        if (fileMap.has(file) && fileMap.get(file).indexOf(word) === -1)
+          fileMap.get(file).push(word);
+        else fileMap.set(file, [word]);
+      });
+    });
+
+    // now check if the files don't contain excluded terms
+    const results = [];
+    for (const [file, wordList] of fileMap) {
+      // check if all requirements are matched
+
+      // as search terms with length < 3 are discarded
+      const filteredTermCount = [...searchTerms].filter(
+        (term) => term.length > 2
+      ).length;
+      if (
+        wordList.length !== searchTerms.size &&
+        wordList.length !== filteredTermCount
+      )
+        continue;
+
+      // ensure that none of the excluded terms is in the search result
+      if (
+        [...excludedTerms].some(
+          (term) =>
+            terms[term] === file ||
+            titleTerms[term] === file ||
+            (terms[term] || []).includes(file) ||
+            (titleTerms[term] || []).includes(file)
+        )
+      )
+        break;
+
+      // select one (max) score for the file.
+      const score = Math.max(...wordList.map((w) => scoreMap.get(file)[w]));
+      // add result to the result list
+      results.push([
+        docNames[file],
+        titles[file],
+        "",
+        null,
+        score,
+        filenames[file],
+      ]);
+    }
+    return results;
+  },
+
+  /**
+   * helper function to return a node containing the
+   * search summary for a given text. keywords is a list
+   * of stemmed words, highlightWords is the list of normal, unstemmed
+   * words. the first one is used to find the occurrence, the
+   * latter for highlighting it.
+   */
+  makeSearchSummary: (htmlText, keywords, highlightWords) => {
+    const text = Search.htmlToText(htmlText).toLowerCase();
+    if (text === "") return null;
+
+    const actualStartPosition = [...keywords]
+      .map((k) => text.indexOf(k.toLowerCase()))
+      .filter((i) => i > -1)
+      .slice(-1)[0];
+    const startWithContext = Math.max(actualStartPosition - 120, 0);
+
+    const top = startWithContext === 0 ? "" : "...";
+    const tail = startWithContext + 240 < text.length ? "..." : "";
+
+    let summary = document.createElement("div");
+    summary.classList.add("context");
+    summary.innerText = top + text.substr(startWithContext, 240).trim() + tail;
+
+    highlightWords.forEach((highlightWord) =>
+      _highlightText(summary, highlightWord, "highlighted")
+    );
+
+    return summary;
+  },
+};
+
+_ready(Search.init);
diff --git a/docs/build/html/_static/underscore-1.13.1.js b/docs/build/html/_static/underscore-1.13.1.js
new file mode 100644
index 0000000..ffd77af
--- /dev/null
+++ b/docs/build/html/_static/underscore-1.13.1.js
@@ -0,0 +1,2042 @@
+(function (global, factory) {
+  typeof exports === 'object' && typeof module !== 'undefined' ? module.exports = factory() :
+  typeof define === 'function' && define.amd ? define('underscore', factory) :
+  (global = typeof globalThis !== 'undefined' ? globalThis : global || self, (function () {
+    var current = global._;
+    var exports = global._ = factory();
+    exports.noConflict = function () { global._ = current; return exports; };
+  }()));
+}(this, (function () {
+  //     Underscore.js 1.13.1
+  //     https://underscorejs.org
+  //     (c) 2009-2021 Jeremy Ashkenas, Julian Gonggrijp, and DocumentCloud and Investigative Reporters & Editors
+  //     Underscore may be freely distributed under the MIT license.
+
+  // Current version.
+  var VERSION = '1.13.1';
+
+  // Establish the root object, `window` (`self`) in the browser, `global`
+  // on the server, or `this` in some virtual machines. We use `self`
+  // instead of `window` for `WebWorker` support.
+  var root = typeof self == 'object' && self.self === self && self ||
+            typeof global == 'object' && global.global === global && global ||
+            Function('return this')() ||
+            {};
+
+  // Save bytes in the minified (but not gzipped) version:
+  var ArrayProto = Array.prototype, ObjProto = Object.prototype;
+  var SymbolProto = typeof Symbol !== 'undefined' ? Symbol.prototype : null;
+
+  // Create quick reference variables for speed access to core prototypes.
+  var push = ArrayProto.push,
+      slice = ArrayProto.slice,
+      toString = ObjProto.toString,
+      hasOwnProperty = ObjProto.hasOwnProperty;
+
+  // Modern feature detection.
+  var supportsArrayBuffer = typeof ArrayBuffer !== 'undefined',
+      supportsDataView = typeof DataView !== 'undefined';
+
+  // All **ECMAScript 5+** native function implementations that we hope to use
+  // are declared here.
+  var nativeIsArray = Array.isArray,
+      nativeKeys = Object.keys,
+      nativeCreate = Object.create,
+      nativeIsView = supportsArrayBuffer && ArrayBuffer.isView;
+
+  // Create references to these builtin functions because we override them.
+  var _isNaN = isNaN,
+      _isFinite = isFinite;
+
+  // Keys in IE < 9 that won't be iterated by `for key in ...` and thus missed.
+  var hasEnumBug = !{toString: null}.propertyIsEnumerable('toString');
+  var nonEnumerableProps = ['valueOf', 'isPrototypeOf', 'toString',
+    'propertyIsEnumerable', 'hasOwnProperty', 'toLocaleString'];
+
+  // The largest integer that can be represented exactly.
+  var MAX_ARRAY_INDEX = Math.pow(2, 53) - 1;
+
+  // Some functions take a variable number of arguments, or a few expected
+  // arguments at the beginning and then a variable number of values to operate
+  // on. This helper accumulates all remaining arguments past the function’s
+  // argument length (or an explicit `startIndex`), into an array that becomes
+  // the last argument. Similar to ES6’s "rest parameter".
+  function restArguments(func, startIndex) {
+    startIndex = startIndex == null ? func.length - 1 : +startIndex;
+    return function() {
+      var length = Math.max(arguments.length - startIndex, 0),
+          rest = Array(length),
+          index = 0;
+      for (; index < length; index++) {
+        rest[index] = arguments[index + startIndex];
+      }
+      switch (startIndex) {
+        case 0: return func.call(this, rest);
+        case 1: return func.call(this, arguments[0], rest);
+        case 2: return func.call(this, arguments[0], arguments[1], rest);
+      }
+      var args = Array(startIndex + 1);
+      for (index = 0; index < startIndex; index++) {
+        args[index] = arguments[index];
+      }
+      args[startIndex] = rest;
+      return func.apply(this, args);
+    };
+  }
+
+  // Is a given variable an object?
+  function isObject(obj) {
+    var type = typeof obj;
+    return type === 'function' || type === 'object' && !!obj;
+  }
+
+  // Is a given value equal to null?
+  function isNull(obj) {
+    return obj === null;
+  }
+
+  // Is a given variable undefined?
+  function isUndefined(obj) {
+    return obj === void 0;
+  }
+
+  // Is a given value a boolean?
+  function isBoolean(obj) {
+    return obj === true || obj === false || toString.call(obj) === '[object Boolean]';
+  }
+
+  // Is a given value a DOM element?
+  function isElement(obj) {
+    return !!(obj && obj.nodeType === 1);
+  }
+
+  // Internal function for creating a `toString`-based type tester.
+  function tagTester(name) {
+    var tag = '[object ' + name + ']';
+    return function(obj) {
+      return toString.call(obj) === tag;
+    };
+  }
+
+  var isString = tagTester('String');
+
+  var isNumber = tagTester('Number');
+
+  var isDate = tagTester('Date');
+
+  var isRegExp = tagTester('RegExp');
+
+  var isError = tagTester('Error');
+
+  var isSymbol = tagTester('Symbol');
+
+  var isArrayBuffer = tagTester('ArrayBuffer');
+
+  var isFunction = tagTester('Function');
+
+  // Optimize `isFunction` if appropriate. Work around some `typeof` bugs in old
+  // v8, IE 11 (#1621), Safari 8 (#1929), and PhantomJS (#2236).
+  var nodelist = root.document && root.document.childNodes;
+  if (typeof /./ != 'function' && typeof Int8Array != 'object' && typeof nodelist != 'function') {
+    isFunction = function(obj) {
+      return typeof obj == 'function' || false;
+    };
+  }
+
+  var isFunction$1 = isFunction;
+
+  var hasObjectTag = tagTester('Object');
+
+  // In IE 10 - Edge 13, `DataView` has string tag `'[object Object]'`.
+  // In IE 11, the most common among them, this problem also applies to
+  // `Map`, `WeakMap` and `Set`.
+  var hasStringTagBug = (
+        supportsDataView && hasObjectTag(new DataView(new ArrayBuffer(8)))
+      ),
+      isIE11 = (typeof Map !== 'undefined' && hasObjectTag(new Map));
+
+  var isDataView = tagTester('DataView');
+
+  // In IE 10 - Edge 13, we need a different heuristic
+  // to determine whether an object is a `DataView`.
+  function ie10IsDataView(obj) {
+    return obj != null && isFunction$1(obj.getInt8) && isArrayBuffer(obj.buffer);
+  }
+
+  var isDataView$1 = (hasStringTagBug ? ie10IsDataView : isDataView);
+
+  // Is a given value an array?
+  // Delegates to ECMA5's native `Array.isArray`.
+  var isArray = nativeIsArray || tagTester('Array');
+
+  // Internal function to check whether `key` is an own property name of `obj`.
+  function has$1(obj, key) {
+    return obj != null && hasOwnProperty.call(obj, key);
+  }
+
+  var isArguments = tagTester('Arguments');
+
+  // Define a fallback version of the method in browsers (ahem, IE < 9), where
+  // there isn't any inspectable "Arguments" type.
+  (function() {
+    if (!isArguments(arguments)) {
+      isArguments = function(obj) {
+        return has$1(obj, 'callee');
+      };
+    }
+  }());
+
+  var isArguments$1 = isArguments;
+
+  // Is a given object a finite number?
+  function isFinite$1(obj) {
+    return !isSymbol(obj) && _isFinite(obj) && !isNaN(parseFloat(obj));
+  }
+
+  // Is the given value `NaN`?
+  function isNaN$1(obj) {
+    return isNumber(obj) && _isNaN(obj);
+  }
+
+  // Predicate-generating function. Often useful outside of Underscore.
+  function constant(value) {
+    return function() {
+      return value;
+    };
+  }
+
+  // Common internal logic for `isArrayLike` and `isBufferLike`.
+  function createSizePropertyCheck(getSizeProperty) {
+    return function(collection) {
+      var sizeProperty = getSizeProperty(collection);
+      return typeof sizeProperty == 'number' && sizeProperty >= 0 && sizeProperty <= MAX_ARRAY_INDEX;
+    }
+  }
+
+  // Internal helper to generate a function to obtain property `key` from `obj`.
+  function shallowProperty(key) {
+    return function(obj) {
+      return obj == null ? void 0 : obj[key];
+    };
+  }
+
+  // Internal helper to obtain the `byteLength` property of an object.
+  var getByteLength = shallowProperty('byteLength');
+
+  // Internal helper to determine whether we should spend extensive checks against
+  // `ArrayBuffer` et al.
+  var isBufferLike = createSizePropertyCheck(getByteLength);
+
+  // Is a given value a typed array?
+  var typedArrayPattern = /\[object ((I|Ui)nt(8|16|32)|Float(32|64)|Uint8Clamped|Big(I|Ui)nt64)Array\]/;
+  function isTypedArray(obj) {
+    // `ArrayBuffer.isView` is the most future-proof, so use it when available.
+    // Otherwise, fall back on the above regular expression.
+    return nativeIsView ? (nativeIsView(obj) && !isDataView$1(obj)) :
+                  isBufferLike(obj) && typedArrayPattern.test(toString.call(obj));
+  }
+
+  var isTypedArray$1 = supportsArrayBuffer ? isTypedArray : constant(false);
+
+  // Internal helper to obtain the `length` property of an object.
+  var getLength = shallowProperty('length');
+
+  // Internal helper to create a simple lookup structure.
+  // `collectNonEnumProps` used to depend on `_.contains`, but this led to
+  // circular imports. `emulatedSet` is a one-off solution that only works for
+  // arrays of strings.
+  function emulatedSet(keys) {
+    var hash = {};
+    for (var l = keys.length, i = 0; i < l; ++i) hash[keys[i]] = true;
+    return {
+      contains: function(key) { return hash[key]; },
+      push: function(key) {
+        hash[key] = true;
+        return keys.push(key);
+      }
+    };
+  }
+
+  // Internal helper. Checks `keys` for the presence of keys in IE < 9 that won't
+  // be iterated by `for key in ...` and thus missed. Extends `keys` in place if
+  // needed.
+  function collectNonEnumProps(obj, keys) {
+    keys = emulatedSet(keys);
+    var nonEnumIdx = nonEnumerableProps.length;
+    var constructor = obj.constructor;
+    var proto = isFunction$1(constructor) && constructor.prototype || ObjProto;
+
+    // Constructor is a special case.
+    var prop = 'constructor';
+    if (has$1(obj, prop) && !keys.contains(prop)) keys.push(prop);
+
+    while (nonEnumIdx--) {
+      prop = nonEnumerableProps[nonEnumIdx];
+      if (prop in obj && obj[prop] !== proto[prop] && !keys.contains(prop)) {
+        keys.push(prop);
+      }
+    }
+  }
+
+  // Retrieve the names of an object's own properties.
+  // Delegates to **ECMAScript 5**'s native `Object.keys`.
+  function keys(obj) {
+    if (!isObject(obj)) return [];
+    if (nativeKeys) return nativeKeys(obj);
+    var keys = [];
+    for (var key in obj) if (has$1(obj, key)) keys.push(key);
+    // Ahem, IE < 9.
+    if (hasEnumBug) collectNonEnumProps(obj, keys);
+    return keys;
+  }
+
+  // Is a given array, string, or object empty?
+  // An "empty" object has no enumerable own-properties.
+  function isEmpty(obj) {
+    if (obj == null) return true;
+    // Skip the more expensive `toString`-based type checks if `obj` has no
+    // `.length`.
+    var length = getLength(obj);
+    if (typeof length == 'number' && (
+      isArray(obj) || isString(obj) || isArguments$1(obj)
+    )) return length === 0;
+    return getLength(keys(obj)) === 0;
+  }
+
+  // Returns whether an object has a given set of `key:value` pairs.
+  function isMatch(object, attrs) {
+    var _keys = keys(attrs), length = _keys.length;
+    if (object == null) return !length;
+    var obj = Object(object);
+    for (var i = 0; i < length; i++) {
+      var key = _keys[i];
+      if (attrs[key] !== obj[key] || !(key in obj)) return false;
+    }
+    return true;
+  }
+
+  // If Underscore is called as a function, it returns a wrapped object that can
+  // be used OO-style. This wrapper holds altered versions of all functions added
+  // through `_.mixin`. Wrapped objects may be chained.
+  function _$1(obj) {
+    if (obj instanceof _$1) return obj;
+    if (!(this instanceof _$1)) return new _$1(obj);
+    this._wrapped = obj;
+  }
+
+  _$1.VERSION = VERSION;
+
+  // Extracts the result from a wrapped and chained object.
+  _$1.prototype.value = function() {
+    return this._wrapped;
+  };
+
+  // Provide unwrapping proxies for some methods used in engine operations
+  // such as arithmetic and JSON stringification.
+  _$1.prototype.valueOf = _$1.prototype.toJSON = _$1.prototype.value;
+
+  _$1.prototype.toString = function() {
+    return String(this._wrapped);
+  };
+
+  // Internal function to wrap or shallow-copy an ArrayBuffer,
+  // typed array or DataView to a new view, reusing the buffer.
+  function toBufferView(bufferSource) {
+    return new Uint8Array(
+      bufferSource.buffer || bufferSource,
+      bufferSource.byteOffset || 0,
+      getByteLength(bufferSource)
+    );
+  }
+
+  // We use this string twice, so give it a name for minification.
+  var tagDataView = '[object DataView]';
+
+  // Internal recursive comparison function for `_.isEqual`.
+  function eq(a, b, aStack, bStack) {
+    // Identical objects are equal. `0 === -0`, but they aren't identical.
+    // See the [Harmony `egal` proposal](https://wiki.ecmascript.org/doku.php?id=harmony:egal).
+    if (a === b) return a !== 0 || 1 / a === 1 / b;
+    // `null` or `undefined` only equal to itself (strict comparison).
+    if (a == null || b == null) return false;
+    // `NaN`s are equivalent, but non-reflexive.
+    if (a !== a) return b !== b;
+    // Exhaust primitive checks
+    var type = typeof a;
+    if (type !== 'function' && type !== 'object' && typeof b != 'object') return false;
+    return deepEq(a, b, aStack, bStack);
+  }
+
+  // Internal recursive comparison function for `_.isEqual`.
+  function deepEq(a, b, aStack, bStack) {
+    // Unwrap any wrapped objects.
+    if (a instanceof _$1) a = a._wrapped;
+    if (b instanceof _$1) b = b._wrapped;
+    // Compare `[[Class]]` names.
+    var className = toString.call(a);
+    if (className !== toString.call(b)) return false;
+    // Work around a bug in IE 10 - Edge 13.
+    if (hasStringTagBug && className == '[object Object]' && isDataView$1(a)) {
+      if (!isDataView$1(b)) return false;
+      className = tagDataView;
+    }
+    switch (className) {
+      // These types are compared by value.
+      case '[object RegExp]':
+        // RegExps are coerced to strings for comparison (Note: '' + /a/i === '/a/i')
+      case '[object String]':
+        // Primitives and their corresponding object wrappers are equivalent; thus, `"5"` is
+        // equivalent to `new String("5")`.
+        return '' + a === '' + b;
+      case '[object Number]':
+        // `NaN`s are equivalent, but non-reflexive.
+        // Object(NaN) is equivalent to NaN.
+        if (+a !== +a) return +b !== +b;
+        // An `egal` comparison is performed for other numeric values.
+        return +a === 0 ? 1 / +a === 1 / b : +a === +b;
+      case '[object Date]':
+      case '[object Boolean]':
+        // Coerce dates and booleans to numeric primitive values. Dates are compared by their
+        // millisecond representations. Note that invalid dates with millisecond representations
+        // of `NaN` are not equivalent.
+        return +a === +b;
+      case '[object Symbol]':
+        return SymbolProto.valueOf.call(a) === SymbolProto.valueOf.call(b);
+      case '[object ArrayBuffer]':
+      case tagDataView:
+        // Coerce to typed array so we can fall through.
+        return deepEq(toBufferView(a), toBufferView(b), aStack, bStack);
+    }
+
+    var areArrays = className === '[object Array]';
+    if (!areArrays && isTypedArray$1(a)) {
+        var byteLength = getByteLength(a);
+        if (byteLength !== getByteLength(b)) return false;
+        if (a.buffer === b.buffer && a.byteOffset === b.byteOffset) return true;
+        areArrays = true;
+    }
+    if (!areArrays) {
+      if (typeof a != 'object' || typeof b != 'object') return false;
+
+      // Objects with different constructors are not equivalent, but `Object`s or `Array`s
+      // from different frames are.
+      var aCtor = a.constructor, bCtor = b.constructor;
+      if (aCtor !== bCtor && !(isFunction$1(aCtor) && aCtor instanceof aCtor &&
+                               isFunction$1(bCtor) && bCtor instanceof bCtor)
+                          && ('constructor' in a && 'constructor' in b)) {
+        return false;
+      }
+    }
+    // Assume equality for cyclic structures. The algorithm for detecting cyclic
+    // structures is adapted from ES 5.1 section 15.12.3, abstract operation `JO`.
+
+    // Initializing stack of traversed objects.
+    // It's done here since we only need them for objects and arrays comparison.
+    aStack = aStack || [];
+    bStack = bStack || [];
+    var length = aStack.length;
+    while (length--) {
+      // Linear search. Performance is inversely proportional to the number of
+      // unique nested structures.
+      if (aStack[length] === a) return bStack[length] === b;
+    }
+
+    // Add the first object to the stack of traversed objects.
+    aStack.push(a);
+    bStack.push(b);
+
+    // Recursively compare objects and arrays.
+    if (areArrays) {
+      // Compare array lengths to determine if a deep comparison is necessary.
+      length = a.length;
+      if (length !== b.length) return false;
+      // Deep compare the contents, ignoring non-numeric properties.
+      while (length--) {
+        if (!eq(a[length], b[length], aStack, bStack)) return false;
+      }
+    } else {
+      // Deep compare objects.
+      var _keys = keys(a), key;
+      length = _keys.length;
+      // Ensure that both objects contain the same number of properties before comparing deep equality.
+      if (keys(b).length !== length) return false;
+      while (length--) {
+        // Deep compare each member
+        key = _keys[length];
+        if (!(has$1(b, key) && eq(a[key], b[key], aStack, bStack))) return false;
+      }
+    }
+    // Remove the first object from the stack of traversed objects.
+    aStack.pop();
+    bStack.pop();
+    return true;
+  }
+
+  // Perform a deep comparison to check if two objects are equal.
+  function isEqual(a, b) {
+    return eq(a, b);
+  }
+
+  // Retrieve all the enumerable property names of an object.
+  function allKeys(obj) {
+    if (!isObject(obj)) return [];
+    var keys = [];
+    for (var key in obj) keys.push(key);
+    // Ahem, IE < 9.
+    if (hasEnumBug) collectNonEnumProps(obj, keys);
+    return keys;
+  }
+
+  // Since the regular `Object.prototype.toString` type tests don't work for
+  // some types in IE 11, we use a fingerprinting heuristic instead, based
+  // on the methods. It's not great, but it's the best we got.
+  // The fingerprint method lists are defined below.
+  function ie11fingerprint(methods) {
+    var length = getLength(methods);
+    return function(obj) {
+      if (obj == null) return false;
+      // `Map`, `WeakMap` and `Set` have no enumerable keys.
+      var keys = allKeys(obj);
+      if (getLength(keys)) return false;
+      for (var i = 0; i < length; i++) {
+        if (!isFunction$1(obj[methods[i]])) return false;
+      }
+      // If we are testing against `WeakMap`, we need to ensure that
+      // `obj` doesn't have a `forEach` method in order to distinguish
+      // it from a regular `Map`.
+      return methods !== weakMapMethods || !isFunction$1(obj[forEachName]);
+    };
+  }
+
+  // In the interest of compact minification, we write
+  // each string in the fingerprints only once.
+  var forEachName = 'forEach',
+      hasName = 'has',
+      commonInit = ['clear', 'delete'],
+      mapTail = ['get', hasName, 'set'];
+
+  // `Map`, `WeakMap` and `Set` each have slightly different
+  // combinations of the above sublists.
+  var mapMethods = commonInit.concat(forEachName, mapTail),
+      weakMapMethods = commonInit.concat(mapTail),
+      setMethods = ['add'].concat(commonInit, forEachName, hasName);
+
+  var isMap = isIE11 ? ie11fingerprint(mapMethods) : tagTester('Map');
+
+  var isWeakMap = isIE11 ? ie11fingerprint(weakMapMethods) : tagTester('WeakMap');
+
+  var isSet = isIE11 ? ie11fingerprint(setMethods) : tagTester('Set');
+
+  var isWeakSet = tagTester('WeakSet');
+
+  // Retrieve the values of an object's properties.
+  function values(obj) {
+    var _keys = keys(obj);
+    var length = _keys.length;
+    var values = Array(length);
+    for (var i = 0; i < length; i++) {
+      values[i] = obj[_keys[i]];
+    }
+    return values;
+  }
+
+  // Convert an object into a list of `[key, value]` pairs.
+  // The opposite of `_.object` with one argument.
+  function pairs(obj) {
+    var _keys = keys(obj);
+    var length = _keys.length;
+    var pairs = Array(length);
+    for (var i = 0; i < length; i++) {
+      pairs[i] = [_keys[i], obj[_keys[i]]];
+    }
+    return pairs;
+  }
+
+  // Invert the keys and values of an object. The values must be serializable.
+  function invert(obj) {
+    var result = {};
+    var _keys = keys(obj);
+    for (var i = 0, length = _keys.length; i < length; i++) {
+      result[obj[_keys[i]]] = _keys[i];
+    }
+    return result;
+  }
+
+  // Return a sorted list of the function names available on the object.
+  function functions(obj) {
+    var names = [];
+    for (var key in obj) {
+      if (isFunction$1(obj[key])) names.push(key);
+    }
+    return names.sort();
+  }
+
+  // An internal function for creating assigner functions.
+  function createAssigner(keysFunc, defaults) {
+    return function(obj) {
+      var length = arguments.length;
+      if (defaults) obj = Object(obj);
+      if (length < 2 || obj == null) return obj;
+      for (var index = 1; index < length; index++) {
+        var source = arguments[index],
+            keys = keysFunc(source),
+            l = keys.length;
+        for (var i = 0; i < l; i++) {
+          var key = keys[i];
+          if (!defaults || obj[key] === void 0) obj[key] = source[key];
+        }
+      }
+      return obj;
+    };
+  }
+
+  // Extend a given object with all the properties in passed-in object(s).
+  var extend = createAssigner(allKeys);
+
+  // Assigns a given object with all the own properties in the passed-in
+  // object(s).
+  // (https://developer.mozilla.org/docs/Web/JavaScript/Reference/Global_Objects/Object/assign)
+  var extendOwn = createAssigner(keys);
+
+  // Fill in a given object with default properties.
+  var defaults = createAssigner(allKeys, true);
+
+  // Create a naked function reference for surrogate-prototype-swapping.
+  function ctor() {
+    return function(){};
+  }
+
+  // An internal function for creating a new object that inherits from another.
+  function baseCreate(prototype) {
+    if (!isObject(prototype)) return {};
+    if (nativeCreate) return nativeCreate(prototype);
+    var Ctor = ctor();
+    Ctor.prototype = prototype;
+    var result = new Ctor;
+    Ctor.prototype = null;
+    return result;
+  }
+
+  // Creates an object that inherits from the given prototype object.
+  // If additional properties are provided then they will be added to the
+  // created object.
+  function create(prototype, props) {
+    var result = baseCreate(prototype);
+    if (props) extendOwn(result, props);
+    return result;
+  }
+
+  // Create a (shallow-cloned) duplicate of an object.
+  function clone(obj) {
+    if (!isObject(obj)) return obj;
+    return isArray(obj) ? obj.slice() : extend({}, obj);
+  }
+
+  // Invokes `interceptor` with the `obj` and then returns `obj`.
+  // The primary purpose of this method is to "tap into" a method chain, in
+  // order to perform operations on intermediate results within the chain.
+  function tap(obj, interceptor) {
+    interceptor(obj);
+    return obj;
+  }
+
+  // Normalize a (deep) property `path` to array.
+  // Like `_.iteratee`, this function can be customized.
+  function toPath$1(path) {
+    return isArray(path) ? path : [path];
+  }
+  _$1.toPath = toPath$1;
+
+  // Internal wrapper for `_.toPath` to enable minification.
+  // Similar to `cb` for `_.iteratee`.
+  function toPath(path) {
+    return _$1.toPath(path);
+  }
+
+  // Internal function to obtain a nested property in `obj` along `path`.
+  function deepGet(obj, path) {
+    var length = path.length;
+    for (var i = 0; i < length; i++) {
+      if (obj == null) return void 0;
+      obj = obj[path[i]];
+    }
+    return length ? obj : void 0;
+  }
+
+  // Get the value of the (deep) property on `path` from `object`.
+  // If any property in `path` does not exist or if the value is
+  // `undefined`, return `defaultValue` instead.
+  // The `path` is normalized through `_.toPath`.
+  function get(object, path, defaultValue) {
+    var value = deepGet(object, toPath(path));
+    return isUndefined(value) ? defaultValue : value;
+  }
+
+  // Shortcut function for checking if an object has a given property directly on
+  // itself (in other words, not on a prototype). Unlike the internal `has`
+  // function, this public version can also traverse nested properties.
+  function has(obj, path) {
+    path = toPath(path);
+    var length = path.length;
+    for (var i = 0; i < length; i++) {
+      var key = path[i];
+      if (!has$1(obj, key)) return false;
+      obj = obj[key];
+    }
+    return !!length;
+  }
+
+  // Keep the identity function around for default iteratees.
+  function identity(value) {
+    return value;
+  }
+
+  // Returns a predicate for checking whether an object has a given set of
+  // `key:value` pairs.
+  function matcher(attrs) {
+    attrs = extendOwn({}, attrs);
+    return function(obj) {
+      return isMatch(obj, attrs);
+    };
+  }
+
+  // Creates a function that, when passed an object, will traverse that object’s
+  // properties down the given `path`, specified as an array of keys or indices.
+  function property(path) {
+    path = toPath(path);
+    return function(obj) {
+      return deepGet(obj, path);
+    };
+  }
+
+  // Internal function that returns an efficient (for current engines) version
+  // of the passed-in callback, to be repeatedly applied in other Underscore
+  // functions.
+  function optimizeCb(func, context, argCount) {
+    if (context === void 0) return func;
+    switch (argCount == null ? 3 : argCount) {
+      case 1: return function(value) {
+        return func.call(context, value);
+      };
+      // The 2-argument case is omitted because we’re not using it.
+      case 3: return function(value, index, collection) {
+        return func.call(context, value, index, collection);
+      };
+      case 4: return function(accumulator, value, index, collection) {
+        return func.call(context, accumulator, value, index, collection);
+      };
+    }
+    return function() {
+      return func.apply(context, arguments);
+    };
+  }
+
+  // An internal function to generate callbacks that can be applied to each
+  // element in a collection, returning the desired result — either `_.identity`,
+  // an arbitrary callback, a property matcher, or a property accessor.
+  function baseIteratee(value, context, argCount) {
+    if (value == null) return identity;
+    if (isFunction$1(value)) return optimizeCb(value, context, argCount);
+    if (isObject(value) && !isArray(value)) return matcher(value);
+    return property(value);
+  }
+
+  // External wrapper for our callback generator. Users may customize
+  // `_.iteratee` if they want additional predicate/iteratee shorthand styles.
+  // This abstraction hides the internal-only `argCount` argument.
+  function iteratee(value, context) {
+    return baseIteratee(value, context, Infinity);
+  }
+  _$1.iteratee = iteratee;
+
+  // The function we call internally to generate a callback. It invokes
+  // `_.iteratee` if overridden, otherwise `baseIteratee`.
+  function cb(value, context, argCount) {
+    if (_$1.iteratee !== iteratee) return _$1.iteratee(value, context);
+    return baseIteratee(value, context, argCount);
+  }
+
+  // Returns the results of applying the `iteratee` to each element of `obj`.
+  // In contrast to `_.map` it returns an object.
+  function mapObject(obj, iteratee, context) {
+    iteratee = cb(iteratee, context);
+    var _keys = keys(obj),
+        length = _keys.length,
+        results = {};
+    for (var index = 0; index < length; index++) {
+      var currentKey = _keys[index];
+      results[currentKey] = iteratee(obj[currentKey], currentKey, obj);
+    }
+    return results;
+  }
+
+  // Predicate-generating function. Often useful outside of Underscore.
+  function noop(){}
+
+  // Generates a function for a given object that returns a given property.
+  function propertyOf(obj) {
+    if (obj == null) return noop;
+    return function(path) {
+      return get(obj, path);
+    };
+  }
+
+  // Run a function **n** times.
+  function times(n, iteratee, context) {
+    var accum = Array(Math.max(0, n));
+    iteratee = optimizeCb(iteratee, context, 1);
+    for (var i = 0; i < n; i++) accum[i] = iteratee(i);
+    return accum;
+  }
+
+  // Return a random integer between `min` and `max` (inclusive).
+  function random(min, max) {
+    if (max == null) {
+      max = min;
+      min = 0;
+    }
+    return min + Math.floor(Math.random() * (max - min + 1));
+  }
+
+  // A (possibly faster) way to get the current timestamp as an integer.
+  var now = Date.now || function() {
+    return new Date().getTime();
+  };
+
+  // Internal helper to generate functions for escaping and unescaping strings
+  // to/from HTML interpolation.
+  function createEscaper(map) {
+    var escaper = function(match) {
+      return map[match];
+    };
+    // Regexes for identifying a key that needs to be escaped.
+    var source = '(?:' + keys(map).join('|') + ')';
+    var testRegexp = RegExp(source);
+    var replaceRegexp = RegExp(source, 'g');
+    return function(string) {
+      string = string == null ? '' : '' + string;
+      return testRegexp.test(string) ? string.replace(replaceRegexp, escaper) : string;
+    };
+  }
+
+  // Internal list of HTML entities for escaping.
+  var escapeMap = {
+    '&': '&amp;',
+    '<': '&lt;',
+    '>': '&gt;',
+    '"': '&quot;',
+    "'": '&#x27;',
+    '`': '&#x60;'
+  };
+
+  // Function for escaping strings to HTML interpolation.
+  var _escape = createEscaper(escapeMap);
+
+  // Internal list of HTML entities for unescaping.
+  var unescapeMap = invert(escapeMap);
+
+  // Function for unescaping strings from HTML interpolation.
+  var _unescape = createEscaper(unescapeMap);
+
+  // By default, Underscore uses ERB-style template delimiters. Change the
+  // following template settings to use alternative delimiters.
+  var templateSettings = _$1.templateSettings = {
+    evaluate: /<%([\s\S]+?)%>/g,
+    interpolate: /<%=([\s\S]+?)%>/g,
+    escape: /<%-([\s\S]+?)%>/g
+  };
+
+  // When customizing `_.templateSettings`, if you don't want to define an
+  // interpolation, evaluation or escaping regex, we need one that is
+  // guaranteed not to match.
+  var noMatch = /(.)^/;
+
+  // Certain characters need to be escaped so that they can be put into a
+  // string literal.
+  var escapes = {
+    "'": "'",
+    '\\': '\\',
+    '\r': 'r',
+    '\n': 'n',
+    '\u2028': 'u2028',
+    '\u2029': 'u2029'
+  };
+
+  var escapeRegExp = /\\|'|\r|\n|\u2028|\u2029/g;
+
+  function escapeChar(match) {
+    return '\\' + escapes[match];
+  }
+
+  // In order to prevent third-party code injection through
+  // `_.templateSettings.variable`, we test it against the following regular
+  // expression. It is intentionally a bit more liberal than just matching valid
+  // identifiers, but still prevents possible loopholes through defaults or
+  // destructuring assignment.
+  var bareIdentifier = /^\s*(\w|\$)+\s*$/;
+
+  // JavaScript micro-templating, similar to John Resig's implementation.
+  // Underscore templating handles arbitrary delimiters, preserves whitespace,
+  // and correctly escapes quotes within interpolated code.
+  // NB: `oldSettings` only exists for backwards compatibility.
+  function template(text, settings, oldSettings) {
+    if (!settings && oldSettings) settings = oldSettings;
+    settings = defaults({}, settings, _$1.templateSettings);
+
+    // Combine delimiters into one regular expression via alternation.
+    var matcher = RegExp([
+      (settings.escape || noMatch).source,
+      (settings.interpolate || noMatch).source,
+      (settings.evaluate || noMatch).source
+    ].join('|') + '|$', 'g');
+
+    // Compile the template source, escaping string literals appropriately.
+    var index = 0;
+    var source = "__p+='";
+    text.replace(matcher, function(match, escape, interpolate, evaluate, offset) {
+      source += text.slice(index, offset).replace(escapeRegExp, escapeChar);
+      index = offset + match.length;
+
+      if (escape) {
+        source += "'+\n((__t=(" + escape + "))==null?'':_.escape(__t))+\n'";
+      } else if (interpolate) {
+        source += "'+\n((__t=(" + interpolate + "))==null?'':__t)+\n'";
+      } else if (evaluate) {
+        source += "';\n" + evaluate + "\n__p+='";
+      }
+
+      // Adobe VMs need the match returned to produce the correct offset.
+      return match;
+    });
+    source += "';\n";
+
+    var argument = settings.variable;
+    if (argument) {
+      // Insure against third-party code injection. (CVE-2021-23358)
+      if (!bareIdentifier.test(argument)) throw new Error(
+        'variable is not a bare identifier: ' + argument
+      );
+    } else {
+      // If a variable is not specified, place data values in local scope.
+      source = 'with(obj||{}){\n' + source + '}\n';
+      argument = 'obj';
+    }
+
+    source = "var __t,__p='',__j=Array.prototype.join," +
+      "print=function(){__p+=__j.call(arguments,'');};\n" +
+      source + 'return __p;\n';
+
+    var render;
+    try {
+      render = new Function(argument, '_', source);
+    } catch (e) {
+      e.source = source;
+      throw e;
+    }
+
+    var template = function(data) {
+      return render.call(this, data, _$1);
+    };
+
+    // Provide the compiled source as a convenience for precompilation.
+    template.source = 'function(' + argument + '){\n' + source + '}';
+
+    return template;
+  }
+
+  // Traverses the children of `obj` along `path`. If a child is a function, it
+  // is invoked with its parent as context. Returns the value of the final
+  // child, or `fallback` if any child is undefined.
+  function result(obj, path, fallback) {
+    path = toPath(path);
+    var length = path.length;
+    if (!length) {
+      return isFunction$1(fallback) ? fallback.call(obj) : fallback;
+    }
+    for (var i = 0; i < length; i++) {
+      var prop = obj == null ? void 0 : obj[path[i]];
+      if (prop === void 0) {
+        prop = fallback;
+        i = length; // Ensure we don't continue iterating.
+      }
+      obj = isFunction$1(prop) ? prop.call(obj) : prop;
+    }
+    return obj;
+  }
+
+  // Generate a unique integer id (unique within the entire client session).
+  // Useful for temporary DOM ids.
+  var idCounter = 0;
+  function uniqueId(prefix) {
+    var id = ++idCounter + '';
+    return prefix ? prefix + id : id;
+  }
+
+  // Start chaining a wrapped Underscore object.
+  function chain(obj) {
+    var instance = _$1(obj);
+    instance._chain = true;
+    return instance;
+  }
+
+  // Internal function to execute `sourceFunc` bound to `context` with optional
+  // `args`. Determines whether to execute a function as a constructor or as a
+  // normal function.
+  function executeBound(sourceFunc, boundFunc, context, callingContext, args) {
+    if (!(callingContext instanceof boundFunc)) return sourceFunc.apply(context, args);
+    var self = baseCreate(sourceFunc.prototype);
+    var result = sourceFunc.apply(self, args);
+    if (isObject(result)) return result;
+    return self;
+  }
+
+  // Partially apply a function by creating a version that has had some of its
+  // arguments pre-filled, without changing its dynamic `this` context. `_` acts
+  // as a placeholder by default, allowing any combination of arguments to be
+  // pre-filled. Set `_.partial.placeholder` for a custom placeholder argument.
+  var partial = restArguments(function(func, boundArgs) {
+    var placeholder = partial.placeholder;
+    var bound = function() {
+      var position = 0, length = boundArgs.length;
+      var args = Array(length);
+      for (var i = 0; i < length; i++) {
+        args[i] = boundArgs[i] === placeholder ? arguments[position++] : boundArgs[i];
+      }
+      while (position < arguments.length) args.push(arguments[position++]);
+      return executeBound(func, bound, this, this, args);
+    };
+    return bound;
+  });
+
+  partial.placeholder = _$1;
+
+  // Create a function bound to a given object (assigning `this`, and arguments,
+  // optionally).
+  var bind = restArguments(function(func, context, args) {
+    if (!isFunction$1(func)) throw new TypeError('Bind must be called on a function');
+    var bound = restArguments(function(callArgs) {
+      return executeBound(func, bound, context, this, args.concat(callArgs));
+    });
+    return bound;
+  });
+
+  // Internal helper for collection methods to determine whether a collection
+  // should be iterated as an array or as an object.
+  // Related: https://people.mozilla.org/~jorendorff/es6-draft.html#sec-tolength
+  // Avoids a very nasty iOS 8 JIT bug on ARM-64. #2094
+  var isArrayLike = createSizePropertyCheck(getLength);
+
+  // Internal implementation of a recursive `flatten` function.
+  function flatten$1(input, depth, strict, output) {
+    output = output || [];
+    if (!depth && depth !== 0) {
+      depth = Infinity;
+    } else if (depth <= 0) {
+      return output.concat(input);
+    }
+    var idx = output.length;
+    for (var i = 0, length = getLength(input); i < length; i++) {
+      var value = input[i];
+      if (isArrayLike(value) && (isArray(value) || isArguments$1(value))) {
+        // Flatten current level of array or arguments object.
+        if (depth > 1) {
+          flatten$1(value, depth - 1, strict, output);
+          idx = output.length;
+        } else {
+          var j = 0, len = value.length;
+          while (j < len) output[idx++] = value[j++];
+        }
+      } else if (!strict) {
+        output[idx++] = value;
+      }
+    }
+    return output;
+  }
+
+  // Bind a number of an object's methods to that object. Remaining arguments
+  // are the method names to be bound. Useful for ensuring that all callbacks
+  // defined on an object belong to it.
+  var bindAll = restArguments(function(obj, keys) {
+    keys = flatten$1(keys, false, false);
+    var index = keys.length;
+    if (index < 1) throw new Error('bindAll must be passed function names');
+    while (index--) {
+      var key = keys[index];
+      obj[key] = bind(obj[key], obj);
+    }
+    return obj;
+  });
+
+  // Memoize an expensive function by storing its results.
+  function memoize(func, hasher) {
+    var memoize = function(key) {
+      var cache = memoize.cache;
+      var address = '' + (hasher ? hasher.apply(this, arguments) : key);
+      if (!has$1(cache, address)) cache[address] = func.apply(this, arguments);
+      return cache[address];
+    };
+    memoize.cache = {};
+    return memoize;
+  }
+
+  // Delays a function for the given number of milliseconds, and then calls
+  // it with the arguments supplied.
+  var delay = restArguments(function(func, wait, args) {
+    return setTimeout(function() {
+      return func.apply(null, args);
+    }, wait);
+  });
+
+  // Defers a function, scheduling it to run after the current call stack has
+  // cleared.
+  var defer = partial(delay, _$1, 1);
+
+  // Returns a function, that, when invoked, will only be triggered at most once
+  // during a given window of time. Normally, the throttled function will run
+  // as much as it can, without ever going more than once per `wait` duration;
+  // but if you'd like to disable the execution on the leading edge, pass
+  // `{leading: false}`. To disable execution on the trailing edge, ditto.
+  function throttle(func, wait, options) {
+    var timeout, context, args, result;
+    var previous = 0;
+    if (!options) options = {};
+
+    var later = function() {
+      previous = options.leading === false ? 0 : now();
+      timeout = null;
+      result = func.apply(context, args);
+      if (!timeout) context = args = null;
+    };
+
+    var throttled = function() {
+      var _now = now();
+      if (!previous && options.leading === false) previous = _now;
+      var remaining = wait - (_now - previous);
+      context = this;
+      args = arguments;
+      if (remaining <= 0 || remaining > wait) {
+        if (timeout) {
+          clearTimeout(timeout);
+          timeout = null;
+        }
+        previous = _now;
+        result = func.apply(context, args);
+        if (!timeout) context = args = null;
+      } else if (!timeout && options.trailing !== false) {
+        timeout = setTimeout(later, remaining);
+      }
+      return result;
+    };
+
+    throttled.cancel = function() {
+      clearTimeout(timeout);
+      previous = 0;
+      timeout = context = args = null;
+    };
+
+    return throttled;
+  }
+
+  // When a sequence of calls of the returned function ends, the argument
+  // function is triggered. The end of a sequence is defined by the `wait`
+  // parameter. If `immediate` is passed, the argument function will be
+  // triggered at the beginning of the sequence instead of at the end.
+  function debounce(func, wait, immediate) {
+    var timeout, previous, args, result, context;
+
+    var later = function() {
+      var passed = now() - previous;
+      if (wait > passed) {
+        timeout = setTimeout(later, wait - passed);
+      } else {
+        timeout = null;
+        if (!immediate) result = func.apply(context, args);
+        // This check is needed because `func` can recursively invoke `debounced`.
+        if (!timeout) args = context = null;
+      }
+    };
+
+    var debounced = restArguments(function(_args) {
+      context = this;
+      args = _args;
+      previous = now();
+      if (!timeout) {
+        timeout = setTimeout(later, wait);
+        if (immediate) result = func.apply(context, args);
+      }
+      return result;
+    });
+
+    debounced.cancel = function() {
+      clearTimeout(timeout);
+      timeout = args = context = null;
+    };
+
+    return debounced;
+  }
+
+  // Returns the first function passed as an argument to the second,
+  // allowing you to adjust arguments, run code before and after, and
+  // conditionally execute the original function.
+  function wrap(func, wrapper) {
+    return partial(wrapper, func);
+  }
+
+  // Returns a negated version of the passed-in predicate.
+  function negate(predicate) {
+    return function() {
+      return !predicate.apply(this, arguments);
+    };
+  }
+
+  // Returns a function that is the composition of a list of functions, each
+  // consuming the return value of the function that follows.
+  function compose() {
+    var args = arguments;
+    var start = args.length - 1;
+    return function() {
+      var i = start;
+      var result = args[start].apply(this, arguments);
+      while (i--) result = args[i].call(this, result);
+      return result;
+    };
+  }
+
+  // Returns a function that will only be executed on and after the Nth call.
+  function after(times, func) {
+    return function() {
+      if (--times < 1) {
+        return func.apply(this, arguments);
+      }
+    };
+  }
+
+  // Returns a function that will only be executed up to (but not including) the
+  // Nth call.
+  function before(times, func) {
+    var memo;
+    return function() {
+      if (--times > 0) {
+        memo = func.apply(this, arguments);
+      }
+      if (times <= 1) func = null;
+      return memo;
+    };
+  }
+
+  // Returns a function that will be executed at most one time, no matter how
+  // often you call it. Useful for lazy initialization.
+  var once = partial(before, 2);
+
+  // Returns the first key on an object that passes a truth test.
+  function findKey(obj, predicate, context) {
+    predicate = cb(predicate, context);
+    var _keys = keys(obj), key;
+    for (var i = 0, length = _keys.length; i < length; i++) {
+      key = _keys[i];
+      if (predicate(obj[key], key, obj)) return key;
+    }
+  }
+
+  // Internal function to generate `_.findIndex` and `_.findLastIndex`.
+  function createPredicateIndexFinder(dir) {
+    return function(array, predicate, context) {
+      predicate = cb(predicate, context);
+      var length = getLength(array);
+      var index = dir > 0 ? 0 : length - 1;
+      for (; index >= 0 && index < length; index += dir) {
+        if (predicate(array[index], index, array)) return index;
+      }
+      return -1;
+    };
+  }
+
+  // Returns the first index on an array-like that passes a truth test.
+  var findIndex = createPredicateIndexFinder(1);
+
+  // Returns the last index on an array-like that passes a truth test.
+  var findLastIndex = createPredicateIndexFinder(-1);
+
+  // Use a comparator function to figure out the smallest index at which
+  // an object should be inserted so as to maintain order. Uses binary search.
+  function sortedIndex(array, obj, iteratee, context) {
+    iteratee = cb(iteratee, context, 1);
+    var value = iteratee(obj);
+    var low = 0, high = getLength(array);
+    while (low < high) {
+      var mid = Math.floor((low + high) / 2);
+      if (iteratee(array[mid]) < value) low = mid + 1; else high = mid;
+    }
+    return low;
+  }
+
+  // Internal function to generate the `_.indexOf` and `_.lastIndexOf` functions.
+  function createIndexFinder(dir, predicateFind, sortedIndex) {
+    return function(array, item, idx) {
+      var i = 0, length = getLength(array);
+      if (typeof idx == 'number') {
+        if (dir > 0) {
+          i = idx >= 0 ? idx : Math.max(idx + length, i);
+        } else {
+          length = idx >= 0 ? Math.min(idx + 1, length) : idx + length + 1;
+        }
+      } else if (sortedIndex && idx && length) {
+        idx = sortedIndex(array, item);
+        return array[idx] === item ? idx : -1;
+      }
+      if (item !== item) {
+        idx = predicateFind(slice.call(array, i, length), isNaN$1);
+        return idx >= 0 ? idx + i : -1;
+      }
+      for (idx = dir > 0 ? i : length - 1; idx >= 0 && idx < length; idx += dir) {
+        if (array[idx] === item) return idx;
+      }
+      return -1;
+    };
+  }
+
+  // Return the position of the first occurrence of an item in an array,
+  // or -1 if the item is not included in the array.
+  // If the array is large and already in sort order, pass `true`
+  // for **isSorted** to use binary search.
+  var indexOf = createIndexFinder(1, findIndex, sortedIndex);
+
+  // Return the position of the last occurrence of an item in an array,
+  // or -1 if the item is not included in the array.
+  var lastIndexOf = createIndexFinder(-1, findLastIndex);
+
+  // Return the first value which passes a truth test.
+  function find(obj, predicate, context) {
+    var keyFinder = isArrayLike(obj) ? findIndex : findKey;
+    var key = keyFinder(obj, predicate, context);
+    if (key !== void 0 && key !== -1) return obj[key];
+  }
+
+  // Convenience version of a common use case of `_.find`: getting the first
+  // object containing specific `key:value` pairs.
+  function findWhere(obj, attrs) {
+    return find(obj, matcher(attrs));
+  }
+
+  // The cornerstone for collection functions, an `each`
+  // implementation, aka `forEach`.
+  // Handles raw objects in addition to array-likes. Treats all
+  // sparse array-likes as if they were dense.
+  function each(obj, iteratee, context) {
+    iteratee = optimizeCb(iteratee, context);
+    var i, length;
+    if (isArrayLike(obj)) {
+      for (i = 0, length = obj.length; i < length; i++) {
+        iteratee(obj[i], i, obj);
+      }
+    } else {
+      var _keys = keys(obj);
+      for (i = 0, length = _keys.length; i < length; i++) {
+        iteratee(obj[_keys[i]], _keys[i], obj);
+      }
+    }
+    return obj;
+  }
+
+  // Return the results of applying the iteratee to each element.
+  function map(obj, iteratee, context) {
+    iteratee = cb(iteratee, context);
+    var _keys = !isArrayLike(obj) && keys(obj),
+        length = (_keys || obj).length,
+        results = Array(length);
+    for (var index = 0; index < length; index++) {
+      var currentKey = _keys ? _keys[index] : index;
+      results[index] = iteratee(obj[currentKey], currentKey, obj);
+    }
+    return results;
+  }
+
+  // Internal helper to create a reducing function, iterating left or right.
+  function createReduce(dir) {
+    // Wrap code that reassigns argument variables in a separate function than
+    // the one that accesses `arguments.length` to avoid a perf hit. (#1991)
+    var reducer = function(obj, iteratee, memo, initial) {
+      var _keys = !isArrayLike(obj) && keys(obj),
+          length = (_keys || obj).length,
+          index = dir > 0 ? 0 : length - 1;
+      if (!initial) {
+        memo = obj[_keys ? _keys[index] : index];
+        index += dir;
+      }
+      for (; index >= 0 && index < length; index += dir) {
+        var currentKey = _keys ? _keys[index] : index;
+        memo = iteratee(memo, obj[currentKey], currentKey, obj);
+      }
+      return memo;
+    };
+
+    return function(obj, iteratee, memo, context) {
+      var initial = arguments.length >= 3;
+      return reducer(obj, optimizeCb(iteratee, context, 4), memo, initial);
+    };
+  }
+
+  // **Reduce** builds up a single result from a list of values, aka `inject`,
+  // or `foldl`.
+  var reduce = createReduce(1);
+
+  // The right-associative version of reduce, also known as `foldr`.
+  var reduceRight = createReduce(-1);
+
+  // Return all the elements that pass a truth test.
+  function filter(obj, predicate, context) {
+    var results = [];
+    predicate = cb(predicate, context);
+    each(obj, function(value, index, list) {
+      if (predicate(value, index, list)) results.push(value);
+    });
+    return results;
+  }
+
+  // Return all the elements for which a truth test fails.
+  function reject(obj, predicate, context) {
+    return filter(obj, negate(cb(predicate)), context);
+  }
+
+  // Determine whether all of the elements pass a truth test.
+  function every(obj, predicate, context) {
+    predicate = cb(predicate, context);
+    var _keys = !isArrayLike(obj) && keys(obj),
+        length = (_keys || obj).length;
+    for (var index = 0; index < length; index++) {
+      var currentKey = _keys ? _keys[index] : index;
+      if (!predicate(obj[currentKey], currentKey, obj)) return false;
+    }
+    return true;
+  }
+
+  // Determine if at least one element in the object passes a truth test.
+  function some(obj, predicate, context) {
+    predicate = cb(predicate, context);
+    var _keys = !isArrayLike(obj) && keys(obj),
+        length = (_keys || obj).length;
+    for (var index = 0; index < length; index++) {
+      var currentKey = _keys ? _keys[index] : index;
+      if (predicate(obj[currentKey], currentKey, obj)) return true;
+    }
+    return false;
+  }
+
+  // Determine if the array or object contains a given item (using `===`).
+  function contains(obj, item, fromIndex, guard) {
+    if (!isArrayLike(obj)) obj = values(obj);
+    if (typeof fromIndex != 'number' || guard) fromIndex = 0;
+    return indexOf(obj, item, fromIndex) >= 0;
+  }
+
+  // Invoke a method (with arguments) on every item in a collection.
+  var invoke = restArguments(function(obj, path, args) {
+    var contextPath, func;
+    if (isFunction$1(path)) {
+      func = path;
+    } else {
+      path = toPath(path);
+      contextPath = path.slice(0, -1);
+      path = path[path.length - 1];
+    }
+    return map(obj, function(context) {
+      var method = func;
+      if (!method) {
+        if (contextPath && contextPath.length) {
+          context = deepGet(context, contextPath);
+        }
+        if (context == null) return void 0;
+        method = context[path];
+      }
+      return method == null ? method : method.apply(context, args);
+    });
+  });
+
+  // Convenience version of a common use case of `_.map`: fetching a property.
+  function pluck(obj, key) {
+    return map(obj, property(key));
+  }
+
+  // Convenience version of a common use case of `_.filter`: selecting only
+  // objects containing specific `key:value` pairs.
+  function where(obj, attrs) {
+    return filter(obj, matcher(attrs));
+  }
+
+  // Return the maximum element (or element-based computation).
+  function max(obj, iteratee, context) {
+    var result = -Infinity, lastComputed = -Infinity,
+        value, computed;
+    if (iteratee == null || typeof iteratee == 'number' && typeof obj[0] != 'object' && obj != null) {
+      obj = isArrayLike(obj) ? obj : values(obj);
+      for (var i = 0, length = obj.length; i < length; i++) {
+        value = obj[i];
+        if (value != null && value > result) {
+          result = value;
+        }
+      }
+    } else {
+      iteratee = cb(iteratee, context);
+      each(obj, function(v, index, list) {
+        computed = iteratee(v, index, list);
+        if (computed > lastComputed || computed === -Infinity && result === -Infinity) {
+          result = v;
+          lastComputed = computed;
+        }
+      });
+    }
+    return result;
+  }
+
+  // Return the minimum element (or element-based computation).
+  function min(obj, iteratee, context) {
+    var result = Infinity, lastComputed = Infinity,
+        value, computed;
+    if (iteratee == null || typeof iteratee == 'number' && typeof obj[0] != 'object' && obj != null) {
+      obj = isArrayLike(obj) ? obj : values(obj);
+      for (var i = 0, length = obj.length; i < length; i++) {
+        value = obj[i];
+        if (value != null && value < result) {
+          result = value;
+        }
+      }
+    } else {
+      iteratee = cb(iteratee, context);
+      each(obj, function(v, index, list) {
+        computed = iteratee(v, index, list);
+        if (computed < lastComputed || computed === Infinity && result === Infinity) {
+          result = v;
+          lastComputed = computed;
+        }
+      });
+    }
+    return result;
+  }
+
+  // Sample **n** random values from a collection using the modern version of the
+  // [Fisher-Yates shuffle](https://en.wikipedia.org/wiki/Fisher–Yates_shuffle).
+  // If **n** is not specified, returns a single random element.
+  // The internal `guard` argument allows it to work with `_.map`.
+  function sample(obj, n, guard) {
+    if (n == null || guard) {
+      if (!isArrayLike(obj)) obj = values(obj);
+      return obj[random(obj.length - 1)];
+    }
+    var sample = isArrayLike(obj) ? clone(obj) : values(obj);
+    var length = getLength(sample);
+    n = Math.max(Math.min(n, length), 0);
+    var last = length - 1;
+    for (var index = 0; index < n; index++) {
+      var rand = random(index, last);
+      var temp = sample[index];
+      sample[index] = sample[rand];
+      sample[rand] = temp;
+    }
+    return sample.slice(0, n);
+  }
+
+  // Shuffle a collection.
+  function shuffle(obj) {
+    return sample(obj, Infinity);
+  }
+
+  // Sort the object's values by a criterion produced by an iteratee.
+  function sortBy(obj, iteratee, context) {
+    var index = 0;
+    iteratee = cb(iteratee, context);
+    return pluck(map(obj, function(value, key, list) {
+      return {
+        value: value,
+        index: index++,
+        criteria: iteratee(value, key, list)
+      };
+    }).sort(function(left, right) {
+      var a = left.criteria;
+      var b = right.criteria;
+      if (a !== b) {
+        if (a > b || a === void 0) return 1;
+        if (a < b || b === void 0) return -1;
+      }
+      return left.index - right.index;
+    }), 'value');
+  }
+
+  // An internal function used for aggregate "group by" operations.
+  function group(behavior, partition) {
+    return function(obj, iteratee, context) {
+      var result = partition ? [[], []] : {};
+      iteratee = cb(iteratee, context);
+      each(obj, function(value, index) {
+        var key = iteratee(value, index, obj);
+        behavior(result, value, key);
+      });
+      return result;
+    };
+  }
+
+  // Groups the object's values by a criterion. Pass either a string attribute
+  // to group by, or a function that returns the criterion.
+  var groupBy = group(function(result, value, key) {
+    if (has$1(result, key)) result[key].push(value); else result[key] = [value];
+  });
+
+  // Indexes the object's values by a criterion, similar to `_.groupBy`, but for
+  // when you know that your index values will be unique.
+  var indexBy = group(function(result, value, key) {
+    result[key] = value;
+  });
+
+  // Counts instances of an object that group by a certain criterion. Pass
+  // either a string attribute to count by, or a function that returns the
+  // criterion.
+  var countBy = group(function(result, value, key) {
+    if (has$1(result, key)) result[key]++; else result[key] = 1;
+  });
+
+  // Split a collection into two arrays: one whose elements all pass the given
+  // truth test, and one whose elements all do not pass the truth test.
+  var partition = group(function(result, value, pass) {
+    result[pass ? 0 : 1].push(value);
+  }, true);
+
+  // Safely create a real, live array from anything iterable.
+  var reStrSymbol = /[^\ud800-\udfff]|[\ud800-\udbff][\udc00-\udfff]|[\ud800-\udfff]/g;
+  function toArray(obj) {
+    if (!obj) return [];
+    if (isArray(obj)) return slice.call(obj);
+    if (isString(obj)) {
+      // Keep surrogate pair characters together.
+      return obj.match(reStrSymbol);
+    }
+    if (isArrayLike(obj)) return map(obj, identity);
+    return values(obj);
+  }
+
+  // Return the number of elements in a collection.
+  function size(obj) {
+    if (obj == null) return 0;
+    return isArrayLike(obj) ? obj.length : keys(obj).length;
+  }
+
+  // Internal `_.pick` helper function to determine whether `key` is an enumerable
+  // property name of `obj`.
+  function keyInObj(value, key, obj) {
+    return key in obj;
+  }
+
+  // Return a copy of the object only containing the allowed properties.
+  var pick = restArguments(function(obj, keys) {
+    var result = {}, iteratee = keys[0];
+    if (obj == null) return result;
+    if (isFunction$1(iteratee)) {
+      if (keys.length > 1) iteratee = optimizeCb(iteratee, keys[1]);
+      keys = allKeys(obj);
+    } else {
+      iteratee = keyInObj;
+      keys = flatten$1(keys, false, false);
+      obj = Object(obj);
+    }
+    for (var i = 0, length = keys.length; i < length; i++) {
+      var key = keys[i];
+      var value = obj[key];
+      if (iteratee(value, key, obj)) result[key] = value;
+    }
+    return result;
+  });
+
+  // Return a copy of the object without the disallowed properties.
+  var omit = restArguments(function(obj, keys) {
+    var iteratee = keys[0], context;
+    if (isFunction$1(iteratee)) {
+      iteratee = negate(iteratee);
+      if (keys.length > 1) context = keys[1];
+    } else {
+      keys = map(flatten$1(keys, false, false), String);
+      iteratee = function(value, key) {
+        return !contains(keys, key);
+      };
+    }
+    return pick(obj, iteratee, context);
+  });
+
+  // Returns everything but the last entry of the array. Especially useful on
+  // the arguments object. Passing **n** will return all the values in
+  // the array, excluding the last N.
+  function initial(array, n, guard) {
+    return slice.call(array, 0, Math.max(0, array.length - (n == null || guard ? 1 : n)));
+  }
+
+  // Get the first element of an array. Passing **n** will return the first N
+  // values in the array. The **guard** check allows it to work with `_.map`.
+  function first(array, n, guard) {
+    if (array == null || array.length < 1) return n == null || guard ? void 0 : [];
+    if (n == null || guard) return array[0];
+    return initial(array, array.length - n);
+  }
+
+  // Returns everything but the first entry of the `array`. Especially useful on
+  // the `arguments` object. Passing an **n** will return the rest N values in the
+  // `array`.
+  function rest(array, n, guard) {
+    return slice.call(array, n == null || guard ? 1 : n);
+  }
+
+  // Get the last element of an array. Passing **n** will return the last N
+  // values in the array.
+  function last(array, n, guard) {
+    if (array == null || array.length < 1) return n == null || guard ? void 0 : [];
+    if (n == null || guard) return array[array.length - 1];
+    return rest(array, Math.max(0, array.length - n));
+  }
+
+  // Trim out all falsy values from an array.
+  function compact(array) {
+    return filter(array, Boolean);
+  }
+
+  // Flatten out an array, either recursively (by default), or up to `depth`.
+  // Passing `true` or `false` as `depth` means `1` or `Infinity`, respectively.
+  function flatten(array, depth) {
+    return flatten$1(array, depth, false);
+  }
+
+  // Take the difference between one array and a number of other arrays.
+  // Only the elements present in just the first array will remain.
+  var difference = restArguments(function(array, rest) {
+    rest = flatten$1(rest, true, true);
+    return filter(array, function(value){
+      return !contains(rest, value);
+    });
+  });
+
+  // Return a version of the array that does not contain the specified value(s).
+  var without = restArguments(function(array, otherArrays) {
+    return difference(array, otherArrays);
+  });
+
+  // Produce a duplicate-free version of the array. If the array has already
+  // been sorted, you have the option of using a faster algorithm.
+  // The faster algorithm will not work with an iteratee if the iteratee
+  // is not a one-to-one function, so providing an iteratee will disable
+  // the faster algorithm.
+  function uniq(array, isSorted, iteratee, context) {
+    if (!isBoolean(isSorted)) {
+      context = iteratee;
+      iteratee = isSorted;
+      isSorted = false;
+    }
+    if (iteratee != null) iteratee = cb(iteratee, context);
+    var result = [];
+    var seen = [];
+    for (var i = 0, length = getLength(array); i < length; i++) {
+      var value = array[i],
+          computed = iteratee ? iteratee(value, i, array) : value;
+      if (isSorted && !iteratee) {
+        if (!i || seen !== computed) result.push(value);
+        seen = computed;
+      } else if (iteratee) {
+        if (!contains(seen, computed)) {
+          seen.push(computed);
+          result.push(value);
+        }
+      } else if (!contains(result, value)) {
+        result.push(value);
+      }
+    }
+    return result;
+  }
+
+  // Produce an array that contains the union: each distinct element from all of
+  // the passed-in arrays.
+  var union = restArguments(function(arrays) {
+    return uniq(flatten$1(arrays, true, true));
+  });
+
+  // Produce an array that contains every item shared between all the
+  // passed-in arrays.
+  function intersection(array) {
+    var result = [];
+    var argsLength = arguments.length;
+    for (var i = 0, length = getLength(array); i < length; i++) {
+      var item = array[i];
+      if (contains(result, item)) continue;
+      var j;
+      for (j = 1; j < argsLength; j++) {
+        if (!contains(arguments[j], item)) break;
+      }
+      if (j === argsLength) result.push(item);
+    }
+    return result;
+  }
+
+  // Complement of zip. Unzip accepts an array of arrays and groups
+  // each array's elements on shared indices.
+  function unzip(array) {
+    var length = array && max(array, getLength).length || 0;
+    var result = Array(length);
+
+    for (var index = 0; index < length; index++) {
+      result[index] = pluck(array, index);
+    }
+    return result;
+  }
+
+  // Zip together multiple lists into a single array -- elements that share
+  // an index go together.
+  var zip = restArguments(unzip);
+
+  // Converts lists into objects. Pass either a single array of `[key, value]`
+  // pairs, or two parallel arrays of the same length -- one of keys, and one of
+  // the corresponding values. Passing by pairs is the reverse of `_.pairs`.
+  function object(list, values) {
+    var result = {};
+    for (var i = 0, length = getLength(list); i < length; i++) {
+      if (values) {
+        result[list[i]] = values[i];
+      } else {
+        result[list[i][0]] = list[i][1];
+      }
+    }
+    return result;
+  }
+
+  // Generate an integer Array containing an arithmetic progression. A port of
+  // the native Python `range()` function. See
+  // [the Python documentation](https://docs.python.org/library/functions.html#range).
+  function range(start, stop, step) {
+    if (stop == null) {
+      stop = start || 0;
+      start = 0;
+    }
+    if (!step) {
+      step = stop < start ? -1 : 1;
+    }
+
+    var length = Math.max(Math.ceil((stop - start) / step), 0);
+    var range = Array(length);
+
+    for (var idx = 0; idx < length; idx++, start += step) {
+      range[idx] = start;
+    }
+
+    return range;
+  }
+
+  // Chunk a single array into multiple arrays, each containing `count` or fewer
+  // items.
+  function chunk(array, count) {
+    if (count == null || count < 1) return [];
+    var result = [];
+    var i = 0, length = array.length;
+    while (i < length) {
+      result.push(slice.call(array, i, i += count));
+    }
+    return result;
+  }
+
+  // Helper function to continue chaining intermediate results.
+  function chainResult(instance, obj) {
+    return instance._chain ? _$1(obj).chain() : obj;
+  }
+
+  // Add your own custom functions to the Underscore object.
+  function mixin(obj) {
+    each(functions(obj), function(name) {
+      var func = _$1[name] = obj[name];
+      _$1.prototype[name] = function() {
+        var args = [this._wrapped];
+        push.apply(args, arguments);
+        return chainResult(this, func.apply(_$1, args));
+      };
+    });
+    return _$1;
+  }
+
+  // Add all mutator `Array` functions to the wrapper.
+  each(['pop', 'push', 'reverse', 'shift', 'sort', 'splice', 'unshift'], function(name) {
+    var method = ArrayProto[name];
+    _$1.prototype[name] = function() {
+      var obj = this._wrapped;
+      if (obj != null) {
+        method.apply(obj, arguments);
+        if ((name === 'shift' || name === 'splice') && obj.length === 0) {
+          delete obj[0];
+        }
+      }
+      return chainResult(this, obj);
+    };
+  });
+
+  // Add all accessor `Array` functions to the wrapper.
+  each(['concat', 'join', 'slice'], function(name) {
+    var method = ArrayProto[name];
+    _$1.prototype[name] = function() {
+      var obj = this._wrapped;
+      if (obj != null) obj = method.apply(obj, arguments);
+      return chainResult(this, obj);
+    };
+  });
+
+  // Named Exports
+
+  var allExports = {
+    __proto__: null,
+    VERSION: VERSION,
+    restArguments: restArguments,
+    isObject: isObject,
+    isNull: isNull,
+    isUndefined: isUndefined,
+    isBoolean: isBoolean,
+    isElement: isElement,
+    isString: isString,
+    isNumber: isNumber,
+    isDate: isDate,
+    isRegExp: isRegExp,
+    isError: isError,
+    isSymbol: isSymbol,
+    isArrayBuffer: isArrayBuffer,
+    isDataView: isDataView$1,
+    isArray: isArray,
+    isFunction: isFunction$1,
+    isArguments: isArguments$1,
+    isFinite: isFinite$1,
+    isNaN: isNaN$1,
+    isTypedArray: isTypedArray$1,
+    isEmpty: isEmpty,
+    isMatch: isMatch,
+    isEqual: isEqual,
+    isMap: isMap,
+    isWeakMap: isWeakMap,
+    isSet: isSet,
+    isWeakSet: isWeakSet,
+    keys: keys,
+    allKeys: allKeys,
+    values: values,
+    pairs: pairs,
+    invert: invert,
+    functions: functions,
+    methods: functions,
+    extend: extend,
+    extendOwn: extendOwn,
+    assign: extendOwn,
+    defaults: defaults,
+    create: create,
+    clone: clone,
+    tap: tap,
+    get: get,
+    has: has,
+    mapObject: mapObject,
+    identity: identity,
+    constant: constant,
+    noop: noop,
+    toPath: toPath$1,
+    property: property,
+    propertyOf: propertyOf,
+    matcher: matcher,
+    matches: matcher,
+    times: times,
+    random: random,
+    now: now,
+    escape: _escape,
+    unescape: _unescape,
+    templateSettings: templateSettings,
+    template: template,
+    result: result,
+    uniqueId: uniqueId,
+    chain: chain,
+    iteratee: iteratee,
+    partial: partial,
+    bind: bind,
+    bindAll: bindAll,
+    memoize: memoize,
+    delay: delay,
+    defer: defer,
+    throttle: throttle,
+    debounce: debounce,
+    wrap: wrap,
+    negate: negate,
+    compose: compose,
+    after: after,
+    before: before,
+    once: once,
+    findKey: findKey,
+    findIndex: findIndex,
+    findLastIndex: findLastIndex,
+    sortedIndex: sortedIndex,
+    indexOf: indexOf,
+    lastIndexOf: lastIndexOf,
+    find: find,
+    detect: find,
+    findWhere: findWhere,
+    each: each,
+    forEach: each,
+    map: map,
+    collect: map,
+    reduce: reduce,
+    foldl: reduce,
+    inject: reduce,
+    reduceRight: reduceRight,
+    foldr: reduceRight,
+    filter: filter,
+    select: filter,
+    reject: reject,
+    every: every,
+    all: every,
+    some: some,
+    any: some,
+    contains: contains,
+    includes: contains,
+    include: contains,
+    invoke: invoke,
+    pluck: pluck,
+    where: where,
+    max: max,
+    min: min,
+    shuffle: shuffle,
+    sample: sample,
+    sortBy: sortBy,
+    groupBy: groupBy,
+    indexBy: indexBy,
+    countBy: countBy,
+    partition: partition,
+    toArray: toArray,
+    size: size,
+    pick: pick,
+    omit: omit,
+    first: first,
+    head: first,
+    take: first,
+    initial: initial,
+    last: last,
+    rest: rest,
+    tail: rest,
+    drop: rest,
+    compact: compact,
+    flatten: flatten,
+    without: without,
+    uniq: uniq,
+    unique: uniq,
+    union: union,
+    intersection: intersection,
+    difference: difference,
+    unzip: unzip,
+    transpose: unzip,
+    zip: zip,
+    object: object,
+    range: range,
+    chunk: chunk,
+    mixin: mixin,
+    'default': _$1
+  };
+
+  // Default Export
+
+  // Add all of the Underscore functions to the wrapper object.
+  var _ = mixin(allExports);
+  // Legacy Node.js API.
+  _._ = _;
+
+  return _;
+
+})));
+//# sourceMappingURL=underscore-umd.js.map
diff --git a/docs/build/html/_static/underscore.js b/docs/build/html/_static/underscore.js
new file mode 100644
index 0000000..cf177d4
--- /dev/null
+++ b/docs/build/html/_static/underscore.js
@@ -0,0 +1,6 @@
+!function(n,r){"object"==typeof exports&&"undefined"!=typeof module?module.exports=r():"function"==typeof define&&define.amd?define("underscore",r):(n="undefined"!=typeof globalThis?globalThis:n||self,function(){var t=n._,e=n._=r();e.noConflict=function(){return n._=t,e}}())}(this,(function(){
+//     Underscore.js 1.13.1
+//     https://underscorejs.org
+//     (c) 2009-2021 Jeremy Ashkenas, Julian Gonggrijp, and DocumentCloud and Investigative Reporters & Editors
+//     Underscore may be freely distributed under the MIT license.
+var n="1.13.1",r="object"==typeof self&&self.self===self&&self||"object"==typeof global&&global.global===global&&global||Function("return this")()||{},t=Array.prototype,e=Object.prototype,u="undefined"!=typeof Symbol?Symbol.prototype:null,o=t.push,i=t.slice,a=e.toString,f=e.hasOwnProperty,c="undefined"!=typeof ArrayBuffer,l="undefined"!=typeof DataView,s=Array.isArray,p=Object.keys,v=Object.create,h=c&&ArrayBuffer.isView,y=isNaN,d=isFinite,g=!{toString:null}.propertyIsEnumerable("toString"),b=["valueOf","isPrototypeOf","toString","propertyIsEnumerable","hasOwnProperty","toLocaleString"],m=Math.pow(2,53)-1;function j(n,r){return r=null==r?n.length-1:+r,function(){for(var t=Math.max(arguments.length-r,0),e=Array(t),u=0;u<t;u++)e[u]=arguments[u+r];switch(r){case 0:return n.call(this,e);case 1:return n.call(this,arguments[0],e);case 2:return n.call(this,arguments[0],arguments[1],e)}var o=Array(r+1);for(u=0;u<r;u++)o[u]=arguments[u];return o[r]=e,n.apply(this,o)}}function _(n){var r=typeof 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ur(n,r,!1)},without:Kr,uniq:Jr,unique:Jr,union:Gr,intersection:function(n){for(var r=[],t=arguments.length,e=0,u=Y(n);e<u;e++){var o=n[e];if(!Er(r,o)){var i;for(i=1;i<t&&Er(arguments[i],o);i++);i===t&&r.push(o)}}return r},difference:Cr,unzip:Hr,transpose:Hr,zip:Qr,object:function(n,r){for(var t={},e=0,u=Y(n);e<u;e++)r?t[n[e]]=r[e]:t[n[e][0]]=n[e][1];return t},range:function(n,r,t){null==r&&(r=n||0,n=0),t||(t=r<n?-1:1);for(var e=Math.max(Math.ceil((r-n)/t),0),u=Array(e),o=0;o<e;o++,n+=t)u[o]=n;return u},chunk:function(n,r){if(null==r||r<1)return[];for(var t=[],e=0,u=n.length;e<u;)t.push(i.call(n,e,e+=r));return t},mixin:Yr,default:tn});return Zr._=Zr,Zr}));
\ No newline at end of file
diff --git a/docs/build/html/genindex.html b/docs/build/html/genindex.html
new file mode 100644
index 0000000..e1deb15
--- /dev/null
+++ b/docs/build/html/genindex.html
@@ -0,0 +1,1454 @@
+
+<!DOCTYPE html>
+
+<html lang="en">
+  <head>
+    <meta charset="utf-8" />
+    <meta name="viewport" content="width=device-width, initial-scale=1.0" />
+    <title>Index &#8212; mbtrack2 0.6.0 documentation</title>
+    <link rel="stylesheet" type="text/css" href="_static/pygments.css" />
+    <link rel="stylesheet" type="text/css" href="_static/nature.css" />
+    <script data-url_root="./" id="documentation_options" src="_static/documentation_options.js"></script>
+    <script src="_static/jquery.js"></script>
+    <script src="_static/underscore.js"></script>
+    <script src="_static/_sphinx_javascript_frameworks_compat.js"></script>
+    <script src="_static/doctools.js"></script>
+    <link rel="index" title="Index" href="#" />
+    <link rel="search" title="Search" href="search.html" /> 
+  </head><body>
+    <div class="related" role="navigation" aria-label="related navigation">
+      <h3>Navigation</h3>
+      <ul>
+        <li class="right" style="margin-right: 10px">
+          <a href="#" title="General Index"
+             accesskey="I">index</a></li>
+        <li class="right" >
+          <a href="py-modindex.html" title="Python Module Index"
+             >modules</a> |</li>
+        <li class="nav-item nav-item-0"><a href="index.html">mbtrack2 0.6.0 documentation</a> &#187;</li>
+        <li class="nav-item nav-item-this"><a href="">Index</a></li> 
+      </ul>
+    </div>  
+
+    <div class="document">
+      <div class="documentwrapper">
+        <div class="bodywrapper">
+          <div class="body" role="main">
+            
+
+<h1 id="index">Index</h1>
+
+<div class="genindex-jumpbox">
+ <a href="#A"><strong>A</strong></a>
+ | <a href="#B"><strong>B</strong></a>
+ | <a href="#C"><strong>C</strong></a>
+ | <a href="#D"><strong>D</strong></a>
+ | <a href="#E"><strong>E</strong></a>
+ | <a href="#F"><strong>F</strong></a>
+ | <a href="#G"><strong>G</strong></a>
+ | <a href="#H"><strong>H</strong></a>
+ | <a href="#I"><strong>I</strong></a>
+ | <a href="#K"><strong>K</strong></a>
+ | <a href="#L"><strong>L</strong></a>
+ | <a href="#M"><strong>M</strong></a>
+ | <a href="#N"><strong>N</strong></a>
+ | <a href="#O"><strong>O</strong></a>
+ | <a href="#P"><strong>P</strong></a>
+ | <a href="#Q"><strong>Q</strong></a>
+ | <a href="#R"><strong>R</strong></a>
+ | <a href="#S"><strong>S</strong></a>
+ | <a href="#T"><strong>T</strong></a>
+ | <a href="#U"><strong>U</strong></a>
+ | <a href="#V"><strong>V</strong></a>
+ | <a href="#W"><strong>W</strong></a>
+ | <a href="#X"><strong>X</strong></a>
+ | <a href="#Y"><strong>Y</strong></a>
+ | <a href="#Z"><strong>Z</strong></a>
+ 
+</div>
+<h2 id="A">A</h2>
+<table style="width: 100%" class="indextable genindextable"><tr>
+  <td style="width: 33%; vertical-align: top;"><ul>
+      <li><a href="mbtrack2.impedance.html#mbtrack2.impedance.impedance_model.ImpedanceModel.add">add() (mbtrack2.impedance.impedance_model.ImpedanceModel method)</a>
+
+      <ul>
+        <li><a href="mbtrack2.impedance.html#mbtrack2.impedance.wakefield.ComplexData.add">(mbtrack2.impedance.wakefield.ComplexData method)</a>
+</li>
+        <li><a href="mbtrack2.impedance.html#mbtrack2.impedance.wakefield.Impedance.add">(mbtrack2.impedance.wakefield.Impedance method)</a>
+</li>
+        <li><a href="mbtrack2.impedance.html#mbtrack2.impedance.wakefield.WakeFunction.add">(mbtrack2.impedance.wakefield.WakeFunction method)</a>
+</li>
+      </ul></li>
+      <li><a href="mbtrack2.impedance.html#mbtrack2.impedance.impedance_model.ImpedanceModel.add_global">add_global() (mbtrack2.impedance.impedance_model.ImpedanceModel method)</a>
+</li>
+  </ul></td>
+  <td style="width: 33%; vertical-align: top;"><ul>
+      <li><a href="mbtrack2.impedance.html#mbtrack2.impedance.wakefield.WakeField.add_several_wakefields">add_several_wakefields() (mbtrack2.impedance.wakefield.WakeField static method)</a>
+</li>
+      <li><a href="mbtrack2.impedance.html#mbtrack2.impedance.wakefield.WakeField.add_wakefields">add_wakefields() (mbtrack2.impedance.wakefield.WakeField static method)</a>
+</li>
+      <li><a href="mbtrack2.utilities.html#mbtrack2.utilities.optics.Optics.alpha">alpha() (mbtrack2.utilities.optics.Optics method)</a>
+</li>
+      <li><a href="mbtrack2.impedance.html#mbtrack2.impedance.tapers.StupakovCircularTaper.angle">angle (mbtrack2.impedance.tapers.StupakovCircularTaper property)</a>
+
+      <ul>
+        <li><a href="mbtrack2.impedance.html#mbtrack2.impedance.tapers.StupakovRectangularTaper.angle">(mbtrack2.impedance.tapers.StupakovRectangularTaper property)</a>
+</li>
+      </ul></li>
+      <li><a href="mbtrack2.impedance.html#mbtrack2.impedance.wakefield.WakeField.append_to_model">append_to_model() (mbtrack2.impedance.wakefield.WakeField method)</a>
+</li>
+  </ul></td>
+</tr></table>
+
+<h2 id="B">B</h2>
+<table style="width: 100%" class="indextable genindextable"><tr>
+  <td style="width: 33%; vertical-align: top;"><ul>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.particles.Beam">Beam (class in mbtrack2.tracking.particles)</a>
+</li>
+      <li><a href="mbtrack2.utilities.html#mbtrack2.utilities.beamloading.BeamLoadingEquilibrium.beam_equilibrium">beam_equilibrium() (mbtrack2.utilities.beamloading.BeamLoadingEquilibrium method)</a>
+</li>
+      <li><a href="mbtrack2.utilities.html#mbtrack2.utilities.misc.beam_loss_factor">beam_loss_factor() (in module mbtrack2.utilities.misc)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.rf.CavityResonator.beam_phase">beam_phase (mbtrack2.tracking.rf.CavityResonator property)</a>
+</li>
+      <li><a href="mbtrack2.utilities.html#mbtrack2.utilities.spectrum.beam_spectrum">beam_spectrum() (in module mbtrack2.utilities.spectrum)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.rf.CavityResonator.beam_voltage">beam_voltage (mbtrack2.tracking.rf.CavityResonator property)</a>
+</li>
+      <li><a href="mbtrack2.utilities.html#mbtrack2.utilities.beamloading.BeamLoadingEquilibrium">BeamLoadingEquilibrium (class in mbtrack2.utilities.beamloading)</a>
+</li>
+      <li><a href="mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.monitors.BeamMonitor">BeamMonitor (class in mbtrack2.tracking.monitors.monitors)</a>
+</li>
+      <li><a href="mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.monitors.BeamSpectrumMonitor">BeamSpectrumMonitor (class in mbtrack2.tracking.monitors.monitors)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.rf.CavityResonator.beta">beta (mbtrack2.tracking.rf.CavityResonator property)</a>
+
+      <ul>
+        <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.synchrotron.Synchrotron.beta">(mbtrack2.tracking.synchrotron.Synchrotron property)</a>
+</li>
+      </ul></li>
+      <li><a href="mbtrack2.utilities.html#mbtrack2.utilities.optics.Optics.beta">beta() (mbtrack2.utilities.optics.Optics method)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.particles.Bunch.binning">binning() (mbtrack2.tracking.particles.Bunch method)</a>
+</li>
+  </ul></td>
+  <td style="width: 33%; vertical-align: top;"><ul>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.particles.Bunch">Bunch (class in mbtrack2.tracking.particles)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.particles.Beam.bunch_charge">bunch_charge (mbtrack2.tracking.particles.Beam property)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.particles.Beam.bunch_cs">bunch_cs (mbtrack2.tracking.particles.Beam property)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.particles.Beam.bunch_current">bunch_current (mbtrack2.tracking.particles.Beam property)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.particles.Beam.bunch_emit">bunch_emit (mbtrack2.tracking.particles.Beam property)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.particles.Beam.bunch_index">bunch_index (mbtrack2.tracking.particles.Beam property)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.particles.Beam.bunch_mean">bunch_mean (mbtrack2.tracking.particles.Beam property)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.parallel.Mpi.bunch_num">bunch_num (mbtrack2.tracking.parallel.Mpi property)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.particles.Beam.bunch_particle">bunch_particle (mbtrack2.tracking.particles.Beam property)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.particles.Beam.bunch_std">bunch_std (mbtrack2.tracking.particles.Beam property)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.parallel.Mpi.bunch_to_rank">bunch_to_rank() (mbtrack2.tracking.parallel.Mpi method)</a>
+</li>
+      <li><a href="mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.monitors.BunchMonitor">BunchMonitor (class in mbtrack2.tracking.monitors.monitors)</a>
+</li>
+      <li><a href="mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.monitors.BunchSpectrumMonitor">BunchSpectrumMonitor (class in mbtrack2.tracking.monitors.monitors)</a>
+</li>
+  </ul></td>
+</tr></table>
+
+<h2 id="C">C</h2>
+<table style="width: 100%" class="indextable genindextable"><tr>
+  <td style="width: 33%; vertical-align: top;"><ul>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.rf.CavityResonator.cavity_phase">cavity_phase (mbtrack2.tracking.rf.CavityResonator property)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.rf.CavityResonator.cavity_phasor">cavity_phasor (mbtrack2.tracking.rf.CavityResonator property)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.rf.CavityResonator.cavity_phasor_record">cavity_phasor_record (mbtrack2.tracking.rf.CavityResonator property)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.rf.CavityResonator.cavity_voltage">cavity_voltage (mbtrack2.tracking.rf.CavityResonator property)</a>
+</li>
+      <li><a href="mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.monitors.CavityMonitor">CavityMonitor (class in mbtrack2.tracking.monitors.monitors)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.rf.CavityResonator">CavityResonator (class in mbtrack2.tracking.rf)</a>
+</li>
+      <li><a href="mbtrack2.instability.html#mbtrack2.instability.instabilities.cbi_threshold">cbi_threshold() (in module mbtrack2.instability.instabilities)</a>
+</li>
+      <li><a href="mbtrack2.utilities.html#mbtrack2.utilities.beamloading.BeamLoadingEquilibrium.center_of_mass">center_of_mass() (mbtrack2.utilities.beamloading.BeamLoadingEquilibrium method)</a>
+</li>
+      <li><a href="mbtrack2.utilities.html#mbtrack2.utilities.optics.PhysicalModel.change_values">change_values() (mbtrack2.utilities.optics.PhysicalModel method)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.particles.Beam.charge">charge (mbtrack2.tracking.particles.Beam property)</a>
+
+      <ul>
+        <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.particles.Bunch.charge">(mbtrack2.tracking.particles.Bunch property)</a>
+</li>
+      </ul></li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.wakepotential.WakePotential.charge_density">charge_density() (mbtrack2.tracking.wakepotential.WakePotential method)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.particles.Bunch.charge_per_mp">charge_per_mp (mbtrack2.tracking.particles.Bunch property)</a>
+</li>
+  </ul></td>
+  <td style="width: 33%; vertical-align: top;"><ul>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.wakepotential.WakePotential.check_sampling">check_sampling() (mbtrack2.tracking.wakepotential.WakePotential method)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.aperture.CircularAperture">CircularAperture (class in mbtrack2.tracking.aperture)</a>
+</li>
+      <li><a href="mbtrack2.impedance.html#mbtrack2.impedance.resistive_wall.CircularResistiveWall">CircularResistiveWall (class in mbtrack2.impedance.resistive_wall)</a>
+</li>
+      <li><a href="mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.monitors.Monitor.close">close() (mbtrack2.tracking.monitors.monitors.Monitor method)</a>
+</li>
+      <li><a href="mbtrack2.impedance.html#mbtrack2.impedance.resistive_wall.Coating">Coating (class in mbtrack2.impedance.resistive_wall)</a>
+</li>
+      <li><a href="mbtrack2.impedance.html#mbtrack2.impedance.wakefield.ComplexData">ComplexData (class in mbtrack2.impedance.wakefield)</a>
+</li>
+      <li><a href="mbtrack2.impedance.html#mbtrack2.impedance.wakefield.ComplexData.component_type">component_type (mbtrack2.impedance.wakefield.ComplexData property)</a>
+</li>
+      <li><a href="mbtrack2.impedance.html#mbtrack2.impedance.wakefield.WakeField.components">components (mbtrack2.impedance.wakefield.WakeField property)</a>
+</li>
+      <li><a href="mbtrack2.impedance.html#mbtrack2.impedance.impedance_model.ImpedanceModel.compute_sum">compute_sum() (mbtrack2.impedance.impedance_model.ImpedanceModel method)</a>
+</li>
+      <li><a href="mbtrack2.impedance.html#mbtrack2.impedance.impedance_model.ImpedanceModel.compute_sum_names">compute_sum_names() (mbtrack2.impedance.impedance_model.ImpedanceModel method)</a>
+</li>
+      <li><a href="mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.tools.copy_files">copy_files() (in module mbtrack2.tracking.monitors.tools)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.particles.Bunch.cs_invariant">cs_invariant (mbtrack2.tracking.particles.Bunch property)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.particles.Beam.current">current (mbtrack2.tracking.particles.Beam property)</a>
+
+      <ul>
+        <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.particles.Bunch.current">(mbtrack2.tracking.particles.Bunch property)</a>
+</li>
+      </ul></li>
+  </ul></td>
+</tr></table>
+
+<h2 id="D">D</h2>
+<table style="width: 100%" class="indextable genindextable"><tr>
+  <td style="width: 33%; vertical-align: top;"><ul>
+      <li><a href="mbtrack2.utilities.html#mbtrack2.utilities.beamloading.BeamLoadingEquilibrium.ddV">ddV() (mbtrack2.utilities.beamloading.BeamLoadingEquilibrium method)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.rf.CavityResonator.ddVRF">ddVRF() (mbtrack2.tracking.rf.CavityResonator method)</a>
+</li>
+      <li><a href="mbtrack2.impedance.html#mbtrack2.impedance.wakefield.WakeFunction.deconvolution">deconvolution() (mbtrack2.impedance.wakefield.WakeFunction method)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.rf.CavityResonator.deltaVRF">deltaVRF() (mbtrack2.tracking.rf.CavityResonator method)</a>
+
+      <ul>
+        <li><a href="mbtrack2.utilities.html#mbtrack2.utilities.beamloading.BeamLoadingEquilibrium.deltaVRF">(mbtrack2.utilities.beamloading.BeamLoadingEquilibrium method)</a>
+</li>
+      </ul></li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.rf.CavityResonator.detune">detune (mbtrack2.tracking.rf.CavityResonator property)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.rf.DirectFeedback.DFB_alpha">DFB_alpha (mbtrack2.tracking.rf.DirectFeedback property)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.rf.DirectFeedback.DFB_fs">DFB_fs() (mbtrack2.tracking.rf.DirectFeedback method)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.rf.DirectFeedback.DFB_gamma">DFB_gamma (mbtrack2.tracking.rf.DirectFeedback property)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.rf.CavityResonator.DFB_ig_phasor">DFB_ig_phasor (mbtrack2.tracking.rf.CavityResonator property)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.rf.DirectFeedback.DFB_parameter_set">DFB_parameter_set() (mbtrack2.tracking.rf.DirectFeedback method)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.rf.DirectFeedback.DFB_phase_shift">DFB_phase_shift (mbtrack2.tracking.rf.DirectFeedback property)</a>
+</li>
+  </ul></td>
+  <td style="width: 33%; vertical-align: top;"><ul>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.rf.DirectFeedback.DFB_psi">DFB_psi (mbtrack2.tracking.rf.DirectFeedback property)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.rf.DirectFeedback.DFB_Rs">DFB_Rs (mbtrack2.tracking.rf.DirectFeedback property)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.rf.DirectFeedback.DFB_Vg">DFB_Vg() (mbtrack2.tracking.rf.DirectFeedback method)</a>
+</li>
+      <li><a href="mbtrack2.impedance.html#mbtrack2.impedance.tapers.StupakovCircularTaper.dip">dip() (mbtrack2.impedance.tapers.StupakovCircularTaper method)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.wakepotential.WakePotential.dipole_moment">dipole_moment() (mbtrack2.tracking.wakepotential.WakePotential method)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.rf.DirectFeedback">DirectFeedback (class in mbtrack2.tracking.rf)</a>
+</li>
+      <li><a href="mbtrack2.utilities.html#mbtrack2.utilities.optics.Optics.dispersion">dispersion() (mbtrack2.utilities.optics.Optics method)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.particles.Beam.distance_between_bunches">distance_between_bunches (mbtrack2.tracking.particles.Beam property)</a>
+</li>
+      <li><a href="mbtrack2.utilities.html#mbtrack2.utilities.misc.double_sided_impedance">double_sided_impedance() (in module mbtrack2.utilities.misc)</a>
+</li>
+      <li><a href="mbtrack2.impedance.html#mbtrack2.impedance.wakefield.WakeField.drop">drop() (mbtrack2.impedance.wakefield.WakeField method)</a>
+</li>
+      <li><a href="mbtrack2.utilities.html#mbtrack2.utilities.beamloading.BeamLoadingEquilibrium.du_dz">du_dz() (mbtrack2.utilities.beamloading.BeamLoadingEquilibrium method)</a>
+</li>
+      <li><a href="mbtrack2.utilities.html#mbtrack2.utilities.beamloading.BeamLoadingEquilibrium.dV">dV() (mbtrack2.utilities.beamloading.BeamLoadingEquilibrium method)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.rf.CavityResonator.dVRF">dVRF() (mbtrack2.tracking.rf.CavityResonator method)</a>
+</li>
+  </ul></td>
+</tr></table>
+
+<h2 id="E">E</h2>
+<table style="width: 100%" class="indextable genindextable"><tr>
+  <td style="width: 33%; vertical-align: top;"><ul>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.synchrotron.Synchrotron.E0">E0 (mbtrack2.tracking.synchrotron.Synchrotron property)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.particles.Particle.E_rest">E_rest (mbtrack2.tracking.particles.Particle property)</a>
+</li>
+      <li><a href="mbtrack2.utilities.html#mbtrack2.utilities.misc.effective_impedance">effective_impedance() (in module mbtrack2.utilities.misc)</a>
+
+      <ul>
+        <li><a href="mbtrack2.impedance.html#mbtrack2.impedance.impedance_model.ImpedanceModel.effective_impedance">(mbtrack2.impedance.impedance_model.ImpedanceModel method)</a>
+</li>
+      </ul></li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.particles.Electron">Electron (class in mbtrack2.tracking.particles)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.element.Element">Element (class in mbtrack2.tracking.element)</a>
+</li>
+  </ul></td>
+  <td style="width: 33%; vertical-align: top;"><ul>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.aperture.ElipticalAperture">ElipticalAperture (class in mbtrack2.tracking.aperture)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.particles.Bunch.emit">emit (mbtrack2.tracking.particles.Bunch property)</a>
+</li>
+      <li><a href="mbtrack2.utilities.html#mbtrack2.utilities.beamloading.BeamLoadingEquilibrium.energy_balance">energy_balance() (mbtrack2.utilities.beamloading.BeamLoadingEquilibrium method)</a>
+</li>
+      <li><a href="mbtrack2.impedance.html#mbtrack2.impedance.impedance_model.ImpedanceModel.energy_loss">energy_loss() (mbtrack2.impedance.impedance_model.ImpedanceModel method)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.synchrotron.Synchrotron.eta">eta() (mbtrack2.tracking.synchrotron.Synchrotron method)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.feedback.ExponentialDamper">ExponentialDamper (class in mbtrack2.tracking.feedback)</a>
+</li>
+  </ul></td>
+</tr></table>
+
+<h2 id="F">F</h2>
+<table style="width: 100%" class="indextable genindextable"><tr>
+  <td style="width: 33%; vertical-align: top;"><ul>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.synchrotron.Synchrotron.f0">f0 (mbtrack2.tracking.synchrotron.Synchrotron property)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.synchrotron.Synchrotron.f1">f1 (mbtrack2.tracking.synchrotron.Synchrotron property)</a>
+</li>
+      <li><a href="mbtrack2.instability.html#mbtrack2.instability.ions.fast_beam_ion">fast_beam_ion() (in module mbtrack2.instability.ions)</a>
+</li>
+      <li><a href="mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.monitors.BeamSpectrumMonitor.fft_resolution">fft_resolution (mbtrack2.tracking.monitors.monitors.BeamSpectrumMonitor property)</a>
+
+      <ul>
+        <li><a href="mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.monitors.BunchSpectrumMonitor.fft_resolution">(mbtrack2.tracking.monitors.monitors.BunchSpectrumMonitor property)</a>
+</li>
+      </ul></li>
+      <li><a href="mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.monitors.Monitor.file">file (mbtrack2.tracking.monitors.monitors.Monitor property)</a>
+</li>
+      <li><a href="mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.monitors.Monitor.file_name">file_name (mbtrack2.tracking.monitors.monitors.Monitor property)</a>
+</li>
+  </ul></td>
+  <td style="width: 33%; vertical-align: top;"><ul>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.particles.Beam.filling_pattern">filling_pattern (mbtrack2.tracking.particles.Beam property)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.rf.CavityResonator.filling_time">filling_time (mbtrack2.tracking.rf.CavityResonator property)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.feedback.FIRDamper">FIRDamper (class in mbtrack2.tracking.feedback)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.rf.CavityResonator.fr">fr (mbtrack2.tracking.rf.CavityResonator property)</a>
+</li>
+      <li><a href="mbtrack2.impedance.html#mbtrack2.impedance.csr.FreeSpaceCSR">FreeSpaceCSR (class in mbtrack2.impedance.csr)</a>
+</li>
+      <li><a href="mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.monitors.BeamSpectrumMonitor.frequency_samples">frequency_samples (mbtrack2.tracking.monitors.monitors.BeamSpectrumMonitor property)</a>
+
+      <ul>
+        <li><a href="mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.monitors.BunchSpectrumMonitor.frequency_samples">(mbtrack2.tracking.monitors.monitors.BunchSpectrumMonitor property)</a>
+</li>
+      </ul></li>
+  </ul></td>
+</tr></table>
+
+<h2 id="G">G</h2>
+<table style="width: 100%" class="indextable genindextable"><tr>
+  <td style="width: 33%; vertical-align: top;"><ul>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.synchrotron.Synchrotron.gamma">gamma (mbtrack2.tracking.synchrotron.Synchrotron property)</a>
+</li>
+      <li><a href="mbtrack2.utilities.html#mbtrack2.utilities.optics.Optics.gamma">gamma() (mbtrack2.utilities.optics.Optics method)</a>
+</li>
+      <li><a href="mbtrack2.impedance.html#mbtrack2.impedance.tapers.StupakovRectangularTaper.gap_prime">gap_prime (mbtrack2.impedance.tapers.StupakovRectangularTaper property)</a>
+</li>
+      <li><a href="mbtrack2.utilities.html#mbtrack2.utilities.spectrum.gaussian_bunch">gaussian_bunch() (in module mbtrack2.utilities.spectrum)</a>
+</li>
+      <li><a href="mbtrack2.utilities.html#mbtrack2.utilities.spectrum.gaussian_bunch_spectrum">gaussian_bunch_spectrum() (in module mbtrack2.utilities.spectrum)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.rf.CavityResonator.generator_phasor">generator_phasor (mbtrack2.tracking.rf.CavityResonator property)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.synchrotron.Synchrotron.get_adts">get_adts() (mbtrack2.tracking.synchrotron.Synchrotron method)</a>
+</li>
+      <li><a href="mbtrack2.utilities.html#mbtrack2.utilities.optics.PhysicalModel.get_aperture">get_aperture() (mbtrack2.utilities.optics.PhysicalModel method)</a>
+</li>
+      <li><a href="mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.monitors.BeamSpectrumMonitor.get_beam_spectrum">get_beam_spectrum() (mbtrack2.tracking.monitors.monitors.BeamSpectrumMonitor method)</a>
+</li>
+  </ul></td>
+  <td style="width: 33%; vertical-align: top;"><ul>
+      <li><a href="mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.monitors.BunchSpectrumMonitor.get_coherent_spectrum">get_coherent_spectrum() (mbtrack2.tracking.monitors.monitors.BunchSpectrumMonitor method)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.feedback.FIRDamper.get_fir">get_fir() (mbtrack2.tracking.feedback.FIRDamper method)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.wakepotential.WakePotential.get_gaussian_wakepotential">get_gaussian_wakepotential() (mbtrack2.tracking.wakepotential.WakePotential method)</a>
+</li>
+      <li><a href="mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.monitors.BunchSpectrumMonitor.get_incoherent_spectrum">get_incoherent_spectrum() (mbtrack2.tracking.monitors.monitors.BunchSpectrumMonitor method)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.wakepotential.LongRangeResistiveWall.get_kick">get_kick() (mbtrack2.tracking.wakepotential.LongRangeResistiveWall method)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.synchrotron.Synchrotron.get_longitudinal_twiss">get_longitudinal_twiss() (mbtrack2.tracking.synchrotron.Synchrotron method)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.synchrotron.Synchrotron.get_mcf_order">get_mcf_order() (mbtrack2.tracking.synchrotron.Synchrotron method)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.wakepotential.WakePotential.get_wakepotential">get_wakepotential() (mbtrack2.tracking.wakepotential.WakePotential method)</a>
+</li>
+      <li><a href="mbtrack2.impedance.html#mbtrack2.impedance.impedance_model.ImpedanceModel.group_attributes">group_attributes() (mbtrack2.impedance.impedance_model.ImpedanceModel method)</a>
+</li>
+  </ul></td>
+</tr></table>
+
+<h2 id="H">H</h2>
+<table style="width: 100%" class="indextable genindextable"><tr>
+  <td style="width: 33%; vertical-align: top;"><ul>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.synchrotron.Synchrotron.h">h (mbtrack2.tracking.synchrotron.Synchrotron property)</a>
+</li>
+  </ul></td>
+  <td style="width: 33%; vertical-align: top;"><ul>
+      <li><a href="mbtrack2.utilities.html#mbtrack2.utilities.misc.head_tail_form_factor">head_tail_form_factor() (in module mbtrack2.utilities.misc)</a>
+</li>
+  </ul></td>
+</tr></table>
+
+<h2 id="I">I</h2>
+<table style="width: 100%" class="indextable genindextable"><tr>
+  <td style="width: 33%; vertical-align: top;"><ul>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.rf.ProportionalIntegralLoop.Ig2Vg">Ig2Vg() (mbtrack2.tracking.rf.ProportionalIntegralLoop method)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.rf.ProportionalIntegralLoop.Ig2Vg_matrix">Ig2Vg_matrix() (mbtrack2.tracking.rf.ProportionalIntegralLoop method)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.rf.CavityResonator.ig_phasor_record">ig_phasor_record (mbtrack2.tracking.rf.CavityResonator property)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.rf.ProportionalIntegralLoop.IIR">IIR() (mbtrack2.tracking.rf.ProportionalIntegralLoop method)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.rf.ProportionalIntegralLoop.IIR_init">IIR_init() (mbtrack2.tracking.rf.ProportionalIntegralLoop method)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.rf.ProportionalIntegralLoop.IIRcutoff">IIRcutoff (mbtrack2.tracking.rf.ProportionalIntegralLoop property)</a>
+</li>
+      <li><a href="mbtrack2.impedance.html#mbtrack2.impedance.wakefield.Impedance">Impedance (class in mbtrack2.impedance.wakefield)</a>
+</li>
+      <li><a href="mbtrack2.impedance.html#mbtrack2.impedance.wakefield.WakeField.impedance_components">impedance_components (mbtrack2.impedance.wakefield.WakeField property)</a>
+</li>
+      <li><a href="mbtrack2.impedance.html#mbtrack2.impedance.impedance_model.ImpedanceModel">ImpedanceModel (class in mbtrack2.impedance.impedance_model)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.particles.Beam.init_beam">init_beam() (mbtrack2.tracking.particles.Beam method)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.feedback.FIRDamper.init_beam_no_mpi">init_beam_no_mpi() (mbtrack2.tracking.feedback.FIRDamper method)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.rf.ProportionalIntegralLoop.init_FFconst">init_FFconst() (mbtrack2.tracking.rf.ProportionalIntegralLoop method)</a>
+</li>
+  </ul></td>
+  <td style="width: 33%; vertical-align: top;"><ul>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.particles.Bunch.init_gaussian">init_gaussian() (mbtrack2.tracking.particles.Bunch method)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.rf.ProportionalIntegralLoop.init_Ig2Vg_matrix">init_Ig2Vg_matrix() (mbtrack2.tracking.rf.ProportionalIntegralLoop method)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.rf.CavityResonator.init_phasor">init_phasor() (mbtrack2.tracking.rf.CavityResonator method)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.rf.CavityResonator.init_phasor_track">init_phasor_track() (mbtrack2.tracking.rf.CavityResonator method)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.rf.CavityResonator.init_tracking">init_tracking() (mbtrack2.tracking.rf.CavityResonator method)</a>
+</li>
+      <li><a href="mbtrack2.impedance.html#mbtrack2.impedance.wakefield.ComplexData.initialize_coefficient">initialize_coefficient() (mbtrack2.impedance.wakefield.ComplexData method)</a>
+</li>
+      <li><a href="mbtrack2.utilities.html#mbtrack2.utilities.beamloading.BeamLoadingEquilibrium.integrate_func">integrate_func() (mbtrack2.utilities.beamloading.BeamLoadingEquilibrium method)</a>
+</li>
+      <li><a href="mbtrack2.instability.html#mbtrack2.instability.ions.ion_cross_section">ion_cross_section() (in module mbtrack2.instability.ions)</a>
+</li>
+      <li><a href="mbtrack2.instability.html#mbtrack2.instability.ions.ion_frequency">ion_frequency() (in module mbtrack2.instability.ions)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.rf.CavityResonator.is_CBI_stable">is_CBI_stable() (mbtrack2.tracking.rf.CavityResonator method)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.rf.CavityResonator.is_DC_Robinson_stable">is_DC_Robinson_stable() (mbtrack2.tracking.rf.CavityResonator method)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.particles.Bunch.is_empty">is_empty (mbtrack2.tracking.particles.Bunch property)</a>
+</li>
+  </ul></td>
+</tr></table>
+
+<h2 id="K">K</h2>
+<table style="width: 100%" class="indextable genindextable"><tr>
+  <td style="width: 33%; vertical-align: top;"><ul>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.synchrotron.Synchrotron.k1">k1 (mbtrack2.tracking.synchrotron.Synchrotron property)</a>
+</li>
+  </ul></td>
+</tr></table>
+
+<h2 id="L">L</h2>
+<table style="width: 100%" class="indextable genindextable"><tr>
+  <td style="width: 33%; vertical-align: top;"><ul>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.synchrotron.Synchrotron.L">L (mbtrack2.tracking.synchrotron.Synchrotron property)</a>
+</li>
+      <li><a href="mbtrack2.instability.html#mbtrack2.instability.instabilities.lcbi_growth_rate">lcbi_growth_rate() (in module mbtrack2.instability.instabilities)</a>
+</li>
+      <li><a href="mbtrack2.instability.html#mbtrack2.instability.instabilities.lcbi_growth_rate_mode">lcbi_growth_rate_mode() (in module mbtrack2.instability.instabilities)</a>
+</li>
+      <li><a href="mbtrack2.instability.html#mbtrack2.instability.instabilities.lcbi_stability_diagram">lcbi_stability_diagram() (in module mbtrack2.instability.instabilities)</a>
+</li>
+      <li><a href="mbtrack2.impedance.html#mbtrack2.impedance.wakefield.WakeField.list_to_attr">list_to_attr() (mbtrack2.impedance.wakefield.WakeField method)</a>
+</li>
+      <li><a href="mbtrack2.impedance.html#mbtrack2.impedance.impedance_model.ImpedanceModel.load">load() (mbtrack2.impedance.impedance_model.ImpedanceModel method)</a>
+
+      <ul>
+        <li><a href="mbtrack2.impedance.html#mbtrack2.impedance.wakefield.WakeField.load">(mbtrack2.impedance.wakefield.WakeField static method)</a>
+</li>
+        <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.particles.Beam.load">(mbtrack2.tracking.particles.Beam method)</a>
+</li>
+        <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.particles.Bunch.load">(mbtrack2.tracking.particles.Bunch method)</a>
+</li>
+      </ul></li>
+      <li><a href="mbtrack2.utilities.html#mbtrack2.utilities.optics.Optics.load_from_AT">load_from_AT() (mbtrack2.utilities.optics.Optics method)</a>
+</li>
+      <li><a href="mbtrack2.utilities.html#mbtrack2.utilities.optics.Optics.local_alpha">local_alpha (mbtrack2.utilities.optics.Optics property)</a>
+</li>
+      <li><a href="mbtrack2.utilities.html#mbtrack2.utilities.optics.Optics.local_beta">local_beta (mbtrack2.utilities.optics.Optics property)</a>
+</li>
+      <li><a href="mbtrack2.utilities.html#mbtrack2.utilities.optics.Optics.local_gamma">local_gamma (mbtrack2.utilities.optics.Optics property)</a>
+</li>
+      <li><a href="mbtrack2.impedance.html#mbtrack2.impedance.tapers.StupakovCircularTaper.long">long() (mbtrack2.impedance.tapers.StupakovCircularTaper method)</a>
+
+      <ul>
+        <li><a href="mbtrack2.impedance.html#mbtrack2.impedance.tapers.StupakovRectangularTaper.long">(mbtrack2.impedance.tapers.StupakovRectangularTaper method)</a>
+</li>
+      </ul></li>
+  </ul></td>
+  <td style="width: 33%; vertical-align: top;"><ul>
+      <li><a href="mbtrack2.impedance.html#mbtrack2.impedance.resonator.PureInductive.long_impedance">long_impedance() (mbtrack2.impedance.resonator.PureInductive method)</a>
+
+      <ul>
+        <li><a href="mbtrack2.impedance.html#mbtrack2.impedance.resonator.PureResistive.long_impedance">(mbtrack2.impedance.resonator.PureResistive method)</a>
+</li>
+        <li><a href="mbtrack2.impedance.html#mbtrack2.impedance.resonator.Resonator.long_impedance">(mbtrack2.impedance.resonator.Resonator method)</a>
+</li>
+      </ul></li>
+      <li><a href="mbtrack2.impedance.html#mbtrack2.impedance.resonator.Resonator.long_wake_function">long_wake_function() (mbtrack2.impedance.resonator.Resonator method)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.aperture.LongitudinalAperture">LongitudinalAperture (class in mbtrack2.tracking.aperture)</a>
+</li>
+      <li><a href="mbtrack2.impedance.html#mbtrack2.impedance.csr.FreeSpaceCSR.LongitudinalImpedance">LongitudinalImpedance() (mbtrack2.impedance.csr.FreeSpaceCSR method)</a>
+
+      <ul>
+        <li><a href="mbtrack2.impedance.html#mbtrack2.impedance.csr.ParallelPlatesCSR.LongitudinalImpedance">(mbtrack2.impedance.csr.ParallelPlatesCSR method)</a>
+</li>
+        <li><a href="mbtrack2.impedance.html#mbtrack2.impedance.resistive_wall.Coating.LongitudinalImpedance">(mbtrack2.impedance.resistive_wall.Coating method)</a>
+</li>
+      </ul></li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.element.LongitudinalMap">LongitudinalMap (class in mbtrack2.tracking.element)</a>
+</li>
+      <li><a href="mbtrack2.impedance.html#mbtrack2.impedance.csr.FreeSpaceCSR.LongitudinalWakeFunction">LongitudinalWakeFunction() (mbtrack2.impedance.csr.FreeSpaceCSR method)</a>
+
+      <ul>
+        <li><a href="mbtrack2.impedance.html#mbtrack2.impedance.csr.ParallelPlatesCSR.LongitudinalWakeFunction">(mbtrack2.impedance.csr.ParallelPlatesCSR method)</a>
+</li>
+        <li><a href="mbtrack2.impedance.html#mbtrack2.impedance.resistive_wall.CircularResistiveWall.LongitudinalWakeFunction">(mbtrack2.impedance.resistive_wall.CircularResistiveWall method)</a>
+</li>
+      </ul></li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.wakepotential.LongRangeResistiveWall">LongRangeResistiveWall (class in mbtrack2.tracking.wakepotential)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.rf.CavityResonator.loss_factor">loss_factor (mbtrack2.tracking.rf.CavityResonator property)</a>
+</li>
+      <li><a href="mbtrack2.impedance.html#mbtrack2.impedance.wakefield.Impedance.loss_factor">loss_factor() (mbtrack2.impedance.wakefield.Impedance method)</a>
+
+      <ul>
+        <li><a href="mbtrack2.impedance.html#mbtrack2.impedance.wakefield.WakeFunction.loss_factor">(mbtrack2.impedance.wakefield.WakeFunction method)</a>
+</li>
+      </ul></li>
+  </ul></td>
+</tr></table>
+
+<h2 id="M">M</h2>
+<table style="width: 100%" class="indextable genindextable"><tr>
+  <td style="width: 33%; vertical-align: top;"><ul>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.rf.CavityResonator.m">m (mbtrack2.tracking.rf.CavityResonator property)</a>
+</li>
+      <li><a href="mbtrack2.instability.html#mbtrack2.instability.instabilities.mbi_threshold">mbi_threshold() (in module mbtrack2.instability.instabilities)</a>
+</li>
+      <li>
+    mbtrack2
+
+      <ul>
+        <li><a href="mbtrack2.html#module-mbtrack2">module</a>
+</li>
+      </ul></li>
+      <li>
+    mbtrack2.impedance
+
+      <ul>
+        <li><a href="mbtrack2.impedance.html#module-mbtrack2.impedance">module</a>
+</li>
+      </ul></li>
+      <li>
+    mbtrack2.impedance.csr
+
+      <ul>
+        <li><a href="mbtrack2.impedance.html#module-mbtrack2.impedance.csr">module</a>
+</li>
+      </ul></li>
+      <li>
+    mbtrack2.impedance.impedance_model
+
+      <ul>
+        <li><a href="mbtrack2.impedance.html#module-mbtrack2.impedance.impedance_model">module</a>
+</li>
+      </ul></li>
+      <li>
+    mbtrack2.impedance.resistive_wall
+
+      <ul>
+        <li><a href="mbtrack2.impedance.html#module-mbtrack2.impedance.resistive_wall">module</a>
+</li>
+      </ul></li>
+      <li>
+    mbtrack2.impedance.resonator
+
+      <ul>
+        <li><a href="mbtrack2.impedance.html#module-mbtrack2.impedance.resonator">module</a>
+</li>
+      </ul></li>
+      <li>
+    mbtrack2.impedance.tapers
+
+      <ul>
+        <li><a href="mbtrack2.impedance.html#module-mbtrack2.impedance.tapers">module</a>
+</li>
+      </ul></li>
+      <li>
+    mbtrack2.impedance.wakefield
+
+      <ul>
+        <li><a href="mbtrack2.impedance.html#module-mbtrack2.impedance.wakefield">module</a>
+</li>
+      </ul></li>
+      <li>
+    mbtrack2.instability
+
+      <ul>
+        <li><a href="mbtrack2.instability.html#module-mbtrack2.instability">module</a>
+</li>
+      </ul></li>
+      <li>
+    mbtrack2.instability.instabilities
+
+      <ul>
+        <li><a href="mbtrack2.instability.html#module-mbtrack2.instability.instabilities">module</a>
+</li>
+      </ul></li>
+      <li>
+    mbtrack2.instability.ions
+
+      <ul>
+        <li><a href="mbtrack2.instability.html#module-mbtrack2.instability.ions">module</a>
+</li>
+      </ul></li>
+      <li>
+    mbtrack2.tracking
+
+      <ul>
+        <li><a href="mbtrack2.tracking.html#module-mbtrack2.tracking">module</a>
+</li>
+      </ul></li>
+      <li>
+    mbtrack2.tracking.aperture
+
+      <ul>
+        <li><a href="mbtrack2.tracking.html#module-mbtrack2.tracking.aperture">module</a>
+</li>
+      </ul></li>
+      <li>
+    mbtrack2.tracking.element
+
+      <ul>
+        <li><a href="mbtrack2.tracking.html#module-mbtrack2.tracking.element">module</a>
+</li>
+      </ul></li>
+      <li>
+    mbtrack2.tracking.feedback
+
+      <ul>
+        <li><a href="mbtrack2.tracking.html#module-mbtrack2.tracking.feedback">module</a>
+</li>
+      </ul></li>
+      <li>
+    mbtrack2.tracking.monitors
+
+      <ul>
+        <li><a href="mbtrack2.tracking.monitors.html#module-mbtrack2.tracking.monitors">module</a>
+</li>
+      </ul></li>
+      <li>
+    mbtrack2.tracking.monitors.monitors
+
+      <ul>
+        <li><a href="mbtrack2.tracking.monitors.html#module-mbtrack2.tracking.monitors.monitors">module</a>
+</li>
+      </ul></li>
+      <li>
+    mbtrack2.tracking.monitors.plotting
+
+      <ul>
+        <li><a href="mbtrack2.tracking.monitors.html#module-mbtrack2.tracking.monitors.plotting">module</a>
+</li>
+      </ul></li>
+      <li>
+    mbtrack2.tracking.monitors.tools
+
+      <ul>
+        <li><a href="mbtrack2.tracking.monitors.html#module-mbtrack2.tracking.monitors.tools">module</a>
+</li>
+      </ul></li>
+      <li>
+    mbtrack2.tracking.parallel
+
+      <ul>
+        <li><a href="mbtrack2.tracking.html#module-mbtrack2.tracking.parallel">module</a>
+</li>
+      </ul></li>
+      <li>
+    mbtrack2.tracking.particles
+
+      <ul>
+        <li><a href="mbtrack2.tracking.html#module-mbtrack2.tracking.particles">module</a>
+</li>
+      </ul></li>
+      <li>
+    mbtrack2.tracking.rf
+
+      <ul>
+        <li><a href="mbtrack2.tracking.html#module-mbtrack2.tracking.rf">module</a>
+</li>
+      </ul></li>
+      <li>
+    mbtrack2.tracking.synchrotron
+
+      <ul>
+        <li><a href="mbtrack2.tracking.html#module-mbtrack2.tracking.synchrotron">module</a>
+</li>
+      </ul></li>
+      <li>
+    mbtrack2.tracking.wakepotential
+
+      <ul>
+        <li><a href="mbtrack2.tracking.html#module-mbtrack2.tracking.wakepotential">module</a>
+</li>
+      </ul></li>
+      <li>
+    mbtrack2.utilities
+
+      <ul>
+        <li><a href="mbtrack2.utilities.html#module-mbtrack2.utilities">module</a>
+</li>
+      </ul></li>
+      <li>
+    mbtrack2.utilities.beamloading
+
+      <ul>
+        <li><a href="mbtrack2.utilities.html#module-mbtrack2.utilities.beamloading">module</a>
+</li>
+      </ul></li>
+  </ul></td>
+  <td style="width: 33%; vertical-align: top;"><ul>
+      <li>
+    mbtrack2.utilities.misc
+
+      <ul>
+        <li><a href="mbtrack2.utilities.html#module-mbtrack2.utilities.misc">module</a>
+</li>
+      </ul></li>
+      <li>
+    mbtrack2.utilities.optics
+
+      <ul>
+        <li><a href="mbtrack2.utilities.html#module-mbtrack2.utilities.optics">module</a>
+</li>
+      </ul></li>
+      <li>
+    mbtrack2.utilities.read_impedance
+
+      <ul>
+        <li><a href="mbtrack2.utilities.html#module-mbtrack2.utilities.read_impedance">module</a>
+</li>
+      </ul></li>
+      <li>
+    mbtrack2.utilities.spectrum
+
+      <ul>
+        <li><a href="mbtrack2.utilities.html#module-mbtrack2.utilities.spectrum">module</a>
+</li>
+      </ul></li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.synchrotron.Synchrotron.mcf_order">mcf_order (mbtrack2.tracking.synchrotron.Synchrotron property)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.particles.Bunch.mean">mean (mbtrack2.tracking.particles.Bunch property)</a>
+</li>
+      <li><a href="mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.tools.merge_files">merge_files() (in module mbtrack2.tracking.monitors.tools)</a>
+</li>
+      <li>
+    module
+
+      <ul>
+        <li><a href="mbtrack2.html#module-mbtrack2">mbtrack2</a>
+</li>
+        <li><a href="mbtrack2.impedance.html#module-mbtrack2.impedance">mbtrack2.impedance</a>
+</li>
+        <li><a href="mbtrack2.impedance.html#module-mbtrack2.impedance.csr">mbtrack2.impedance.csr</a>
+</li>
+        <li><a href="mbtrack2.impedance.html#module-mbtrack2.impedance.impedance_model">mbtrack2.impedance.impedance_model</a>
+</li>
+        <li><a href="mbtrack2.impedance.html#module-mbtrack2.impedance.resistive_wall">mbtrack2.impedance.resistive_wall</a>
+</li>
+        <li><a href="mbtrack2.impedance.html#module-mbtrack2.impedance.resonator">mbtrack2.impedance.resonator</a>
+</li>
+        <li><a href="mbtrack2.impedance.html#module-mbtrack2.impedance.tapers">mbtrack2.impedance.tapers</a>
+</li>
+        <li><a href="mbtrack2.impedance.html#module-mbtrack2.impedance.wakefield">mbtrack2.impedance.wakefield</a>
+</li>
+        <li><a href="mbtrack2.instability.html#module-mbtrack2.instability">mbtrack2.instability</a>
+</li>
+        <li><a href="mbtrack2.instability.html#module-mbtrack2.instability.instabilities">mbtrack2.instability.instabilities</a>
+</li>
+        <li><a href="mbtrack2.instability.html#module-mbtrack2.instability.ions">mbtrack2.instability.ions</a>
+</li>
+        <li><a href="mbtrack2.tracking.html#module-mbtrack2.tracking">mbtrack2.tracking</a>
+</li>
+        <li><a href="mbtrack2.tracking.html#module-mbtrack2.tracking.aperture">mbtrack2.tracking.aperture</a>
+</li>
+        <li><a href="mbtrack2.tracking.html#module-mbtrack2.tracking.element">mbtrack2.tracking.element</a>
+</li>
+        <li><a href="mbtrack2.tracking.html#module-mbtrack2.tracking.feedback">mbtrack2.tracking.feedback</a>
+</li>
+        <li><a href="mbtrack2.tracking.monitors.html#module-mbtrack2.tracking.monitors">mbtrack2.tracking.monitors</a>
+</li>
+        <li><a href="mbtrack2.tracking.monitors.html#module-mbtrack2.tracking.monitors.monitors">mbtrack2.tracking.monitors.monitors</a>
+</li>
+        <li><a href="mbtrack2.tracking.monitors.html#module-mbtrack2.tracking.monitors.plotting">mbtrack2.tracking.monitors.plotting</a>
+</li>
+        <li><a href="mbtrack2.tracking.monitors.html#module-mbtrack2.tracking.monitors.tools">mbtrack2.tracking.monitors.tools</a>
+</li>
+        <li><a href="mbtrack2.tracking.html#module-mbtrack2.tracking.parallel">mbtrack2.tracking.parallel</a>
+</li>
+        <li><a href="mbtrack2.tracking.html#module-mbtrack2.tracking.particles">mbtrack2.tracking.particles</a>
+</li>
+        <li><a href="mbtrack2.tracking.html#module-mbtrack2.tracking.rf">mbtrack2.tracking.rf</a>
+</li>
+        <li><a href="mbtrack2.tracking.html#module-mbtrack2.tracking.synchrotron">mbtrack2.tracking.synchrotron</a>
+</li>
+        <li><a href="mbtrack2.tracking.html#module-mbtrack2.tracking.wakepotential">mbtrack2.tracking.wakepotential</a>
+</li>
+        <li><a href="mbtrack2.utilities.html#module-mbtrack2.utilities">mbtrack2.utilities</a>
+</li>
+        <li><a href="mbtrack2.utilities.html#module-mbtrack2.utilities.beamloading">mbtrack2.utilities.beamloading</a>
+</li>
+        <li><a href="mbtrack2.utilities.html#module-mbtrack2.utilities.misc">mbtrack2.utilities.misc</a>
+</li>
+        <li><a href="mbtrack2.utilities.html#module-mbtrack2.utilities.optics">mbtrack2.utilities.optics</a>
+</li>
+        <li><a href="mbtrack2.utilities.html#module-mbtrack2.utilities.read_impedance">mbtrack2.utilities.read_impedance</a>
+</li>
+        <li><a href="mbtrack2.utilities.html#module-mbtrack2.utilities.spectrum">mbtrack2.utilities.spectrum</a>
+</li>
+      </ul></li>
+      <li><a href="mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.monitors.Monitor">Monitor (class in mbtrack2.tracking.monitors.monitors)</a>
+</li>
+      <li><a href="mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.monitors.Monitor.monitor_init">monitor_init() (mbtrack2.tracking.monitors.monitors.Monitor method)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.particles.Bunch.mp_number">mp_number (mbtrack2.tracking.particles.Bunch property)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.parallel.Mpi">Mpi (class in mbtrack2.tracking.parallel)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.particles.Beam.mpi_close">mpi_close() (mbtrack2.tracking.particles.Beam method)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.particles.Beam.mpi_gather">mpi_gather() (mbtrack2.tracking.particles.Beam method)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.particles.Beam.mpi_init">mpi_init() (mbtrack2.tracking.particles.Beam method)</a>
+</li>
+      <li><a href="mbtrack2.utilities.html#mbtrack2.utilities.optics.Optics.mu">mu() (mbtrack2.utilities.optics.Optics method)</a>
+</li>
+      <li><a href="mbtrack2.impedance.html#mbtrack2.impedance.wakefield.ComplexData.multiply">multiply() (mbtrack2.impedance.wakefield.ComplexData method)</a>
+
+      <ul>
+        <li><a href="mbtrack2.impedance.html#mbtrack2.impedance.wakefield.Impedance.multiply">(mbtrack2.impedance.wakefield.Impedance method)</a>
+</li>
+        <li><a href="mbtrack2.impedance.html#mbtrack2.impedance.wakefield.WakeFunction.multiply">(mbtrack2.impedance.wakefield.WakeFunction method)</a>
+</li>
+      </ul></li>
+  </ul></td>
+</tr></table>
+
+<h2 id="N">N</h2>
+<table style="width: 100%" class="indextable genindextable"><tr>
+  <td style="width: 33%; vertical-align: top;"><ul>
+      <li><a href="mbtrack2.impedance.html#mbtrack2.impedance.wakefield.ComplexData.name_and_coefficients_table">name_and_coefficients_table() (mbtrack2.impedance.wakefield.ComplexData method)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.rf.CavityResonator.Ncav">Ncav (mbtrack2.tracking.rf.CavityResonator property)</a>
+</li>
+  </ul></td>
+  <td style="width: 33%; vertical-align: top;"><ul>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.parallel.Mpi.next_bunch">next_bunch (mbtrack2.tracking.parallel.Mpi property)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.particles.Beam.not_empty">not_empty (mbtrack2.tracking.particles.Beam property)</a>
+</li>
+  </ul></td>
+</tr></table>
+
+<h2 id="O">O</h2>
+<table style="width: 100%" class="indextable genindextable"><tr>
+  <td style="width: 33%; vertical-align: top;"><ul>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.synchrotron.Synchrotron.omega0">omega0 (mbtrack2.tracking.synchrotron.Synchrotron property)</a>
+</li>
+  </ul></td>
+  <td style="width: 33%; vertical-align: top;"><ul>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.synchrotron.Synchrotron.omega1">omega1 (mbtrack2.tracking.synchrotron.Synchrotron property)</a>
+</li>
+      <li><a href="mbtrack2.utilities.html#mbtrack2.utilities.optics.Optics">Optics (class in mbtrack2.utilities.optics)</a>
+</li>
+  </ul></td>
+</tr></table>
+
+<h2 id="P">P</h2>
+<table style="width: 100%" class="indextable genindextable"><tr>
+  <td style="width: 33%; vertical-align: top;"><ul>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.element.Element.parallel">parallel() (mbtrack2.tracking.element.Element static method)</a>
+</li>
+      <li><a href="mbtrack2.impedance.html#mbtrack2.impedance.csr.ParallelPlatesCSR">ParallelPlatesCSR (class in mbtrack2.impedance.csr)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.particles.Particle">Particle (class in mbtrack2.tracking.particles)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.particles.Beam.particle_number">particle_number (mbtrack2.tracking.particles.Beam property)</a>
+
+      <ul>
+        <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.particles.Bunch.particle_number">(mbtrack2.tracking.particles.Bunch property)</a>
+</li>
+      </ul></li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.rf.CavityResonator.Pb">Pb() (mbtrack2.tracking.rf.CavityResonator method)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.rf.CavityResonator.Pc">Pc (mbtrack2.tracking.rf.CavityResonator property)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.rf.DirectFeedback.phase_shift">phase_shift (mbtrack2.tracking.rf.DirectFeedback property)</a>
+</li>
+      <li><a href="mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.monitors.PhaseSpaceMonitor">PhaseSpaceMonitor (class in mbtrack2.tracking.monitors.monitors)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.rf.CavityResonator.phasor_decay">phasor_decay() (mbtrack2.tracking.rf.CavityResonator method)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.rf.CavityResonator.phasor_evol">phasor_evol() (mbtrack2.tracking.rf.CavityResonator method)</a>
+</li>
+      <li><a href="mbtrack2.utilities.html#mbtrack2.utilities.optics.PhysicalModel">PhysicalModel (class in mbtrack2.utilities.optics)</a>
+</li>
+      <li><a href="mbtrack2.impedance.html#mbtrack2.impedance.wakefield.Impedance.plot">plot() (mbtrack2.impedance.wakefield.Impedance method)</a>
+
+      <ul>
+        <li><a href="mbtrack2.impedance.html#mbtrack2.impedance.wakefield.WakeFunction.plot">(mbtrack2.impedance.wakefield.WakeFunction method)</a>
+</li>
+        <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.particles.Beam.plot">(mbtrack2.tracking.particles.Beam method)</a>
+</li>
+        <li><a href="mbtrack2.utilities.html#mbtrack2.utilities.optics.Optics.plot">(mbtrack2.utilities.optics.Optics method)</a>
+</li>
+      </ul></li>
+      <li><a href="mbtrack2.utilities.html#mbtrack2.utilities.optics.PhysicalModel.plot_aperture">plot_aperture() (mbtrack2.utilities.optics.PhysicalModel method)</a>
+</li>
+      <li><a href="mbtrack2.impedance.html#mbtrack2.impedance.impedance_model.ImpedanceModel.plot_area">plot_area() (mbtrack2.impedance.impedance_model.ImpedanceModel method)</a>
+</li>
+      <li><a href="mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.plotting.plot_beamdata">plot_beamdata() (in module mbtrack2.tracking.monitors.plotting)</a>
+</li>
+      <li><a href="mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.plotting.plot_beamspectrum">plot_beamspectrum() (in module mbtrack2.tracking.monitors.plotting)</a>
+</li>
+      <li><a href="mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.plotting.plot_bunchdata">plot_bunchdata() (in module mbtrack2.tracking.monitors.plotting)</a>
+</li>
+      <li><a href="mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.plotting.plot_bunchspectrum">plot_bunchspectrum() (in module mbtrack2.tracking.monitors.plotting)</a>
+</li>
+      <li><a href="mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.plotting.plot_cavitydata">plot_cavitydata() (in module mbtrack2.tracking.monitors.plotting)</a>
+</li>
+      <li><a href="mbtrack2.instability.html#mbtrack2.instability.ions.plot_critical_mass">plot_critical_mass() (in module mbtrack2.instability.ions)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.rf.CavityResonator.plot_DC_Robinson_stability">plot_DC_Robinson_stability() (mbtrack2.tracking.rf.CavityResonator method)</a>
+</li>
+      <li><a href="mbtrack2.utilities.html#mbtrack2.utilities.beamloading.BeamLoadingEquilibrium.plot_dV">plot_dV() (mbtrack2.utilities.beamloading.BeamLoadingEquilibrium method)</a>
+</li>
+  </ul></td>
+  <td style="width: 33%; vertical-align: top;"><ul>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.feedback.FIRDamper.plot_fir">plot_fir() (mbtrack2.tracking.feedback.FIRDamper method)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.wakepotential.WakePotential.plot_gaussian_wake">plot_gaussian_wake() (mbtrack2.tracking.wakepotential.WakePotential method)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.wakepotential.WakePotential.plot_last_wake">plot_last_wake() (mbtrack2.tracking.wakepotential.WakePotential method)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.particles.Bunch.plot_phasespace">plot_phasespace() (mbtrack2.tracking.particles.Bunch method)</a>
+</li>
+      <li><a href="mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.plotting.plot_phasespacedata">plot_phasespacedata() (in module mbtrack2.tracking.monitors.plotting)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.rf.CavityResonator.plot_phasor">plot_phasor() (mbtrack2.tracking.rf.CavityResonator method)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.particles.Bunch.plot_profile">plot_profile() (mbtrack2.tracking.particles.Bunch method)</a>
+</li>
+      <li><a href="mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.plotting.plot_profiledata">plot_profiledata() (in module mbtrack2.tracking.monitors.plotting)</a>
+</li>
+      <li><a href="mbtrack2.utilities.html#mbtrack2.utilities.optics.PhysicalModel.plot_resistivity">plot_resistivity() (mbtrack2.utilities.optics.PhysicalModel method)</a>
+</li>
+      <li><a href="mbtrack2.utilities.html#mbtrack2.utilities.beamloading.BeamLoadingEquilibrium.plot_rho">plot_rho() (mbtrack2.utilities.beamloading.BeamLoadingEquilibrium method)</a>
+</li>
+      <li><a href="mbtrack2.utilities.html#mbtrack2.utilities.beamloading.BeamLoadingEquilibrium.plot_voltage">plot_voltage() (mbtrack2.utilities.beamloading.BeamLoadingEquilibrium method)</a>
+</li>
+      <li><a href="mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.plotting.plot_wakedata">plot_wakedata() (in module mbtrack2.tracking.monitors.plotting)</a>
+</li>
+      <li><a href="mbtrack2.impedance.html#mbtrack2.impedance.impedance_model.ImpedanceModel.power_loss_spectrum">power_loss_spectrum() (mbtrack2.impedance.impedance_model.ImpedanceModel method)</a>
+</li>
+      <li><a href="mbtrack2.impedance.html#mbtrack2.impedance.wakefield.ComplexData.power_x">power_x (mbtrack2.impedance.wakefield.ComplexData property)</a>
+</li>
+      <li><a href="mbtrack2.impedance.html#mbtrack2.impedance.wakefield.ComplexData.power_y">power_y (mbtrack2.impedance.wakefield.ComplexData property)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.rf.CavityResonator.Pr">Pr() (mbtrack2.tracking.rf.CavityResonator method)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.wakepotential.WakePotential.prepare_wakefunction">prepare_wakefunction() (mbtrack2.tracking.wakepotential.WakePotential method)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.parallel.Mpi.previous_bunch">previous_bunch (mbtrack2.tracking.parallel.Mpi property)</a>
+</li>
+      <li><a href="mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.monitors.ProfileMonitor">ProfileMonitor (class in mbtrack2.tracking.monitors.monitors)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.rf.ProportionalIntegralLoop">ProportionalIntegralLoop (class in mbtrack2.tracking.rf)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.rf.ProportionalLoop">ProportionalLoop (class in mbtrack2.tracking.rf)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.particles.Proton">Proton (class in mbtrack2.tracking.particles)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.rf.CavityResonator.psi">psi (mbtrack2.tracking.rf.CavityResonator property)</a>
+</li>
+      <li><a href="mbtrack2.utilities.html#mbtrack2.utilities.beamloading.BeamLoadingEquilibrium.PTBL_threshold">PTBL_threshold() (mbtrack2.utilities.beamloading.BeamLoadingEquilibrium method)</a>
+</li>
+      <li><a href="mbtrack2.impedance.html#mbtrack2.impedance.resonator.PureInductive">PureInductive (class in mbtrack2.impedance.resonator)</a>
+</li>
+      <li><a href="mbtrack2.impedance.html#mbtrack2.impedance.resonator.PureResistive">PureResistive (class in mbtrack2.impedance.resonator)</a>
+</li>
+  </ul></td>
+</tr></table>
+
+<h2 id="Q">Q</h2>
+<table style="width: 100%" class="indextable genindextable"><tr>
+  <td style="width: 33%; vertical-align: top;"><ul>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.rf.CavityResonator.Q">Q (mbtrack2.tracking.rf.CavityResonator property)</a>
+</li>
+  </ul></td>
+  <td style="width: 33%; vertical-align: top;"><ul>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.rf.CavityResonator.QL">QL (mbtrack2.tracking.rf.CavityResonator property)</a>
+</li>
+      <li><a href="mbtrack2.impedance.html#mbtrack2.impedance.tapers.StupakovRectangularTaper.quad">quad() (mbtrack2.impedance.tapers.StupakovRectangularTaper method)</a>
+</li>
+  </ul></td>
+</tr></table>
+
+<h2 id="R">R</h2>
+<table style="width: 100%" class="indextable genindextable"><tr>
+  <td style="width: 33%; vertical-align: top;"><ul>
+      <li><a href="mbtrack2.impedance.html#mbtrack2.impedance.tapers.StupakovCircularTaper.radius_prime">radius_prime (mbtrack2.impedance.tapers.StupakovCircularTaper property)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.parallel.Mpi.rank_to_bunch">rank_to_bunch() (mbtrack2.tracking.parallel.Mpi method)</a>
+</li>
+      <li><a href="mbtrack2.utilities.html#mbtrack2.utilities.read_impedance.read_ABCI">read_ABCI() (in module mbtrack2.utilities.read_impedance)</a>
+</li>
+      <li><a href="mbtrack2.utilities.html#mbtrack2.utilities.read_impedance.read_CST">read_CST() (in module mbtrack2.utilities.read_impedance)</a>
+</li>
+      <li><a href="mbtrack2.utilities.html#mbtrack2.utilities.read_impedance.read_ECHO2D">read_ECHO2D() (in module mbtrack2.utilities.read_impedance)</a>
+</li>
+      <li><a href="mbtrack2.utilities.html#mbtrack2.utilities.read_impedance.read_IW2D">read_IW2D() (in module mbtrack2.utilities.read_impedance)</a>
+</li>
+      <li><a href="mbtrack2.utilities.html#mbtrack2.utilities.read_impedance.read_IW2D_folder">read_IW2D_folder() (in module mbtrack2.utilities.read_impedance)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.aperture.RectangularAperture">RectangularAperture (class in mbtrack2.tracking.aperture)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.wakepotential.WakePotential.reduce_sampling">reduce_sampling() (mbtrack2.tracking.wakepotential.WakePotential method)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.wakepotential.WakePotential.reference_loss">reference_loss() (mbtrack2.tracking.wakepotential.WakePotential method)</a>
+</li>
+  </ul></td>
+  <td style="width: 33%; vertical-align: top;"><ul>
+      <li><a href="mbtrack2.impedance.html#mbtrack2.impedance.impedance_model.ImpedanceModel.rename_attribute">rename_attribute() (mbtrack2.impedance.impedance_model.ImpedanceModel method)</a>
+</li>
+      <li><a href="mbtrack2.utilities.html#mbtrack2.utilities.optics.PhysicalModel.resistive_wall_effective_radius">resistive_wall_effective_radius() (mbtrack2.utilities.optics.PhysicalModel method)</a>
+</li>
+      <li><a href="mbtrack2.impedance.html#mbtrack2.impedance.resonator.Resonator">Resonator (class in mbtrack2.impedance.resonator)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.rf.RFCavity">RFCavity (class in mbtrack2.tracking.rf)</a>
+</li>
+      <li><a href="mbtrack2.utilities.html#mbtrack2.utilities.beamloading.BeamLoadingEquilibrium.rho">rho() (mbtrack2.utilities.beamloading.BeamLoadingEquilibrium method)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.rf.CavityResonator.RL">RL (mbtrack2.tracking.rf.CavityResonator property)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.rf.CavityResonator.Rs">Rs (mbtrack2.tracking.rf.CavityResonator property)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.rf.CavityResonator.Rs_per_cavity">Rs_per_cavity (mbtrack2.tracking.rf.CavityResonator property)</a>
+</li>
+      <li><a href="mbtrack2.instability.html#mbtrack2.instability.instabilities.rwmbi_growth_rate">rwmbi_growth_rate() (in module mbtrack2.instability.instabilities)</a>
+</li>
+      <li><a href="mbtrack2.instability.html#mbtrack2.instability.instabilities.rwmbi_threshold">rwmbi_threshold() (in module mbtrack2.instability.instabilities)</a>
+</li>
+  </ul></td>
+</tr></table>
+
+<h2 id="S">S</h2>
+<table style="width: 100%" class="indextable genindextable"><tr>
+  <td style="width: 33%; vertical-align: top;"><ul>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.rf.CavityResonator.sample_voltage">sample_voltage() (mbtrack2.tracking.rf.CavityResonator method)</a>
+</li>
+      <li><a href="mbtrack2.impedance.html#mbtrack2.impedance.impedance_model.ImpedanceModel.save">save() (mbtrack2.impedance.impedance_model.ImpedanceModel method)</a>
+
+      <ul>
+        <li><a href="mbtrack2.impedance.html#mbtrack2.impedance.wakefield.WakeField.save">(mbtrack2.impedance.wakefield.WakeField method)</a>
+</li>
+        <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.particles.Beam.save">(mbtrack2.tracking.particles.Beam method)</a>
+</li>
+        <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.particles.Bunch.save">(mbtrack2.tracking.particles.Bunch method)</a>
+</li>
+      </ul></li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.rf.CavityResonator.set_generator">set_generator() (mbtrack2.tracking.rf.CavityResonator method)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.rf.CavityResonator.set_optimal_coupling">set_optimal_coupling() (mbtrack2.tracking.rf.CavityResonator method)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.rf.CavityResonator.set_optimal_detune">set_optimal_detune() (mbtrack2.tracking.rf.CavityResonator method)</a>
+</li>
+      <li><a href="mbtrack2.utilities.html#mbtrack2.utilities.optics.Optics.setup_interpolation">setup_interpolation() (mbtrack2.utilities.optics.Optics method)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.parallel.Mpi.share_distributions">share_distributions() (mbtrack2.tracking.parallel.Mpi method)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.parallel.Mpi.share_means">share_means() (mbtrack2.tracking.parallel.Mpi method)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.parallel.Mpi.share_stds">share_stds() (mbtrack2.tracking.parallel.Mpi method)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.synchrotron.Synchrotron.sigma">sigma() (mbtrack2.tracking.synchrotron.Synchrotron method)</a>
+</li>
+      <li><a href="mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.monitors.BeamSpectrumMonitor.signal_resolution">signal_resolution (mbtrack2.tracking.monitors.monitors.BeamSpectrumMonitor property)</a>
+
+      <ul>
+        <li><a href="mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.monitors.BunchSpectrumMonitor.signal_resolution">(mbtrack2.tracking.monitors.monitors.BunchSpectrumMonitor property)</a>
+</li>
+      </ul></li>
+  </ul></td>
+  <td style="width: 33%; vertical-align: top;"><ul>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.element.SkewQuadrupole">SkewQuadrupole (class in mbtrack2.tracking.element)</a>
+</li>
+      <li><a href="mbtrack2.impedance.html#mbtrack2.impedance.resistive_wall.skin_depth">skin_depth() (in module mbtrack2.impedance.resistive_wall)</a>
+</li>
+      <li><a href="mbtrack2.utilities.html#mbtrack2.utilities.spectrum.spectral_density">spectral_density() (in module mbtrack2.utilities.spectrum)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.particles.Bunch.std">std (mbtrack2.tracking.particles.Bunch property)</a>
+</li>
+      <li><a href="mbtrack2.utilities.html#mbtrack2.utilities.beamloading.BeamLoadingEquilibrium.std_rho">std_rho() (mbtrack2.utilities.beamloading.BeamLoadingEquilibrium method)</a>
+</li>
+      <li><a href="mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.plotting.streak_beamdata">streak_beamdata() (in module mbtrack2.tracking.monitors.plotting)</a>
+</li>
+      <li><a href="mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.plotting.streak_beamspectrum">streak_beamspectrum() (in module mbtrack2.tracking.monitors.plotting)</a>
+</li>
+      <li><a href="mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.plotting.streak_bunchspectrum">streak_bunchspectrum() (in module mbtrack2.tracking.monitors.plotting)</a>
+</li>
+      <li><a href="mbtrack2.impedance.html#mbtrack2.impedance.tapers.StupakovCircularTaper">StupakovCircularTaper (class in mbtrack2.impedance.tapers)</a>
+</li>
+      <li><a href="mbtrack2.impedance.html#mbtrack2.impedance.tapers.StupakovRectangularTaper">StupakovRectangularTaper (class in mbtrack2.impedance.tapers)</a>
+</li>
+      <li><a href="mbtrack2.impedance.html#mbtrack2.impedance.impedance_model.ImpedanceModel.sum_beta">sum_beta() (mbtrack2.impedance.impedance_model.ImpedanceModel method)</a>
+</li>
+      <li><a href="mbtrack2.impedance.html#mbtrack2.impedance.csr.ParallelPlatesCSR.sum_func">sum_func() (mbtrack2.impedance.csr.ParallelPlatesCSR method)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.synchrotron.Synchrotron">Synchrotron (class in mbtrack2.tracking.synchrotron)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.synchrotron.Synchrotron.synchrotron_tune">synchrotron_tune() (mbtrack2.tracking.synchrotron.Synchrotron method)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.element.SynchrotronRadiation">SynchrotronRadiation (class in mbtrack2.tracking.element)</a>
+</li>
+  </ul></td>
+</tr></table>
+
+<h2 id="T">T</h2>
+<table style="width: 100%" class="indextable genindextable"><tr>
+  <td style="width: 33%; vertical-align: top;"><ul>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.synchrotron.Synchrotron.T0">T0 (mbtrack2.tracking.synchrotron.Synchrotron property)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.synchrotron.Synchrotron.T1">T1 (mbtrack2.tracking.synchrotron.Synchrotron property)</a>
+</li>
+      <li><a href="mbtrack2.utilities.html#mbtrack2.utilities.optics.PhysicalModel.taper">taper() (mbtrack2.utilities.optics.PhysicalModel method)</a>
+</li>
+      <li><a href="mbtrack2.impedance.html#mbtrack2.impedance.csr.ParallelPlatesCSR.threshold">threshold (mbtrack2.impedance.csr.ParallelPlatesCSR property)</a>
+</li>
+      <li><a href="mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.monitors.BeamMonitor.to_buffer">to_buffer() (mbtrack2.tracking.monitors.monitors.BeamMonitor method)</a>
+
+      <ul>
+        <li><a href="mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.monitors.BeamSpectrumMonitor.to_buffer">(mbtrack2.tracking.monitors.monitors.BeamSpectrumMonitor method)</a>
+</li>
+        <li><a href="mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.monitors.BunchSpectrumMonitor.to_buffer">(mbtrack2.tracking.monitors.monitors.BunchSpectrumMonitor method)</a>
+</li>
+        <li><a href="mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.monitors.Monitor.to_buffer">(mbtrack2.tracking.monitors.monitors.Monitor method)</a>
+</li>
+        <li><a href="mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.monitors.PhaseSpaceMonitor.to_buffer">(mbtrack2.tracking.monitors.monitors.PhaseSpaceMonitor method)</a>
+</li>
+        <li><a href="mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.monitors.ProfileMonitor.to_buffer">(mbtrack2.tracking.monitors.monitors.ProfileMonitor method)</a>
+</li>
+        <li><a href="mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.monitors.WakePotentialMonitor.to_buffer">(mbtrack2.tracking.monitors.monitors.WakePotentialMonitor method)</a>
+</li>
+      </ul></li>
+      <li><a href="mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.monitors.BeamMonitor.to_buffer_no_mpi">to_buffer_no_mpi() (mbtrack2.tracking.monitors.monitors.BeamMonitor method)</a>
+</li>
+      <li><a href="mbtrack2.impedance.html#mbtrack2.impedance.wakefield.WakeFunction.to_impedance">to_impedance() (mbtrack2.impedance.wakefield.WakeFunction method)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.synchrotron.Synchrotron.to_pyat">to_pyat() (mbtrack2.tracking.synchrotron.Synchrotron method)</a>
+</li>
+      <li><a href="mbtrack2.utilities.html#mbtrack2.utilities.beamloading.BeamLoadingEquilibrium.to_solve">to_solve() (mbtrack2.utilities.beamloading.BeamLoadingEquilibrium method)</a>
+</li>
+      <li><a href="mbtrack2.impedance.html#mbtrack2.impedance.wakefield.Impedance.to_wakefunction">to_wakefunction() (mbtrack2.impedance.wakefield.Impedance method)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.aperture.CircularAperture.track">track() (mbtrack2.tracking.aperture.CircularAperture method)</a>
+
+      <ul>
+        <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.aperture.ElipticalAperture.track">(mbtrack2.tracking.aperture.ElipticalAperture method)</a>
+</li>
+        <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.aperture.LongitudinalAperture.track">(mbtrack2.tracking.aperture.LongitudinalAperture method)</a>
+</li>
+        <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.aperture.RectangularAperture.track">(mbtrack2.tracking.aperture.RectangularAperture method)</a>
+</li>
+        <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.element.Element.track">(mbtrack2.tracking.element.Element method)</a>
+</li>
+        <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.element.LongitudinalMap.track">(mbtrack2.tracking.element.LongitudinalMap method)</a>
+</li>
+        <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.element.SkewQuadrupole.track">(mbtrack2.tracking.element.SkewQuadrupole method)</a>
+</li>
+        <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.element.SynchrotronRadiation.track">(mbtrack2.tracking.element.SynchrotronRadiation method)</a>
+</li>
+        <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.element.TransverseMap.track">(mbtrack2.tracking.element.TransverseMap method)</a>
+</li>
+        <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.element.TransverseMapSector.track">(mbtrack2.tracking.element.TransverseMapSector method)</a>
+</li>
+        <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.feedback.ExponentialDamper.track">(mbtrack2.tracking.feedback.ExponentialDamper method)</a>
+</li>
+        <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.feedback.FIRDamper.track">(mbtrack2.tracking.feedback.FIRDamper method)</a>
+</li>
+        <li><a href="mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.monitors.BeamMonitor.track">(mbtrack2.tracking.monitors.monitors.BeamMonitor method)</a>
+</li>
+        <li><a href="mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.monitors.BeamSpectrumMonitor.track">(mbtrack2.tracking.monitors.monitors.BeamSpectrumMonitor method)</a>
+</li>
+        <li><a href="mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.monitors.BunchMonitor.track">(mbtrack2.tracking.monitors.monitors.BunchMonitor method)</a>
+</li>
+        <li><a href="mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.monitors.BunchSpectrumMonitor.track">(mbtrack2.tracking.monitors.monitors.BunchSpectrumMonitor method)</a>
+</li>
+        <li><a href="mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.monitors.CavityMonitor.track">(mbtrack2.tracking.monitors.monitors.CavityMonitor method)</a>
+</li>
+        <li><a href="mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.monitors.PhaseSpaceMonitor.track">(mbtrack2.tracking.monitors.monitors.PhaseSpaceMonitor method)</a>
+</li>
+        <li><a href="mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.monitors.ProfileMonitor.track">(mbtrack2.tracking.monitors.monitors.ProfileMonitor method)</a>
+</li>
+        <li><a href="mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.monitors.WakePotentialMonitor.track">(mbtrack2.tracking.monitors.monitors.WakePotentialMonitor method)</a>
+</li>
+        <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.rf.CavityResonator.track">(mbtrack2.tracking.rf.CavityResonator method)</a>
+</li>
+        <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.rf.DirectFeedback.track">(mbtrack2.tracking.rf.DirectFeedback method)</a>
+</li>
+        <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.rf.ProportionalIntegralLoop.track">(mbtrack2.tracking.rf.ProportionalIntegralLoop method)</a>
+</li>
+        <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.rf.ProportionalLoop.track">(mbtrack2.tracking.rf.ProportionalLoop method)</a>
+</li>
+        <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.rf.RFCavity.track">(mbtrack2.tracking.rf.RFCavity method)</a>
+</li>
+        <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.rf.TunerLoop.track">(mbtrack2.tracking.rf.TunerLoop method)</a>
+</li>
+        <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.wakepotential.LongRangeResistiveWall.track">(mbtrack2.tracking.wakepotential.LongRangeResistiveWall method)</a>
+</li>
+        <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.wakepotential.WakePotential.track">(mbtrack2.tracking.wakepotential.WakePotential method)</a>
+</li>
+      </ul></li>
+  </ul></td>
+  <td style="width: 33%; vertical-align: top;"><ul>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.wakepotential.LongRangeResistiveWall.track_bunch">track_bunch() (mbtrack2.tracking.wakepotential.LongRangeResistiveWall method)</a>
+</li>
+      <li><a href="mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.monitors.Monitor.track_bunch_data">track_bunch_data() (mbtrack2.tracking.monitors.monitors.Monitor method)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.feedback.FIRDamper.track_sb">track_sb() (mbtrack2.tracking.feedback.FIRDamper method)</a>
+</li>
+      <li><a href="mbtrack2.impedance.html#mbtrack2.impedance.resonator.Resonator.transverse_impedance">transverse_impedance() (mbtrack2.impedance.resonator.Resonator method)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.element.transverse_map_sector_generator">transverse_map_sector_generator() (in module mbtrack2.tracking.element)</a>
+</li>
+      <li><a href="mbtrack2.impedance.html#mbtrack2.impedance.resonator.Resonator.transverse_wake_function">transverse_wake_function() (mbtrack2.impedance.resonator.Resonator method)</a>
+</li>
+      <li><a href="mbtrack2.impedance.html#mbtrack2.impedance.resistive_wall.Coating.TransverseImpedance">TransverseImpedance() (mbtrack2.impedance.resistive_wall.Coating method)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.element.TransverseMap">TransverseMap (class in mbtrack2.tracking.element)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.element.TransverseMapSector">TransverseMapSector (class in mbtrack2.tracking.element)</a>
+</li>
+      <li><a href="mbtrack2.impedance.html#mbtrack2.impedance.resistive_wall.CircularResistiveWall.TransverseWakeFunction">TransverseWakeFunction() (mbtrack2.impedance.resistive_wall.CircularResistiveWall method)</a>
+</li>
+      <li><a href="mbtrack2.utilities.html#mbtrack2.utilities.misc.tune_shift_from_effective_impedance">tune_shift_from_effective_impedance() (in module mbtrack2.utilities.misc)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.rf.TunerLoop">TunerLoop (class in mbtrack2.tracking.rf)</a>
+</li>
+  </ul></td>
+</tr></table>
+
+<h2 id="U">U</h2>
+<table style="width: 100%" class="indextable genindextable"><tr>
+  <td style="width: 33%; vertical-align: top;"><ul>
+      <li><a href="mbtrack2.utilities.html#mbtrack2.utilities.beamloading.BeamLoadingEquilibrium.u">u() (mbtrack2.utilities.beamloading.BeamLoadingEquilibrium method)</a>
+</li>
+      <li><a href="mbtrack2.utilities.html#mbtrack2.utilities.beamloading.BeamLoadingEquilibrium.uexp">uexp() (mbtrack2.utilities.beamloading.BeamLoadingEquilibrium method)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.particles.Beam.update_distance_between_bunches">update_distance_between_bunches() (mbtrack2.tracking.particles.Beam method)</a>
+</li>
+  </ul></td>
+  <td style="width: 33%; vertical-align: top;"><ul>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.rf.CavityResonator.update_feedback">update_feedback() (mbtrack2.tracking.rf.CavityResonator method)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.particles.Beam.update_filling_pattern">update_filling_pattern() (mbtrack2.tracking.particles.Beam method)</a>
+</li>
+      <li><a href="mbtrack2.utilities.html#mbtrack2.utilities.beamloading.BeamLoadingEquilibrium.update_potentials">update_potentials() (mbtrack2.utilities.beamloading.BeamLoadingEquilibrium method)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.wakepotential.LongRangeResistiveWall.update_tables">update_tables() (mbtrack2.tracking.wakepotential.LongRangeResistiveWall method)</a>
+</li>
+  </ul></td>
+</tr></table>
+
+<h2 id="V">V</h2>
+<table style="width: 100%" class="indextable genindextable"><tr>
+  <td style="width: 33%; vertical-align: top;"><ul>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.rf.RFCavity.value">value() (mbtrack2.tracking.rf.RFCavity method)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.rf.CavityResonator.Vb">Vb() (mbtrack2.tracking.rf.CavityResonator method)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.rf.CavityResonator.Vbr">Vbr() (mbtrack2.tracking.rf.CavityResonator method)</a>
+</li>
+  </ul></td>
+  <td style="width: 33%; vertical-align: top;"><ul>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.rf.ProportionalIntegralLoop.Vg2Ig">Vg2Ig() (mbtrack2.tracking.rf.ProportionalIntegralLoop method)</a>
+</li>
+      <li><a href="mbtrack2.utilities.html#mbtrack2.utilities.beamloading.BeamLoadingEquilibrium.voltage">voltage() (mbtrack2.utilities.beamloading.BeamLoadingEquilibrium method)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.rf.CavityResonator.VRF">VRF() (mbtrack2.tracking.rf.CavityResonator method)</a>
+</li>
+  </ul></td>
+</tr></table>
+
+<h2 id="W">W</h2>
+<table style="width: 100%" class="indextable genindextable"><tr>
+  <td style="width: 33%; vertical-align: top;"><ul>
+      <li><a href="mbtrack2.impedance.html#mbtrack2.impedance.wakefield.WakeField.wake_components">wake_components (mbtrack2.impedance.wakefield.WakeField property)</a>
+</li>
+      <li><a href="mbtrack2.impedance.html#mbtrack2.impedance.wakefield.WakeField">WakeField (class in mbtrack2.impedance.wakefield)</a>
+</li>
+      <li><a href="mbtrack2.impedance.html#mbtrack2.impedance.wakefield.WakeFunction">WakeFunction (class in mbtrack2.impedance.wakefield)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.wakepotential.WakePotential">WakePotential (class in mbtrack2.tracking.wakepotential)</a>
+</li>
+      <li><a href="mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.monitors.WakePotentialMonitor">WakePotentialMonitor (class in mbtrack2.tracking.monitors.monitors)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.wakepotential.LongRangeResistiveWall.Wdip">Wdip() (mbtrack2.tracking.wakepotential.LongRangeResistiveWall method)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.wakepotential.LongRangeResistiveWall.Wlong">Wlong() (mbtrack2.tracking.wakepotential.LongRangeResistiveWall method)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.rf.CavityResonator.wr">wr (mbtrack2.tracking.rf.CavityResonator property)</a>
+</li>
+  </ul></td>
+  <td style="width: 33%; vertical-align: top;"><ul>
+      <li><a href="mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.monitors.BeamMonitor.write">write() (mbtrack2.tracking.monitors.monitors.BeamMonitor method)</a>
+
+      <ul>
+        <li><a href="mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.monitors.BeamSpectrumMonitor.write">(mbtrack2.tracking.monitors.monitors.BeamSpectrumMonitor method)</a>
+</li>
+        <li><a href="mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.monitors.BunchSpectrumMonitor.write">(mbtrack2.tracking.monitors.monitors.BunchSpectrumMonitor method)</a>
+</li>
+        <li><a href="mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.monitors.Monitor.write">(mbtrack2.tracking.monitors.monitors.Monitor method)</a>
+</li>
+        <li><a href="mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.monitors.ProfileMonitor.write">(mbtrack2.tracking.monitors.monitors.ProfileMonitor method)</a>
+</li>
+        <li><a href="mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.monitors.WakePotentialMonitor.write">(mbtrack2.tracking.monitors.monitors.WakePotentialMonitor method)</a>
+</li>
+      </ul></li>
+      <li><a href="mbtrack2.tracking.monitors.html#mbtrack2.tracking.monitors.monitors.BeamMonitor.write_no_mpi">write_no_mpi() (mbtrack2.tracking.monitors.monitors.BeamMonitor method)</a>
+</li>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.parallel.Mpi.write_table">write_table() (mbtrack2.tracking.parallel.Mpi method)</a>
+</li>
+  </ul></td>
+</tr></table>
+
+<h2 id="X">X</h2>
+<table style="width: 100%" class="indextable genindextable"><tr>
+  <td style="width: 33%; vertical-align: top;"><ul>
+      <li><a href="mbtrack2.impedance.html#mbtrack2.impedance.tapers.StupakovRectangularTaper.xdip">xdip() (mbtrack2.impedance.tapers.StupakovRectangularTaper method)</a>
+</li>
+  </ul></td>
+</tr></table>
+
+<h2 id="Y">Y</h2>
+<table style="width: 100%" class="indextable genindextable"><tr>
+  <td style="width: 33%; vertical-align: top;"><ul>
+      <li><a href="mbtrack2.impedance.html#mbtrack2.impedance.tapers.StupakovRectangularTaper.ydip">ydip() (mbtrack2.impedance.tapers.StupakovRectangularTaper method)</a>
+</li>
+  </ul></td>
+  <td style="width: 33%; vertical-align: top;"><ul>
+      <li><a href="mbtrack2.utilities.html#mbtrack2.utilities.misc.yokoya_elliptic">yokoya_elliptic() (in module mbtrack2.utilities.misc)</a>
+</li>
+  </ul></td>
+</tr></table>
+
+<h2 id="Z">Z</h2>
+<table style="width: 100%" class="indextable genindextable"><tr>
+  <td style="width: 33%; vertical-align: top;"><ul>
+      <li><a href="mbtrack2.tracking.html#mbtrack2.tracking.rf.CavityResonator.Z">Z() (mbtrack2.tracking.rf.CavityResonator method)</a>
+</li>
+      <li><a href="mbtrack2.impedance.html#mbtrack2.impedance.tapers.StupakovCircularTaper.Z0">Z0 (mbtrack2.impedance.tapers.StupakovCircularTaper property)</a>
+
+      <ul>
+        <li><a href="mbtrack2.impedance.html#mbtrack2.impedance.tapers.StupakovRectangularTaper.Z0">(mbtrack2.impedance.tapers.StupakovRectangularTaper property)</a>
+</li>
+      </ul></li>
+  </ul></td>
+  <td style="width: 33%; vertical-align: top;"><ul>
+      <li><a href="mbtrack2.impedance.html#mbtrack2.impedance.tapers.StupakovCircularTaper.Z_over_n">Z_over_n() (mbtrack2.impedance.tapers.StupakovCircularTaper method)</a>
+
+      <ul>
+        <li><a href="mbtrack2.impedance.html#mbtrack2.impedance.tapers.StupakovRectangularTaper.Z_over_n">(mbtrack2.impedance.tapers.StupakovRectangularTaper method)</a>
+</li>
+      </ul></li>
+  </ul></td>
+</tr></table>
+
+
+
+            <div class="clearer"></div>
+          </div>
+        </div>
+      </div>
+      <div class="sphinxsidebar" role="navigation" aria-label="main navigation">
+        <div class="sphinxsidebarwrapper">
+<div id="searchbox" style="display: none" role="search">
+  <h3 id="searchlabel">Quick search</h3>
+    <div class="searchformwrapper">
+    <form class="search" action="search.html" method="get">
+      <input type="text" name="q" aria-labelledby="searchlabel" autocomplete="off" autocorrect="off" autocapitalize="off" spellcheck="false"/>
+      <input type="submit" value="Go" />
+    </form>
+    </div>
+</div>
+<script>document.getElementById('searchbox').style.display = "block"</script>
+        </div>
+      </div>
+      <div class="clearer"></div>
+    </div>
+    <div class="related" role="navigation" aria-label="related navigation">
+      <h3>Navigation</h3>
+      <ul>
+        <li class="right" style="margin-right: 10px">
+          <a href="#" title="General Index"
+             >index</a></li>
+        <li class="right" >
+          <a href="py-modindex.html" title="Python Module Index"
+             >modules</a> |</li>
+        <li class="nav-item nav-item-0"><a href="index.html">mbtrack2 0.6.0 documentation</a> &#187;</li>
+        <li class="nav-item nav-item-this"><a href="">Index</a></li> 
+      </ul>
+    </div>
+    <div class="footer" role="contentinfo">
+        &#169; Copyright 2024, A. Gamelin et al.
+      Created using <a href="https://www.sphinx-doc.org/">Sphinx</a> 5.0.2.
+    </div>
+  </body>
+</html>
\ No newline at end of file
diff --git a/docs/build/html/index.html b/docs/build/html/index.html
new file mode 100644
index 0000000..0650629
--- /dev/null
+++ b/docs/build/html/index.html
@@ -0,0 +1,107 @@
+
+<!DOCTYPE html>
+
+<html lang="en">
+  <head>
+    <meta charset="utf-8" />
+    <meta name="viewport" content="width=device-width, initial-scale=1.0" /><meta name="generator" content="Docutils 0.18.1: http://docutils.sourceforge.net/" />
+
+    <title>Welcome to mbtrack2’s documentation! &#8212; mbtrack2 0.6.0 documentation</title>
+    <link rel="stylesheet" type="text/css" href="_static/pygments.css" />
+    <link rel="stylesheet" type="text/css" href="_static/nature.css" />
+    <script data-url_root="./" id="documentation_options" src="_static/documentation_options.js"></script>
+    <script src="_static/jquery.js"></script>
+    <script src="_static/underscore.js"></script>
+    <script src="_static/_sphinx_javascript_frameworks_compat.js"></script>
+    <script src="_static/doctools.js"></script>
+    <link rel="index" title="Index" href="genindex.html" />
+    <link rel="search" title="Search" href="search.html" /> 
+  </head><body>
+    <div class="related" role="navigation" aria-label="related navigation">
+      <h3>Navigation</h3>
+      <ul>
+        <li class="right" style="margin-right: 10px">
+          <a href="genindex.html" title="General Index"
+             accesskey="I">index</a></li>
+        <li class="right" >
+          <a href="py-modindex.html" title="Python Module Index"
+             >modules</a> |</li>
+        <li class="nav-item nav-item-0"><a href="#">mbtrack2 0.6.0 documentation</a> &#187;</li>
+        <li class="nav-item nav-item-this"><a href="">Welcome to mbtrack2’s documentation!</a></li> 
+      </ul>
+    </div>  
+
+    <div class="document">
+      <div class="documentwrapper">
+        <div class="bodywrapper">
+          <div class="body" role="main">
+            
+  <section id="welcome-to-mbtrack2-s-documentation">
+<h1>Welcome to mbtrack2’s documentation!<a class="headerlink" href="#welcome-to-mbtrack2-s-documentation" title="Permalink to this heading">¶</a></h1>
+<div class="toctree-wrapper compound">
+</div>
+</section>
+<section id="indices-and-tables">
+<h1>Indices and tables<a class="headerlink" href="#indices-and-tables" title="Permalink to this heading">¶</a></h1>
+<ul class="simple">
+<li><p><a class="reference internal" href="genindex.html"><span class="std std-ref">Index</span></a></p></li>
+<li><p><a class="reference internal" href="py-modindex.html"><span class="std std-ref">Module Index</span></a></p></li>
+<li><p><a class="reference internal" href="search.html"><span class="std std-ref">Search Page</span></a></p></li>
+</ul>
+</section>
+
+
+            <div class="clearer"></div>
+          </div>
+        </div>
+      </div>
+      <div class="sphinxsidebar" role="navigation" aria-label="main navigation">
+        <div class="sphinxsidebarwrapper">
+  <div>
+    <h3><a href="#">Table of Contents</a></h3>
+    <ul>
+<li><a class="reference internal" href="#">Welcome to mbtrack2’s documentation!</a></li>
+<li><a class="reference internal" href="#indices-and-tables">Indices and tables</a></li>
+</ul>
+
+  </div>
+  <div role="note" aria-label="source link">
+    <h3>This Page</h3>
+    <ul class="this-page-menu">
+      <li><a href="_sources/index.rst.txt"
+            rel="nofollow">Show Source</a></li>
+    </ul>
+   </div>
+<div id="searchbox" style="display: none" role="search">
+  <h3 id="searchlabel">Quick search</h3>
+    <div class="searchformwrapper">
+    <form class="search" action="search.html" method="get">
+      <input type="text" name="q" aria-labelledby="searchlabel" autocomplete="off" autocorrect="off" autocapitalize="off" spellcheck="false"/>
+      <input type="submit" value="Go" />
+    </form>
+    </div>
+</div>
+<script>document.getElementById('searchbox').style.display = "block"</script>
+        </div>
+      </div>
+      <div class="clearer"></div>
+    </div>
+    <div class="related" role="navigation" aria-label="related navigation">
+      <h3>Navigation</h3>
+      <ul>
+        <li class="right" style="margin-right: 10px">
+          <a href="genindex.html" title="General Index"
+             >index</a></li>
+        <li class="right" >
+          <a href="py-modindex.html" title="Python Module Index"
+             >modules</a> |</li>
+        <li class="nav-item nav-item-0"><a href="#">mbtrack2 0.6.0 documentation</a> &#187;</li>
+        <li class="nav-item nav-item-this"><a href="">Welcome to mbtrack2’s documentation!</a></li> 
+      </ul>
+    </div>
+    <div class="footer" role="contentinfo">
+        &#169; Copyright 2024, A. Gamelin et al.
+      Created using <a href="https://www.sphinx-doc.org/">Sphinx</a> 5.0.2.
+    </div>
+  </body>
+</html>
\ No newline at end of file
diff --git a/docs/build/html/mbtrack2.html b/docs/build/html/mbtrack2.html
new file mode 100644
index 0000000..4563121
--- /dev/null
+++ b/docs/build/html/mbtrack2.html
@@ -0,0 +1,162 @@
+
+<!DOCTYPE html>
+
+<html lang="en">
+  <head>
+    <meta charset="utf-8" />
+    <meta name="viewport" content="width=device-width, initial-scale=1.0" /><meta name="generator" content="Docutils 0.18.1: http://docutils.sourceforge.net/" />
+
+    <title>mbtrack2 package &#8212; mbtrack2 0.6.0 documentation</title>
+    <link rel="stylesheet" type="text/css" href="_static/pygments.css" />
+    <link rel="stylesheet" type="text/css" href="_static/nature.css" />
+    <script data-url_root="./" id="documentation_options" src="_static/documentation_options.js"></script>
+    <script src="_static/jquery.js"></script>
+    <script src="_static/underscore.js"></script>
+    <script src="_static/_sphinx_javascript_frameworks_compat.js"></script>
+    <script src="_static/doctools.js"></script>
+    <link rel="index" title="Index" href="genindex.html" />
+    <link rel="search" title="Search" href="search.html" /> 
+  </head><body>
+    <div class="related" role="navigation" aria-label="related navigation">
+      <h3>Navigation</h3>
+      <ul>
+        <li class="right" style="margin-right: 10px">
+          <a href="genindex.html" title="General Index"
+             accesskey="I">index</a></li>
+        <li class="right" >
+          <a href="py-modindex.html" title="Python Module Index"
+             >modules</a> |</li>
+        <li class="nav-item nav-item-0"><a href="index.html">mbtrack2 0.6.0 documentation</a> &#187;</li>
+        <li class="nav-item nav-item-this"><a href="">mbtrack2 package</a></li> 
+      </ul>
+    </div>  
+
+    <div class="document">
+      <div class="documentwrapper">
+        <div class="bodywrapper">
+          <div class="body" role="main">
+            
+  <section id="mbtrack2-package">
+<h1>mbtrack2 package<a class="headerlink" href="#mbtrack2-package" title="Permalink to this heading">¶</a></h1>
+<section id="subpackages">
+<h2>Subpackages<a class="headerlink" href="#subpackages" title="Permalink to this heading">¶</a></h2>
+<div class="toctree-wrapper compound">
+<ul>
+<li class="toctree-l1"><a class="reference internal" href="mbtrack2.impedance.html">mbtrack2.impedance package</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="mbtrack2.impedance.html#submodules">Submodules</a></li>
+<li class="toctree-l2"><a class="reference internal" href="mbtrack2.impedance.html#module-mbtrack2.impedance.csr">mbtrack2.impedance.csr module</a></li>
+<li class="toctree-l2"><a class="reference internal" href="mbtrack2.impedance.html#module-mbtrack2.impedance.impedance_model">mbtrack2.impedance.impedance_model module</a></li>
+<li class="toctree-l2"><a class="reference internal" href="mbtrack2.impedance.html#module-mbtrack2.impedance.resistive_wall">mbtrack2.impedance.resistive_wall module</a></li>
+<li class="toctree-l2"><a class="reference internal" href="mbtrack2.impedance.html#module-mbtrack2.impedance.resonator">mbtrack2.impedance.resonator module</a></li>
+<li class="toctree-l2"><a class="reference internal" href="mbtrack2.impedance.html#module-mbtrack2.impedance.tapers">mbtrack2.impedance.tapers module</a></li>
+<li class="toctree-l2"><a class="reference internal" href="mbtrack2.impedance.html#module-mbtrack2.impedance.wakefield">mbtrack2.impedance.wakefield module</a></li>
+<li class="toctree-l2"><a class="reference internal" href="mbtrack2.impedance.html#module-mbtrack2.impedance">Module contents</a></li>
+</ul>
+</li>
+<li class="toctree-l1"><a class="reference internal" href="mbtrack2.instability.html">mbtrack2.instability package</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="mbtrack2.instability.html#submodules">Submodules</a></li>
+<li class="toctree-l2"><a class="reference internal" href="mbtrack2.instability.html#module-mbtrack2.instability.instabilities">mbtrack2.instability.instabilities module</a></li>
+<li class="toctree-l2"><a class="reference internal" href="mbtrack2.instability.html#module-mbtrack2.instability.ions">mbtrack2.instability.ions module</a></li>
+<li class="toctree-l2"><a class="reference internal" href="mbtrack2.instability.html#module-mbtrack2.instability">Module contents</a></li>
+</ul>
+</li>
+<li class="toctree-l1"><a class="reference internal" href="mbtrack2.tracking.html">mbtrack2.tracking package</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="mbtrack2.tracking.html#subpackages">Subpackages</a><ul>
+<li class="toctree-l3"><a class="reference internal" href="mbtrack2.tracking.monitors.html">mbtrack2.tracking.monitors package</a><ul>
+<li class="toctree-l4"><a class="reference internal" href="mbtrack2.tracking.monitors.html#submodules">Submodules</a></li>
+<li class="toctree-l4"><a class="reference internal" href="mbtrack2.tracking.monitors.html#module-mbtrack2.tracking.monitors.monitors">mbtrack2.tracking.monitors.monitors module</a></li>
+<li class="toctree-l4"><a class="reference internal" href="mbtrack2.tracking.monitors.html#module-mbtrack2.tracking.monitors.plotting">mbtrack2.tracking.monitors.plotting module</a></li>
+<li class="toctree-l4"><a class="reference internal" href="mbtrack2.tracking.monitors.html#module-mbtrack2.tracking.monitors.tools">mbtrack2.tracking.monitors.tools module</a></li>
+<li class="toctree-l4"><a class="reference internal" href="mbtrack2.tracking.monitors.html#module-mbtrack2.tracking.monitors">Module contents</a></li>
+</ul>
+</li>
+</ul>
+</li>
+<li class="toctree-l2"><a class="reference internal" href="mbtrack2.tracking.html#submodules">Submodules</a></li>
+<li class="toctree-l2"><a class="reference internal" href="mbtrack2.tracking.html#module-mbtrack2.tracking.aperture">mbtrack2.tracking.aperture module</a></li>
+<li class="toctree-l2"><a class="reference internal" href="mbtrack2.tracking.html#module-mbtrack2.tracking.element">mbtrack2.tracking.element module</a></li>
+<li class="toctree-l2"><a class="reference internal" href="mbtrack2.tracking.html#module-mbtrack2.tracking.feedback">mbtrack2.tracking.feedback module</a></li>
+<li class="toctree-l2"><a class="reference internal" href="mbtrack2.tracking.html#module-mbtrack2.tracking.parallel">mbtrack2.tracking.parallel module</a></li>
+<li class="toctree-l2"><a class="reference internal" href="mbtrack2.tracking.html#module-mbtrack2.tracking.particles">mbtrack2.tracking.particles module</a></li>
+<li class="toctree-l2"><a class="reference internal" href="mbtrack2.tracking.html#module-mbtrack2.tracking.rf">mbtrack2.tracking.rf module</a></li>
+<li class="toctree-l2"><a class="reference internal" href="mbtrack2.tracking.html#module-mbtrack2.tracking.synchrotron">mbtrack2.tracking.synchrotron module</a></li>
+<li class="toctree-l2"><a class="reference internal" href="mbtrack2.tracking.html#module-mbtrack2.tracking.wakepotential">mbtrack2.tracking.wakepotential module</a></li>
+<li class="toctree-l2"><a class="reference internal" href="mbtrack2.tracking.html#module-mbtrack2.tracking">Module contents</a></li>
+</ul>
+</li>
+<li class="toctree-l1"><a class="reference internal" href="mbtrack2.utilities.html">mbtrack2.utilities package</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="mbtrack2.utilities.html#submodules">Submodules</a></li>
+<li class="toctree-l2"><a class="reference internal" href="mbtrack2.utilities.html#module-mbtrack2.utilities.beamloading">mbtrack2.utilities.beamloading module</a></li>
+<li class="toctree-l2"><a class="reference internal" href="mbtrack2.utilities.html#module-mbtrack2.utilities.misc">mbtrack2.utilities.misc module</a></li>
+<li class="toctree-l2"><a class="reference internal" href="mbtrack2.utilities.html#module-mbtrack2.utilities.optics">mbtrack2.utilities.optics module</a></li>
+<li class="toctree-l2"><a class="reference internal" href="mbtrack2.utilities.html#module-mbtrack2.utilities.read_impedance">mbtrack2.utilities.read_impedance module</a></li>
+<li class="toctree-l2"><a class="reference internal" href="mbtrack2.utilities.html#module-mbtrack2.utilities.spectrum">mbtrack2.utilities.spectrum module</a></li>
+<li class="toctree-l2"><a class="reference internal" href="mbtrack2.utilities.html#module-mbtrack2.utilities">Module contents</a></li>
+</ul>
+</li>
+</ul>
+</div>
+</section>
+<section id="module-mbtrack2">
+<span id="module-contents"></span><h2>Module contents<a class="headerlink" href="#module-mbtrack2" title="Permalink to this heading">¶</a></h2>
+</section>
+</section>
+
+
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+            
+  <section id="mbtrack2-impedance-package">
+<h1>mbtrack2.impedance package<a class="headerlink" href="#mbtrack2-impedance-package" title="Permalink to this heading">¶</a></h1>
+<section id="submodules">
+<h2>Submodules<a class="headerlink" href="#submodules" title="Permalink to this heading">¶</a></h2>
+</section>
+<section id="module-mbtrack2.impedance.csr">
+<span id="mbtrack2-impedance-csr-module"></span><h2>mbtrack2.impedance.csr module<a class="headerlink" href="#module-mbtrack2.impedance.csr" title="Permalink to this heading">¶</a></h2>
+<p>Define coherent synchrotron radiation (CSR) wakefields in various models.</p>
+<dl class="py class">
+<dt class="sig sig-object py" id="mbtrack2.impedance.csr.FreeSpaceCSR">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">mbtrack2.impedance.csr.</span></span><span class="sig-name descname"><span class="pre">FreeSpaceCSR</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">time</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">frequency</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">length</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">radius</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/impedance/csr.html#FreeSpaceCSR"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.impedance.csr.FreeSpaceCSR" title="Permalink to this definition">¶</a></dt>
+<dd><p>Bases: <a class="reference internal" href="#mbtrack2.impedance.wakefield.WakeField" title="mbtrack2.impedance.wakefield.WakeField"><code class="xref py py-class docutils literal notranslate"><span class="pre">WakeField</span></code></a></p>
+<p>Free space steady-state coherent synchrotron radiation Wakefield element,
+based on [1].</p>
+<p>Impedance is computed using Eq. (A10) of [2].</p>
+<dl class="simple">
+<dt>time<span class="classifier">array of float</span></dt><dd><p>Time points where the wake function will be evaluated in [s].</p>
+</dd>
+<dt>frequency<span class="classifier">array of float</span></dt><dd><p>Frequency points where the impedance will be evaluated in [Hz].</p>
+</dd>
+<dt>length<span class="classifier">float </span></dt><dd><p>Length of the impedacen to consider in [m].</p>
+</dd>
+<dt>radius<span class="classifier">float </span></dt><dd><p>Dipole radius of curvature in [m].</p>
+</dd>
+</dl>
+<p>[1] : Faltens, A. N. D. R. I. S., &amp; Laslett, L. J. (1973). Longitudinal 
+coupling impedance of a stationary electron ring in a cylindrical 
+geometry. part. Accel., 4, 151-157.
+[2] : Agoh, T., and K. Yokoya. “Calculation of coherent synchrotron 
+radiation using mesh.” Physical Review Special Topics-Accelerators and 
+Beams 7.5 (2004): 054403.</p>
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.impedance.csr.FreeSpaceCSR.LongitudinalImpedance">
+<span class="sig-name descname"><span class="pre">LongitudinalImpedance</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">frequency</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/impedance/csr.html#FreeSpaceCSR.LongitudinalImpedance"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.impedance.csr.FreeSpaceCSR.LongitudinalImpedance" title="Permalink to this definition">¶</a></dt>
+<dd><p>Compute the free space steady-state CSR impedance.
+Based on Eq. (A10) of [1].</p>
+<p>This formula is valid only if omega &lt;&lt; (3 * gamma^3 * c) / (2 * R).</p>
+<dl class="simple">
+<dt>frequency<span class="classifier">float array</span></dt><dd><p>Frequency in [Hz].</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>Zl<span class="classifier">complex array</span></dt><dd><p>Longitudinal impedance in [ohm].</p>
+</dd>
+</dl>
+<p>[1] : Agoh, T., and K. Yokoya. “Calculation of coherent synchrotron 
+radiation using mesh.” Physical Review Special Topics-Accelerators and 
+Beams 7.5 (2004): 054403.</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.impedance.csr.FreeSpaceCSR.LongitudinalWakeFunction">
+<span class="sig-name descname"><span class="pre">LongitudinalWakeFunction</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">time</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/impedance/csr.html#FreeSpaceCSR.LongitudinalWakeFunction"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.impedance.csr.FreeSpaceCSR.LongitudinalWakeFunction" title="Permalink to this definition">¶</a></dt>
+<dd></dd></dl>
+
+</dd></dl>
+
+<dl class="py class">
+<dt class="sig sig-object py" id="mbtrack2.impedance.csr.ParallelPlatesCSR">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">mbtrack2.impedance.csr.</span></span><span class="sig-name descname"><span class="pre">ParallelPlatesCSR</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">time</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">frequency</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">length</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">radius</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">distance</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/impedance/csr.html#ParallelPlatesCSR"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.impedance.csr.ParallelPlatesCSR" title="Permalink to this definition">¶</a></dt>
+<dd><p>Bases: <a class="reference internal" href="#mbtrack2.impedance.wakefield.WakeField" title="mbtrack2.impedance.wakefield.WakeField"><code class="xref py py-class docutils literal notranslate"><span class="pre">WakeField</span></code></a></p>
+<p>Perfectly conducting parallel plates steady-state coherent synchrotron 
+radiation Wakefield element, based on [1].</p>
+<dl class="simple">
+<dt>time<span class="classifier">array of float</span></dt><dd><p>Time points where the wake function will be evaluated in [s].</p>
+</dd>
+<dt>frequency<span class="classifier">array of float</span></dt><dd><p>Frequency points where the impedance will be evaluated in [Hz].</p>
+</dd>
+<dt>length<span class="classifier">float </span></dt><dd><p>Length of the impedacen to consider in [m].</p>
+</dd>
+<dt>radius<span class="classifier">float </span></dt><dd><p>Dipole radius of curvature in [m].</p>
+</dd>
+<dt>distance<span class="classifier">float</span></dt><dd><p>Vertical distance between the parallel plates in [m].</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>threshold<span class="classifier">float</span></dt><dd><p>Shielding threshold in the parallel plates model in [Hz].</p>
+</dd>
+</dl>
+<p>[1] : Agoh, T., and K. Yokoya. “Calculation of coherent synchrotron 
+radiation using mesh.” Physical Review Special Topics-Accelerators and 
+Beams 7.5 (2004): 054403.</p>
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.impedance.csr.ParallelPlatesCSR.LongitudinalImpedance">
+<span class="sig-name descname"><span class="pre">LongitudinalImpedance</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">frequency</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">tol</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1e-05</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/impedance/csr.html#ParallelPlatesCSR.LongitudinalImpedance"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.impedance.csr.ParallelPlatesCSR.LongitudinalImpedance" title="Permalink to this definition">¶</a></dt>
+<dd><p>Compute the CSR impedance using the perfectly conducting parallel 
+plates steady-state model.</p>
+<p>Impedance is computed using Eq. (A1) of [1].</p>
+<dl class="simple">
+<dt>frequency<span class="classifier">float array</span></dt><dd><p>Frequency in [Hz].</p>
+</dd>
+<dt>tol<span class="classifier">float, optinal</span></dt><dd><p>Desired maximum final error on sum_func.</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>Zl<span class="classifier">complex array</span></dt><dd><p>Longitudinal impedance in [ohm].</p>
+</dd>
+</dl>
+<p>[1] : Agoh, T., and K. Yokoya. “Calculation of coherent synchrotron 
+radiation using mesh.” Physical Review Special Topics-Accelerators and 
+Beams 7.5 (2004): 054403.</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.impedance.csr.ParallelPlatesCSR.LongitudinalWakeFunction">
+<span class="sig-name descname"><span class="pre">LongitudinalWakeFunction</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">time</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/impedance/csr.html#ParallelPlatesCSR.LongitudinalWakeFunction"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.impedance.csr.ParallelPlatesCSR.LongitudinalWakeFunction" title="Permalink to this definition">¶</a></dt>
+<dd></dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.impedance.csr.ParallelPlatesCSR.sum_func">
+<span class="sig-name descname"><span class="pre">sum_func</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">p</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">k</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/impedance/csr.html#ParallelPlatesCSR.sum_func"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.impedance.csr.ParallelPlatesCSR.sum_func" title="Permalink to this definition">¶</a></dt>
+<dd><p>Utility function for LongitudinalImpedance.</p>
+<p>p : int
+k : float</p>
+<p>sum_value : mpc</p>
+</dd></dl>
+
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.impedance.csr.ParallelPlatesCSR.threshold">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">threshold</span></span><a class="headerlink" href="#mbtrack2.impedance.csr.ParallelPlatesCSR.threshold" title="Permalink to this definition">¶</a></dt>
+<dd><p>Shielding threshold in the parallel plates model in [Hz].</p>
+</dd></dl>
+
+</dd></dl>
+
+</section>
+<section id="module-mbtrack2.impedance.impedance_model">
+<span id="mbtrack2-impedance-impedance-model-module"></span><h2>mbtrack2.impedance.impedance_model module<a class="headerlink" href="#module-mbtrack2.impedance.impedance_model" title="Permalink to this heading">¶</a></h2>
+<p>Module where the ImpedanceModel class is defined.</p>
+<dl class="py class">
+<dt class="sig sig-object py" id="mbtrack2.impedance.impedance_model.ImpedanceModel">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">mbtrack2.impedance.impedance_model.</span></span><span class="sig-name descname"><span class="pre">ImpedanceModel</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">ring</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/impedance/impedance_model.html#ImpedanceModel"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.impedance.impedance_model.ImpedanceModel" title="Permalink to this definition">¶</a></dt>
+<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">object</span></code></p>
+<p>Define the impedance model of the machine.</p>
+<p>The model must be completed with successive add(…) and add_global(…)
+calls, then compute_sum() must be run.</p>
+<p>The transverse impedance and wake functions are beta weighted and divided
+by the beta at the tracking location (ring.optics.local_beta).</p>
+<p>ring : Synchrotron object</p>
+<dl class="simple">
+<dt>wakefields<span class="classifier">list of WakeField objects</span></dt><dd><p>WakeFields in the model.</p>
+</dd>
+<dt>positions<span class="classifier">list of arrays</span></dt><dd><p>Positions corresponding the different WakeFields.</p>
+</dd>
+<dt>names<span class="classifier">list of str</span></dt><dd><p>Names of the WakeField objects.</p>
+</dd>
+<dt>sum<span class="classifier">WakeField</span></dt><dd><p>Sum of every WakeField in the model weigthed by beta functions.</p>
+</dd>
+<dt><a href="#id1"><span class="problematic" id="id2">sum_</span></a>”name”<span class="classifier">WakeField</span></dt><dd><p>Sum of the “name” Wakefield weigthed by beta functions.</p>
+</dd>
+<dt>sum_names<span class="classifier">array</span></dt><dd><p>Names of attributes where the WakeFields are summed by name.</p>
+</dd>
+<dt>globals<span class="classifier">list of WakeField objects</span></dt><dd><p>Globals WakeFields in the model.</p>
+</dd>
+<dt>globals_names<span class="classifier">list of str</span></dt><dd><p>Names of the global WakeFields objects.</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>add(wakefield, positions, name)</dt><dd><p>Add the same WakeField object at different locations to the model.</p>
+</dd>
+<dt>add_global(wakefield, name)</dt><dd><p>Add a “global” WakeField object which will added to the sum WakeField
+but not weighted by beta functions.</p>
+</dd>
+<dt>sum_beta(wake, beta)</dt><dd><p>Weight a WakeField object by an array of beta functions.</p>
+</dd>
+<dt>compute_sum_names()</dt><dd><p>Compute the weighted WakeField for each WakeField object type.</p>
+</dd>
+<dt>compute_sum()</dt><dd><p>Compute the sum of all weighted WakeField into self.sum.</p>
+</dd>
+<dt>plot_area(Z_type=”Zlong”, component=”real”, sigma=None, attr_list=None)</dt><dd><p>Plot the contributions of different kind of WakeFields.</p>
+</dd>
+<dt>save(file)</dt><dd><p>Save impedance model to file.</p>
+</dd>
+<dt>load(file)</dt><dd><p>Load impedance model from file.</p>
+</dd>
+</dl>
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.impedance.impedance_model.ImpedanceModel.add">
+<span class="sig-name descname"><span class="pre">add</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">wakefield</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">positions</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">name</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/impedance/impedance_model.html#ImpedanceModel.add"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.impedance.impedance_model.ImpedanceModel.add" title="Permalink to this definition">¶</a></dt>
+<dd><p>Add the same WakeField object at different locations to the model.</p>
+<dl class="simple">
+<dt>wakefield<span class="classifier">WakeField</span></dt><dd><p>WakeField object to add to the model.</p>
+</dd>
+<dt>positions<span class="classifier">array, float or int</span></dt><dd><p>Array of longitudinal positions where the elements are loacted.</p>
+</dd>
+<dt>name<span class="classifier">str, optional</span></dt><dd><p>Name of the element type. If None, the name of the WakeField object
+is used. The default is None.</p>
+</dd>
+</dl>
+<p>None.</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.impedance.impedance_model.ImpedanceModel.add_global">
+<span class="sig-name descname"><span class="pre">add_global</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">wakefield</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">name</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/impedance/impedance_model.html#ImpedanceModel.add_global"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.impedance.impedance_model.ImpedanceModel.add_global" title="Permalink to this definition">¶</a></dt>
+<dd><p>Add a “global” WakeField object which will added to the sum WakeField
+but not weighted by beta functions.</p>
+<p>To use with “distributed” elements, for example a resistive wall
+wakefield computed from an effective radius (so which has already been
+weighted by beta functions).</p>
+<dl class="simple">
+<dt>wakefield<span class="classifier">WakeField</span></dt><dd><p>WakeField object to add to the model.</p>
+</dd>
+<dt>name<span class="classifier">str, optional</span></dt><dd><p>Name of the element type. If None, the name of the WakeField object
+is used. The default is None.</p>
+</dd>
+</dl>
+<p>None.</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.impedance.impedance_model.ImpedanceModel.compute_sum">
+<span class="sig-name descname"><span class="pre">compute_sum</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/impedance/impedance_model.html#ImpedanceModel.compute_sum"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.impedance.impedance_model.ImpedanceModel.compute_sum" title="Permalink to this definition">¶</a></dt>
+<dd><p>Compute the sum of all weighted WakeField into self.sum.</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.impedance.impedance_model.ImpedanceModel.compute_sum_names">
+<span class="sig-name descname"><span class="pre">compute_sum_names</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/impedance/impedance_model.html#ImpedanceModel.compute_sum_names"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.impedance.impedance_model.ImpedanceModel.compute_sum_names" title="Permalink to this definition">¶</a></dt>
+<dd><p>Compute the weighted WakeField for each WakeField object type.
+The new summed WakeField object are set to into self.sum_name.</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.impedance.impedance_model.ImpedanceModel.effective_impedance">
+<span class="sig-name descname"><span class="pre">effective_impedance</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">m</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">mu</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">sigma</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">M</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">tuneS</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">xi</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">mode</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'Hermite'</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/impedance/impedance_model.html#ImpedanceModel.effective_impedance"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.impedance.impedance_model.ImpedanceModel.effective_impedance" title="Permalink to this definition">¶</a></dt>
+<dd><p>Compute the longitudinal and transverse effective impedance.</p>
+<dl class="simple">
+<dt>mu<span class="classifier">int</span></dt><dd><p>coupled bunch mode number, goes from 0 to (M-1) where M is the
+number of bunches</p>
+</dd>
+<dt>m<span class="classifier">int</span></dt><dd><p>head-tail (or azimutal/synchrotron) mode number</p>
+</dd>
+<dt>sigma<span class="classifier">float</span></dt><dd><p>RMS bunch length in [s]</p>
+</dd>
+<dt>M<span class="classifier">int</span></dt><dd><p>Number of bunches.</p>
+</dd>
+<dt>tuneS<span class="classifier">float</span></dt><dd><p>Synchrotron tune.</p>
+</dd>
+<dt>xi<span class="classifier">float, optional</span></dt><dd><p>(non-normalized) chromaticity</p>
+</dd>
+<dt>mode: str, optional</dt><dd><p>type of the mode taken into account for the computation:
+-“Hermite” modes for Gaussian bunches</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>summary<span class="classifier">DataFrame</span></dt><dd><p>Longitudinal and transverse effective impedance.</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.impedance.impedance_model.ImpedanceModel.energy_loss">
+<span class="sig-name descname"><span class="pre">energy_loss</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">sigma</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">M</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">bunch_spacing</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">I</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">n_points</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">10000000.0</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/impedance/impedance_model.html#ImpedanceModel.energy_loss"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.impedance.impedance_model.ImpedanceModel.energy_loss" title="Permalink to this definition">¶</a></dt>
+<dd><p>Compute the beam and bunch loss factor and energy losses for each type 
+of element in the model assuming Gaussian bunches and constant spacing
+between bunches.</p>
+<dl class="simple">
+<dt>sigma<span class="classifier">float</span></dt><dd><p>RMS bunch length in [s].</p>
+</dd>
+<dt>M<span class="classifier">int</span></dt><dd><p>Number of bunches in the beam.</p>
+</dd>
+<dt>bunch_spacing<span class="classifier">float</span></dt><dd><p>Time between two bunches in [s].</p>
+</dd>
+<dt>I<span class="classifier">float</span></dt><dd><p>Total beam current in [A].</p>
+</dd>
+<dt>n_points<span class="classifier">float, optional</span></dt><dd><p>Number of points used in the frequency spectrums.</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>summary<span class="classifier">Dataframe</span></dt><dd><p>Contains the beam and bunch loss factor and energy loss for the 
+full model and for each type of different component.</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.impedance.impedance_model.ImpedanceModel.group_attributes">
+<span class="sig-name descname"><span class="pre">group_attributes</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">string_in_name</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">names_to_group</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">property_list</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">['Zlong']</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/impedance/impedance_model.html#ImpedanceModel.group_attributes"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.impedance.impedance_model.ImpedanceModel.group_attributes" title="Permalink to this definition">¶</a></dt>
+<dd><p>Groups attributes in the ImpedanceModel based on a given string pattern.
+Args:</p>
+<blockquote>
+<div><p>string_in_name (str): The string pattern used to match attribute names for grouping. If names_to_group is given, this is a name of a new attribute instead.
+names_to_group (list, optional): List of attribute names to be explicitly grouped.</p>
+<blockquote>
+<div><p>If not provided, attributes matching the string pattern will be automatically grouped.
+Defaults to None.</p>
+</div></blockquote>
+<dl class="simple">
+<dt>property_list (list, optional): List of property names to be grouped for each attribute.</dt><dd><p>Defaults to [‘Zlong’].</p>
+</dd>
+</dl>
+</div></blockquote>
+<dl class="simple">
+<dt>Returns:</dt><dd><p>int: Returns 0 indicating the successful grouping of attributes.</p>
+</dd>
+<dt>Notes:</dt><dd><ul class="simple">
+<li><p>This method groups attributes in the ImpedanceModel class based on a given string pattern.</p></li>
+<li><p>If names_to_group is not provided, it automatically selects attributes from the existing sum_names that match the given string pattern.</p></li>
+<li><p>A new WakeField instance is created and assigned to the attribute named ‘string_in_name’.</p></li>
+<li><p>The specified properties from the first attribute in names_to_group are appended to the new WakeField instance.</p></li>
+<li><p>The values of the specified properties from the remaining attributes in names_to_group are added to the corresponding properties in the new WakeField instance.</p></li>
+<li><p>The names_to_group attributes are removed from the ImpedanceModel class.</p></li>
+<li><p>The new grouped attribute is added to sum_names, and the first attribute in names_to_group is removed from sum_names.</p></li>
+</ul>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.impedance.impedance_model.ImpedanceModel.load">
+<span class="sig-name descname"><span class="pre">load</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">file</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/impedance/impedance_model.html#ImpedanceModel.load"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.impedance.impedance_model.ImpedanceModel.load" title="Permalink to this definition">¶</a></dt>
+<dd><p>Load impedance model from file.</p>
+<p>The same pandas version is needed on both saving and loading computer
+for the pickle to work.</p>
+<dl class="simple">
+<dt>file<span class="classifier">str</span></dt><dd><p>File where the impedance model is saved.</p>
+</dd>
+</dl>
+<p>None.</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.impedance.impedance_model.ImpedanceModel.plot_area">
+<span class="sig-name descname"><span class="pre">plot_area</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">Z_type</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'Zlong'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">component</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'real'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">sigma</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">attr_list</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">zoom</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/impedance/impedance_model.html#ImpedanceModel.plot_area"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.impedance.impedance_model.ImpedanceModel.plot_area" title="Permalink to this definition">¶</a></dt>
+<dd><p>Plot the contributions of different kind of WakeFields.</p>
+<dl class="simple">
+<dt>Z_type<span class="classifier">str, optional</span></dt><dd><p>Type of impedance to plot.</p>
+</dd>
+<dt>component<span class="classifier">str, optional</span></dt><dd><p>Component to plot, can be “real” or “imag”.</p>
+</dd>
+<dt>sigma<span class="classifier">float, optional</span></dt><dd><p>RMS bunch length in [s] to use for the spectral density. If equal
+to None, the spectral density is not plotted.</p>
+</dd>
+<dt>attr_list<span class="classifier">list or array of str, optional</span></dt><dd><p>Attributes to plot.</p>
+</dd>
+<dt>zoom<span class="classifier">bool</span></dt><dd><p>If True, add a zoomed plot on top right corner.</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.impedance.impedance_model.ImpedanceModel.power_loss_spectrum">
+<span class="sig-name descname"><span class="pre">power_loss_spectrum</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">sigma</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">M</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">bunch_spacing</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">I</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">n_points</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">10000000.0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">max_overlap</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">plot</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/impedance/impedance_model.html#ImpedanceModel.power_loss_spectrum"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.impedance.impedance_model.ImpedanceModel.power_loss_spectrum" title="Permalink to this definition">¶</a></dt>
+<dd><p>Compute the power loss spectrum of the summed longitudinal impedance 
+as in Eq. (4) of [1].</p>
+<p>Assume Gaussian bunches and constant spacing between bunches.</p>
+<dl>
+<dt>sigma<span class="classifier">float</span></dt><dd><p>RMS bunch length in [s].</p>
+</dd>
+<dt>M<span class="classifier">int</span></dt><dd><p>Number of bunches in the beam.</p>
+</dd>
+<dt>bunch_spacing<span class="classifier">float</span></dt><dd><p>Time between two bunches in [s].</p>
+</dd>
+<dt>I<span class="classifier">float</span></dt><dd><p>Total beam current in [A].</p>
+</dd>
+<dt>n_points<span class="classifier">float, optional</span></dt><dd><p>Number of points used in the frequency spectrum.</p>
+</dd>
+<dt>max_overlap<span class="classifier">bool, optional</span></dt><dd><p>If True, the bunch spectrum (scaled to the number of bunches) is 
+used instead of the beam spectrum to compute the maximum value of 
+the power loss spectrum at each frequency. Should only be used to 
+maximise the power loss at a given frequency (e.g. for HOMs) and 
+not for the full spectrum.</p>
+</dd>
+<dt>plot<span class="classifier">bool, optional</span></dt><dd><dl>
+<dt>If True, plots:</dt><dd><ul class="simple">
+<li><p>the overlap between the real part of the longitudinal impedance</p></li>
+</ul>
+<p>and the beam spectrum.
+- the power loss spectrum.</p>
+</dd>
+</dl>
+</dd>
+</dl>
+<dl class="simple">
+<dt>pf0<span class="classifier">array</span></dt><dd><p>Frequency points.</p>
+</dd>
+<dt>power_loss<span class="classifier">array</span></dt><dd><p>Power loss spectrum in [W].</p>
+</dd>
+</dl>
+<p>[1] : L. Teofili, et al. “A Multi-Physics Approach to Simulate the RF 
+Heating 3D Power Map Induced by the Proton Beam in a Beam Intercepting 
+Device”, in IPAC’18, 2018, doi:10.18429/JACoW-IPAC2018-THPAK093</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.impedance.impedance_model.ImpedanceModel.rename_attribute">
+<span class="sig-name descname"><span class="pre">rename_attribute</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">old_name</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">new_name</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/impedance/impedance_model.html#ImpedanceModel.rename_attribute"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.impedance.impedance_model.ImpedanceModel.rename_attribute" title="Permalink to this definition">¶</a></dt>
+<dd><p>Renames an attribute in the ImpedanceModel.
+Args:</p>
+<blockquote>
+<div><p>old_name (str): The current name of the attribute to be renamed.
+new_name (str): The new name for the attribute.</p>
+</div></blockquote>
+<dl class="simple">
+<dt>Raises:</dt><dd><p>KeyError: If the old_name doesn’t exist as an attribute in the ImpedanceModel.</p>
+</dd>
+<dt>Notes:</dt><dd><ul class="simple">
+<li><p>This method renames an attribute in the ImpedanceModel class.</p></li>
+<li><p>The attribute with the old_name is removed from the class’s dictionary (__dict__) using the pop() method.</p></li>
+<li><p>The attribute is then added back to the class’s dictionary with the new_name using the __dict__ attribute.</p></li>
+<li><p>If the old_name doesn’t exist as an attribute in the ImpedanceModel, a KeyError is raised.</p></li>
+</ul>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.impedance.impedance_model.ImpedanceModel.save">
+<span class="sig-name descname"><span class="pre">save</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">file</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/impedance/impedance_model.html#ImpedanceModel.save"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.impedance.impedance_model.ImpedanceModel.save" title="Permalink to this definition">¶</a></dt>
+<dd><p>Save impedance model to file.</p>
+<p>The same pandas version is needed on both saving and loading computer
+for the pickle to work.</p>
+<dl class="simple">
+<dt>file<span class="classifier">str</span></dt><dd><p>File where the impedance model is saved.</p>
+</dd>
+</dl>
+<p>None.</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.impedance.impedance_model.ImpedanceModel.sum_beta">
+<span class="sig-name descname"><span class="pre">sum_beta</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">wake</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">beta</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/impedance/impedance_model.html#ImpedanceModel.sum_beta"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.impedance.impedance_model.ImpedanceModel.sum_beta" title="Permalink to this definition">¶</a></dt>
+<dd><p>Weight a WakeField object by an array of beta functions.</p>
+<dl class="simple">
+<dt>wake<span class="classifier">WakeField</span></dt><dd><p>WakeField element object.</p>
+</dd>
+<dt>beta<span class="classifier">array of shape (2, N)</span></dt><dd><p>Beta function at the locations of the elements.</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>wake_sum<span class="classifier">WakeField</span></dt><dd><p>WakeField object weighted by beta functions.</p>
+</dd>
+</dl>
+</dd></dl>
+
+</dd></dl>
+
+</section>
+<section id="module-mbtrack2.impedance.resistive_wall">
+<span id="mbtrack2-impedance-resistive-wall-module"></span><h2>mbtrack2.impedance.resistive_wall module<a class="headerlink" href="#module-mbtrack2.impedance.resistive_wall" title="Permalink to this heading">¶</a></h2>
+<p>Define resistive wall elements based on the WakeField class.</p>
+<dl class="py class">
+<dt class="sig sig-object py" id="mbtrack2.impedance.resistive_wall.CircularResistiveWall">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">mbtrack2.impedance.resistive_wall.</span></span><span class="sig-name descname"><span class="pre">CircularResistiveWall</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">time</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">frequency</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">length</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">rho</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">radius</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">exact</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">atol</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1e-20</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/impedance/resistive_wall.html#CircularResistiveWall"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.impedance.resistive_wall.CircularResistiveWall" title="Permalink to this definition">¶</a></dt>
+<dd><p>Bases: <a class="reference internal" href="#mbtrack2.impedance.wakefield.WakeField" title="mbtrack2.impedance.wakefield.WakeField"><code class="xref py py-class docutils literal notranslate"><span class="pre">WakeField</span></code></a></p>
+<p>Resistive wall WakeField element for a circular beam pipe.</p>
+<p>Impedance from approximated formulas from Eq. (2.77) of Chao book [1].
+Wake function formulas from [2].</p>
+<dl class="simple">
+<dt>time<span class="classifier">array of float</span></dt><dd><p>Time points where the wake function will be evaluated in [s].</p>
+</dd>
+<dt>frequency<span class="classifier">array of float</span></dt><dd><p>Frequency points where the impedance will be evaluated in [Hz].</p>
+</dd>
+<dt>length<span class="classifier">float </span></dt><dd><p>Beam pipe length in [m].</p>
+</dd>
+<dt>rho<span class="classifier">float</span></dt><dd><p>Resistivity in [ohm.m].</p>
+</dd>
+<dt>radius<span class="classifier">float </span></dt><dd><p>Beam pipe radius in [m].</p>
+</dd>
+<dt>exact<span class="classifier">bool, optional</span></dt><dd><p>If False, approxmiated formulas are used for the wake function 
+computations.</p>
+</dd>
+<dt>atol<span class="classifier">float, optional</span></dt><dd><p>Absolute tolerance used to enforce fundamental theorem of beam loading
+for the exact expression of the longitudinal wake function.
+Default is 1e-20.</p>
+</dd>
+</dl>
+<p>[1] : Chao, A. W. (1993). Physics of collective beam instabilities in high 
+energy accelerators. Wiley.
+[2] : Skripka, Galina, et al. “Simultaneous computation of intrabunch and 
+interbunch collective beam motions in storage rings.” Nuclear Instruments 
+and Methods in Physics Research Section A: Accelerators, Spectrometers, 
+Detectors and Associated Equipment 806 (2016): 221-230.</p>
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.impedance.resistive_wall.CircularResistiveWall.LongitudinalWakeFunction">
+<span class="sig-name descname"><span class="pre">LongitudinalWakeFunction</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">time</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">exact</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">atol</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1e-20</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/impedance/resistive_wall.html#CircularResistiveWall.LongitudinalWakeFunction"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.impedance.resistive_wall.CircularResistiveWall.LongitudinalWakeFunction" title="Permalink to this definition">¶</a></dt>
+<dd><p>Compute the longitudinal wake function of a circular resistive wall 
+using Eq. (22), or approxmiated expression Eq. (24), of [1]. The 
+approxmiated expression is valid if the time is large compared to the 
+characteristic time t0.</p>
+<p>If some time value is smaller than atol, then the fundamental theorem 
+of beam loading is applied: Wl(0) = Wl(0+)/2.</p>
+<dl class="simple">
+<dt>time<span class="classifier">array of float</span></dt><dd><p>Time points where the wake function is evaluated in [s].</p>
+</dd>
+<dt>exact<span class="classifier">bool, optional</span></dt><dd><p>If True, the exact expression is used. The default is False.</p>
+</dd>
+<dt>atol<span class="classifier">float, optional</span></dt><dd><p>Absolute tolerance used to enforce fundamental theorem of beam loading
+for the exact expression of the longitudinal wake function.
+Default is 1e-20.</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>wl<span class="classifier">array of float</span></dt><dd><p>Longitudinal wake function in [V/C].</p>
+</dd>
+</dl>
+<p>[1] : Skripka, Galina, et al. “Simultaneous computation of intrabunch and 
+interbunch collective beam motions in storage rings.” Nuclear Instruments 
+and Methods in Physics Research Section A: Accelerators, Spectrometers, 
+Detectors and Associated Equipment 806 (2016): 221-230.</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.impedance.resistive_wall.CircularResistiveWall.TransverseWakeFunction">
+<span class="sig-name descname"><span class="pre">TransverseWakeFunction</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">time</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">exact</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/impedance/resistive_wall.html#CircularResistiveWall.TransverseWakeFunction"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.impedance.resistive_wall.CircularResistiveWall.TransverseWakeFunction" title="Permalink to this definition">¶</a></dt>
+<dd><p>Compute the transverse wake function of a circular resistive wall 
+using Eq. (25), or approxmiated expression Eq. (26), of [1]. The 
+approxmiated expression is valid if the time is large compared to the 
+characteristic time t0.</p>
+<p>Exact expression (Eq. (25) from [1]) is corrected by factor (c * t0).</p>
+<dl class="simple">
+<dt>time<span class="classifier">array of float</span></dt><dd><p>Time points where the wake function is evaluated in [s].</p>
+</dd>
+<dt>exact<span class="classifier">bool, optional</span></dt><dd><p>If True, the exact expression is used. The default is False.</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>wt<span class="classifier">array of float</span></dt><dd><p>Transverse wake function in [V/C].</p>
+</dd>
+</dl>
+<p>[1] : Skripka, Galina, et al. “Simultaneous computation of intrabunch and 
+interbunch collective beam motions in storage rings.” Nuclear Instruments 
+and Methods in Physics Research Section A: Accelerators, Spectrometers, 
+Detectors and Associated Equipment 806 (2016): 221-230.</p>
+</dd></dl>
+
+</dd></dl>
+
+<dl class="py class">
+<dt class="sig sig-object py" id="mbtrack2.impedance.resistive_wall.Coating">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">mbtrack2.impedance.resistive_wall.</span></span><span class="sig-name descname"><span class="pre">Coating</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">frequency</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">length</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">rho1</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">rho2</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">radius</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">thickness</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">approx</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/impedance/resistive_wall.html#Coating"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.impedance.resistive_wall.Coating" title="Permalink to this definition">¶</a></dt>
+<dd><p>Bases: <a class="reference internal" href="#mbtrack2.impedance.wakefield.WakeField" title="mbtrack2.impedance.wakefield.WakeField"><code class="xref py py-class docutils literal notranslate"><span class="pre">WakeField</span></code></a></p>
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.impedance.resistive_wall.Coating.LongitudinalImpedance">
+<span class="sig-name descname"><span class="pre">LongitudinalImpedance</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">f</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">approx</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/impedance/resistive_wall.html#Coating.LongitudinalImpedance"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.impedance.resistive_wall.Coating.LongitudinalImpedance" title="Permalink to this definition">¶</a></dt>
+<dd><p>Compute the longitudinal impedance of a coating using Eq. (5), or 
+approxmiated expression Eq. (8), of [1]. The approxmiated expression 
+is valid if the skin depth of the coating is large compared to the 
+coating thickness.</p>
+<dl class="simple">
+<dt>f<span class="classifier">array of float</span></dt><dd><p>Frequency points where the impedance is evaluated in [Hz].</p>
+</dd>
+<dt>approx<span class="classifier">bool</span></dt><dd><p>If True, used approxmiated formula.</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>Zl<span class="classifier">array</span></dt><dd><p>Longitudinal impedance values in [ohm].</p>
+</dd>
+</dl>
+<p>[1] : Migliorati, M., E. Belli, and M. Zobov. “Impact of the resistive 
+wall impedance on beam dynamics in the Future Circular e+ e− Collider.” 
+Physical Review Accelerators and Beams 21.4 (2018): 041001.</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.impedance.resistive_wall.Coating.TransverseImpedance">
+<span class="sig-name descname"><span class="pre">TransverseImpedance</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">f</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">approx</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/impedance/resistive_wall.html#Coating.TransverseImpedance"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.impedance.resistive_wall.Coating.TransverseImpedance" title="Permalink to this definition">¶</a></dt>
+<dd><p>Compute the transverse impedance of a coating using Eq. (6), or 
+approxmiated expression Eq. (9), of [1]. The approxmiated expression 
+is valid if the skin depth of the coating is large compared to the 
+coating thickness.</p>
+<dl class="simple">
+<dt>f<span class="classifier">array of float</span></dt><dd><p>Frequency points where the impedance is evaluated in [Hz].</p>
+</dd>
+<dt>approx<span class="classifier">bool</span></dt><dd><p>If True, used approxmiated formula.</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>Zt<span class="classifier">array</span></dt><dd><p>Transverse impedance values in [ohm].</p>
+</dd>
+</dl>
+<p>[1] : Migliorati, M., E. Belli, and M. Zobov. “Impact of the resistive 
+wall impedance on beam dynamics in the Future Circular e+ e− Collider.” 
+Physical Review Accelerators and Beams 21.4 (2018): 041001.</p>
+</dd></dl>
+
+</dd></dl>
+
+<dl class="py function">
+<dt class="sig sig-object py" id="mbtrack2.impedance.resistive_wall.skin_depth">
+<span class="sig-prename descclassname"><span class="pre">mbtrack2.impedance.resistive_wall.</span></span><span class="sig-name descname"><span class="pre">skin_depth</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">frequency</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">rho</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">mu_r</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">epsilon_r</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/impedance/resistive_wall.html#skin_depth"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.impedance.resistive_wall.skin_depth" title="Permalink to this definition">¶</a></dt>
+<dd><p>General formula for the skin depth.</p>
+<dl class="simple">
+<dt>frequency<span class="classifier">array of float</span></dt><dd><p>Frequency points in [Hz].</p>
+</dd>
+<dt>rho<span class="classifier">float</span></dt><dd><p>Resistivity in [ohm.m].</p>
+</dd>
+<dt>mu_r<span class="classifier">float, optional</span></dt><dd><p>Relative magnetic permeability.</p>
+</dd>
+<dt>epsilon_r<span class="classifier">float, optional</span></dt><dd><p>Relative electric permittivity.</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>delta<span class="classifier">array of float</span></dt><dd><p>Skin depth in [m].</p>
+</dd>
+</dl>
+</dd></dl>
+
+</section>
+<section id="module-mbtrack2.impedance.resonator">
+<span id="mbtrack2-impedance-resonator-module"></span><h2>mbtrack2.impedance.resonator module<a class="headerlink" href="#module-mbtrack2.impedance.resonator" title="Permalink to this heading">¶</a></h2>
+<p>This module defines the impedances and wake functions from the resonator model 
+based on the WakeField class.</p>
+<dl class="py class">
+<dt class="sig sig-object py" id="mbtrack2.impedance.resonator.PureInductive">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">mbtrack2.impedance.resonator.</span></span><span class="sig-name descname"><span class="pre">PureInductive</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">L</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">n_wake</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1000000.0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">n_imp</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1000000.0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">imp_freq_lim</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">100000000000.0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">nout</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">trim</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/impedance/resonator.html#PureInductive"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.impedance.resonator.PureInductive" title="Permalink to this definition">¶</a></dt>
+<dd><p>Bases: <a class="reference internal" href="#mbtrack2.impedance.wakefield.WakeField" title="mbtrack2.impedance.wakefield.WakeField"><code class="xref py py-class docutils literal notranslate"><span class="pre">WakeField</span></code></a></p>
+<p>Pure inductive Wakefield element which computes associated longitudinal 
+impedance and wake function.</p>
+<dl class="simple">
+<dt>L<span class="classifier">float</span></dt><dd><p>Inductance value in [Ohm/Hz].</p>
+</dd>
+<dt>n_wake<span class="classifier">int or float, optional</span></dt><dd><p>Number of points used in the wake function.</p>
+</dd>
+<dt>n_imp<span class="classifier">int or float, optional</span></dt><dd><p>Number of points used in the impedance.</p>
+</dd>
+<dt>imp_freq_lim<span class="classifier">float, optional</span></dt><dd><p>Maximum frequency used in the impedance.</p>
+</dd>
+</dl>
+<p>nout, trim : see Impedance.to_wakefunction</p>
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.impedance.resonator.PureInductive.long_impedance">
+<span class="sig-name descname"><span class="pre">long_impedance</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">f</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/impedance/resonator.html#PureInductive.long_impedance"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.impedance.resonator.PureInductive.long_impedance" title="Permalink to this definition">¶</a></dt>
+<dd></dd></dl>
+
+</dd></dl>
+
+<dl class="py class">
+<dt class="sig sig-object py" id="mbtrack2.impedance.resonator.PureResistive">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">mbtrack2.impedance.resonator.</span></span><span class="sig-name descname"><span class="pre">PureResistive</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">R</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">n_wake</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1000000.0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">n_imp</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1000000.0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">imp_freq_lim</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">100000000000.0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">nout</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">trim</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/impedance/resonator.html#PureResistive"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.impedance.resonator.PureResistive" title="Permalink to this definition">¶</a></dt>
+<dd><p>Bases: <a class="reference internal" href="#mbtrack2.impedance.wakefield.WakeField" title="mbtrack2.impedance.wakefield.WakeField"><code class="xref py py-class docutils literal notranslate"><span class="pre">WakeField</span></code></a></p>
+<p>Pure resistive Wakefield element which computes associated longitudinal 
+impedance and wake function.</p>
+<dl class="simple">
+<dt>R<span class="classifier">float</span></dt><dd><p>Resistance value in [Ohm].</p>
+</dd>
+<dt>n_wake<span class="classifier">int or float, optional</span></dt><dd><p>Number of points used in the wake function.</p>
+</dd>
+<dt>n_imp<span class="classifier">int or float, optional</span></dt><dd><p>Number of points used in the impedance.</p>
+</dd>
+<dt>imp_freq_lim<span class="classifier">float, optional</span></dt><dd><p>Maximum frequency used in the impedance.</p>
+</dd>
+</dl>
+<p>nout, trim : see Impedance.to_wakefunction</p>
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.impedance.resonator.PureResistive.long_impedance">
+<span class="sig-name descname"><span class="pre">long_impedance</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">f</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/impedance/resonator.html#PureResistive.long_impedance"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.impedance.resonator.PureResistive.long_impedance" title="Permalink to this definition">¶</a></dt>
+<dd></dd></dl>
+
+</dd></dl>
+
+<dl class="py class">
+<dt class="sig sig-object py" id="mbtrack2.impedance.resonator.Resonator">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">mbtrack2.impedance.resonator.</span></span><span class="sig-name descname"><span class="pre">Resonator</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">time</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">frequency</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">Rs</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">fr</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">Q</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">plane</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">atol</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1e-20</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/impedance/resonator.html#Resonator"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.impedance.resonator.Resonator" title="Permalink to this definition">¶</a></dt>
+<dd><p>Bases: <a class="reference internal" href="#mbtrack2.impedance.wakefield.WakeField" title="mbtrack2.impedance.wakefield.WakeField"><code class="xref py py-class docutils literal notranslate"><span class="pre">WakeField</span></code></a></p>
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.impedance.resonator.Resonator.long_impedance">
+<span class="sig-name descname"><span class="pre">long_impedance</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">f</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/impedance/resonator.html#Resonator.long_impedance"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.impedance.resonator.Resonator.long_impedance" title="Permalink to this definition">¶</a></dt>
+<dd></dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.impedance.resonator.Resonator.long_wake_function">
+<span class="sig-name descname"><span class="pre">long_wake_function</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">t</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">atol</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/impedance/resonator.html#Resonator.long_wake_function"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.impedance.resonator.Resonator.long_wake_function" title="Permalink to this definition">¶</a></dt>
+<dd></dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.impedance.resonator.Resonator.transverse_impedance">
+<span class="sig-name descname"><span class="pre">transverse_impedance</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">f</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/impedance/resonator.html#Resonator.transverse_impedance"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.impedance.resonator.Resonator.transverse_impedance" title="Permalink to this definition">¶</a></dt>
+<dd></dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.impedance.resonator.Resonator.transverse_wake_function">
+<span class="sig-name descname"><span class="pre">transverse_wake_function</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">t</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/impedance/resonator.html#Resonator.transverse_wake_function"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.impedance.resonator.Resonator.transverse_wake_function" title="Permalink to this definition">¶</a></dt>
+<dd></dd></dl>
+
+</dd></dl>
+
+</section>
+<section id="module-mbtrack2.impedance.tapers">
+<span id="mbtrack2-impedance-tapers-module"></span><h2>mbtrack2.impedance.tapers module<a class="headerlink" href="#module-mbtrack2.impedance.tapers" title="Permalink to this heading">¶</a></h2>
+<p>Module where taper elements are defined.</p>
+<dl class="py class">
+<dt class="sig sig-object py" id="mbtrack2.impedance.tapers.StupakovCircularTaper">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">mbtrack2.impedance.tapers.</span></span><span class="sig-name descname"><span class="pre">StupakovCircularTaper</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">frequency</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">radius_entrance</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">radius_exit</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">length</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">m_max</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">100</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">n_points</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">10000</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/impedance/tapers.html#StupakovCircularTaper"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.impedance.tapers.StupakovCircularTaper" title="Permalink to this definition">¶</a></dt>
+<dd><p>Bases: <a class="reference internal" href="#mbtrack2.impedance.wakefield.WakeField" title="mbtrack2.impedance.wakefield.WakeField"><code class="xref py py-class docutils literal notranslate"><span class="pre">WakeField</span></code></a></p>
+<p>Circular taper WakeField element, using the low frequency 
+approxmiation. Assume constant taper angle. Formulas from [1].</p>
+<p>! Valid for low w</p>
+<p>frequency: frequency points where the impedance will be evaluated in [Hz]
+radius_entrance : radius at taper entrance in [m]
+radius_exit : radius at taper exit in [m]
+length : taper length in [m]</p>
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.impedance.tapers.StupakovCircularTaper.Z0">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">Z0</span></span><a class="headerlink" href="#mbtrack2.impedance.tapers.StupakovCircularTaper.Z0" title="Permalink to this definition">¶</a></dt>
+<dd></dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.impedance.tapers.StupakovCircularTaper.Z_over_n">
+<span class="sig-name descname"><span class="pre">Z_over_n</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">f0</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/impedance/tapers.html#StupakovCircularTaper.Z_over_n"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.impedance.tapers.StupakovCircularTaper.Z_over_n" title="Permalink to this definition">¶</a></dt>
+<dd></dd></dl>
+
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.impedance.tapers.StupakovCircularTaper.angle">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">angle</span></span><a class="headerlink" href="#mbtrack2.impedance.tapers.StupakovCircularTaper.angle" title="Permalink to this definition">¶</a></dt>
+<dd></dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.impedance.tapers.StupakovCircularTaper.dip">
+<span class="sig-name descname"><span class="pre">dip</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">frequency</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/impedance/tapers.html#StupakovCircularTaper.dip"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.impedance.tapers.StupakovCircularTaper.dip" title="Permalink to this definition">¶</a></dt>
+<dd></dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.impedance.tapers.StupakovCircularTaper.long">
+<span class="sig-name descname"><span class="pre">long</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">frequency</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/impedance/tapers.html#StupakovCircularTaper.long"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.impedance.tapers.StupakovCircularTaper.long" title="Permalink to this definition">¶</a></dt>
+<dd></dd></dl>
+
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.impedance.tapers.StupakovCircularTaper.radius_prime">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">radius_prime</span></span><a class="headerlink" href="#mbtrack2.impedance.tapers.StupakovCircularTaper.radius_prime" title="Permalink to this definition">¶</a></dt>
+<dd></dd></dl>
+
+</dd></dl>
+
+<dl class="py class">
+<dt class="sig sig-object py" id="mbtrack2.impedance.tapers.StupakovRectangularTaper">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">mbtrack2.impedance.tapers.</span></span><span class="sig-name descname"><span class="pre">StupakovRectangularTaper</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">frequency</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">gap_entrance</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">gap_exit</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">length</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">width</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">m_max</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">100</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">n_points</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">10000</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/impedance/tapers.html#StupakovRectangularTaper"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.impedance.tapers.StupakovRectangularTaper" title="Permalink to this definition">¶</a></dt>
+<dd><p>Bases: <a class="reference internal" href="#mbtrack2.impedance.wakefield.WakeField" title="mbtrack2.impedance.wakefield.WakeField"><code class="xref py py-class docutils literal notranslate"><span class="pre">WakeField</span></code></a></p>
+<p>Rectangular vertical taper WakeField element, using the low frequency 
+approxmiation. Assume constant taper angle. Formulas from [1].</p>
+<p>! Valid for low w</p>
+<p>frequency: frequency points where the impedance will be evaluated in [Hz]
+gap_entrance : full vertical gap at taper entrance in [m]
+gap_exit: full vertical gap at taper exit in [m]
+length: taper length in [m]
+width : full horizontal width of the taper in [m]</p>
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.impedance.tapers.StupakovRectangularTaper.Z0">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">Z0</span></span><a class="headerlink" href="#mbtrack2.impedance.tapers.StupakovRectangularTaper.Z0" title="Permalink to this definition">¶</a></dt>
+<dd></dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.impedance.tapers.StupakovRectangularTaper.Z_over_n">
+<span class="sig-name descname"><span class="pre">Z_over_n</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">f0</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/impedance/tapers.html#StupakovRectangularTaper.Z_over_n"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.impedance.tapers.StupakovRectangularTaper.Z_over_n" title="Permalink to this definition">¶</a></dt>
+<dd></dd></dl>
+
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.impedance.tapers.StupakovRectangularTaper.angle">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">angle</span></span><a class="headerlink" href="#mbtrack2.impedance.tapers.StupakovRectangularTaper.angle" title="Permalink to this definition">¶</a></dt>
+<dd></dd></dl>
+
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.impedance.tapers.StupakovRectangularTaper.gap_prime">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">gap_prime</span></span><a class="headerlink" href="#mbtrack2.impedance.tapers.StupakovRectangularTaper.gap_prime" title="Permalink to this definition">¶</a></dt>
+<dd></dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.impedance.tapers.StupakovRectangularTaper.long">
+<span class="sig-name descname"><span class="pre">long</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">frequency</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/impedance/tapers.html#StupakovRectangularTaper.long"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.impedance.tapers.StupakovRectangularTaper.long" title="Permalink to this definition">¶</a></dt>
+<dd></dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.impedance.tapers.StupakovRectangularTaper.quad">
+<span class="sig-name descname"><span class="pre">quad</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/impedance/tapers.html#StupakovRectangularTaper.quad"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.impedance.tapers.StupakovRectangularTaper.quad" title="Permalink to this definition">¶</a></dt>
+<dd></dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.impedance.tapers.StupakovRectangularTaper.xdip">
+<span class="sig-name descname"><span class="pre">xdip</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/impedance/tapers.html#StupakovRectangularTaper.xdip"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.impedance.tapers.StupakovRectangularTaper.xdip" title="Permalink to this definition">¶</a></dt>
+<dd></dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.impedance.tapers.StupakovRectangularTaper.ydip">
+<span class="sig-name descname"><span class="pre">ydip</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/impedance/tapers.html#StupakovRectangularTaper.ydip"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.impedance.tapers.StupakovRectangularTaper.ydip" title="Permalink to this definition">¶</a></dt>
+<dd></dd></dl>
+
+</dd></dl>
+
+</section>
+<section id="module-mbtrack2.impedance.wakefield">
+<span id="mbtrack2-impedance-wakefield-module"></span><h2>mbtrack2.impedance.wakefield module<a class="headerlink" href="#module-mbtrack2.impedance.wakefield" title="Permalink to this heading">¶</a></h2>
+<p>This module defines general classes to describes wakefields, impedances and 
+wake functions.</p>
+<dl class="py class">
+<dt class="sig sig-object py" id="mbtrack2.impedance.wakefield.ComplexData">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">mbtrack2.impedance.wakefield.</span></span><span class="sig-name descname"><span class="pre">ComplexData</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">variable</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">array([-</span> <span class="pre">1.e+15,</span> <span class="pre">1.e+15])</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">function</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">array([0,</span> <span class="pre">0])</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/impedance/wakefield.html#ComplexData"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.impedance.wakefield.ComplexData" title="Permalink to this definition">¶</a></dt>
+<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">object</span></code></p>
+<p>Define a general data structure for a complex function based on a pandas 
+DataFrame.</p>
+<dl class="simple">
+<dt>variable<span class="classifier">list, numpy array</span></dt><dd><p>contains the function variable values</p>
+</dd>
+<dt>function<span class="classifier">list or numpy array of comp lex numbers</span></dt><dd><p>contains the values taken by the complex function</p>
+</dd>
+</dl>
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.impedance.wakefield.ComplexData.add">
+<span class="sig-name descname"><span class="pre">add</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">structure_to_add</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">method</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'zero'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">interp_kind</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'cubic'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">index_name</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'variable'</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/impedance/wakefield.html#ComplexData.add"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.impedance.wakefield.ComplexData.add" title="Permalink to this definition">¶</a></dt>
+<dd><p>Method to add two structures. If the data don’t have the same length,
+different cases are handled.</p>
+<dl>
+<dt>structure_to_add<span class="classifier">ComplexData object, int, float or complex.</span></dt><dd><p>structure to be added.</p>
+</dd>
+<dt>method<span class="classifier">str, optional</span></dt><dd><p>manage how the addition is done, possibilties are: 
+-common: the common range of the index (variable) from the two</p>
+<blockquote>
+<div><p>structures is used. The input data are cross-interpolated
+so that the result data contains the points at all initial
+points in the common domain.</p>
+</div></blockquote>
+<p>-extrapolate: extrapolate the value of both ComplexData.
+-zero: outside of the common range, the missing values are zero. In</p>
+<blockquote>
+<div><p>the common range, behave as “common” method.</p>
+</div></blockquote>
+</dd>
+<dt>interp_kind<span class="classifier">str, optional</span></dt><dd><p>interpolation method which is passed to pandas and to
+scipy.interpolate.interp1d.</p>
+</dd>
+<dt>index_name<span class="classifier">str, optional</span></dt><dd><p>name of the dataframe index passed to the method</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>ComplexData </dt><dd><p>Contains the sum of the two inputs.</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.impedance.wakefield.ComplexData.component_type">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">component_type</span></span><a class="headerlink" href="#mbtrack2.impedance.wakefield.ComplexData.component_type" title="Permalink to this definition">¶</a></dt>
+<dd></dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.impedance.wakefield.ComplexData.initialize_coefficient">
+<span class="sig-name descname"><span class="pre">initialize_coefficient</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/impedance/wakefield.html#ComplexData.initialize_coefficient"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.impedance.wakefield.ComplexData.initialize_coefficient" title="Permalink to this definition">¶</a></dt>
+<dd><p>Define the impedance coefficients and the plane of the impedance that
+are presents in attributes of the class.</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.impedance.wakefield.ComplexData.multiply">
+<span class="sig-name descname"><span class="pre">multiply</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">factor</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/impedance/wakefield.html#ComplexData.multiply"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.impedance.wakefield.ComplexData.multiply" title="Permalink to this definition">¶</a></dt>
+<dd><p>Multiply a data strucure with a float or an int.
+If the multiplication is done with something else, throw a warning.</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.impedance.wakefield.ComplexData.name_and_coefficients_table">
+<span class="sig-name descname"><span class="pre">name_and_coefficients_table</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/impedance/wakefield.html#ComplexData.name_and_coefficients_table"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.impedance.wakefield.ComplexData.name_and_coefficients_table" title="Permalink to this definition">¶</a></dt>
+<dd><p>Return a table associating the human readbale names of an impedance
+component and its associated coefficients and plane.</p>
+</dd></dl>
+
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.impedance.wakefield.ComplexData.power_x">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">power_x</span></span><a class="headerlink" href="#mbtrack2.impedance.wakefield.ComplexData.power_x" title="Permalink to this definition">¶</a></dt>
+<dd></dd></dl>
+
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.impedance.wakefield.ComplexData.power_y">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">power_y</span></span><a class="headerlink" href="#mbtrack2.impedance.wakefield.ComplexData.power_y" title="Permalink to this definition">¶</a></dt>
+<dd></dd></dl>
+
+</dd></dl>
+
+<dl class="py class">
+<dt class="sig sig-object py" id="mbtrack2.impedance.wakefield.Impedance">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">mbtrack2.impedance.wakefield.</span></span><span class="sig-name descname"><span class="pre">Impedance</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">variable</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">array([-</span> <span class="pre">1.e+15,</span> <span class="pre">1.e+15])</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">function</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">array([0,</span> <span class="pre">0])</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">component_type</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'long'</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/impedance/wakefield.html#Impedance"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.impedance.wakefield.Impedance" title="Permalink to this definition">¶</a></dt>
+<dd><p>Bases: <a class="reference internal" href="#mbtrack2.impedance.wakefield.ComplexData" title="mbtrack2.impedance.wakefield.ComplexData"><code class="xref py py-class docutils literal notranslate"><span class="pre">ComplexData</span></code></a></p>
+<p>Define an Impedance object based on a ComplexData object.</p>
+<dl class="simple">
+<dt>variable<span class="classifier">array-like</span></dt><dd><p>Frequency domain structure of the impedance in [Hz].</p>
+</dd>
+<dt>function<span class="classifier">array-like</span></dt><dd><p>Impedance values in [Ohm].</p>
+</dd>
+<dt>component_type<span class="classifier">str, optinal</span></dt><dd><p>Type of the impedance: “long”, “xdip”, “xquad”, …</p>
+</dd>
+</dl>
+<p>data : DataFrame
+impedance_type : str</p>
+<dl class="simple">
+<dt>loss_factor(sigma)</dt><dd><p>Compute the loss factor or the kick factor for a Gaussian bunch.</p>
+</dd>
+<dt>to_wakefunction()</dt><dd><p>Return a WakeFunction object from the impedance data.</p>
+</dd>
+<dt>plot()</dt><dd><p>Plot the impedance data.</p>
+</dd>
+</dl>
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.impedance.wakefield.Impedance.add">
+<span class="sig-name descname"><span class="pre">add</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">structure_to_add</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">beta_x</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">beta_y</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">method</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'zero'</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/impedance/wakefield.html#Impedance.add"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.impedance.wakefield.Impedance.add" title="Permalink to this definition">¶</a></dt>
+<dd><p>Method to add two Impedance objects. The two structures are
+compared so that the addition is self-consistent.
+Beta functions can be precised as well.</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.impedance.wakefield.Impedance.loss_factor">
+<span class="sig-name descname"><span class="pre">loss_factor</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">sigma</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/impedance/wakefield.html#Impedance.loss_factor"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.impedance.wakefield.Impedance.loss_factor" title="Permalink to this definition">¶</a></dt>
+<dd><p>Compute the loss factor or the kick factor for a Gaussian bunch. 
+Formulas from Eq. (2) p239 and Eq.(7) p240 of [1].</p>
+<dl class="simple">
+<dt>sigma<span class="classifier">float</span></dt><dd><p>RMS bunch length in [s]</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>kloss: float</dt><dd><p>Loss factor in [V/C] or kick factor in [V/C/m] depanding on the 
+impedance type.</p>
+</dd>
+</dl>
+<p>[1] : Handbook of accelerator physics and engineering, 3rd printing.</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.impedance.wakefield.Impedance.multiply">
+<span class="sig-name descname"><span class="pre">multiply</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">factor</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/impedance/wakefield.html#Impedance.multiply"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.impedance.wakefield.Impedance.multiply" title="Permalink to this definition">¶</a></dt>
+<dd><p>Multiply a Impedance object with a float or an int.
+If the multiplication is done with something else, throw a warning.</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.impedance.wakefield.Impedance.plot">
+<span class="sig-name descname"><span class="pre">plot</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/impedance/wakefield.html#Impedance.plot"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.impedance.wakefield.Impedance.plot" title="Permalink to this definition">¶</a></dt>
+<dd><p>Plot the impedance data.</p>
+<dl>
+<dt>ax<span class="classifier">class:<cite>matplotlib.axes.Axes</cite></span></dt><dd><p>Impedance data.</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.impedance.wakefield.Impedance.to_wakefunction">
+<span class="sig-name descname"><span class="pre">to_wakefunction</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">nout</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">trim</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/impedance/wakefield.html#Impedance.to_wakefunction"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.impedance.wakefield.Impedance.to_wakefunction" title="Permalink to this definition">¶</a></dt>
+<dd><p>Return a WakeFunction object from the impedance data.
+The impedance data is assumed to be sampled equally.</p>
+<dl class="simple">
+<dt>nout<span class="classifier">int or float, optional</span></dt><dd><p>Length of the transformed axis of the output. If None, it is taken
+to be 2*(n-1) where n is the length of the input. If nout &gt; n, the
+input is padded with zeros. If nout &lt; n, the input it cropped.
+Note that, for any nout value, nout//2+1 input points are required.</p>
+</dd>
+<dt>trim<span class="classifier">bool or float, optional</span></dt><dd><p>If True, the pseudo wake function is trimmed at time=0 and is forced 
+to zero where time&lt;0. 
+If False, the original result is preserved.
+If a float is given, the pseudo wake function is trimmed from 
+time &lt;= trim to 0.</p>
+</dd>
+</dl>
+</dd></dl>
+
+</dd></dl>
+
+<dl class="py class">
+<dt class="sig sig-object py" id="mbtrack2.impedance.wakefield.WakeField">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">mbtrack2.impedance.wakefield.</span></span><span class="sig-name descname"><span class="pre">WakeField</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">structure_list</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">name</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/impedance/wakefield.html#WakeField"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.impedance.wakefield.WakeField" title="Permalink to this definition">¶</a></dt>
+<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">object</span></code></p>
+<p>Defines a WakeField which corresponds to a single physical element which 
+produces different types of wakes, represented by their Impedance or 
+WakeFunction objects.</p>
+<dl class="simple">
+<dt>structure_list<span class="classifier">list, optional</span></dt><dd><p>list of Impedance/WakeFunction objects to add to the WakeField.</p>
+</dd>
+</dl>
+<p>name : str, optional</p>
+<dl class="simple">
+<dt>impedance_components<span class="classifier">array of str</span></dt><dd><p>Impedance components present for this element.</p>
+</dd>
+<dt>wake_components<span class="classifier">array of str</span></dt><dd><p>WakeFunction components present for this element.</p>
+</dd>
+<dt>components<span class="classifier">array of str</span></dt><dd><p>Impedance or WakeFunction components present for this element.</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>append_to_model(structure_to_add)</dt><dd><p>Add Impedance/WakeFunction to WakeField.</p>
+</dd>
+<dt>list_to_attr(structure_list)</dt><dd><p>Add list of Impedance/WakeFunction to WakeField.</p>
+</dd>
+<dt>add_wakefields(wake1, beta1, wake2, beta2)</dt><dd><p>Add two WakeFields taking into account beta functions.</p>
+</dd>
+<dt>add_several_wakefields(wakefields, beta)</dt><dd><p>Add a list of WakeFields taking into account beta functions.</p>
+</dd>
+<dt>drop(component)</dt><dd><p>Delete a component or a list of component from the WakeField.</p>
+</dd>
+<dt>save(file)</dt><dd><p>Save WakeField element to file.</p>
+</dd>
+<dt>load(file)</dt><dd><p>Load WakeField element from file.</p>
+</dd>
+</dl>
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.impedance.wakefield.WakeField.add_several_wakefields">
+<em class="property"><span class="pre">static</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">add_several_wakefields</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">wakefields</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">beta</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/impedance/wakefield.html#WakeField.add_several_wakefields"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.impedance.wakefield.WakeField.add_several_wakefields" title="Permalink to this definition">¶</a></dt>
+<dd><p>Add a list of WakeFields taking into account beta functions.</p>
+<dl class="simple">
+<dt>wakefields<span class="classifier">list of WakeField</span></dt><dd><p>WakeFields to add.</p>
+</dd>
+<dt>beta<span class="classifier">array of shape (len(wakefields), 2)</span></dt><dd><p>Beta functions at the WakeField postions.</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>wake_sum<span class="classifier">WakeField</span></dt><dd><p>WakeField with summed components.</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.impedance.wakefield.WakeField.add_wakefields">
+<em class="property"><span class="pre">static</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">add_wakefields</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">wake1</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">beta1</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">wake2</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">beta2</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/impedance/wakefield.html#WakeField.add_wakefields"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.impedance.wakefield.WakeField.add_wakefields" title="Permalink to this definition">¶</a></dt>
+<dd><p>Add two WakeFields taking into account beta functions.</p>
+<dl class="simple">
+<dt>wake1<span class="classifier">WakeField</span></dt><dd><p>WakeField to add.</p>
+</dd>
+<dt>beta1<span class="classifier">array of shape (2,)</span></dt><dd><p>Beta functions at wake1 postion.</p>
+</dd>
+<dt>wake2<span class="classifier">WakeField</span></dt><dd><p>WakeField to add.</p>
+</dd>
+<dt>beta2<span class="classifier">array of shape (2,)</span></dt><dd><p>Beta functions at wake2 postion.</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>wake_sum<span class="classifier">WakeField</span></dt><dd><p>WakeField with summed components.</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.impedance.wakefield.WakeField.append_to_model">
+<span class="sig-name descname"><span class="pre">append_to_model</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">structure_to_add</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/impedance/wakefield.html#WakeField.append_to_model"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.impedance.wakefield.WakeField.append_to_model" title="Permalink to this definition">¶</a></dt>
+<dd><p>Add Impedance/WakeFunction component to WakeField.</p>
+<p>structure_to_add : Impedance or WakeFunction object</p>
+</dd></dl>
+
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.impedance.wakefield.WakeField.components">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">components</span></span><a class="headerlink" href="#mbtrack2.impedance.wakefield.WakeField.components" title="Permalink to this definition">¶</a></dt>
+<dd><p>Return an array of the component names for the element.</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.impedance.wakefield.WakeField.drop">
+<span class="sig-name descname"><span class="pre">drop</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">component</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/impedance/wakefield.html#WakeField.drop"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.impedance.wakefield.WakeField.drop" title="Permalink to this definition">¶</a></dt>
+<dd><p>Delete a component or a list of component from the WakeField.</p>
+<dl class="simple">
+<dt>component<span class="classifier">str or list of str</span></dt><dd><p>Component or list of components to drop.
+If “Z”, drop all impedance components.
+If “W””, drop all wake function components.</p>
+</dd>
+</dl>
+<p>None.</p>
+</dd></dl>
+
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.impedance.wakefield.WakeField.impedance_components">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">impedance_components</span></span><a class="headerlink" href="#mbtrack2.impedance.wakefield.WakeField.impedance_components" title="Permalink to this definition">¶</a></dt>
+<dd><p>Return an array of the impedance component names for the element.</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.impedance.wakefield.WakeField.list_to_attr">
+<span class="sig-name descname"><span class="pre">list_to_attr</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">structure_list</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/impedance/wakefield.html#WakeField.list_to_attr"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.impedance.wakefield.WakeField.list_to_attr" title="Permalink to this definition">¶</a></dt>
+<dd><p>Add list of Impedance/WakeFunction components to WakeField.</p>
+<p>structure_list : list of Impedance or WakeFunction objects.</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.impedance.wakefield.WakeField.load">
+<em class="property"><span class="pre">static</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">load</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">file</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/impedance/wakefield.html#WakeField.load"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.impedance.wakefield.WakeField.load" title="Permalink to this definition">¶</a></dt>
+<dd><p>Load WakeField element from file.</p>
+<p>The same pandas version is needed on both saving and loading computer
+for the pickle to work.</p>
+<dl class="simple">
+<dt>file<span class="classifier">str</span></dt><dd><p>File where the WakeField element is saved.</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>wakefield<span class="classifier">WakeField</span></dt><dd><p>Loaded wakefield.</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.impedance.wakefield.WakeField.save">
+<span class="sig-name descname"><span class="pre">save</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">file</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/impedance/wakefield.html#WakeField.save"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.impedance.wakefield.WakeField.save" title="Permalink to this definition">¶</a></dt>
+<dd><p>Save WakeField element to file.</p>
+<p>The same pandas version is needed on both saving and loading computer
+for the pickle to work.</p>
+<dl class="simple">
+<dt>file<span class="classifier">str</span></dt><dd><p>File where the WakeField element is saved.</p>
+</dd>
+</dl>
+<p>None.</p>
+</dd></dl>
+
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.impedance.wakefield.WakeField.wake_components">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">wake_components</span></span><a class="headerlink" href="#mbtrack2.impedance.wakefield.WakeField.wake_components" title="Permalink to this definition">¶</a></dt>
+<dd><p>Return an array of the wake function component names for the element.</p>
+</dd></dl>
+
+</dd></dl>
+
+<dl class="py class">
+<dt class="sig sig-object py" id="mbtrack2.impedance.wakefield.WakeFunction">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">mbtrack2.impedance.wakefield.</span></span><span class="sig-name descname"><span class="pre">WakeFunction</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">variable</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">array([-</span> <span class="pre">1.e+15,</span> <span class="pre">1.e+15])</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">function</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">array([0,</span> <span class="pre">0])</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">component_type</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'long'</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/impedance/wakefield.html#WakeFunction"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.impedance.wakefield.WakeFunction" title="Permalink to this definition">¶</a></dt>
+<dd><p>Bases: <a class="reference internal" href="#mbtrack2.impedance.wakefield.ComplexData" title="mbtrack2.impedance.wakefield.ComplexData"><code class="xref py py-class docutils literal notranslate"><span class="pre">ComplexData</span></code></a></p>
+<p>Define a WakeFunction object based on a ComplexData object.</p>
+<dl class="simple">
+<dt>variable<span class="classifier">array-like</span></dt><dd><p>Time domain structure of the wake function in [s].</p>
+</dd>
+<dt>function<span class="classifier">array-like</span></dt><dd><p>Wake function values in [V/C] for “long” and in [V/C/m] for others.</p>
+</dd>
+<dt>component_type<span class="classifier">str, optinal</span></dt><dd><p>Type of the wake function: “long”, “xdip”, “xquad”, …</p>
+</dd>
+</dl>
+<p>data : DataFrame
+wake_type : str</p>
+<dl class="simple">
+<dt>to_impedance()</dt><dd><p>Return an Impedance object from the WakeFunction data.</p>
+</dd>
+<dt>deconvolution(freq_lim, sigma, mu)</dt><dd><p>Compute a wake function from wake potential data.</p>
+</dd>
+<dt>plot()</dt><dd><p>Plot the wake function data.</p>
+</dd>
+<dt>loss_factor(sigma)</dt><dd><p>Compute the loss factor or the kick factor for a Gaussian bunch.</p>
+</dd>
+</dl>
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.impedance.wakefield.WakeFunction.add">
+<span class="sig-name descname"><span class="pre">add</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">structure_to_add</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">method</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'zero'</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/impedance/wakefield.html#WakeFunction.add"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.impedance.wakefield.WakeFunction.add" title="Permalink to this definition">¶</a></dt>
+<dd><p>Method to add two WakeFunction objects. The two structures are
+compared so that the addition is self-consistent.</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.impedance.wakefield.WakeFunction.deconvolution">
+<span class="sig-name descname"><span class="pre">deconvolution</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">freq_lim</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">sigma</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">mu</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">nout</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/impedance/wakefield.html#WakeFunction.deconvolution"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.impedance.wakefield.WakeFunction.deconvolution" title="Permalink to this definition">¶</a></dt>
+<dd><p>Compute a wake function from wake potential data.</p>
+<p>The present data loaded into the WakeFunction object is assumed to be 
+an uniformly sampled wake potential from a Gaussian bunch distribution 
+with RMS bunch length sigma and offset mu.</p>
+<dl class="simple">
+<dt>The offset mu depends on the code used to compute the wake potential:</dt><dd><ul class="simple">
+<li><p>for CST, it is the first time sample, so self.data.index[0].</p></li>
+<li><p>for ABCI, it is “-1 * ISIG * SIG / c”.</p></li>
+</ul>
+</dd>
+</dl>
+<dl class="simple">
+<dt>freq_lim<span class="classifier">float</span></dt><dd><p>The maximum frequency for calculating the impedance [Hz].</p>
+</dd>
+<dt>sigma<span class="classifier">float</span></dt><dd><p>RMS of the Gaussian distribution in [s].</p>
+</dd>
+<dt>mu<span class="classifier">float</span></dt><dd><p>Offset of the Gaussian distribution in [s].</p>
+</dd>
+<dt>nout<span class="classifier">int or float, optional</span></dt><dd><p>Length of the transformed axis of the output. If None, it is taken
+to be 2*(n-1) where n is the length of the input. If nout &gt; n, the
+input is padded with zeros. If nout &lt; n, the input it cropped.
+Note that, for any nout value, nout//2+1 input points are required.
+The default is None.</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.impedance.wakefield.WakeFunction.loss_factor">
+<span class="sig-name descname"><span class="pre">loss_factor</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">sigma</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/impedance/wakefield.html#WakeFunction.loss_factor"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.impedance.wakefield.WakeFunction.loss_factor" title="Permalink to this definition">¶</a></dt>
+<dd><p>Compute the loss factor or the kick factor for a Gaussian bunch. 
+Formulas from Eq. (5.6), Eq. (5.12) and Eq. (5.17) of [1].</p>
+<dl class="simple">
+<dt>sigma<span class="classifier">float</span></dt><dd><p>RMS bunch length in [s]</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>kloss: float</dt><dd><p>Loss factor in [V/C] or kick factor in [V/C/m] depanding on the 
+impedance type.</p>
+</dd>
+</dl>
+<p>[1] : Zotter, Bruno W., and Semyon A. Kheifets. Impedances and wakes 
+in high-energy particle accelerators. World Scientific, 1998.</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.impedance.wakefield.WakeFunction.multiply">
+<span class="sig-name descname"><span class="pre">multiply</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">factor</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/impedance/wakefield.html#WakeFunction.multiply"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.impedance.wakefield.WakeFunction.multiply" title="Permalink to this definition">¶</a></dt>
+<dd><p>Multiply a WakeFunction object with a float or an int.
+If the multiplication is done with something else, throw a warning.</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.impedance.wakefield.WakeFunction.plot">
+<span class="sig-name descname"><span class="pre">plot</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/impedance/wakefield.html#WakeFunction.plot"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.impedance.wakefield.WakeFunction.plot" title="Permalink to this definition">¶</a></dt>
+<dd><p>Plot the wake function data.</p>
+<dl>
+<dt>ax<span class="classifier">class:<cite>matplotlib.axes.Axes</cite></span></dt><dd><p>Wake function data.</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.impedance.wakefield.WakeFunction.to_impedance">
+<span class="sig-name descname"><span class="pre">to_impedance</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">freq_lim</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">nout</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">sigma</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">mu</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/impedance/wakefield.html#WakeFunction.to_impedance"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.impedance.wakefield.WakeFunction.to_impedance" title="Permalink to this definition">¶</a></dt>
+<dd><p>Return an Impedance object from the WakeFunction data.
+The WakeFunction data is assumed to be sampled equally.</p>
+<p>If both sigma and mu are given, the impedance data is divided by the
+Fourier transform of a Gaussian distribution. It then can be used to go 
+from wake potential data to impedance.</p>
+<dl class="simple">
+<dt>freq_lim<span class="classifier">float</span></dt><dd><p>The maximum frequency for calculating the impedance [Hz].</p>
+</dd>
+<dt>nout<span class="classifier">int or float, optional</span></dt><dd><p>Length of the transformed axis of the output. If None, it is taken
+to be 2*(n-1) where n is the length of the input. If nout &gt; n, the
+input is padded with zeros. If nout &lt; n, the input it cropped.
+Note that, for any nout value, nout//2+1 input points are required.
+The default is None.</p>
+</dd>
+<dt>sigma<span class="classifier">float</span></dt><dd><p>RMS of the Gaussian distribution in [s].
+The default is None.</p>
+</dd>
+<dt>mu<span class="classifier">float</span></dt><dd><p>Offset of the Gaussian distribution in [s].
+The default is None.</p>
+</dd>
+</dl>
+</dd></dl>
+
+</dd></dl>
+
+</section>
+<section id="module-mbtrack2.impedance">
+<span id="module-contents"></span><h2>Module contents<a class="headerlink" href="#module-mbtrack2.impedance" title="Permalink to this heading">¶</a></h2>
+</section>
+</section>
+
+
+            <div class="clearer"></div>
+          </div>
+        </div>
+      </div>
+      <div class="sphinxsidebar" role="navigation" aria-label="main navigation">
+        <div class="sphinxsidebarwrapper">
+  <div>
+    <h3><a href="index.html">Table of Contents</a></h3>
+    <ul>
+<li><a class="reference internal" href="#">mbtrack2.impedance package</a><ul>
+<li><a class="reference internal" href="#submodules">Submodules</a></li>
+<li><a class="reference internal" href="#module-mbtrack2.impedance.csr">mbtrack2.impedance.csr module</a></li>
+<li><a class="reference internal" href="#module-mbtrack2.impedance.impedance_model">mbtrack2.impedance.impedance_model module</a></li>
+<li><a class="reference internal" href="#module-mbtrack2.impedance.resistive_wall">mbtrack2.impedance.resistive_wall module</a></li>
+<li><a class="reference internal" href="#module-mbtrack2.impedance.resonator">mbtrack2.impedance.resonator module</a></li>
+<li><a class="reference internal" href="#module-mbtrack2.impedance.tapers">mbtrack2.impedance.tapers module</a></li>
+<li><a class="reference internal" href="#module-mbtrack2.impedance.wakefield">mbtrack2.impedance.wakefield module</a></li>
+<li><a class="reference internal" href="#module-mbtrack2.impedance">Module contents</a></li>
+</ul>
+</li>
+</ul>
+
+  </div>
+  <div role="note" aria-label="source link">
+    <h3>This Page</h3>
+    <ul class="this-page-menu">
+      <li><a href="_sources/mbtrack2.impedance.rst.txt"
+            rel="nofollow">Show Source</a></li>
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+             accesskey="I">index</a></li>
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+          <a href="py-modindex.html" title="Python Module Index"
+             >modules</a> |</li>
+        <li class="nav-item nav-item-0"><a href="index.html">mbtrack2 0.6.0 documentation</a> &#187;</li>
+        <li class="nav-item nav-item-this"><a href="">mbtrack2.instability package</a></li> 
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+            
+  <section id="mbtrack2-instability-package">
+<h1>mbtrack2.instability package<a class="headerlink" href="#mbtrack2-instability-package" title="Permalink to this heading">¶</a></h1>
+<section id="submodules">
+<h2>Submodules<a class="headerlink" href="#submodules" title="Permalink to this heading">¶</a></h2>
+</section>
+<section id="module-mbtrack2.instability.instabilities">
+<span id="mbtrack2-instability-instabilities-module"></span><h2>mbtrack2.instability.instabilities module<a class="headerlink" href="#module-mbtrack2.instability.instabilities" title="Permalink to this heading">¶</a></h2>
+<p>General calculations about instability thresholds.</p>
+<dl class="py function">
+<dt class="sig sig-object py" id="mbtrack2.instability.instabilities.cbi_threshold">
+<span class="sig-prename descclassname"><span class="pre">mbtrack2.instability.instabilities.</span></span><span class="sig-name descname"><span class="pre">cbi_threshold</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">ring</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">I</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">Vrf</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">f</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">beta</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">Ncav</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/instability/instabilities.html#cbi_threshold"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.instability.instabilities.cbi_threshold" title="Permalink to this definition">¶</a></dt>
+<dd><p>Compute the longitudinal and transverse coupled bunch instability 
+thresolds driven by HOMs [1].</p>
+<p>Approximate formula, does not take into account variation with Q.
+For better estimate use lcbi_growth_rate.</p>
+<p>ring : Synchrotron object
+I : float</p>
+<blockquote>
+<div><p>Total beam current in [A].</p>
+</div></blockquote>
+<dl class="simple">
+<dt>Vrf<span class="classifier">float</span></dt><dd><p>Total RF voltage in [V].</p>
+</dd>
+<dt>f<span class="classifier">float</span></dt><dd><p>Frequency of the HOM in [Hz].</p>
+</dd>
+<dt>beta<span class="classifier">array-like of shape (2,)</span></dt><dd><p>Horizontal and vertical beta function at the HOM position in [m].</p>
+</dd>
+<dt>Ncav<span class="classifier">int, optional</span></dt><dd><p>Number of RF cavity.</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>Zlong<span class="classifier">float</span></dt><dd><p>Maximum longitudinal impedance of the HOM in [ohm].</p>
+</dd>
+<dt>Zxdip<span class="classifier">float</span></dt><dd><p>Maximum horizontal dipolar impedance of the HOM in [ohm/m].</p>
+</dd>
+<dt>Zydip<span class="classifier">float</span></dt><dd><p>Maximum vertical dipolar impedance of the HOM in [ohm/m].</p>
+</dd>
+</dl>
+<p>[1] : Ruprecht, Martin, et al. “Calculation of Transverse Coupled Bunch 
+Instabilities in Electron Storage Rings Driven By Quadrupole Higher Order 
+Modes.” 7th Int. Particle Accelerator Conf.(IPAC’16), Busan, Korea.</p>
+</dd></dl>
+
+<dl class="py function">
+<dt class="sig sig-object py" id="mbtrack2.instability.instabilities.lcbi_growth_rate">
+<span class="sig-prename descclassname"><span class="pre">mbtrack2.instability.instabilities.</span></span><span class="sig-name descname"><span class="pre">lcbi_growth_rate</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">ring</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">I</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">M</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">synchrotron_tune</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">Vrf</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">fr</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">RL</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">QL</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">Z</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/instability/instabilities.html#lcbi_growth_rate"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.instability.instabilities.lcbi_growth_rate" title="Permalink to this definition">¶</a></dt>
+<dd><p>Compute the maximum growth rate for longitudinal coupled bunch instability 
+driven an impedance [1].</p>
+<p>Use either a list of resonators (fr, RL, QL) or an Impedance object (Z).</p>
+<p>ring : Synchrotron object
+I : float</p>
+<blockquote>
+<div><p>Total beam current in [A].</p>
+</div></blockquote>
+<dl class="simple">
+<dt>M<span class="classifier">int</span></dt><dd><p>Nomber of bunches in the beam.</p>
+</dd>
+<dt>synchrotron_tune<span class="classifier">float, optional</span></dt><dd><p>Synchrotron tune.</p>
+</dd>
+<dt>Vrf<span class="classifier">float, optinal</span></dt><dd><p>Total RF voltage in [V] used to compute synchrotron tune if not given.</p>
+</dd>
+<dt>fr<span class="classifier">float or list, optional</span></dt><dd><p>Frequency of the HOM in [Hz].</p>
+</dd>
+<dt>RL<span class="classifier">float or list, optional</span></dt><dd><p>Loaded shunt impedance of the HOM in [Ohm].</p>
+</dd>
+<dt>QL<span class="classifier">float or list, optional</span></dt><dd><p>Loaded quality factor of the HOM.</p>
+</dd>
+<dt>Z<span class="classifier">Impedance, optional</span></dt><dd><p>Longitunial impedance to consider.</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>growth_rate<span class="classifier">float</span></dt><dd><p>Maximum coupled bunch instability growth rate in [s-1].</p>
+</dd>
+<dt>mu<span class="classifier">int</span></dt><dd><p>Coupled bunch mode number corresponding to the maximum coupled bunch 
+instability growth rate.</p>
+</dd>
+<dt>growth_rates<span class="classifier">array</span></dt><dd><p>Coupled bunch instability growth rates for the different mode numbers 
+in [s-1].</p>
+</dd>
+</dl>
+<p>[1] : Eq. 51 p139 of Akai, Kazunori. “RF System for Electron Storage 
+Rings.” Physics And Engineering Of High Performance Electron Storage Rings 
+And Application Of Superconducting Technology. 2002. 118-149.</p>
+</dd></dl>
+
+<dl class="py function">
+<dt class="sig sig-object py" id="mbtrack2.instability.instabilities.lcbi_growth_rate_mode">
+<span class="sig-prename descclassname"><span class="pre">mbtrack2.instability.instabilities.</span></span><span class="sig-name descname"><span class="pre">lcbi_growth_rate_mode</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">ring</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">I</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">M</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">mu</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">synchrotron_tune</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">Vrf</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">fr</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">RL</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">QL</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">Z</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/instability/instabilities.html#lcbi_growth_rate_mode"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.instability.instabilities.lcbi_growth_rate_mode" title="Permalink to this definition">¶</a></dt>
+<dd><p>Compute the longitudinal coupled bunch instability growth rate driven by
+an impedance for a given coupled bunch mode mu [1].</p>
+<p>Use either a list of resonators (fr, RL, QL) or an Impedance object (Z).</p>
+<p>ring : Synchrotron object
+I : float</p>
+<blockquote>
+<div><p>Total beam current in [A].</p>
+</div></blockquote>
+<dl class="simple">
+<dt>M<span class="classifier">int</span></dt><dd><p>Nomber of bunches in the beam.</p>
+</dd>
+<dt>mu<span class="classifier">int</span></dt><dd><p>Coupled bunch mode number (= 0, …, M-1).</p>
+</dd>
+<dt>synchrotron_tune<span class="classifier">float, optional</span></dt><dd><p>Synchrotron tune.</p>
+</dd>
+<dt>Vrf<span class="classifier">float, optinal</span></dt><dd><p>Total RF voltage in [V] used to compute synchrotron tune if not given.</p>
+</dd>
+<dt>fr<span class="classifier">float or list, optional</span></dt><dd><p>Frequency of the resonator in [Hz].</p>
+</dd>
+<dt>RL<span class="classifier">float or list, optional</span></dt><dd><p>Loaded shunt impedance of the resonator in [Ohm].</p>
+</dd>
+<dt>QL<span class="classifier">float or list, optional</span></dt><dd><p>Loaded quality factor of the resonator.</p>
+</dd>
+<dt>Z<span class="classifier">Impedance, optional</span></dt><dd><p>Longitunial impedance to consider.</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>float</dt><dd><p>Coupled bunch instability growth rate for the mode mu in [s-1].</p>
+</dd>
+</dl>
+<p>[1] : Eq. 51 p139 of Akai, Kazunori. “RF System for Electron Storage 
+Rings.” Physics And Engineering Of High Performance Electron Storage Rings 
+And Application Of Superconducting Technology. 2002. 118-149.</p>
+</dd></dl>
+
+<dl class="py function">
+<dt class="sig sig-object py" id="mbtrack2.instability.instabilities.lcbi_stability_diagram">
+<span class="sig-prename descclassname"><span class="pre">mbtrack2.instability.instabilities.</span></span><span class="sig-name descname"><span class="pre">lcbi_stability_diagram</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">ring</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">I</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">M</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">modes</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">cavity_list</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">detune_range</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">synchrotron_tune</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">Vrf</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/instability/instabilities.html#lcbi_stability_diagram"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.instability.instabilities.lcbi_stability_diagram" title="Permalink to this definition">¶</a></dt>
+<dd><p>Plot longitudinal coupled bunch instability stability diagram for a 
+arbitrary list of CavityResonator objects around a detuning range.</p>
+<p>Last object in the cavity_list is assumed to be the one with the variable 
+detuning.</p>
+<dl class="simple">
+<dt>ring<span class="classifier">Synchrotron object</span></dt><dd><p>Ring parameters.</p>
+</dd>
+<dt>I<span class="classifier">float</span></dt><dd><p>Total beam current in [A].</p>
+</dd>
+<dt>M<span class="classifier">int</span></dt><dd><p>Nomber of bunches in the beam.</p>
+</dd>
+<dt>modes<span class="classifier">list</span></dt><dd><p>Coupled bunch mode numbers to consider.</p>
+</dd>
+<dt>cavity_list<span class="classifier">list</span></dt><dd><dl class="simple">
+<dt>List of CavityResonator objects to consider, which can be:</dt><dd><ul class="simple">
+<li><p>active cavities</p></li>
+<li><p>passive cavities</p></li>
+<li><p>HOMs</p></li>
+<li><p>mode dampers</p></li>
+</ul>
+</dd>
+</dl>
+</dd>
+<dt>detune_range<span class="classifier">array</span></dt><dd><p>Detuning range (list of points) of the last CavityResonator object.</p>
+</dd>
+<dt>synchrotron_tune<span class="classifier">float, optional</span></dt><dd><p>Synchrotron tune.</p>
+</dd>
+<dt>Vrf<span class="classifier">float, optinal</span></dt><dd><p>Total RF voltage in [V] used to compute synchrotron tune if not given.</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>fig<span class="classifier">Figure</span></dt><dd><p>Show the shunt impedance threshold for different coupled bunch modes.</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py function">
+<dt class="sig sig-object py" id="mbtrack2.instability.instabilities.mbi_threshold">
+<span class="sig-prename descclassname"><span class="pre">mbtrack2.instability.instabilities.</span></span><span class="sig-name descname"><span class="pre">mbi_threshold</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">ring</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">sigma</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">R</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">b</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/instability/instabilities.html#mbi_threshold"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.instability.instabilities.mbi_threshold" title="Permalink to this definition">¶</a></dt>
+<dd><p>Compute the microbunching instability (MBI) threshold for a bunched beam
+considering the steady-state parallel plate model [1][2].</p>
+<p>ring : Synchrotron object
+sigma : float</p>
+<blockquote>
+<div><p>RMS bunch length in [s]</p>
+</div></blockquote>
+<dl class="simple">
+<dt>R<span class="classifier">float</span></dt><dd><p>dipole bending radius in [m]</p>
+</dd>
+<dt>b<span class="classifier">float</span></dt><dd><p>vertical distance between the conducting parallel plates in [m]</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>I<span class="classifier">float</span></dt><dd><p>MBI current threshold in [A]</p>
+</dd>
+</dl>
+<p>[1] : Y. Cai, “Theory of microwave instability and coherent synchrotron 
+radiation in electron storage rings”, SLAC-PUB-14561
+[2] : D. Zhou, “Coherent synchrotron radiation and microwave instability in 
+electron storage rings”, PhD thesis, p112</p>
+</dd></dl>
+
+<dl class="py function">
+<dt class="sig sig-object py" id="mbtrack2.instability.instabilities.rwmbi_growth_rate">
+<span class="sig-prename descclassname"><span class="pre">mbtrack2.instability.instabilities.</span></span><span class="sig-name descname"><span class="pre">rwmbi_growth_rate</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">ring</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">current</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">beff</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">rho_material</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">plane</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'x'</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/instability/instabilities.html#rwmbi_growth_rate"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.instability.instabilities.rwmbi_growth_rate" title="Permalink to this definition">¶</a></dt>
+<dd><p>Compute the growth rate of the transverse coupled-bunch instability induced
+by resistive wall impedance [1].</p>
+<p>ring : Synchrotron object
+current : float</p>
+<blockquote>
+<div><p>Total beam current in [A].</p>
+</div></blockquote>
+<dl class="simple">
+<dt>beff<span class="classifier">float</span></dt><dd><p>Effective radius of the vacuum chamber in [m].</p>
+</dd>
+<dt>rho_material<span class="classifier">float</span></dt><dd><p>Resistivity of the chamber’s wall material in [Ohm.m].</p>
+</dd>
+<dt>plane<span class="classifier">str, optional</span></dt><dd><p>The plane in which the instability will be computed. Use ‘x’ for the 
+horizontal plane, and ‘y’ for the vertical.</p>
+</dd>
+</dl>
+<p>[1] Eq. (31) in R. Nagaoka and K. L. F. Bane, “Collective effects in a
+diffraction-limited storage ring”, J. Synchrotron Rad. Vol 21, 2014. pp.937-960</p>
+</dd></dl>
+
+<dl class="py function">
+<dt class="sig sig-object py" id="mbtrack2.instability.instabilities.rwmbi_threshold">
+<span class="sig-prename descclassname"><span class="pre">mbtrack2.instability.instabilities.</span></span><span class="sig-name descname"><span class="pre">rwmbi_threshold</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">ring</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">beff</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">rho_material</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">plane</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'x'</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/instability/instabilities.html#rwmbi_threshold"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.instability.instabilities.rwmbi_threshold" title="Permalink to this definition">¶</a></dt>
+<dd><p>Compute the threshold current of the transverse coupled-bunch instability 
+induced by resistive wall impedance [1].</p>
+<p>ring : Synchrotron object
+beff : float</p>
+<blockquote>
+<div><p>Effective radius of the vacuum chamber in [m].</p>
+</div></blockquote>
+<dl class="simple">
+<dt>rho_material<span class="classifier">float</span></dt><dd><p>Resistivity of the chamber’s wall material in [Ohm.m].</p>
+</dd>
+<dt>plane<span class="classifier">str, optional</span></dt><dd><p>The plane in which the instability will be computed. Use ‘x’ for the 
+horizontal plane, and ‘y’ for the vertical.</p>
+</dd>
+</dl>
+<p>[1] Eq. (32) in R. Nagaoka and K. L. F. Bane, “Collective effects in a
+diffraction-limited storage ring”, J. Synchrotron Rad. Vol 21, 2014. pp.937-960</p>
+</dd></dl>
+
+</section>
+<section id="module-mbtrack2.instability.ions">
+<span id="mbtrack2-instability-ions-module"></span><h2>mbtrack2.instability.ions module<a class="headerlink" href="#module-mbtrack2.instability.ions" title="Permalink to this heading">¶</a></h2>
+<p>Various calculations about ion trapping and instabilities in electron storage 
+rings.</p>
+<dl class="py function">
+<dt class="sig sig-object py" id="mbtrack2.instability.ions.fast_beam_ion">
+<span class="sig-prename descclassname"><span class="pre">mbtrack2.instability.ions.</span></span><span class="sig-name descname"><span class="pre">fast_beam_ion</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">ring</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">Nb</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">nb</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">Lsep</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">sigmax</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">sigmay</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">P</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">T</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">beta</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">model</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'linear'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">delta_omega</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">ion</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'CO'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">dim</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'y'</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/instability/ions.html#fast_beam_ion"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.instability.ions.fast_beam_ion" title="Permalink to this definition">¶</a></dt>
+<dd><p>Compute fast beam ion instability rise time [1].</p>
+<p>Warning ! 
+If model=”linear”, the rise time is an assymptotic grow time 
+(i.e. y ~ exp(sqrt(t/tau))) [1].
+If model=”decoherence”, the rise time is an e-folding time 
+(i.e. y ~ exp(t/tau)) [2].
+If model=”non-linear”, the rise time is a linear growth time
+(i.e. y ~ t/tau) [3].</p>
+<dl class="simple">
+<dt>The linear model assumes that [1]:</dt><dd><p>x,y &lt;&lt; sigmax,sigmay</p>
+</dd>
+<dt>The decoherence model assumes that [2]:</dt><dd><p>Lsep &lt;&lt; c / (2 * pi * ion_frequency) 
+Lsep &lt;&lt; c / (2 * pi * betatron_frequency)</p>
+</dd>
+<dt>The non-linear model assumes that [3]:</dt><dd><p>x,y &gt;&gt; sigmax,sigmay</p>
+</dd>
+</dl>
+<p>ring : Synchrotron object
+Nb : float</p>
+<blockquote>
+<div><p>Number of electron per bunch.</p>
+</div></blockquote>
+<dl class="simple">
+<dt>nb<span class="classifier">float</span></dt><dd><p>Number of bunches.</p>
+</dd>
+<dt>Lsep<span class="classifier">float</span></dt><dd><p>Bunch spacing in [m].</p>
+</dd>
+<dt>sigmax<span class="classifier">float</span></dt><dd><p>Horizontal beam size in [m].</p>
+</dd>
+<dt>sigmay<span class="classifier">float</span></dt><dd><p>Vertical beam size in [m].</p>
+</dd>
+<dt>P<span class="classifier">float</span></dt><dd><p>Partial pressure of the molecular ion in [Pa].</p>
+</dd>
+<dt>T<span class="classifier">float</span></dt><dd><p>Tempertature in [K].</p>
+</dd>
+<dt>beta<span class="classifier">float</span></dt><dd><p>Average betatron function around the ring in [m].</p>
+</dd>
+<dt>model<span class="classifier">str, optional</span></dt><dd><p>If “linear”, use [1].
+If “decoherence”, use [2].
+If “non-linear”, use [3].</p>
+</dd>
+<dt>delta_omega<span class="classifier">float, optional</span></dt><dd><p>RMS variation of the ion oscillation angular frequnecy around the ring
+in [Hz].</p>
+</dd>
+<dt>ion<span class="classifier">str, optional</span></dt><dd><p>Ion type. The default is “CO”.</p>
+</dd>
+<dt>dim<span class="classifier">“y” o “x”, optional</span></dt><dd><p>Dimension to consider. The default is “y”.</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>tau<span class="classifier">float</span></dt><dd><p>Instability rise time in [s].</p>
+</dd>
+</dl>
+<p>[1] : T. O. Raubenheimer and F. Zimmermann, “Fast beam-ion instability. I. 
+linear theory and simulations”, Physical Review E 52 (1995).
+[2] : G. V. Stupakov, T. O. Raubenheimer, and F. Zimmermann, “Fast beam-ion 
+instability. II. effect of ion decoherence”, Physical Review E 52 (1995).
+[3] : Chao, A. W., &amp; Mess, K. H. (Eds.). (2013). Handbook of accelerator 
+physics and engineering. World scientific. 3rd Printing. p417.</p>
+</dd></dl>
+
+<dl class="py function">
+<dt class="sig sig-object py" id="mbtrack2.instability.ions.ion_cross_section">
+<span class="sig-prename descclassname"><span class="pre">mbtrack2.instability.ions.</span></span><span class="sig-name descname"><span class="pre">ion_cross_section</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">ring</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">ion</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/instability/ions.html#ion_cross_section"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.instability.ions.ion_cross_section" title="Permalink to this definition">¶</a></dt>
+<dd><p>Compute the collisional ionization cross section.</p>
+<p>Compute the inelastic collision cross section between a molecule or an atom
+by a relativistic electron using the relativistic Bethe asymptotic formula 
+[1].</p>
+<p>Values of M02 and C02 from [2].</p>
+<p>ring : Synchrotron object
+ion : str</p>
+<blockquote>
+<div><p>Ion type.</p>
+</div></blockquote>
+<dl class="simple">
+<dt>sigma<span class="classifier">float</span></dt><dd><p>Cross section in [m**2].</p>
+</dd>
+</dl>
+<p>[1] : M. Inokuti, “Inelastic collisions of fast charged particles with 
+atoms and molecules-the bethe theory revisited”, Reviews of modern physics 
+43 (1971).
+[2] : P. F. Tavares, “Bremsstrahlung detection of ions trapped in the EPA 
+electron beam”, Part. Accel. 43 (1993).</p>
+</dd></dl>
+
+<dl class="py function">
+<dt class="sig sig-object py" id="mbtrack2.instability.ions.ion_frequency">
+<span class="sig-prename descclassname"><span class="pre">mbtrack2.instability.ions.</span></span><span class="sig-name descname"><span class="pre">ion_frequency</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">N</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">Lsep</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">sigmax</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">sigmay</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">ion</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'CO'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">dim</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'y'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">express</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'coupling'</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/instability/ions.html#ion_frequency"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.instability.ions.ion_frequency" title="Permalink to this definition">¶</a></dt>
+<dd><p>Compute the ion oscillation frequnecy.</p>
+<dl class="simple">
+<dt>N<span class="classifier">float</span></dt><dd><p>Number of electrons per bunch.</p>
+</dd>
+<dt>Lsep<span class="classifier">float</span></dt><dd><p>Bunch spacing in [m].</p>
+</dd>
+<dt>sigmax<span class="classifier">float or array</span></dt><dd><p>Horizontal beam size in [m].</p>
+</dd>
+<dt>sigmay<span class="classifier">float or array</span></dt><dd><p>Vertical beam size in [m].</p>
+</dd>
+<dt>ion<span class="classifier">str, optional</span></dt><dd><p>Ion type. The default is “CO”.</p>
+</dd>
+<dt>dim<span class="classifier">“y” o “x”, optional</span></dt><dd><p>Dimension to consider. The default is “y”.</p>
+</dd>
+<dt>express<span class="classifier">str, optional</span></dt><dd><p>Expression to use to compute the ion oscillation frequency. 
+The default is “coupling” corresponding to Gaussian electron and ion 
+distributions with coupling [1].
+Also possible is “no_coupling” corresponding to Gaussian electron and 
+ion distributions without coupling [2].</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>f<span class="classifier">float or array</span></dt><dd><p>Ion oscillation frequencies in [Hz].</p>
+</dd>
+</dl>
+<p>[1] : T. O. Raubenheimer and F. Zimmermann, “Fast beam-ion instability. I. 
+linear theory and simulations”, Physical Review E 52 (1995).
+[2] : G. V. Stupakov, T. O. Raubenheimer, and F. Zimmermann, “Fast beam-ion 
+instability. II. effect of ion decoherence”, Physical Review E 52 (1995).</p>
+</dd></dl>
+
+<dl class="py function">
+<dt class="sig sig-object py" id="mbtrack2.instability.ions.plot_critical_mass">
+<span class="sig-prename descclassname"><span class="pre">mbtrack2.instability.ions.</span></span><span class="sig-name descname"><span class="pre">plot_critical_mass</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">ring</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">bunch_charge</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">bunch_spacing</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">n_points</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">10000.0</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/instability/ions.html#plot_critical_mass"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.instability.ions.plot_critical_mass" title="Permalink to this definition">¶</a></dt>
+<dd><p>Plot ion critical mass, using Eq. (7.70) p147 of [1]</p>
+<p>ring : Synchrotron object
+bunch_charge : float</p>
+<blockquote>
+<div><p>Bunch charge in [C].</p>
+</div></blockquote>
+<dl class="simple">
+<dt>bunch_spacing<span class="classifier">float</span></dt><dd><p>Time in between two adjacent bunches in [s].</p>
+</dd>
+<dt>n_points<span class="classifier">float or int, optional</span></dt><dd><p>Number of point used in the plot. The default is 1e4.</p>
+</dd>
+</dl>
+<p>fig : figure</p>
+<p>[1] : Gamelin, A. (2018). Collective effects in a transient microbunching 
+regime and ion cloud mitigation in ThomX (Doctoral dissertation, 
+Université Paris-Saclay).</p>
+</dd></dl>
+
+</section>
+<section id="module-mbtrack2.instability">
+<span id="module-contents"></span><h2>Module contents<a class="headerlink" href="#module-mbtrack2.instability" title="Permalink to this heading">¶</a></h2>
+</section>
+</section>
+
+
+            <div class="clearer"></div>
+          </div>
+        </div>
+      </div>
+      <div class="sphinxsidebar" role="navigation" aria-label="main navigation">
+        <div class="sphinxsidebarwrapper">
+  <div>
+    <h3><a href="index.html">Table of Contents</a></h3>
+    <ul>
+<li><a class="reference internal" href="#">mbtrack2.instability package</a><ul>
+<li><a class="reference internal" href="#submodules">Submodules</a></li>
+<li><a class="reference internal" href="#module-mbtrack2.instability.instabilities">mbtrack2.instability.instabilities module</a></li>
+<li><a class="reference internal" href="#module-mbtrack2.instability.ions">mbtrack2.instability.ions module</a></li>
+<li><a class="reference internal" href="#module-mbtrack2.instability">Module contents</a></li>
+</ul>
+</li>
+</ul>
+
+  </div>
+  <div role="note" aria-label="source link">
+    <h3>This Page</h3>
+    <ul class="this-page-menu">
+      <li><a href="_sources/mbtrack2.instability.rst.txt"
+            rel="nofollow">Show Source</a></li>
+    </ul>
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+    </form>
+    </div>
+</div>
+<script>document.getElementById('searchbox').style.display = "block"</script>
+        </div>
+      </div>
+      <div class="clearer"></div>
+    </div>
+    <div class="related" role="navigation" aria-label="related navigation">
+      <h3>Navigation</h3>
+      <ul>
+        <li class="right" style="margin-right: 10px">
+          <a href="genindex.html" title="General Index"
+             >index</a></li>
+        <li class="right" >
+          <a href="py-modindex.html" title="Python Module Index"
+             >modules</a> |</li>
+        <li class="nav-item nav-item-0"><a href="index.html">mbtrack2 0.6.0 documentation</a> &#187;</li>
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\ No newline at end of file
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new file mode 100644
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+
+<!DOCTYPE html>
+
+<html lang="en">
+  <head>
+    <meta charset="utf-8" />
+    <meta name="viewport" content="width=device-width, initial-scale=1.0" /><meta name="generator" content="Docutils 0.18.1: http://docutils.sourceforge.net/" />
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+    <title>mbtrack2.tracking package &#8212; mbtrack2 0.6.0 documentation</title>
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+             >modules</a> |</li>
+        <li class="nav-item nav-item-0"><a href="index.html">mbtrack2 0.6.0 documentation</a> &#187;</li>
+        <li class="nav-item nav-item-this"><a href="">mbtrack2.tracking package</a></li> 
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+    <div class="document">
+      <div class="documentwrapper">
+        <div class="bodywrapper">
+          <div class="body" role="main">
+            
+  <section id="mbtrack2-tracking-package">
+<h1>mbtrack2.tracking package<a class="headerlink" href="#mbtrack2-tracking-package" title="Permalink to this heading">¶</a></h1>
+<section id="subpackages">
+<h2>Subpackages<a class="headerlink" href="#subpackages" title="Permalink to this heading">¶</a></h2>
+<div class="toctree-wrapper compound">
+<ul>
+<li class="toctree-l1"><a class="reference internal" href="mbtrack2.tracking.monitors.html">mbtrack2.tracking.monitors package</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="mbtrack2.tracking.monitors.html#submodules">Submodules</a></li>
+<li class="toctree-l2"><a class="reference internal" href="mbtrack2.tracking.monitors.html#module-mbtrack2.tracking.monitors.monitors">mbtrack2.tracking.monitors.monitors module</a></li>
+<li class="toctree-l2"><a class="reference internal" href="mbtrack2.tracking.monitors.html#module-mbtrack2.tracking.monitors.plotting">mbtrack2.tracking.monitors.plotting module</a></li>
+<li class="toctree-l2"><a class="reference internal" href="mbtrack2.tracking.monitors.html#module-mbtrack2.tracking.monitors.tools">mbtrack2.tracking.monitors.tools module</a></li>
+<li class="toctree-l2"><a class="reference internal" href="mbtrack2.tracking.monitors.html#module-mbtrack2.tracking.monitors">Module contents</a></li>
+</ul>
+</li>
+</ul>
+</div>
+</section>
+<section id="submodules">
+<h2>Submodules<a class="headerlink" href="#submodules" title="Permalink to this heading">¶</a></h2>
+</section>
+<section id="module-mbtrack2.tracking.aperture">
+<span id="mbtrack2-tracking-aperture-module"></span><h2>mbtrack2.tracking.aperture module<a class="headerlink" href="#module-mbtrack2.tracking.aperture" title="Permalink to this heading">¶</a></h2>
+<p>This module defines aperture elements for tracking.</p>
+<dl class="py class">
+<dt class="sig sig-object py" id="mbtrack2.tracking.aperture.CircularAperture">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">mbtrack2.tracking.aperture.</span></span><span class="sig-name descname"><span class="pre">CircularAperture</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">radius</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/aperture.html#CircularAperture"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.aperture.CircularAperture" title="Permalink to this definition">¶</a></dt>
+<dd><p>Bases: <a class="reference internal" href="#mbtrack2.tracking.element.Element" title="mbtrack2.tracking.element.Element"><code class="xref py py-class docutils literal notranslate"><span class="pre">Element</span></code></a></p>
+<p>Circular aperture element. The particles which are outside of the circle 
+are ‘lost’ and not used in the tracking any more.</p>
+<dl class="simple">
+<dt>radius<span class="classifier">float</span></dt><dd><p>radius of the circle in [m]</p>
+</dd>
+</dl>
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.aperture.CircularAperture.track">
+<span class="sig-name descname"><span class="pre">track</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">bunch</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/aperture.html#CircularAperture.track"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.aperture.CircularAperture.track" title="Permalink to this definition">¶</a></dt>
+<dd><p>Tracking method for the element.
+No bunch to bunch interaction, so written for Bunch objects and
+&#64;Element.parallel is used to handle Beam objects.</p>
+<p>bunch : Bunch or Beam object</p>
+</dd></dl>
+
+</dd></dl>
+
+<dl class="py class">
+<dt class="sig sig-object py" id="mbtrack2.tracking.aperture.ElipticalAperture">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">mbtrack2.tracking.aperture.</span></span><span class="sig-name descname"><span class="pre">ElipticalAperture</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">X_radius</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">Y_radius</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/aperture.html#ElipticalAperture"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.aperture.ElipticalAperture" title="Permalink to this definition">¶</a></dt>
+<dd><p>Bases: <a class="reference internal" href="#mbtrack2.tracking.element.Element" title="mbtrack2.tracking.element.Element"><code class="xref py py-class docutils literal notranslate"><span class="pre">Element</span></code></a></p>
+<p>Eliptical aperture element. The particles which are outside of the elipse 
+are ‘lost’ and not used in the tracking any more.</p>
+<dl class="simple">
+<dt>X_radius<span class="classifier">float</span></dt><dd><p>horizontal radius of the elipse in [m]</p>
+</dd>
+<dt>Y_radius<span class="classifier">float</span></dt><dd><p>vertical radius of the elipse in [m]</p>
+</dd>
+</dl>
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.aperture.ElipticalAperture.track">
+<span class="sig-name descname"><span class="pre">track</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">bunch</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/aperture.html#ElipticalAperture.track"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.aperture.ElipticalAperture.track" title="Permalink to this definition">¶</a></dt>
+<dd><p>Tracking method for the element.
+No bunch to bunch interaction, so written for Bunch objects and
+&#64;Element.parallel is used to handle Beam objects.</p>
+<p>bunch : Bunch or Beam object</p>
+</dd></dl>
+
+</dd></dl>
+
+<dl class="py class">
+<dt class="sig sig-object py" id="mbtrack2.tracking.aperture.LongitudinalAperture">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">mbtrack2.tracking.aperture.</span></span><span class="sig-name descname"><span class="pre">LongitudinalAperture</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">tau_up</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">tau_low</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/aperture.html#LongitudinalAperture"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.aperture.LongitudinalAperture" title="Permalink to this definition">¶</a></dt>
+<dd><p>Bases: <a class="reference internal" href="#mbtrack2.tracking.element.Element" title="mbtrack2.tracking.element.Element"><code class="xref py py-class docutils literal notranslate"><span class="pre">Element</span></code></a></p>
+<p>Longitudinal aperture element. The particles which are outside of the 
+longitudinal bounds are ‘lost’ and not used in the tracking any more.</p>
+<p>ring : Synchrotron object
+tau_up : float</p>
+<blockquote>
+<div><p>Upper longitudinal bound in [s].</p>
+</div></blockquote>
+<dl class="simple">
+<dt>tau_low<span class="classifier">float, optional</span></dt><dd><p>Lower longitudinal bound in [s].</p>
+</dd>
+</dl>
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.aperture.LongitudinalAperture.track">
+<span class="sig-name descname"><span class="pre">track</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">bunch</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/aperture.html#LongitudinalAperture.track"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.aperture.LongitudinalAperture.track" title="Permalink to this definition">¶</a></dt>
+<dd><p>Tracking method for the element.
+No bunch to bunch interaction, so written for Bunch objects and
+&#64;Element.parallel is used to handle Beam objects.</p>
+<p>bunch : Bunch or Beam object</p>
+</dd></dl>
+
+</dd></dl>
+
+<dl class="py class">
+<dt class="sig sig-object py" id="mbtrack2.tracking.aperture.RectangularAperture">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">mbtrack2.tracking.aperture.</span></span><span class="sig-name descname"><span class="pre">RectangularAperture</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">X_right</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">Y_top</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">X_left</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">Y_bottom</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/aperture.html#RectangularAperture"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.aperture.RectangularAperture" title="Permalink to this definition">¶</a></dt>
+<dd><p>Bases: <a class="reference internal" href="#mbtrack2.tracking.element.Element" title="mbtrack2.tracking.element.Element"><code class="xref py py-class docutils literal notranslate"><span class="pre">Element</span></code></a></p>
+<p>Rectangular aperture element. The particles which are outside of the 
+rectangle are ‘lost’ and not used in the tracking any more.</p>
+<dl class="simple">
+<dt>X_right<span class="classifier">float</span></dt><dd><p>right horizontal aperture of the rectangle in [m]</p>
+</dd>
+<dt>Y_top<span class="classifier">float</span></dt><dd><p>top vertical aperture of the rectangle in [m]</p>
+</dd>
+<dt>X_left<span class="classifier">float, optional</span></dt><dd><p>left horizontal aperture of the rectangle in [m]</p>
+</dd>
+<dt>Y_bottom<span class="classifier">float, optional</span></dt><dd><p>bottom vertical aperture of the rectangle in [m]</p>
+</dd>
+</dl>
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.aperture.RectangularAperture.track">
+<span class="sig-name descname"><span class="pre">track</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">bunch</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/aperture.html#RectangularAperture.track"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.aperture.RectangularAperture.track" title="Permalink to this definition">¶</a></dt>
+<dd><p>Tracking method for the element.
+No bunch to bunch interaction, so written for Bunch objects and
+&#64;Element.parallel is used to handle Beam objects.</p>
+<p>bunch : Bunch or Beam object</p>
+</dd></dl>
+
+</dd></dl>
+
+</section>
+<section id="module-mbtrack2.tracking.element">
+<span id="mbtrack2-tracking-element-module"></span><h2>mbtrack2.tracking.element module<a class="headerlink" href="#module-mbtrack2.tracking.element" title="Permalink to this heading">¶</a></h2>
+<p>This module defines the most basic elements for tracking, including Element,
+an abstract base class which is to be used as mother class to every elements
+included in the tracking.</p>
+<dl class="py class">
+<dt class="sig sig-object py" id="mbtrack2.tracking.element.Element">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">mbtrack2.tracking.element.</span></span><span class="sig-name descname"><span class="pre">Element</span></span><a class="reference internal" href="_modules/mbtrack2/tracking/element.html#Element"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.element.Element" title="Permalink to this definition">¶</a></dt>
+<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">object</span></code></p>
+<p>Abstract Element class used for subclass inheritance to define all kinds 
+of objects which intervene in the tracking.</p>
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.element.Element.parallel">
+<em class="property"><span class="pre">static</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">parallel</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">track</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/element.html#Element.parallel"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.element.Element.parallel" title="Permalink to this definition">¶</a></dt>
+<dd><p>Defines the decorator &#64;parallel which handle the embarrassingly 
+parallel case which happens when there is no bunch to bunch 
+interaction in the tracking routine.</p>
+<p>Adding &#64;Element.parallel allows to write the track method of the 
+Element subclass for a Bunch object instead of a Beam object.</p>
+<dl class="simple">
+<dt>track<span class="classifier">function, method of an Element subclass</span></dt><dd><p>track method of an Element subclass which takes a Bunch object as
+input</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>track_wrapper: function, method of an Element subclass</dt><dd><p>track method of an Element subclass which takes a Beam object or a
+Bunch object as input</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.element.Element.track">
+<em class="property"><span class="pre">abstract</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">track</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">beam</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/element.html#Element.track"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.element.Element.track" title="Permalink to this definition">¶</a></dt>
+<dd><p>Track a beam object through this Element.
+This method needs to be overloaded in each Element subclass.</p>
+<p>beam : Beam object</p>
+</dd></dl>
+
+</dd></dl>
+
+<dl class="py class">
+<dt class="sig sig-object py" id="mbtrack2.tracking.element.LongitudinalMap">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">mbtrack2.tracking.element.</span></span><span class="sig-name descname"><span class="pre">LongitudinalMap</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">ring</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/element.html#LongitudinalMap"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.element.LongitudinalMap" title="Permalink to this definition">¶</a></dt>
+<dd><p>Bases: <a class="reference internal" href="#mbtrack2.tracking.element.Element" title="mbtrack2.tracking.element.Element"><code class="xref py py-class docutils literal notranslate"><span class="pre">Element</span></code></a></p>
+<p>Longitudinal map for a single turn in the synchrotron.</p>
+<p>ring : Synchrotron object</p>
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.element.LongitudinalMap.track">
+<span class="sig-name descname"><span class="pre">track</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">bunch</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/element.html#LongitudinalMap.track"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.element.LongitudinalMap.track" title="Permalink to this definition">¶</a></dt>
+<dd><p>Tracking method for the element.
+No bunch to bunch interaction, so written for Bunch objects and
+&#64;Element.parallel is used to handle Beam objects.</p>
+<p>bunch : Bunch or Beam object</p>
+</dd></dl>
+
+</dd></dl>
+
+<dl class="py class">
+<dt class="sig sig-object py" id="mbtrack2.tracking.element.SkewQuadrupole">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">mbtrack2.tracking.element.</span></span><span class="sig-name descname"><span class="pre">SkewQuadrupole</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">strength</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/element.html#SkewQuadrupole"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.element.SkewQuadrupole" title="Permalink to this definition">¶</a></dt>
+<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">object</span></code></p>
+<p>Thin skew quadrupole element used to introduce betatron coupling (the 
+length of the quadrupole is neglected).</p>
+<dl class="simple">
+<dt>strength<span class="classifier">float</span></dt><dd><p>Integrated strength of the skew quadrupole [m].</p>
+</dd>
+</dl>
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.element.SkewQuadrupole.track">
+<span class="sig-name descname"><span class="pre">track</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">bunch</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/element.html#SkewQuadrupole.track"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.element.SkewQuadrupole.track" title="Permalink to this definition">¶</a></dt>
+<dd><p>Tracking method for the element.
+No bunch to bunch interaction, so written for Bunch objects and
+&#64;Element.parallel is used to handle Beam objects.</p>
+<p>bunch : Bunch or Beam object</p>
+</dd></dl>
+
+</dd></dl>
+
+<dl class="py class">
+<dt class="sig sig-object py" id="mbtrack2.tracking.element.SynchrotronRadiation">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">mbtrack2.tracking.element.</span></span><span class="sig-name descname"><span class="pre">SynchrotronRadiation</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">ring</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">switch</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">array([True,</span> <span class="pre">True,</span> <span class="pre">True])</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/element.html#SynchrotronRadiation"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.element.SynchrotronRadiation" title="Permalink to this definition">¶</a></dt>
+<dd><p>Bases: <a class="reference internal" href="#mbtrack2.tracking.element.Element" title="mbtrack2.tracking.element.Element"><code class="xref py py-class docutils literal notranslate"><span class="pre">Element</span></code></a></p>
+<p>Element to handle synchrotron radiation, radiation damping and quantum 
+excitation, for a single turn in the synchrotron.</p>
+<p>ring : Synchrotron object
+switch : bool array of shape (3,), optional</p>
+<blockquote>
+<div><p>allow to choose on which plane the synchrotron radiation is active</p>
+</div></blockquote>
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.element.SynchrotronRadiation.track">
+<span class="sig-name descname"><span class="pre">track</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">bunch</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/element.html#SynchrotronRadiation.track"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.element.SynchrotronRadiation.track" title="Permalink to this definition">¶</a></dt>
+<dd><p>Tracking method for the element.
+No bunch to bunch interaction, so written for Bunch objects and
+&#64;Element.parallel is used to handle Beam objects.</p>
+<p>bunch : Bunch or Beam object</p>
+</dd></dl>
+
+</dd></dl>
+
+<dl class="py class">
+<dt class="sig sig-object py" id="mbtrack2.tracking.element.TransverseMap">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">mbtrack2.tracking.element.</span></span><span class="sig-name descname"><span class="pre">TransverseMap</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">ring</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/element.html#TransverseMap"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.element.TransverseMap" title="Permalink to this definition">¶</a></dt>
+<dd><p>Bases: <a class="reference internal" href="#mbtrack2.tracking.element.Element" title="mbtrack2.tracking.element.Element"><code class="xref py py-class docutils literal notranslate"><span class="pre">Element</span></code></a></p>
+<p>Transverse map for a single turn in the synchrotron.</p>
+<p>ring : Synchrotron object</p>
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.element.TransverseMap.track">
+<span class="sig-name descname"><span class="pre">track</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">bunch</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/element.html#TransverseMap.track"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.element.TransverseMap.track" title="Permalink to this definition">¶</a></dt>
+<dd><p>Tracking method for the element.
+No bunch to bunch interaction, so written for Bunch objects and
+&#64;Element.parallel is used to handle Beam objects.</p>
+<p>bunch : Bunch or Beam object</p>
+</dd></dl>
+
+</dd></dl>
+
+<dl class="py class">
+<dt class="sig sig-object py" id="mbtrack2.tracking.element.TransverseMapSector">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">mbtrack2.tracking.element.</span></span><span class="sig-name descname"><span class="pre">TransverseMapSector</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">ring</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">alpha0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">beta0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">dispersion0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">alpha1</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">beta1</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">dispersion1</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">phase_diff</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">chro_diff</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">adts</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/element.html#TransverseMapSector"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.element.TransverseMapSector" title="Permalink to this definition">¶</a></dt>
+<dd><p>Bases: <a class="reference internal" href="#mbtrack2.tracking.element.Element" title="mbtrack2.tracking.element.Element"><code class="xref py py-class docutils literal notranslate"><span class="pre">Element</span></code></a></p>
+<p>Transverse map for a sector of the synchrotron, from an initial 
+position s0 to a final position s1.</p>
+<dl class="simple">
+<dt>ring<span class="classifier">Synchrotron object</span></dt><dd><p>Ring parameters.</p>
+</dd>
+<dt>alpha0<span class="classifier">array of shape (2,)</span></dt><dd><p>Alpha Twiss function at the initial location of the sector.</p>
+</dd>
+<dt>beta0<span class="classifier">array of shape (2,)</span></dt><dd><p>Beta Twiss function at the initial location of the sector.</p>
+</dd>
+<dt>dispersion0<span class="classifier">array of shape (4,)</span></dt><dd><p>Dispersion function at the initial location of the sector.</p>
+</dd>
+<dt>alpha1<span class="classifier">array of shape (2,)</span></dt><dd><p>Alpha Twiss function at the final location of the sector.</p>
+</dd>
+<dt>beta1<span class="classifier">array of shape (2,)</span></dt><dd><p>Beta Twiss function at the final location of the sector.</p>
+</dd>
+<dt>dispersion1<span class="classifier">array of shape (4,)</span></dt><dd><p>Dispersion function at the final location of the sector.</p>
+</dd>
+<dt>phase_diff<span class="classifier">array of shape (2,)</span></dt><dd><p>Phase difference between the initial and final location of the 
+sector.</p>
+</dd>
+<dt>chro_diff<span class="classifier">array of shape (2,)</span></dt><dd><p>Chromaticity difference between the initial and final location of 
+the sector.</p>
+</dd>
+<dt>adts<span class="classifier">array of shape (4,), optional</span></dt><dd><p>Amplitude-dependent tune shift of the sector, see Synchrotron class 
+for details. The default is None.</p>
+</dd>
+</dl>
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.element.TransverseMapSector.track">
+<span class="sig-name descname"><span class="pre">track</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">bunch</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/element.html#TransverseMapSector.track"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.element.TransverseMapSector.track" title="Permalink to this definition">¶</a></dt>
+<dd><p>Tracking method for the element.
+No bunch to bunch interaction, so written for Bunch objects and
+&#64;Element.parallel is used to handle Beam objects.</p>
+<p>bunch : Bunch or Beam object</p>
+</dd></dl>
+
+</dd></dl>
+
+<dl class="py function">
+<dt class="sig sig-object py" id="mbtrack2.tracking.element.transverse_map_sector_generator">
+<span class="sig-prename descclassname"><span class="pre">mbtrack2.tracking.element.</span></span><span class="sig-name descname"><span class="pre">transverse_map_sector_generator</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">ring</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">positions</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/element.html#transverse_map_sector_generator"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.element.transverse_map_sector_generator" title="Permalink to this definition">¶</a></dt>
+<dd><p>Convenience function which generate a list of TransverseMapSector elements
+from a ring with an AT lattice.</p>
+<p>Tracking through all the sectors is equivalent to a full turn (and thus to 
+the TransverseMap object).</p>
+<dl class="simple">
+<dt>ring<span class="classifier">Synchrotron object</span></dt><dd><p>Ring parameters, must .</p>
+</dd>
+<dt>positions<span class="classifier">array</span></dt><dd><p>List of longitudinal positions in [m] to use as starting and end points
+of the TransverseMapSector elements.
+The array should contain the initial position (s=0) but not the end 
+position (s=ring.L), so like position = np.array([0, pos1, pos2, …]).</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>sectors<span class="classifier">list</span></dt><dd><p>List of TransverseMapSector elements.</p>
+</dd>
+</dl>
+</dd></dl>
+
+</section>
+<section id="module-mbtrack2.tracking.feedback">
+<span id="mbtrack2-tracking-feedback-module"></span><h2>mbtrack2.tracking.feedback module<a class="headerlink" href="#module-mbtrack2.tracking.feedback" title="Permalink to this heading">¶</a></h2>
+<p>This module defines both exponential and FIR based bunch by bunch damper 
+feedback for tracking.</p>
+<dl class="py class">
+<dt class="sig sig-object py" id="mbtrack2.tracking.feedback.ExponentialDamper">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">mbtrack2.tracking.feedback.</span></span><span class="sig-name descname"><span class="pre">ExponentialDamper</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">ring</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">plane</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">damping_time</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">phase_diff</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/feedback.html#ExponentialDamper"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.feedback.ExponentialDamper" title="Permalink to this definition">¶</a></dt>
+<dd><p>Bases: <a class="reference internal" href="#mbtrack2.tracking.element.Element" title="mbtrack2.tracking.element.Element"><code class="xref py py-class docutils literal notranslate"><span class="pre">Element</span></code></a></p>
+<p>Simple bunch by bunch damper feedback system based on exponential damping.</p>
+<dl class="simple">
+<dt>ring<span class="classifier">Synchrotron object</span></dt><dd><p>Synchrotron to use.</p>
+</dd>
+<dt>plane<span class="classifier">{“x”,”y”,”s”}</span></dt><dd><p>Allow to choose on which plane the damper is active.</p>
+</dd>
+<dt>damping_time<span class="classifier">float</span></dt><dd><p>Damping time in [s].</p>
+</dd>
+<dt>phase_diff<span class="classifier">array of shape (3,)</span></dt><dd><p>Phase difference between the damper and the position monitor in [rad].</p>
+</dd>
+</dl>
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.feedback.ExponentialDamper.track">
+<span class="sig-name descname"><span class="pre">track</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">bunch</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/feedback.html#ExponentialDamper.track"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.feedback.ExponentialDamper.track" title="Permalink to this definition">¶</a></dt>
+<dd><p>Tracking method for the feedback system
+No bunch to bunch interaction, so written for Bunch object and
+&#64;Element.parallel is used to handle Beam object.</p>
+<p>bunch : Bunch or Beam object</p>
+</dd></dl>
+
+</dd></dl>
+
+<dl class="py class">
+<dt class="sig sig-object py" id="mbtrack2.tracking.feedback.FIRDamper">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">mbtrack2.tracking.feedback.</span></span><span class="sig-name descname"><span class="pre">FIRDamper</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">ring</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">plane</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">tune</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">turn_delay</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">tap_number</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">gain</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">phase</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">bpm_error</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">max_kick</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/feedback.html#FIRDamper"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.feedback.FIRDamper" title="Permalink to this definition">¶</a></dt>
+<dd><p>Bases: <a class="reference internal" href="#mbtrack2.tracking.element.Element" title="mbtrack2.tracking.element.Element"><code class="xref py py-class docutils literal notranslate"><span class="pre">Element</span></code></a></p>
+<p>Bunch by bunch damper feedback system based on FIR filters.</p>
+<p>FIR computation is based on [1].</p>
+<dl class="simple">
+<dt>ring<span class="classifier">Synchrotron object</span></dt><dd><p>Synchrotron to use.</p>
+</dd>
+<dt>plane<span class="classifier">{“x”,”y”,”s”}</span></dt><dd><p>Allow to choose on which plane the damper is active.</p>
+</dd>
+<dt>tune<span class="classifier">float</span></dt><dd><p>Reference (betatron or synchrotron) tune for which the damper system 
+is set.</p>
+</dd>
+<dt>turn_delay<span class="classifier">int</span></dt><dd><p>Number of turn delay before the kick is applied.</p>
+</dd>
+<dt>tap_number<span class="classifier">int</span></dt><dd><p>Number of tap for the FIR filter.</p>
+</dd>
+<dt>gain<span class="classifier">float</span></dt><dd><p>Gain of the FIR filter.</p>
+</dd>
+<dt>phase<span class="classifier">float</span></dt><dd><p>Phase of the FIR filter in [degree].</p>
+</dd>
+<dt>bpm_error<span class="classifier">float, optional</span></dt><dd><p>RMS measurement error applied to the computed mean position.
+Unit is [m] if the plane is “x” or “y” and [s] if the plane is “s”.
+The default is None.</p>
+</dd>
+<dt>max_kick<span class="classifier">float, optional</span></dt><dd><p>Maximum kick strength limitation.
+Unit is [rad] if the plane is “x” or “y” and no unit (delta) if the 
+plane is “s”.
+The default is None.</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>pos<span class="classifier">array</span></dt><dd><p>Stored beam postions.</p>
+</dd>
+<dt>kick<span class="classifier">array</span></dt><dd><p>Stored damper kicks.</p>
+</dd>
+<dt>coef<span class="classifier">array</span></dt><dd><p>Coefficients of the FIR filter.</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>get_fir(tap_number, tune, phase, turn_delay, gain)</dt><dd><p>Initialize the FIR filter and return an array containing the FIR 
+coefficients.</p>
+</dd>
+<dt>plot_fir()</dt><dd><p>Plot the gain and the phase of the FIR filter.</p>
+</dd>
+<dt>track(beam_or_bunch)</dt><dd><p>Tracking method.</p>
+</dd>
+</dl>
+<p>[1] T.Nakamura, S.Daté, K. Kobayashi, T. Ohshima. Proceedings of EPAC 
+2004. Transverse bunch by bunch feedback system for the Spring-8 
+storage ring.</p>
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.feedback.FIRDamper.get_fir">
+<span class="sig-name descname"><span class="pre">get_fir</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">tap_number</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">tune</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">phase</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">turn_delay</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">gain</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/feedback.html#FIRDamper.get_fir"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.feedback.FIRDamper.get_fir" title="Permalink to this definition">¶</a></dt>
+<dd><p>Compute the FIR coefficients.</p>
+<p>FIR computation is based on [1].</p>
+<dl class="simple">
+<dt>FIR_coef<span class="classifier">array</span></dt><dd><p>Array containing the FIR coefficients.</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.feedback.FIRDamper.init_beam_no_mpi">
+<span class="sig-name descname"><span class="pre">init_beam_no_mpi</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">beam</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/feedback.html#FIRDamper.init_beam_no_mpi"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.feedback.FIRDamper.init_beam_no_mpi" title="Permalink to this definition">¶</a></dt>
+<dd><p>Change array sizes if Beam is used without mpi.</p>
+<dl class="simple">
+<dt>beam<span class="classifier">Beam</span></dt><dd><p>Beam to track.</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.feedback.FIRDamper.plot_fir">
+<span class="sig-name descname"><span class="pre">plot_fir</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/feedback.html#FIRDamper.plot_fir"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.feedback.FIRDamper.plot_fir" title="Permalink to this definition">¶</a></dt>
+<dd><p>Plot the gain and the phase of the FIR filter.</p>
+<dl class="simple">
+<dt>fig<span class="classifier">Figure</span></dt><dd><p>Plot of the gain and phase.</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.feedback.FIRDamper.track">
+<span class="sig-name descname"><span class="pre">track</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">beam_or_bunch</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/feedback.html#FIRDamper.track"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.feedback.FIRDamper.track" title="Permalink to this definition">¶</a></dt>
+<dd><p>Tracking method.</p>
+<dl class="simple">
+<dt>beam_or_bunch<span class="classifier">Beam or Bunch</span></dt><dd><p>Data to track.</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.feedback.FIRDamper.track_sb">
+<span class="sig-name descname"><span class="pre">track_sb</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">bunch</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">bunch_number</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/feedback.html#FIRDamper.track_sb"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.feedback.FIRDamper.track_sb" title="Permalink to this definition">¶</a></dt>
+<dd><p>Core of the tracking method.</p>
+<dl class="simple">
+<dt>bunch<span class="classifier">Bunch</span></dt><dd><p>Bunch to track.</p>
+</dd>
+<dt>bunch_number<span class="classifier">int, optional</span></dt><dd><p>Number of bunch in beam.not_empty. 
+The default is 0.</p>
+</dd>
+</dl>
+</dd></dl>
+
+</dd></dl>
+
+</section>
+<section id="module-mbtrack2.tracking.parallel">
+<span id="mbtrack2-tracking-parallel-module"></span><h2>mbtrack2.tracking.parallel module<a class="headerlink" href="#module-mbtrack2.tracking.parallel" title="Permalink to this heading">¶</a></h2>
+<p>Module to handle parallel computation</p>
+<dl class="py class">
+<dt class="sig sig-object py" id="mbtrack2.tracking.parallel.Mpi">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">mbtrack2.tracking.parallel.</span></span><span class="sig-name descname"><span class="pre">Mpi</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">filling_pattern</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/parallel.html#Mpi"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.parallel.Mpi" title="Permalink to this definition">¶</a></dt>
+<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">object</span></code></p>
+<p>Class which handle parallel computation via the mpi4py module [1].</p>
+<dl class="simple">
+<dt>filling_pattern<span class="classifier">bool array of shape (h,)</span></dt><dd><p>Filling pattern of the beam, like Beam.filling_pattern</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>comm<span class="classifier">MPI.Intracomm object</span></dt><dd><p>MPI intra-comminicator of the processor group, used to manage 
+communication between processors.</p>
+</dd>
+<dt>rank<span class="classifier">int</span></dt><dd><p>Rank of the processor which run the program</p>
+</dd>
+<dt>size<span class="classifier">int</span></dt><dd><p>Number of processor within the processor group (in fact in the 
+intra-comminicator group)</p>
+</dd>
+<dt>table<span class="classifier">int array of shape (size, 2)</span></dt><dd><p>Table of correspondance between the rank of the processor and its 
+associated bunch number</p>
+</dd>
+<dt>bunch_num<span class="classifier">int</span></dt><dd><p>Return the bunch number corresponding to the current processor</p>
+</dd>
+<dt>next_bunch<span class="classifier">int</span></dt><dd><p>Return the rank of the next tracked bunch</p>
+</dd>
+<dt>previous_bunch<span class="classifier">int</span></dt><dd><p>Return the rank of the previous tracked bunch</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>write_table(filling_pattern)</dt><dd><p>Write a table with the rank and the corresponding bunch number for each
+bunch of the filling pattern</p>
+</dd>
+<dt>rank_to_bunch(rank)</dt><dd><p>Return the bunch number corresponding to rank</p>
+</dd>
+<dt>bunch_to_rank(bunch_num)</dt><dd><p>Return the rank corresponding to the bunch number bunch_num</p>
+</dd>
+<dt>share_distributions(beam)</dt><dd><p>Compute the bunch profiles and share it between the different bunches.</p>
+</dd>
+<dt>share_means(beam)</dt><dd><p>Compute the bunch means and share it between the different bunches.</p>
+</dd>
+<dt>share_stds(beam)</dt><dd><p>Compute the bunch standard deviations and share it between the 
+different bunches.</p>
+</dd>
+</dl>
+<p>[1] L. Dalcin, P. Kler, R. Paz, and A. Cosimo, Parallel Distributed 
+Computing using Python, Advances in Water Resources, 34(9):1124-1139, 2011.</p>
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.tracking.parallel.Mpi.bunch_num">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">bunch_num</span></span><a class="headerlink" href="#mbtrack2.tracking.parallel.Mpi.bunch_num" title="Permalink to this definition">¶</a></dt>
+<dd><p>Return the bunch number corresponding to the current processor</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.parallel.Mpi.bunch_to_rank">
+<span class="sig-name descname"><span class="pre">bunch_to_rank</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">bunch_num</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/parallel.html#Mpi.bunch_to_rank"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.parallel.Mpi.bunch_to_rank" title="Permalink to this definition">¶</a></dt>
+<dd><p>Return the rank corresponding to the bunch number bunch_num</p>
+<dl class="simple">
+<dt>bunch_num<span class="classifier">int</span></dt><dd><p>Bunch number</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>rank<span class="classifier">int</span></dt><dd><p>Rank of the processor which tracks the input bunch number</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.tracking.parallel.Mpi.next_bunch">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">next_bunch</span></span><a class="headerlink" href="#mbtrack2.tracking.parallel.Mpi.next_bunch" title="Permalink to this definition">¶</a></dt>
+<dd><p>Return the rank of the next tracked bunch</p>
+</dd></dl>
+
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.tracking.parallel.Mpi.previous_bunch">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">previous_bunch</span></span><a class="headerlink" href="#mbtrack2.tracking.parallel.Mpi.previous_bunch" title="Permalink to this definition">¶</a></dt>
+<dd><p>Return the rank of the previous tracked bunch</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.parallel.Mpi.rank_to_bunch">
+<span class="sig-name descname"><span class="pre">rank_to_bunch</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">rank</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/parallel.html#Mpi.rank_to_bunch"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.parallel.Mpi.rank_to_bunch" title="Permalink to this definition">¶</a></dt>
+<dd><p>Return the bunch number corresponding to rank</p>
+<dl class="simple">
+<dt>rank<span class="classifier">int</span></dt><dd><p>Rank of a processor</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>bunch_num<span class="classifier">int</span></dt><dd><p>Bunch number corresponding to the input rank</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.parallel.Mpi.share_distributions">
+<span class="sig-name descname"><span class="pre">share_distributions</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">beam</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">dimensions</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'tau'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">n_bin</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">75</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/parallel.html#Mpi.share_distributions"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.parallel.Mpi.share_distributions" title="Permalink to this definition">¶</a></dt>
+<dd><p>Compute the bunch profiles and share it between the different bunches.</p>
+<p>beam : Beam object
+dimension : str or list of str, optional</p>
+<blockquote>
+<div><p>Dimensions in which the binning is done. The default is “tau”.</p>
+</div></blockquote>
+<dl class="simple">
+<dt>n_bin<span class="classifier">int or list of int, optional</span></dt><dd><p>Number of bins. The default is 75.</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.parallel.Mpi.share_means">
+<span class="sig-name descname"><span class="pre">share_means</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">beam</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/parallel.html#Mpi.share_means"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.parallel.Mpi.share_means" title="Permalink to this definition">¶</a></dt>
+<dd><p>Compute the bunch means and share it between the different bunches.</p>
+<p>beam : Beam object</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.parallel.Mpi.share_stds">
+<span class="sig-name descname"><span class="pre">share_stds</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">beam</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/parallel.html#Mpi.share_stds"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.parallel.Mpi.share_stds" title="Permalink to this definition">¶</a></dt>
+<dd><p>Compute the bunch standard deviations and share it between the 
+different bunches.</p>
+<p>beam : Beam object</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.parallel.Mpi.write_table">
+<span class="sig-name descname"><span class="pre">write_table</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">filling_pattern</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/parallel.html#Mpi.write_table"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.parallel.Mpi.write_table" title="Permalink to this definition">¶</a></dt>
+<dd><p>Write a table with the rank and the corresponding bunch number for each
+bunch of the filling pattern</p>
+<dl class="simple">
+<dt>filling_pattern<span class="classifier">bool array of shape (h,)</span></dt><dd><p>Filling pattern of the beam, like Beam.filling_pattern</p>
+</dd>
+</dl>
+</dd></dl>
+
+</dd></dl>
+
+</section>
+<section id="module-mbtrack2.tracking.particles">
+<span id="mbtrack2-tracking-particles-module"></span><h2>mbtrack2.tracking.particles module<a class="headerlink" href="#module-mbtrack2.tracking.particles" title="Permalink to this heading">¶</a></h2>
+<p>Module where particles, bunches and beams are described as objects.</p>
+<dl class="py class">
+<dt class="sig sig-object py" id="mbtrack2.tracking.particles.Beam">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">mbtrack2.tracking.particles.</span></span><span class="sig-name descname"><span class="pre">Beam</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">ring</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">bunch_list</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/particles.html#Beam"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.particles.Beam" title="Permalink to this definition">¶</a></dt>
+<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">object</span></code></p>
+<p>Define a Beam object composed of several Bunch objects.</p>
+<p>ring : Synchrotron object
+bunch_list : list of Bunch object, optional</p>
+<dl class="simple">
+<dt>current<span class="classifier">float</span></dt><dd><p>Total beam current in [A]</p>
+</dd>
+<dt>charge<span class="classifier">float</span></dt><dd><p>Total bunch charge in [C]</p>
+</dd>
+<dt>particle_number<span class="classifier">int</span></dt><dd><p>Total number of particle in the beam</p>
+</dd>
+<dt>filling_pattern<span class="classifier">bool array of shape (ring.h,)</span></dt><dd><p>Filling pattern of the beam</p>
+</dd>
+<dt>bunch_current<span class="classifier">array of shape (ring.h,)</span></dt><dd><p>Current in each bunch in [A]</p>
+</dd>
+<dt>bunch_charge<span class="classifier">array of shape (ring.h,)</span></dt><dd><p>Charge in each bunch in [C]</p>
+</dd>
+<dt>bunch_particle<span class="classifier">array of shape (ring.h,)</span></dt><dd><p>Particle number in each bunch</p>
+</dd>
+<dt>bunch_mean<span class="classifier">array of shape (6, ring.h)</span></dt><dd><p>Mean position of alive particles for each bunch</p>
+</dd>
+<dt>bunch_std<span class="classifier">array of shape (6, ring.h)</span></dt><dd><p>Standard deviation of the position of alive particles for each bunch</p>
+</dd>
+<dt>bunch_emit<span class="classifier">array of shape (6, ring.h)</span></dt><dd><p>Bunch emittance of alive particles for each bunch</p>
+</dd>
+</dl>
+<p>mpi : Mpi object
+mpi_switch : bool</p>
+<blockquote>
+<div><p>Status of MPI parallelisation, should not be changed directly but with
+mpi_init() and mpi_close()</p>
+</div></blockquote>
+<dl class="simple">
+<dt>bunch_index<span class="classifier">array of shape (len(self,))</span></dt><dd><p>Return an array with the positions of the non-empty bunches</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>init_beam(filling_pattern, current_per_bunch=1e-3, mp_per_bunch=1e3)</dt><dd><p>Initialize beam with a given filling pattern and marco-particle number 
+per bunch. Then initialize the different bunches with a 6D gaussian
+phase space.</p>
+</dd>
+<dt>mpi_init()</dt><dd><p>Switch on MPI parallelisation and initialise a Mpi object</p>
+</dd>
+<dt>mpi_gather()</dt><dd><p>Gather beam, all bunches of the different processors are sent to 
+all processors. Rather slow</p>
+</dd>
+<dt>mpi_share_distributions()</dt><dd><p>Compute the bunch profile and share it between the different bunches.</p>
+</dd>
+<dt>mpi_close()</dt><dd><p>Call mpi_gather and switch off MPI parallelisation</p>
+</dd>
+<dt>plot(var, option=None)</dt><dd><p>Plot variables with respect to bunch number.</p>
+</dd>
+<dt>save(file_name)</dt><dd><p>Save beam object data in an HDF5 file format.</p>
+</dd>
+<dt>load(file_name, mpi)</dt><dd><p>Load data from a HDF5 file recorded by Beam save method.</p>
+</dd>
+</dl>
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.tracking.particles.Beam.bunch_charge">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">bunch_charge</span></span><a class="headerlink" href="#mbtrack2.tracking.particles.Beam.bunch_charge" title="Permalink to this definition">¶</a></dt>
+<dd><p>Return an array with the charge in each bunch in [C]</p>
+</dd></dl>
+
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.tracking.particles.Beam.bunch_cs">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">bunch_cs</span></span><a class="headerlink" href="#mbtrack2.tracking.particles.Beam.bunch_cs" title="Permalink to this definition">¶</a></dt>
+<dd><p>Return an array with the average Courant-Snyder invariant for each 
+bunch</p>
+</dd></dl>
+
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.tracking.particles.Beam.bunch_current">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">bunch_current</span></span><a class="headerlink" href="#mbtrack2.tracking.particles.Beam.bunch_current" title="Permalink to this definition">¶</a></dt>
+<dd><p>Return an array with the current in each bunch in [A]</p>
+</dd></dl>
+
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.tracking.particles.Beam.bunch_emit">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">bunch_emit</span></span><a class="headerlink" href="#mbtrack2.tracking.particles.Beam.bunch_emit" title="Permalink to this definition">¶</a></dt>
+<dd><p>Return an array with the bunch emittance of alive particles for each
+bunches and each plane</p>
+</dd></dl>
+
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.tracking.particles.Beam.bunch_index">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">bunch_index</span></span><a class="headerlink" href="#mbtrack2.tracking.particles.Beam.bunch_index" title="Permalink to this definition">¶</a></dt>
+<dd><p>Return an array with the positions of the non-empty bunches.</p>
+</dd></dl>
+
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.tracking.particles.Beam.bunch_mean">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">bunch_mean</span></span><a class="headerlink" href="#mbtrack2.tracking.particles.Beam.bunch_mean" title="Permalink to this definition">¶</a></dt>
+<dd><p>Return an array with the mean position of alive particles for each
+bunches</p>
+</dd></dl>
+
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.tracking.particles.Beam.bunch_particle">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">bunch_particle</span></span><a class="headerlink" href="#mbtrack2.tracking.particles.Beam.bunch_particle" title="Permalink to this definition">¶</a></dt>
+<dd><p>Return an array with the particle number in each bunch</p>
+</dd></dl>
+
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.tracking.particles.Beam.bunch_std">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">bunch_std</span></span><a class="headerlink" href="#mbtrack2.tracking.particles.Beam.bunch_std" title="Permalink to this definition">¶</a></dt>
+<dd><p>Return an array with the standard deviation of the position of alive 
+particles for each bunches</p>
+</dd></dl>
+
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.tracking.particles.Beam.charge">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">charge</span></span><a class="headerlink" href="#mbtrack2.tracking.particles.Beam.charge" title="Permalink to this definition">¶</a></dt>
+<dd><p>Total beam charge in [C]</p>
+</dd></dl>
+
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.tracking.particles.Beam.current">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">current</span></span><a class="headerlink" href="#mbtrack2.tracking.particles.Beam.current" title="Permalink to this definition">¶</a></dt>
+<dd><p>Total beam current in [A]</p>
+</dd></dl>
+
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.tracking.particles.Beam.distance_between_bunches">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">distance_between_bunches</span></span><a class="headerlink" href="#mbtrack2.tracking.particles.Beam.distance_between_bunches" title="Permalink to this definition">¶</a></dt>
+<dd><p>Return an array which contains the distance to the next bunch in 
+units of the RF period (ring.T1)</p>
+</dd></dl>
+
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.tracking.particles.Beam.filling_pattern">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">filling_pattern</span></span><a class="headerlink" href="#mbtrack2.tracking.particles.Beam.filling_pattern" title="Permalink to this definition">¶</a></dt>
+<dd><p>Return an array with the filling pattern of the beam as bool</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.particles.Beam.init_beam">
+<span class="sig-name descname"><span class="pre">init_beam</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">filling_pattern</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">current_per_bunch</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0.001</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">mp_per_bunch</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1000.0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">track_alive</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">mpi</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/particles.html#Beam.init_beam"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.particles.Beam.init_beam" title="Permalink to this definition">¶</a></dt>
+<dd><p>Initialize beam with a given filling pattern and marco-particle number 
+per bunch. Then initialize the different bunches with a 6D gaussian
+phase space.</p>
+<p>If the filling pattern is an array of bool then the current per bunch 
+is uniform, else the filling pattern can be an array with the current
+in each bunch.</p>
+<dl class="simple">
+<dt>filling_pattern<span class="classifier">numpy array or list of length ring.h</span></dt><dd><p>Filling pattern of the beam, can be a list or an array of bool, 
+then current_per_bunch is used. Or can be an array with the current
+in each bunch.</p>
+</dd>
+<dt>current_per_bunch<span class="classifier">float, optional</span></dt><dd><p>Current per bunch in [A]</p>
+</dd>
+<dt>mp_per_bunch<span class="classifier">float, optional</span></dt><dd><p>Macro-particle number per bunch</p>
+</dd>
+<dt>track_alive<span class="classifier">bool, optional</span></dt><dd><p>If False, the code no longer take into account alive/dead particles.
+Should be set to True if element such as apertures are used.
+Can be set to False to gain a speed increase.</p>
+</dd>
+<dt>mpi<span class="classifier">bool, optional</span></dt><dd><p>If True, only a single bunch is fully initialized on each core, the
+other bunches are initialized with a single marco-particle.</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.particles.Beam.load">
+<span class="sig-name descname"><span class="pre">load</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">file_name</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">mpi</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">track_alive</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/particles.html#Beam.load"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.particles.Beam.load" title="Permalink to this definition">¶</a></dt>
+<dd><p>Load data from a HDF5 file recorded by Beam save method.</p>
+<dl class="simple">
+<dt>file_name<span class="classifier">str</span></dt><dd><p>Path to the HDF5 file where the Beam data is stored.</p>
+</dd>
+<dt>mpi<span class="classifier">bool</span></dt><dd><p>If True, only a single bunch is fully initialized on each core, the
+other bunches are initialized with a single marco-particle.</p>
+</dd>
+<dt>track_alive<span class="classifier">bool, optional</span></dt><dd><p>If False, the code no longer take into account alive/dead particles.
+Should be set to True if element such as apertures are used.
+Can be set to False to gain a speed increase.
+The default is True.</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.particles.Beam.mpi_close">
+<span class="sig-name descname"><span class="pre">mpi_close</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/particles.html#Beam.mpi_close"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.particles.Beam.mpi_close" title="Permalink to this definition">¶</a></dt>
+<dd><p>Call mpi_gather and switch off MPI parallelisation</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.particles.Beam.mpi_gather">
+<span class="sig-name descname"><span class="pre">mpi_gather</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/particles.html#Beam.mpi_gather"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.particles.Beam.mpi_gather" title="Permalink to this definition">¶</a></dt>
+<dd><p>Gather beam, all bunches of the different processors are sent to 
+all processors. Rather slow</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.particles.Beam.mpi_init">
+<span class="sig-name descname"><span class="pre">mpi_init</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/particles.html#Beam.mpi_init"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.particles.Beam.mpi_init" title="Permalink to this definition">¶</a></dt>
+<dd><p>Switch on MPI parallelisation and initialise a Mpi object</p>
+</dd></dl>
+
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.tracking.particles.Beam.not_empty">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">not_empty</span></span><a class="headerlink" href="#mbtrack2.tracking.particles.Beam.not_empty" title="Permalink to this definition">¶</a></dt>
+<dd><p>Return a generator to iterate over not empty bunches.</p>
+</dd></dl>
+
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.tracking.particles.Beam.particle_number">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">particle_number</span></span><a class="headerlink" href="#mbtrack2.tracking.particles.Beam.particle_number" title="Permalink to this definition">¶</a></dt>
+<dd><p>Total number of particles in the beam</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.particles.Beam.plot">
+<span class="sig-name descname"><span class="pre">plot</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">var</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">option</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/particles.html#Beam.plot"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.particles.Beam.plot" title="Permalink to this definition">¶</a></dt>
+<dd><p>Plot variables with respect to bunch number.</p>
+<dl>
+<dt>var<span class="classifier">str {“bunch_current”, “bunch_charge”, “bunch_particle”, </span></dt><dd><blockquote>
+<div><p>“bunch_mean”, “bunch_std”, “bunch_emit”}</p>
+</div></blockquote>
+<p>Variable to be plotted.</p>
+</dd>
+<dt>option<span class="classifier">str, optional</span></dt><dd><p>If var is “bunch_mean”, “bunch_std”, or “bunch_emit, option needs 
+to be specified.
+For “bunch_mean” and “bunch_std”,</p>
+<blockquote>
+<div><p>option = {“x”,”xp”,”y”,”yp”,”tau”,”delta”}.</p>
+</div></blockquote>
+<p>For “bunch_emit”, option = {“x”,”y”,”s”}.
+The default is None.</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>fig<span class="classifier">Figure</span></dt><dd><p>Figure object with the plot on it.</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.particles.Beam.save">
+<span class="sig-name descname"><span class="pre">save</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">file_name</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/particles.html#Beam.save"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.particles.Beam.save" title="Permalink to this definition">¶</a></dt>
+<dd><p>Save beam object data in an HDF5 file format.</p>
+<p>The output file is named as “&lt;file_name&gt;.hdf5”.</p>
+<dl class="simple">
+<dt>file_name<span class="classifier">str</span></dt><dd><p>Name of the output file.</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.particles.Beam.update_distance_between_bunches">
+<span class="sig-name descname"><span class="pre">update_distance_between_bunches</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/particles.html#Beam.update_distance_between_bunches"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.particles.Beam.update_distance_between_bunches" title="Permalink to this definition">¶</a></dt>
+<dd><p>Update the distance_between_bunches array</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.particles.Beam.update_filling_pattern">
+<span class="sig-name descname"><span class="pre">update_filling_pattern</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/particles.html#Beam.update_filling_pattern"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.particles.Beam.update_filling_pattern" title="Permalink to this definition">¶</a></dt>
+<dd><p>Update the beam filling pattern.</p>
+</dd></dl>
+
+</dd></dl>
+
+<dl class="py class">
+<dt class="sig sig-object py" id="mbtrack2.tracking.particles.Bunch">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">mbtrack2.tracking.particles.</span></span><span class="sig-name descname"><span class="pre">Bunch</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">ring</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">mp_number</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1000.0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">current</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0.001</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">track_alive</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">alive</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">load_from_file</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">load_suffix</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/particles.html#Bunch"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.particles.Bunch" title="Permalink to this definition">¶</a></dt>
+<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">object</span></code></p>
+<p>Define a bunch object.</p>
+<p>ring : Synchrotron object
+mp_number : float, optional</p>
+<blockquote>
+<div><p>Macro-particle number.</p>
+</div></blockquote>
+<dl class="simple">
+<dt>current<span class="classifier">float, optional</span></dt><dd><p>Bunch current in [A].</p>
+</dd>
+<dt>track_alive<span class="classifier">bool, optional</span></dt><dd><p>If False, the code no longer take into account alive/dead particles.
+Should be set to True if element such as apertures are used.
+Can be set to False to gain a speed increase.</p>
+</dd>
+<dt>alive<span class="classifier">bool, optional</span></dt><dd><p>If False, the bunch is defined as empty.</p>
+</dd>
+<dt>load_from_file<span class="classifier">str, optional</span></dt><dd><p>Name of bunch save file generated by save method.
+If None, the bunch is initialized using the input parameters.
+Otherwise, the bunch from the file is loaded and the other inputs are 
+ignored.
+Default is None.</p>
+</dd>
+<dt>load_suffix<span class="classifier">str or int, optional</span></dt><dd><p>Suffix to the group name used to load the data from the HDF5 file.
+Default is None.</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>mp_number<span class="classifier">int</span></dt><dd><p>Macro-particle number.</p>
+</dd>
+<dt>alive<span class="classifier">array of bool of shape (mp_number,)</span></dt><dd><p>Array used to monitor which particle is dead or alive.</p>
+</dd>
+<dt>charge<span class="classifier">float</span></dt><dd><p>Bunch charge in [C].</p>
+</dd>
+<dt>charge_per_mp<span class="classifier">float</span></dt><dd><p>Charge per macro-particle in [C].</p>
+</dd>
+<dt>particle_number<span class="classifier">int</span></dt><dd><p>Number of particles in the bunch.</p>
+</dd>
+<dt>current<span class="classifier">float</span></dt><dd><p>Bunch current in [A].</p>
+</dd>
+<dt>is_empty<span class="classifier">bool</span></dt><dd><p>Return True if the bunch is empty.</p>
+</dd>
+<dt>mean<span class="classifier">array of shape (6,)</span></dt><dd><p>Mean position of alive particles for each coordinates.</p>
+</dd>
+<dt>std<span class="classifier">array of shape (6,)</span></dt><dd><p>Standard deviation of the position of alive particles for each 
+coordinates.</p>
+</dd>
+<dt>emit<span class="classifier">array of shape (3,)</span></dt><dd><p>Bunch emittance for each plane [1]. !!! -&gt; Correct for long ?</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>init_gaussian(cov=None, mean=None, <a href="#id1"><span class="problematic" id="id2">**</span></a>kwargs)</dt><dd><p>Initialize bunch particles with 6D gaussian phase space.</p>
+</dd>
+<dt>plot_phasespace(x_var=”tau”, y_var=”delta”, plot_type=”j”)</dt><dd><p>Plot phase space.</p>
+</dd>
+<dt>save(file_name)</dt><dd><p>Save bunch object data (6D phase space, current, and state) in an HDF5 
+file format.</p>
+</dd>
+<dt>load(file_name)</dt><dd><p>Load data from a HDF5 file recorded by Bunch save method.</p>
+</dd>
+</dl>
+<p>[1] Wiedemann, H. (2015). Particle accelerator physics. 4th edition. 
+Springer, Eq.(8.39) of p224.</p>
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.particles.Bunch.binning">
+<span class="sig-name descname"><span class="pre">binning</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">dimension</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'tau'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">n_bin</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">75</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/particles.html#Bunch.binning"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.particles.Bunch.binning" title="Permalink to this definition">¶</a></dt>
+<dd><p>Bin macro-particles.</p>
+<dl class="simple">
+<dt>dimension<span class="classifier">str, optional</span></dt><dd><p>Dimension in which the binning is done. The default is “tau”.</p>
+</dd>
+<dt>n_bin<span class="classifier">int, optional</span></dt><dd><p>Number of bins. The default is 75.</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>bins<span class="classifier">array of shape (n_bin,)</span></dt><dd><p>Bins where the particles are sorted.</p>
+</dd>
+<dt>sorted_index<span class="classifier">array of shape (self.mp_number,)</span></dt><dd><p>Bin number of each macro-particles.</p>
+</dd>
+<dt>profile<span class="classifier">array of shape (n_bin - 1,)</span></dt><dd><p>Number of marco-particles in each bin.</p>
+</dd>
+<dt>center<span class="classifier">array of shape (n_bin - 1,)</span></dt><dd><p>Center of each bin.</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.tracking.particles.Bunch.charge">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">charge</span></span><a class="headerlink" href="#mbtrack2.tracking.particles.Bunch.charge" title="Permalink to this definition">¶</a></dt>
+<dd><p>Bunch charge in [C]</p>
+</dd></dl>
+
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.tracking.particles.Bunch.charge_per_mp">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">charge_per_mp</span></span><a class="headerlink" href="#mbtrack2.tracking.particles.Bunch.charge_per_mp" title="Permalink to this definition">¶</a></dt>
+<dd><p>Charge per macro-particle [C]</p>
+</dd></dl>
+
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.tracking.particles.Bunch.cs_invariant">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">cs_invariant</span></span><a class="headerlink" href="#mbtrack2.tracking.particles.Bunch.cs_invariant" title="Permalink to this definition">¶</a></dt>
+<dd><p>Return the average Courant-Snyder invariant of each plane.</p>
+</dd></dl>
+
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.tracking.particles.Bunch.current">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">current</span></span><a class="headerlink" href="#mbtrack2.tracking.particles.Bunch.current" title="Permalink to this definition">¶</a></dt>
+<dd><p>Bunch current [A]</p>
+</dd></dl>
+
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.tracking.particles.Bunch.emit">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">emit</span></span><a class="headerlink" href="#mbtrack2.tracking.particles.Bunch.emit" title="Permalink to this definition">¶</a></dt>
+<dd><p>Return the bunch emittance for each plane.</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.particles.Bunch.init_gaussian">
+<span class="sig-name descname"><span class="pre">init_gaussian</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">cov</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">mean</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/particles.html#Bunch.init_gaussian"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.particles.Bunch.init_gaussian" title="Permalink to this definition">¶</a></dt>
+<dd><p>Initialize bunch particles with 6D gaussian phase space.
+Covariance matrix is taken from [1] and dispersion is added following
+the method explained in [2].</p>
+<dl class="simple">
+<dt>cov<span class="classifier">(6,6) array, optional</span></dt><dd><p>Covariance matrix of the bunch distribution</p>
+</dd>
+<dt>mean<span class="classifier">(6,) array, optional</span></dt><dd><p>Mean of the bunch distribution</p>
+</dd>
+</dl>
+<p>[1] Wiedemann, H. (2015). Particle accelerator physics. 4th 
+edition. Springer, Eq.(8.38) of p223.
+[2] <a class="reference external" href="http://www.pp.rhul.ac.uk/bdsim/manual-develop/dev_beamgeneration.html">http://www.pp.rhul.ac.uk/bdsim/manual-develop/dev_beamgeneration.html</a></p>
+</dd></dl>
+
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.tracking.particles.Bunch.is_empty">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">is_empty</span></span><a class="headerlink" href="#mbtrack2.tracking.particles.Bunch.is_empty" title="Permalink to this definition">¶</a></dt>
+<dd><p>Return True if the bunch is empty.</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.particles.Bunch.load">
+<span class="sig-name descname"><span class="pre">load</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">file_name</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">suffix</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">track_alive</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/particles.html#Bunch.load"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.particles.Bunch.load" title="Permalink to this definition">¶</a></dt>
+<dd><p>Load data from a HDF5 file recorded by Bunch save method.</p>
+<dl class="simple">
+<dt>file_name<span class="classifier">str</span></dt><dd><p>Path to the HDF5 file where the Bunch data is stored.</p>
+</dd>
+<dt>suffix<span class="classifier">str or int, optional</span></dt><dd><p>Suffix to the group name used to load the data from the HDF5 file.
+If None, it is not used.</p>
+</dd>
+<dt>track_alive<span class="classifier">bool, optional</span></dt><dd><p>If False, the code no longer take into account alive/dead particles.
+Should be set to True if element such as apertures are used.
+Can be set to False to gain a speed increase.</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.tracking.particles.Bunch.mean">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">mean</span></span><a class="headerlink" href="#mbtrack2.tracking.particles.Bunch.mean" title="Permalink to this definition">¶</a></dt>
+<dd><p>Return the mean position of alive particles for each coordinates.</p>
+</dd></dl>
+
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.tracking.particles.Bunch.mp_number">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">mp_number</span></span><a class="headerlink" href="#mbtrack2.tracking.particles.Bunch.mp_number" title="Permalink to this definition">¶</a></dt>
+<dd><p>Macro-particle number</p>
+</dd></dl>
+
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.tracking.particles.Bunch.particle_number">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">particle_number</span></span><a class="headerlink" href="#mbtrack2.tracking.particles.Bunch.particle_number" title="Permalink to this definition">¶</a></dt>
+<dd><p>Particle number</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.particles.Bunch.plot_phasespace">
+<span class="sig-name descname"><span class="pre">plot_phasespace</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x_var</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'tau'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">y_var</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'delta'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">kind</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'scatter'</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/particles.html#Bunch.plot_phasespace"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.particles.Bunch.plot_phasespace" title="Permalink to this definition">¶</a></dt>
+<dd><p>Plot phase space.</p>
+<dl class="simple">
+<dt>x_var<span class="classifier">str </span></dt><dd><p>Dimension to plot on horizontal axis.</p>
+</dd>
+<dt>y_var<span class="classifier">str </span></dt><dd><p>Dimension to plot on vertical axis.</p>
+</dd>
+<dt>kind<span class="classifier">str, {“scatter”, “kde”, “hist”, “hex”, “reg”, “resid”}</span></dt><dd><p>Kind of plot to draw. See seeborn documentation.
+The defualt value is “scatter”.</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>fig<span class="classifier">Figure</span></dt><dd><p>Figure object with the plot on it.</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.particles.Bunch.plot_profile">
+<span class="sig-name descname"><span class="pre">plot_profile</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">dimension</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'tau'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">n_bin</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">75</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/particles.html#Bunch.plot_profile"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.particles.Bunch.plot_profile" title="Permalink to this definition">¶</a></dt>
+<dd><p>Plot bunch profile.</p>
+<dl class="simple">
+<dt>dimension<span class="classifier">str, optional</span></dt><dd><p>Dimension to plot. The default is “tau”.</p>
+</dd>
+<dt>n_bin<span class="classifier">int, optional</span></dt><dd><p>Number of bins. The default is 75.</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.particles.Bunch.save">
+<span class="sig-name descname"><span class="pre">save</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">file_name</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">suffix</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">mpi_comm</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/particles.html#Bunch.save"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.particles.Bunch.save" title="Permalink to this definition">¶</a></dt>
+<dd><p>Save bunch object data (6D phase space, current, and state) in an HDF5 
+file format.</p>
+<p>The output file is named as “&lt;file_name&gt;.hdf5”.</p>
+<dl class="simple">
+<dt>file_name<span class="classifier">str</span></dt><dd><p>Name of the output file.</p>
+</dd>
+<dt>suffix<span class="classifier">str or int, optional</span></dt><dd><p>Suffix to the group name used to save the data into the HDF5 file.
+If None, it is not used.</p>
+</dd>
+<dt>mpi_comm<span class="classifier">MPI communicator, optional</span></dt><dd><p>For internal use if mpi is used in Beam objects.
+Default is None.</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.tracking.particles.Bunch.std">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">std</span></span><a class="headerlink" href="#mbtrack2.tracking.particles.Bunch.std" title="Permalink to this definition">¶</a></dt>
+<dd><p>Return the standard deviation of the position of alive 
+particles for each coordinates.</p>
+</dd></dl>
+
+</dd></dl>
+
+<dl class="py class">
+<dt class="sig sig-object py" id="mbtrack2.tracking.particles.Electron">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">mbtrack2.tracking.particles.</span></span><span class="sig-name descname"><span class="pre">Electron</span></span><a class="reference internal" href="_modules/mbtrack2/tracking/particles.html#Electron"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.particles.Electron" title="Permalink to this definition">¶</a></dt>
+<dd><p>Bases: <a class="reference internal" href="#mbtrack2.tracking.particles.Particle" title="mbtrack2.tracking.particles.Particle"><code class="xref py py-class docutils literal notranslate"><span class="pre">Particle</span></code></a></p>
+<p>Define an electron</p>
+</dd></dl>
+
+<dl class="py class">
+<dt class="sig sig-object py" id="mbtrack2.tracking.particles.Particle">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">mbtrack2.tracking.particles.</span></span><span class="sig-name descname"><span class="pre">Particle</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">mass</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">charge</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/particles.html#Particle"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.particles.Particle" title="Permalink to this definition">¶</a></dt>
+<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">object</span></code></p>
+<p>Define a particle object.</p>
+<dl class="simple">
+<dt>mass<span class="classifier">float</span></dt><dd><p>total particle mass in [kg]</p>
+</dd>
+<dt>charge<span class="classifier">float</span></dt><dd><p>electrical charge in [C]</p>
+</dd>
+<dt>E_rest<span class="classifier">float</span></dt><dd><p>particle rest energy in [eV]</p>
+</dd>
+</dl>
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.tracking.particles.Particle.E_rest">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">E_rest</span></span><a class="headerlink" href="#mbtrack2.tracking.particles.Particle.E_rest" title="Permalink to this definition">¶</a></dt>
+<dd></dd></dl>
+
+</dd></dl>
+
+<dl class="py class">
+<dt class="sig sig-object py" id="mbtrack2.tracking.particles.Proton">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">mbtrack2.tracking.particles.</span></span><span class="sig-name descname"><span class="pre">Proton</span></span><a class="reference internal" href="_modules/mbtrack2/tracking/particles.html#Proton"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.particles.Proton" title="Permalink to this definition">¶</a></dt>
+<dd><p>Bases: <a class="reference internal" href="#mbtrack2.tracking.particles.Particle" title="mbtrack2.tracking.particles.Particle"><code class="xref py py-class docutils literal notranslate"><span class="pre">Particle</span></code></a></p>
+<p>Define a proton</p>
+</dd></dl>
+
+</section>
+<section id="module-mbtrack2.tracking.rf">
+<span id="mbtrack2-tracking-rf-module"></span><h2>mbtrack2.tracking.rf module<a class="headerlink" href="#module-mbtrack2.tracking.rf" title="Permalink to this heading">¶</a></h2>
+<p>This module handles radio-frequency (RF) cavitiy elements.</p>
+<dl class="py class">
+<dt class="sig sig-object py" id="mbtrack2.tracking.rf.CavityResonator">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">mbtrack2.tracking.rf.</span></span><span class="sig-name descname"><span class="pre">CavityResonator</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">ring</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">m</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">Rs</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">Q</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">QL</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">detune</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">Ncav</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">Vc</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">theta</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">n_bin</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">75</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/rf.html#CavityResonator"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.rf.CavityResonator" title="Permalink to this definition">¶</a></dt>
+<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">object</span></code></p>
+<p>Cavity resonator class for active or passive RF cavity with beam
+loading or HOM, based on [1,2].</p>
+<p>Use cosine definition.</p>
+<p>If used with mpi, beam.mpi.share_distributions must be called before the 
+track method call.</p>
+<dl class="simple">
+<dt>Different kind of RF feeback and loops can be added using:</dt><dd><p>cavity_resonator.feedback.append(loop)</p>
+</dd>
+</dl>
+<p>ring : Synchrotron object
+m : int or float</p>
+<blockquote>
+<div><p>Harmonic number of the cavity.</p>
+</div></blockquote>
+<dl class="simple">
+<dt>Rs<span class="classifier">float</span></dt><dd><p>Shunt impedance of the cavities in [Ohm], defined as 0.5*Vc*Vc/Pc.
+If Ncav = 1, used for the total shunt impedance.
+If Ncav &gt; 1, used for the shunt impedance per cavity.</p>
+</dd>
+<dt>Q<span class="classifier">float</span></dt><dd><p>Quality factor of the cavity.</p>
+</dd>
+<dt>QL<span class="classifier">float</span></dt><dd><p>Loaded quality factor of the cavity.</p>
+</dd>
+<dt>detune<span class="classifier">float</span></dt><dd><p>Detuing of the cavity in [Hz], defined as (fr - m*ring.f1).</p>
+</dd>
+<dt>Ncav<span class="classifier">int, optional</span></dt><dd><p>Number of cavities.</p>
+</dd>
+<dt>Vc<span class="classifier">float, optinal</span></dt><dd><p>Total cavity voltage objective value in [V].</p>
+</dd>
+<dt>theta<span class="classifier">float, optional</span></dt><dd><p>Total cavity phase objective value in [rad].</p>
+</dd>
+<dt>n_bin<span class="classifier">int, optional</span></dt><dd><p>Number of bins used for the beam loading computation. 
+Only used if MPI is not used, otherwise n_bin must be specified in the 
+beam.mpi.share_distributions method.
+The default is 75.</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>beam_phasor<span class="classifier">complex</span></dt><dd><p>Beam phasor in [V].</p>
+</dd>
+<dt>beam_phasor_record<span class="classifier">array of complex</span></dt><dd><p>Last beam phasor value of each bunch in [V].</p>
+</dd>
+<dt>generator_phasor<span class="classifier">complex</span></dt><dd><p>Generator phasor in [V].</p>
+</dd>
+<dt>generator_phasor_record<span class="classifier">array of complex</span></dt><dd><p>Last generator phasor value of each bunch in [V].</p>
+</dd>
+<dt>cavity_phasor<span class="classifier">complex</span></dt><dd><p>Cavity phasor in [V].</p>
+</dd>
+<dt>cavity_phasor_record<span class="classifier">array of complex</span></dt><dd><p>Last cavity phasor value of each bunch in [V].</p>
+</dd>
+<dt>ig_phasor_record<span class="classifier">array of complex</span></dt><dd><p>Last current generator phasor of each bunch in [A].
+Only used for some feedback types.</p>
+</dd>
+<dt>cavity_voltage<span class="classifier">float</span></dt><dd><p>Cavity total voltage in [V].</p>
+</dd>
+<dt>cavity_phase<span class="classifier">float</span></dt><dd><p>Cavity total phase in [rad].</p>
+</dd>
+<dt>loss_factor<span class="classifier">float</span></dt><dd><p>Cavity loss factor in [V/C].</p>
+</dd>
+<dt>Rs_per_cavity<span class="classifier">float</span></dt><dd><p>Shunt impedance of a single cavity in [Ohm], defined as 0.5*Vc*Vc/Pc.</p>
+</dd>
+<dt>beta<span class="classifier">float</span></dt><dd><p>Coupling coefficient of the cavity.</p>
+</dd>
+<dt>fr<span class="classifier">float</span></dt><dd><p>Resonance frequency of the cavity in [Hz].</p>
+</dd>
+<dt>wr<span class="classifier">float</span></dt><dd><p>Angular resonance frequency in [Hz.rad].</p>
+</dd>
+<dt>psi<span class="classifier">float</span></dt><dd><p>Tuning angle in [rad].</p>
+</dd>
+<dt>filling_time<span class="classifier">float</span></dt><dd><p>Cavity filling time in [s].</p>
+</dd>
+<dt>Pc<span class="classifier">float</span></dt><dd><p>Power dissipated in the cavity walls in [W].</p>
+</dd>
+<dt>Pg<span class="classifier">float</span></dt><dd><p>Generator power in [W].</p>
+</dd>
+<dt>Vgr<span class="classifier">float</span></dt><dd><p>Generator voltage at resonance in [V].</p>
+</dd>
+<dt>theta_gr<span class="classifier">float</span></dt><dd><p>Generator phase at resonance in [rad].</p>
+</dd>
+<dt>Vg<span class="classifier">float</span></dt><dd><p>Generator voltage in [V].</p>
+</dd>
+<dt>theta_g<span class="classifier">float</span></dt><dd><p>Generator phase in [rad].</p>
+</dd>
+<dt>tracking<span class="classifier">bool</span></dt><dd><p>True if the tracking has been initialized.</p>
+</dd>
+<dt>bunch_index<span class="classifier">int</span></dt><dd><p>Number of the tracked bunch in the current core.</p>
+</dd>
+<dt>distance<span class="classifier">array</span></dt><dd><p>Distance between bunches.</p>
+</dd>
+</dl>
+<p>valid_bunch_index : array</p>
+<dl class="simple">
+<dt>Vbr(I0)</dt><dd><p>Return beam voltage at resonance in [V].</p>
+</dd>
+<dt>Vb(I0)</dt><dd><p>Return beam voltage in [V].</p>
+</dd>
+<dt>Pb(I0)</dt><dd><p>Return power transmitted to the beam in [W].</p>
+</dd>
+<dt>Pr(I0)</dt><dd><p>Return power reflected back to the generator in [W].</p>
+</dd>
+<dt>Z(f)</dt><dd><p>Cavity impedance in [Ohm] for a given frequency f in [Hz].</p>
+</dd>
+<dt>set_optimal_coupling(I0)</dt><dd><p>Set coupling to optimal value.</p>
+</dd>
+<dt>set_optimal_detune(I0)</dt><dd><p>Set detuning to optimal conditions.</p>
+</dd>
+<dt>set_generator(I0)</dt><dd><p>Set generator parameters.</p>
+</dd>
+<dt>plot_phasor(I0)</dt><dd><p>Plot phasor diagram.</p>
+</dd>
+<dt>is_DC_Robinson_stable(I0)</dt><dd><p>Check DC Robinson stability.</p>
+</dd>
+<dt>plot_DC_Robinson_stability()</dt><dd><p>Plot DC Robinson stability limit.</p>
+</dd>
+<dt>init_tracking(beam)</dt><dd><p>Initialization of the tracking.</p>
+</dd>
+<dt>track(beam)</dt><dd><p>Tracking method.</p>
+</dd>
+<dt>phasor_decay(time)</dt><dd><p>Compute the beam phasor decay during a given time span.</p>
+</dd>
+<dt>phasor_evol(profile, bin_length, charge_per_mp)</dt><dd><p>Compute the beam phasor evolution during the crossing of a bunch.</p>
+</dd>
+<dt>VRF(z, I0)</dt><dd><p>Return the total RF voltage.</p>
+</dd>
+<dt>dVRF(z, I0)</dt><dd><p>Return derivative of total RF voltage.</p>
+</dd>
+<dt>ddVRF(z, I0)</dt><dd><p>Return the second derivative of total RF voltage.</p>
+</dd>
+<dt>deltaVRF(z, I0)</dt><dd><p>Return the generator voltage minus beam loading voltage.</p>
+</dd>
+<dt>update_feedback()</dt><dd><p>Force feedback update from current CavityResonator parameters.</p>
+</dd>
+<dt>sample_voltage()</dt><dd><p>Sample the voltage seen by a zero charge particle during an RF period.</p>
+</dd>
+</dl>
+<p>[1] Wilson, P. B. (1994). Fundamental-mode rf design in e+ e− storage ring 
+factories. In Frontiers of Particle Beams: Factories with e+ e-Rings 
+(pp. 293-311). Springer, Berlin, Heidelberg.</p>
+<p>[2] Naoto Yamamoto, Alexis Gamelin, and Ryutaro Nagaoka. “Investigation 
+of Longitudinal Beam Dynamics With Harmonic Cavities by Using the Code 
+Mbtrack.” IPAC’19, Melbourne, Australia, 2019.</p>
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.tracking.rf.CavityResonator.DFB_ig_phasor">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">DFB_ig_phasor</span></span><a class="headerlink" href="#mbtrack2.tracking.rf.CavityResonator.DFB_ig_phasor" title="Permalink to this definition">¶</a></dt>
+<dd><p>Last direct feedback current generator phasor of each bunch in [A]</p>
+</dd></dl>
+
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.tracking.rf.CavityResonator.Ncav">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">Ncav</span></span><a class="headerlink" href="#mbtrack2.tracking.rf.CavityResonator.Ncav" title="Permalink to this definition">¶</a></dt>
+<dd><p>Number of cavities</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.rf.CavityResonator.Pb">
+<span class="sig-name descname"><span class="pre">Pb</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">I0</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/rf.html#CavityResonator.Pb"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.rf.CavityResonator.Pb" title="Permalink to this definition">¶</a></dt>
+<dd><p>Return power transmitted to the beam in [W] - near Eq. (4.2.3) in [1].</p>
+<dl class="simple">
+<dt>I0<span class="classifier">float</span></dt><dd><p>Beam current in [A].</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>float</dt><dd><p>Power transmitted to the beam in [W].</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.tracking.rf.CavityResonator.Pc">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">Pc</span></span><a class="headerlink" href="#mbtrack2.tracking.rf.CavityResonator.Pc" title="Permalink to this definition">¶</a></dt>
+<dd><p>Power dissipated in the cavity walls in [W]</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.rf.CavityResonator.Pr">
+<span class="sig-name descname"><span class="pre">Pr</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">I0</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/rf.html#CavityResonator.Pr"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.rf.CavityResonator.Pr" title="Permalink to this definition">¶</a></dt>
+<dd><p>Power reflected back to the generator in [W].</p>
+<dl class="simple">
+<dt>I0<span class="classifier">float</span></dt><dd><p>Beam current in [A].</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>float</dt><dd><p>Power reflected back to the generator in [W].</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.tracking.rf.CavityResonator.Q">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">Q</span></span><a class="headerlink" href="#mbtrack2.tracking.rf.CavityResonator.Q" title="Permalink to this definition">¶</a></dt>
+<dd><p>Quality factor</p>
+</dd></dl>
+
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.tracking.rf.CavityResonator.QL">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">QL</span></span><a class="headerlink" href="#mbtrack2.tracking.rf.CavityResonator.QL" title="Permalink to this definition">¶</a></dt>
+<dd><p>Loaded quality factor</p>
+</dd></dl>
+
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.tracking.rf.CavityResonator.RL">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">RL</span></span><a class="headerlink" href="#mbtrack2.tracking.rf.CavityResonator.RL" title="Permalink to this definition">¶</a></dt>
+<dd><p>Loaded shunt impedance [ohm]</p>
+</dd></dl>
+
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.tracking.rf.CavityResonator.Rs">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">Rs</span></span><a class="headerlink" href="#mbtrack2.tracking.rf.CavityResonator.Rs" title="Permalink to this definition">¶</a></dt>
+<dd><p>Shunt impedance [ohm]</p>
+</dd></dl>
+
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.tracking.rf.CavityResonator.Rs_per_cavity">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">Rs_per_cavity</span></span><a class="headerlink" href="#mbtrack2.tracking.rf.CavityResonator.Rs_per_cavity" title="Permalink to this definition">¶</a></dt>
+<dd><p>Shunt impedance of a single cavity in [Ohm], defined as 
+0.5*Vc*Vc/Pc.</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.rf.CavityResonator.VRF">
+<span class="sig-name descname"><span class="pre">VRF</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">z</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">I0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">F</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">PHI</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/rf.html#CavityResonator.VRF"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.rf.CavityResonator.VRF" title="Permalink to this definition">¶</a></dt>
+<dd><p>Total RF voltage taking into account form factor amplitude F and form factor phase PHI</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.rf.CavityResonator.Vb">
+<span class="sig-name descname"><span class="pre">Vb</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">I0</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/rf.html#CavityResonator.Vb"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.rf.CavityResonator.Vb" title="Permalink to this definition">¶</a></dt>
+<dd><p>Return beam voltage in [V].</p>
+<dl class="simple">
+<dt>I0<span class="classifier">float</span></dt><dd><p>Beam current in [A].</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>float</dt><dd><p>Beam voltage in [V].</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.rf.CavityResonator.Vbr">
+<span class="sig-name descname"><span class="pre">Vbr</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">I0</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/rf.html#CavityResonator.Vbr"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.rf.CavityResonator.Vbr" title="Permalink to this definition">¶</a></dt>
+<dd><p>Return beam voltage at resonance in [V].</p>
+<dl class="simple">
+<dt>I0<span class="classifier">float</span></dt><dd><p>Beam current in [A].</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>float</dt><dd><p>Beam voltage at resonance in [V].</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.rf.CavityResonator.Z">
+<span class="sig-name descname"><span class="pre">Z</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">f</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/rf.html#CavityResonator.Z"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.rf.CavityResonator.Z" title="Permalink to this definition">¶</a></dt>
+<dd><p>Cavity impedance in [Ohm] for a given frequency f in [Hz]</p>
+</dd></dl>
+
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.tracking.rf.CavityResonator.beam_phase">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">beam_phase</span></span><a class="headerlink" href="#mbtrack2.tracking.rf.CavityResonator.beam_phase" title="Permalink to this definition">¶</a></dt>
+<dd><p>Beam loading phase in [rad]</p>
+</dd></dl>
+
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.tracking.rf.CavityResonator.beam_voltage">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">beam_voltage</span></span><a class="headerlink" href="#mbtrack2.tracking.rf.CavityResonator.beam_voltage" title="Permalink to this definition">¶</a></dt>
+<dd><p>Beam loading voltage in [V]</p>
+</dd></dl>
+
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.tracking.rf.CavityResonator.beta">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">beta</span></span><a class="headerlink" href="#mbtrack2.tracking.rf.CavityResonator.beta" title="Permalink to this definition">¶</a></dt>
+<dd><p>Coupling coefficient</p>
+</dd></dl>
+
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.tracking.rf.CavityResonator.cavity_phase">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">cavity_phase</span></span><a class="headerlink" href="#mbtrack2.tracking.rf.CavityResonator.cavity_phase" title="Permalink to this definition">¶</a></dt>
+<dd><p>Cavity total phase in [rad]</p>
+</dd></dl>
+
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.tracking.rf.CavityResonator.cavity_phasor">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">cavity_phasor</span></span><a class="headerlink" href="#mbtrack2.tracking.rf.CavityResonator.cavity_phasor" title="Permalink to this definition">¶</a></dt>
+<dd><p>Cavity total phasor in [V]</p>
+</dd></dl>
+
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.tracking.rf.CavityResonator.cavity_phasor_record">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">cavity_phasor_record</span></span><a class="headerlink" href="#mbtrack2.tracking.rf.CavityResonator.cavity_phasor_record" title="Permalink to this definition">¶</a></dt>
+<dd><p>Last cavity phasor value of each bunch in [V]</p>
+</dd></dl>
+
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.tracking.rf.CavityResonator.cavity_voltage">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">cavity_voltage</span></span><a class="headerlink" href="#mbtrack2.tracking.rf.CavityResonator.cavity_voltage" title="Permalink to this definition">¶</a></dt>
+<dd><p>Cavity total voltage in [V]</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.rf.CavityResonator.dVRF">
+<span class="sig-name descname"><span class="pre">dVRF</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">z</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">I0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">F</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">PHI</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/rf.html#CavityResonator.dVRF"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.rf.CavityResonator.dVRF" title="Permalink to this definition">¶</a></dt>
+<dd><p>Return derivative of total RF voltage taking into account form factor amplitude F and form factor phase PHI</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.rf.CavityResonator.ddVRF">
+<span class="sig-name descname"><span class="pre">ddVRF</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">z</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">I0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">F</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">PHI</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/rf.html#CavityResonator.ddVRF"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.rf.CavityResonator.ddVRF" title="Permalink to this definition">¶</a></dt>
+<dd><p>Return the second derivative of total RF voltage taking into account form factor amplitude F and form factor phase PHI</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.rf.CavityResonator.deltaVRF">
+<span class="sig-name descname"><span class="pre">deltaVRF</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">z</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">I0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">F</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">PHI</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/rf.html#CavityResonator.deltaVRF"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.rf.CavityResonator.deltaVRF" title="Permalink to this definition">¶</a></dt>
+<dd><p>Return the generator voltage minus beam loading voltage taking into account form factor amplitude F and form factor phase PHI</p>
+</dd></dl>
+
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.tracking.rf.CavityResonator.detune">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">detune</span></span><a class="headerlink" href="#mbtrack2.tracking.rf.CavityResonator.detune" title="Permalink to this definition">¶</a></dt>
+<dd><p>Cavity detuning [Hz] - defined as (fr - m*f1)</p>
+</dd></dl>
+
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.tracking.rf.CavityResonator.filling_time">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">filling_time</span></span><a class="headerlink" href="#mbtrack2.tracking.rf.CavityResonator.filling_time" title="Permalink to this definition">¶</a></dt>
+<dd><p>Cavity filling time in [s]</p>
+</dd></dl>
+
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.tracking.rf.CavityResonator.fr">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">fr</span></span><a class="headerlink" href="#mbtrack2.tracking.rf.CavityResonator.fr" title="Permalink to this definition">¶</a></dt>
+<dd><p>Resonance frequency of the cavity in [Hz]</p>
+</dd></dl>
+
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.tracking.rf.CavityResonator.generator_phasor">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">generator_phasor</span></span><a class="headerlink" href="#mbtrack2.tracking.rf.CavityResonator.generator_phasor" title="Permalink to this definition">¶</a></dt>
+<dd><p>Generator phasor in [V]</p>
+</dd></dl>
+
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.tracking.rf.CavityResonator.ig_phasor_record">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">ig_phasor_record</span></span><a class="headerlink" href="#mbtrack2.tracking.rf.CavityResonator.ig_phasor_record" title="Permalink to this definition">¶</a></dt>
+<dd><p>Last current generator phasor of each bunch in [A]</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.rf.CavityResonator.init_phasor">
+<span class="sig-name descname"><span class="pre">init_phasor</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">beam</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/rf.html#CavityResonator.init_phasor"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.rf.CavityResonator.init_phasor" title="Permalink to this definition">¶</a></dt>
+<dd><p>Initialize the beam phasor for a given beam distribution using an
+analytic formula [1].</p>
+<p>No modifications on the Beam object.</p>
+<p>beam : Beam object</p>
+<p>[1] mbtrack2 manual.</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.rf.CavityResonator.init_phasor_track">
+<span class="sig-name descname"><span class="pre">init_phasor_track</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">beam</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/rf.html#CavityResonator.init_phasor_track"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.rf.CavityResonator.init_phasor_track" title="Permalink to this definition">¶</a></dt>
+<dd><p>Initialize the beam phasor for a given beam distribution using a
+tracking like method.</p>
+<p>Follow the same steps as the track method but in the “rf” reference 
+frame and without any modifications on the beam.</p>
+<p>beam : Beam object</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.rf.CavityResonator.init_tracking">
+<span class="sig-name descname"><span class="pre">init_tracking</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">beam</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/rf.html#CavityResonator.init_tracking"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.rf.CavityResonator.init_tracking" title="Permalink to this definition">¶</a></dt>
+<dd><p>Initialization of the tracking.</p>
+<p>beam : Beam object</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.rf.CavityResonator.is_CBI_stable">
+<span class="sig-name descname"><span class="pre">is_CBI_stable</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">I0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">synchrotron_tune</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">modes</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">bool_return</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/rf.html#CavityResonator.is_CBI_stable"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.rf.CavityResonator.is_CBI_stable" title="Permalink to this definition">¶</a></dt>
+<dd><p>Check Coupled-Bunch-Instability stability, 
+Effect of Direct RF feedback is not included.</p>
+<p>This method is a wraper around lcbi_growth_rate to caluclate the CBI 
+growth rate from the CavityResonator own impedance.</p>
+<p>See lcbi_growth_rate for details.</p>
+<dl>
+<dt>I0<span class="classifier">float</span></dt><dd><p>Beam current in [A].</p>
+</dd>
+<dt>synchrotron_tune<span class="classifier">float, optinal</span></dt><dd><p>Fractional number of longitudinal tune.
+If None, synchrotron_tune is computed using self.Vc as total 
+voltage.
+Default is None.</p>
+</dd>
+<dt>modes<span class="classifier">float or list of float, optional</span></dt><dd><p>Coupled Bunch Instability mode numbers to consider.
+If not None, return growth_rates of the input coupled bunch modes.
+Default is None.</p>
+</dd>
+<dt>bool_return<span class="classifier">bool, optional</span></dt><dd><dl>
+<dt>If True:</dt><dd><ul class="simple">
+<li><p>return True if the most unstable mode is stronger than</p></li>
+</ul>
+<p>longitudinal damping time.
+- return False if it is not the case.</p>
+</dd>
+</dl>
+<p>Default is False.</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>growth_rate<span class="classifier">float</span></dt><dd><p>Maximum coupled bunch instability growth rate in [s-1].</p>
+</dd>
+<dt>mu<span class="classifier">int</span></dt><dd><p>Coupled bunch mode number corresponding to the maximum coupled bunch 
+instability growth rate.</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.rf.CavityResonator.is_DC_Robinson_stable">
+<span class="sig-name descname"><span class="pre">is_DC_Robinson_stable</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">I0</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/rf.html#CavityResonator.is_DC_Robinson_stable"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.rf.CavityResonator.is_DC_Robinson_stable" title="Permalink to this definition">¶</a></dt>
+<dd><p>Check DC Robinson stability - Eq. (6.1.1) [1]</p>
+<dl class="simple">
+<dt>I0<span class="classifier">float</span></dt><dd><p>Beam current in [A].</p>
+</dd>
+</dl>
+<p>bool</p>
+</dd></dl>
+
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.tracking.rf.CavityResonator.loss_factor">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">loss_factor</span></span><a class="headerlink" href="#mbtrack2.tracking.rf.CavityResonator.loss_factor" title="Permalink to this definition">¶</a></dt>
+<dd><p>Cavity loss factor in [V/C]</p>
+</dd></dl>
+
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.tracking.rf.CavityResonator.m">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">m</span></span><a class="headerlink" href="#mbtrack2.tracking.rf.CavityResonator.m" title="Permalink to this definition">¶</a></dt>
+<dd><p>Harmonic number of the cavity</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.rf.CavityResonator.phasor_decay">
+<span class="sig-name descname"><span class="pre">phasor_decay</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">time</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">ref_frame</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'beam'</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/rf.html#CavityResonator.phasor_decay"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.rf.CavityResonator.phasor_decay" title="Permalink to this definition">¶</a></dt>
+<dd><p>Compute the beam phasor decay during a given time span, assuming that 
+no particles are crossing the cavity during the time span.</p>
+<dl class="simple">
+<dt>time<span class="classifier">float</span></dt><dd><p>Time span in [s], can be positive or negative.</p>
+</dd>
+<dt>ref_frame<span class="classifier">string, optional</span></dt><dd><p>Reference frame to be used, can be “beam” or “rf”.</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.rf.CavityResonator.phasor_evol">
+<span class="sig-name descname"><span class="pre">phasor_evol</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">profile</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">bin_length</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">charge_per_mp</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">ref_frame</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'beam'</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/rf.html#CavityResonator.phasor_evol"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.rf.CavityResonator.phasor_evol" title="Permalink to this definition">¶</a></dt>
+<dd><p>Compute the beam phasor evolution during the crossing of a bunch using 
+an analytic formula [1].</p>
+<p>Assume that the phasor decay happens before the beam loading.</p>
+<dl class="simple">
+<dt>profile<span class="classifier">array</span></dt><dd><p>Longitudinal profile of the bunch in [number of macro-particle].</p>
+</dd>
+<dt>bin_length<span class="classifier">float</span></dt><dd><p>Length of a bin in [s].</p>
+</dd>
+<dt>charge_per_mp<span class="classifier">float</span></dt><dd><p>Charge per macro-particle in [C].</p>
+</dd>
+<dt>ref_frame<span class="classifier">string, optional</span></dt><dd><p>Reference frame to be used, can be “beam” or “rf”.</p>
+</dd>
+</dl>
+<p>[1] mbtrack2 manual.</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.rf.CavityResonator.plot_DC_Robinson_stability">
+<span class="sig-name descname"><span class="pre">plot_DC_Robinson_stability</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">detune_range</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">[-</span> <span class="pre">100000.0,</span> <span class="pre">100000.0]</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/rf.html#CavityResonator.plot_DC_Robinson_stability"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.rf.CavityResonator.plot_DC_Robinson_stability" title="Permalink to this definition">¶</a></dt>
+<dd><p>Plot DC Robinson stability limit.</p>
+<dl class="simple">
+<dt>detune_range<span class="classifier">list or array, optional</span></dt><dd><p>Range of tuning to plot in [Hz].</p>
+</dd>
+</dl>
+<p>Figure.</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.rf.CavityResonator.plot_phasor">
+<span class="sig-name descname"><span class="pre">plot_phasor</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">I0</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/rf.html#CavityResonator.plot_phasor"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.rf.CavityResonator.plot_phasor" title="Permalink to this definition">¶</a></dt>
+<dd><p>Plot phasor diagram showing the vector addition of generator and beam 
+loading voltage.</p>
+<dl class="simple">
+<dt>I0<span class="classifier">float</span></dt><dd><p>Beam current in [A].</p>
+</dd>
+</dl>
+<p>Figure.</p>
+</dd></dl>
+
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.tracking.rf.CavityResonator.psi">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">psi</span></span><a class="headerlink" href="#mbtrack2.tracking.rf.CavityResonator.psi" title="Permalink to this definition">¶</a></dt>
+<dd><p>Tuning angle in [rad]</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.rf.CavityResonator.sample_voltage">
+<span class="sig-name descname"><span class="pre">sample_voltage</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">n_points</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">10000.0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">index</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/rf.html#CavityResonator.sample_voltage"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.rf.CavityResonator.sample_voltage" title="Permalink to this definition">¶</a></dt>
+<dd><p>Sample the voltage seen by a zero charge particle during an RF period.</p>
+<dl class="simple">
+<dt>n_points<span class="classifier">int or float, optional</span></dt><dd><p>Number of sample points. The default is 1e4.</p>
+</dd>
+<dt>index<span class="classifier">int, optional</span></dt><dd><p>RF bucket number to sample. Be carful if index &gt; 0 as no new beam 
+loading is not taken into account here.
+The default is 0.</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>pos<span class="classifier">array of float</span></dt><dd><p>Array of position from -T1/2 to T1/2.</p>
+</dd>
+<dt>voltage_rec<span class="classifier">array of float</span></dt><dd><p>Recoring of the voltage.</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.rf.CavityResonator.set_generator">
+<span class="sig-name descname"><span class="pre">set_generator</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">I0</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/rf.html#CavityResonator.set_generator"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.rf.CavityResonator.set_generator" title="Permalink to this definition">¶</a></dt>
+<dd><p>Set generator parameters (Pg, Vgr, theta_gr, Vg and theta_g) for a 
+given current and set of parameters.</p>
+<dl class="simple">
+<dt>I0<span class="classifier">float</span></dt><dd><p>Beam current in [A].</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.rf.CavityResonator.set_optimal_coupling">
+<span class="sig-name descname"><span class="pre">set_optimal_coupling</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">I0</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/rf.html#CavityResonator.set_optimal_coupling"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.rf.CavityResonator.set_optimal_coupling" title="Permalink to this definition">¶</a></dt>
+<dd><p>Set coupling to optimal value - Eq. (4.2.3) in [1].</p>
+<dl class="simple">
+<dt>I0<span class="classifier">float</span></dt><dd><p>Beam current in [A].</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.rf.CavityResonator.set_optimal_detune">
+<span class="sig-name descname"><span class="pre">set_optimal_detune</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">I0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">F</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/rf.html#CavityResonator.set_optimal_detune"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.rf.CavityResonator.set_optimal_detune" title="Permalink to this definition">¶</a></dt>
+<dd><p>Set detuning to optimal conditions - second Eq. (4.2.1) in [1].</p>
+<dl class="simple">
+<dt>I0<span class="classifier">float</span></dt><dd><p>Beam current in [A].</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.rf.CavityResonator.track">
+<span class="sig-name descname"><span class="pre">track</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">beam</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/rf.html#CavityResonator.track"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.rf.CavityResonator.track" title="Permalink to this definition">¶</a></dt>
+<dd><p>Track a Beam object through the CavityResonator object.</p>
+<p>Can be used with or without mpi.
+If used with mpi, beam.mpi.share_distributions must be called before.</p>
+<p>The beam phasor is given at t=0 (synchronous particle) of the first 
+non empty bunch.</p>
+<p>beam : Beam object</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.rf.CavityResonator.update_feedback">
+<span class="sig-name descname"><span class="pre">update_feedback</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/rf.html#CavityResonator.update_feedback"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.rf.CavityResonator.update_feedback" title="Permalink to this definition">¶</a></dt>
+<dd><p>Force feedback update from current CavityResonator parameters.</p>
+</dd></dl>
+
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.tracking.rf.CavityResonator.wr">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">wr</span></span><a class="headerlink" href="#mbtrack2.tracking.rf.CavityResonator.wr" title="Permalink to this definition">¶</a></dt>
+<dd><p>Angular resonance frequency in [Hz.rad]</p>
+</dd></dl>
+
+</dd></dl>
+
+<dl class="py class">
+<dt class="sig sig-object py" id="mbtrack2.tracking.rf.DirectFeedback">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">mbtrack2.tracking.rf.</span></span><span class="sig-name descname"><span class="pre">DirectFeedback</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">DFB_gain</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">DFB_phase_shift</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">DFB_sample_num</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">DFB_every</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">DFB_delay</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/rf.html#DirectFeedback"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.rf.DirectFeedback" title="Permalink to this definition">¶</a></dt>
+<dd><p>Bases: <a class="reference internal" href="#mbtrack2.tracking.rf.ProportionalIntegralLoop" title="mbtrack2.tracking.rf.ProportionalIntegralLoop"><code class="xref py py-class docutils literal notranslate"><span class="pre">ProportionalIntegralLoop</span></code></a></p>
+<p>Direct RF FB (DFB) via generator current (ig) using PI controller [1,2].</p>
+<p>The DirectFeedback inherits from ProportionalIntegralLoop so all 
+mandatory parameters from ProportionalIntegralLoop should be passed as
+kwargs when initializing a DirectFeedback object.</p>
+<p>To avoid cavity-beam unmatching (large synchrotron oscilation of beam),
+the CavityResonator generator parameters should be set before 
+initialization.</p>
+<dl class="simple">
+<dt>The loop must be added to the CavityResonator object using:</dt><dd><p>cav_res.feedback.append(loop)</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>DFB_gain<span class="classifier">float</span></dt><dd><p>Gain of the DFB.</p>
+</dd>
+<dt>DFB_phase_shift<span class="classifier">float</span></dt><dd><p>Phase shift of the DFB.</p>
+</dd>
+<dt>DFB_sample_num<span class="classifier">int, optional</span></dt><dd><p>Sample number to monitor Vc for the DFB.
+The averaged Vc value in DFB_sample_num is monitored.
+Units are in bucket numbers.
+If None, value from the ProportionalIntegralLoop is used.
+Default is None.</p>
+</dd>
+<dt>DFB_every<span class="classifier">int, optional</span></dt><dd><p>Interval to monitor and change Vc for the DFB.
+Units are in bucket numbers.
+If None, value from the ProportionalIntegralLoop is used.
+Default is None.</p>
+</dd>
+<dt>DFB_delay<span class="classifier">int, optional</span></dt><dd><p>Loop delay of the DFB.
+Units are in bucket numbers.
+If None, value from the ProportionalIntegralLoop is used.
+Default is None.</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>phase_shift<span class="classifier">float</span></dt><dd><p>Phase shift applied to DFB, defined as psi - DFB_phase_shift.</p>
+</dd>
+<dt>DFB_psi: float</dt><dd><p>Return detuning angle value with Direct RF feedback in [rad].</p>
+</dd>
+<dt>DFB_alpha<span class="classifier">float</span></dt><dd><p>Return the amplitude ratio alpha of the DFB.</p>
+</dd>
+<dt>DFB_gamma<span class="classifier">float</span></dt><dd><p>Return the gain gamma of the DFB.</p>
+</dd>
+<dt>DFB_Rs<span class="classifier">float</span></dt><dd><p>Return the shunt impedance of the DFB in [ohm].</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>DFB_parameter_set(DFB_gain, DFB_phase_shift)</dt><dd><p>Set DFB gain and phase shift parameters.</p>
+</dd>
+<dt>track()</dt><dd><p>Tracking method for the Direct RF feedback.</p>
+</dd>
+<dt>DFB_Vg()</dt><dd><p>Return the generator voltage main and DFB components in [V].</p>
+</dd>
+<dt>DFB_fs()</dt><dd><p>Return the modified synchrotron frequency in [Hz].</p>
+</dd>
+</dl>
+<p>[1] : Akai, K. (2022). Stability analysis of rf accelerating mode with 
+feedback loops under heavy beam loading in SuperKEKB. PRAB, 25(10), 
+102002.
+[2] : N. Yamamoto et al. (2023). Stability survey of a double RF system 
+with RF feedback loops for bunch lengthening in a low-emittance synchrotron 
+ring. In Proc. IPAC’23. doi:10.18429/JACoW-IPAC2023-WEPL161</p>
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.tracking.rf.DirectFeedback.DFB_Rs">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">DFB_Rs</span></span><a class="headerlink" href="#mbtrack2.tracking.rf.DirectFeedback.DFB_Rs" title="Permalink to this definition">¶</a></dt>
+<dd><p>Return the shunt impedance of the DFB in [ohm].</p>
+<p>Eq. (15) of [1].</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.rf.DirectFeedback.DFB_Vg">
+<span class="sig-name descname"><span class="pre">DFB_Vg</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">vc</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">-</span> <span class="pre">1</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/rf.html#DirectFeedback.DFB_Vg"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.rf.DirectFeedback.DFB_Vg" title="Permalink to this definition">¶</a></dt>
+<dd><p>Return the generator voltage main and DFB components in [V].</p>
+</dd></dl>
+
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.tracking.rf.DirectFeedback.DFB_alpha">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">DFB_alpha</span></span><a class="headerlink" href="#mbtrack2.tracking.rf.DirectFeedback.DFB_alpha" title="Permalink to this definition">¶</a></dt>
+<dd><p>Return the amplitude ratio alpha of the DFB.</p>
+<p>Near Eq. (13) of [1].</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.rf.DirectFeedback.DFB_fs">
+<span class="sig-name descname"><span class="pre">DFB_fs</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">vg_main</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">-</span> <span class="pre">1</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">vg_drf</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">-</span> <span class="pre">1</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/rf.html#DirectFeedback.DFB_fs"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.rf.DirectFeedback.DFB_fs" title="Permalink to this definition">¶</a></dt>
+<dd><p>Return the modified synchrotron frequency in [Hz].</p>
+</dd></dl>
+
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.tracking.rf.DirectFeedback.DFB_gamma">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">DFB_gamma</span></span><a class="headerlink" href="#mbtrack2.tracking.rf.DirectFeedback.DFB_gamma" title="Permalink to this definition">¶</a></dt>
+<dd><p>Return the gain gamma of the DFB.</p>
+<p>Near Eq. (13) of [1].</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.rf.DirectFeedback.DFB_parameter_set">
+<span class="sig-name descname"><span class="pre">DFB_parameter_set</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">DFB_gain</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">DFB_phase_shift</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/rf.html#DirectFeedback.DFB_parameter_set"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.rf.DirectFeedback.DFB_parameter_set" title="Permalink to this definition">¶</a></dt>
+<dd><p>Set DFB gain and phase shift parameters.</p>
+<dl class="simple">
+<dt>DFB_gain<span class="classifier">float</span></dt><dd><p>Gain of the DFB.</p>
+</dd>
+<dt>DFB_phase_shift<span class="classifier">float</span></dt><dd><p>Phase shift of the DFB.</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.tracking.rf.DirectFeedback.DFB_phase_shift">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">DFB_phase_shift</span></span><a class="headerlink" href="#mbtrack2.tracking.rf.DirectFeedback.DFB_phase_shift" title="Permalink to this definition">¶</a></dt>
+<dd><p>Return DFB phase shift.</p>
+</dd></dl>
+
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.tracking.rf.DirectFeedback.DFB_psi">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">DFB_psi</span></span><a class="headerlink" href="#mbtrack2.tracking.rf.DirectFeedback.DFB_psi" title="Permalink to this definition">¶</a></dt>
+<dd><p>Return detuning angle value with Direct RF feedback in [rad].</p>
+<p>Fig.4 of ref [1].</p>
+</dd></dl>
+
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.tracking.rf.DirectFeedback.phase_shift">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">phase_shift</span></span><a class="headerlink" href="#mbtrack2.tracking.rf.DirectFeedback.phase_shift" title="Permalink to this definition">¶</a></dt>
+<dd><p>Return phase shift applied to DFB.
+Defined as self.cav_res.psi - self.DFB_phase_shift.</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.rf.DirectFeedback.track">
+<span class="sig-name descname"><span class="pre">track</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/rf.html#DirectFeedback.track"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.rf.DirectFeedback.track" title="Permalink to this definition">¶</a></dt>
+<dd><p>Tracking method for the Direct RF feedback.</p>
+<p>None.</p>
+</dd></dl>
+
+</dd></dl>
+
+<dl class="py class">
+<dt class="sig sig-object py" id="mbtrack2.tracking.rf.ProportionalIntegralLoop">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">mbtrack2.tracking.rf.</span></span><span class="sig-name descname"><span class="pre">ProportionalIntegralLoop</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">ring</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">cav_res</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">gain</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">sample_num</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">every</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">delay</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">IIR_cutoff</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">FF</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/rf.html#ProportionalIntegralLoop"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.rf.ProportionalIntegralLoop" title="Permalink to this definition">¶</a></dt>
+<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">object</span></code></p>
+<p>Proportional Integral (PI) loop to control a CavityResonator amplitude and 
+phase via generator current (ig) [1,2].</p>
+<p>Feedback reference targets (setpoints) are cav_res.Vc and cav_res.theta.</p>
+<p>The ProportionalIntegralLoop should be initialized only after generator 
+parameters are set.</p>
+<dl class="simple">
+<dt>The loop must be added to the CavityResonator object using:</dt><dd><p>cav_res.feedback.append(loop)</p>
+</dd>
+</dl>
+<p>When the reference target is changed, it might be needed to re-initialize 
+the feedforward constant by calling init_FFconst().</p>
+<p>ring : Synchrotron object
+cav_res : CavityResonator object</p>
+<blockquote>
+<div><p>CavityResonator in which the loop will be added.</p>
+</div></blockquote>
+<dl class="simple">
+<dt>gain<span class="classifier">float list</span></dt><dd><p>Proportional gain (Pgain) and integral gain (Igain) of the feedback 
+system in the form of a list [Pgain, Igain].
+In case of normal conducting cavity (QL~1e4), the Pgain of ~1.0 and 
+Igain of ~1e4(5) are usually used.
+In case of super conducting cavity (QL &gt; 1e6), the Pgain of ~100 
+can be used.
+In a “bad” parameter set, unstable oscillation of the cavity voltage 
+can be caused. So, a parameter scan of the gain should be made.
+Igain * ring.T1 / dtau is Ki defined as a the coefficients for 
+integral part in of [1], where dtau is a clock period of the PI controller.</p>
+</dd>
+<dt>sample_num<span class="classifier">int</span></dt><dd><p>Number of bunch over which the mean cavity voltage is computed.
+Units are in bucket numbers.</p>
+</dd>
+<dt>every<span class="classifier">int</span></dt><dd><p>Sampling and clock period of the feedback controller
+Time interval between two cavity voltage monitoring and feedback.
+Units are in bucket numbers.</p>
+</dd>
+<dt>delay<span class="classifier">int</span></dt><dd><p>Loop delay of the PI feedback system. 
+Units are in bucket numbers.</p>
+</dd>
+<dt>IIR_cutoff<span class="classifier">float, optinal</span></dt><dd><p>Cutoff frequency of the IIR filter in [Hz].
+If 0, cutoff frequency is infinity.
+Default is 0.</p>
+</dd>
+<dt>FF<span class="classifier">bool, optional</span></dt><dd><p>Boolean switch to use feedforward constant.
+True is recommended to prevent a cavity voltage drop in the beginning 
+of the tracking.
+In case of small Pgain (QL ~ 1e4), cavity voltage drop may cause 
+beam loss due to static Robinson.
+Default is True.</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>track()</dt><dd><p>Tracking method for the Cavity PI control feedback.</p>
+</dd>
+<dt>init_Ig2Vg_matrix()</dt><dd><p>Initialize matrix for Ig2Vg_matrix.</p>
+</dd>
+<dt>init_FFconst()</dt><dd><p>Initialize feedforward constant.</p>
+</dd>
+<dt>Ig2Vg_matrix()</dt><dd><p>Return Vg from Ig using matrix formalism.</p>
+</dd>
+<dt>Ig2Vg()</dt><dd><p>Go from Ig to Vg and apply values.</p>
+</dd>
+<dt>Vg2Ig(Vg)</dt><dd><p>Return Ig from Vg (assuming constant Vg).</p>
+</dd>
+<dt>IIR_init(cutoff)</dt><dd><p>Initialization for the IIR filter.</p>
+</dd>
+<dt>IIR(input)</dt><dd><p>Return IIR filter output.</p>
+</dd>
+<dt>IIRcutoff()</dt><dd><p>Return IIR cutoff frequency in [Hz].</p>
+</dd>
+</dl>
+<p>Assumption : delay &gt;&gt; every ~ sample_num</p>
+<p>Adjusting ig(Vg) parameter to keep the cavity voltage constant (to target values).
+The “track” method is</p>
+<blockquote>
+<div><p>1) Monitoring the cavity voltage phasor
+Mean cavity voltage value between specified bunch number (sample_num) is monitored
+with specified interval period (every).
+2) Changing the ig phasor
+The ig phasor is changed according the difference of the specified
+reference values with specified gain (gain).
+By using ig instead of Vg, the cavity response can be taken account.
+3) ig changes are reflected to Vg after the specifed delay (delay) of the system</p>
+</div></blockquote>
+<dl>
+<dt>Vc–&gt;(rot)–&gt;IIR–&gt;(-)–&gt;(V-&gt;I,fac)–&gt;PI–&gt;Ig –&gt; Vg</dt><dd><blockquote>
+<div><div class="line-block">
+<div class="line"><br /></div>
+</div>
+</div></blockquote>
+<p>Ref</p>
+</dd>
+</dl>
+<dl>
+<dt>PF; E0=2.5GeV, C=187m, frf=500MHz</dt><dd><p>QL=11800, fs0=23kHz
+==&gt; gain=[0.5,1e4], sample_num=8, every=7(13ns), delay=500(1us)</p>
+<blockquote>
+<div><p>is one reasonable parameter set.</p>
+</div></blockquote>
+<dl class="simple">
+<dt>The practical clock period is 13ns.</dt><dd><p>==&gt; Igain_PF = Igain_mbtrack * Trf / 13ns = Igain_mbtrack * 0.153</p>
+</dd>
+</dl>
+</dd>
+</dl>
+<p>[1] : <a class="reference external" href="https://en.wikipedia.org/wiki/PID_controller">https://en.wikipedia.org/wiki/PID_controller</a>
+[2] : Yamamoto, N., Takahashi, T., &amp; Sakanaka, S. (2018). Reduction and 
+compensation of the transient beam loading effect in a double rf system 
+of synchrotron light sources. PRAB, 21(1), 012001.</p>
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.rf.ProportionalIntegralLoop.IIR">
+<span class="sig-name descname"><span class="pre">IIR</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">input</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/rf.html#ProportionalIntegralLoop.IIR"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.rf.ProportionalIntegralLoop.IIR" title="Permalink to this definition">¶</a></dt>
+<dd><p>Return IIR filter output.</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.rf.ProportionalIntegralLoop.IIR_init">
+<span class="sig-name descname"><span class="pre">IIR_init</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">cutoff</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/rf.html#ProportionalIntegralLoop.IIR_init"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.rf.ProportionalIntegralLoop.IIR_init" title="Permalink to this definition">¶</a></dt>
+<dd><p>Initialization for the IIR filter.</p>
+<dl class="simple">
+<dt>cutoff<span class="classifier">float</span></dt><dd><p>Cutoff frequency of the IIR filter in [Hz].
+If 0, cutoff frequency is infinity.</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.tracking.rf.ProportionalIntegralLoop.IIRcutoff">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">IIRcutoff</span></span><a class="headerlink" href="#mbtrack2.tracking.rf.ProportionalIntegralLoop.IIRcutoff" title="Permalink to this definition">¶</a></dt>
+<dd><p>Return IIR cutoff frequency in [Hz].</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.rf.ProportionalIntegralLoop.Ig2Vg">
+<span class="sig-name descname"><span class="pre">Ig2Vg</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/rf.html#ProportionalIntegralLoop.Ig2Vg"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.rf.ProportionalIntegralLoop.Ig2Vg" title="Permalink to this definition">¶</a></dt>
+<dd><p>Go from Ig to Vg.</p>
+<p>Apply new values to cav_res.generator_phasor_record, cav_res.Vg and
+cav_res.theta_g from ig_phasor_record.</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.rf.ProportionalIntegralLoop.Ig2Vg_matrix">
+<span class="sig-name descname"><span class="pre">Ig2Vg_matrix</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/rf.html#ProportionalIntegralLoop.Ig2Vg_matrix"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.rf.ProportionalIntegralLoop.Ig2Vg_matrix" title="Permalink to this definition">¶</a></dt>
+<dd><p>Return Vg from Ig using matrix formalism.
+Warning: self.init_Ig2Vg should be called after each CavityResonator 
+parameter change.</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.rf.ProportionalIntegralLoop.Vg2Ig">
+<span class="sig-name descname"><span class="pre">Vg2Ig</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">Vg</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/rf.html#ProportionalIntegralLoop.Vg2Ig"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.rf.ProportionalIntegralLoop.Vg2Ig" title="Permalink to this definition">¶</a></dt>
+<dd><p>Return Ig from Vg (assuming constant Vg).</p>
+<p>Eq.25 of ref [2] assuming the dVg/dt = 0.</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.rf.ProportionalIntegralLoop.init_FFconst">
+<span class="sig-name descname"><span class="pre">init_FFconst</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/rf.html#ProportionalIntegralLoop.init_FFconst"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.rf.ProportionalIntegralLoop.init_FFconst" title="Permalink to this definition">¶</a></dt>
+<dd><p>Initialize feedforward constant.</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.rf.ProportionalIntegralLoop.init_Ig2Vg_matrix">
+<span class="sig-name descname"><span class="pre">init_Ig2Vg_matrix</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/rf.html#ProportionalIntegralLoop.init_Ig2Vg_matrix"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.rf.ProportionalIntegralLoop.init_Ig2Vg_matrix" title="Permalink to this definition">¶</a></dt>
+<dd><p>Initialize matrix for Ig2Vg_matrix.</p>
+<p>Shoud be called before first use of Ig2Vg_matrix and after each cavity 
+parameter change.</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.rf.ProportionalIntegralLoop.track">
+<span class="sig-name descname"><span class="pre">track</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">apply_changes</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/rf.html#ProportionalIntegralLoop.track"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.rf.ProportionalIntegralLoop.track" title="Permalink to this definition">¶</a></dt>
+<dd><p>Tracking method for the Cavity PI control feedback.</p>
+<p>None.</p>
+</dd></dl>
+
+</dd></dl>
+
+<dl class="py class">
+<dt class="sig sig-object py" id="mbtrack2.tracking.rf.ProportionalLoop">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">mbtrack2.tracking.rf.</span></span><span class="sig-name descname"><span class="pre">ProportionalLoop</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">ring</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">cav_res</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">gain_A</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">gain_P</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">delay</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/rf.html#ProportionalLoop"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.rf.ProportionalLoop" title="Permalink to this definition">¶</a></dt>
+<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">object</span></code></p>
+<p>Proportional feedback loop to control a CavityResonator amplitude and phase.</p>
+<p>Feedback setpoints are cav_res.Vc and cav_res.theta.</p>
+<dl class="simple">
+<dt>The loop must be added to the CavityResonator object using:</dt><dd><p>cav_res.feedback.append(loop)</p>
+</dd>
+</dl>
+<p>ring : Synchrotron object
+cav_res : CavityResonator</p>
+<blockquote>
+<div><p>The CavityResonator which is to be controlled.</p>
+</div></blockquote>
+<dl class="simple">
+<dt>gain_A<span class="classifier">float</span></dt><dd><p>Amplitude (voltage) gain of the feedback.</p>
+</dd>
+<dt>gain_P<span class="classifier">float</span></dt><dd><p>Phase gain of the feedback.</p>
+</dd>
+<dt>delay<span class="classifier">int</span></dt><dd><p>Feedback delay in unit of turns.
+Must be supperior or equal to 1.</p>
+</dd>
+</dl>
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.rf.ProportionalLoop.track">
+<span class="sig-name descname"><span class="pre">track</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/rf.html#ProportionalLoop.track"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.rf.ProportionalLoop.track" title="Permalink to this definition">¶</a></dt>
+<dd><p>Tracking method for the amplitude and phase loop.</p>
+<p>None.</p>
+</dd></dl>
+
+</dd></dl>
+
+<dl class="py class">
+<dt class="sig sig-object py" id="mbtrack2.tracking.rf.RFCavity">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">mbtrack2.tracking.rf.</span></span><span class="sig-name descname"><span class="pre">RFCavity</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">ring</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">m</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">Vc</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">theta</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/rf.html#RFCavity"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.rf.RFCavity" title="Permalink to this definition">¶</a></dt>
+<dd><p>Bases: <a class="reference internal" href="#mbtrack2.tracking.element.Element" title="mbtrack2.tracking.element.Element"><code class="xref py py-class docutils literal notranslate"><span class="pre">Element</span></code></a></p>
+<p>Perfect RF cavity class for main and harmonic RF cavities.
+Use cosine definition.</p>
+<p>ring : Synchrotron object
+m : int</p>
+<blockquote>
+<div><p>Harmonic number of the cavity</p>
+</div></blockquote>
+<dl class="simple">
+<dt>Vc<span class="classifier">float</span></dt><dd><p>Amplitude of cavity voltage [V]</p>
+</dd>
+<dt>theta<span class="classifier">float</span></dt><dd><p>Phase of Cavity voltage</p>
+</dd>
+</dl>
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.rf.RFCavity.track">
+<span class="sig-name descname"><span class="pre">track</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">bunch</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/rf.html#RFCavity.track"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.rf.RFCavity.track" title="Permalink to this definition">¶</a></dt>
+<dd><p>Tracking method for the element.
+No bunch to bunch interaction, so written for Bunch objects and
+&#64;Element.parallel is used to handle Beam objects.</p>
+<p>bunch : Bunch or Beam object</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.rf.RFCavity.value">
+<span class="sig-name descname"><span class="pre">value</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">val</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/rf.html#RFCavity.value"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.rf.RFCavity.value" title="Permalink to this definition">¶</a></dt>
+<dd></dd></dl>
+
+</dd></dl>
+
+<dl class="py class">
+<dt class="sig sig-object py" id="mbtrack2.tracking.rf.TunerLoop">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">mbtrack2.tracking.rf.</span></span><span class="sig-name descname"><span class="pre">TunerLoop</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">ring</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">cav_res</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">gain</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0.01</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">avering_period</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">offset</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/rf.html#TunerLoop"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.rf.TunerLoop" title="Permalink to this definition">¶</a></dt>
+<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">object</span></code></p>
+<p>Cavity tuner loop used to control a CavityResonator tuning (psi or detune)
+in order to keep the phase between cavity and generator current constant.</p>
+<p>Only a proportional controller is assumed.</p>
+<dl class="simple">
+<dt>The loop must be added to the CavityResonator object using:</dt><dd><p>cav_res.feedback.append(loop)</p>
+</dd>
+</dl>
+<p>ring : Synchrotron object
+cav_res : CavityResonator</p>
+<blockquote>
+<div><p>The CavityResonator which is to be controlled.</p>
+</div></blockquote>
+<dl class="simple">
+<dt>gain<span class="classifier">float</span></dt><dd><p>Proportional gain of the tuner loop.
+If not specified, 0.01 is used.</p>
+</dd>
+<dt>avering_period:</dt><dd><p>Period during which the phase difference is monitored and averaged. 
+Then the feedback correction is applied every avering_period turn.
+Unit is turn number.
+A value longer than one synchrotron period (1/fs) is recommended.
+If not specified, 2-synchrotron period (2/fs) is used, although it is
+too fast compared to the actual situation.</p>
+</dd>
+<dt>offset<span class="classifier">float</span></dt><dd><p>Tuning offset in [rad].</p>
+</dd>
+</dl>
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.rf.TunerLoop.track">
+<span class="sig-name descname"><span class="pre">track</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/rf.html#TunerLoop.track"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.rf.TunerLoop.track" title="Permalink to this definition">¶</a></dt>
+<dd><p>Tracking method for the tuner loop.</p>
+<p>None.</p>
+</dd></dl>
+
+</dd></dl>
+
+</section>
+<section id="module-mbtrack2.tracking.synchrotron">
+<span id="mbtrack2-tracking-synchrotron-module"></span><h2>mbtrack2.tracking.synchrotron module<a class="headerlink" href="#module-mbtrack2.tracking.synchrotron" title="Permalink to this heading">¶</a></h2>
+<p>Module where the Synchrotron class is defined.</p>
+<dl class="py class">
+<dt class="sig sig-object py" id="mbtrack2.tracking.synchrotron.Synchrotron">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">mbtrack2.tracking.synchrotron.</span></span><span class="sig-name descname"><span class="pre">Synchrotron</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">h</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">optics</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">particle</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/synchrotron.html#Synchrotron"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.synchrotron.Synchrotron" title="Permalink to this definition">¶</a></dt>
+<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">object</span></code></p>
+<p>Synchrotron class to store main properties.</p>
+<p>Optional parameters are optional only if the Optics object passed to the 
+class uses a loaded lattice.</p>
+<dl>
+<dt>h<span class="classifier">int</span></dt><dd><p>Harmonic number of the accelerator.</p>
+</dd>
+<dt>optics<span class="classifier">Optics object</span></dt><dd><p>Object where the optic functions are stored.</p>
+</dd>
+<dt>particle<span class="classifier">Particle object</span></dt><dd><p>Particle which is accelerated.</p>
+</dd>
+<dt>tau<span class="classifier">array of shape (3,)</span></dt><dd><p>Horizontal, vertical and longitudinal damping times in [s].</p>
+</dd>
+<dt>sigma_delta<span class="classifier">float</span></dt><dd><p>Equilibrium energy spread.</p>
+</dd>
+<dt>sigma_0<span class="classifier">float</span></dt><dd><p>Natural bunch length in [s].</p>
+</dd>
+<dt>emit<span class="classifier">array of shape (2,)</span></dt><dd><p>Horizontal and vertical equilibrium emittance in [m.rad].</p>
+</dd>
+<dt>L<span class="classifier">float, optional</span></dt><dd><p>Ring circumference in [m].</p>
+</dd>
+<dt>E0<span class="classifier">float, optional</span></dt><dd><p>Nominal (total) energy of the ring in [eV].</p>
+</dd>
+<dt>ac<span class="classifier">float, optional</span></dt><dd><p>Momentum compaction factor.</p>
+</dd>
+<dt>tune<span class="classifier">array of shape (2,), optional</span></dt><dd><p>Horizontal and vertical tunes.</p>
+</dd>
+<dt>chro<span class="classifier">array of shape (2,), optional</span></dt><dd><p>Horizontal and vertical (non-normalized) chromaticities.</p>
+</dd>
+<dt>U0<span class="classifier">float, optional</span></dt><dd><p>Energy loss per turn in [eV].</p>
+</dd>
+<dt>adts<span class="classifier">list of arrays or None, optional</span></dt><dd><p>List that contains arrays of polynomial’s coefficients, in decreasing 
+powers, used to determine Amplitude-Dependent Tune Shifts (ADTS). 
+The order of the elements strictly needs to be
+[coef_xx, coef_yx, coef_xy, coef_yy], where x and y denote the horizontal
+and the vertical plane, respectively, and coef_PQ means the polynomial’s
+coefficients of the ADTS in plane P due to the amplitude in plane Q.</p>
+<p>For example, if the tune shift in y due to the Courant-Snyder invariant 
+Jx is characterized by the equation dQy(x) = 3*Jx**2 + 2*Jx + 1, then 
+coef_yx takes the form np.array([3, 2, 1]).</p>
+<p>Use None, to exclude the ADTS from calculation.</p>
+</dd>
+<dt>mcf_order<span class="classifier">array, optional</span></dt><dd><p>Higher-orders momentum compaction factor in decreasing powers.
+Input here the coefficients considering only the derivatives and which
+do not include any factorial factor.
+The 1st order should be included in the array and be at the last 
+position.</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>T0<span class="classifier">float</span></dt><dd><p>Revolution time in [s].</p>
+</dd>
+<dt>f0<span class="classifier">float</span></dt><dd><p>Revolution frequency in [Hz].</p>
+</dd>
+<dt>omega0<span class="classifier">float</span></dt><dd><p>Angular revolution frequency in [Hz.rad]</p>
+</dd>
+<dt>T1<span class="classifier">flaot</span></dt><dd><p>Fundamental RF period in [s].</p>
+</dd>
+<dt>f1<span class="classifier">float</span></dt><dd><p>Fundamental RF frequency in [Hz].</p>
+</dd>
+<dt>omega1<span class="classifier">float</span></dt><dd><p>Fundamental RF angular frequency in [Hz.rad].</p>
+</dd>
+<dt>k1<span class="classifier">float</span></dt><dd><p>Fundamental RF wave number in [m**-1].</p>
+</dd>
+<dt>gamma<span class="classifier">float</span></dt><dd><p>Relativistic Lorentz gamma.</p>
+</dd>
+<dt>beta<span class="classifier">float</span></dt><dd><p>Relativistic Lorentz beta.</p>
+</dd>
+<dt>long_alpha<span class="classifier">float</span></dt><dd><p>Longitudinal alpha Twiss parameter at the tracking location.
+Initialized at zero.</p>
+</dd>
+<dt>long_beta<span class="classifier">float</span></dt><dd><p>Longitudinal beta Twiss parameter at the tracking location in [s].
+Initialized at zero.</p>
+</dd>
+<dt>long_gamma<span class="classifier">float</span></dt><dd><p>Longitudinal gamma Twiss parameter at the tracking location in [s-1].
+Initialized at zero.</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>synchrotron_tune(V)</dt><dd><p>Compute the (unperturbed) synchrotron tune from main RF voltage.</p>
+</dd>
+<dt>sigma(position)</dt><dd><p>Return the RMS beam size at equilibrium in [m].</p>
+</dd>
+<dt>eta(delta)</dt><dd><p>Momentum compaction taking into account higher orders if provided in
+mcf_order.</p>
+</dd>
+<dt>mcf(delta)</dt><dd><p>Momentum compaction factor taking into account higher orders if 
+provided in mcf_order.</p>
+</dd>
+<dt>get_adts()</dt><dd><p>Compute and add Amplitude-Dependent Tune Shifts (ADTS) sextupolar 
+componenet from AT lattice.</p>
+</dd>
+<dt>get_mcf_order()</dt><dd><p>Compute momentum compaction factor up to 3rd order from AT lattice.</p>
+</dd>
+<dt>get_longitudinal_twiss(V)</dt><dd><p>Compute the longitudinal Twiss parameters and the synchrotron tune for 
+single or multi-harmonic RF systems.</p>
+</dd>
+<dt>to_pyat(Vrf)</dt><dd><p>Return a pyAT simple_ring element from the Synchrotron element data.</p>
+</dd>
+</dl>
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.tracking.synchrotron.Synchrotron.E0">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">E0</span></span><a class="headerlink" href="#mbtrack2.tracking.synchrotron.Synchrotron.E0" title="Permalink to this definition">¶</a></dt>
+<dd><p>Nominal (total) energy of the ring [eV]</p>
+</dd></dl>
+
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.tracking.synchrotron.Synchrotron.L">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">L</span></span><a class="headerlink" href="#mbtrack2.tracking.synchrotron.Synchrotron.L" title="Permalink to this definition">¶</a></dt>
+<dd><p>Ring circumference [m]</p>
+</dd></dl>
+
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.tracking.synchrotron.Synchrotron.T0">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">T0</span></span><a class="headerlink" href="#mbtrack2.tracking.synchrotron.Synchrotron.T0" title="Permalink to this definition">¶</a></dt>
+<dd><p>Revolution time [s]</p>
+</dd></dl>
+
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.tracking.synchrotron.Synchrotron.T1">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">T1</span></span><a class="headerlink" href="#mbtrack2.tracking.synchrotron.Synchrotron.T1" title="Permalink to this definition">¶</a></dt>
+<dd><p>“Fundamental RF period [s]</p>
+</dd></dl>
+
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.tracking.synchrotron.Synchrotron.beta">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">beta</span></span><a class="headerlink" href="#mbtrack2.tracking.synchrotron.Synchrotron.beta" title="Permalink to this definition">¶</a></dt>
+<dd><p>Relativistic beta</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.synchrotron.Synchrotron.eta">
+<span class="sig-name descname"><span class="pre">eta</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">delta</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/synchrotron.html#Synchrotron.eta"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.synchrotron.Synchrotron.eta" title="Permalink to this definition">¶</a></dt>
+<dd><p>Momentum compaction taking into account higher orders if provided in
+mcf_order.</p>
+<dl class="simple">
+<dt>delta<span class="classifier">float or array like bunch[“delta”], optional</span></dt><dd><p>Relative energy deviation. The default is 0.</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>float or array</dt><dd><p>Momentum compaction.</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.tracking.synchrotron.Synchrotron.f0">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">f0</span></span><a class="headerlink" href="#mbtrack2.tracking.synchrotron.Synchrotron.f0" title="Permalink to this definition">¶</a></dt>
+<dd><p>Revolution frequency [Hz]</p>
+</dd></dl>
+
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.tracking.synchrotron.Synchrotron.f1">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">f1</span></span><a class="headerlink" href="#mbtrack2.tracking.synchrotron.Synchrotron.f1" title="Permalink to this definition">¶</a></dt>
+<dd><p>Fundamental RF frequency [Hz]</p>
+</dd></dl>
+
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.tracking.synchrotron.Synchrotron.gamma">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">gamma</span></span><a class="headerlink" href="#mbtrack2.tracking.synchrotron.Synchrotron.gamma" title="Permalink to this definition">¶</a></dt>
+<dd><p>Relativistic gamma</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.synchrotron.Synchrotron.get_adts">
+<span class="sig-name descname"><span class="pre">get_adts</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/synchrotron.html#Synchrotron.get_adts"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.synchrotron.Synchrotron.get_adts" title="Permalink to this definition">¶</a></dt>
+<dd><p>Compute and add Amplitude-Dependent Tune Shifts (ADTS) sextupolar 
+componenet from AT lattice.</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.synchrotron.Synchrotron.get_longitudinal_twiss">
+<span class="sig-name descname"><span class="pre">get_longitudinal_twiss</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">V</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">phase</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">harmonics</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">add</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/synchrotron.html#Synchrotron.get_longitudinal_twiss"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.synchrotron.Synchrotron.get_longitudinal_twiss" title="Permalink to this definition">¶</a></dt>
+<dd><p>Compute the longitudinal Twiss parameters and the synchrotron tune for 
+single or multi-harmonic RF systems.</p>
+<p>Hypthesis:
+- Use the linear approximation (tau ~ 0).
+- For higher haromics only, cos(phi) ~ 0 must be true.</p>
+<dl class="simple">
+<dt>V<span class="classifier">float or array-like of float</span></dt><dd><p>RF voltage in [V].</p>
+</dd>
+<dt>phase<span class="classifier">float or array-like of float, optional</span></dt><dd><p>RF phase using cosine convention in [rad].
+Default is None.</p>
+</dd>
+<dt>harmonics<span class="classifier">int or array-like of int, optional</span></dt><dd><p>Harmonics of the cavities to consider.
+Default is None.</p>
+</dd>
+<dt>add<span class="classifier">bool, optional</span></dt><dd><p>If True,</p>
+</dd>
+</dl>
+<ul class="simple">
+<li><p>If a single voltage value is given, assume a single RF system set at</p></li>
+</ul>
+<p>the synchronous phase.
+- If a single pair of voltage/phase value is given, assume a single RF 
+system at this setting.
+- Otherwise, compute the synchrotron tune for a multi-harmonic RF 
+system.</p>
+<dl class="simple">
+<dt>tuneS<span class="classifier">float</span></dt><dd><p>Synchrotron tune in the linear approximation.</p>
+</dd>
+<dt>long_alpha<span class="classifier">float</span></dt><dd><p>Longitudinal alpha Twiss parameter at the tracking location.</p>
+</dd>
+<dt>long_beta<span class="classifier">float</span></dt><dd><p>Longitudinal beta Twiss parameter at the tracking location in [s].</p>
+</dd>
+<dt>long_gamma<span class="classifier">float</span></dt><dd><p>Longitudinal gamma Twiss parameter at the tracking location in [s-1].</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.synchrotron.Synchrotron.get_mcf_order">
+<span class="sig-name descname"><span class="pre">get_mcf_order</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">add</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">show_fit</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/synchrotron.html#Synchrotron.get_mcf_order"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.synchrotron.Synchrotron.get_mcf_order" title="Permalink to this definition">¶</a></dt>
+<dd><p>Compute momentum compaction factor up to 3rd order from AT lattice.</p>
+<dl class="simple">
+<dt>add<span class="classifier">bool, optional</span></dt><dd><p>If True, add the computed coefficient to the Synchrotron object.
+If False, the result is returned.
+The default is True.</p>
+</dd>
+<dt>show_fit<span class="classifier">bool, optional</span></dt><dd><p>If True, show a plot with the data and fit.
+The default is False.</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>pvalue<span class="classifier">array, optional</span></dt><dd><p>Momentum compaction factor up to 3rd order</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.tracking.synchrotron.Synchrotron.h">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">h</span></span><a class="headerlink" href="#mbtrack2.tracking.synchrotron.Synchrotron.h" title="Permalink to this definition">¶</a></dt>
+<dd><p>Harmonic number</p>
+</dd></dl>
+
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.tracking.synchrotron.Synchrotron.k1">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">k1</span></span><a class="headerlink" href="#mbtrack2.tracking.synchrotron.Synchrotron.k1" title="Permalink to this definition">¶</a></dt>
+<dd><p>Fundamental RF wave number [m**-1]</p>
+</dd></dl>
+
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.tracking.synchrotron.Synchrotron.mcf_order">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">mcf_order</span></span><a class="headerlink" href="#mbtrack2.tracking.synchrotron.Synchrotron.mcf_order" title="Permalink to this definition">¶</a></dt>
+<dd><p>Higher-orders momentum compaction factor</p>
+</dd></dl>
+
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.tracking.synchrotron.Synchrotron.omega0">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">omega0</span></span><a class="headerlink" href="#mbtrack2.tracking.synchrotron.Synchrotron.omega0" title="Permalink to this definition">¶</a></dt>
+<dd><p>Angular revolution frequency [Hz rad]</p>
+</dd></dl>
+
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.tracking.synchrotron.Synchrotron.omega1">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">omega1</span></span><a class="headerlink" href="#mbtrack2.tracking.synchrotron.Synchrotron.omega1" title="Permalink to this definition">¶</a></dt>
+<dd><p>Fundamental RF angular frequency[Hz rad]</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.synchrotron.Synchrotron.sigma">
+<span class="sig-name descname"><span class="pre">sigma</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">position</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/synchrotron.html#Synchrotron.sigma"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.synchrotron.Synchrotron.sigma" title="Permalink to this definition">¶</a></dt>
+<dd><p>Return the RMS beam size at equilibrium in [m].</p>
+<dl class="simple">
+<dt>position<span class="classifier">float or array, optional</span></dt><dd><p>Longitudinal position in [m] where the beam size is computed. 
+If None, the local values are used.</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>sigma<span class="classifier">array</span></dt><dd><p>RMS beam size in [m] at position location or at local positon if 
+position is None.</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.synchrotron.Synchrotron.synchrotron_tune">
+<span class="sig-name descname"><span class="pre">synchrotron_tune</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">V</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/synchrotron.html#Synchrotron.synchrotron_tune"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.synchrotron.Synchrotron.synchrotron_tune" title="Permalink to this definition">¶</a></dt>
+<dd><p>Compute the (unperturbed) synchrotron tune from main RF voltage.</p>
+<dl class="simple">
+<dt>V<span class="classifier">float</span></dt><dd><p>Main RF voltage in [V].</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>tuneS<span class="classifier">float</span></dt><dd><p>Synchrotron tune.</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.synchrotron.Synchrotron.to_pyat">
+<span class="sig-name descname"><span class="pre">to_pyat</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">Vrf</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">harmonic_number</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">TimeLag</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/synchrotron.html#Synchrotron.to_pyat"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.synchrotron.Synchrotron.to_pyat" title="Permalink to this definition">¶</a></dt>
+<dd><p>Return a pyAT simple_ring element from the Synchrotron element data.</p>
+<p>See pyAT documentation for informations about simple_ring.</p>
+<dl class="simple">
+<dt>Vrf<span class="classifier">float or array-like of float</span></dt><dd><p>RF Voltage in [V]. If sevral cavities are provided, harmonic_number
+and TimeLag should be provided.</p>
+</dd>
+<dt>harmonic_number<span class="classifier">float or array-like of float, optional</span></dt><dd><p>Harmonic numbers of the RF cavities. The default is None.</p>
+</dd>
+<dt>TimeLag<span class="classifier">float or array-like of float, optional</span></dt><dd><p>Set the timelag of the cavities in pyAT definition. 
+The default is False.</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>at_simple_ring<span class="classifier">at.physics.fastring.simple_ring</span></dt><dd><p>A pyAT simple_ring element.</p>
+</dd>
+</dl>
+</dd></dl>
+
+</dd></dl>
+
+</section>
+<section id="module-mbtrack2.tracking.wakepotential">
+<span id="mbtrack2-tracking-wakepotential-module"></span><h2>mbtrack2.tracking.wakepotential module<a class="headerlink" href="#module-mbtrack2.tracking.wakepotential" title="Permalink to this heading">¶</a></h2>
+<p>This module defines the WakePotential and LongRangeResistiveWall classes which 
+deal with the single bunch and multi-bunch wakes.</p>
+<dl class="py class">
+<dt class="sig sig-object py" id="mbtrack2.tracking.wakepotential.LongRangeResistiveWall">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">mbtrack2.tracking.wakepotential.</span></span><span class="sig-name descname"><span class="pre">LongRangeResistiveWall</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">ring</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">beam</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">length</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">rho</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">radius</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">types</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">['Wlong',</span> <span class="pre">'Wxdip',</span> <span class="pre">'Wydip']</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">nt</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">50</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">x3</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">y3</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/wakepotential.html#LongRangeResistiveWall"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.wakepotential.LongRangeResistiveWall" title="Permalink to this definition">¶</a></dt>
+<dd><p>Bases: <a class="reference internal" href="#mbtrack2.tracking.element.Element" title="mbtrack2.tracking.element.Element"><code class="xref py py-class docutils literal notranslate"><span class="pre">Element</span></code></a></p>
+<p>Element to deal with multi-bunch and multi-turn wakes from resistive wall 
+using the algorithm defined in [1].</p>
+<dl>
+<dt>Main approximations:</dt><dd><ul class="simple">
+<li><p>Bunches are treated as point charge.</p></li>
+<li><p>Assymptotic expression for the resistive wall wake functions are</p></li>
+</ul>
+<p>used.
+- Multi-turn wakes are limited to nt turns.</p>
+</dd>
+</dl>
+<p>Self-bunch interaction is not included in this element and should be dealed
+with the WakePotential class.</p>
+<p>ring : Synchrotron object
+beam : Beam object
+length : float</p>
+<blockquote>
+<div><p>Length of the resistive pipe to consider in [m].</p>
+</div></blockquote>
+<dl class="simple">
+<dt>rho<span class="classifier">float</span></dt><dd><p>Effective resistivity to consider in [ohm.m] as in [1].</p>
+</dd>
+<dt>radius<span class="classifier">float</span></dt><dd><p>Beam pipe radius to consider in [m].</p>
+</dd>
+<dt>types<span class="classifier">str or list, optional</span></dt><dd><p>Wake types to consider. 
+The default is [“Wlong”,”Wxdip”,”Wydip”].</p>
+</dd>
+<dt>nt<span class="classifier">int or float, optional</span></dt><dd><p>Number of turns to consider for the long range wakes. 
+The default is 50.</p>
+</dd>
+<dt>x3<span class="classifier">float, optional</span></dt><dd><p>Horizontal effective radius of the 3rd power in [m], as Eq.27 in [1].
+The default is radius.</p>
+</dd>
+<dt>y3<span class="classifier">float, optional</span></dt><dd><p>Vertical effective radius of the 3rd power in [m], as Eq.27 in [1].
+The default is radius.</p>
+</dd>
+</dl>
+<p>[1] : Skripka, Galina, et al. “Simultaneous computation of intrabunch and 
+interbunch collective beam motions in storage rings.” NIM.A (2016).</p>
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.wakepotential.LongRangeResistiveWall.Wdip">
+<span class="sig-name descname"><span class="pre">Wdip</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">t</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">plane</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/wakepotential.html#LongRangeResistiveWall.Wdip"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.wakepotential.LongRangeResistiveWall.Wdip" title="Permalink to this definition">¶</a></dt>
+<dd><p>Approxmiate expression for the transverse resistive wall wake 
+function - Eq.26 of [1].</p>
+<dl class="simple">
+<dt>t<span class="classifier">float</span></dt><dd><p>Time in [s].</p>
+</dd>
+<dt>plane<span class="classifier">str</span></dt><dd><p>“x” or “y”.</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>wdip<span class="classifier">float</span></dt><dd><p>Wake function in [V/C/m].</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.wakepotential.LongRangeResistiveWall.Wlong">
+<span class="sig-name descname"><span class="pre">Wlong</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">t</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/wakepotential.html#LongRangeResistiveWall.Wlong"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.wakepotential.LongRangeResistiveWall.Wlong" title="Permalink to this definition">¶</a></dt>
+<dd><p>Approxmiate expression for the longitudinal resistive wall wake 
+function - Eq.24 of [1].</p>
+<dl class="simple">
+<dt>t<span class="classifier">float</span></dt><dd><p>Time in [s].</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>wl<span class="classifier">float</span></dt><dd><p>Wake function in [V/C].</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.wakepotential.LongRangeResistiveWall.get_kick">
+<span class="sig-name descname"><span class="pre">get_kick</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">rank</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">wake_type</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/wakepotential.html#LongRangeResistiveWall.get_kick"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.wakepotential.LongRangeResistiveWall.get_kick" title="Permalink to this definition">¶</a></dt>
+<dd><p>Compute the wake kick to apply.</p>
+<dl class="simple">
+<dt>rank<span class="classifier">int</span></dt><dd><p>Rank of the bunch, as defined in Mpi class.</p>
+</dd>
+<dt>wake_type<span class="classifier">float</span></dt><dd><p>Type of the wake to compute.</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>sum_kick<span class="classifier">float</span></dt><dd><p>Sum of the kicks from the different bunches at different turns.</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.wakepotential.LongRangeResistiveWall.track">
+<span class="sig-name descname"><span class="pre">track</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">beam</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/wakepotential.html#LongRangeResistiveWall.track"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.wakepotential.LongRangeResistiveWall.track" title="Permalink to this definition">¶</a></dt>
+<dd><p>Track a beam.</p>
+<p>beam : Beam object</p>
+<p>None.</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.wakepotential.LongRangeResistiveWall.track_bunch">
+<span class="sig-name descname"><span class="pre">track_bunch</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">bunch</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">rank</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/wakepotential.html#LongRangeResistiveWall.track_bunch"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.wakepotential.LongRangeResistiveWall.track_bunch" title="Permalink to this definition">¶</a></dt>
+<dd><p>Track a bunch.</p>
+<p>Should only be used within the track method and not standalone.</p>
+<p>bunch : Bunch object
+rank : int</p>
+<blockquote>
+<div><p>Rank of the bunch, as defined in Mpi class.</p>
+</div></blockquote>
+<p>None.</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.wakepotential.LongRangeResistiveWall.update_tables">
+<span class="sig-name descname"><span class="pre">update_tables</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">beam</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/wakepotential.html#LongRangeResistiveWall.update_tables"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.wakepotential.LongRangeResistiveWall.update_tables" title="Permalink to this definition">¶</a></dt>
+<dd><p>Update tables.</p>
+<p>Table tau[i,j] is defined as the time difference of the bunch i center 
+of mass with respect to center of the RF bucket number 0 at turn j.
+Turn 0 corresponds to the tracked turn.</p>
+<p>Positive time corresponds to past events and negative time to future 
+events.</p>
+<p>beam : Beam object</p>
+<p>None.</p>
+</dd></dl>
+
+</dd></dl>
+
+<dl class="py class">
+<dt class="sig sig-object py" id="mbtrack2.tracking.wakepotential.WakePotential">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">mbtrack2.tracking.wakepotential.</span></span><span class="sig-name descname"><span class="pre">WakePotential</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">ring</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">wakefield</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">n_bin</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">80</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">interp_on_postion</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/wakepotential.html#WakePotential"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.wakepotential.WakePotential" title="Permalink to this definition">¶</a></dt>
+<dd><p>Bases: <a class="reference internal" href="#mbtrack2.tracking.element.Element" title="mbtrack2.tracking.element.Element"><code class="xref py py-class docutils literal notranslate"><span class="pre">Element</span></code></a></p>
+<p>Compute a wake potential from uniformly sampled wake functions by 
+performing a convolution with a bunch charge profile.</p>
+<p>Two different time bases are used. The first one is controled by the n_bin
+parameter and is used to compute the bunch profile. Then the bunch profile
+is interpolated on the wake function time base which is used to perform the
+convolution to get the wake potential.</p>
+<p>ring : Synchrotron object
+wakefield : Wakefield object</p>
+<blockquote>
+<div><p>Wakefield object which contains the wake functions to be used. The wake
+functions must be uniformly sampled!</p>
+</div></blockquote>
+<dl class="simple">
+<dt>n_bin<span class="classifier">int, optional</span></dt><dd><p>Number of bins for constructing the longitudinal bunch profile.</p>
+</dd>
+<dt>interp_on_postion<span class="classifier">bool, optional</span></dt><dd><p>If True, the computed wake potential is interpolated on the exact 
+particle location. If False, the wake potential is interpolated on the 
+bin center and each particle of the bin get the same value.
+Default is True.</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>rho<span class="classifier">array of shape (n_bin, )</span></dt><dd><p>Bunch charge density profile in the unit [1/s].</p>
+</dd>
+<dt>Wp<span class="classifier">array </span></dt><dd><p>Wake potential profile.</p>
+</dd>
+<dt>Wp_interp<span class="classifier">array of shape (mp_number, )</span></dt><dd><p>Wake potential, obtained from interpolating Wp, exerted on each macro-particle.</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>charge_density(bunch)</dt><dd><p>Compute bunch charge density profile in [1/s].</p>
+</dd>
+<dt>dipole_moment(bunch, plane, tau0)</dt><dd><p>Return the dipole moment of the bunch computed on the same time array 
+as the wake function.</p>
+</dd>
+<dt>prepare_wakefunction(wake_type)</dt><dd><p>Prepare the wake function of a given wake_type to be used for the wake
+potential computation.</p>
+</dd>
+<dt>get_wakepotential(bunch, wake_type)</dt><dd><p>Return the wake potential computed on the wake function time array 
+limited to the bunch profile.</p>
+</dd>
+<dt>track(bunch)</dt><dd><p>Tracking method for the element.</p>
+</dd>
+<dt>plot_last_wake(wake_type)</dt><dd><p>Plot the last wake potential of a given type computed during the last
+call of the track method.</p>
+</dd>
+<dt>reference_loss(bunch)</dt><dd><p>Calculate the loss factor and kick factor from the wake potential and 
+compare it to a reference value assuming a Gaussian bunch computed in 
+the frequency domain.</p>
+</dd>
+<dt>check_sampling()</dt><dd><p>Check if the wake function sampling is uniform.</p>
+</dd>
+<dt>reduce_sampling(factor)</dt><dd><p>Reduce wake function samping by an integer factor.</p>
+</dd>
+</dl>
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.wakepotential.WakePotential.charge_density">
+<span class="sig-name descname"><span class="pre">charge_density</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">bunch</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/wakepotential.html#WakePotential.charge_density"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.wakepotential.WakePotential.charge_density" title="Permalink to this definition">¶</a></dt>
+<dd><p>Compute bunch charge density profile in [1/s].</p>
+<p>bunch : Bunch object</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.wakepotential.WakePotential.check_sampling">
+<span class="sig-name descname"><span class="pre">check_sampling</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/wakepotential.html#WakePotential.check_sampling"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.wakepotential.WakePotential.check_sampling" title="Permalink to this definition">¶</a></dt>
+<dd><p>Check if the wake function sampling is uniform.</p>
+<p>ValueError</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.wakepotential.WakePotential.dipole_moment">
+<span class="sig-name descname"><span class="pre">dipole_moment</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">bunch</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">plane</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">tau0</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/wakepotential.html#WakePotential.dipole_moment"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.wakepotential.WakePotential.dipole_moment" title="Permalink to this definition">¶</a></dt>
+<dd><p>Return the dipole moment of the bunch computed on the same time array 
+as the wake function.</p>
+<p>bunch : Bunch object
+plane : str</p>
+<blockquote>
+<div><p>Plane on which the dipole moment is computed, “x” or “y”.</p>
+</div></blockquote>
+<dl class="simple">
+<dt>tau0<span class="classifier">array</span></dt><dd><p>Time array on which the dipole moment will be interpolated, in [s].</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>dipole<span class="classifier">array</span></dt><dd><p>Dipole moment of the bunch.</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.wakepotential.WakePotential.get_gaussian_wakepotential">
+<span class="sig-name descname"><span class="pre">get_gaussian_wakepotential</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">sigma</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">wake_type</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">dipole</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0.001</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/wakepotential.html#WakePotential.get_gaussian_wakepotential"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.wakepotential.WakePotential.get_gaussian_wakepotential" title="Permalink to this definition">¶</a></dt>
+<dd><p>Return the wake potential computed using a perfect gaussian profile.</p>
+<dl class="simple">
+<dt>sigma<span class="classifier">float</span></dt><dd><p>RMS bunch length in [s].</p>
+</dd>
+<dt>wake_type<span class="classifier">str</span></dt><dd><p>Wake function type: “Wlong”, “Wxdip”, …</p>
+</dd>
+<dt>dipole<span class="classifier">float, optional</span></dt><dd><p>Dipole moment to consider in [m], (uniform dipole moment).</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>tau0<span class="classifier">array</span></dt><dd><p>Time base in [s].</p>
+</dd>
+<dt>W0<span class="classifier">array</span></dt><dd><p>Wake function.</p>
+</dd>
+<dt>Wp<span class="classifier">array</span></dt><dd><p>Wake potential.</p>
+</dd>
+<dt>profile0<span class="classifier">array</span></dt><dd><p>Gaussian bunch profile.</p>
+</dd>
+<dt>dipole0<span class="classifier">array</span></dt><dd><p>Dipole moment.</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.wakepotential.WakePotential.get_wakepotential">
+<span class="sig-name descname"><span class="pre">get_wakepotential</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">bunch</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">wake_type</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/wakepotential.html#WakePotential.get_wakepotential"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.wakepotential.WakePotential.get_wakepotential" title="Permalink to this definition">¶</a></dt>
+<dd><p>Return the wake potential computed on the wake function time array 
+limited to the bunch profile.</p>
+<p>bunch : Bunch object
+wake_type : str</p>
+<blockquote>
+<div><p>Wake function type: “Wlong”, “Wxdip”, …</p>
+</div></blockquote>
+<dl class="simple">
+<dt>Wp<span class="classifier">array</span></dt><dd><p>Wake potential.</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.wakepotential.WakePotential.plot_gaussian_wake">
+<span class="sig-name descname"><span class="pre">plot_gaussian_wake</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">sigma</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">wake_type</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">dipole</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0.001</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">plot_rho</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">plot_dipole</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">plot_wake_function</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/wakepotential.html#WakePotential.plot_gaussian_wake"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.wakepotential.WakePotential.plot_gaussian_wake" title="Permalink to this definition">¶</a></dt>
+<dd><p>Plot the wake potential of a given type for a perfect gaussian bunch.</p>
+<dl class="simple">
+<dt>sigma<span class="classifier">float</span></dt><dd><p>RMS bunch length in [s].</p>
+</dd>
+<dt>wake_type<span class="classifier">str</span></dt><dd><p>Type of the wake to plot: “Wlong”, “Wxdip”, …</p>
+</dd>
+<dt>dipole<span class="classifier">float, optional</span></dt><dd><p>Dipole moment to consider in [m], (uniform dipole moment).</p>
+</dd>
+<dt>plot_rho<span class="classifier">bool, optional</span></dt><dd><p>Plot the normalised bunch profile. The default is True.</p>
+</dd>
+<dt>plot_dipole<span class="classifier">bool, optional</span></dt><dd><p>Plot the normalised dipole moment. The default is False.</p>
+</dd>
+<dt>plot_wake_function<span class="classifier">bool, optional</span></dt><dd><p>Plot the normalised wake function. The default is True.</p>
+</dd>
+</dl>
+<p>fig : figure</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.wakepotential.WakePotential.plot_last_wake">
+<span class="sig-name descname"><span class="pre">plot_last_wake</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">wake_type</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">plot_rho</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">plot_dipole</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">plot_wake_function</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/wakepotential.html#WakePotential.plot_last_wake"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.wakepotential.WakePotential.plot_last_wake" title="Permalink to this definition">¶</a></dt>
+<dd><p>Plot the last wake potential of a given type computed during the last
+call of the track method.</p>
+<dl class="simple">
+<dt>wake_type<span class="classifier">str</span></dt><dd><p>Type of the wake to plot: “Wlong”, “Wxdip”, …</p>
+</dd>
+<dt>plot_rho<span class="classifier">bool, optional</span></dt><dd><p>Plot the normalised bunch profile. The default is True.</p>
+</dd>
+<dt>plot_dipole<span class="classifier">bool, optional</span></dt><dd><p>Plot the normalised dipole moment. The default is False.</p>
+</dd>
+<dt>plot_wake_function<span class="classifier">bool, optional</span></dt><dd><p>Plot the normalised wake function. The default is True.</p>
+</dd>
+</dl>
+<p>fig : figure</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.wakepotential.WakePotential.prepare_wakefunction">
+<span class="sig-name descname"><span class="pre">prepare_wakefunction</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">wake_type</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">tau</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">save_data</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/wakepotential.html#WakePotential.prepare_wakefunction"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.wakepotential.WakePotential.prepare_wakefunction" title="Permalink to this definition">¶</a></dt>
+<dd><p>Prepare the wake function of a given wake_type to be used for the wake
+potential computation.</p>
+<p>The new time array keeps the same sampling time as given in the 
+WakeFunction definition but is restricted to the bunch profile time 
+array.</p>
+<dl class="simple">
+<dt>wake_type<span class="classifier">str</span></dt><dd><p>Type of the wake function to prepare: “Wlong”, “Wxdip”, …</p>
+</dd>
+<dt>tau<span class="classifier">array</span></dt><dd><p>Time domain array of the bunch profile in [s].</p>
+</dd>
+<dt>save_data<span class="classifier">bool, optional</span></dt><dd><p>If True, the results are saved as atributes.</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>tau0<span class="classifier">array</span></dt><dd><p>Time base of the wake function in [s].</p>
+</dd>
+<dt>dtau0<span class="classifier">float</span></dt><dd><p>Difference between two points of the wake function time base in 
+[s].</p>
+</dd>
+<dt>W0<span class="classifier">array</span></dt><dd><p>Wake function array in [V/C] or [V/C/m].</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.wakepotential.WakePotential.reduce_sampling">
+<span class="sig-name descname"><span class="pre">reduce_sampling</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">factor</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/wakepotential.html#WakePotential.reduce_sampling"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.wakepotential.WakePotential.reduce_sampling" title="Permalink to this definition">¶</a></dt>
+<dd><p>Reduce wake function samping by an integer factor.</p>
+<p>Used to reduce computation time for long bunches.</p>
+<p>factor : int</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.wakepotential.WakePotential.reference_loss">
+<span class="sig-name descname"><span class="pre">reference_loss</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">bunch</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/wakepotential.html#WakePotential.reference_loss"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.wakepotential.WakePotential.reference_loss" title="Permalink to this definition">¶</a></dt>
+<dd><p>Calculate the loss factor and kick factor from the wake potential and 
+compare it to a reference value assuming a Gaussian bunch computed in 
+the frequency domain.</p>
+<p>bunch : Bunch object</p>
+<dl class="simple">
+<dt>loss_data<span class="classifier">DataFrame</span></dt><dd><p>An output showing the loss/kick factors compared to the reference 
+values.</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.wakepotential.WakePotential.track">
+<span class="sig-name descname"><span class="pre">track</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">bunch</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/wakepotential.html#WakePotential.track"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.wakepotential.WakePotential.track" title="Permalink to this definition">¶</a></dt>
+<dd><p>Tracking method for the element.
+No bunch to bunch interaction, so written for Bunch objects and
+&#64;Element.parallel is used to handle Beam objects.</p>
+<p>bunch : Bunch or Beam object.</p>
+</dd></dl>
+
+</dd></dl>
+
+</section>
+<section id="module-mbtrack2.tracking">
+<span id="module-contents"></span><h2>Module contents<a class="headerlink" href="#module-mbtrack2.tracking" title="Permalink to this heading">¶</a></h2>
+</section>
+</section>
+
+
+            <div class="clearer"></div>
+          </div>
+        </div>
+      </div>
+      <div class="sphinxsidebar" role="navigation" aria-label="main navigation">
+        <div class="sphinxsidebarwrapper">
+  <div>
+    <h3><a href="index.html">Table of Contents</a></h3>
+    <ul>
+<li><a class="reference internal" href="#">mbtrack2.tracking package</a><ul>
+<li><a class="reference internal" href="#subpackages">Subpackages</a></li>
+<li><a class="reference internal" href="#submodules">Submodules</a></li>
+<li><a class="reference internal" href="#module-mbtrack2.tracking.aperture">mbtrack2.tracking.aperture module</a></li>
+<li><a class="reference internal" href="#module-mbtrack2.tracking.element">mbtrack2.tracking.element module</a></li>
+<li><a class="reference internal" href="#module-mbtrack2.tracking.feedback">mbtrack2.tracking.feedback module</a></li>
+<li><a class="reference internal" href="#module-mbtrack2.tracking.parallel">mbtrack2.tracking.parallel module</a></li>
+<li><a class="reference internal" href="#module-mbtrack2.tracking.particles">mbtrack2.tracking.particles module</a></li>
+<li><a class="reference internal" href="#module-mbtrack2.tracking.rf">mbtrack2.tracking.rf module</a></li>
+<li><a class="reference internal" href="#module-mbtrack2.tracking.synchrotron">mbtrack2.tracking.synchrotron module</a></li>
+<li><a class="reference internal" href="#module-mbtrack2.tracking.wakepotential">mbtrack2.tracking.wakepotential module</a></li>
+<li><a class="reference internal" href="#module-mbtrack2.tracking">Module contents</a></li>
+</ul>
+</li>
+</ul>
+
+  </div>
+  <div role="note" aria-label="source link">
+    <h3>This Page</h3>
+    <ul class="this-page-menu">
+      <li><a href="_sources/mbtrack2.tracking.rst.txt"
+            rel="nofollow">Show Source</a></li>
+    </ul>
+   </div>
+<div id="searchbox" style="display: none" role="search">
+  <h3 id="searchlabel">Quick search</h3>
+    <div class="searchformwrapper">
+    <form class="search" action="search.html" method="get">
+      <input type="text" name="q" aria-labelledby="searchlabel" autocomplete="off" autocorrect="off" autocapitalize="off" spellcheck="false"/>
+      <input type="submit" value="Go" />
+    </form>
+    </div>
+</div>
+<script>document.getElementById('searchbox').style.display = "block"</script>
+        </div>
+      </div>
+      <div class="clearer"></div>
+    </div>
+    <div class="related" role="navigation" aria-label="related navigation">
+      <h3>Navigation</h3>
+      <ul>
+        <li class="right" style="margin-right: 10px">
+          <a href="genindex.html" title="General Index"
+             >index</a></li>
+        <li class="right" >
+          <a href="py-modindex.html" title="Python Module Index"
+             >modules</a> |</li>
+        <li class="nav-item nav-item-0"><a href="index.html">mbtrack2 0.6.0 documentation</a> &#187;</li>
+        <li class="nav-item nav-item-this"><a href="">mbtrack2.tracking package</a></li> 
+      </ul>
+    </div>
+    <div class="footer" role="contentinfo">
+        &#169; Copyright 2024, A. Gamelin et al.
+      Created using <a href="https://www.sphinx-doc.org/">Sphinx</a> 5.0.2.
+    </div>
+  </body>
+</html>
\ No newline at end of file
diff --git a/docs/build/html/mbtrack2.tracking.monitors.html b/docs/build/html/mbtrack2.tracking.monitors.html
new file mode 100644
index 0000000..e4fe450
--- /dev/null
+++ b/docs/build/html/mbtrack2.tracking.monitors.html
@@ -0,0 +1,1259 @@
+
+<!DOCTYPE html>
+
+<html lang="en">
+  <head>
+    <meta charset="utf-8" />
+    <meta name="viewport" content="width=device-width, initial-scale=1.0" /><meta name="generator" content="Docutils 0.18.1: http://docutils.sourceforge.net/" />
+
+    <title>mbtrack2.tracking.monitors package &#8212; mbtrack2 0.6.0 documentation</title>
+    <link rel="stylesheet" type="text/css" href="_static/pygments.css" />
+    <link rel="stylesheet" type="text/css" href="_static/nature.css" />
+    <script data-url_root="./" id="documentation_options" src="_static/documentation_options.js"></script>
+    <script src="_static/jquery.js"></script>
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+    <link rel="index" title="Index" href="genindex.html" />
+    <link rel="search" title="Search" href="search.html" /> 
+  </head><body>
+    <div class="related" role="navigation" aria-label="related navigation">
+      <h3>Navigation</h3>
+      <ul>
+        <li class="right" style="margin-right: 10px">
+          <a href="genindex.html" title="General Index"
+             accesskey="I">index</a></li>
+        <li class="right" >
+          <a href="py-modindex.html" title="Python Module Index"
+             >modules</a> |</li>
+        <li class="nav-item nav-item-0"><a href="index.html">mbtrack2 0.6.0 documentation</a> &#187;</li>
+        <li class="nav-item nav-item-this"><a href="">mbtrack2.tracking.monitors package</a></li> 
+      </ul>
+    </div>  
+
+    <div class="document">
+      <div class="documentwrapper">
+        <div class="bodywrapper">
+          <div class="body" role="main">
+            
+  <section id="mbtrack2-tracking-monitors-package">
+<h1>mbtrack2.tracking.monitors package<a class="headerlink" href="#mbtrack2-tracking-monitors-package" title="Permalink to this heading">¶</a></h1>
+<section id="submodules">
+<h2>Submodules<a class="headerlink" href="#submodules" title="Permalink to this heading">¶</a></h2>
+</section>
+<section id="module-mbtrack2.tracking.monitors.monitors">
+<span id="mbtrack2-tracking-monitors-monitors-module"></span><h2>mbtrack2.tracking.monitors.monitors module<a class="headerlink" href="#module-mbtrack2.tracking.monitors.monitors" title="Permalink to this heading">¶</a></h2>
+<p>This module defines the different monitor class which are used to save data
+during tracking.</p>
+<dl class="py class">
+<dt class="sig sig-object py" id="mbtrack2.tracking.monitors.monitors.BeamMonitor">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">mbtrack2.tracking.monitors.monitors.</span></span><span class="sig-name descname"><span class="pre">BeamMonitor</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">h</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">save_every</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">buffer_size</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">total_size</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">file_name</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">mpi_mode</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/monitors/monitors.html#BeamMonitor"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.monitors.monitors.BeamMonitor" title="Permalink to this definition">¶</a></dt>
+<dd><p>Bases: <a class="reference internal" href="#mbtrack2.tracking.monitors.monitors.Monitor" title="mbtrack2.tracking.monitors.monitors.Monitor"><code class="xref py py-class docutils literal notranslate"><span class="pre">Monitor</span></code></a></p>
+<p>Monitor the full beam and save each bunch attributes (mean, std, emit and 
+current).</p>
+<dl>
+<dt>h<span class="classifier">int</span></dt><dd><p>Harmonic number of the ring.</p>
+</dd>
+<dt>save_every<span class="classifier">int or float</span></dt><dd><p>Set the frequency of the save. The data is saved every save_every 
+call of the montior.</p>
+</dd>
+<dt>buffer_size<span class="classifier">int or float</span></dt><dd><p>Size of the save buffer.</p>
+</dd>
+<dt>total_size<span class="classifier">int or float</span></dt><dd><p>Total size of the save. The following relationships between the 
+parameters must exist:</p>
+<blockquote>
+<div><p>total_size % buffer_size == 0
+number of call to track / save_every == total_size</p>
+</div></blockquote>
+</dd>
+<dt>file_name<span class="classifier">string, optional</span></dt><dd><p>Name of the HDF5 where the data will be stored. Must be specified
+the first time a subclass of Monitor is instancied and must be None
+the following times.</p>
+</dd>
+<dt>mpi_mode<span class="classifier">bool, optional</span></dt><dd><p>If True, open the HDF5 file in parallel mode, which is needed to
+allow several cores to write in the same file at the same time.
+If False, open the HDF5 file in standard mode.</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>track(beam)</dt><dd><p>Save data</p>
+</dd>
+</dl>
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.monitors.monitors.BeamMonitor.to_buffer">
+<span class="sig-name descname"><span class="pre">to_buffer</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">bunch</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">bunch_num</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/monitors/monitors.html#BeamMonitor.to_buffer"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.monitors.monitors.BeamMonitor.to_buffer" title="Permalink to this definition">¶</a></dt>
+<dd><p>Save data to buffer, if mpi is being used.</p>
+<p>bunch : Bunch object
+bunch_num : int</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.monitors.monitors.BeamMonitor.to_buffer_no_mpi">
+<span class="sig-name descname"><span class="pre">to_buffer_no_mpi</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">beam</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/monitors/monitors.html#BeamMonitor.to_buffer_no_mpi"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.monitors.monitors.BeamMonitor.to_buffer_no_mpi" title="Permalink to this definition">¶</a></dt>
+<dd><p>Save data to buffer, if mpi is not being used.</p>
+<p>beam : Beam object</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.monitors.monitors.BeamMonitor.track">
+<span class="sig-name descname"><span class="pre">track</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">beam</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/monitors/monitors.html#BeamMonitor.track"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.monitors.monitors.BeamMonitor.track" title="Permalink to this definition">¶</a></dt>
+<dd><p>Save data</p>
+<p>beam : Beam object</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.monitors.monitors.BeamMonitor.write">
+<span class="sig-name descname"><span class="pre">write</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">bunch_num</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/monitors/monitors.html#BeamMonitor.write"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.monitors.monitors.BeamMonitor.write" title="Permalink to this definition">¶</a></dt>
+<dd><p>Write data from buffer to the HDF5 file, if mpi is being used.</p>
+<p>bunch_num : int</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.monitors.monitors.BeamMonitor.write_no_mpi">
+<span class="sig-name descname"><span class="pre">write_no_mpi</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/monitors/monitors.html#BeamMonitor.write_no_mpi"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.monitors.monitors.BeamMonitor.write_no_mpi" title="Permalink to this definition">¶</a></dt>
+<dd><p>Write data from buffer to the HDF5 file, if mpi is not being used.</p>
+</dd></dl>
+
+</dd></dl>
+
+<dl class="py class">
+<dt class="sig sig-object py" id="mbtrack2.tracking.monitors.monitors.BeamSpectrumMonitor">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">mbtrack2.tracking.monitors.monitors.</span></span><span class="sig-name descname"><span class="pre">BeamSpectrumMonitor</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">ring</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">save_every</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">buffer_size</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">total_size</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">dim</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'all'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">n_fft</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">file_name</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">mpi_mode</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/monitors/monitors.html#BeamSpectrumMonitor"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.monitors.monitors.BeamSpectrumMonitor" title="Permalink to this definition">¶</a></dt>
+<dd><p>Bases: <a class="reference internal" href="#mbtrack2.tracking.monitors.monitors.Monitor" title="mbtrack2.tracking.monitors.monitors.Monitor"><code class="xref py py-class docutils literal notranslate"><span class="pre">Monitor</span></code></a></p>
+<p>Monitor coherent beam spectrum.</p>
+<p>ring : Synchrotron object
+save_every : int or float</p>
+<blockquote>
+<div><p>Set the frequency of the save. The spectrums are computed every 
+save_every call of the montior.</p>
+</div></blockquote>
+<dl>
+<dt>buffer_size<span class="classifier">int or float</span></dt><dd><p>Size of the save buffer.</p>
+</dd>
+<dt>total_size<span class="classifier">int or float</span></dt><dd><p>Total size of the save. The following relationships between the 
+parameters must exist:</p>
+<blockquote>
+<div><p>total_size % buffer_size == 0
+number of call to track / save_every == total_size - 1</p>
+</div></blockquote>
+</dd>
+<dt>dim<span class="classifier">str, optional</span></dt><dd><p>Dimensions in which the spectrums have to be computed.
+Can be:</p>
+<blockquote>
+<div><ul class="simple">
+<li><p>“all”</p></li>
+<li><p>“tau”</p></li>
+<li><p>“x”</p></li>
+<li><p>“y”</p></li>
+<li><p>“xy” or “yx”</p></li>
+<li><p>“xtau” or “taux”</p></li>
+<li><p>“ytau” or “tauy”</p></li>
+</ul>
+</div></blockquote>
+</dd>
+<dt>n_fft<span class="classifier">int or float, optional</span></dt><dd><p>The number of points used for FFT computation, if n_fft is bigger than
+save_every zero-padding is applied.
+If None, save_every is used.</p>
+</dd>
+<dt>file_name<span class="classifier">string, optional</span></dt><dd><p>Name of the HDF5 where the data will be stored. Must be specified
+the first time a subclass of Monitor is instancied and must be None
+the following times.</p>
+</dd>
+<dt>mpi_mode<span class="classifier">bool, optional</span></dt><dd><p>If True, open the HDF5 file in parallel mode, which is needed to
+allow several cores to write in the same file at the same time.
+If False, open the HDF5 file in standard mode.</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>fft_resolution<span class="classifier">float</span></dt><dd><p>Return the fft resolution in [Hz].</p>
+</dd>
+<dt>signal_resolution<span class="classifier">float</span></dt><dd><p>Return the signal resolution in [Hz].</p>
+</dd>
+<dt>frequency_samples<span class="classifier">array of float</span></dt><dd><p>Return the fft frequency samples in [Hz].</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>track(bunch):</dt><dd><p>Save spectrum data.</p>
+</dd>
+</dl>
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.tracking.monitors.monitors.BeamSpectrumMonitor.fft_resolution">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">fft_resolution</span></span><a class="headerlink" href="#mbtrack2.tracking.monitors.monitors.BeamSpectrumMonitor.fft_resolution" title="Permalink to this definition">¶</a></dt>
+<dd><p>Return the fft resolution in [Hz].</p>
+<p>It is defined as the sampling frequency over the number of samples.</p>
+</dd></dl>
+
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.tracking.monitors.monitors.BeamSpectrumMonitor.frequency_samples">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">frequency_samples</span></span><a class="headerlink" href="#mbtrack2.tracking.monitors.monitors.BeamSpectrumMonitor.frequency_samples" title="Permalink to this definition">¶</a></dt>
+<dd><p>Return the fft frequency samples in [Hz].</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.monitors.monitors.BeamSpectrumMonitor.get_beam_spectrum">
+<span class="sig-name descname"><span class="pre">get_beam_spectrum</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">mean</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/monitors/monitors.html#BeamSpectrumMonitor.get_beam_spectrum"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.monitors.monitors.BeamSpectrumMonitor.get_beam_spectrum" title="Permalink to this definition">¶</a></dt>
+<dd><p>Compute the beam coherent spectrum i.e. the absolute value of the FT 
+of the mean position of every bunch.</p>
+<dl class="simple">
+<dt>coherent<span class="classifier">array</span></dt><dd><p>The beam coherent spectrum.</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.tracking.monitors.monitors.BeamSpectrumMonitor.signal_resolution">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">signal_resolution</span></span><a class="headerlink" href="#mbtrack2.tracking.monitors.monitors.BeamSpectrumMonitor.signal_resolution" title="Permalink to this definition">¶</a></dt>
+<dd><p>Return the signal resolution in [Hz].</p>
+<p>It is defined as the inverse of the signal length.</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.monitors.monitors.BeamSpectrumMonitor.to_buffer">
+<span class="sig-name descname"><span class="pre">to_buffer</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">beam</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/monitors/monitors.html#BeamSpectrumMonitor.to_buffer"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.monitors.monitors.BeamSpectrumMonitor.to_buffer" title="Permalink to this definition">¶</a></dt>
+<dd><p>A method to hold saved data before writing it to the output file.</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.monitors.monitors.BeamSpectrumMonitor.track">
+<span class="sig-name descname"><span class="pre">track</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">beam</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/monitors/monitors.html#BeamSpectrumMonitor.track"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.monitors.monitors.BeamSpectrumMonitor.track" title="Permalink to this definition">¶</a></dt>
+<dd><p>Save mean data.</p>
+<p>beam : Beam object</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.monitors.monitors.BeamSpectrumMonitor.write">
+<span class="sig-name descname"><span class="pre">write</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/monitors/monitors.html#BeamSpectrumMonitor.write"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.monitors.monitors.BeamSpectrumMonitor.write" title="Permalink to this definition">¶</a></dt>
+<dd><p>Write data from buffer to output file.</p>
+</dd></dl>
+
+</dd></dl>
+
+<dl class="py class">
+<dt class="sig sig-object py" id="mbtrack2.tracking.monitors.monitors.BunchMonitor">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">mbtrack2.tracking.monitors.monitors.</span></span><span class="sig-name descname"><span class="pre">BunchMonitor</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">bunch_number</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">save_every</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">buffer_size</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">total_size</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">file_name</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">mpi_mode</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/monitors/monitors.html#BunchMonitor"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.monitors.monitors.BunchMonitor" title="Permalink to this definition">¶</a></dt>
+<dd><p>Bases: <a class="reference internal" href="#mbtrack2.tracking.monitors.monitors.Monitor" title="mbtrack2.tracking.monitors.monitors.Monitor"><code class="xref py py-class docutils literal notranslate"><span class="pre">Monitor</span></code></a></p>
+<p>Monitor a single bunch and save attributes 
+(mean, std, emit, current, and cs_invariant).</p>
+<dl>
+<dt>bunch_number<span class="classifier">int</span></dt><dd><p>Bunch to monitor</p>
+</dd>
+<dt>save_every<span class="classifier">int or float</span></dt><dd><p>Set the frequency of the save. The data is saved every save_every 
+call of the montior.</p>
+</dd>
+<dt>buffer_size<span class="classifier">int or float</span></dt><dd><p>Size of the save buffer.</p>
+</dd>
+<dt>total_size<span class="classifier">int or float</span></dt><dd><p>Total size of the save. The following relationships between the 
+parameters must exist:</p>
+<blockquote>
+<div><p>total_size % buffer_size == 0
+number of call to track / save_every == total_size</p>
+</div></blockquote>
+</dd>
+<dt>file_name<span class="classifier">string, optional</span></dt><dd><p>Name of the HDF5 where the data will be stored. Must be specified
+the first time a subclass of Monitor is instancied and must be None
+the following times.</p>
+</dd>
+<dt>mpi_mode<span class="classifier">bool, optional</span></dt><dd><p>If True, open the HDF5 file in parallel mode, which is needed to
+allow several cores to write in the same file at the same time.
+If False, open the HDF5 file in standard mode.</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>track(object_to_save)</dt><dd><p>Save data</p>
+</dd>
+</dl>
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.monitors.monitors.BunchMonitor.track">
+<span class="sig-name descname"><span class="pre">track</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">object_to_save</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/monitors/monitors.html#BunchMonitor.track"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.monitors.monitors.BunchMonitor.track" title="Permalink to this definition">¶</a></dt>
+<dd><p>Save data</p>
+<p>object_to_save : Bunch or Beam object</p>
+</dd></dl>
+
+</dd></dl>
+
+<dl class="py class">
+<dt class="sig sig-object py" id="mbtrack2.tracking.monitors.monitors.BunchSpectrumMonitor">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">mbtrack2.tracking.monitors.monitors.</span></span><span class="sig-name descname"><span class="pre">BunchSpectrumMonitor</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">ring</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">bunch_number</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">mp_number</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">sample_size</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">save_every</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">buffer_size</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">total_size</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">dim</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'all'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">n_fft</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">file_name</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">mpi_mode</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/monitors/monitors.html#BunchSpectrumMonitor"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.monitors.monitors.BunchSpectrumMonitor" title="Permalink to this definition">¶</a></dt>
+<dd><p>Bases: <a class="reference internal" href="#mbtrack2.tracking.monitors.monitors.Monitor" title="mbtrack2.tracking.monitors.monitors.Monitor"><code class="xref py py-class docutils literal notranslate"><span class="pre">Monitor</span></code></a></p>
+<p>Monitor the coherent and incoherent bunch spectrums.</p>
+<p>ring : Synchrotron object
+bunch_number : int</p>
+<blockquote>
+<div><p>Bunch to monitor</p>
+</div></blockquote>
+<dl>
+<dt>mp_number<span class="classifier">int or float</span></dt><dd><p>Total number of macro-particles in the bunch.</p>
+</dd>
+<dt>sample_size<span class="classifier">int or float</span></dt><dd><p>Number of macro-particles to be used for tune and FFT computation.
+This number cannot exceed mp_number.</p>
+</dd>
+<dt>save_every<span class="classifier">int or float</span></dt><dd><p>Set the frequency of the save. The spectrums are computed every 
+save_every call of the montior.</p>
+</dd>
+<dt>buffer_size<span class="classifier">int or float</span></dt><dd><p>Size of the save buffer.</p>
+</dd>
+<dt>total_size<span class="classifier">int or float</span></dt><dd><p>Total size of the save. The following relationships between the 
+parameters must exist:</p>
+<blockquote>
+<div><p>total_size % buffer_size == 0
+number of call to track / save_every == total_size - 1</p>
+</div></blockquote>
+</dd>
+<dt>dim<span class="classifier">str, optional</span></dt><dd><p>Dimensions in which the spectrums have to be computed.
+Can be:</p>
+<blockquote>
+<div><ul class="simple">
+<li><p>“all”</p></li>
+<li><p>“tau”</p></li>
+<li><p>“x”</p></li>
+<li><p>“y”</p></li>
+<li><p>“xy” or “yx”</p></li>
+<li><p>“xtau” or “taux”</p></li>
+<li><p>“ytau” or “tauy”</p></li>
+</ul>
+</div></blockquote>
+</dd>
+<dt>n_fft<span class="classifier">int or float, optional</span></dt><dd><p>The number of points used for FFT computation, if n_fft is bigger than
+save_every zero-padding is applied.
+If None, save_every is used.</p>
+</dd>
+<dt>file_name<span class="classifier">string, optional</span></dt><dd><p>Name of the HDF5 where the data will be stored. Must be specified
+the first time a subclass of Monitor is instancied and must be None
+the following times.</p>
+</dd>
+<dt>mpi_mode<span class="classifier">bool, optional</span></dt><dd><p>If True, open the HDF5 file in parallel mode, which is needed to
+allow several cores to write in the same file at the same time.
+If False, open the HDF5 file in standard mode.</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>fft_resolution<span class="classifier">float</span></dt><dd><p>Return the fft resolution in [Hz].</p>
+</dd>
+<dt>signal_resolution<span class="classifier">float</span></dt><dd><p>Return the signal resolution in [Hz].</p>
+</dd>
+<dt>frequency_samples<span class="classifier">array of float</span></dt><dd><p>Return the fft frequency samples in [Hz].</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>track(bunch):</dt><dd><p>Save spectrum data.</p>
+</dd>
+</dl>
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.tracking.monitors.monitors.BunchSpectrumMonitor.fft_resolution">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">fft_resolution</span></span><a class="headerlink" href="#mbtrack2.tracking.monitors.monitors.BunchSpectrumMonitor.fft_resolution" title="Permalink to this definition">¶</a></dt>
+<dd><p>Return the fft resolution in [Hz].</p>
+<p>It is defined as the sampling frequency over the number of samples.</p>
+</dd></dl>
+
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.tracking.monitors.monitors.BunchSpectrumMonitor.frequency_samples">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">frequency_samples</span></span><a class="headerlink" href="#mbtrack2.tracking.monitors.monitors.BunchSpectrumMonitor.frequency_samples" title="Permalink to this definition">¶</a></dt>
+<dd><p>Return the fft frequency samples in [Hz].</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.monitors.monitors.BunchSpectrumMonitor.get_coherent_spectrum">
+<span class="sig-name descname"><span class="pre">get_coherent_spectrum</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">mean</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/monitors/monitors.html#BunchSpectrumMonitor.get_coherent_spectrum"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.monitors.monitors.BunchSpectrumMonitor.get_coherent_spectrum" title="Permalink to this definition">¶</a></dt>
+<dd><p>Compute the coherent spectrum i.e. the absolute value of the FT of the
+mean position of the bunch.</p>
+<dl class="simple">
+<dt>coherent<span class="classifier">array</span></dt><dd><p>Bunch coherent spectrum.</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.monitors.monitors.BunchSpectrumMonitor.get_incoherent_spectrum">
+<span class="sig-name descname"><span class="pre">get_incoherent_spectrum</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">positions</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/monitors/monitors.html#BunchSpectrumMonitor.get_incoherent_spectrum"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.monitors.monitors.BunchSpectrumMonitor.get_incoherent_spectrum" title="Permalink to this definition">¶</a></dt>
+<dd><p>Compute the incoherent spectrum i.e. the average of the absolute value 
+of the FT of the position of every particule of the bunch.</p>
+<dl class="simple">
+<dt>incoherent<span class="classifier">array</span></dt><dd><p>Bunch incoherent spectrum.</p>
+</dd>
+<dt>mean_incoherent<span class="classifier">float</span></dt><dd><p>Mean frequency of the maximum of each individual particle spectrum
+in [Hz].</p>
+</dd>
+<dt>std_incoherent<span class="classifier">float</span></dt><dd><p>Standard deviation of the frequency of the maximum of each 
+individual particle spectrum in [Hz].</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.tracking.monitors.monitors.BunchSpectrumMonitor.signal_resolution">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">signal_resolution</span></span><a class="headerlink" href="#mbtrack2.tracking.monitors.monitors.BunchSpectrumMonitor.signal_resolution" title="Permalink to this definition">¶</a></dt>
+<dd><p>Return the signal resolution in [Hz].</p>
+<p>It is defined as the inverse of the signal length.</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.monitors.monitors.BunchSpectrumMonitor.to_buffer">
+<span class="sig-name descname"><span class="pre">to_buffer</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">bunch</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/monitors/monitors.html#BunchSpectrumMonitor.to_buffer"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.monitors.monitors.BunchSpectrumMonitor.to_buffer" title="Permalink to this definition">¶</a></dt>
+<dd><p>A method to hold saved data before writing it to the output file.</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.monitors.monitors.BunchSpectrumMonitor.track">
+<span class="sig-name descname"><span class="pre">track</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">object_to_save</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/monitors/monitors.html#BunchSpectrumMonitor.track"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.monitors.monitors.BunchSpectrumMonitor.track" title="Permalink to this definition">¶</a></dt>
+<dd><p>Save spectrum data.</p>
+<p>object_to_save : Beam or Bunch object</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.monitors.monitors.BunchSpectrumMonitor.write">
+<span class="sig-name descname"><span class="pre">write</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/monitors/monitors.html#BunchSpectrumMonitor.write"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.monitors.monitors.BunchSpectrumMonitor.write" title="Permalink to this definition">¶</a></dt>
+<dd><p>Write data from buffer to output file.</p>
+</dd></dl>
+
+</dd></dl>
+
+<dl class="py class">
+<dt class="sig sig-object py" id="mbtrack2.tracking.monitors.monitors.CavityMonitor">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">mbtrack2.tracking.monitors.monitors.</span></span><span class="sig-name descname"><span class="pre">CavityMonitor</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">cavity_name</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">ring</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">save_every</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">buffer_size</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">total_size</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">file_name</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">mpi_mode</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/monitors/monitors.html#CavityMonitor"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.monitors.monitors.CavityMonitor" title="Permalink to this definition">¶</a></dt>
+<dd><p>Bases: <a class="reference internal" href="#mbtrack2.tracking.monitors.monitors.Monitor" title="mbtrack2.tracking.monitors.monitors.Monitor"><code class="xref py py-class docutils literal notranslate"><span class="pre">Monitor</span></code></a></p>
+<p>Monitor a CavityResonator object and save attributes.</p>
+<dl class="simple">
+<dt>cavity_name<span class="classifier">str</span></dt><dd><p>Name of the CavityResonator object to monitor.</p>
+</dd>
+</dl>
+<p>ring : Synchrotron object
+save_every : int or float</p>
+<blockquote>
+<div><p>Set the frequency of the save. The data is saved every save_every 
+call of the montior.</p>
+</div></blockquote>
+<dl>
+<dt>buffer_size<span class="classifier">int or float</span></dt><dd><p>Size of the save buffer.</p>
+</dd>
+<dt>total_size<span class="classifier">int or float</span></dt><dd><p>Total size of the save. The following relationships between the 
+parameters must exist:</p>
+<blockquote>
+<div><p>total_size % buffer_size == 0
+number of call to track / save_every == total_size</p>
+</div></blockquote>
+</dd>
+<dt>file_name<span class="classifier">string, optional</span></dt><dd><p>Name of the HDF5 where the data will be stored. Must be specified
+the first time a subclass of Monitor is instancied and must be None
+the following times.</p>
+</dd>
+<dt>mpi_mode<span class="classifier">bool, optional</span></dt><dd><p>If True, open the HDF5 file in parallel mode, which is needed to
+allow several cores to write in the same file at the same time.
+If False, open the HDF5 file in standard mode.</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>track(beam, cavity)</dt><dd><p>Save data</p>
+</dd>
+</dl>
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.monitors.monitors.CavityMonitor.track">
+<span class="sig-name descname"><span class="pre">track</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">beam</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">cavity</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/monitors/monitors.html#CavityMonitor.track"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.monitors.monitors.CavityMonitor.track" title="Permalink to this definition">¶</a></dt>
+<dd><p>Save data</p>
+<p>beam : Beam object
+cavity : CavityResonator object</p>
+</dd></dl>
+
+</dd></dl>
+
+<dl class="py class">
+<dt class="sig sig-object py" id="mbtrack2.tracking.monitors.monitors.Monitor">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">mbtrack2.tracking.monitors.monitors.</span></span><span class="sig-name descname"><span class="pre">Monitor</span></span><a class="reference internal" href="_modules/mbtrack2/tracking/monitors/monitors.html#Monitor"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.monitors.monitors.Monitor" title="Permalink to this definition">¶</a></dt>
+<dd><p>Bases: <a class="reference internal" href="mbtrack2.tracking.html#mbtrack2.tracking.element.Element" title="mbtrack2.tracking.element.Element"><code class="xref py py-class docutils literal notranslate"><span class="pre">Element</span></code></a></p>
+<p>Abstract Monitor class used for subclass inheritance to define all the
+different kind of monitors objects.</p>
+<p>The Monitor class is based on h5py module to be able to write data on 
+structured binary files. The class provides a common file where the 
+different Monitor subclass can write.</p>
+<dl class="simple">
+<dt>file<span class="classifier">HDF5 file</span></dt><dd><p>Common file where all monitors, Monitor subclass elements, write the
+saved data. Based on class attribute _file_storage.</p>
+</dd>
+<dt>file_name<span class="classifier">string</span></dt><dd><p>Name of the HDF5 file where the data is stored. Based on class 
+attribute _file_name_storage.</p>
+</dd>
+</dl>
+<dl>
+<dt>monitor_init(group_name, save_every, buffer_size, total_size,</dt><dd><blockquote>
+<div><p>dict_buffer, dict_file, file_name=None, mpi_mode=True)</p>
+</div></blockquote>
+<p>Method called to initialize Monitor subclass.</p>
+</dd>
+<dt>write()</dt><dd><p>Write data from buffer to the HDF5 file.</p>
+</dd>
+<dt>to_buffer(object_to_save)</dt><dd><p>Save data to buffer.</p>
+</dd>
+<dt>close()</dt><dd><p>Close the HDF5 file shared by all Monitor subclass, must be called 
+by at least an instance of a Montior subclass at the end of the 
+tracking.</p>
+</dd>
+<dt>track_bunch_data(object_to_save)</dt><dd><p>Track method to use when saving bunch data.</p>
+</dd>
+</dl>
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.monitors.monitors.Monitor.close">
+<span class="sig-name descname"><span class="pre">close</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/monitors/monitors.html#Monitor.close"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.monitors.monitors.Monitor.close" title="Permalink to this definition">¶</a></dt>
+<dd><p>Close the HDF5 file shared by all Monitor subclass, must be called 
+by at least an instance of a Montior subclass at the end of the 
+tracking.</p>
+</dd></dl>
+
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.tracking.monitors.monitors.Monitor.file">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">file</span></span><a class="headerlink" href="#mbtrack2.tracking.monitors.monitors.Monitor.file" title="Permalink to this definition">¶</a></dt>
+<dd><p>Name of the HDF5 file where the data is stored.</p>
+</dd></dl>
+
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.tracking.monitors.monitors.Monitor.file_name">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">file_name</span></span><a class="headerlink" href="#mbtrack2.tracking.monitors.monitors.Monitor.file_name" title="Permalink to this definition">¶</a></dt>
+<dd><p>Common file where all monitors, Monitor subclass elements, write the
+saved data.</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.monitors.monitors.Monitor.monitor_init">
+<span class="sig-name descname"><span class="pre">monitor_init</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">group_name</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">save_every</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">buffer_size</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">total_size</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">dict_buffer</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">dict_file</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">file_name</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">mpi_mode</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">dict_dtype</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/monitors/monitors.html#Monitor.monitor_init"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.monitors.monitors.Monitor.monitor_init" title="Permalink to this definition">¶</a></dt>
+<dd><p>Method called to initialize Monitor subclass.</p>
+<dl>
+<dt>group_name<span class="classifier">string</span></dt><dd><p>Name of the HDF5 group in which the data for the current monitor 
+will be saved.</p>
+</dd>
+<dt>save_every<span class="classifier">int or float</span></dt><dd><p>Set the frequency of the save. The data is saved every save_every 
+call of the montior.</p>
+</dd>
+<dt>buffer_size<span class="classifier">int or float</span></dt><dd><p>Size of the save buffer.</p>
+</dd>
+<dt>total_size<span class="classifier">int or float</span></dt><dd><p>Total size of the save. The following relationships between the 
+parameters must exist:</p>
+<blockquote>
+<div><p>total_size % buffer_size == 0
+number of call to track / save_every == total_size</p>
+</div></blockquote>
+</dd>
+<dt>dict_buffer<span class="classifier">dict</span></dt><dd><p>Dictionary with keys as the attribute name to save and values as
+the shape of the buffer to create to hold the attribute, like 
+(key.shape, buffer_size)</p>
+</dd>
+<dt>dict_file<span class="classifier">dict</span></dt><dd><p>Dictionary with keys as the attribute name to save and values as
+the shape of the dataset to create to hold the attribute, like 
+(key.shape, total_size)</p>
+</dd>
+<dt>file_name<span class="classifier">string, optional</span></dt><dd><p>Name of the HDF5 where the data will be stored. Must be specified
+the first time a subclass of Monitor is instancied and must be None
+the following times.</p>
+</dd>
+<dt>mpi_mode<span class="classifier">bool, optional</span></dt><dd><p>If True, open the HDF5 file in parallel mode, which is needed to
+allow several cores to write in the same file at the same time.
+If False, open the HDF5 file in standard mode.</p>
+</dd>
+<dt>dict_dtype<span class="classifier">dict, optional</span></dt><dd><p>Dictionary with keys as the attribute name to save and values as
+the dtype to use to save the values.
+If None, float is used for all attributes.</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.monitors.monitors.Monitor.to_buffer">
+<span class="sig-name descname"><span class="pre">to_buffer</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">object_to_save</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/monitors/monitors.html#Monitor.to_buffer"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.monitors.monitors.Monitor.to_buffer" title="Permalink to this definition">¶</a></dt>
+<dd><p>Save data to buffer.</p>
+<dl class="simple">
+<dt>object_to_save<span class="classifier">python object</span></dt><dd><p>Depends on the Monitor subclass, typically a Beam or Bunch object.</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.monitors.monitors.Monitor.track_bunch_data">
+<span class="sig-name descname"><span class="pre">track_bunch_data</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">object_to_save</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">check_empty</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/monitors/monitors.html#Monitor.track_bunch_data"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.monitors.monitors.Monitor.track_bunch_data" title="Permalink to this definition">¶</a></dt>
+<dd><p>Track method to use when saving bunch data.</p>
+<p>object_to_save : Beam or Bunch
+check_emptiness: bool</p>
+<blockquote>
+<div><p>If True, check if the bunch is empty. If it is, then do nothing.</p>
+</div></blockquote>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.monitors.monitors.Monitor.write">
+<span class="sig-name descname"><span class="pre">write</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/monitors/monitors.html#Monitor.write"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.monitors.monitors.Monitor.write" title="Permalink to this definition">¶</a></dt>
+<dd><p>Write data from buffer to the HDF5 file.</p>
+</dd></dl>
+
+</dd></dl>
+
+<dl class="py class">
+<dt class="sig sig-object py" id="mbtrack2.tracking.monitors.monitors.PhaseSpaceMonitor">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">mbtrack2.tracking.monitors.monitors.</span></span><span class="sig-name descname"><span class="pre">PhaseSpaceMonitor</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">bunch_number</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">mp_number</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">save_every</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">buffer_size</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">total_size</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">file_name</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">mpi_mode</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/monitors/monitors.html#PhaseSpaceMonitor"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.monitors.monitors.PhaseSpaceMonitor" title="Permalink to this definition">¶</a></dt>
+<dd><p>Bases: <a class="reference internal" href="#mbtrack2.tracking.monitors.monitors.Monitor" title="mbtrack2.tracking.monitors.monitors.Monitor"><code class="xref py py-class docutils literal notranslate"><span class="pre">Monitor</span></code></a></p>
+<p>Monitor a single bunch and save the full phase space.</p>
+<dl>
+<dt>bunch_number<span class="classifier">int</span></dt><dd><p>Bunch to monitor</p>
+</dd>
+<dt>mp_number<span class="classifier">int or float</span></dt><dd><p>Number of macroparticle in the phase space to save. If less than the 
+total number of macroparticles, a random fraction of the bunch is saved.</p>
+</dd>
+<dt>save_every<span class="classifier">int or float</span></dt><dd><p>Set the frequency of the save. The data is saved every save_every 
+call of the montior.</p>
+</dd>
+<dt>buffer_size<span class="classifier">int or float</span></dt><dd><p>Size of the save buffer.</p>
+</dd>
+<dt>total_size<span class="classifier">int or float</span></dt><dd><p>Total size of the save. The following relationships between the 
+parameters must exist:</p>
+<blockquote>
+<div><p>total_size % buffer_size == 0
+number of call to track / save_every == total_size</p>
+</div></blockquote>
+</dd>
+<dt>file_name<span class="classifier">string, optional</span></dt><dd><p>Name of the HDF5 where the data will be stored. Must be specified
+the first time a subclass of Monitor is instancied and must be None
+the following times.</p>
+</dd>
+<dt>mpi_mode<span class="classifier">bool, optional</span></dt><dd><p>If True, open the HDF5 file in parallel mode, which is needed to
+allow several cores to write in the same file at the same time.
+If False, open the HDF5 file in standard mode.</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>track(object_to_save)</dt><dd><p>Save data</p>
+</dd>
+</dl>
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.monitors.monitors.PhaseSpaceMonitor.to_buffer">
+<span class="sig-name descname"><span class="pre">to_buffer</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">bunch</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/monitors/monitors.html#PhaseSpaceMonitor.to_buffer"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.monitors.monitors.PhaseSpaceMonitor.to_buffer" title="Permalink to this definition">¶</a></dt>
+<dd><p>Save data to buffer.</p>
+<p>bunch : Bunch object</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.monitors.monitors.PhaseSpaceMonitor.track">
+<span class="sig-name descname"><span class="pre">track</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">object_to_save</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/monitors/monitors.html#PhaseSpaceMonitor.track"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.monitors.monitors.PhaseSpaceMonitor.track" title="Permalink to this definition">¶</a></dt>
+<dd><p>Save data</p>
+<p>object_to_save : Bunch or Beam object</p>
+</dd></dl>
+
+</dd></dl>
+
+<dl class="py class">
+<dt class="sig sig-object py" id="mbtrack2.tracking.monitors.monitors.ProfileMonitor">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">mbtrack2.tracking.monitors.monitors.</span></span><span class="sig-name descname"><span class="pre">ProfileMonitor</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">bunch_number</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">save_every</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">buffer_size</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">total_size</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">dimensions</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'tau'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">n_bin</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">75</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">file_name</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">mpi_mode</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/monitors/monitors.html#ProfileMonitor"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.monitors.monitors.ProfileMonitor" title="Permalink to this definition">¶</a></dt>
+<dd><p>Bases: <a class="reference internal" href="#mbtrack2.tracking.monitors.monitors.Monitor" title="mbtrack2.tracking.monitors.monitors.Monitor"><code class="xref py py-class docutils literal notranslate"><span class="pre">Monitor</span></code></a></p>
+<p>Monitor a single bunch and save bunch profiles.</p>
+<dl>
+<dt>bunch_number<span class="classifier">int</span></dt><dd><p>Bunch to monitor.</p>
+</dd>
+<dt>save_every<span class="classifier">int or float</span></dt><dd><p>Set the frequency of the save. The data is saved every save_every 
+call of the montior.</p>
+</dd>
+<dt>buffer_size<span class="classifier">int or float</span></dt><dd><p>Size of the save buffer.</p>
+</dd>
+<dt>total_size<span class="classifier">int or float</span></dt><dd><p>Total size of the save. The following relationships between the 
+parameters must exist:</p>
+<blockquote>
+<div><p>total_size % buffer_size == 0
+number of call to track / save_every == total_size</p>
+</div></blockquote>
+</dd>
+<dt>dimensions<span class="classifier">str or list of str, optional</span></dt><dd><p>Dimensions to save.</p>
+</dd>
+<dt>n_bin<span class="classifier">int or list of int, optional</span></dt><dd><p>Number of bin to use in each dimension.</p>
+</dd>
+<dt>file_name<span class="classifier">string, optional</span></dt><dd><p>Name of the HDF5 where the data will be stored. Must be specified
+the first time a subclass of Monitor is instancied and must be None
+the following times.</p>
+</dd>
+<dt>mpi_mode<span class="classifier">bool, optional</span></dt><dd><p>If True, open the HDF5 file in parallel mode, which is needed to
+allow several cores to write in the same file at the same time.
+If False, open the HDF5 file in standard mode.</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>track(object_to_save)</dt><dd><p>Save data.</p>
+</dd>
+</dl>
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.monitors.monitors.ProfileMonitor.to_buffer">
+<span class="sig-name descname"><span class="pre">to_buffer</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">bunch</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/monitors/monitors.html#ProfileMonitor.to_buffer"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.monitors.monitors.ProfileMonitor.to_buffer" title="Permalink to this definition">¶</a></dt>
+<dd><p>Save data to buffer.</p>
+<p>bunch : Bunch object</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.monitors.monitors.ProfileMonitor.track">
+<span class="sig-name descname"><span class="pre">track</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">object_to_save</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/monitors/monitors.html#ProfileMonitor.track"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.monitors.monitors.ProfileMonitor.track" title="Permalink to this definition">¶</a></dt>
+<dd><p>Save data.</p>
+<p>object_to_save : Bunch or Beam object</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.monitors.monitors.ProfileMonitor.write">
+<span class="sig-name descname"><span class="pre">write</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/monitors/monitors.html#ProfileMonitor.write"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.monitors.monitors.ProfileMonitor.write" title="Permalink to this definition">¶</a></dt>
+<dd><p>Write data from buffer to the HDF5 file.</p>
+</dd></dl>
+
+</dd></dl>
+
+<dl class="py class">
+<dt class="sig sig-object py" id="mbtrack2.tracking.monitors.monitors.WakePotentialMonitor">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">mbtrack2.tracking.monitors.monitors.</span></span><span class="sig-name descname"><span class="pre">WakePotentialMonitor</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">bunch_number</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">wake_types</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">n_bin</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">save_every</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">buffer_size</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">total_size</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">file_name</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">mpi_mode</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/monitors/monitors.html#WakePotentialMonitor"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.monitors.monitors.WakePotentialMonitor" title="Permalink to this definition">¶</a></dt>
+<dd><p>Bases: <a class="reference internal" href="#mbtrack2.tracking.monitors.monitors.Monitor" title="mbtrack2.tracking.monitors.monitors.Monitor"><code class="xref py py-class docutils literal notranslate"><span class="pre">Monitor</span></code></a></p>
+<p>Monitor the wake potential from a single bunch and save attributes (tau, 
+…).</p>
+<dl>
+<dt>bunch_number<span class="classifier">int</span></dt><dd><p>Bunch to monitor.</p>
+</dd>
+<dt>wake_types<span class="classifier">str or list of str</span></dt><dd><p>Wake types to save: “Wlong, “Wxdip”, …</p>
+</dd>
+<dt>n_bin<span class="classifier">int</span></dt><dd><p>Number of bin to be used to interpolate the wake potential on a fixed
+grid.</p>
+</dd>
+<dt>save_every<span class="classifier">int or float</span></dt><dd><p>Set the frequency of the save. The data is saved every save_every 
+call of the montior.</p>
+</dd>
+<dt>buffer_size<span class="classifier">int or float</span></dt><dd><p>Size of the save buffer.</p>
+</dd>
+<dt>total_size<span class="classifier">int or float</span></dt><dd><p>Total size of the save. The following relationships between the 
+parameters must exist:</p>
+<blockquote>
+<div><p>total_size % buffer_size == 0
+number of call to track / save_every == total_size</p>
+</div></blockquote>
+</dd>
+<dt>file_name<span class="classifier">string, optional</span></dt><dd><p>Name of the HDF5 where the data will be stored. Must be specified
+the first time a subclass of Monitor is instancied and must be None
+the following times.</p>
+</dd>
+<dt>mpi_mode<span class="classifier">bool, optional</span></dt><dd><p>If True, open the HDF5 file in parallel mode, which is needed to
+allow several cores to write in the same file at the same time.
+If False, open the HDF5 file in standard mode.</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>track(object_to_save, wake_potential_to_save)</dt><dd><p>Save data.</p>
+</dd>
+</dl>
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.monitors.monitors.WakePotentialMonitor.to_buffer">
+<span class="sig-name descname"><span class="pre">to_buffer</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">wp</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/monitors/monitors.html#WakePotentialMonitor.to_buffer"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.monitors.monitors.WakePotentialMonitor.to_buffer" title="Permalink to this definition">¶</a></dt>
+<dd><p>Save data to buffer.</p>
+<p>wp : WakePotential object</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.monitors.monitors.WakePotentialMonitor.track">
+<span class="sig-name descname"><span class="pre">track</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">object_to_save</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">wake_potential_to_save</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/monitors/monitors.html#WakePotentialMonitor.track"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.monitors.monitors.WakePotentialMonitor.track" title="Permalink to this definition">¶</a></dt>
+<dd><p>Save data.</p>
+<p>object_to_save : Bunch or Beam object
+wake_potential_to_save : WakePotential object</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.tracking.monitors.monitors.WakePotentialMonitor.write">
+<span class="sig-name descname"><span class="pre">write</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/monitors/monitors.html#WakePotentialMonitor.write"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.monitors.monitors.WakePotentialMonitor.write" title="Permalink to this definition">¶</a></dt>
+<dd><p>Write data from buffer to the HDF5 file.</p>
+</dd></dl>
+
+</dd></dl>
+
+</section>
+<section id="module-mbtrack2.tracking.monitors.plotting">
+<span id="mbtrack2-tracking-monitors-plotting-module"></span><h2>mbtrack2.tracking.monitors.plotting module<a class="headerlink" href="#module-mbtrack2.tracking.monitors.plotting" title="Permalink to this heading">¶</a></h2>
+<p>Module for plotting the data recorded by the monitor module during the 
+tracking.</p>
+<dl class="py function">
+<dt class="sig sig-object py" id="mbtrack2.tracking.monitors.plotting.plot_beamdata">
+<span class="sig-prename descclassname"><span class="pre">mbtrack2.tracking.monitors.plotting.</span></span><span class="sig-name descname"><span class="pre">plot_beamdata</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">filenames</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">dataset</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'mean'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">dimension</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'tau'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">stat_var</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'mean'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">x_var</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'time'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">turn</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">legend</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/monitors/plotting.html#plot_beamdata"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.monitors.plotting.plot_beamdata" title="Permalink to this definition">¶</a></dt>
+<dd><p>Plot 2D data recorded by BeamMonitor.</p>
+<dl>
+<dt>filenames<span class="classifier">str or list of str</span></dt><dd><p>Names of the HDF5 files to be plotted.</p>
+</dd>
+<dt>dataset<span class="classifier">{“current”,”emit”,”mean”,”std”,”cs_invariant”}</span></dt><dd><p>HDF5 file’s dataset to be plotted. The default is “mean”.</p>
+</dd>
+<dt>dimension<span class="classifier">str</span></dt><dd><blockquote>
+<div><dl class="simple">
+<dt>The dimension of the dataset to plot:</dt><dd><p>for “emit”, dimension = {“x”,”y”,”s”},
+for “cs_invariant”, dimension = {“x”,”y”,”s”},
+for “mean” and “std”, dimension = {“x”,”xp”,”y”,”yp”,”tau”,”delta”}.
+not used if “current”.</p>
+</dd>
+</dl>
+</div></blockquote>
+<p>The default is “tau”.</p>
+</dd>
+<dt>stat_var<span class="classifier">{“mean”, “std”}</span></dt><dd><p>Statistical value of the dimension.</p>
+</dd>
+<dt>x_var<span class="classifier">{“time”, “index”}</span></dt><dd><dl class="simple">
+<dt>Choice of the horizontal axis:</dt><dd><p>“time” corresponds to turn number.
+“index” corresponds to bunch index.</p>
+</dd>
+</dl>
+</dd>
+<dt>turn<span class="classifier">int or float, optional</span></dt><dd><p>Choice of the turn to plot when x_var = “index”.
+If None, the last turn is plotted.</p>
+</dd>
+<dt>legend<span class="classifier">list of str, optional</span></dt><dd><p>Legend to add for each file.</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>fig<span class="classifier">Figure</span></dt><dd><p>Figure object with the plot on it.</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py function">
+<dt class="sig sig-object py" id="mbtrack2.tracking.monitors.plotting.plot_beamspectrum">
+<span class="sig-prename descclassname"><span class="pre">mbtrack2.tracking.monitors.plotting.</span></span><span class="sig-name descname"><span class="pre">plot_beamspectrum</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">filenames</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">dim</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'tau'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">turns</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">f0</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">log_scale</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">legend</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">norm</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/monitors/plotting.html#plot_beamspectrum"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.monitors.plotting.plot_beamspectrum" title="Permalink to this definition">¶</a></dt>
+<dd><p>Plot coherent beam spectrum data.</p>
+<dl class="simple">
+<dt>filenames<span class="classifier">str or list of str</span></dt><dd><p>Names of the HDF5 files to be plotted.</p>
+</dd>
+<dt>dim<span class="classifier">{“x”,”y”,”tau”}, optional</span></dt><dd><p>The dimension of the dataset to plot.
+The default is “tau”.</p>
+</dd>
+<dt>turns<span class="classifier">array or None, optional</span></dt><dd><p>Numbers of the turns to plot.
+If None, all turns are shown. 
+The default is None.</p>
+</dd>
+<dt>f0<span class="classifier">float or None, optional</span></dt><dd><p>If not None, the frequency axis is noramlised by f0. 
+The default is None.</p>
+</dd>
+<dt>log_scale<span class="classifier">bool, optional</span></dt><dd><p>If True, the spectrum plots are shown in y-log scale. 
+The default is True.</p>
+</dd>
+<dt>legend<span class="classifier">list of str, optional</span></dt><dd><p>Legend to add for each file.
+The default is None.</p>
+</dd>
+<dt>norm<span class="classifier">bool, optional</span></dt><dd><p>If True, normalise the data of each spectrum by its geometric mean.
+The default is False.</p>
+</dd>
+</dl>
+<p>fig : Figure</p>
+</dd></dl>
+
+<dl class="py function">
+<dt class="sig sig-object py" id="mbtrack2.tracking.monitors.plotting.plot_bunchdata">
+<span class="sig-prename descclassname"><span class="pre">mbtrack2.tracking.monitors.plotting.</span></span><span class="sig-name descname"><span class="pre">plot_bunchdata</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">filenames</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">bunch_number</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">dataset</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">dimension</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'x'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">legend</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/monitors/plotting.html#plot_bunchdata"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.monitors.plotting.plot_bunchdata" title="Permalink to this definition">¶</a></dt>
+<dd><p>Plot data recorded by BunchMonitor.</p>
+<dl>
+<dt>filenames<span class="classifier">str or list of str</span></dt><dd><p>Names of the HDF5 files to be plotted.</p>
+</dd>
+<dt>bunch_number<span class="classifier">int or list of int</span></dt><dd><p>Bunch to plot. This has to be identical to ‘bunch_number’ parameter in 
+‘BunchMonitor’ object.</p>
+</dd>
+<dt>dataset<span class="classifier">{“current”, “emit”, “mean”, “std”, “cs_invariant”}</span></dt><dd><p>HDF5 file’s dataset to be plotted.</p>
+</dd>
+<dt>dimension<span class="classifier">str, optional</span></dt><dd><p>The dimension of the dataset to plot. Use “None” for “current”,
+otherwise use the following :</p>
+<blockquote>
+<div><p>for “emit”, dimension = {“x”,”y”,”s”},
+for “cs_invariant”, dimension = {“x”,”y”,”s”},
+for “mean” and “std”, dimension = {“x”,”xp”,”y”,”yp”,”tau”,”delta”},
+for “action”, dimension = {“x”,”y”}.</p>
+</div></blockquote>
+</dd>
+<dt>legend<span class="classifier">list of str, optional</span></dt><dd><p>Legend to add for each file.</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>fig<span class="classifier">Figure</span></dt><dd><p>Figure object with the plot on it.</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py function">
+<dt class="sig sig-object py" id="mbtrack2.tracking.monitors.plotting.plot_bunchspectrum">
+<span class="sig-prename descclassname"><span class="pre">mbtrack2.tracking.monitors.plotting.</span></span><span class="sig-name descname"><span class="pre">plot_bunchspectrum</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">filenames</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">bunch_number</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">dataset</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'incoherent'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">dim</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'tau'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">turns</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">fs</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">log_scale</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">legend</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">norm</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/monitors/plotting.html#plot_bunchspectrum"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.monitors.plotting.plot_bunchspectrum" title="Permalink to this definition">¶</a></dt>
+<dd><p>Plot coherent and incoherent spectrum data.</p>
+<dl class="simple">
+<dt>filenames<span class="classifier">str or list of str</span></dt><dd><p>Names of the HDF5 files to be plotted.</p>
+</dd>
+<dt>bunch_number<span class="classifier">int or list of int</span></dt><dd><p>Bunch to plot. This has to be identical to ‘bunch_number’ parameter in 
+‘BunchSpectrumMonitor’ object.</p>
+</dd>
+<dt>dataset<span class="classifier">{“mean_incoherent”, “coherent”, “incoherent”}</span></dt><dd><p>HDF5 file’s dataset to be plotted. 
+The default is “incoherent”.</p>
+</dd>
+<dt>dim<span class="classifier">{“x”,”y”,”tau”}, optional</span></dt><dd><p>The dimension of the dataset to plot.
+The default is “tau”.</p>
+</dd>
+<dt>turns<span class="classifier">array or None, optional</span></dt><dd><p>Numbers of the turns to plot.
+If None, all turns are shown. 
+The default is None.</p>
+</dd>
+<dt>fs<span class="classifier">float or None, optional</span></dt><dd><p>If not None, the frequency axis is noramlised by fs. 
+The default is None.</p>
+</dd>
+<dt>log_scale<span class="classifier">bool, optional</span></dt><dd><p>If True, the spectrum plots are shown in y-log scale. 
+The default is True.</p>
+</dd>
+<dt>legend<span class="classifier">list of str, optional</span></dt><dd><p>Legend to add for each file.
+The default is None.</p>
+</dd>
+<dt>norm<span class="classifier">bool, optional</span></dt><dd><p>If True, normalise the data of each spectrum by its geometric mean.
+The default is False.</p>
+</dd>
+</dl>
+<p>fig : Figure</p>
+</dd></dl>
+
+<dl class="py function">
+<dt class="sig sig-object py" id="mbtrack2.tracking.monitors.plotting.plot_cavitydata">
+<span class="sig-prename descclassname"><span class="pre">mbtrack2.tracking.monitors.plotting.</span></span><span class="sig-name descname"><span class="pre">plot_cavitydata</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">filename</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">cavity_name</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">phasor</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'cavity'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">plot_type</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'bunch'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">bunch_number</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">turn</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">cm_lim</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">show_objective</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/monitors/plotting.html#plot_cavitydata"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.monitors.plotting.plot_cavitydata" title="Permalink to this definition">¶</a></dt>
+<dd><p>Plot data recorded by CavityMonitor.</p>
+<dl>
+<dt>filename<span class="classifier">str </span></dt><dd><p>Name of the HDF5 file that contains the data.</p>
+</dd>
+<dt>cavity_name<span class="classifier">str</span></dt><dd><p>Name of the CavityResonator object.</p>
+</dd>
+<dt>phasor<span class="classifier">str, optional</span></dt><dd><p>Type of the phasor to plot. Can be “beam”, “cavity”, “generator” or 
+“ig”.</p>
+</dd>
+<dt>plot_type<span class="classifier">str, optional</span></dt><dd><dl>
+<dt>Type of plot:</dt><dd><ul class="simple">
+<li><p>“bunch” plots the phasor voltage and angle versus time for a</p></li>
+</ul>
+<p>given bunch.
+- “turn” plots the phasor voltage and ange versus bunch index for
+a given turn.
+- “streak_amplitude” plots the phasor amplitude versus bunch index 
+and time.
+- “streak_angle” plots the phasor angle versus bunch index and 
+time.
+- “detune” or “psi” plots the detuning or tuning angle versus time.
+- “power” plots the generator, cavity, beam and reflected power
+versus time. Needs BeamMonitor data with same save_every as 
+CavityMonitor.
+- “mean” plots the mean phasor voltage and angle versus time for 
+non empty bunches. Needs BeamMonitor data with same save_every as 
+CavityMonitor.
+- “tuner_diff” plots the tuner difference from optimal tuning 
+condition (for a given bunch) and the tuning angle versus time.</p>
+</dd>
+</dl>
+</dd>
+<dt>bunch_number<span class="classifier">int, optional</span></dt><dd><p>Bunch number to select. The default is 0.</p>
+</dd>
+<dt>turn<span class="classifier">int, optional</span></dt><dd><p>Turn to plot. The default is None.</p>
+</dd>
+<dt>cm_lim<span class="classifier">list [vmin, vmax], optional</span></dt><dd><p>Colormap scale for the “streak” plots.</p>
+</dd>
+<dt>show_objective<span class="classifier">bool, optional</span></dt><dd><p>If True, shows the Cavity voltage and phase objective value (Vc and 
+theta) in plot type “mean” and “bunch” for “cavity” phasor.
+Default is False.</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>fig<span class="classifier">Figure</span></dt><dd><p>Figure object with the plot on it.</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py function">
+<dt class="sig sig-object py" id="mbtrack2.tracking.monitors.plotting.plot_phasespacedata">
+<span class="sig-prename descclassname"><span class="pre">mbtrack2.tracking.monitors.plotting.</span></span><span class="sig-name descname"><span class="pre">plot_phasespacedata</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">filename</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">bunch_number</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">x_var</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">y_var</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">turn</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">only_alive</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">plot_size</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">plot_kind</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'kde'</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/monitors/plotting.html#plot_phasespacedata"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.monitors.plotting.plot_phasespacedata" title="Permalink to this definition">¶</a></dt>
+<dd><p>Plot data recorded by PhaseSpaceMonitor.</p>
+<dl class="simple">
+<dt>filename<span class="classifier">str</span></dt><dd><p>Name of the HDF5 file that contains the data.</p>
+</dd>
+<dt>bunch_number<span class="classifier">int</span></dt><dd><p>Bunch to plot. This has to be identical to ‘bunch_number’ parameter in 
+‘PhaseSpaceMonitor’ object.</p>
+</dd>
+<dt>x_var, y_var<span class="classifier">str {“x”, “xp”, “y”, “yp”, “tau”, “delta”}</span></dt><dd><p>If dataset is “particles”, the variables to be plotted on the 
+horizontal and the vertical axes need to be specified.</p>
+</dd>
+<dt>turn<span class="classifier">int</span></dt><dd><p>Turn at which the data will be extracted.</p>
+</dd>
+<dt>only_alive<span class="classifier">bool, optional</span></dt><dd><p>When only_alive is True, only alive particles are plotted and dead 
+particles will be discarded.</p>
+</dd>
+<dt>plot_size<span class="classifier">[0,1], optional</span></dt><dd><p>Number of macro-particles to plot relative to the total number 
+of macro-particles recorded. This option helps reduce processing time
+when the data is big.</p>
+</dd>
+<dt>plot_kind<span class="classifier">{‘scatter’, ‘kde’, ‘hex’, ‘reg’, ‘resid’}, optional</span></dt><dd><p>The plot style. The default is ‘kde’.</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>fig<span class="classifier">Figure</span></dt><dd><p>Figure object with the plot on it.</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py function">
+<dt class="sig sig-object py" id="mbtrack2.tracking.monitors.plotting.plot_profiledata">
+<span class="sig-prename descclassname"><span class="pre">mbtrack2.tracking.monitors.plotting.</span></span><span class="sig-name descname"><span class="pre">plot_profiledata</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">filename</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">bunch_number</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">dimension</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'tau'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">start</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">stop</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">step</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">profile_plot</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">streak_plot</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/monitors/plotting.html#plot_profiledata"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.monitors.plotting.plot_profiledata" title="Permalink to this definition">¶</a></dt>
+<dd><p>Plot data recorded by ProfileMonitor</p>
+<dl class="simple">
+<dt>filename<span class="classifier">str</span></dt><dd><p>Name of the HDF5 file that contains the data.</p>
+</dd>
+<dt>bunch_number<span class="classifier">int</span></dt><dd><p>Bunch to plot. This has to be identical to ‘bunch_number’ parameter in 
+‘ProfileMonitor’ object.</p>
+</dd>
+<dt>dimension<span class="classifier">str, optional</span></dt><dd><p>Dimension to plot. The default is “tau”</p>
+</dd>
+<dt>start<span class="classifier">int, optional</span></dt><dd><p>First turn to plot. The default is 0.</p>
+</dd>
+<dt>stop<span class="classifier">int, optional</span></dt><dd><p>Last turn to plot. If None, the last turn of the record is selected.</p>
+</dd>
+<dt>step<span class="classifier">int, optional</span></dt><dd><p>Plotting step. This has to be divisible by ‘save_every’ parameter in
+‘ProfileMonitor’ object, i.e. step % save_every == 0. If None, step is
+equivalent to save_every.</p>
+</dd>
+<dt>profile_plot<span class="classifier">bool, optional</span></dt><dd><p>If Ture, bunch profile plot is plotted.</p>
+</dd>
+<dt>streak_plot<span class="classifier">bool, optional</span></dt><dd><p>If True, strek plot is plotted.</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>fig<span class="classifier">Figure</span></dt><dd><p>Figure object with the plot on it.</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py function">
+<dt class="sig sig-object py" id="mbtrack2.tracking.monitors.plotting.plot_wakedata">
+<span class="sig-prename descclassname"><span class="pre">mbtrack2.tracking.monitors.plotting.</span></span><span class="sig-name descname"><span class="pre">plot_wakedata</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">filename</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">bunch_number</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">wake_type</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'Wlong'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">start</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">stop</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">step</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">profile_plot</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">streak_plot</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">bunch_profile</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">dipole</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/monitors/plotting.html#plot_wakedata"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.monitors.plotting.plot_wakedata" title="Permalink to this definition">¶</a></dt>
+<dd><p>Plot data recorded by WakePotentialMonitor</p>
+<dl class="simple">
+<dt>filename<span class="classifier">str</span></dt><dd><p>Name of the HDF5 file that contains the data.</p>
+</dd>
+<dt>bunch_number<span class="classifier">int</span></dt><dd><p>Bunch to plot. This has to be identical to ‘bunch_number’ parameter in 
+‘WakePotentialMonitor’ object.</p>
+</dd>
+<dt>wake_type<span class="classifier">str, optional</span></dt><dd><p>Wake type to plot: “Wlong”, “Wxdip”, …</p>
+</dd>
+<dt>start<span class="classifier">int, optional</span></dt><dd><p>First turn to plot. The default is 0.</p>
+</dd>
+<dt>stop<span class="classifier">int, optional</span></dt><dd><p>Last turn to plot. If None, the last turn of the record is selected.</p>
+</dd>
+<dt>step<span class="classifier">int, optional</span></dt><dd><p>Plotting step. This has to be divisible by ‘save_every’ parameter in
+‘WakePotentialMonitor’ object, i.e. step % save_every == 0. If None, 
+step is equivalent to save_every.</p>
+</dd>
+<dt>profile_plot<span class="classifier">bool, optional</span></dt><dd><p>If Ture, wake potential profile plot is plotted.</p>
+</dd>
+<dt>streak_plot<span class="classifier">bool, optional</span></dt><dd><p>If True, strek plot is plotted.</p>
+</dd>
+<dt>bunch_profile<span class="classifier">bool, optional.</span></dt><dd><p>If True, the bunch profile is plotted.</p>
+</dd>
+<dt>dipole<span class="classifier">bool, optional</span></dt><dd><p>If True, the dipole moment is plotted.</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>fig<span class="classifier">Figure</span></dt><dd><p>Figure object with the plot on it.</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py function">
+<dt class="sig sig-object py" id="mbtrack2.tracking.monitors.plotting.streak_beamdata">
+<span class="sig-prename descclassname"><span class="pre">mbtrack2.tracking.monitors.plotting.</span></span><span class="sig-name descname"><span class="pre">streak_beamdata</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">filename</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">dataset</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'mean'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">dimension</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'tau'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">cm_lim</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/monitors/plotting.html#streak_beamdata"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.monitors.plotting.streak_beamdata" title="Permalink to this definition">¶</a></dt>
+<dd><p>Plot 3D data recorded by BeamMonitor.</p>
+<dl>
+<dt>filename<span class="classifier">str</span></dt><dd><p>Name of the HDF5 file that contains the data.</p>
+</dd>
+<dt>dataset<span class="classifier">{“current”,”emit”,”mean”,”std”,”cs_invariant”}</span></dt><dd><p>HDF5 file’s dataset to be plotted. The default is “mean”.</p>
+</dd>
+<dt>dimension<span class="classifier">str</span></dt><dd><blockquote>
+<div><dl class="simple">
+<dt>The dimension of the dataset to plot:</dt><dd><p>for “emit”, dimension = {“x”,”y”,”s”},
+for “cs_invariant”, dimension = {“x”,”y”,”s”},
+for “mean” and “std”, dimension = {“x”,”xp”,”y”,”yp”,”tau”,”delta”}.
+not used if “current”.</p>
+</dd>
+</dl>
+</div></blockquote>
+<p>The default is “tau”.</p>
+</dd>
+<dt>cm_lim<span class="classifier">list [vmin, vmax], optional</span></dt><dd><p>Colormap scale for the “streak” plot.</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>fig<span class="classifier">Figure</span></dt><dd><p>Figure object with the plot on it.</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py function">
+<dt class="sig sig-object py" id="mbtrack2.tracking.monitors.plotting.streak_beamspectrum">
+<span class="sig-prename descclassname"><span class="pre">mbtrack2.tracking.monitors.plotting.</span></span><span class="sig-name descname"><span class="pre">streak_beamspectrum</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">filename</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">dim</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'tau'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">f0</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">log_scale</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">fmin</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">fmax</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">turns</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">norm</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">ylim</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/monitors/plotting.html#streak_beamspectrum"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.monitors.plotting.streak_beamspectrum" title="Permalink to this definition">¶</a></dt>
+<dd><p>Plot 3D data recorded by the BeamSpectrumMonitor.</p>
+<dl class="simple">
+<dt>filenames<span class="classifier">str</span></dt><dd><p>Name of the HDF5 file to be plotted.</p>
+</dd>
+<dt>dim<span class="classifier">{“x”,”y”,”tau”}, optional</span></dt><dd><p>The dimension of the dataset to plot.
+The default is “tau”.</p>
+</dd>
+<dt>f0<span class="classifier">float or None, optional</span></dt><dd><p>If not None, the frequency axis is noramlised by f0.</p>
+</dd>
+<dt>log_scale<span class="classifier">bool, optional</span></dt><dd><p>If True, the spectrum plots are shown in y-log scale. 
+The default is True.</p>
+</dd>
+<dt>fmin<span class="classifier">float, optional</span></dt><dd><p>If not None, the plot is limitted to values bigger than fmin.</p>
+</dd>
+<dt>fmax<span class="classifier">float, optional</span></dt><dd><p>If not None, the plot is limitted to values smaller than fmax.</p>
+</dd>
+<dt>turns<span class="classifier">array, optional</span></dt><dd><p>If not None, only the turn numbers in the turns array are plotted.</p>
+</dd>
+<dt>norm<span class="classifier">bool, optional</span></dt><dd><p>If True, normalise the data of each spectrum by its geometric mean.
+The default is False.</p>
+</dd>
+<dt>ylim<span class="classifier">array, optional</span></dt><dd><p>If not None, should be array like in the form [ymin, ymax] where ymin 
+and ymax are the minimum and maxmimum values used in the y axis.</p>
+</dd>
+</dl>
+<p>fig : Figure</p>
+</dd></dl>
+
+<dl class="py function">
+<dt class="sig sig-object py" id="mbtrack2.tracking.monitors.plotting.streak_bunchspectrum">
+<span class="sig-prename descclassname"><span class="pre">mbtrack2.tracking.monitors.plotting.</span></span><span class="sig-name descname"><span class="pre">streak_bunchspectrum</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">filename</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">bunch_number</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">dataset</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'incoherent'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">dim</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'tau'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">fs</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">log_scale</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">fmin</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">fmax</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">turns</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">norm</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">ylim</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/monitors/plotting.html#streak_bunchspectrum"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.monitors.plotting.streak_bunchspectrum" title="Permalink to this definition">¶</a></dt>
+<dd><p>Plot 3D data recorded by the BunchSpectrumMonitor.</p>
+<dl class="simple">
+<dt>filenames<span class="classifier">str</span></dt><dd><p>Name of the HDF5 file to be plotted.</p>
+</dd>
+<dt>bunch_number<span class="classifier">int</span></dt><dd><p>Bunch to plot. This has to be identical to ‘bunch_number’ parameter in 
+‘BunchSpectrumMonitor’ object.</p>
+</dd>
+<dt>dataset<span class="classifier">{“coherent”, “incoherent”}</span></dt><dd><p>HDF5 file’s dataset to be plotted. 
+The default is “incoherent”.</p>
+</dd>
+<dt>dim<span class="classifier">{“x”,”y”,”tau”}, optional</span></dt><dd><p>The dimension of the dataset to plot.
+The default is “tau”.</p>
+</dd>
+<dt>fs<span class="classifier">float or None, optional</span></dt><dd><p>If not None, the frequency axis is noramlised by fs.</p>
+</dd>
+<dt>log_scale<span class="classifier">bool, optional</span></dt><dd><p>If True, the spectrum plots are shown in y-log scale. 
+The default is True.</p>
+</dd>
+<dt>fmin<span class="classifier">float, optional</span></dt><dd><p>If not None, the plot is limitted to values bigger than fmin.</p>
+</dd>
+<dt>fmax<span class="classifier">float, optional</span></dt><dd><p>If not None, the plot is limitted to values smaller than fmax.</p>
+</dd>
+<dt>turns<span class="classifier">array, optional</span></dt><dd><p>If not None, only the turn numbers in the turns array are plotted.</p>
+</dd>
+<dt>norm<span class="classifier">bool, optional</span></dt><dd><p>If True, normalise the data of each spectrum by its geometric mean.
+The default is False.</p>
+</dd>
+<dt>ylim<span class="classifier">array, optional</span></dt><dd><p>If not None, should be array like in the form [ymin, ymax] where ymin 
+and ymax are the minimum and maxmimum values used in the y axis.</p>
+</dd>
+</dl>
+<p>fig : Figure</p>
+</dd></dl>
+
+</section>
+<section id="module-mbtrack2.tracking.monitors.tools">
+<span id="mbtrack2-tracking-monitors-tools-module"></span><h2>mbtrack2.tracking.monitors.tools module<a class="headerlink" href="#module-mbtrack2.tracking.monitors.tools" title="Permalink to this heading">¶</a></h2>
+<p>This module defines utilities functions, helping to deals with tracking output 
+and hdf5 files.</p>
+<dl class="py function">
+<dt class="sig sig-object py" id="mbtrack2.tracking.monitors.tools.copy_files">
+<span class="sig-prename descclassname"><span class="pre">mbtrack2.tracking.monitors.tools.</span></span><span class="sig-name descname"><span class="pre">copy_files</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">source</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">copy</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">version</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/monitors/tools.html#copy_files"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.monitors.tools.copy_files" title="Permalink to this definition">¶</a></dt>
+<dd><p>Copy a source hdf5 file into another hdf5 file using a different HDF5 
+version.</p>
+<p>The function assumes that the source file has only a single group layer.</p>
+<dl class="simple">
+<dt>source<span class="classifier">str</span></dt><dd><p>Name of the source file.</p>
+</dd>
+<dt>copy<span class="classifier">str</span></dt><dd><p>Name of the copy file.</p>
+</dd>
+<dt>version<span class="classifier">str, optional</span></dt><dd><p>Version number of the copy file.</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py function">
+<dt class="sig sig-object py" id="mbtrack2.tracking.monitors.tools.merge_files">
+<span class="sig-prename descclassname"><span class="pre">mbtrack2.tracking.monitors.tools.</span></span><span class="sig-name descname"><span class="pre">merge_files</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">files_prefix</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">files_number</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">start_idx</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">file_name</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/tracking/monitors/tools.html#merge_files"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.tracking.monitors.tools.merge_files" title="Permalink to this definition">¶</a></dt>
+<dd><p>Merge several hdf5 files into one.</p>
+<p>The function assumes that the files to merge have names in the follwing 
+format:</p>
+<blockquote>
+<div><ul class="simple">
+<li><p>“files_prefix_0.hdf5”</p></li>
+<li><p>“files_prefix_1.hdf5”</p></li>
+</ul>
+<p>…
+- “files_prefix_files_number.hdf5”</p>
+</div></blockquote>
+<dl class="simple">
+<dt>files_prefix<span class="classifier">str</span></dt><dd><p>Name of the files to merge.</p>
+</dd>
+<dt>files_number<span class="classifier">int</span></dt><dd><p>Number of files to merge.</p>
+</dd>
+<dt>start_idx<span class="classifier">int, optional</span></dt><dd><p>Start index of the hdf5 files.</p>
+</dd>
+<dt>file_name<span class="classifier">str, optional</span></dt><dd><p>Name of the file with the merged data. If None, files_prefix without
+number is used.</p>
+</dd>
+</dl>
+</dd></dl>
+
+</section>
+<section id="module-mbtrack2.tracking.monitors">
+<span id="module-contents"></span><h2>Module contents<a class="headerlink" href="#module-mbtrack2.tracking.monitors" title="Permalink to this heading">¶</a></h2>
+</section>
+</section>
+
+
+            <div class="clearer"></div>
+          </div>
+        </div>
+      </div>
+      <div class="sphinxsidebar" role="navigation" aria-label="main navigation">
+        <div class="sphinxsidebarwrapper">
+  <div>
+    <h3><a href="index.html">Table of Contents</a></h3>
+    <ul>
+<li><a class="reference internal" href="#">mbtrack2.tracking.monitors package</a><ul>
+<li><a class="reference internal" href="#submodules">Submodules</a></li>
+<li><a class="reference internal" href="#module-mbtrack2.tracking.monitors.monitors">mbtrack2.tracking.monitors.monitors module</a></li>
+<li><a class="reference internal" href="#module-mbtrack2.tracking.monitors.plotting">mbtrack2.tracking.monitors.plotting module</a></li>
+<li><a class="reference internal" href="#module-mbtrack2.tracking.monitors.tools">mbtrack2.tracking.monitors.tools module</a></li>
+<li><a class="reference internal" href="#module-mbtrack2.tracking.monitors">Module contents</a></li>
+</ul>
+</li>
+</ul>
+
+  </div>
+  <div role="note" aria-label="source link">
+    <h3>This Page</h3>
+    <ul class="this-page-menu">
+      <li><a href="_sources/mbtrack2.tracking.monitors.rst.txt"
+            rel="nofollow">Show Source</a></li>
+    </ul>
+   </div>
+<div id="searchbox" style="display: none" role="search">
+  <h3 id="searchlabel">Quick search</h3>
+    <div class="searchformwrapper">
+    <form class="search" action="search.html" method="get">
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+      <input type="submit" value="Go" />
+    </form>
+    </div>
+</div>
+<script>document.getElementById('searchbox').style.display = "block"</script>
+        </div>
+      </div>
+      <div class="clearer"></div>
+    </div>
+    <div class="related" role="navigation" aria-label="related navigation">
+      <h3>Navigation</h3>
+      <ul>
+        <li class="right" style="margin-right: 10px">
+          <a href="genindex.html" title="General Index"
+             >index</a></li>
+        <li class="right" >
+          <a href="py-modindex.html" title="Python Module Index"
+             >modules</a> |</li>
+        <li class="nav-item nav-item-0"><a href="index.html">mbtrack2 0.6.0 documentation</a> &#187;</li>
+        <li class="nav-item nav-item-this"><a href="">mbtrack2.tracking.monitors package</a></li> 
+      </ul>
+    </div>
+    <div class="footer" role="contentinfo">
+        &#169; Copyright 2024, A. Gamelin et al.
+      Created using <a href="https://www.sphinx-doc.org/">Sphinx</a> 5.0.2.
+    </div>
+  </body>
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+<!DOCTYPE html>
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+    <meta name="viewport" content="width=device-width, initial-scale=1.0" /><meta name="generator" content="Docutils 0.18.1: http://docutils.sourceforge.net/" />
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+    <title>mbtrack2.utilities package &#8212; mbtrack2 0.6.0 documentation</title>
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+             accesskey="I">index</a></li>
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+          <a href="py-modindex.html" title="Python Module Index"
+             >modules</a> |</li>
+        <li class="nav-item nav-item-0"><a href="index.html">mbtrack2 0.6.0 documentation</a> &#187;</li>
+        <li class="nav-item nav-item-this"><a href="">mbtrack2.utilities package</a></li> 
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+
+    <div class="document">
+      <div class="documentwrapper">
+        <div class="bodywrapper">
+          <div class="body" role="main">
+            
+  <section id="mbtrack2-utilities-package">
+<h1>mbtrack2.utilities package<a class="headerlink" href="#mbtrack2-utilities-package" title="Permalink to this heading">¶</a></h1>
+<section id="submodules">
+<h2>Submodules<a class="headerlink" href="#submodules" title="Permalink to this heading">¶</a></h2>
+</section>
+<section id="module-mbtrack2.utilities.beamloading">
+<span id="mbtrack2-utilities-beamloading-module"></span><h2>mbtrack2.utilities.beamloading module<a class="headerlink" href="#module-mbtrack2.utilities.beamloading" title="Permalink to this heading">¶</a></h2>
+<p>Module where the BeamLoadingEquilibrium class is defined.</p>
+<dl class="py class">
+<dt class="sig sig-object py" id="mbtrack2.utilities.beamloading.BeamLoadingEquilibrium">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">mbtrack2.utilities.beamloading.</span></span><span class="sig-name descname"><span class="pre">BeamLoadingEquilibrium</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">ring</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">cavity_list</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">I0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">auto_set_MC_theta</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">F</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">PHI</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">B1</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">-</span> <span class="pre">0.2</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">B2</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0.2</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/utilities/beamloading.html#BeamLoadingEquilibrium"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.utilities.beamloading.BeamLoadingEquilibrium" title="Permalink to this definition">¶</a></dt>
+<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">object</span></code></p>
+<p>Class used to compute beam equilibrium profile for a given storage ring 
+and a list of RF cavities of any harmonic. The class assumes an uniform 
+filling of the storage ring. Based on an extension of [1].</p>
+<p>[1] Venturini, M. (2018). Passive higher-harmonic rf cavities with general
+settings and multibunch instabilities in electron storage rings.
+Physical Review Accelerators and Beams, 21(11), 114404.</p>
+<p>ring : Synchrotron object
+cavity_list : list of CavityResonator objects
+I0 : beam current in [A].
+auto_set_MC_theta : if True, allow class to change cavity phase for</p>
+<blockquote>
+<div><p>CavityResonator objetcs with m = 1 (i.e. main cavities)</p>
+</div></blockquote>
+<p>F : list of form factor amplitude
+PHI : list of form factor phase
+B1 : lower intergration boundary
+B2 : upper intergration boundary</p>
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.utilities.beamloading.BeamLoadingEquilibrium.PTBL_threshold">
+<span class="sig-name descname"><span class="pre">PTBL_threshold</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">I0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">m</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">MC_index</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">HC_index</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/utilities/beamloading.html#BeamLoadingEquilibrium.PTBL_threshold"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.utilities.beamloading.BeamLoadingEquilibrium.PTBL_threshold" title="Permalink to this definition">¶</a></dt>
+<dd><p>Compute the periodic transient beam loading (PTBL) instability 
+threshold based on [1].</p>
+<p>The beam_equilibrium method should be called before the PTBL_threshold 
+one.</p>
+<p>Eq. (22) and (23) have been modified for cosine voltage convention 
+for the main cavity.</p>
+<dl class="simple">
+<dt>I0<span class="classifier">float</span></dt><dd><p>Beam total current in [A].</p>
+</dd>
+<dt>m<span class="classifier">int, optional</span></dt><dd><p>Number of bunches in the beam. 
+The default is None. If None, uniform filling is assumed.</p>
+</dd>
+<dt>MC_index<span class="classifier">int, optional</span></dt><dd><p>Index of the main cavity in cavity_list. The default is 0.</p>
+</dd>
+<dt>HC_index<span class="classifier">int, optional</span></dt><dd><p>Index of the harmonic cavity in cavity_list. The default is 1.</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>eta<span class="classifier">float</span></dt><dd><p>Amplification factor, if bigger than 1 then the beam is possibly 
+in the PTBL regime, Eq. (22) of [1].</p>
+</dd>
+<dt>RQth<span class="classifier">float</span></dt><dd><p>R/Q threshold, Eq. (24) of [1].</p>
+</dd>
+<dt>f<span class="classifier">float</span></dt><dd><p>f function, Eq. (23) of [1].</p>
+</dd>
+</dl>
+<p>[1] : He, T. (2022). Novel perturbation method for judging the 
+stability of the equilibrium solution in the presence of passive 
+harmonic cavities. Physical Review Accelerators and Beams, 25(9), 
+094402.</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.utilities.beamloading.BeamLoadingEquilibrium.beam_equilibrium">
+<span class="sig-name descname"><span class="pre">beam_equilibrium</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x0</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">tol</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0.0001</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">method</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'hybr'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">options</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">plot</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">CM</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">verbiose</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/utilities/beamloading.html#BeamLoadingEquilibrium.beam_equilibrium"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.utilities.beamloading.BeamLoadingEquilibrium.beam_equilibrium" title="Permalink to this definition">¶</a></dt>
+<dd><p>Solve system of non-linear equation to find the form factors F
+and PHI at equilibrum. Can be used to compute the equilibrium bunch
+profile.</p>
+<p>x0 : initial guess
+tol : tolerance for termination of the algorithm
+method : method used by scipy.optimize.root to solve the system
+options : options given to scipy.optimize.root
+plot : if True, plot the equilibrium bunch profile
+CM : if True, the system imposes zero center of mass offset,
+if False, the system imposes energy balance.
+verbiose : if True, print out informations about convergence.</p>
+<p>sol : OptimizeResult object representing the solution</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.utilities.beamloading.BeamLoadingEquilibrium.center_of_mass">
+<span class="sig-name descname"><span class="pre">center_of_mass</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/utilities/beamloading.html#BeamLoadingEquilibrium.center_of_mass"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.utilities.beamloading.BeamLoadingEquilibrium.center_of_mass" title="Permalink to this definition">¶</a></dt>
+<dd><p>Return center of mass position in [s]</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.utilities.beamloading.BeamLoadingEquilibrium.dV">
+<span class="sig-name descname"><span class="pre">dV</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">z</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/utilities/beamloading.html#BeamLoadingEquilibrium.dV"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.utilities.beamloading.BeamLoadingEquilibrium.dV" title="Permalink to this definition">¶</a></dt>
+<dd><p>Return derivative of the RF system total voltage at position z</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.utilities.beamloading.BeamLoadingEquilibrium.ddV">
+<span class="sig-name descname"><span class="pre">ddV</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">z</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/utilities/beamloading.html#BeamLoadingEquilibrium.ddV"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.utilities.beamloading.BeamLoadingEquilibrium.ddV" title="Permalink to this definition">¶</a></dt>
+<dd><p>Return the second derivative of the RF system total voltage at position z</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.utilities.beamloading.BeamLoadingEquilibrium.deltaVRF">
+<span class="sig-name descname"><span class="pre">deltaVRF</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">z</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/utilities/beamloading.html#BeamLoadingEquilibrium.deltaVRF"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.utilities.beamloading.BeamLoadingEquilibrium.deltaVRF" title="Permalink to this definition">¶</a></dt>
+<dd><p>Return the generator voltage minus beam loading voltage of the total RF system at position z</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.utilities.beamloading.BeamLoadingEquilibrium.du_dz">
+<span class="sig-name descname"><span class="pre">du_dz</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">z</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/utilities/beamloading.html#BeamLoadingEquilibrium.du_dz"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.utilities.beamloading.BeamLoadingEquilibrium.du_dz" title="Permalink to this definition">¶</a></dt>
+<dd><p>Partial derivative of the scaled potential u(z) by z</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.utilities.beamloading.BeamLoadingEquilibrium.energy_balance">
+<span class="sig-name descname"><span class="pre">energy_balance</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/utilities/beamloading.html#BeamLoadingEquilibrium.energy_balance"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.utilities.beamloading.BeamLoadingEquilibrium.energy_balance" title="Permalink to this definition">¶</a></dt>
+<dd><p>Return energy balance for the synchronous particle
+(z = 0 ,delta = 0).</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.utilities.beamloading.BeamLoadingEquilibrium.integrate_func">
+<span class="sig-name descname"><span class="pre">integrate_func</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">f</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">g</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/utilities/beamloading.html#BeamLoadingEquilibrium.integrate_func"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.utilities.beamloading.BeamLoadingEquilibrium.integrate_func" title="Permalink to this definition">¶</a></dt>
+<dd><p>Return Integral[f*g]/Integral[f] between B1 and B2</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.utilities.beamloading.BeamLoadingEquilibrium.plot_dV">
+<span class="sig-name descname"><span class="pre">plot_dV</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">z1</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">z2</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/utilities/beamloading.html#BeamLoadingEquilibrium.plot_dV"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.utilities.beamloading.BeamLoadingEquilibrium.plot_dV" title="Permalink to this definition">¶</a></dt>
+<dd><p>Plot the derivative of RF system total voltage between z1 and z2</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.utilities.beamloading.BeamLoadingEquilibrium.plot_rho">
+<span class="sig-name descname"><span class="pre">plot_rho</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">z1</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">z2</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/utilities/beamloading.html#BeamLoadingEquilibrium.plot_rho"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.utilities.beamloading.BeamLoadingEquilibrium.plot_rho" title="Permalink to this definition">¶</a></dt>
+<dd><p>Plot the bunch equilibrium profile between z1 and z2</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.utilities.beamloading.BeamLoadingEquilibrium.plot_voltage">
+<span class="sig-name descname"><span class="pre">plot_voltage</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">z1</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">z2</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/utilities/beamloading.html#BeamLoadingEquilibrium.plot_voltage"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.utilities.beamloading.BeamLoadingEquilibrium.plot_voltage" title="Permalink to this definition">¶</a></dt>
+<dd><p>Plot the RF system total voltage between z1 and z2</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.utilities.beamloading.BeamLoadingEquilibrium.rho">
+<span class="sig-name descname"><span class="pre">rho</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">z</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/utilities/beamloading.html#BeamLoadingEquilibrium.rho"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.utilities.beamloading.BeamLoadingEquilibrium.rho" title="Permalink to this definition">¶</a></dt>
+<dd><p>Return bunch equilibrium profile at postion z</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.utilities.beamloading.BeamLoadingEquilibrium.std_rho">
+<span class="sig-name descname"><span class="pre">std_rho</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">z1</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">z2</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/utilities/beamloading.html#BeamLoadingEquilibrium.std_rho"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.utilities.beamloading.BeamLoadingEquilibrium.std_rho" title="Permalink to this definition">¶</a></dt>
+<dd><p>Return the rms bunch equilibrium size in [m]</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.utilities.beamloading.BeamLoadingEquilibrium.to_solve">
+<span class="sig-name descname"><span class="pre">to_solve</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">CM</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/utilities/beamloading.html#BeamLoadingEquilibrium.to_solve"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.utilities.beamloading.BeamLoadingEquilibrium.to_solve" title="Permalink to this definition">¶</a></dt>
+<dd><p>System of non-linear equation to solve to find the form factors F
+and PHI at equilibrum.
+The system is composed of Eq. (B6) and (B7) of [1] for each cavity.
+If auto_set_MC_theta == True, the system also find the main cavity 
+phase to impose energy balance or cancel center of mass offset.
+If CM is True, the system imposes zero center of mass offset,
+if False, the system imposes energy balance.</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.utilities.beamloading.BeamLoadingEquilibrium.u">
+<span class="sig-name descname"><span class="pre">u</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">z</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/utilities/beamloading.html#BeamLoadingEquilibrium.u"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.utilities.beamloading.BeamLoadingEquilibrium.u" title="Permalink to this definition">¶</a></dt>
+<dd><p>Scaled potential u(z)</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.utilities.beamloading.BeamLoadingEquilibrium.uexp">
+<span class="sig-name descname"><span class="pre">uexp</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">z</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/utilities/beamloading.html#BeamLoadingEquilibrium.uexp"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.utilities.beamloading.BeamLoadingEquilibrium.uexp" title="Permalink to this definition">¶</a></dt>
+<dd></dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.utilities.beamloading.BeamLoadingEquilibrium.update_potentials">
+<span class="sig-name descname"><span class="pre">update_potentials</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/utilities/beamloading.html#BeamLoadingEquilibrium.update_potentials"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.utilities.beamloading.BeamLoadingEquilibrium.update_potentials" title="Permalink to this definition">¶</a></dt>
+<dd><p>Update potentials with cavity and ring data.</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.utilities.beamloading.BeamLoadingEquilibrium.voltage">
+<span class="sig-name descname"><span class="pre">voltage</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">z</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/utilities/beamloading.html#BeamLoadingEquilibrium.voltage"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.utilities.beamloading.BeamLoadingEquilibrium.voltage" title="Permalink to this definition">¶</a></dt>
+<dd><p>Return the RF system total voltage at position z</p>
+</dd></dl>
+
+</dd></dl>
+
+</section>
+<section id="module-mbtrack2.utilities.misc">
+<span id="mbtrack2-utilities-misc-module"></span><h2>mbtrack2.utilities.misc module<a class="headerlink" href="#module-mbtrack2.utilities.misc" title="Permalink to this heading">¶</a></h2>
+<p>This module defines miscellaneous utilities functions.</p>
+<dl class="py function">
+<dt class="sig sig-object py" id="mbtrack2.utilities.misc.beam_loss_factor">
+<span class="sig-prename descclassname"><span class="pre">mbtrack2.utilities.misc.</span></span><span class="sig-name descname"><span class="pre">beam_loss_factor</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">impedance</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">frequency</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">spectrum</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">ring</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/utilities/misc.html#beam_loss_factor"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.utilities.misc.beam_loss_factor" title="Permalink to this definition">¶</a></dt>
+<dd><p>Compute “beam” loss factor using the beam spectrum, uses a sum instead of 
+integral compared to loss_factor [1].</p>
+<p>impedance : Impedance of type “long”
+frequency : array</p>
+<blockquote>
+<div><p>Sample points of spectrum.</p>
+</div></blockquote>
+<dl class="simple">
+<dt>spectrum<span class="classifier">array</span></dt><dd><p>Beam spectrum to consider.</p>
+</dd>
+</dl>
+<p>ring : Synchrotron object</p>
+<dl class="simple">
+<dt>kloss_beam<span class="classifier">float</span></dt><dd><p>Beam loss factor in [V/C].</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>[1]<span class="classifier">Handbook of accelerator physics and engineering, 3rd printing. </span></dt><dd><p>Eq (3) p239.</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py function">
+<dt class="sig sig-object py" id="mbtrack2.utilities.misc.double_sided_impedance">
+<span class="sig-prename descclassname"><span class="pre">mbtrack2.utilities.misc.</span></span><span class="sig-name descname"><span class="pre">double_sided_impedance</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">impedance</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/utilities/misc.html#double_sided_impedance"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.utilities.misc.double_sided_impedance" title="Permalink to this definition">¶</a></dt>
+<dd><p>Add negative frequency points to single sided impedance spectrum following
+symetries depending on impedance type.</p>
+<dl class="simple">
+<dt>impedance<span class="classifier">Impedance object</span></dt><dd><p>Single sided impedance.</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py function">
+<dt class="sig sig-object py" id="mbtrack2.utilities.misc.effective_impedance">
+<span class="sig-prename descclassname"><span class="pre">mbtrack2.utilities.misc.</span></span><span class="sig-name descname"><span class="pre">effective_impedance</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">ring</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">imp</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">m</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">mu</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">sigma</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">M</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">tuneS</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">xi</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">mode</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'Hermite'</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/utilities/misc.html#effective_impedance"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.utilities.misc.effective_impedance" title="Permalink to this definition">¶</a></dt>
+<dd><p>Compute the effective (longitudinal or transverse) impedance. 
+Formulas from Eq. (1) and (2) p238 of [1].</p>
+<p>ring : Synchrotron object
+imp : Impedance object
+mu : int</p>
+<blockquote>
+<div><p>coupled bunch mode number, goes from 0 to (M-1) where M is the
+number of bunches</p>
+</div></blockquote>
+<dl class="simple">
+<dt>m<span class="classifier">int</span></dt><dd><p>head-tail (or azimutal/synchrotron) mode number</p>
+</dd>
+<dt>sigma<span class="classifier">float</span></dt><dd><p>RMS bunch length in [s]</p>
+</dd>
+<dt>M<span class="classifier">int</span></dt><dd><p>Number of bunches.</p>
+</dd>
+<dt>tuneS<span class="classifier">float</span></dt><dd><p>Synchrotron tune.</p>
+</dd>
+<dt>xi<span class="classifier">float, optional</span></dt><dd><p>(non-normalized) chromaticity</p>
+</dd>
+<dt>mode: str, optional</dt><dd><p>type of the mode taken into account for the computation:
+-“Hermite” modes for Gaussian bunches</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>Zeff<span class="classifier">float </span></dt><dd><p>effective impedance in [ohm] or in [ohm/m] depanding on the impedance
+type.</p>
+</dd>
+</dl>
+<p>[1] : Handbook of accelerator physics and engineering, 3rd printing.</p>
+</dd></dl>
+
+<dl class="py function">
+<dt class="sig sig-object py" id="mbtrack2.utilities.misc.head_tail_form_factor">
+<span class="sig-prename descclassname"><span class="pre">mbtrack2.utilities.misc.</span></span><span class="sig-name descname"><span class="pre">head_tail_form_factor</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">ring</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">imp</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">m</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">sigma</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">tuneS</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">xi</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">mode</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'Hermite'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">mu</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/utilities/misc.html#head_tail_form_factor"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.utilities.misc.head_tail_form_factor" title="Permalink to this definition">¶</a></dt>
+<dd></dd></dl>
+
+<dl class="py function">
+<dt class="sig sig-object py" id="mbtrack2.utilities.misc.tune_shift_from_effective_impedance">
+<span class="sig-prename descclassname"><span class="pre">mbtrack2.utilities.misc.</span></span><span class="sig-name descname"><span class="pre">tune_shift_from_effective_impedance</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">Zeff</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/utilities/misc.html#tune_shift_from_effective_impedance"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.utilities.misc.tune_shift_from_effective_impedance" title="Permalink to this definition">¶</a></dt>
+<dd></dd></dl>
+
+<dl class="py function">
+<dt class="sig sig-object py" id="mbtrack2.utilities.misc.yokoya_elliptic">
+<span class="sig-prename descclassname"><span class="pre">mbtrack2.utilities.misc.</span></span><span class="sig-name descname"><span class="pre">yokoya_elliptic</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x_radius</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">y_radius</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/utilities/misc.html#yokoya_elliptic"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.utilities.misc.yokoya_elliptic" title="Permalink to this definition">¶</a></dt>
+<dd><p>Compute Yokoya factors for an elliptic beam pipe.
+Function adapted from N. Mounet IW2D.</p>
+<dl class="simple">
+<dt>x_radius<span class="classifier">float</span></dt><dd><p>Horizontal semi-axis of the ellipse in [m].</p>
+</dd>
+<dt>y_radius<span class="classifier">float</span></dt><dd><p>Vertical semi-axis of the ellipse in [m].</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>yoklong<span class="classifier">float</span></dt><dd><p>Yokoya factor for the longitudinal impedance.</p>
+</dd>
+<dt>yokxdip<span class="classifier">float</span></dt><dd><p>Yokoya factor for the dipolar horizontal impedance.</p>
+</dd>
+<dt>yokydip<span class="classifier">float</span></dt><dd><p>Yokoya factor for the dipolar vertical impedance.</p>
+</dd>
+<dt>yokxquad<span class="classifier">float</span></dt><dd><p>Yokoya factor for the quadrupolar horizontal impedance.</p>
+</dd>
+<dt>yokyquad<span class="classifier">float</span></dt><dd><p>Yokoya factor for the quadrupolar vertical impedance.</p>
+</dd>
+</dl>
+</dd></dl>
+
+</section>
+<section id="module-mbtrack2.utilities.optics">
+<span id="mbtrack2-utilities-optics-module"></span><h2>mbtrack2.utilities.optics module<a class="headerlink" href="#module-mbtrack2.utilities.optics" title="Permalink to this heading">¶</a></h2>
+<p>Module where the class to store the optic functions and the lattice physical 
+parameters are defined.</p>
+<dl class="py class">
+<dt class="sig sig-object py" id="mbtrack2.utilities.optics.Optics">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">mbtrack2.utilities.optics.</span></span><span class="sig-name descname"><span class="pre">Optics</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">lattice_file</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">local_beta</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">local_alpha</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">local_dispersion</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/utilities/optics.html#Optics"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.utilities.optics.Optics" title="Permalink to this definition">¶</a></dt>
+<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">object</span></code></p>
+<p>Class used to handle optic functions.</p>
+<dl class="simple">
+<dt>lattice_file<span class="classifier">str, optional if local_beta, local_alpha and </span></dt><dd><p>local_dispersion are specified.
+AT lattice file path.</p>
+</dd>
+<dt>local_beta<span class="classifier">array of shape (2,), optional if lattice_file is specified.</span></dt><dd><p>Beta function at the location of the tracking. Default is mean beta if
+lattice has been loaded.</p>
+</dd>
+<dt>local_alpha<span class="classifier">array of shape (2,), optional if lattice_file is specified.</span></dt><dd><p>Alpha function at the location of the tracking. Default is mean alpha 
+if lattice has been loaded.</p>
+</dd>
+<dt>local_dispersion<span class="classifier">array of shape (4,), optional if lattice_file is </span></dt><dd><p>specified.
+Dispersion function and derivative at the location of the tracking. 
+Default is zero if lattice has been loaded.</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>use_local_values<span class="classifier">bool</span></dt><dd><p>True if no lattice has been loaded.</p>
+</dd>
+<dt>local_gamma<span class="classifier">array of shape (2,)</span></dt><dd><p>Gamma function at the location of the tracking.</p>
+</dd>
+</dl>
+<p>lattice : AT lattice</p>
+<dl class="simple">
+<dt>load_from_AT(lattice_file, <a href="#id1"><span class="problematic" id="id2">**</span></a>kwargs)</dt><dd><p>Load a lattice from accelerator toolbox (AT).</p>
+</dd>
+<dt>setup_interpolation()</dt><dd><p>Setup interpolation of the optic functions.</p>
+</dd>
+<dt>beta(position)</dt><dd><p>Return beta functions at specific locations given by position.</p>
+</dd>
+<dt>alpha(position)</dt><dd><p>Return alpha functions at specific locations given by position.</p>
+</dd>
+<dt>gamma(position)</dt><dd><p>Return gamma functions at specific locations given by position.</p>
+</dd>
+<dt>dispersion(position)</dt><dd><p>Return dispersion functions at specific locations given by position.</p>
+</dd>
+<dt>plot(self, var, option, n_points=1000)</dt><dd><p>Plot optical variables.</p>
+</dd>
+</dl>
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.utilities.optics.Optics.alpha">
+<span class="sig-name descname"><span class="pre">alpha</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">position</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/utilities/optics.html#Optics.alpha"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.utilities.optics.Optics.alpha" title="Permalink to this definition">¶</a></dt>
+<dd><p>Return alpha functions at specific locations given by position. If no
+lattice has been loaded, local values are returned.</p>
+<dl class="simple">
+<dt>position<span class="classifier">array or float</span></dt><dd><p>Longitudinal position at which the alpha functions are returned.</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>alpha<span class="classifier">array</span></dt><dd><p>Alpha functions.</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.utilities.optics.Optics.beta">
+<span class="sig-name descname"><span class="pre">beta</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">position</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/utilities/optics.html#Optics.beta"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.utilities.optics.Optics.beta" title="Permalink to this definition">¶</a></dt>
+<dd><p>Return beta functions at specific locations given by position. If no
+lattice has been loaded, local values are returned.</p>
+<dl class="simple">
+<dt>position<span class="classifier">array or float</span></dt><dd><p>Longitudinal position at which the beta functions are returned.</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>beta<span class="classifier">array</span></dt><dd><p>Beta functions.</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.utilities.optics.Optics.dispersion">
+<span class="sig-name descname"><span class="pre">dispersion</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">position</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/utilities/optics.html#Optics.dispersion"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.utilities.optics.Optics.dispersion" title="Permalink to this definition">¶</a></dt>
+<dd><p>Return dispersion functions at specific locations given by position. 
+If no lattice has been loaded, local values are returned.</p>
+<dl class="simple">
+<dt>position<span class="classifier">array or float</span></dt><dd><p>Longitudinal position at which the dispersion functions are 
+returned.</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>dispersion<span class="classifier">array</span></dt><dd><p>Dispersion functions.</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.utilities.optics.Optics.gamma">
+<span class="sig-name descname"><span class="pre">gamma</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">position</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/utilities/optics.html#Optics.gamma"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.utilities.optics.Optics.gamma" title="Permalink to this definition">¶</a></dt>
+<dd><p>Return gamma functions at specific locations given by position. If no
+lattice has been loaded, local values are returned.</p>
+<dl class="simple">
+<dt>position<span class="classifier">array or float</span></dt><dd><p>Longitudinal position at which the gamma functions are returned.</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>gamma<span class="classifier">array</span></dt><dd><p>Gamma functions.</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.utilities.optics.Optics.load_from_AT">
+<span class="sig-name descname"><span class="pre">load_from_AT</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">lattice_file</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/utilities/optics.html#Optics.load_from_AT"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.utilities.optics.Optics.load_from_AT" title="Permalink to this definition">¶</a></dt>
+<dd><p>Load a lattice from accelerator toolbox (AT).</p>
+<dl class="simple">
+<dt>lattice_file<span class="classifier">str</span></dt><dd><p>AT lattice file path.</p>
+</dd>
+<dt>n_points<span class="classifier">int or float, optional</span></dt><dd><p>Minimum number of points to use for the optic function arrays.</p>
+</dd>
+<dt>periodicity<span class="classifier">int, optional</span></dt><dd><p>Lattice periodicity, if not specified the AT lattice periodicity is
+used.</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.utilities.optics.Optics.local_alpha">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">local_alpha</span></span><a class="headerlink" href="#mbtrack2.utilities.optics.Optics.local_alpha" title="Permalink to this definition">¶</a></dt>
+<dd><p>Return alpha function at the location defined by the lattice file.</p>
+</dd></dl>
+
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.utilities.optics.Optics.local_beta">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">local_beta</span></span><a class="headerlink" href="#mbtrack2.utilities.optics.Optics.local_beta" title="Permalink to this definition">¶</a></dt>
+<dd><p>Return beta function at the location defined by the lattice file.</p>
+</dd></dl>
+
+<dl class="py property">
+<dt class="sig sig-object py" id="mbtrack2.utilities.optics.Optics.local_gamma">
+<em class="property"><span class="pre">property</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">local_gamma</span></span><a class="headerlink" href="#mbtrack2.utilities.optics.Optics.local_gamma" title="Permalink to this definition">¶</a></dt>
+<dd><p>Return beta function at the location defined by the lattice file.</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.utilities.optics.Optics.mu">
+<span class="sig-name descname"><span class="pre">mu</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">position</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/utilities/optics.html#Optics.mu"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.utilities.optics.Optics.mu" title="Permalink to this definition">¶</a></dt>
+<dd><p>Return phase advances at specific locations given by position. 
+If no lattice has been loaded, None is returned.</p>
+<dl class="simple">
+<dt>position<span class="classifier">array or float</span></dt><dd><p>Longitudinal position at which the phase advances are returned.</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>mu<span class="classifier">array</span></dt><dd><p>Phase advances.</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.utilities.optics.Optics.plot">
+<span class="sig-name descname"><span class="pre">plot</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">var</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">option</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">n_points</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1000</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/utilities/optics.html#Optics.plot"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.utilities.optics.Optics.plot" title="Permalink to this definition">¶</a></dt>
+<dd><p>Plot optical variables.</p>
+<dl class="simple">
+<dt>var<span class="classifier">{“beta”, “alpha”, “gamma”, “dispersion”, “mu”}</span></dt><dd><p>Optical variable to be plotted.</p>
+</dd>
+<dt>option<span class="classifier">str</span></dt><dd><p>If var = “beta”, “alpha” and “gamma”, option = {“x”,”y”} specifying
+the axis of interest.
+If var = “dispersion”, option = {“x”,”px”,”y”,”py”} specifying the 
+axis of interest for the dispersion function or its derivative.</p>
+</dd>
+<dt>n_points<span class="classifier">int</span></dt><dd><p>Number of points on the plot. The default value is 1000.</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.utilities.optics.Optics.setup_interpolation">
+<span class="sig-name descname"><span class="pre">setup_interpolation</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/utilities/optics.html#Optics.setup_interpolation"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.utilities.optics.Optics.setup_interpolation" title="Permalink to this definition">¶</a></dt>
+<dd><p>Setup interpolation of the optic functions.</p>
+</dd></dl>
+
+</dd></dl>
+
+<dl class="py class">
+<dt class="sig sig-object py" id="mbtrack2.utilities.optics.PhysicalModel">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">mbtrack2.utilities.optics.</span></span><span class="sig-name descname"><span class="pre">PhysicalModel</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">ring</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">x_right</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">y_top</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">shape</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">rho</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">x_left</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">y_bottom</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">n_points</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">10000.0</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/utilities/optics.html#PhysicalModel"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.utilities.optics.PhysicalModel" title="Permalink to this definition">¶</a></dt>
+<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">object</span></code></p>
+<p>Store the lattice physical parameters such as apperture and resistivity.</p>
+<p>ring : Synchrotron object
+x_right : float</p>
+<blockquote>
+<div><p>Default value for the right horizontal aperture in [m].</p>
+</div></blockquote>
+<dl class="simple">
+<dt>y_top<span class="classifier">float</span></dt><dd><p>Default value for the top vertical aperture in [m].</p>
+</dd>
+<dt>shape<span class="classifier">str</span></dt><dd><p>Default value for the shape of the chamber cross section 
+(elli/circ/rect).</p>
+</dd>
+<dt>rho<span class="classifier">float</span></dt><dd><p>Default value for the resistivity of the chamber material [ohm.m].</p>
+</dd>
+<dt>x_left<span class="classifier">float, optional</span></dt><dd><p>Default value for the left horizontal aperture in [m].</p>
+</dd>
+<dt>y_bottom<span class="classifier">float, optional</span></dt><dd><p>Default value for the bottom vertical aperture in [m].</p>
+</dd>
+<dt>n_points<span class="classifier">int or float, optional</span></dt><dd><p>Number of points to use in class arrays</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>position<span class="classifier">array of shape (n_points,)</span></dt><dd><p>Longitudinal position in [m].</p>
+</dd>
+<dt>x_right<span class="classifier">array of shape (n_points,)</span></dt><dd><p>Right horizontal aperture in [m].</p>
+</dd>
+<dt>y_top<span class="classifier">array of shape (n_points,)</span></dt><dd><p>Top vertical aperture in [m].</p>
+</dd>
+<dt>shape<span class="classifier">array of shape (n_points - 1,)</span></dt><dd><p>Shape of the chamber cross section (elli/circ/rect).</p>
+</dd>
+<dt>rho<span class="classifier">array of shape (n_points - 1,)</span></dt><dd><p>Resistivity of the chamber material in [ohm.m].</p>
+</dd>
+<dt>x_left<span class="classifier">array of shape (n_points,)</span></dt><dd><p>Left horizontal aperture in [m].</p>
+</dd>
+<dt>y_bottom<span class="classifier">array of shape (n_points,)</span></dt><dd><p>Bottom vertical aperture in [m].</p>
+</dd>
+<dt>length<span class="classifier">array of shape (n_points - 1,)</span></dt><dd><p>Length of each segments between two longitudinal positions in [m].</p>
+</dd>
+<dt>center<span class="classifier">array of shape (n_points - 1,)</span></dt><dd><p>Center of each segments between two longitudinal positions in [m].</p>
+</dd>
+</dl>
+<dl>
+<dt>change_values(start_position, end_position, x_right, y_top, shape, rho)</dt><dd><p>Change the physical parameters between start_position and end_position.</p>
+</dd>
+<dt>taper(start_position, end_position, x_right_start, x_right_end, </dt><dd><blockquote>
+<div><p>y_top_start, y_top_end, shape, rho)</p>
+</div></blockquote>
+<p>Change the physical parameters to have a tapered transition between 
+start_position and end_position.</p>
+</dd>
+<dt>plot_aperture()</dt><dd><p>Plot horizontal and vertical apertures.</p>
+</dd>
+<dt>resistive_wall_effective_radius(optics)</dt><dd><p>Return the effective radius of the chamber for resistive wall 
+calculations.</p>
+</dd>
+</dl>
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.utilities.optics.PhysicalModel.change_values">
+<span class="sig-name descname"><span class="pre">change_values</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">start_position</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">end_position</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">x_right</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">y_top</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">shape</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">rho</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">x_left</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">y_bottom</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">sym</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/utilities/optics.html#PhysicalModel.change_values"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.utilities.optics.PhysicalModel.change_values" title="Permalink to this definition">¶</a></dt>
+<dd><p>Change the physical parameters between start_position and end_position.</p>
+<p>start_position : float
+end_position : float
+x_right : float, optional</p>
+<blockquote>
+<div><p>Right horizontal aperture in [m].</p>
+</div></blockquote>
+<dl class="simple">
+<dt>y_top<span class="classifier">float, optional</span></dt><dd><p>Top vertical aperture in [m].</p>
+</dd>
+<dt>shape<span class="classifier">str, optional</span></dt><dd><p>Shape of the chamber cross section (elli/circ/rect).</p>
+</dd>
+<dt>rho<span class="classifier">float, optional</span></dt><dd><p>Resistivity of the chamber material [ohm.m].</p>
+</dd>
+<dt>x_left<span class="classifier">float, optional</span></dt><dd><p>Left horizontal aperture in [m].</p>
+</dd>
+<dt>y_bottom<span class="classifier">float, optional</span></dt><dd><p>Bottom vertical aperture in [m].</p>
+</dd>
+<dt>sym<span class="classifier">bool, optional</span></dt><dd><p>If True, right/left and top/bottum symmetry is applied.</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.utilities.optics.PhysicalModel.get_aperture">
+<span class="sig-name descname"><span class="pre">get_aperture</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">s</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/utilities/optics.html#PhysicalModel.get_aperture"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.utilities.optics.PhysicalModel.get_aperture" title="Permalink to this definition">¶</a></dt>
+<dd></dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.utilities.optics.PhysicalModel.plot_aperture">
+<span class="sig-name descname"><span class="pre">plot_aperture</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/utilities/optics.html#PhysicalModel.plot_aperture"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.utilities.optics.PhysicalModel.plot_aperture" title="Permalink to this definition">¶</a></dt>
+<dd><p>Plot horizontal and vertical apertures.</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.utilities.optics.PhysicalModel.plot_resistivity">
+<span class="sig-name descname"><span class="pre">plot_resistivity</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/utilities/optics.html#PhysicalModel.plot_resistivity"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.utilities.optics.PhysicalModel.plot_resistivity" title="Permalink to this definition">¶</a></dt>
+<dd><p>Plot resistivity along the ring.</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.utilities.optics.PhysicalModel.resistive_wall_effective_radius">
+<span class="sig-name descname"><span class="pre">resistive_wall_effective_radius</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">optics</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">x_right</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">y_top</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/utilities/optics.html#PhysicalModel.resistive_wall_effective_radius"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.utilities.optics.PhysicalModel.resistive_wall_effective_radius" title="Permalink to this definition">¶</a></dt>
+<dd><p>Return the effective radius of the chamber for resistive wall 
+calculations as defined in Eq. 27 of [1].</p>
+<p>Section with rho = 0 ohm.m are not considered in this calculation.</p>
+<p>optics : Optics object
+x_right : bool, optional</p>
+<blockquote>
+<div><p>If True, x_right is used, if Fasle, x_left is used.</p>
+</div></blockquote>
+<dl class="simple">
+<dt>y_top<span class="classifier">bool, optional</span></dt><dd><p>If True, y_top is used, if Fasle, y_bottom is used.</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>L<span class="classifier">float</span></dt><dd><p>Total length considered in [m].</p>
+</dd>
+<dt>rho_star<span class="classifier">float</span></dt><dd><p>Effective resistivity of the chamber material in [ohm.m].</p>
+</dd>
+<dt>a1_L<span class="classifier">float</span></dt><dd><p>Effective longitudinal radius of the chamber of the first power in
+[m].</p>
+</dd>
+<dt>a2_L<span class="classifier">float</span></dt><dd><p>Effective longitudinal radius of the chamber of the second power 
+in [m].</p>
+</dd>
+<dt>a3_H<span class="classifier">float</span></dt><dd><p>Effective horizontal radius of the chamber of the third power in
+[m].</p>
+</dd>
+<dt>a4_H<span class="classifier">float</span></dt><dd><p>Effective horizontal radius of the chamber of the fourth power in
+[m].</p>
+</dd>
+<dt>a3_V<span class="classifier">float</span></dt><dd><p>Effective vertical radius of the chamber of the third power in [m].</p>
+</dd>
+<dt>a4_V<span class="classifier">float</span></dt><dd><p>Effective vertical radius of the chamber of the fourth power in 
+[m].</p>
+</dd>
+</dl>
+<p>[1] Skripka, Galina, et al. “Simultaneous computation of intrabunch 
+and interbunch collective beam motions in storage rings.” Nuclear 
+Instruments and Methods in Physics Research Section A: Accelerators, 
+Spectrometers, Detectors and Associated Equipment 806 (2016): 221-230.</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="mbtrack2.utilities.optics.PhysicalModel.taper">
+<span class="sig-name descname"><span class="pre">taper</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">start_position</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">end_position</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">x_right_start</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">x_right_end</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">y_top_start</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">y_top_end</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">shape</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">rho</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">x_left_start</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">x_left_end</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">y_bottom_start</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">y_bottom_end</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">sym</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/utilities/optics.html#PhysicalModel.taper"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.utilities.optics.PhysicalModel.taper" title="Permalink to this definition">¶</a></dt>
+<dd><p>Change the physical parameters to have a tapered transition between 
+start_position and end_position.</p>
+<p>start_position : float
+end_position : float
+x_right_start : float</p>
+<blockquote>
+<div><p>Right horizontal aperture at the start of the taper in [m].</p>
+</div></blockquote>
+<dl class="simple">
+<dt>x_right_end<span class="classifier">float</span></dt><dd><p>Right horizontal aperture at the end of the taper in [m].</p>
+</dd>
+<dt>y_top_start<span class="classifier">float</span></dt><dd><p>Top vertical aperture at the start of the taper in [m].</p>
+</dd>
+<dt>y_top_end<span class="classifier">float</span></dt><dd><p>Top vertical aperture at the end of the taper in [m].</p>
+</dd>
+<dt>shape<span class="classifier">str</span></dt><dd><p>Shape of the chamber cross section (elli/circ/rect).</p>
+</dd>
+<dt>rho<span class="classifier">float</span></dt><dd><p>Resistivity of the chamber material [ohm.m].</p>
+</dd>
+<dt>x_left_start<span class="classifier">float, optional</span></dt><dd><p>Left horizontal aperture at the start of the taper in [m].</p>
+</dd>
+<dt>x_left_end<span class="classifier">float, optional</span></dt><dd><p>Left horizontal aperture at the end of the taper in [m].</p>
+</dd>
+<dt>y_bottom_start<span class="classifier">float, optional</span></dt><dd><p>Bottom vertical aperture at the start of the taper in [m].</p>
+</dd>
+<dt>y_bottom_end<span class="classifier">float, optional</span></dt><dd><p>Bottom vertical aperture at the end of the taper in [m].</p>
+</dd>
+<dt>sym<span class="classifier">bool, optional</span></dt><dd><p>If True, right/left and top/bottum symmetry is applied.</p>
+</dd>
+</dl>
+</dd></dl>
+
+</dd></dl>
+
+</section>
+<section id="module-mbtrack2.utilities.read_impedance">
+<span id="mbtrack2-utilities-read-impedance-module"></span><h2>mbtrack2.utilities.read_impedance module<a class="headerlink" href="#module-mbtrack2.utilities.read_impedance" title="Permalink to this heading">¶</a></h2>
+<p>Module where function used to import impedance and wakes from other codes are
+defined.</p>
+<dl class="py function">
+<dt class="sig sig-object py" id="mbtrack2.utilities.read_impedance.read_ABCI">
+<span class="sig-prename descclassname"><span class="pre">mbtrack2.utilities.read_impedance.</span></span><span class="sig-name descname"><span class="pre">read_ABCI</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">file</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">azimuthal</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">output</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/utilities/read_impedance.html#read_ABCI"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.utilities.read_impedance.read_ABCI" title="Permalink to this definition">¶</a></dt>
+<dd><p>Read ABCI output files [1].</p>
+<dl class="simple">
+<dt>file<span class="classifier">str</span></dt><dd><p>Path to ABCI .pot file.</p>
+</dd>
+<dt>azimuthal<span class="classifier">bool, optional</span></dt><dd><p>If True, the transverse wake potential and impedance is loaded from the
+“AZIMUTHAL” data.
+If False, it is loaded from the “TRANSVERSE” data. In that case, a -1
+factor is applied on the wake to agree with mbtrack2 sign convention.
+The default is False.</p>
+</dd>
+<dt>output<span class="classifier">bool, optional</span></dt><dd><p>If True, print out the loaded components header.
+Default is False.</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>wake<span class="classifier">WakeField</span></dt><dd><p>Object where the ABCI computed impedance and wake are stored.</p>
+</dd>
+</dl>
+<p>[1] : ABCI - <a class="reference external" href="https://abci.kek.jp/abci.htm">https://abci.kek.jp/abci.htm</a></p>
+</dd></dl>
+
+<dl class="py function">
+<dt class="sig sig-object py" id="mbtrack2.utilities.read_impedance.read_CST">
+<span class="sig-prename descclassname"><span class="pre">mbtrack2.utilities.read_impedance.</span></span><span class="sig-name descname"><span class="pre">read_CST</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">file</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">component_type</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'long'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">divide_by</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">imp</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/utilities/read_impedance.html#read_CST"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.utilities.read_impedance.read_CST" title="Permalink to this definition">¶</a></dt>
+<dd><p>Read CST text file format into an Impedance or WakeFunction object.</p>
+<dl class="simple">
+<dt>file<span class="classifier">str</span></dt><dd><p>Path to the text file to read.</p>
+</dd>
+<dt>component_type<span class="classifier">str, optional</span></dt><dd><p>Type of the Impedance or WakeFunction object to load.
+Default is ‘long’.</p>
+</dd>
+<dt>divide_by<span class="classifier">float, optional</span></dt><dd><p>Divide the impedance by a value. Mainly used to normalize transverse
+impedance by displacement.
+Default is None.</p>
+</dd>
+<dt>imp<span class="classifier">bool, optional.</span></dt><dd><p>If True a Impedance object is loaded, if False a WakeFunction object is
+loaded.
+Default is True.</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>result<span class="classifier">Impedance or WakeFunction object.</span></dt><dd><p>Data from file.</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py function">
+<dt class="sig sig-object py" id="mbtrack2.utilities.read_impedance.read_ECHO2D">
+<span class="sig-prename descclassname"><span class="pre">mbtrack2.utilities.read_impedance.</span></span><span class="sig-name descname"><span class="pre">read_ECHO2D</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">file</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">component_type</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'long'</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/utilities/read_impedance.html#read_ECHO2D"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.utilities.read_impedance.read_ECHO2D" title="Permalink to this definition">¶</a></dt>
+<dd><p>Read ECHO2D text file format (after matlab post-processing) into a
+WakeFunction object.</p>
+<dl class="simple">
+<dt>file<span class="classifier">str</span></dt><dd><p>Path to the text file to read.</p>
+</dd>
+<dt>component_type<span class="classifier">str, optional</span></dt><dd><p>Type of the WakeFunction object to load.
+Default is ‘long’.</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>result<span class="classifier">WakeFunction object.</span></dt><dd><p>Data from file.</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py function">
+<dt class="sig sig-object py" id="mbtrack2.utilities.read_impedance.read_IW2D">
+<span class="sig-prename descclassname"><span class="pre">mbtrack2.utilities.read_impedance.</span></span><span class="sig-name descname"><span class="pre">read_IW2D</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">file</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">file_type</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'Zlong'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">output</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/utilities/read_impedance.html#read_IW2D"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.utilities.read_impedance.read_IW2D" title="Permalink to this definition">¶</a></dt>
+<dd><p>Read IW2D file format into an Impedance object or a WakeField object.</p>
+<dl class="simple">
+<dt>file<span class="classifier">str</span></dt><dd><p>Path to the file to read.</p>
+</dd>
+<dt>file_type<span class="classifier">str, optional</span></dt><dd><p>Type of the Impedance or WakeField object.</p>
+</dd>
+<dt>output<span class="classifier">bool, optional</span></dt><dd><p>If True, print out the interpolated values.
+Default is False.</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>result<span class="classifier">Impedance or WakeField object</span></dt><dd><p>Data from file.</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py function">
+<dt class="sig sig-object py" id="mbtrack2.utilities.read_impedance.read_IW2D_folder">
+<span class="sig-prename descclassname"><span class="pre">mbtrack2.utilities.read_impedance.</span></span><span class="sig-name descname"><span class="pre">read_IW2D_folder</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">folder</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">suffix</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">select</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'WZ'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">output</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/utilities/read_impedance.html#read_IW2D_folder"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.utilities.read_impedance.read_IW2D_folder" title="Permalink to this definition">¶</a></dt>
+<dd><p>Read IW2D results into a WakeField object.</p>
+<dl class="simple">
+<dt>folder<span class="classifier">str</span></dt><dd><p>Path to the folder to read.</p>
+</dd>
+<dt>suffix<span class="classifier">str</span></dt><dd><p>End of the name of each files. For example, in “Zlong_test.dat” the
+suffix should be “_test.dat”.</p>
+</dd>
+<dt>select<span class="classifier">str, optional</span></dt><dd><p>Select which object to load. “W” for WakeFunction, “Z” for Impedance
+and “WZ” or “ZW” for both.</p>
+</dd>
+<dt>output<span class="classifier">bool, optional</span></dt><dd><p>If True, print out the interpolated values.
+Default is False.</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>result<span class="classifier">WakeField object</span></dt><dd><p>WakeField object with Impedance and WakeFunction objects from the
+different files.</p>
+</dd>
+</dl>
+</dd></dl>
+
+</section>
+<section id="module-mbtrack2.utilities.spectrum">
+<span id="mbtrack2-utilities-spectrum-module"></span><h2>mbtrack2.utilities.spectrum module<a class="headerlink" href="#module-mbtrack2.utilities.spectrum" title="Permalink to this heading">¶</a></h2>
+<p>Module where bunch and beam spectrums and profile are defined.</p>
+<dl class="py function">
+<dt class="sig sig-object py" id="mbtrack2.utilities.spectrum.beam_spectrum">
+<span class="sig-prename descclassname"><span class="pre">mbtrack2.utilities.spectrum.</span></span><span class="sig-name descname"><span class="pre">beam_spectrum</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">frequency</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">M</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">bunch_spacing</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">sigma</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">bunch_spectrum</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/utilities/spectrum.html#beam_spectrum"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.utilities.spectrum.beam_spectrum" title="Permalink to this definition">¶</a></dt>
+<dd><p>Compute the beam spectrum assuming constant spacing between bunches [1].</p>
+<dl class="simple">
+<dt>frequency<span class="classifier">list or numpy array</span></dt><dd><p>sample points of the beam spectrum in [Hz].</p>
+</dd>
+<dt>M<span class="classifier">int</span></dt><dd><p>Number of bunches.</p>
+</dd>
+<dt>bunch_spacing<span class="classifier">float</span></dt><dd><p>Time between two bunches in [s].</p>
+</dd>
+<dt>sigma<span class="classifier">float, optional</span></dt><dd><p>If bunch_spectrum is None then a Gaussian bunch with sigma RMS bunch 
+length in [s] is assumed.</p>
+</dd>
+<dt>bunch_spectrum<span class="classifier">array, optional</span></dt><dd><p>Bunch spectrum sampled at points given in frequency.</p>
+</dd>
+</dl>
+<p>beam_spectrum : array</p>
+<dl class="simple">
+<dt>[1] Rumolo, G - Beam Instabilities - CAS - CERN Accelerator School: </dt><dd><p>Advanced Accelerator Physics Course - 2014, Eq. 9</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py function">
+<dt class="sig sig-object py" id="mbtrack2.utilities.spectrum.gaussian_bunch">
+<span class="sig-prename descclassname"><span class="pre">mbtrack2.utilities.spectrum.</span></span><span class="sig-name descname"><span class="pre">gaussian_bunch</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">time</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">sigma</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/utilities/spectrum.html#gaussian_bunch"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.utilities.spectrum.gaussian_bunch" title="Permalink to this definition">¶</a></dt>
+<dd><p>Compute a Gaussian bunch profile.</p>
+<dl class="simple">
+<dt>time<span class="classifier">array</span></dt><dd><p>sample points of the bunch profile in [s].</p>
+</dd>
+<dt>sigma<span class="classifier">float</span></dt><dd><p>RMS bunch length in [s].</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>bunch_profile<span class="classifier">array</span></dt><dd><p>Bunch profile in [s**-1] sampled at points given in time.</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py function">
+<dt class="sig sig-object py" id="mbtrack2.utilities.spectrum.gaussian_bunch_spectrum">
+<span class="sig-prename descclassname"><span class="pre">mbtrack2.utilities.spectrum.</span></span><span class="sig-name descname"><span class="pre">gaussian_bunch_spectrum</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">frequency</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">sigma</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/utilities/spectrum.html#gaussian_bunch_spectrum"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.utilities.spectrum.gaussian_bunch_spectrum" title="Permalink to this definition">¶</a></dt>
+<dd><p>Compute a Gaussian bunch spectrum [1].</p>
+<dl class="simple">
+<dt>frequency<span class="classifier">array</span></dt><dd><p>sample points of the beam spectrum in [Hz].</p>
+</dd>
+<dt>sigma<span class="classifier">float</span></dt><dd><p>RMS bunch length in [s].</p>
+</dd>
+</dl>
+<dl class="simple">
+<dt>bunch_spectrum<span class="classifier">array</span></dt><dd><p>Bunch spectrum sampled at points given in frequency.</p>
+</dd>
+</dl>
+<p>[1] : Gamelin, A. (2018). Collective effects in a transient microbunching 
+regime and ion cloud mitigation in ThomX. p86, Eq. 4.19</p>
+</dd></dl>
+
+<dl class="py function">
+<dt class="sig sig-object py" id="mbtrack2.utilities.spectrum.spectral_density">
+<span class="sig-prename descclassname"><span class="pre">mbtrack2.utilities.spectrum.</span></span><span class="sig-name descname"><span class="pre">spectral_density</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">frequency</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">sigma</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">m</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">k</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">mode</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'Hermite'</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/mbtrack2/utilities/spectrum.html#spectral_density"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#mbtrack2.utilities.spectrum.spectral_density" title="Permalink to this definition">¶</a></dt>
+<dd><p>Compute the spectral density of different modes for various values of the
+head-tail mode number, based on Table 1 p238 of [1].</p>
+<dl class="simple">
+<dt>frequency<span class="classifier">list or numpy array</span></dt><dd><p>sample points of the spectral density in [Hz]</p>
+</dd>
+<dt>sigma<span class="classifier">float</span></dt><dd><p>RMS bunch length in [s]</p>
+</dd>
+<dt>m<span class="classifier">int, optional</span></dt><dd><p>head-tail (or azimutal/synchrotron) mode number</p>
+</dd>
+<dt>k<span class="classifier">int, optional</span></dt><dd><p>radial mode number (such that <a href="#id3"><span class="problematic" id="id4">|q|=m+2k, where |q|</span></a> is the head-tail mode number)</p>
+</dd>
+<dt>mode: str, optional</dt><dd><p>type of the mode taken into account for the computation:
+-“Hermite” modes for Gaussian bunches (typical for electrons)
+-“Chebyshev” for airbag bunches
+-“Legendre” for parabolic bunches (typical for protons)
+-“Sacherer” or “Sinusoidal” simplifying approximation of Legendre modes from [3]</p>
+</dd>
+</dl>
+<p>numpy array</p>
+<p>[1] : Handbook of accelerator physics and engineering, 3rd printing.
+[2] : Ng, K. Y. (2005). Physics of intensity dependent beam instabilities. WORLD SCIENTIFIC. <a class="reference external" href="https://doi.org/10.1142/5835">https://doi.org/10.1142/5835</a>
+[3] : Sacherer, F. J. (1972). Methods for computing bunched beam instabilities. CERN Tech. rep. CERN/SI-BR/72-5 <a class="reference external" href="https://cds.cern.ch/record/2291670?ln=en">https://cds.cern.ch/record/2291670?ln=en</a></p>
+</dd></dl>
+
+</section>
+<section id="module-mbtrack2.utilities">
+<span id="module-contents"></span><h2>Module contents<a class="headerlink" href="#module-mbtrack2.utilities" title="Permalink to this heading">¶</a></h2>
+</section>
+</section>
+
+
+            <div class="clearer"></div>
+          </div>
+        </div>
+      </div>
+      <div class="sphinxsidebar" role="navigation" aria-label="main navigation">
+        <div class="sphinxsidebarwrapper">
+  <div>
+    <h3><a href="index.html">Table of Contents</a></h3>
+    <ul>
+<li><a class="reference internal" href="#">mbtrack2.utilities package</a><ul>
+<li><a class="reference internal" href="#submodules">Submodules</a></li>
+<li><a class="reference internal" href="#module-mbtrack2.utilities.beamloading">mbtrack2.utilities.beamloading module</a></li>
+<li><a class="reference internal" href="#module-mbtrack2.utilities.misc">mbtrack2.utilities.misc module</a></li>
+<li><a class="reference internal" href="#module-mbtrack2.utilities.optics">mbtrack2.utilities.optics module</a></li>
+<li><a class="reference internal" href="#module-mbtrack2.utilities.read_impedance">mbtrack2.utilities.read_impedance module</a></li>
+<li><a class="reference internal" href="#module-mbtrack2.utilities.spectrum">mbtrack2.utilities.spectrum module</a></li>
+<li><a class="reference internal" href="#module-mbtrack2.utilities">Module contents</a></li>
+</ul>
+</li>
+</ul>
+
+  </div>
+  <div role="note" aria-label="source link">
+    <h3>This Page</h3>
+    <ul class="this-page-menu">
+      <li><a href="_sources/mbtrack2.utilities.rst.txt"
+            rel="nofollow">Show Source</a></li>
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+<div id="searchbox" style="display: none" role="search">
+  <h3 id="searchlabel">Quick search</h3>
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+             >modules</a> |</li>
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+
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+  <head>
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+          <a href="#" title="Python Module Index"
+             >modules</a> |</li>
+        <li class="nav-item nav-item-0"><a href="index.html">mbtrack2 0.6.0 documentation</a> &#187;</li>
+        <li class="nav-item nav-item-this"><a href="">Python Module Index</a></li> 
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+            
+
+   <h1>Python Module Index</h1>
+
+   <div class="modindex-jumpbox">
+   <a href="#cap-m"><strong>m</strong></a>
+   </div>
+
+   <table class="indextable modindextable">
+     <tr class="pcap"><td></td><td>&#160;</td><td></td></tr>
+     <tr class="cap" id="cap-m"><td></td><td>
+       <strong>m</strong></td><td></td></tr>
+     <tr>
+       <td><img src="_static/minus.png" class="toggler"
+              id="toggle-1" style="display: none" alt="-" /></td>
+       <td>
+       <a href="mbtrack2.html#module-mbtrack2"><code class="xref">mbtrack2</code></a></td><td>
+       <em></em></td></tr>
+     <tr class="cg-1">
+       <td></td>
+       <td>&#160;&#160;&#160;
+       <a href="mbtrack2.impedance.html#module-mbtrack2.impedance"><code class="xref">mbtrack2.impedance</code></a></td><td>
+       <em></em></td></tr>
+     <tr class="cg-1">
+       <td></td>
+       <td>&#160;&#160;&#160;
+       <a href="mbtrack2.impedance.html#module-mbtrack2.impedance.csr"><code class="xref">mbtrack2.impedance.csr</code></a></td><td>
+       <em></em></td></tr>
+     <tr class="cg-1">
+       <td></td>
+       <td>&#160;&#160;&#160;
+       <a href="mbtrack2.impedance.html#module-mbtrack2.impedance.impedance_model"><code class="xref">mbtrack2.impedance.impedance_model</code></a></td><td>
+       <em></em></td></tr>
+     <tr class="cg-1">
+       <td></td>
+       <td>&#160;&#160;&#160;
+       <a href="mbtrack2.impedance.html#module-mbtrack2.impedance.resistive_wall"><code class="xref">mbtrack2.impedance.resistive_wall</code></a></td><td>
+       <em></em></td></tr>
+     <tr class="cg-1">
+       <td></td>
+       <td>&#160;&#160;&#160;
+       <a href="mbtrack2.impedance.html#module-mbtrack2.impedance.resonator"><code class="xref">mbtrack2.impedance.resonator</code></a></td><td>
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+     <tr class="cg-1">
+       <td></td>
+       <td>&#160;&#160;&#160;
+       <a href="mbtrack2.impedance.html#module-mbtrack2.impedance.tapers"><code class="xref">mbtrack2.impedance.tapers</code></a></td><td>
+       <em></em></td></tr>
+     <tr class="cg-1">
+       <td></td>
+       <td>&#160;&#160;&#160;
+       <a href="mbtrack2.impedance.html#module-mbtrack2.impedance.wakefield"><code class="xref">mbtrack2.impedance.wakefield</code></a></td><td>
+       <em></em></td></tr>
+     <tr class="cg-1">
+       <td></td>
+       <td>&#160;&#160;&#160;
+       <a href="mbtrack2.instability.html#module-mbtrack2.instability"><code class="xref">mbtrack2.instability</code></a></td><td>
+       <em></em></td></tr>
+     <tr class="cg-1">
+       <td></td>
+       <td>&#160;&#160;&#160;
+       <a href="mbtrack2.instability.html#module-mbtrack2.instability.instabilities"><code class="xref">mbtrack2.instability.instabilities</code></a></td><td>
+       <em></em></td></tr>
+     <tr class="cg-1">
+       <td></td>
+       <td>&#160;&#160;&#160;
+       <a href="mbtrack2.instability.html#module-mbtrack2.instability.ions"><code class="xref">mbtrack2.instability.ions</code></a></td><td>
+       <em></em></td></tr>
+     <tr class="cg-1">
+       <td></td>
+       <td>&#160;&#160;&#160;
+       <a href="mbtrack2.tracking.html#module-mbtrack2.tracking"><code class="xref">mbtrack2.tracking</code></a></td><td>
+       <em></em></td></tr>
+     <tr class="cg-1">
+       <td></td>
+       <td>&#160;&#160;&#160;
+       <a href="mbtrack2.tracking.html#module-mbtrack2.tracking.aperture"><code class="xref">mbtrack2.tracking.aperture</code></a></td><td>
+       <em></em></td></tr>
+     <tr class="cg-1">
+       <td></td>
+       <td>&#160;&#160;&#160;
+       <a href="mbtrack2.tracking.html#module-mbtrack2.tracking.element"><code class="xref">mbtrack2.tracking.element</code></a></td><td>
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+     <tr class="cg-1">
+       <td></td>
+       <td>&#160;&#160;&#160;
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+     <tr class="cg-1">
+       <td></td>
+       <td>&#160;&#160;&#160;
+       <a href="mbtrack2.tracking.monitors.html#module-mbtrack2.tracking.monitors"><code class="xref">mbtrack2.tracking.monitors</code></a></td><td>
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+     <tr class="cg-1">
+       <td></td>
+       <td>&#160;&#160;&#160;
+       <a href="mbtrack2.tracking.monitors.html#module-mbtrack2.tracking.monitors.monitors"><code class="xref">mbtrack2.tracking.monitors.monitors</code></a></td><td>
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+     <tr class="cg-1">
+       <td></td>
+       <td>&#160;&#160;&#160;
+       <a href="mbtrack2.tracking.monitors.html#module-mbtrack2.tracking.monitors.plotting"><code class="xref">mbtrack2.tracking.monitors.plotting</code></a></td><td>
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+     <tr class="cg-1">
+       <td></td>
+       <td>&#160;&#160;&#160;
+       <a href="mbtrack2.tracking.monitors.html#module-mbtrack2.tracking.monitors.tools"><code class="xref">mbtrack2.tracking.monitors.tools</code></a></td><td>
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+     <tr class="cg-1">
+       <td></td>
+       <td>&#160;&#160;&#160;
+       <a href="mbtrack2.tracking.html#module-mbtrack2.tracking.parallel"><code class="xref">mbtrack2.tracking.parallel</code></a></td><td>
+       <em></em></td></tr>
+     <tr class="cg-1">
+       <td></td>
+       <td>&#160;&#160;&#160;
+       <a href="mbtrack2.tracking.html#module-mbtrack2.tracking.particles"><code class="xref">mbtrack2.tracking.particles</code></a></td><td>
+       <em></em></td></tr>
+     <tr class="cg-1">
+       <td></td>
+       <td>&#160;&#160;&#160;
+       <a href="mbtrack2.tracking.html#module-mbtrack2.tracking.rf"><code class="xref">mbtrack2.tracking.rf</code></a></td><td>
+       <em></em></td></tr>
+     <tr class="cg-1">
+       <td></td>
+       <td>&#160;&#160;&#160;
+       <a href="mbtrack2.tracking.html#module-mbtrack2.tracking.synchrotron"><code class="xref">mbtrack2.tracking.synchrotron</code></a></td><td>
+       <em></em></td></tr>
+     <tr class="cg-1">
+       <td></td>
+       <td>&#160;&#160;&#160;
+       <a href="mbtrack2.tracking.html#module-mbtrack2.tracking.wakepotential"><code class="xref">mbtrack2.tracking.wakepotential</code></a></td><td>
+       <em></em></td></tr>
+     <tr class="cg-1">
+       <td></td>
+       <td>&#160;&#160;&#160;
+       <a href="mbtrack2.utilities.html#module-mbtrack2.utilities"><code class="xref">mbtrack2.utilities</code></a></td><td>
+       <em></em></td></tr>
+     <tr class="cg-1">
+       <td></td>
+       <td>&#160;&#160;&#160;
+       <a href="mbtrack2.utilities.html#module-mbtrack2.utilities.beamloading"><code class="xref">mbtrack2.utilities.beamloading</code></a></td><td>
+       <em></em></td></tr>
+     <tr class="cg-1">
+       <td></td>
+       <td>&#160;&#160;&#160;
+       <a href="mbtrack2.utilities.html#module-mbtrack2.utilities.misc"><code class="xref">mbtrack2.utilities.misc</code></a></td><td>
+       <em></em></td></tr>
+     <tr class="cg-1">
+       <td></td>
+       <td>&#160;&#160;&#160;
+       <a href="mbtrack2.utilities.html#module-mbtrack2.utilities.optics"><code class="xref">mbtrack2.utilities.optics</code></a></td><td>
+       <em></em></td></tr>
+     <tr class="cg-1">
+       <td></td>
+       <td>&#160;&#160;&#160;
+       <a href="mbtrack2.utilities.html#module-mbtrack2.utilities.read_impedance"><code class="xref">mbtrack2.utilities.read_impedance</code></a></td><td>
+       <em></em></td></tr>
+     <tr class="cg-1">
+       <td></td>
+       <td>&#160;&#160;&#160;
+       <a href="mbtrack2.utilities.html#module-mbtrack2.utilities.spectrum"><code class="xref">mbtrack2.utilities.spectrum</code></a></td><td>
+       <em></em></td></tr>
+   </table>
+
+
+            <div class="clearer"></div>
+          </div>
+        </div>
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diff --git a/docs/build/html/search.html b/docs/build/html/search.html
new file mode 100644
index 0000000..0ba1cc4
--- /dev/null
+++ b/docs/build/html/search.html
@@ -0,0 +1,103 @@
+
+<!DOCTYPE html>
+
+<html lang="en">
+  <head>
+    <meta charset="utf-8" />
+    <meta name="viewport" content="width=device-width, initial-scale=1.0" />
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+  </form>
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+          <a href="py-modindex.html" title="Python Module Index"
+             >modules</a> |</li>
+        <li class="nav-item nav-item-0"><a href="index.html">mbtrack2 0.6.0 documentation</a> &#187;</li>
+        <li class="nav-item nav-item-this"><a href="">Search</a></li> 
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diff --git a/docs/build/html/searchindex.js b/docs/build/html/searchindex.js
new file mode 100644
index 0000000..cff3f41
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"Bunch"], [4, 1, 1, "", "Electron"], [4, 1, 1, "", "Particle"], [4, 1, 1, "", "Proton"]], "mbtrack2.tracking.particles.Beam": [[4, 3, 1, "", "bunch_charge"], [4, 3, 1, "", "bunch_cs"], [4, 3, 1, "", "bunch_current"], [4, 3, 1, "", "bunch_emit"], [4, 3, 1, "", "bunch_index"], [4, 3, 1, "", "bunch_mean"], [4, 3, 1, "", "bunch_particle"], [4, 3, 1, "", "bunch_std"], [4, 3, 1, "", "charge"], [4, 3, 1, "", "current"], [4, 3, 1, "", "distance_between_bunches"], [4, 3, 1, "", "filling_pattern"], [4, 2, 1, "", "init_beam"], [4, 2, 1, "", "load"], [4, 2, 1, "", "mpi_close"], [4, 2, 1, "", "mpi_gather"], [4, 2, 1, "", "mpi_init"], [4, 3, 1, "", "not_empty"], [4, 3, 1, "", "particle_number"], [4, 2, 1, "", "plot"], [4, 2, 1, "", "save"], [4, 2, 1, "", "update_distance_between_bunches"], [4, 2, 1, "", "update_filling_pattern"]], "mbtrack2.tracking.particles.Bunch": [[4, 2, 1, "", "binning"], [4, 3, 1, "", "charge"], [4, 3, 1, "", "charge_per_mp"], [4, 3, 1, "", "cs_invariant"], [4, 3, 1, "", "current"], [4, 3, 1, "", "emit"], [4, 2, 1, "", "init_gaussian"], [4, 3, 1, "", "is_empty"], [4, 2, 1, "", "load"], [4, 3, 1, "", "mean"], [4, 3, 1, "", "mp_number"], [4, 3, 1, "", "particle_number"], [4, 2, 1, "", "plot_phasespace"], [4, 2, 1, "", "plot_profile"], [4, 2, 1, "", "save"], [4, 3, 1, "", "std"]], "mbtrack2.tracking.particles.Particle": [[4, 3, 1, "", "E_rest"]], "mbtrack2.tracking.rf": [[4, 1, 1, "", "CavityResonator"], [4, 1, 1, "", "DirectFeedback"], [4, 1, 1, "", "ProportionalIntegralLoop"], [4, 1, 1, "", "ProportionalLoop"], [4, 1, 1, "", "RFCavity"], [4, 1, 1, "", "TunerLoop"]], "mbtrack2.tracking.rf.CavityResonator": [[4, 3, 1, "", "DFB_ig_phasor"], [4, 3, 1, "", "Ncav"], [4, 2, 1, "", "Pb"], [4, 3, 1, "", "Pc"], [4, 2, 1, "", "Pr"], [4, 3, 1, "", "Q"], [4, 3, 1, "", "QL"], [4, 3, 1, "", "RL"], [4, 3, 1, "", "Rs"], [4, 3, 1, "", "Rs_per_cavity"], [4, 2, 1, "", "VRF"], [4, 2, 1, "", "Vb"], [4, 2, 1, "", "Vbr"], [4, 2, 1, "", "Z"], [4, 3, 1, "", "beam_phase"], [4, 3, 1, "", "beam_voltage"], [4, 3, 1, "", "beta"], [4, 3, 1, "", "cavity_phase"], [4, 3, 1, "", "cavity_phasor"], [4, 3, 1, "", "cavity_phasor_record"], [4, 3, 1, "", "cavity_voltage"], [4, 2, 1, "", "dVRF"], [4, 2, 1, "", "ddVRF"], [4, 2, 1, "", "deltaVRF"], [4, 3, 1, "", "detune"], [4, 3, 1, "", "filling_time"], [4, 3, 1, "", "fr"], [4, 3, 1, "", "generator_phasor"], [4, 3, 1, "", "ig_phasor_record"], [4, 2, 1, "", "init_phasor"], [4, 2, 1, "", "init_phasor_track"], [4, 2, 1, "", "init_tracking"], [4, 2, 1, "", "is_CBI_stable"], [4, 2, 1, "", "is_DC_Robinson_stable"], [4, 3, 1, "", "loss_factor"], [4, 3, 1, "", "m"], [4, 2, 1, "", "phasor_decay"], [4, 2, 1, "", "phasor_evol"], [4, 2, 1, "", "plot_DC_Robinson_stability"], [4, 2, 1, "", "plot_phasor"], [4, 3, 1, "", "psi"], [4, 2, 1, "", "sample_voltage"], [4, 2, 1, "", "set_generator"], [4, 2, 1, "", "set_optimal_coupling"], [4, 2, 1, "", "set_optimal_detune"], [4, 2, 1, "", "track"], [4, 2, 1, "", "update_feedback"], [4, 3, 1, "", "wr"]], "mbtrack2.tracking.rf.DirectFeedback": [[4, 3, 1, "", "DFB_Rs"], [4, 2, 1, "", "DFB_Vg"], [4, 3, 1, "", "DFB_alpha"], [4, 2, 1, "", "DFB_fs"], [4, 3, 1, "", "DFB_gamma"], [4, 2, 1, "", "DFB_parameter_set"], [4, 3, 1, "", "DFB_phase_shift"], [4, 3, 1, "", "DFB_psi"], [4, 3, 1, "", "phase_shift"], [4, 2, 1, "", "track"]], "mbtrack2.tracking.rf.ProportionalIntegralLoop": [[4, 2, 1, "", "IIR"], [4, 2, 1, "", "IIR_init"], [4, 3, 1, "", "IIRcutoff"], [4, 2, 1, "", "Ig2Vg"], [4, 2, 1, "", "Ig2Vg_matrix"], [4, 2, 1, "", "Vg2Ig"], [4, 2, 1, "", "init_FFconst"], [4, 2, 1, "", "init_Ig2Vg_matrix"], [4, 2, 1, "", "track"]], "mbtrack2.tracking.rf.ProportionalLoop": [[4, 2, 1, "", "track"]], "mbtrack2.tracking.rf.RFCavity": [[4, 2, 1, "", "track"], [4, 2, 1, "", "value"]], "mbtrack2.tracking.rf.TunerLoop": [[4, 2, 1, "", "track"]], "mbtrack2.tracking.synchrotron": [[4, 1, 1, "", "Synchrotron"]], "mbtrack2.tracking.synchrotron.Synchrotron": [[4, 3, 1, "", "E0"], [4, 3, 1, "", "L"], [4, 3, 1, "", "T0"], [4, 3, 1, "", "T1"], [4, 3, 1, "", "beta"], [4, 2, 1, "", "eta"], [4, 3, 1, "", "f0"], [4, 3, 1, "", "f1"], [4, 3, 1, "", "gamma"], [4, 2, 1, "", "get_adts"], [4, 2, 1, "", "get_longitudinal_twiss"], [4, 2, 1, "", "get_mcf_order"], [4, 3, 1, "", "h"], [4, 3, 1, "", "k1"], [4, 3, 1, "", "mcf_order"], [4, 3, 1, "", "omega0"], [4, 3, 1, "", "omega1"], [4, 2, 1, "", "sigma"], [4, 2, 1, "", "synchrotron_tune"], [4, 2, 1, "", "to_pyat"]], "mbtrack2.tracking.wakepotential": [[4, 1, 1, "", "LongRangeResistiveWall"], [4, 1, 1, "", "WakePotential"]], "mbtrack2.tracking.wakepotential.LongRangeResistiveWall": [[4, 2, 1, "", "Wdip"], [4, 2, 1, "", "Wlong"], [4, 2, 1, "", "get_kick"], [4, 2, 1, "", "track"], [4, 2, 1, "", "track_bunch"], [4, 2, 1, "", "update_tables"]], "mbtrack2.tracking.wakepotential.WakePotential": [[4, 2, 1, "", "charge_density"], [4, 2, 1, "", "check_sampling"], [4, 2, 1, "", "dipole_moment"], [4, 2, 1, "", "get_gaussian_wakepotential"], [4, 2, 1, "", "get_wakepotential"], [4, 2, 1, "", "plot_gaussian_wake"], [4, 2, 1, "", "plot_last_wake"], [4, 2, 1, "", "prepare_wakefunction"], [4, 2, 1, "", "reduce_sampling"], [4, 2, 1, "", "reference_loss"], [4, 2, 1, "", "track"]], "mbtrack2.utilities": [[6, 0, 0, "-", "beamloading"], [6, 0, 0, "-", "misc"], [6, 0, 0, "-", "optics"], [6, 0, 0, "-", "read_impedance"], [6, 0, 0, "-", "spectrum"]], "mbtrack2.utilities.beamloading": [[6, 1, 1, "", "BeamLoadingEquilibrium"]], "mbtrack2.utilities.beamloading.BeamLoadingEquilibrium": [[6, 2, 1, "", "PTBL_threshold"], [6, 2, 1, "", "beam_equilibrium"], [6, 2, 1, "", "center_of_mass"], [6, 2, 1, "", "dV"], [6, 2, 1, "", "ddV"], [6, 2, 1, "", "deltaVRF"], [6, 2, 1, "", "du_dz"], [6, 2, 1, "", "energy_balance"], [6, 2, 1, "", "integrate_func"], [6, 2, 1, "", "plot_dV"], [6, 2, 1, "", "plot_rho"], [6, 2, 1, "", "plot_voltage"], [6, 2, 1, "", "rho"], [6, 2, 1, "", "std_rho"], [6, 2, 1, "", "to_solve"], [6, 2, 1, "", "u"], [6, 2, 1, "", "uexp"], [6, 2, 1, "", "update_potentials"], [6, 2, 1, "", "voltage"]], "mbtrack2.utilities.misc": [[6, 4, 1, "", "beam_loss_factor"], [6, 4, 1, "", "double_sided_impedance"], [6, 4, 1, "", "effective_impedance"], [6, 4, 1, "", "head_tail_form_factor"], [6, 4, 1, "", "tune_shift_from_effective_impedance"], [6, 4, 1, "", "yokoya_elliptic"]], "mbtrack2.utilities.optics": [[6, 1, 1, "", "Optics"], [6, 1, 1, "", "PhysicalModel"]], "mbtrack2.utilities.optics.Optics": [[6, 2, 1, "", "alpha"], [6, 2, 1, "", "beta"], [6, 2, 1, "", "dispersion"], [6, 2, 1, "", "gamma"], [6, 2, 1, "", "load_from_AT"], [6, 3, 1, "", "local_alpha"], [6, 3, 1, "", "local_beta"], [6, 3, 1, "", "local_gamma"], [6, 2, 1, "", "mu"], [6, 2, 1, "", "plot"], [6, 2, 1, "", "setup_interpolation"]], "mbtrack2.utilities.optics.PhysicalModel": [[6, 2, 1, "", "change_values"], [6, 2, 1, "", "get_aperture"], [6, 2, 1, "", "plot_aperture"], [6, 2, 1, "", "plot_resistivity"], [6, 2, 1, "", "resistive_wall_effective_radius"], [6, 2, 1, "", "taper"]], "mbtrack2.utilities.read_impedance": [[6, 4, 1, "", "read_ABCI"], [6, 4, 1, "", "read_CST"], [6, 4, 1, "", "read_ECHO2D"], [6, 4, 1, "", "read_IW2D"], [6, 4, 1, "", "read_IW2D_folder"]], "mbtrack2.utilities.spectrum": [[6, 4, 1, "", "beam_spectrum"], [6, 4, 1, "", "gaussian_bunch"], [6, 4, 1, "", "gaussian_bunch_spectrum"], [6, 4, 1, "", "spectral_density"]]}, "objtypes": {"0": "py:module", "1": "py:class", "2": "py:method", "3": "py:property", "4": "py:function"}, "objnames": {"0": ["py", "module", "Python module"], "1": ["py", "class", "Python class"], "2": ["py", "method", "Python method"], "3": ["py", "property", "Python property"], "4": ["py", "function", "Python function"]}, "titleterms": {"welcom": 0, "mbtrack2": [0, 1, 2, 3, 4, 5, 6], "s": 0, "document": 0, "indic": 0, "tabl": 0, "packag": [1, 2, 3, 4, 5, 6], "subpackag": [1, 4], "modul": [1, 2, 3, 4, 5, 6], "content": [1, 2, 3, 4, 5, 6], "imped": 2, "submodul": [2, 3, 4, 5, 6], "csr": 2, "impedance_model": 2, "resistive_wal": 2, "reson": 2, "taper": 2, "wakefield": 2, "instabl": 3, "ion": 3, "track": [4, 5], "apertur": 4, "element": 4, "feedback": 4, "parallel": 4, "particl": 4, "rf": 4, "synchrotron": 4, "wakepotenti": 4, "monitor": 5, "plot": 5, "tool": 5, "util": 6, "beamload": 6, "misc": 6, "optic": 6, "read_imped": 6, "spectrum": 6}, "envversion": {"sphinx.domains.c": 2, "sphinx.domains.changeset": 1, "sphinx.domains.citation": 1, "sphinx.domains.cpp": 6, "sphinx.domains.index": 1, "sphinx.domains.javascript": 2, "sphinx.domains.math": 2, "sphinx.domains.python": 3, "sphinx.domains.rst": 2, "sphinx.domains.std": 2, "sphinx.ext.viewcode": 1, "sphinx": 56}})
\ No newline at end of file
diff --git a/docs/make.bat b/docs/make.bat
new file mode 100644
index 0000000..747ffb7
--- /dev/null
+++ b/docs/make.bat
@@ -0,0 +1,35 @@
+@ECHO OFF
+
+pushd %~dp0
+
+REM Command file for Sphinx documentation
+
+if "%SPHINXBUILD%" == "" (
+	set SPHINXBUILD=sphinx-build
+)
+set SOURCEDIR=source
+set BUILDDIR=build
+
+%SPHINXBUILD% >NUL 2>NUL
+if errorlevel 9009 (
+	echo.
+	echo.The 'sphinx-build' command was not found. Make sure you have Sphinx
+	echo.installed, then set the SPHINXBUILD environment variable to point
+	echo.to the full path of the 'sphinx-build' executable. Alternatively you
+	echo.may add the Sphinx directory to PATH.
+	echo.
+	echo.If you don't have Sphinx installed, grab it from
+	echo.https://www.sphinx-doc.org/
+	exit /b 1
+)
+
+if "%1" == "" goto help
+
+%SPHINXBUILD% -M %1 %SOURCEDIR% %BUILDDIR% %SPHINXOPTS% %O%
+goto end
+
+:help
+%SPHINXBUILD% -M help %SOURCEDIR% %BUILDDIR% %SPHINXOPTS% %O%
+
+:end
+popd
diff --git a/docs/source/Makefile b/docs/source/Makefile
new file mode 100644
index 0000000..d4bb2cb
--- /dev/null
+++ b/docs/source/Makefile
@@ -0,0 +1,20 @@
+# Minimal makefile for Sphinx documentation
+#
+
+# You can set these variables from the command line, and also
+# from the environment for the first two.
+SPHINXOPTS    ?=
+SPHINXBUILD   ?= sphinx-build
+SOURCEDIR     = .
+BUILDDIR      = _build
+
+# Put it first so that "make" without argument is like "make help".
+help:
+	@$(SPHINXBUILD) -M help "$(SOURCEDIR)" "$(BUILDDIR)" $(SPHINXOPTS) $(O)
+
+.PHONY: help Makefile
+
+# Catch-all target: route all unknown targets to Sphinx using the new
+# "make mode" option.  $(O) is meant as a shortcut for $(SPHINXOPTS).
+%: Makefile
+	@$(SPHINXBUILD) -M $@ "$(SOURCEDIR)" "$(BUILDDIR)" $(SPHINXOPTS) $(O)
diff --git a/docs/source/conf.py b/docs/source/conf.py
new file mode 100644
index 0000000..2ff33b5
--- /dev/null
+++ b/docs/source/conf.py
@@ -0,0 +1,60 @@
+# Configuration file for the Sphinx documentation builder.
+#
+# This file only contains a selection of the most common options. For a full
+# list see the documentation:
+# https://www.sphinx-doc.org/en/master/usage/configuration.html
+
+# -- Path setup --------------------------------------------------------------
+
+# If extensions (or modules to document with autodoc) are in another directory,
+# add these directories to sys.path here. If the directory is relative to the
+# documentation root, use os.path.abspath to make it absolute, like shown here.
+#
+# import os
+# import sys
+# sys.path.insert(0, os.path.abspath('.'))
+
+
+# -- Project information -----------------------------------------------------
+
+project = 'mbtrack2'
+copyright = '2024, A. Gamelin et al'
+author = 'A. Gamelin et al'
+
+# The full version, including alpha/beta/rc tags
+release = '0.6.0'
+
+
+# -- General configuration ---------------------------------------------------
+
+# Add any Sphinx extension module names here, as strings. They can be
+# extensions coming with Sphinx (named 'sphinx.ext.*') or your custom
+# ones.
+extensions = [
+    'sphinx.ext.autodoc',
+    'sphinx.ext.viewcode',
+]
+
+# Add any paths that contain templates here, relative to this directory.
+templates_path = ['_templates']
+
+# List of patterns, relative to source directory, that match files and
+# directories to ignore when looking for source files.
+# This pattern also affects html_static_path and html_extra_path.
+exclude_patterns = []
+
+
+# -- Options for HTML output -------------------------------------------------
+
+# The theme to use for HTML and HTML Help pages.  See the documentation for
+# a list of builtin themes.
+#
+html_theme = 'nature'
+
+# Add any paths that contain custom static files (such as style sheets) here,
+# relative to this directory. They are copied after the builtin static files,
+# so a file named "default.css" will overwrite the builtin "default.css".
+html_static_path = ['_static']
+
+
+# -- Extension configuration -------------------------------------------------
diff --git a/docs/source/index.rst b/docs/source/index.rst
new file mode 100644
index 0000000..e4a144e
--- /dev/null
+++ b/docs/source/index.rst
@@ -0,0 +1,20 @@
+.. mbtrack2 documentation master file, created by
+   sphinx-quickstart on Sun Apr 28 19:57:17 2024.
+   You can adapt this file completely to your liking, but it should at least
+   contain the root `toctree` directive.
+
+Welcome to mbtrack2's documentation!
+====================================
+
+.. toctree::
+   :maxdepth: 2
+   :caption: Contents:
+
+
+
+Indices and tables
+==================
+
+* :ref:`genindex`
+* :ref:`modindex`
+* :ref:`search`
diff --git a/docs/source/make.bat b/docs/source/make.bat
new file mode 100644
index 0000000..32bb245
--- /dev/null
+++ b/docs/source/make.bat
@@ -0,0 +1,35 @@
+@ECHO OFF
+
+pushd %~dp0
+
+REM Command file for Sphinx documentation
+
+if "%SPHINXBUILD%" == "" (
+	set SPHINXBUILD=sphinx-build
+)
+set SOURCEDIR=.
+set BUILDDIR=_build
+
+%SPHINXBUILD% >NUL 2>NUL
+if errorlevel 9009 (
+	echo.
+	echo.The 'sphinx-build' command was not found. Make sure you have Sphinx
+	echo.installed, then set the SPHINXBUILD environment variable to point
+	echo.to the full path of the 'sphinx-build' executable. Alternatively you
+	echo.may add the Sphinx directory to PATH.
+	echo.
+	echo.If you don't have Sphinx installed, grab it from
+	echo.https://www.sphinx-doc.org/
+	exit /b 1
+)
+
+if "%1" == "" goto help
+
+%SPHINXBUILD% -M %1 %SOURCEDIR% %BUILDDIR% %SPHINXOPTS% %O%
+goto end
+
+:help
+%SPHINXBUILD% -M help %SOURCEDIR% %BUILDDIR% %SPHINXOPTS% %O%
+
+:end
+popd
diff --git a/docs/source/mbtrack2.impedance.rst b/docs/source/mbtrack2.impedance.rst
new file mode 100644
index 0000000..2d40343
--- /dev/null
+++ b/docs/source/mbtrack2.impedance.rst
@@ -0,0 +1,61 @@
+mbtrack2.impedance package
+==========================
+
+Submodules
+----------
+
+mbtrack2.impedance.csr module
+-----------------------------
+
+.. automodule:: mbtrack2.impedance.csr
+   :members:
+   :undoc-members:
+   :show-inheritance:
+
+mbtrack2.impedance.impedance\_model module
+------------------------------------------
+
+.. automodule:: mbtrack2.impedance.impedance_model
+   :members:
+   :undoc-members:
+   :show-inheritance:
+
+mbtrack2.impedance.resistive\_wall module
+-----------------------------------------
+
+.. automodule:: mbtrack2.impedance.resistive_wall
+   :members:
+   :undoc-members:
+   :show-inheritance:
+
+mbtrack2.impedance.resonator module
+-----------------------------------
+
+.. automodule:: mbtrack2.impedance.resonator
+   :members:
+   :undoc-members:
+   :show-inheritance:
+
+mbtrack2.impedance.tapers module
+--------------------------------
+
+.. automodule:: mbtrack2.impedance.tapers
+   :members:
+   :undoc-members:
+   :show-inheritance:
+
+mbtrack2.impedance.wakefield module
+-----------------------------------
+
+.. automodule:: mbtrack2.impedance.wakefield
+   :members:
+   :undoc-members:
+   :show-inheritance:
+
+Module contents
+---------------
+
+.. automodule:: mbtrack2.impedance
+   :members:
+   :undoc-members:
+   :show-inheritance:
diff --git a/docs/source/mbtrack2.instability.rst b/docs/source/mbtrack2.instability.rst
new file mode 100644
index 0000000..7b7e8f4
--- /dev/null
+++ b/docs/source/mbtrack2.instability.rst
@@ -0,0 +1,29 @@
+mbtrack2.instability package
+============================
+
+Submodules
+----------
+
+mbtrack2.instability.instabilities module
+-----------------------------------------
+
+.. automodule:: mbtrack2.instability.instabilities
+   :members:
+   :undoc-members:
+   :show-inheritance:
+
+mbtrack2.instability.ions module
+--------------------------------
+
+.. automodule:: mbtrack2.instability.ions
+   :members:
+   :undoc-members:
+   :show-inheritance:
+
+Module contents
+---------------
+
+.. automodule:: mbtrack2.instability
+   :members:
+   :undoc-members:
+   :show-inheritance:
diff --git a/docs/source/mbtrack2.rst b/docs/source/mbtrack2.rst
new file mode 100644
index 0000000..7d99aeb
--- /dev/null
+++ b/docs/source/mbtrack2.rst
@@ -0,0 +1,21 @@
+mbtrack2 package
+================
+
+Subpackages
+-----------
+
+.. toctree::
+   :maxdepth: 4
+
+   mbtrack2.impedance
+   mbtrack2.instability
+   mbtrack2.tracking
+   mbtrack2.utilities
+
+Module contents
+---------------
+
+.. automodule:: mbtrack2
+   :members:
+   :undoc-members:
+   :show-inheritance:
diff --git a/docs/source/mbtrack2.tracking.monitors.rst b/docs/source/mbtrack2.tracking.monitors.rst
new file mode 100644
index 0000000..36cd62a
--- /dev/null
+++ b/docs/source/mbtrack2.tracking.monitors.rst
@@ -0,0 +1,37 @@
+mbtrack2.tracking.monitors package
+==================================
+
+Submodules
+----------
+
+mbtrack2.tracking.monitors.monitors module
+------------------------------------------
+
+.. automodule:: mbtrack2.tracking.monitors.monitors
+   :members:
+   :undoc-members:
+   :show-inheritance:
+
+mbtrack2.tracking.monitors.plotting module
+------------------------------------------
+
+.. automodule:: mbtrack2.tracking.monitors.plotting
+   :members:
+   :undoc-members:
+   :show-inheritance:
+
+mbtrack2.tracking.monitors.tools module
+---------------------------------------
+
+.. automodule:: mbtrack2.tracking.monitors.tools
+   :members:
+   :undoc-members:
+   :show-inheritance:
+
+Module contents
+---------------
+
+.. automodule:: mbtrack2.tracking.monitors
+   :members:
+   :undoc-members:
+   :show-inheritance:
diff --git a/docs/source/mbtrack2.tracking.rst b/docs/source/mbtrack2.tracking.rst
new file mode 100644
index 0000000..36df13c
--- /dev/null
+++ b/docs/source/mbtrack2.tracking.rst
@@ -0,0 +1,85 @@
+mbtrack2.tracking package
+=========================
+
+Subpackages
+-----------
+
+.. toctree::
+   :maxdepth: 4
+
+   mbtrack2.tracking.monitors
+
+Submodules
+----------
+
+mbtrack2.tracking.aperture module
+---------------------------------
+
+.. automodule:: mbtrack2.tracking.aperture
+   :members:
+   :undoc-members:
+   :show-inheritance:
+
+mbtrack2.tracking.element module
+--------------------------------
+
+.. automodule:: mbtrack2.tracking.element
+   :members:
+   :undoc-members:
+   :show-inheritance:
+
+mbtrack2.tracking.feedback module
+---------------------------------
+
+.. automodule:: mbtrack2.tracking.feedback
+   :members:
+   :undoc-members:
+   :show-inheritance:
+
+mbtrack2.tracking.parallel module
+---------------------------------
+
+.. automodule:: mbtrack2.tracking.parallel
+   :members:
+   :undoc-members:
+   :show-inheritance:
+
+mbtrack2.tracking.particles module
+----------------------------------
+
+.. automodule:: mbtrack2.tracking.particles
+   :members:
+   :undoc-members:
+   :show-inheritance:
+
+mbtrack2.tracking.rf module
+---------------------------
+
+.. automodule:: mbtrack2.tracking.rf
+   :members:
+   :undoc-members:
+   :show-inheritance:
+
+mbtrack2.tracking.synchrotron module
+------------------------------------
+
+.. automodule:: mbtrack2.tracking.synchrotron
+   :members:
+   :undoc-members:
+   :show-inheritance:
+
+mbtrack2.tracking.wakepotential module
+--------------------------------------
+
+.. automodule:: mbtrack2.tracking.wakepotential
+   :members:
+   :undoc-members:
+   :show-inheritance:
+
+Module contents
+---------------
+
+.. automodule:: mbtrack2.tracking
+   :members:
+   :undoc-members:
+   :show-inheritance:
diff --git a/docs/source/mbtrack2.utilities.rst b/docs/source/mbtrack2.utilities.rst
new file mode 100644
index 0000000..e23f1f6
--- /dev/null
+++ b/docs/source/mbtrack2.utilities.rst
@@ -0,0 +1,53 @@
+mbtrack2.utilities package
+==========================
+
+Submodules
+----------
+
+mbtrack2.utilities.beamloading module
+-------------------------------------
+
+.. automodule:: mbtrack2.utilities.beamloading
+   :members:
+   :undoc-members:
+   :show-inheritance:
+
+mbtrack2.utilities.misc module
+------------------------------
+
+.. automodule:: mbtrack2.utilities.misc
+   :members:
+   :undoc-members:
+   :show-inheritance:
+
+mbtrack2.utilities.optics module
+--------------------------------
+
+.. automodule:: mbtrack2.utilities.optics
+   :members:
+   :undoc-members:
+   :show-inheritance:
+
+mbtrack2.utilities.read\_impedance module
+-----------------------------------------
+
+.. automodule:: mbtrack2.utilities.read_impedance
+   :members:
+   :undoc-members:
+   :show-inheritance:
+
+mbtrack2.utilities.spectrum module
+----------------------------------
+
+.. automodule:: mbtrack2.utilities.spectrum
+   :members:
+   :undoc-members:
+   :show-inheritance:
+
+Module contents
+---------------
+
+.. automodule:: mbtrack2.utilities
+   :members:
+   :undoc-members:
+   :show-inheritance:
-- 
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