diff --git a/.gitlab-ci.yml b/.gitlab-ci.yml
new file mode 100644
index 0000000000000000000000000000000000000000..40cdc34baf22bff3699e850b500f86582060bf71
--- /dev/null
+++ b/.gitlab-ci.yml
@@ -0,0 +1,83 @@
+stages:
+ - test
+ - build_docker
+ - build_pip
+
+.python_job:
+ image: gitlab-registry.synchrotron-soleil.fr/pa/collective-effects/python_mpi:latest
+ before_script:
+ - pip install poetry
+ - poetry install
+ - source `poetry env info --path`/bin/activate
+
+include:
+ - template: Jobs/Dependency-Scanning.gitlab-ci.yml
+
+testing:
+ extends: .python_job
+ stage: test
+ rules:
+ - if: '$CI_COMMIT_BRANCH == "stable"'
+ - if: '$CI_COMMIT_BRANCH == "develop"'
+ - if: '$CI_MERGE_REQUEST_TARGET_BRANCH_NAME == "stable"'
+ - if: '$CI_MERGE_REQUEST_TARGET_BRANCH_NAME == "develop"'
+ script:
+ - cd tests
+ - poetry run pytest --junitxml=report.xml
+ artifacts:
+ when: always
+ reports:
+ junit: /builds/PA/collective-effects/mbtrack2/tests/report.xml
+
+formatters:
+ extends: .python_job
+ stage: test
+ rules:
+ - if: '$CI_COMMIT_BRANCH == "stable"'
+ - if: '$CI_COMMIT_BRANCH == "develop"'
+ - if: '$CI_MERGE_REQUEST_TARGET_BRANCH_NAME == "stable"'
+ - if: '$CI_MERGE_REQUEST_TARGET_BRANCH_NAME == "develop"'
+ script:
+ - poetry run isort --check --diff mbtrack2/
+ - poetry run yapf -d -r mbtrack2/
+
+docker_develop:
+ stage: build_docker
+ rules:
+ - if: '$CI_COMMIT_BRANCH == "develop"'
+ image: docker:latest
+ services:
+ - docker:dind
+ variables:
+ CONTAINER_RELEASE_IMAGE: ${CI_REGISTRY_IMAGE}:develop
+ script:
+ - echo "${CI_REGISTRY_PASSWORD}" | docker login -u ${CI_REGISTRY_USER} --password-stdin ${CI_REGISTRY}
+ - docker build --pull -t ${CONTAINER_RELEASE_IMAGE} .
+ - docker push ${CONTAINER_RELEASE_IMAGE}
+
+docker_stable:
+ stage: build_docker
+ rules:
+ - if: '$CI_COMMIT_TAG'
+ image: docker:latest
+ services:
+ - docker:dind
+ variables:
+ CONTAINER_RELEASE_IMAGE: ${CI_REGISTRY_IMAGE}:latest
+ CONTAINER_TAG_IMAGE: ${CI_REGISTRY_IMAGE}:${CI_COMMIT_TAG}
+ script:
+ - echo "${CI_REGISTRY_PASSWORD}" | docker login -u ${CI_REGISTRY_USER} --password-stdin ${CI_REGISTRY}
+ - docker build --pull -t ${CONTAINER_RELEASE_IMAGE} .
+ - docker image tag ${CONTAINER_RELEASE_IMAGE} ${CONTAINER_TAG_IMAGE}
+ - docker push ${CONTAINER_RELEASE_IMAGE}
+ - docker push ${CONTAINER_TAG_IMAGE}
+
+pip_stable:
+ extends: .python_job
+ stage: build_pip
+ rules:
+ - if: '$CI_COMMIT_TAG'
+ script:
+ - poetry config repositories.gitlab ${CI_API_V4_URL}/projects/${CI_PROJECT_ID}/packages/pypi
+ - poetry build
+ - poetry publish --repository gitlab -u gitlab-ci-token -p ${CI_JOB_TOKEN}
diff --git a/CONTRIBUTORS.md b/CONTRIBUTORS.md
index 7464840088806af9649a343612171d6533d22de4..325b2f0eedbfbeb779b4940e8fb0db8b01d16f09 100644
--- a/CONTRIBUTORS.md
+++ b/CONTRIBUTORS.md
@@ -6,4 +6,5 @@ The following people contributed to the developpement of this code (chronologic
+ Naoto Yamamoto
+ David Amorim
+ Antonin Sauret
-+ Vadim Gubaidulin
\ No newline at end of file
++ Vadim Gubaidulin
++ Keon Hee Kim
\ No newline at end of file
diff --git a/Dockerfile b/Dockerfile
new file mode 100644
index 0000000000000000000000000000000000000000..18257107f17c4a6026d7dd4e3d99187cd914bd71
--- /dev/null
+++ b/Dockerfile
@@ -0,0 +1,8 @@
+FROM gitlab-registry.synchrotron-soleil.fr/pa/collective-effects/python_mpi:latest
+LABEL name mbtrack2
+USER dockeruser
+WORKDIR '/home/dockeruser'
+ENV PATH ${PATH}:/home/dockeruser/miniconda3/bin:/home/dockeruser/miniconda3/condabin
+RUN pip3 install accelerator-toolbox==0.5.0
+COPY --chown=dockeruser mbtrack2 /home/dockeruser/mbtrack2
+ENV PYTHONPATH=/home/dockeruser/
\ No newline at end of file
diff --git a/README.md b/README.md
index 44f9bcf9f11af399601309587396112afe8f524a..9591f8b37b4778b9cfb41f1f256f3db03510f67a 100644
--- a/README.md
+++ b/README.md
@@ -1,6 +1,10 @@
mbtrack2
========
+[](https://gitlab.synchrotron-soleil.fr/PA/collective-effects/mbtrack2/-/releases) [](https://pypi.org/project/mbtrack2/)
+[](https://gitlab.synchrotron-soleil.fr/PA/collective-effects/mbtrack2/-/blob/stable/LICENSE)
+[](https://mbtrack2.readthedocs.io/)
+
mbtrack2 is a coherent object-oriented framework written in python to work on collective effects in synchrotrons.
mbtrack2 is composed of different modules allowing to easily write scripts for single bunch or multi-bunch tracking using MPI parallelization in a transparent way. The base of the tracking model of mbtrack2 is inspired by mbtrack, a C multi-bunch tracking code initially developed at SOLEIL.
@@ -56,14 +60,22 @@ To test your installation run:
from mbtrack2 import *
```
+### Using docker
+
+A docker image is available:
+
+```
+docker pull gitlab-registry.synchrotron-soleil.fr/pa/collective-effects/mbtrack2
+```
+
References
----------
If used in a publication, please cite mbtrack2 paper and the zenodo archive for the corresponding code version (and any other paper in this list for more specific features).
-[](https://doi.org/10.5281/zenodo.10871040)
+[](https://doi.org/10.5281/zenodo.12749990)
### mbtrack2 general features
A. Gamelin, W. Foosang, and R. Nagaoka, “mbtrack2, a Collective Effect Library in Pythonâ€, presented at the 12th Int. Particle Accelerator Conf. (IPAC'21), Campinas, Brazil, May 2021, paper MOPAB070.
-### RF cavities with beam loading and RF feedbacks
-Yamamoto, Naoto, Alexis Gamelin, and Ryutaro Nagaoka. "Investigation of Longitudinal Beam Dynamics With Harmonic Cavities by Using the Code Mbtrack." Proc. 10th International Partile Accelerator Conference (IPAC’19), Melbourne, Australia, 19-24 May 2019. 2019.
\ No newline at end of file
+### RF cavities with beam loading and RF feedbacks
+Yamamoto, Naoto, Alexis Gamelin, and Ryutaro Nagaoka. "Investigation of Longitudinal Beam Dynamics With Harmonic Cavities by Using the Code Mbtrack." Proc. 10th International Partile Accelerator Conference (IPAC’19), Melbourne, Australia, 19-24 May 2019. 2019.
diff --git a/docs/Makefile b/docs/Makefile
new file mode 100644
index 0000000000000000000000000000000000000000..d0c3cbf1020d5c292abdedf27627c6abe25e2293
--- /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/doctrees/index.doctree b/docs/build/doctrees/index.doctree
new file mode 100644
index 0000000000000000000000000000000000000000..eb57e0b46145d7b096ddc76b4d820a8b7f7e194d
Binary files /dev/null and b/docs/build/doctrees/index.doctree differ
diff --git a/docs/build/doctrees/mbtrack2.doctree b/docs/build/doctrees/mbtrack2.doctree
new file mode 100644
index 0000000000000000000000000000000000000000..a5b1a56ba89b1f4b956901a54adba4bb6d3221d8
Binary files /dev/null and b/docs/build/doctrees/mbtrack2.doctree differ
diff --git a/docs/build/doctrees/mbtrack2.impedance.doctree b/docs/build/doctrees/mbtrack2.impedance.doctree
new file mode 100644
index 0000000000000000000000000000000000000000..ae1970528e641c512933c55c51fb4aacd33ef86e
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diff --git a/docs/build/doctrees/mbtrack2.instability.doctree b/docs/build/doctrees/mbtrack2.instability.doctree
new file mode 100644
index 0000000000000000000000000000000000000000..aaa04af300ac58f2443964a6adb89ed606b2c06a
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diff --git a/docs/build/doctrees/mbtrack2.tracking.doctree b/docs/build/doctrees/mbtrack2.tracking.doctree
new file mode 100644
index 0000000000000000000000000000000000000000..459d2142496649c20ffc34fed4ab8e1bc500e201
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diff --git a/docs/build/doctrees/mbtrack2.tracking.monitors.doctree b/docs/build/doctrees/mbtrack2.tracking.monitors.doctree
new file mode 100644
index 0000000000000000000000000000000000000000..0ecdc292209877337041fa2013e0ff4343617295
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diff --git a/docs/build/doctrees/mbtrack2.utilities.doctree b/docs/build/doctrees/mbtrack2.utilities.doctree
new file mode 100644
index 0000000000000000000000000000000000000000..19e22ab5a32453b1da96ce148913985adfc2c17b
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diff --git a/docs/build/html/.buildinfo b/docs/build/html/.buildinfo
new file mode 100644
index 0000000000000000000000000000000000000000..7c9c50a20abe1055dd514b743ad75a2d128fd3b9
--- /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 0000000000000000000000000000000000000000..9822c3adefc06cace1e2881aab84a321c8a83769
--- /dev/null
+++ b/docs/build/html/_modules/index.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" />
+ <title>Overview: module code — 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> »</li>
+ <li class="nav-item nav-item-this"><a href="">Overview: module code</a></li>
+ </ul>
+ </div>
+
+ <div class="document">
+ <div class="documentwrapper">
+ <div class="bodywrapper">
+ <div class="body" role="main">
+
+ <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>
+<li><a href="mbtrack2/tracking/element.html">mbtrack2.tracking.element</a></li>
+<li><a href="mbtrack2/tracking/feedback.html">mbtrack2.tracking.feedback</a></li>
+<li><a href="mbtrack2/tracking/monitors/monitors.html">mbtrack2.tracking.monitors.monitors</a></li>
+<li><a href="mbtrack2/tracking/monitors/plotting.html">mbtrack2.tracking.monitors.plotting</a></li>
+<li><a href="mbtrack2/tracking/monitors/tools.html">mbtrack2.tracking.monitors.tools</a></li>
+<li><a href="mbtrack2/tracking/parallel.html">mbtrack2.tracking.parallel</a></li>
+<li><a href="mbtrack2/tracking/particles.html">mbtrack2.tracking.particles</a></li>
+<li><a href="mbtrack2/tracking/rf.html">mbtrack2.tracking.rf</a></li>
+<li><a href="mbtrack2/tracking/synchrotron.html">mbtrack2.tracking.synchrotron</a></li>
+<li><a href="mbtrack2/tracking/wakepotential.html">mbtrack2.tracking.wakepotential</a></li>
+<li><a href="mbtrack2/utilities/beamloading.html">mbtrack2.utilities.beamloading</a></li>
+<li><a href="mbtrack2/utilities/misc.html">mbtrack2.utilities.misc</a></li>
+<li><a href="mbtrack2/utilities/optics.html">mbtrack2.utilities.optics</a></li>
+<li><a href="mbtrack2/utilities/read_impedance.html">mbtrack2.utilities.read_impedance</a></li>
+<li><a href="mbtrack2/utilities/spectrum.html">mbtrack2.utilities.spectrum</a></li>
+</ul>
+
+ <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> »</li>
+ <li class="nav-item nav-item-this"><a href="">Overview: module code</a></li>
+ </ul>
+ </div>
+ <div class="footer" role="contentinfo">
+ © 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/csr.html b/docs/build/html/_modules/mbtrack2/impedance/csr.html
new file mode 100644
index 0000000000000000000000000000000000000000..39459734430c5f0fab646413c7fe850a1c513311
--- /dev/null
+++ b/docs/build/html/_modules/mbtrack2/impedance/csr.html
@@ -0,0 +1,292 @@
+
+<!DOCTYPE html>
+
+<html lang="en">
+ <head>
+ <meta charset="utf-8" />
+ <meta name="viewport" content="width=device-width, initial-scale=1.0" />
+ <title>mbtrack2.impedance.csr — 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> »</li>
+ <li class="nav-item nav-item-1"><a href="../../index.html" accesskey="U">Module code</a> »</li>
+ <li class="nav-item nav-item-this"><a href="">mbtrack2.impedance.csr</a></li>
+ </ul>
+ </div>
+
+ <div class="document">
+ <div class="documentwrapper">
+ <div class="bodywrapper">
+ <div class="body" role="main">
+
+ <h1>Source code for mbtrack2.impedance.csr</h1><div class="highlight"><pre>
+<span></span><span class="c1"># -*- coding: utf-8 -*-</span>
+<span class="sd">"""</span>
+<span class="sd">Define coherent synchrotron radiation (CSR) wakefields in various models.</span>
+<span class="sd">"""</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">"""</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., & 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. "Calculation of coherent synchrotron </span>
+<span class="sd"> radiation using mesh." Physical Review Special Topics-Accelerators and </span>
+<span class="sd"> Beams 7.5 (2004): 054403.</span>
+
+<span class="sd"> """</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">'long'</span><span class="p">)</span>
+ <span class="c1"># Wlong = WakeFunction(variable = time, function = Wl, component_type="long")</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">"""</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 << (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. "Calculation of coherent synchrotron </span>
+<span class="sd"> radiation using mesh." Physical Review Special Topics-Accelerators and </span>
+<span class="sd"> Beams 7.5 (2004): 054403.</span>
+<span class="sd"> """</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">"""</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. "Calculation of coherent synchrotron </span>
+<span class="sd"> radiation using mesh." Physical Review Special Topics-Accelerators and </span>
+<span class="sd"> Beams 7.5 (2004): 054403.</span>
+
+<span class="sd"> """</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">'long'</span><span class="p">)</span>
+ <span class="c1"># Wlong = WakeFunction(variable = time, function = Wl, component_type="long")</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">"""Shielding threshold in the parallel plates model in [Hz]."""</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">"""</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. "Calculation of coherent synchrotron </span>
+<span class="sd"> radiation using mesh." Physical Review Special Topics-Accelerators and </span>
+<span class="sd"> Beams 7.5 (2004): 054403.</span>
+<span class="sd"> """</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">'r+s'</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">"""</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"> """</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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diff --git a/docs/build/html/_modules/mbtrack2/impedance/impedance_model.html b/docs/build/html/_modules/mbtrack2/impedance/impedance_model.html
new file mode 100644
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+++ b/docs/build/html/_modules/mbtrack2/impedance/impedance_model.html
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+<!DOCTYPE html>
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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">"""</span>
+<span class="sd">Module where the ImpedanceModel class is defined.</span>
+<span class="sd">"""</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">"""</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_"name" : WakeField</span>
+<span class="sd"> Sum of the "name" 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 "global" 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="Zlong", component="real", 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"> """</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">"""</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"> """</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">"Please give a valid name."</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">"This name is already taken."</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">"""</span>
+<span class="sd"> Add a "global" 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 "distributed" 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"> """</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">"Please give a valid name."</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">"This name is already taken."</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">"""</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"> """</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">"x"</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">"y"</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">"""</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"> """</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">"sum_"</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">"""</span>
+<span class="sd"> Compute the sum of all weighted WakeField into self.sum.</span>
+<span class="sd"> """</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">"sum"</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">"sum"</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">"sum"</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">'Zlong'</span><span class="p">]):</span>
+<span class="w"> </span><span class="sd">"""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 ['Zlong'].</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 'string_in_name'.</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."""</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">"""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'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's dictionary (__dict__) using the pop() method.</span>
+<span class="sd"> - The attribute is then added back to the class's dictionary with the new_name using the __dict__ attribute.</span>
+<span class="sd"> - If the old_name doesn't exist as an attribute in the ImpedanceModel, a KeyError is raised.</span>
+<span class="sd"> """</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">"Zlong"</span><span class="p">,</span>
+ <span class="n">component</span><span class="o">=</span><span class="s2">"real"</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">"""</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 "real" or "imag". </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"> """</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">"Zlong"</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span>
+ <span class="s2">"Zxdip"</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span>
+ <span class="s2">"Zydip"</span><span class="p">:</span> <span class="mi">2</span><span class="p">,</span>
+ <span class="s2">"Zxquad"</span><span class="p">:</span> <span class="mi">3</span><span class="p">,</span>
+ <span class="s2">"Zyquad"</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">"$Z_\mathrm</span><span class="si">{long}</span><span class="s2"> \; (\mathrm</span><span class="si">{k}</span><span class="s2">\Omega)$"</span><span class="p">,</span>
+ <span class="sa">r</span><span class="s2">"$\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">)$"</span><span class="p">,</span>
+ <span class="sa">r</span><span class="s2">"$\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">)$"</span><span class="p">,</span>
+ <span class="sa">r</span><span class="s2">"$\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">)$"</span><span class="p">,</span>
+ <span class="sa">r</span><span class="s2">"$\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">)$"</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">"Spectral density for sigma = "</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">" s"</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">'tab10'</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">"sum_"</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">'r'</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">"upper left"</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">"Frequency (GHz)"</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">" - "</span> <span class="o">+</span> <span class="n">component</span> <span class="o">+</span> <span class="s2">" part"</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">" - "</span> <span class="o">+</span> <span class="n">component</span> <span class="o">+</span> <span class="s2">" part"</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">"30%"</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">"Frequency (kHz)"</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">"$[\mathrm</span><span class="si">{G}</span><span class="s2">\Omega]$"</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">"Hermite"</span><span class="p">):</span>
+<span class="w"> </span><span class="sd">"""</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"> -"Hermite" 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"> """</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">"Zlong"</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">"Zxdip"</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">"Zydip"</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">"Z/n [mOhm]"</span><span class="p">,</span> <span class="s2">"sum betax x Zxeff [kOhm]"</span><span class="p">,</span>
+ <span class="s2">"sum betay x Zyeff [kOhm]"</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">"""</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"> """</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">>=</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">"Zlong"</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">"loss factor (beam) [V/pC]"</span><span class="p">,</span>
+ <span class="s2">"loss factor (bunch) [V/pC]"</span>
+ <span class="p">])</span>
+
+ <span class="n">summary</span><span class="p">[</span><span class="s2">"P (beam) [W]"</span><span class="p">]</span> <span class="o">=</span> <span class="n">summary</span><span class="p">[</span><span class="s2">"loss factor (beam) [V/pC]"</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">"P (bunch) [W]"</span><span class="p">]</span> <span class="o">=</span> <span class="n">summary</span><span class="p">[</span><span class="s2">"loss factor (bunch) [V/pC]"</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">"""</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. "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", in IPAC'18, 2018, doi:10.18429/JACoW-IPAC2018-THPAK093</span>
+
+<span class="sd"> """</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">>=</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">"r"</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s2">"Re[Z] [Ohm]"</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">"b"</span><span class="p">,</span>
+ <span class="n">label</span><span class="o">=</span><span class="s2">"Beam spectrum [a.u.]"</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">"Frequency [Hz]"</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">"Re[Z] [Ohm]"</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">"Beam spectrum [a.u.]"</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">"best"</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">"Frequency [Hz]"</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">"Power loss [W]"</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">"""</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"> """</span>
+ <span class="n">to_save</span> <span class="o">=</span> <span class="p">{</span>
+ <span class="s2">"wakefields"</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">"positions"</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">"names"</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">"globals"</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">"globals_names"</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">"wb"</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">"""</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"> """</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">'rb'</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">"wakefields"</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">"positions"</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">"names"</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">"globals"</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">"globals_names"</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>
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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">"""</span>
+<span class="sd">Define resistive wall elements based on the WakeField class.</span>
+<span class="sd">"""</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">"""</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"> """</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">"""</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. "Simultaneous computation of intrabunch and </span>
+<span class="sd"> interbunch collective beam motions in storage rings." 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"> """</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">'long'</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">'xdip'</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">'ydip'</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">"long"</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">"xdip"</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">"ydip"</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">"""</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. "Simultaneous computation of intrabunch and </span>
+<span class="sd"> interbunch collective beam motions in storage rings." 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"> """</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"><</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">></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">"""</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. "Simultaneous computation of intrabunch and </span>
+<span class="sd"> interbunch collective beam motions in storage rings." 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"> """</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"><</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">></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">"""</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. "Impact of the resistive </span>
+<span class="sd"> wall impedance on beam dynamics in the Future Circular e+ e− Collider." </span>
+<span class="sd"> Physical Review Accelerators and Beams 21.4 (2018): 041001.</span>
+
+<span class="sd"> """</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">'long'</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">'xdip'</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">'ydip'</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">"""</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. "Impact of the resistive </span>
+<span class="sd"> wall impedance on beam dynamics in the Future Circular e+ e− Collider." </span>
+<span class="sd"> Physical Review Accelerators and Beams 21.4 (2018): 041001.</span>
+
+<span class="sd"> """</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"><</span> <span class="mf">0.01</span><span class="p">:</span>
+ <span class="nb">print</span><span class="p">(</span>
+ <span class="s2">"Approximation is not valid. Returning impedance anyway."</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">"""</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. "Impact of the resistive </span>
+<span class="sd"> wall impedance on beam dynamics in the Future Circular e+ e− Collider." </span>
+<span class="sd"> Physical Review Accelerators and Beams 21.4 (2018): 041001.</span>
+
+<span class="sd"> """</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"><</span> <span class="mf">0.01</span><span class="p">:</span>
+ <span class="nb">print</span><span class="p">(</span>
+ <span class="s2">"Approximation is not valid. Returning impedance anyway."</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>
+
+ <div class="clearer"></div>
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diff --git a/docs/build/html/_modules/mbtrack2/impedance/resonator.html b/docs/build/html/_modules/mbtrack2/impedance/resonator.html
new file mode 100644
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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">"""</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">"""</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">"""</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 < 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: "long", "x" or "y".</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, "Impedances and Wakes in High-Energy </span>
+<span class="sd"> Particle Ac-celerators", Eq. (3.10) and (3.15), pp.51-53.</span>
+
+<span class="sd"> """</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">>=</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">"long"</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">"long"</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">"long"</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">"x"</span> <span class="ow">or</span> <span class="n">dim</span> <span class="o">==</span> <span class="s2">"y"</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">"dip"</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">"dip"</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">"Plane must be: long, x or y"</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">>=</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"><</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"><</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"><</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"><</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"><</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"><</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">>=</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"><</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"><</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">"""</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"> """</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">"long"</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">"""</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"> """</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">"long"</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>
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+ <li class="nav-item nav-item-1"><a href="../../index.html" >Module code</a> »</li>
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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 0000000000000000000000000000000000000000..ce74a42fbbd6f95c80bff9aee9a349da0a3675fc
--- /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 — mbtrack2 0.6.0 documentation</title>
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+ <link rel="stylesheet" type="text/css" href="../../../_static/nature.css" />
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+ <li class="nav-item nav-item-1"><a href="../../index.html" accesskey="U">Module code</a> »</li>
+ <li class="nav-item nav-item-this"><a href="">mbtrack2.impedance.tapers</a></li>
+ </ul>
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+ <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">"""</span>
+<span class="sd">Module where taper elements are defined.</span>
+<span class="sd">"""</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">"""</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"> """</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">'long'</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">'xdip'</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">'ydip'</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">'xquad'</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">'yquad'</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">"""</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"> """</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">'long'</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">'xdip'</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">'ydip'</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>
+ </div>
+ </div>
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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 0000000000000000000000000000000000000000..2a1e6d5d440e4e9a299663ba4c7f1a342a198de8
--- /dev/null
+++ b/docs/build/html/_modules/mbtrack2/impedance/wakefield.html
@@ -0,0 +1,1142 @@
+
+<!DOCTYPE html>
+
+<html lang="en">
+ <head>
+ <meta charset="utf-8" />
+ <meta name="viewport" content="width=device-width, initial-scale=1.0" />
+ <title>mbtrack2.impedance.wakefield — mbtrack2 0.6.0 documentation</title>
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+ <li class="nav-item nav-item-1"><a href="../../index.html" accesskey="U">Module code</a> »</li>
+ <li class="nav-item nav-item-this"><a href="">mbtrack2.impedance.wakefield</a></li>
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+ </div>
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+ <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">"""</span>
+<span class="sd">This module defines general classes to describes wakefields, impedances and </span>
+<span class="sd">wake functions.</span>
+<span class="sd">"""</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">"""</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"> """</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">'real'</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">'imag'</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">'variable'</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">'zero'</span><span class="p">,</span>
+ <span class="n">interp_kind</span><span class="o">=</span><span class="s1">'cubic'</span><span class="p">,</span>
+ <span class="n">index_name</span><span class="o">=</span><span class="s2">"variable"</span><span class="p">):</span>
+<span class="w"> </span><span class="sd">"""</span>
+<span class="sd"> Method to add two structures. If the data don'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 "common" 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"> """</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">'first'</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">'first'</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">'common'</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"><=</span> <span class="n">max_variable</span><span class="p">)</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">>=</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"><=</span> <span class="n">max_variable</span><span class="p">)</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">>=</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">'extrapolate'</span><span class="p">:</span>
+ <span class="nb">print</span><span class="p">(</span><span class="s1">'Not there yet'</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">'zero'</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"><=</span> <span class="n">max_variable</span><span class="p">)</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">>=</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"><=</span> <span class="n">max_variable</span><span class="p">)</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">>=</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">'zero'</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">'zero'</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">"""</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"> """</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">'The multiplication factor is not a float '</span>
+ <span class="s1">'or an int.'</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">"cubic"</span><span class="p">):</span>
+<span class="w"> </span><span class="sd">"""</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"> """</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">"real"</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">"imag"</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">"""Return representation of data"""</span>
+ <span class="k">return</span> <span class="sa">f</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">'</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">"""</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"> """</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">'Component type </span><span class="si">{}</span><span class="s1"> does not exist'</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">"a"</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">"b"</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">"c"</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">"d"</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">"plane"</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">"""</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"> """</span>
+
+ <span class="n">component_dict</span> <span class="o">=</span> <span class="p">{</span>
+ <span class="s1">'long'</span><span class="p">:</span> <span class="p">{</span>
+ <span class="s1">'a'</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span>
+ <span class="s1">'b'</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span>
+ <span class="s1">'c'</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span>
+ <span class="s1">'d'</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span>
+ <span class="s1">'plane'</span><span class="p">:</span> <span class="s1">'z'</span>
+ <span class="p">},</span>
+ <span class="s1">'xcst'</span><span class="p">:</span> <span class="p">{</span>
+ <span class="s1">'a'</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span>
+ <span class="s1">'b'</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span>
+ <span class="s1">'c'</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span>
+ <span class="s1">'d'</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span>
+ <span class="s1">'plane'</span><span class="p">:</span> <span class="s1">'x'</span>
+ <span class="p">},</span>
+ <span class="s1">'ycst'</span><span class="p">:</span> <span class="p">{</span>
+ <span class="s1">'a'</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span>
+ <span class="s1">'b'</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span>
+ <span class="s1">'c'</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span>
+ <span class="s1">'d'</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span>
+ <span class="s1">'plane'</span><span class="p">:</span> <span class="s1">'y'</span>
+ <span class="p">},</span>
+ <span class="s1">'xdip'</span><span class="p">:</span> <span class="p">{</span>
+ <span class="s1">'a'</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span>
+ <span class="s1">'b'</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span>
+ <span class="s1">'c'</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span>
+ <span class="s1">'d'</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span>
+ <span class="s1">'plane'</span><span class="p">:</span> <span class="s1">'x'</span>
+ <span class="p">},</span>
+ <span class="s1">'ydip'</span><span class="p">:</span> <span class="p">{</span>
+ <span class="s1">'a'</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span>
+ <span class="s1">'b'</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span>
+ <span class="s1">'c'</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span>
+ <span class="s1">'d'</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span>
+ <span class="s1">'plane'</span><span class="p">:</span> <span class="s1">'y'</span>
+ <span class="p">},</span>
+ <span class="s1">'xydip'</span><span class="p">:</span> <span class="p">{</span>
+ <span class="s1">'a'</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span>
+ <span class="s1">'b'</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span>
+ <span class="s1">'c'</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span>
+ <span class="s1">'d'</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span>
+ <span class="s1">'plane'</span><span class="p">:</span> <span class="s1">'x'</span>
+ <span class="p">},</span>
+ <span class="s1">'yxdip'</span><span class="p">:</span> <span class="p">{</span>
+ <span class="s1">'a'</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span>
+ <span class="s1">'b'</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span>
+ <span class="s1">'c'</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span>
+ <span class="s1">'d'</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span>
+ <span class="s1">'plane'</span><span class="p">:</span> <span class="s1">'y'</span>
+ <span class="p">},</span>
+ <span class="s1">'xquad'</span><span class="p">:</span> <span class="p">{</span>
+ <span class="s1">'a'</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span>
+ <span class="s1">'b'</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span>
+ <span class="s1">'c'</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span>
+ <span class="s1">'d'</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span>
+ <span class="s1">'plane'</span><span class="p">:</span> <span class="s1">'x'</span>
+ <span class="p">},</span>
+ <span class="s1">'yquad'</span><span class="p">:</span> <span class="p">{</span>
+ <span class="s1">'a'</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span>
+ <span class="s1">'b'</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span>
+ <span class="s1">'c'</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span>
+ <span class="s1">'d'</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span>
+ <span class="s1">'plane'</span><span class="p">:</span> <span class="s1">'y'</span>
+ <span class="p">},</span>
+ <span class="s1">'xyquad'</span><span class="p">:</span> <span class="p">{</span>
+ <span class="s1">'a'</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span>
+ <span class="s1">'b'</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span>
+ <span class="s1">'c'</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span>
+ <span class="s1">'d'</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span>
+ <span class="s1">'plane'</span><span class="p">:</span> <span class="s1">'x'</span>
+ <span class="p">},</span>
+ <span class="s1">'yxquad'</span><span class="p">:</span> <span class="p">{</span>
+ <span class="s1">'a'</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span>
+ <span class="s1">'b'</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span>
+ <span class="s1">'c'</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span>
+ <span class="s1">'d'</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span>
+ <span class="s1">'plane'</span><span class="p">:</span> <span class="s1">'y'</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">'x'</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">'y'</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">"""</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 "long" and in [V/C/m] for others.</span>
+<span class="sd"> component_type : str, optinal</span>
+<span class="sd"> Type of the wake function: "long", "xdip", "xquad", ...</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"> """</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">'long'</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">"time [s]"</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">"""Return representation of data"""</span>
+ <span class="k">return</span> <span class="sa">f</span><span class="s1">'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">'</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">'zero'</span><span class="p">):</span>
+<span class="w"> </span><span class="sd">"""</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"> """</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">"time [s]"</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">"time [s]"</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">'The two WakeFunction objects do not have the '</span>
+ <span class="s1">'same coordinates or plane or type. '</span>
+ <span class="s1">'Returning initial WakeFunction object.'</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">"""</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"> """</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">"""</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 > n, the</span>
+<span class="sd"> input is padded with zeros. If nout < 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"> """</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">"real"</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"><</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">"long"</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">"xdip"</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">"ydip"</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">" is not correct."</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">"""</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 "-1 * ISIG * SIG / c".</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 > n, the</span>
+<span class="sd"> input is padded with zeros. If nout < 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"> """</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">"""</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"> """</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">"real"</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">"long"</span><span class="p">:</span>
+ <span class="n">unit</span> <span class="o">=</span> <span class="s2">" [V/C]"</span>
+ <span class="k">else</span><span class="p">:</span>
+ <span class="n">unit</span> <span class="o">=</span> <span class="s2">" [V/C/m]"</span>
+ <span class="n">label</span> <span class="o">=</span> <span class="sa">r</span><span class="s2">"$W_{"</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">"}$"</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">"""</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"> """</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">"real"</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">"""</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: "long", "xdip", "xquad", ...</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"> """</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">'long'</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">'frequency [Hz]'</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">"""Return representation of data"""</span>
+ <span class="k">return</span> <span class="sa">f</span><span class="s1">'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">'</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">'zero'</span><span class="p">):</span>
+<span class="w"> </span><span class="sd">"""</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"> """</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">"frequency [Hz]"</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">"frequency [Hz]"</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">'The two Impedance objects do not have the '</span>
+ <span class="s1">'same coordinates or plane or type. '</span>
+ <span class="s1">'Returning initial Impedance object.'</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">"""</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"> """</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">"""</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"> """</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">></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">"long"</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">"real"</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">"xdip"</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">"ydip"</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">"imag"</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">"xquad"</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">"yquad"</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">"imag"</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">"Impedance type not recognized."</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">"""</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 > n, the</span>
+<span class="sd"> input is padded with zeros. If nout < 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<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 <= trim to 0. </span>
+<span class="sd"> """</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">'real'</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">'imag'</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">"long"</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"><</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">"""</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"> """</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">"long"</span><span class="p">:</span>
+ <span class="n">unit</span> <span class="o">=</span> <span class="s2">" [ohm]"</span>
+ <span class="k">else</span><span class="p">:</span>
+ <span class="n">unit</span> <span class="o">=</span> <span class="s2">" [ohm/m]"</span>
+ <span class="n">label</span> <span class="o">=</span> <span class="sa">r</span><span class="s2">"$Z_{"</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">"}$"</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">"""</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"> """</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">"""Return representation of WakeField components."""</span>
+ <span class="k">return</span> <span class="sa">f</span><span class="s1">'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">'</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">"""Iterate over components"""</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">"""Allow to add two WakeField element with different components."""</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">"""</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"> """</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">"Z"</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">"There is already a component of the type "</span>
+ <span class="s2">"</span><span class="si">{}</span><span class="s2"> in this element."</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">"W"</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">"There is already a component of the type "</span>
+ <span class="s2">"</span><span class="si">{}</span><span class="s2"> in this element."</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">"</span><span class="si">{}</span><span class="s2"> is not an Impedance nor a WakeFunction."</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">"""</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"> """</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">"""</span>
+<span class="sd"> Return an array of the impedance component names for the element.</span>
+<span class="sd"> """</span>
+ <span class="n">valid</span> <span class="o">=</span> <span class="p">[</span>
+ <span class="s2">"Zlong"</span><span class="p">,</span> <span class="s2">"Zxdip"</span><span class="p">,</span> <span class="s2">"Zydip"</span><span class="p">,</span> <span class="s2">"Zxquad"</span><span class="p">,</span> <span class="s2">"Zyquad"</span><span class="p">,</span> <span class="s2">"Zxcst"</span><span class="p">,</span> <span class="s2">"Zycst"</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">"""</span>
+<span class="sd"> Return an array of the wake function component names for the element.</span>
+<span class="sd"> """</span>
+ <span class="n">valid</span> <span class="o">=</span> <span class="p">[</span>
+ <span class="s2">"Wlong"</span><span class="p">,</span> <span class="s2">"Wxdip"</span><span class="p">,</span> <span class="s2">"Wydip"</span><span class="p">,</span> <span class="s2">"Wxquad"</span><span class="p">,</span> <span class="s2">"Wyquad"</span><span class="p">,</span> <span class="s2">"Wxcst"</span><span class="p">,</span> <span class="s2">"Wycst"</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">"""</span>
+<span class="sd"> Return an array of the component names for the element.</span>
+<span class="sd"> """</span>
+ <span class="n">valid</span> <span class="o">=</span> <span class="p">[</span>
+ <span class="s2">"Wlong"</span><span class="p">,</span> <span class="s2">"Wxdip"</span><span class="p">,</span> <span class="s2">"Wydip"</span><span class="p">,</span> <span class="s2">"Wxquad"</span><span class="p">,</span> <span class="s2">"Wyquad"</span><span class="p">,</span> <span class="s2">"Wxcst"</span><span class="p">,</span> <span class="s2">"Wycst"</span><span class="p">,</span>
+ <span class="s2">"Zlong"</span><span class="p">,</span> <span class="s2">"Zxdip"</span><span class="p">,</span> <span class="s2">"Zydip"</span><span class="p">,</span> <span class="s2">"Zxquad"</span><span class="p">,</span> <span class="s2">"Zyquad"</span><span class="p">,</span> <span class="s2">"Zxcst"</span><span class="p">,</span> <span class="s2">"Zycst"</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">"""</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 "Z", drop all impedance components.</span>
+<span class="sd"> If "W"", drop all wake function components.</span>
+
+<span class="sd"> Returns</span>
+<span class="sd"> -------</span>
+<span class="sd"> None.</span>
+
+<span class="sd"> """</span>
+ <span class="k">if</span> <span class="n">component</span> <span class="o">==</span> <span class="s2">"Z"</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">"W"</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">"component should be a str or list of str."</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">"""</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"> """</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">"wb"</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">"""</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"> """</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">'rb'</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">"""</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"> """</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">"""</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"> """</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">></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">"Error in input."</span><span class="p">)</span></div></div>
+</pre></div>
+
+ <div class="clearer"></div>
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+++ b/docs/build/html/_modules/mbtrack2/instability/instabilities.html
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+<!DOCTYPE html>
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+<html lang="en">
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+
+ <h1>Source code for mbtrack2.instability.instabilities</h1><div class="highlight"><pre>
+<span></span><span class="c1"># -*- coding: utf-8 -*-</span>
+<span class="sd">"""</span>
+<span class="sd">General calculations about instability thresholds.</span>
+<span class="sd">"""</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">"""</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, "Theory of microwave instability and coherent synchrotron </span>
+<span class="sd"> radiation in electron storage rings", SLAC-PUB-14561</span>
+<span class="sd"> [2] : D. Zhou, "Coherent synchrotron radiation and microwave instability in </span>
+<span class="sd"> electron storage rings", PhD thesis, p112</span>
+<span class="sd"> """</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">"""</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. "Calculation of Transverse Coupled Bunch </span>
+<span class="sd"> Instabilities in Electron Storage Rings Driven By Quadrupole Higher Order </span>
+<span class="sd"> Modes." 7th Int. Particle Accelerator Conf.(IPAC'16), Busan, Korea. </span>
+<span class="sd"> """</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">"""</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. "RF System for Electron Storage </span>
+<span class="sd"> Rings." 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"> """</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">"Either synchrotron_tune or Vrf is needed."</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">"""</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. "RF System for Electron Storage </span>
+<span class="sd"> Rings." 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"> """</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">"""</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"> """</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">"$\mu$ = "</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">"$\Delta f$ [kHz]"</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">"$R_{s,max}$ $[M\Omega]$"</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">"log"</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">'x'</span><span class="p">):</span>
+<span class="w"> </span><span class="sd">"""</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'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 'x' for the </span>
+<span class="sd"> horizontal plane, and 'y' 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, "Collective effects in a</span>
+<span class="sd"> diffraction-limited storage ring", J. Synchrotron Rad. Vol 21, 2014. pp.937-960 </span>
+
+<span class="sd"> """</span>
+ <span class="n">plane_dict</span> <span class="o">=</span> <span class="p">{</span><span class="s1">'x'</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="s1">'y'</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">'x'</span><span class="p">):</span>
+<span class="w"> </span><span class="sd">"""</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'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 'x' for the </span>
+<span class="sd"> horizontal plane, and 'y' 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, "Collective effects in a</span>
+<span class="sd"> diffraction-limited storage ring", J. Synchrotron Rad. Vol 21, 2014. pp.937-960 </span>
+
+<span class="sd"> """</span>
+ <span class="n">plane_dict</span> <span class="o">=</span> <span class="p">{</span><span class="s1">'x'</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="s1">'y'</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>
+
+ <div class="clearer"></div>
+ </div>
+ </div>
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diff --git a/docs/build/html/_modules/mbtrack2/instability/ions.html b/docs/build/html/_modules/mbtrack2/instability/ions.html
new file mode 100644
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--- /dev/null
+++ b/docs/build/html/_modules/mbtrack2/instability/ions.html
@@ -0,0 +1,393 @@
+
+<!DOCTYPE html>
+
+<html lang="en">
+ <head>
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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">"""</span>
+<span class="sd">Various calculations about ion trapping and instabilities in electron storage </span>
+<span class="sd">rings.</span>
+<span class="sd">"""</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">"classical electron radius"</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">"""</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, "Inelastic collisions of fast charged particles with </span>
+<span class="sd"> atoms and molecules-the bethe theory revisited", Reviews of modern physics </span>
+<span class="sd"> 43 (1971).</span>
+<span class="sd"> [2] : P. F. Tavares, "Bremsstrahlung detection of ions trapped in the EPA </span>
+<span class="sd"> electron beam", Part. Accel. 43 (1993).</span>
+
+<span class="sd"> """</span>
+ <span class="k">if</span> <span class="n">ion</span> <span class="o">==</span> <span class="s2">"CO"</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">"H2"</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">"CO"</span><span class="p">,</span>
+ <span class="n">dim</span><span class="o">=</span><span class="s2">"y"</span><span class="p">,</span>
+ <span class="n">express</span><span class="o">=</span><span class="s2">"coupling"</span><span class="p">):</span>
+<span class="w"> </span><span class="sd">"""</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 "CO".</span>
+<span class="sd"> dim : "y" o "x", optional</span>
+<span class="sd"> Dimension to consider. The default is "y".</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 "coupling" corresponding to Gaussian electron and ion </span>
+<span class="sd"> distributions with coupling [1].</span>
+<span class="sd"> Also possible is "no_coupling" 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, "Fast beam-ion instability. I. </span>
+<span class="sd"> linear theory and simulations", Physical Review E 52 (1995).</span>
+<span class="sd"> [2] : G. V. Stupakov, T. O. Raubenheimer, and F. Zimmermann, "Fast beam-ion </span>
+<span class="sd"> instability. II. effect of ion decoherence", Physical Review E 52 (1995).</span>
+
+<span class="sd"> """</span>
+
+ <span class="k">if</span> <span class="n">ion</span> <span class="o">==</span> <span class="s2">"CO"</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">"H2"</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">"CH4"</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">"H2O"</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">"CO2"</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">"y"</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">"x"</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">"coupling"</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">"no_coupling"</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">"linear"</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">"CO"</span><span class="p">,</span>
+ <span class="n">dim</span><span class="o">=</span><span class="s2">"y"</span><span class="p">):</span>
+<span class="w"> </span><span class="sd">"""</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="linear", 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="decoherence", 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="non-linear", 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 << sigmax,sigmay</span>
+<span class="sd"> </span>
+<span class="sd"> The decoherence model assumes that [2]:</span>
+<span class="sd"> Lsep << c / (2 * pi * ion_frequency) </span>
+<span class="sd"> Lsep << 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 >> 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 "linear", use [1].</span>
+<span class="sd"> If "decoherence", use [2].</span>
+<span class="sd"> If "non-linear", 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 "CO".</span>
+<span class="sd"> dim : "y" o "x", optional</span>
+<span class="sd"> Dimension to consider. The default is "y".</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, "Fast beam-ion instability. I. </span>
+<span class="sd"> linear theory and simulations", Physical Review E 52 (1995).</span>
+<span class="sd"> [2] : G. V. Stupakov, T. O. Raubenheimer, and F. Zimmermann, "Fast beam-ion </span>
+<span class="sd"> instability. II. effect of ion decoherence", Physical Review E 52 (1995).</span>
+<span class="sd"> [3] : Chao, A. W., & 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"> """</span>
+ <span class="k">if</span> <span class="n">dim</span> <span class="o">==</span> <span class="s2">"y"</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">"x"</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">"CO"</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">"H2"</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">"decoherence"</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">"non-linear"</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">"linear"</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">"model unknown"</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">"""</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"> """</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">"$A_x^c$"</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">"$A_y^c$"</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">"log"</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">"$H_2^+$"</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">"$H_2O^+$"</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">"$CH_4^+$"</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">"$CO^+$"</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">"$CO_2^+$"</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">"Critical mass"</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">"Longitudinal position [m]"</span><span class="p">)</span>
+
+ <span class="k">return</span> <span class="n">fig</span></div>
+</pre></div>
+
+ <div class="clearer"></div>
+ </div>
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@@ -0,0 +1,245 @@
+
+<!DOCTYPE html>
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+
+ <h1>Source code for mbtrack2.tracking.aperture</h1><div class="highlight"><pre>
+<span></span><span class="c1"># -*- coding: utf-8 -*-</span>
+<span class="sd">"""</span>
+<span class="sd">This module defines aperture elements for tracking.</span>
+<span class="sd">"""</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">"""</span>
+<span class="sd"> Circular aperture element. The particles which are outside of the circle </span>
+<span class="sd"> are 'lost' 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"> """</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">"""</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"> """</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">"x"</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">"y"</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">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">"""</span>
+<span class="sd"> Eliptical aperture element. The particles which are outside of the elipse </span>
+<span class="sd"> are 'lost' 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"> """</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">"""</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"> """</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">"x"</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">"y"</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"><</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">"""</span>
+<span class="sd"> Rectangular aperture element. The particles which are outside of the </span>
+<span class="sd"> rectangle are 'lost' 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"> """</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">"""</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"> """</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">"x"</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="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">"x"</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="p">(</span><span class="n">bunch</span><span class="o">.</span><span class="n">particles</span><span class="p">[</span><span class="s2">"x"</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="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">"y"</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="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">"y"</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="p">(</span><span class="n">bunch</span><span class="o">.</span><span class="n">particles</span><span class="p">[</span><span class="s2">"y"</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="n">alive</span> <span class="o">=</span> <span class="n">alive_X</span> <span class="o">&</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">"""</span>
+<span class="sd"> Longitudinal aperture element. The particles which are outside of the </span>
+<span class="sd"> longitudinal bounds are 'lost' 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"> """</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">"""</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"> """</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">"tau"</span><span class="p">]</span> <span class="o"><</span> <span class="bp">self</span><span class="o">.</span><span class="n">tau_up</span><span class="p">)</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">"tau"</span><span class="p">]</span> <span class="o">></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">
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+ <li class="nav-item nav-item-1"><a href="../../index.html" >Module code</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/element.html b/docs/build/html/_modules/mbtrack2/tracking/element.html
new file mode 100644
index 0000000000000000000000000000000000000000..9c89459448b0f56e113742a3515944318254c030
--- /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 — mbtrack2 0.6.0 documentation</title>
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+ <li class="nav-item nav-item-1"><a href="../../index.html" accesskey="U">Module code</a> »</li>
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+ <div class="documentwrapper">
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+ <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">"""</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">"""</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">"""</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"> """</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">"""</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"> """</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">"""</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"> """</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">"""</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"> """</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">"""</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"> """</span>
+ <span class="n">bunch</span><span class="p">[</span><span class="s2">"delta"</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">"tau"</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">"delta"</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">"delta"</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">"""</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"> """</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">"""</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"> """</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">"delta"</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">"delta"</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">"xp"</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">"xp"</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">"yp"</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">"yp"</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">"""</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"> """</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">"""</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"> """</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">"delta"</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">"delta"</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">'x'</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">'x'</span><span class="p">]</span><span class="o">*</span><span class="n">bunch</span><span class="p">[</span><span class="s1">'xp'</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">'xp'</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">'y'</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">'y'</span><span class="p">]</span><span class="o">*</span><span class="n">bunch</span><span class="p">[</span><span class="s1">'yp'</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">'yp'</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">"delta"</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">"delta"</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">"x"</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">"xp"</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">"delta"</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">"x"</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">"xp"</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">"delta"</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">"y"</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">"yp"</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">"delta"</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">"y"</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">"yp"</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">"delta"</span><span class="p">]</span>
+
+ <span class="n">bunch</span><span class="p">[</span><span class="s2">"x"</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">"xp"</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">"y"</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">"yp"</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">"""</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"> """</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">"""</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"> """</span>
+
+ <span class="n">bunch</span><span class="p">[</span><span class="s1">'xp'</span><span class="p">]</span> <span class="o">=</span> <span class="n">bunch</span><span class="p">[</span><span class="s1">'xp'</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">'y'</span><span class="p">]</span>
+ <span class="n">bunch</span><span class="p">[</span><span class="s1">'yp'</span><span class="p">]</span> <span class="o">=</span> <span class="n">bunch</span><span class="p">[</span><span class="s1">'yp'</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">'x'</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">"""</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"> """</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">"""</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"> """</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">"delta"</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">"delta"</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">'x'</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">'x'</span><span class="p">]</span><span class="o">*</span><span class="bp">self</span><span class="p">[</span><span class="s1">'xp'</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">'xp'</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">'y'</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">'y'</span><span class="p">]</span><span class="o">*</span><span class="n">bunch</span><span class="p">[</span><span class="s1">'yp'</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">'yp'</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">"delta"</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">"delta"</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">"x"</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">"xp"</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">"delta"</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">"x"</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">"xp"</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">"delta"</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">"y"</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">"yp"</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">"delta"</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">"y"</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">"yp"</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">"delta"</span><span class="p">]</span>
+
+ <span class="n">bunch</span><span class="p">[</span><span class="s2">"x"</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">"xp"</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">"y"</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">"yp"</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">"""</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"> """</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">"END"</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">"s_pos"</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">'mu'</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">'mu'</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">'mu'</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">'mu'</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">"The Synchrotron object must be loaded from an AT lattice"</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>
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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 0000000000000000000000000000000000000000..3db407b7b7d6a0137df6b73bcb1270663b652f57
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+ <h1>Source code for mbtrack2.tracking.feedback</h1><div class="highlight"><pre>
+<span></span><span class="c1"># -*- coding: utf-8 -*-</span>
+<span class="sd">"""</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">"""</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">""" </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 : {"x","y","s"}</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"> """</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">"x"</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">"xp"</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">"y"</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">"yp"</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">"s"</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">"delta"</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">"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">"</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">"""</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"> """</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">""" </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 : {"x","y","s"}</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 "x" or "y" and [s] if the plane is "s".</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 "x" or "y" and no unit (delta) if the </span>
+<span class="sd"> plane is "s".</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"> """</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">"x"</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">"xp"</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">"y"</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">"yp"</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">"s"</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">"delta"</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">"""</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"> """</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">"""</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"> """</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">"Gain"</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">"Tune"</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">"Phase in degree"</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">"""</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"> """</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">"beam_or_bunch must be a Beam or Bunch"</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">"""</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"> """</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">"""</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"> """</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">></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"><</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>
+ </div>
+ <div class="sphinxsidebar" role="navigation" aria-label="main navigation">
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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> »</li>
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+ Created using <a href="https://www.sphinx-doc.org/">Sphinx</a> 5.0.2.
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+</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 0000000000000000000000000000000000000000..713b2e2acd016fddad1d841c933a8fa359714c1b
--- /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 — 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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+ >modules</a> |</li>
+ <li class="nav-item nav-item-0"><a href="../../../../index.html">mbtrack2 0.6.0 documentation</a> »</li>
+ <li class="nav-item nav-item-1"><a href="../../../index.html" accesskey="U">Module code</a> »</li>
+ <li class="nav-item nav-item-this"><a href="">mbtrack2.tracking.monitors.monitors</a></li>
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+ <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">"""</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">"""</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">"""</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"> """</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">"""Common file where all monitors, Monitor subclass elements, write the</span>
+<span class="sd"> saved data."""</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">"The HDF5 file name for monitors is not set."</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">"""Name of the HDF5 file where the data is stored."""</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">"The HDF5 file to store data is not set."</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">"""</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"> """</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">".hdf5"</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">"a"</span><span class="p">,</span>
+ <span class="n">libver</span><span class="o">=</span><span class="s1">'earliest'</span><span class="p">,</span>
+ <span class="n">driver</span><span class="o">=</span><span class="s1">'mpio'</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">"a"</span><span class="p">,</span> <span class="n">libver</span><span class="o">=</span><span class="s1">'earliest'</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">"File is already open."</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">"File name for monitors is already attributed."</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">"total_size must be divisible by buffer_size."</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">"time"</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">"""Write data from buffer to the HDF5 file."""</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">"time"</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">"""</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"> """</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">"""</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"> """</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">"""</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"> """</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">"object_to_save should be a Beam or Bunch object."</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">"""</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"> """</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">"BunchData_"</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">"mean"</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">"std"</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">"emit"</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">"current"</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">"cs_invariant"</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">"mean"</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">"std"</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">"emit"</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">"current"</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">"cs_invariant"</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">"""</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"> """</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">"""</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"> """</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">"PhaseSpaceData_"</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">"particles"</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">"alive"</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">"particles"</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">"alive"</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">"""</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"> """</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">"""</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"> """</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">"""</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"> """</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">"Beam"</span>
+ <span class="n">dict_buffer</span> <span class="o">=</span> <span class="p">{</span>
+ <span class="s2">"mean"</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">"std"</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">"emit"</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">"current"</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">"cs_invariant"</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">"mean"</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">"std"</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">"emit"</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">"current"</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">"cs_invariant"</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">"""</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"> """</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">"""</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"> """</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">"""</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"> """</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">"""</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"> """</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">"time"</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">"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">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">"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">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">"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">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">"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">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">"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">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">"""</span>
+<span class="sd"> Write data from buffer to the HDF5 file, if mpi is not being used.</span>
+<span class="sd"> """</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">"time"</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">"mean"</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">"std"</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">"emit"</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">"current"</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">"cs_invariant"</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">"""</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"> """</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">"tau"</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">"ProfileData_"</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">"_bin"</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">"_bin"</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">"""</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"> """</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">"_bin"</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">"""Write data from buffer to the HDF5 file."""</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">"time"</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">"_bin"</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">"_bin"</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">"""</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"> """</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">"""</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: "Wlong, "Wxdip", ...</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"> """</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">"WakePotentialData_"</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">"tau_"</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">"tau_"</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">"profile_"</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">"profile_"</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">"Wxdip"</span> <span class="ow">or</span> <span class="n">dim</span> <span class="o">==</span> <span class="s2">"Wydip"</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">"dipole_"</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">"dipole_"</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">"""</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"> """</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">"tau0_"</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">"profile0_"</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">"Wxdip"</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">"dipole_x"</span><span class="p">)</span>
+ <span class="k">if</span> <span class="n">dim</span> <span class="o">==</span> <span class="s2">"Wydip"</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">"dipole_y"</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">"Wxdip"</span> <span class="ow">or</span> <span class="n">dim</span> <span class="o">==</span> <span class="s2">"Wydip"</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">"tau_"</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">"profile_"</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">"Wxdip"</span> <span class="ow">or</span> <span class="n">dim</span> <span class="o">==</span> <span class="s2">"Wydip"</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">"dipole_"</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">"""Write data from buffer to the HDF5 file."""</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">"time"</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">"tau_"</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">"tau_"</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">"profile_"</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">"profile_"</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">"Wxdip"</span> <span class="ow">or</span> <span class="n">dim</span> <span class="o">==</span> <span class="s2">"Wydip"</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">"dipole_"</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">"dipole_"</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">"""</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"> """</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">"WakePotentialMonitor for Beam "</span> <span class="o">+</span>
+ <span class="s2">"objects is only available "</span> <span class="o">+</span>
+ <span class="s2">"with MPI mode."</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">"object_to_save should be a Beam or Bunch object."</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">"""</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"> - "all"</span>
+<span class="sd"> - "tau"</span>
+<span class="sd"> - "x"</span>
+<span class="sd"> - "y"</span>
+<span class="sd"> - "xy" or "yx"</span>
+<span class="sd"> - "xtau" or "taux"</span>
+<span class="sd"> - "ytau" or "tauy"</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"> """</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">"all"</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">"x"</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="s2">"y"</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span> <span class="s2">"tau"</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">"all"</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">"x"</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="s2">"y"</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span> <span class="s2">"tau"</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">"tau"</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">"tau"</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">"x"</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">"x"</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">"y"</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">"y"</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">"xy"</span> <span class="ow">or</span> <span class="n">dim</span> <span class="o">==</span> <span class="s2">"yx"</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">"x"</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="s2">"y"</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">"xtau"</span> <span class="ow">or</span> <span class="n">dim</span> <span class="o">==</span> <span class="s2">"taux"</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">"x"</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="s2">"tau"</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">"ytau"</span> <span class="ow">or</span> <span class="n">dim</span> <span class="o">==</span> <span class="s2">"tauy"</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">"y"</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="s2">"tau"</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">"dim is not correct."</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">"BunchSpectrum_"</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">"incoherent"</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">"coherent"</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">"mean_incoherent"</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">"std_incoherent"</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">"incoherent"</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">"coherent"</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">"mean_incoherent"</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">"std_incoherent"</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">"freq"</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">"""</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"> """</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">"""</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"> """</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">"""</span>
+<span class="sd"> Return the fft frequency samples in [Hz].</span>
+<span class="sd"> """</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">"""</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"> """</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">"object_to_save should be a Beam or Bunch object."</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">></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">"""</span>
+<span class="sd"> A method to hold saved data before writing it to the output file.</span>
+
+<span class="sd"> """</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">"""</span>
+<span class="sd"> Write data from buffer to output file.</span>
+
+<span class="sd"> """</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">"time"</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">"incoherent"</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">"mean_incoherent"</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">"std_incoherent"</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">"coherent"</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">"""</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"> """</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">"""</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"> """</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">"""</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"> - "all"</span>
+<span class="sd"> - "tau"</span>
+<span class="sd"> - "x"</span>
+<span class="sd"> - "y"</span>
+<span class="sd"> - "xy" or "yx"</span>
+<span class="sd"> - "xtau" or "taux"</span>
+<span class="sd"> - "ytau" or "tauy"</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"> """</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">"all"</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">"x"</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="s2">"y"</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span> <span class="s2">"tau"</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">"all"</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">"x"</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="s2">"y"</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span> <span class="s2">"tau"</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">"tau"</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">"tau"</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">"x"</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">"x"</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">"y"</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">"y"</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">"xy"</span> <span class="ow">or</span> <span class="n">dim</span> <span class="o">==</span> <span class="s2">"yx"</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">"x"</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="s2">"y"</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">"xtau"</span> <span class="ow">or</span> <span class="n">dim</span> <span class="o">==</span> <span class="s2">"taux"</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">"x"</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="s2">"tau"</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">"ytau"</span> <span class="ow">or</span> <span class="n">dim</span> <span class="o">==</span> <span class="s2">"tauy"</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">"y"</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="s2">"tau"</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">"dim is not correct."</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">"BeamSpectrum"</span>
+
+ <span class="n">dict_buffer</span> <span class="o">=</span> <span class="p">{</span><span class="s2">"coherent"</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">"coherent"</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">"freq"</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">"""</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"> """</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">"""</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"> """</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">"""</span>
+<span class="sd"> Return the fft frequency samples in [Hz].</span>
+<span class="sd"> """</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">"""</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"> """</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">"""</span>
+<span class="sd"> A method to hold saved data before writing it to the output file.</span>
+
+<span class="sd"> """</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">'F'</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">'F'</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">"""</span>
+<span class="sd"> Write data from buffer to output file.</span>
+
+<span class="sd"> """</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">"time"</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">"coherent"</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">"""</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"> """</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">"""</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"> """</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">"cavity_phasor_record"</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">"beam_phasor_record"</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">"generator_phasor_record"</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">"ig_phasor_record"</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">"DFB_ig_phasor"</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">"detune"</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">"psi"</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">"Vg"</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">"theta_g"</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">"Pg"</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">"Rs"</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">"Q"</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">"QL"</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">"Vc"</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">"theta"</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">"cavity_phasor_record"</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">"beam_phasor_record"</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">"generator_phasor_record"</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">"ig_phasor_record"</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">"DFB_ig_phasor"</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">"detune"</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">"psi"</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">"Vg"</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">"theta_g"</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">"Pg"</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">"Rs"</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">"Q"</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">"QL"</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">"Vc"</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">"theta"</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">"cavity_phasor_record"</span><span class="p">:</span> <span class="nb">complex</span><span class="p">,</span>
+ <span class="s2">"beam_phasor_record"</span><span class="p">:</span> <span class="nb">complex</span><span class="p">,</span>
+ <span class="s2">"generator_phasor_record"</span><span class="p">:</span> <span class="nb">complex</span><span class="p">,</span>
+ <span class="s2">"ig_phasor_record"</span><span class="p">:</span> <span class="nb">complex</span><span class="p">,</span>
+ <span class="s2">"DFB_ig_phasor"</span><span class="p">:</span> <span class="nb">complex</span><span class="p">,</span>
+ <span class="s2">"detune"</span><span class="p">:</span> <span class="nb">float</span><span class="p">,</span>
+ <span class="s2">"psi"</span><span class="p">:</span> <span class="nb">float</span><span class="p">,</span>
+ <span class="s2">"Vg"</span><span class="p">:</span> <span class="nb">float</span><span class="p">,</span>
+ <span class="s2">"theta_g"</span><span class="p">:</span> <span class="nb">float</span><span class="p">,</span>
+ <span class="s2">"Pg"</span><span class="p">:</span> <span class="nb">float</span><span class="p">,</span>
+ <span class="s2">"Rs"</span><span class="p">:</span> <span class="nb">float</span><span class="p">,</span>
+ <span class="s2">"Q"</span><span class="p">:</span> <span class="nb">float</span><span class="p">,</span>
+ <span class="s2">"QL"</span><span class="p">:</span> <span class="nb">float</span><span class="p">,</span>
+ <span class="s2">"Vc"</span><span class="p">:</span> <span class="nb">float</span><span class="p">,</span>
+ <span class="s2">"theta"</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">"""</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"> """</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">"cavity should be a CavityResonator object."</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>
+
+ <div class="clearer"></div>
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new file mode 100644
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--- /dev/null
+++ b/docs/build/html/_modules/mbtrack2/tracking/monitors/plotting.html
@@ -0,0 +1,1545 @@
+
+<!DOCTYPE html>
+
+<html lang="en">
+ <head>
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+ <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">"""</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">"""</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">"mean"</span><span class="p">,</span>
+ <span class="n">dimension</span><span class="o">=</span><span class="s2">"tau"</span><span class="p">,</span>
+ <span class="n">stat_var</span><span class="o">=</span><span class="s2">"mean"</span><span class="p">,</span>
+ <span class="n">x_var</span><span class="o">=</span><span class="s2">"time"</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">"""</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 : {"current","emit","mean","std","cs_invariant"}</span>
+<span class="sd"> HDF5 file's dataset to be plotted. The default is "mean".</span>
+<span class="sd"> dimension : str</span>
+<span class="sd"> The dimension of the dataset to plot:</span>
+<span class="sd"> for "emit", dimension = {"x","y","s"},</span>
+<span class="sd"> for "cs_invariant", dimension = {"x","y","s"},</span>
+<span class="sd"> for "mean" and "std", dimension = {"x","xp","y","yp","tau","delta"}.</span>
+<span class="sd"> not used if "current".</span>
+<span class="sd"> The default is "tau".</span>
+<span class="sd"> stat_var : {"mean", "std"}</span>
+<span class="sd"> Statistical value of the dimension.</span>
+<span class="sd"> x_var : {"time", "index"}</span>
+<span class="sd"> Choice of the horizontal axis:</span>
+<span class="sd"> "time" corresponds to turn number.</span>
+<span class="sd"> "index" 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 = "index".</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"> """</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">"r"</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">"Beam"</span><span class="p">][</span><span class="s2">"time"</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">"Beam"</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">"time"</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">"Number of turns"</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">"Beam"</span><span class="p">][</span><span class="s2">"current"</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">"current"</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">"Total current (mA)"</span>
+ <span class="k">elif</span> <span class="n">dataset</span> <span class="o">==</span> <span class="s2">"emit"</span><span class="p">:</span>
+ <span class="n">dimension_dict</span> <span class="o">=</span> <span class="p">{</span><span class="s2">"x"</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="s2">"y"</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span> <span class="s2">"s"</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">"$</span><span class="se">\\</span><span class="s2">epsilon_</span><span class="si">{x}</span><span class="s2">$ (m.rad)"</span><span class="p">,</span> <span class="s2">"$</span><span class="se">\\</span><span class="s2">epsilon_</span><span class="si">{y}</span><span class="s2">$ (m.rad)"</span><span class="p">,</span>
+ <span class="s2">"$</span><span class="se">\\</span><span class="s2">epsilon_</span><span class="si">{s}</span><span class="s2">$ (s)"</span>
+ <span class="p">]</span>
+ <span class="k">if</span> <span class="n">stat_var</span> <span class="o">==</span> <span class="s2">"mean"</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">"std"</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">" "</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">"cs_invariant"</span><span class="p">:</span>
+ <span class="n">dimension_dict</span> <span class="o">=</span> <span class="p">{</span><span class="s2">"x"</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="s2">"y"</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span> <span class="s2">"s"</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">'$J_x$ (m)'</span><span class="p">,</span> <span class="s1">'$J_y$ (m)'</span><span class="p">,</span> <span class="s1">'$J_s$ (s)'</span><span class="p">]</span>
+ <span class="k">if</span> <span class="n">stat_var</span> <span class="o">==</span> <span class="s2">"mean"</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">"std"</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">" "</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">"mean"</span> <span class="ow">or</span> <span class="n">dataset</span> <span class="o">==</span> <span class="s2">"std"</span><span class="p">:</span>
+ <span class="n">dimension_dict</span> <span class="o">=</span> <span class="p">{</span>
+ <span class="s2">"x"</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span>
+ <span class="s2">"xp"</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span>
+ <span class="s2">"y"</span><span class="p">:</span> <span class="mi">2</span><span class="p">,</span>
+ <span class="s2">"yp"</span><span class="p">:</span> <span class="mi">3</span><span class="p">,</span>
+ <span class="s2">"tau"</span><span class="p">:</span> <span class="mi">4</span><span class="p">,</span>
+ <span class="s2">"delta"</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">"x (um)"</span><span class="p">,</span> <span class="s2">"x' ($</span><span class="se">\\</span><span class="s2">mu$rad)"</span><span class="p">,</span> <span class="s2">"y (um)"</span><span class="p">,</span> <span class="s2">"y' ($</span><span class="se">\\</span><span class="s2">mu$rad)"</span><span class="p">,</span>
+ <span class="s2">"$</span><span class="se">\\</span><span class="s2">tau$ (ps)"</span><span class="p">,</span> <span class="s2">"$</span><span class="se">\\</span><span class="s2">delta$"</span>
+ <span class="p">]</span>
+ <span class="k">if</span> <span class="n">stat_var</span> <span class="o">==</span> <span class="s2">"mean"</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">"std"</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">"mean"</span><span class="p">:</span> <span class="s2">"mean of "</span><span class="p">,</span> <span class="s2">"std"</span><span class="p">:</span> <span class="s2">"std of "</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">" "</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">"index"</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">"Beam"</span><span class="p">][</span><span class="s2">"mean"</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">"Bunch index"</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">"Turn is not valid."</span><span class="p">)</span>
+
+ <span class="k">if</span> <span class="n">dataset</span> <span class="o">==</span> <span class="s2">"current"</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">"Bunch current (mA)"</span>
+ <span class="k">elif</span> <span class="n">dataset</span> <span class="o">==</span> <span class="s2">"emit"</span><span class="p">:</span>
+ <span class="n">dimension_dict</span> <span class="o">=</span> <span class="p">{</span><span class="s2">"x"</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="s2">"y"</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span> <span class="s2">"s"</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">"$</span><span class="se">\\</span><span class="s2">epsilon_</span><span class="si">{x}</span><span class="s2">$ (m.rad)"</span><span class="p">,</span> <span class="s2">"$</span><span class="se">\\</span><span class="s2">epsilon_</span><span class="si">{y}</span><span class="s2">$ (m.rad)"</span><span class="p">,</span>
+ <span class="s2">"$</span><span class="se">\\</span><span class="s2">epsilon_</span><span class="si">{s}</span><span class="s2">$ (s)"</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">"cs_invariant"</span><span class="p">:</span>
+ <span class="n">dimension_dict</span> <span class="o">=</span> <span class="p">{</span><span class="s2">"x"</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="s2">"y"</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span> <span class="s2">"s"</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">'$J_x$ (m)'</span><span class="p">,</span> <span class="s1">'$J_y$ (m)'</span><span class="p">,</span> <span class="s1">'$J_s$ (s)'</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">"mean"</span> <span class="ow">or</span> <span class="n">dataset</span> <span class="o">==</span> <span class="s2">"std"</span><span class="p">:</span>
+ <span class="n">dimension_dict</span> <span class="o">=</span> <span class="p">{</span>
+ <span class="s2">"x"</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span>
+ <span class="s2">"xp"</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span>
+ <span class="s2">"y"</span><span class="p">:</span> <span class="mi">2</span><span class="p">,</span>
+ <span class="s2">"yp"</span><span class="p">:</span> <span class="mi">3</span><span class="p">,</span>
+ <span class="s2">"tau"</span><span class="p">:</span> <span class="mi">4</span><span class="p">,</span>
+ <span class="s2">"delta"</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">"x (um)"</span><span class="p">,</span> <span class="s2">"x' ($</span><span class="se">\\</span><span class="s2">mu$rad)"</span><span class="p">,</span> <span class="s2">"y (um)"</span><span class="p">,</span> <span class="s2">"y' ($</span><span class="se">\\</span><span class="s2">mu$rad)"</span><span class="p">,</span>
+ <span class="s2">"$</span><span class="se">\\</span><span class="s2">tau$ (ps)"</span><span class="p">,</span> <span class="s2">"$</span><span class="se">\\</span><span class="s2">delta$"</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">" "</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">"x_var should be time or index"</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">"mean"</span><span class="p">,</span> <span class="n">dimension</span><span class="o">=</span><span class="s2">"tau"</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">"""</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 : {"current","emit","mean","std","cs_invariant"}</span>
+<span class="sd"> HDF5 file's dataset to be plotted. The default is "mean".</span>
+<span class="sd"> dimension : str</span>
+<span class="sd"> The dimension of the dataset to plot:</span>
+<span class="sd"> for "emit", dimension = {"x","y","s"},</span>
+<span class="sd"> for "cs_invariant", dimension = {"x","y","s"},</span>
+<span class="sd"> for "mean" and "std", dimension = {"x","xp","y","yp","tau","delta"}.</span>
+<span class="sd"> not used if "current".</span>
+<span class="sd"> The default is "tau".</span>
+<span class="sd"> cm_lim : list [vmin, vmax], optional</span>
+<span class="sd"> Colormap scale for the "streak" 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"> """</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">"r"</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">"Beam"</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">"time"</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">"mean"</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">"Bunch index"</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">"Number of turns"</span>
+ <span class="k">if</span> <span class="n">dataset</span> <span class="o">==</span> <span class="s2">"current"</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">"current"</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">"Bunch current (mA)"</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">"emit"</span><span class="p">:</span>
+ <span class="n">dimension_dict</span> <span class="o">=</span> <span class="p">{</span><span class="s2">"x"</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="s2">"y"</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span> <span class="s2">"s"</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">"$</span><span class="se">\\</span><span class="s2">epsilon_</span><span class="si">{x}</span><span class="s2">$ (m.rad)"</span><span class="p">,</span> <span class="s2">"$</span><span class="se">\\</span><span class="s2">epsilon_</span><span class="si">{y}</span><span class="s2">$ (m.rad)"</span><span class="p">,</span>
+ <span class="s2">"$</span><span class="se">\\</span><span class="s2">epsilon_</span><span class="si">{s}</span><span class="s2">$ (s)"</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">"emit"</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">"cs_invariant"</span><span class="p">:</span>
+ <span class="n">dimension_dict</span> <span class="o">=</span> <span class="p">{</span><span class="s2">"x"</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="s2">"y"</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span> <span class="s2">"s"</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">'$J_x$ (m)'</span><span class="p">,</span> <span class="s1">'$J_y$ (m)'</span><span class="p">,</span> <span class="s1">'$J_s$ (s)'</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">"cs_invariant"</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">"x"</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span>
+ <span class="s2">"xp"</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span>
+ <span class="s2">"y"</span><span class="p">:</span> <span class="mi">2</span><span class="p">,</span>
+ <span class="s2">"yp"</span><span class="p">:</span> <span class="mi">3</span><span class="p">,</span>
+ <span class="s2">"tau"</span><span class="p">:</span> <span class="mi">4</span><span class="p">,</span>
+ <span class="s2">"delta"</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">"x (um)"</span><span class="p">,</span> <span class="s2">"x' ($</span><span class="se">\\</span><span class="s2">mu$rad)"</span><span class="p">,</span> <span class="s2">"y (um)"</span><span class="p">,</span> <span class="s2">"y' ($</span><span class="se">\\</span><span class="s2">mu$rad)"</span><span class="p">,</span>
+ <span class="s2">"$</span><span class="se">\\</span><span class="s2">tau$ (ps)"</span><span class="p">,</span> <span class="s2">"$</span><span class="se">\\</span><span class="s2">delta$"</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">"mean"</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">" CM"</span>
+ <span class="k">elif</span> <span class="n">dataset</span> <span class="o">==</span> <span class="s2">"std"</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">" RMS"</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">"mean"</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">'lower'</span><span class="p">,</span>
+ <span class="n">aspect</span><span class="o">=</span><span class="s1">'auto'</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">"x"</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">"""</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 'bunch_number' parameter in </span>
+<span class="sd"> 'BunchMonitor' object.</span>
+<span class="sd"> dataset : {"current", "emit", "mean", "std", "cs_invariant"}</span>
+<span class="sd"> HDF5 file's dataset to be plotted.</span>
+<span class="sd"> dimension : str, optional</span>
+<span class="sd"> The dimension of the dataset to plot. Use "None" for "current",</span>
+<span class="sd"> otherwise use the following : </span>
+<span class="sd"> for "emit", dimension = {"x","y","s"},</span>
+<span class="sd"> for "cs_invariant", dimension = {"x","y","s"},</span>
+<span class="sd"> for "mean" and "std", dimension = {"x","xp","y","yp","tau","delta"},</span>
+<span class="sd"> for "action", dimension = {"x","y"}.</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"> """</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">"r"</span><span class="p">)</span>
+ <span class="n">group</span> <span class="o">=</span> <span class="s2">"BunchData_</span><span class="si">{0}</span><span class="s2">"</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">"current"</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">"current (mA)"</span>
+
+ <span class="k">elif</span> <span class="n">dataset</span> <span class="o">==</span> <span class="s2">"emit"</span><span class="p">:</span>
+ <span class="n">dimension_dict</span> <span class="o">=</span> <span class="p">{</span><span class="s2">"x"</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="s2">"y"</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span> <span class="s2">"s"</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">"x"</span><span class="p">:</span> <span class="n">label</span> <span class="o">=</span> <span class="s2">"hor. emittance (m.rad)"</span>
+ <span class="k">elif</span> <span class="n">dimension</span> <span class="o">==</span> <span class="s2">"y"</span><span class="p">:</span> <span class="n">label</span> <span class="o">=</span> <span class="s2">"ver. emittance (m.rad)"</span>
+ <span class="k">elif</span> <span class="n">dimension</span> <span class="o">==</span> <span class="s2">"s"</span><span class="p">:</span> <span class="n">label</span> <span class="o">=</span> <span class="s2">"long. emittance (s)"</span>
+
+ <span class="k">elif</span> <span class="n">dataset</span> <span class="o">==</span> <span class="s2">"mean"</span> <span class="ow">or</span> <span class="n">dataset</span> <span class="o">==</span> <span class="s2">"std"</span><span class="p">:</span>
+ <span class="n">dimension_dict</span> <span class="o">=</span> <span class="p">{</span>
+ <span class="s2">"x"</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span>
+ <span class="s2">"xp"</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span>
+ <span class="s2">"y"</span><span class="p">:</span> <span class="mi">2</span><span class="p">,</span>
+ <span class="s2">"yp"</span><span class="p">:</span> <span class="mi">3</span><span class="p">,</span>
+ <span class="s2">"tau"</span><span class="p">:</span> <span class="mi">4</span><span class="p">,</span>
+ <span class="s2">"delta"</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">"mean"</span><span class="p">:</span>
+ <span class="n">label_list</span> <span class="o">=</span> <span class="p">[</span>
+ <span class="s2">"x ($</span><span class="se">\\</span><span class="s2">mu$m)"</span><span class="p">,</span> <span class="s2">"x' ($</span><span class="se">\\</span><span class="s2">mu$rad)"</span><span class="p">,</span> <span class="s2">"y ($</span><span class="se">\\</span><span class="s2">mu$m)"</span><span class="p">,</span>
+ <span class="s2">"y' ($</span><span class="se">\\</span><span class="s2">mu$rad)"</span><span class="p">,</span> <span class="s2">"$</span><span class="se">\\</span><span class="s2">tau$ (ps)"</span><span class="p">,</span> <span class="s2">"$</span><span class="se">\\</span><span class="s2">delta$"</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">"$</span><span class="se">\\</span><span class="s2">sigma_x$ ($</span><span class="se">\\</span><span class="s2">mu$m)"</span><span class="p">,</span> <span class="s2">"$</span><span class="se">\\</span><span class="s2">sigma_{x'}$ ($</span><span class="se">\\</span><span class="s2">mu$rad)"</span><span class="p">,</span>
+ <span class="s2">"$</span><span class="se">\\</span><span class="s2">sigma_y$ ($</span><span class="se">\\</span><span class="s2">mu$m)"</span><span class="p">,</span> <span class="s2">"$</span><span class="se">\\</span><span class="s2">sigma_{y'}$ ($</span><span class="se">\\</span><span class="s2">mu$rad)"</span><span class="p">,</span>
+ <span class="s2">"$</span><span class="se">\\</span><span class="s2">sigma_{</span><span class="se">\\</span><span class="s2">tau}$ (ps)"</span><span class="p">,</span> <span class="s2">"$</span><span class="se">\\</span><span class="s2">sigma_{</span><span class="se">\\</span><span class="s2">delta}$"</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">"cs_invariant"</span><span class="p">:</span>
+ <span class="n">dimension_dict</span> <span class="o">=</span> <span class="p">{</span><span class="s2">"x"</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="s2">"y"</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span> <span class="s2">"s"</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">'$J_x$ (m)'</span><span class="p">,</span> <span class="s1">'$J_y$ (m)'</span><span class="p">,</span> <span class="s1">'$J_s$ (s)'</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">"time"</span><span class="p">][:]</span>
+ <span class="n">xlabel</span> <span class="o">=</span> <span class="s2">"Number of turns"</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">'kde'</span><span class="p">):</span>
+<span class="w"> </span><span class="sd">"""</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 'bunch_number' parameter in </span>
+<span class="sd"> 'PhaseSpaceMonitor' object.</span>
+<span class="sd"> x_var, y_var : str {"x", "xp", "y", "yp", "tau", "delta"}</span>
+<span class="sd"> If dataset is "particles", 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 : {'scatter', 'kde', 'hex', 'reg', 'resid'}, optional</span>
+<span class="sd"> The plot style. The default is 'kde'. </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"> """</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">"r"</span><span class="p">)</span>
+
+ <span class="n">group</span> <span class="o">=</span> <span class="s2">"PhaseSpaceData_</span><span class="si">{0}</span><span class="s2">"</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">"particles"</span>
+
+ <span class="n">option_dict</span> <span class="o">=</span> <span class="p">{</span><span class="s2">"x"</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="s2">"xp"</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span> <span class="s2">"y"</span><span class="p">:</span> <span class="mi">2</span><span class="p">,</span> <span class="s2">"yp"</span><span class="p">:</span> <span class="mi">3</span><span class="p">,</span> <span class="s2">"tau"</span><span class="p">:</span> <span class="mi">4</span><span class="p">,</span> <span class="s2">"delta"</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">"x (mm)"</span><span class="p">,</span> <span class="s2">"x' (mrad)"</span><span class="p">,</span> <span class="s2">"y (mm)"</span><span class="p">,</span> <span class="s2">"y' (mrad)"</span><span class="p">,</span> <span class="s2">"$</span><span class="se">\\</span><span class="s2">tau$ (ps)"</span><span class="p">,</span>
+ <span class="s2">"$</span><span class="se">\\</span><span class="s2">delta$"</span>
+ <span class="p">]</span>
+
+ <span class="c1"># find the index of "turn" 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">"time"</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">"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">."</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">"time"</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">"alive"</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"><</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">"plot_size must be in range [0,1]."</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">"tau"</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">"""</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 'bunch_number' parameter in </span>
+<span class="sd"> 'ProfileMonitor' object.</span>
+<span class="sd"> dimension : str, optional</span>
+<span class="sd"> Dimension to plot. The default is "tau"</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 'save_every' parameter in</span>
+<span class="sd"> 'ProfileMonitor' 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"> """</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">"r"</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">'ProfileData_</span><span class="si">{0}</span><span class="s1">'</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">"</span><span class="si">{0}</span><span class="s2">_bin"</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">"time"</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">"stop not found. Choose from </span><span class="si">{0}</span><span class="s2">"</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">"start not found. Choose from </span><span class="si">{0}</span><span class="s2">"</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">"step must be divisible by the recording step "</span>
+ <span class="s2">"which is </span><span class="si">{0}</span><span class="s2">."</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">"x"</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="s2">"xp"</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span> <span class="s2">"y"</span><span class="p">:</span> <span class="mi">2</span><span class="p">,</span> <span class="s2">"yp"</span><span class="p">:</span> <span class="mi">3</span><span class="p">,</span> <span class="s2">"tau"</span><span class="p">:</span> <span class="mi">4</span><span class="p">,</span> <span class="s2">"delta"</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">"x (um)"</span><span class="p">,</span> <span class="s2">"x' ($</span><span class="se">\\</span><span class="s2">mu$rad)"</span><span class="p">,</span> <span class="s2">"y (um)"</span><span class="p">,</span> <span class="s2">"y' ($</span><span class="se">\\</span><span class="s2">mu$rad)"</span><span class="p">,</span> <span class="s2">"$</span><span class="se">\\</span><span class="s2">tau$ (ps)"</span><span class="p">,</span>
+ <span class="s2">"$</span><span class="se">\\</span><span class="s2">delta$"</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">"turn </span><span class="si">{0}</span><span class="s2">"</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">"number of macro-particles"</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">'lower'</span><span class="p">,</span>
+ <span class="n">aspect</span><span class="o">=</span><span class="s1">'auto'</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">"Number of turns"</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">"Number of macro-particles"</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">"Wlong"</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">"""</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 'bunch_number' parameter in </span>
+<span class="sd"> 'WakePotentialMonitor' object.</span>
+<span class="sd"> wake_type : str, optional</span>
+<span class="sd"> Wake type to plot: "Wlong", "Wxdip", ... </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 'save_every' parameter in</span>
+<span class="sd"> 'WakePotentialMonitor' 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"> """</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">"r"</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">'WakePotentialData_</span><span class="si">{0}</span><span class="s1">'</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">"time"</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">"stop not found. Choose from </span><span class="si">{0}</span><span class="s2">"</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">"start not found. Choose from </span><span class="si">{0}</span><span class="s2">"</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">"step must be divisible by the recording step "</span>
+ <span class="s2">"which is </span><span class="si">{0}</span><span class="s2">."</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">"Wlong"</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span>
+ <span class="s2">"Wxdip"</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span>
+ <span class="s2">"Wydip"</span><span class="p">:</span> <span class="mi">2</span><span class="p">,</span>
+ <span class="s2">"Wxquad"</span><span class="p">:</span> <span class="mi">3</span><span class="p">,</span>
+ <span class="s2">"Wyquad"</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">"$W_p$ (V/pC)"</span><span class="p">,</span> <span class="s2">"$W_{p,x}^D (V/pC)$"</span><span class="p">,</span> <span class="s2">"$W_{p,y}^D (V/pC)$"</span><span class="p">,</span>
+ <span class="s2">"$W_{p,x}^Q (V/pC/mm)$"</span><span class="p">,</span> <span class="s2">"$W_{p,y}^Q (V/pC/mm)$"</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">"tau_"</span> <span class="o">+</span> <span class="n">wake_type</span>
+ <span class="n">wake_type</span> <span class="o">=</span> <span class="s2">"profile_"</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">"$</span><span class="se">\\</span><span class="s2">rho$ (a.u.)"</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">"tau_"</span> <span class="o">+</span> <span class="n">wake_type</span>
+ <span class="n">wake_type</span> <span class="o">=</span> <span class="s2">"dipole_"</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">"Dipole moment (m)"</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">"tau_"</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">"turn </span><span class="si">{0}</span><span class="s2">"</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">"$</span><span class="se">\\</span><span class="s2">tau$ (ps)"</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">'lower'</span><span class="p">,</span>
+ <span class="n">aspect</span><span class="o">=</span><span class="s1">'auto'</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">"$</span><span class="se">\\</span><span class="s2">tau$ (ps)"</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">"Number of turns"</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">"incoherent"</span><span class="p">,</span>
+ <span class="n">dim</span><span class="o">=</span><span class="s2">"tau"</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">"""</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 'bunch_number' parameter in </span>
+<span class="sd"> 'BunchSpectrumMonitor' object.</span>
+<span class="sd"> dataset : {"mean_incoherent", "coherent", "incoherent"}</span>
+<span class="sd"> HDF5 file's dataset to be plotted. </span>
+<span class="sd"> The default is "incoherent".</span>
+<span class="sd"> dim : {"x","y","tau"}, optional</span>
+<span class="sd"> The dimension of the dataset to plot.</span>
+<span class="sd"> The default is "tau".</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"> """</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">"r"</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">"BunchSpectrum_</span><span class="si">{0}</span><span class="s2">"</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">"time"</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">"freq"</span><span class="p">])</span>
+ <span class="n">dim_dict</span> <span class="o">=</span> <span class="p">{</span><span class="s2">"x"</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="s2">"y"</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span> <span class="s2">"tau"</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">"mean_incoherent"</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">"mean_incoherent"</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">"std_incoherent"</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">"Turn number"</span>
+ <span class="n">ylabel</span> <span class="o">=</span> <span class="s2">"Mean incoherent frequency [Hz]"</span>
+ <span class="k">elif</span> <span class="n">dataset</span> <span class="o">==</span> <span class="s2">"incoherent"</span> <span class="ow">or</span> <span class="n">dataset</span> <span class="o">==</span> <span class="s2">"coherent"</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">"Frequency [Hz]"</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">"$f/f_</span><span class="si">{s}</span><span class="s2">$"</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">'log'</span><span class="p">)</span>
+
+ <span class="n">ylabel</span> <span class="o">=</span> <span class="s2">"FFT amplitude [a.u.]"</span>
+ <span class="k">if</span> <span class="n">dataset</span> <span class="o">==</span> <span class="s2">"incoherent"</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">"Incoherent spectrum"</span><span class="p">)</span>
+ <span class="k">elif</span> <span class="n">dataset</span> <span class="o">==</span> <span class="s2">"coherent"</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">"Coherent spectrum"</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">"incoherent"</span><span class="p">,</span>
+ <span class="n">dim</span><span class="o">=</span><span class="s2">"tau"</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">"""</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 'bunch_number' parameter in </span>
+<span class="sd"> 'BunchSpectrumMonitor' object.</span>
+<span class="sd"> dataset : {"coherent", "incoherent"}</span>
+<span class="sd"> HDF5 file's dataset to be plotted. </span>
+<span class="sd"> The default is "incoherent".</span>
+<span class="sd"> dim : {"x","y","tau"}, optional</span>
+<span class="sd"> The dimension of the dataset to plot.</span>
+<span class="sd"> The default is "tau".</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"> """</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">"r"</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">"BunchSpectrum_</span><span class="si">{0}</span><span class="s2">"</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">"time"</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">"freq"</span><span class="p">])</span>
+ <span class="n">dim_dict</span> <span class="o">=</span> <span class="p">{</span><span class="s2">"x"</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="s2">"y"</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span> <span class="s2">"tau"</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">"Frequency [Hz]"</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">"$f/f_</span><span class="si">{s}</span><span class="s2">$"</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">></span> <span class="n">fmin</span><span class="p">)</span> <span class="o">&</span> <span class="p">(</span><span class="n">x_var</span> <span class="o"><</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">"Turn number"</span>
+ <span class="k">else</span><span class="p">:</span>
+ <span class="n">ylabel</span> <span class="o">=</span> <span class="s2">""</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">"incoherent"</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">"Incoherent spectrum"</span><span class="p">)</span>
+ <span class="k">elif</span> <span class="n">dataset</span> <span class="o">==</span> <span class="s2">"coherent"</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">"Coherent spectrum"</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">'lower'</span><span class="p">,</span>
+ <span class="n">aspect</span><span class="o">=</span><span class="s1">'auto'</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">"none"</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">"FFT amplitude [a.u.]"</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">"tau"</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">"""</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 : {"x","y","tau"}, optional</span>
+<span class="sd"> The dimension of the dataset to plot.</span>
+<span class="sd"> The default is "tau".</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"> """</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">"r"</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">"BeamSpectrum"</span><span class="p">]</span>
+
+ <span class="n">dataset</span> <span class="o">=</span> <span class="s2">"coherent"</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">"time"</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">"freq"</span><span class="p">])</span>
+ <span class="n">dim_dict</span> <span class="o">=</span> <span class="p">{</span><span class="s2">"x"</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="s2">"y"</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span> <span class="s2">"tau"</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">"Frequency [Hz]"</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">"$f/f_</span><span class="si">{0}</span><span class="s2">$"</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">'log'</span><span class="p">)</span>
+
+ <span class="n">ylabel</span> <span class="o">=</span> <span class="s2">"FFT amplitude [a.u.]"</span>
+ <span class="n">ax</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s2">"Beam coherent spectrum"</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">"tau"</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">"""</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 : {"x","y","tau"}, optional</span>
+<span class="sd"> The dimension of the dataset to plot.</span>
+<span class="sd"> The default is "tau".</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"> """</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">"r"</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">"BeamSpectrum"</span><span class="p">]</span>
+ <span class="n">dataset</span> <span class="o">=</span> <span class="s2">"coherent"</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">"time"</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">"freq"</span><span class="p">])</span>
+ <span class="n">dim_dict</span> <span class="o">=</span> <span class="p">{</span><span class="s2">"x"</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="s2">"y"</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span> <span class="s2">"tau"</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">"Frequency [Hz]"</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">"$f/f_</span><span class="si">{0}</span><span class="s2">$"</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">></span> <span class="n">fmin</span><span class="p">)</span> <span class="o">&</span> <span class="p">(</span><span class="n">x_var</span> <span class="o"><</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">"Turn number"</span>
+ <span class="k">else</span><span class="p">:</span>
+ <span class="n">ylabel</span> <span class="o">=</span> <span class="s2">""</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">"Beam coherent spectrum"</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">'lower'</span><span class="p">,</span>
+ <span class="n">aspect</span><span class="o">=</span><span class="s1">'auto'</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">"none"</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">"FFT amplitude [a.u.]"</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">"cavity"</span><span class="p">,</span>
+ <span class="n">plot_type</span><span class="o">=</span><span class="s2">"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="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">"""</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 "beam", "cavity", "generator" or </span>
+<span class="sd"> "ig".</span>
+<span class="sd"> plot_type : str, optional</span>
+<span class="sd"> Type of plot:</span>
+<span class="sd"> - "bunch" plots the phasor voltage and angle versus time for a </span>
+<span class="sd"> given bunch.</span>
+<span class="sd"> - "turn" plots the phasor voltage and ange versus bunch index for</span>
+<span class="sd"> a given turn.</span>
+<span class="sd"> - "streak_amplitude" plots the phasor amplitude versus bunch index </span>
+<span class="sd"> and time.</span>
+<span class="sd"> - "streak_angle" plots the phasor angle versus bunch index and </span>
+<span class="sd"> time.</span>
+<span class="sd"> - "detune" or "psi" plots the detuning or tuning angle versus time.</span>
+<span class="sd"> - "power" 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"> - "mean" 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"> - "tuner_diff" 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 "streak" 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 "mean" and "bunch" for "cavity" 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"> """</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">"r"</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">"time"</span><span class="p">])</span>
+
+ <span class="n">ph</span> <span class="o">=</span> <span class="p">{</span><span class="s2">"cavity"</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="s2">"beam"</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span> <span class="s2">"generator"</span><span class="p">:</span> <span class="mi">2</span><span class="p">,</span> <span class="s2">"ig"</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">"Cavity"</span><span class="p">,</span> <span class="s2">"Beam"</span><span class="p">,</span> <span class="s2">"Generator"</span><span class="p">,</span> <span class="s2">"Generator"</span><span class="p">]</span>
+ <span class="n">units</span> <span class="o">=</span> <span class="p">[</span><span class="s2">" voltage [MV]"</span><span class="p">,</span> <span class="s2">" voltage [MV]"</span><span class="p">,</span> <span class="s2">" voltage [MV]"</span><span class="p">,</span> <span class="s2">" current [A]"</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">"bunch"</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">"mean"</span><span class="p">):</span>
+
+ <span class="k">if</span> <span class="n">plot_type</span> <span class="o">==</span> <span class="s2">"bunch"</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">"cavity_phasor_record"</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">"beam_phasor_record"</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">"generator_phasor_record"</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">"ig_phasor_record"</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">"mean"</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">"Beam"</span><span class="p">][</span><span class="s2">"current"</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">"Beam monitor is needed to show mean voltage."</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">"cavity_phasor_record"</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">"beam_phasor_record"</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">"generator_phasor_record"</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">"ig_phasor_record"</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">" phase [rad]"</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">"r"</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">"b"</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">"Vc"</span><span class="p">])</span> <span class="o">*</span> <span class="mf">1e-6</span><span class="p">,</span>
+ <span class="s2">"r--"</span><span class="p">,</span>
+ <span class="n">label</span><span class="o">=</span><span class="s2">"Cavity voltage objective value [MV]"</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">"theta"</span><span class="p">]),</span>
+ <span class="s2">"b--"</span><span class="p">,</span>
+ <span class="n">label</span><span class="o">=</span><span class="s2">"Cavity phase objective value [rad]"</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">"Turn number"</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">"best"</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">"r"</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">"b"</span><span class="p">)</span>
+
+ <span class="k">if</span> <span class="n">plot_type</span> <span class="o">==</span> <span class="s2">"turn"</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">"Turn is not valid."</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">"cavity_phasor_record"</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">"beam_phasor_record"</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">"generator_phasor_record"</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">"ig_phasor_record"</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">" phase [rad]"</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">"r"</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">"b"</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">"Bunch index"</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">"best"</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">"r"</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">"b"</span><span class="p">)</span>
+
+ <span class="k">if</span> <span class="n">plot_type</span> <span class="o">==</span> <span class="s2">"streak_amplitude"</span> <span class="ow">or</span> <span class="n">plot_type</span> <span class="o">==</span> <span class="s2">"streak_phase"</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">"cavity_phasor_record"</span><span class="p">][:,</span> <span class="p">:],</span>
+ <span class="n">cavity_data</span><span class="p">[</span><span class="s2">"beam_phasor_record"</span><span class="p">][:,</span> <span class="p">:],</span>
+ <span class="n">cavity_data</span><span class="p">[</span><span class="s2">"generator_phasor_record"</span><span class="p">][:,</span> <span class="p">:],</span>
+ <span class="n">cavity_data</span><span class="p">[</span><span class="s2">"ig_phasor_record"</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">"streak_amplitude"</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">"streak_phase"</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">" phase [rad]"</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">'lower'</span><span class="p">,</span> <span class="n">aspect</span><span class="o">=</span><span class="s1">'auto'</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">"Bunch index"</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">"Number of turns"</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">"detune"</span> <span class="ow">or</span> <span class="n">plot_type</span> <span class="o">==</span> <span class="s2">"psi"</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">"detune"</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">"detune"</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">"Detuning $\Delta f$ [kHz]"</span>
+ <span class="k">elif</span> <span class="n">plot_type</span> <span class="o">==</span> <span class="s2">"psi"</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">"psi"</span><span class="p">])</span>
+ <span class="n">ylabel</span> <span class="o">=</span> <span class="sa">r</span><span class="s2">"Tuning angle $\psi$"</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">"Number of turns"</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">"power"</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">"cavity_phasor_record"</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">"cavity_phasor_record"</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">"Beam"</span><span class="p">][</span><span class="s2">"current"</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">"Beam"</span><span class="p">][</span><span class="s2">"current"</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">"Beam monitor is needed to compute power."</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">"Rs"</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">"Pg"</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">"Generator power $P_g$ [kW]"</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">"Beam power $P_b$ [kW]"</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">"Dissipated cavity power $P_c$ [kW]"</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">"Reflected power $P_r$ [kW]"</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">"Number of turns"</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">"Power [kW]"</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">"tuner_diff"</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">"cavity_phasor_record"</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">"psi"</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">"theta_g"</span><span class="p">])</span>
+
+ <span class="n">ylabel1</span> <span class="o">=</span> <span class="s2">"Tuner diff. from optimal [rad]"</span>
+ <span class="n">ylabel2</span> <span class="o">=</span> <span class="sa">r</span><span class="s2">"Tuning angle $\psi$ [rad]"</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">"r"</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">"b"</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">"Turn number"</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">"best"</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">"r"</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">"b"</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>
+
+ <div class="clearer"></div>
+ </div>
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diff --git a/docs/build/html/_modules/mbtrack2/tracking/monitors/tools.html b/docs/build/html/_modules/mbtrack2/tracking/monitors/tools.html
new file mode 100644
index 0000000000000000000000000000000000000000..257687b5f8b733042b4232cee71f62b60bf96697
--- /dev/null
+++ b/docs/build/html/_modules/mbtrack2/tracking/monitors/tools.html
@@ -0,0 +1,190 @@
+
+<!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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+ <div class="body" role="main">
+
+ <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">"""</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">"""</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">"""</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"> - "files_prefix_0.hdf5"</span>
+<span class="sd"> - "files_prefix_1.hdf5"</span>
+<span class="sd"> ...</span>
+<span class="sd"> - "files_prefix_files_number.hdf5"</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"> """</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">".hdf5"</span><span class="p">,</span> <span class="s2">"a"</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">"_"</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">".hdf5"</span><span class="p">,</span> <span class="s2">"r"</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">"freq"</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">"_"</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">".hdf5"</span><span class="p">,</span> <span class="s2">"r"</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">"freq"</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">"time"</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">"""</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"> """</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">'v108'</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">".hdf5"</span><span class="p">,</span> <span class="s2">"r"</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">".hdf5"</span><span class="p">,</span> <span class="s2">"a"</span><span class="p">,</span> <span class="n">libver</span><span class="o">=</span><span class="p">(</span><span class="s1">'earliest'</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>
+
+ <div class="clearer"></div>
+ </div>
+ </div>
+ </div>
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new file mode 100644
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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">"""</span>
+<span class="sd">Module to handle parallel computation</span>
+<span class="sd">"""</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">"""</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"> """</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">"""</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"> """</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">"The number of processors must be equal to the"</span>
+ <span class="s2">"number of (non-empty) bunches."</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">"""</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"> """</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">"""</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"> """</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">"The bunch "</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">" is not tracked on any processor."</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">"""Return the bunch number corresponding to the current processor"""</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">"""Return the rank of the next tracked bunch"""</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">"""Return the rank of the previous tracked bunch"""</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">"tau"</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">"""</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 "tau".</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"> """</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">"Error, mpi is not initialised."</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">"_center"</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">"_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="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">"_profile"</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">"_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="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">"_sorted_index"</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">"""</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"> """</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">"Error, mpi is not initialised."</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">"""</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"> """</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">"Error, mpi is not initialised."</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>
+
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diff --git a/docs/build/html/_modules/mbtrack2/tracking/particles.html b/docs/build/html/_modules/mbtrack2/tracking/particles.html
new file mode 100644
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--- /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" />
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+
+ <h1>Source code for mbtrack2.tracking.particles</h1><div class="highlight"><pre>
+<span></span><span class="c1"># -*- coding: utf-8 -*-</span>
+<span class="sd">"""</span>
+<span class="sd">Module where particles, bunches and beams are described as objects.</span>
+<span class="sd">"""</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">"""</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"> """</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">""" Define an electron"""</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">""" Define a proton"""</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">"""</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]. !!! -> 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="tau", y_var="delta", plot_type="j")</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"> """</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">"x"</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">"xp"</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">"y"</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">"yp"</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">"tau"</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">"delta"</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">"""Return the number of alive particles"""</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">"""Return the columns label for alive particles"""</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">"""Set value to the columns label for alive particles"""</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">"""Iterate over labels"""</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">"""Return representation of alive particles"""</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">'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">'</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">"""Macro-particle number"""</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">"""Charge per macro-particle [C]"""</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">"""Bunch charge in [C]"""</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">"""Particle number"""</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">"""Bunch current [A]"""</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">"""Return True if the bunch is empty."""</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">"""</span>
+<span class="sd"> Return the mean position of alive particles for each coordinates.</span>
+<span class="sd"> """</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">"""</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"> """</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">"""</span>
+<span class="sd"> Return the bunch emittance for each plane.</span>
+<span class="sd"> """</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">"""</span>
+<span class="sd"> Return the average Courant-Snyder invariant of each plane.</span>
+
+<span class="sd"> """</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">'x'</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">'x'</span><span class="p">])</span><span class="o">*</span><span class="bp">self</span><span class="p">[</span><span class="s1">'xp'</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">'xp'</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">'y'</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">'y'</span><span class="p">]</span><span class="o">*</span><span class="bp">self</span><span class="p">[</span><span class="s1">'yp'</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">'yp'</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">'tau'</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">'tau'</span><span class="p">]</span><span class="o">*</span><span class="bp">self</span><span class="p">[</span><span class="s1">'delta'</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">'delta'</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">"""</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"> """</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">"sigma_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">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">"sigma_delta"</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">"optics"</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">"x"</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">"xp"</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">"y"</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">"yp"</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">"tau"</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">"delta"</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">"tau"</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">"""</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 "tau".</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"> """</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">'left'</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">"tau"</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">"""</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 "tau".</span>
+<span class="sd"> n_bin : int, optional</span>
+<span class="sd"> Number of bins. The default is 75.</span>
+
+<span class="sd"> """</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">"tau"</span><span class="p">,</span> <span class="n">y_var</span><span class="o">=</span><span class="s2">"delta"</span><span class="p">,</span> <span class="n">kind</span><span class="o">=</span><span class="s2">"scatter"</span><span class="p">):</span>
+<span class="w"> </span><span class="sd">"""</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, {"scatter", "kde", "hist", "hex", "reg", "resid"}</span>
+<span class="sd"> Kind of plot to draw. See seeborn documentation.</span>
+<span class="sd"> The defualt value is "scatter".</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"> """</span>
+
+ <span class="n">label_dict</span> <span class="o">=</span> <span class="p">{</span>
+ <span class="s2">"x"</span><span class="p">:</span> <span class="s2">"x (mm)"</span><span class="p">,</span>
+ <span class="s2">"xp"</span><span class="p">:</span> <span class="s2">"x' (mrad)"</span><span class="p">,</span>
+ <span class="s2">"y"</span><span class="p">:</span> <span class="s2">"y (mm)"</span><span class="p">,</span>
+ <span class="s2">"yp"</span><span class="p">:</span> <span class="s2">"y' (mrad)"</span><span class="p">,</span>
+ <span class="s2">"tau"</span><span class="p">:</span> <span class="s2">"$</span><span class="se">\\</span><span class="s2">tau$ (ps)"</span><span class="p">,</span>
+ <span class="s2">"delta"</span><span class="p">:</span> <span class="s2">"$</span><span class="se">\\</span><span class="s2">delta$"</span>
+ <span class="p">}</span>
+ <span class="n">scale</span> <span class="o">=</span> <span class="p">{</span>
+ <span class="s2">"x"</span><span class="p">:</span> <span class="mf">1e3</span><span class="p">,</span>
+ <span class="s2">"xp"</span><span class="p">:</span> <span class="mf">1e3</span><span class="p">,</span>
+ <span class="s2">"y"</span><span class="p">:</span> <span class="mf">1e3</span><span class="p">,</span>
+ <span class="s2">"yp"</span><span class="p">:</span> <span class="mf">1e3</span><span class="p">,</span>
+ <span class="s2">"tau"</span><span class="p">:</span> <span class="mf">1e12</span><span class="p">,</span>
+ <span class="s2">"delta"</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">"""</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 "<file_name>.hdf5".</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"> """</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">".hdf5"</span><span class="p">,</span> <span class="s2">"a"</span><span class="p">,</span> <span class="n">libver</span><span class="o">=</span><span class="s2">"earliest"</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">".hdf5"</span><span class="p">,</span>
+ <span class="s2">"a"</span><span class="p">,</span>
+ <span class="n">libver</span><span class="o">=</span><span class="s1">'earliest'</span><span class="p">,</span>
+ <span class="n">driver</span><span class="o">=</span><span class="s1">'mpio'</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">"Bunch"</span>
+ <span class="k">else</span><span class="p">:</span>
+ <span class="n">group_name</span> <span class="o">=</span> <span class="s2">"Bunch_"</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">"alive"</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">"phasespace"</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">"current"</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">"alive"</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">"current"</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">"phasespace"</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">"""</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"> """</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">"r"</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">"Bunch"</span>
+ <span class="k">else</span><span class="p">:</span>
+ <span class="n">group_name</span> <span class="o">=</span> <span class="s2">"Bunch_"</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">'alive'</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">"phasespace"</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">'alive'</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">'current'</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">'current'</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">"""</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"> """</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">"The length of the bunch list is </span><span class="si">{}</span><span class="s2"> "</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">"but should be </span><span class="si">{}</span><span class="s2">"</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">"""Return the number of (not empty) bunches"""</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">"""Return the bunch number i"""</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">"""Set value to the bunch number i"""</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">"""Iterate over all bunches"""</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">"""Return representation of the beam filling pattern"""</span>
+ <span class="k">return</span> <span class="sa">f</span><span class="s1">'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">'</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">"""Return a generator to iterate over not empty 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="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">"""Return an array which contains the distance to the next bunch in </span>
+<span class="sd"> units of the RF period (ring.T1)"""</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">"""Update the distance_between_bunches array"""</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">"""</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"> """</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">"The length of filling pattern is </span><span class="si">{}</span><span class="s2"> "</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">"but should be </span><span class="si">{}</span><span class="s2">"</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">"bool"</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">"float64"</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">"</span><span class="si">{}</span><span class="s2"> should be bool or float64"</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">"""Update the beam filling pattern."""</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">"""Return an array with the filling pattern of the beam as bool"""</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">"""Return an array with the positions of the non-empty bunches."""</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">"""Return an array with the current in each bunch in [A]"""</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">"""Return an array with the charge in each bunch in [C]"""</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">"""Return an array with the particle number in each bunch"""</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">"""Total beam current in [A]"""</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">"""Total beam charge in [C]"""</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">"""Total number of particles in the beam"""</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">"""Return an array with the mean position of alive particles for each</span>
+<span class="sd"> bunches"""</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">"""Return an array with the standard deviation of the position of alive </span>
+<span class="sd"> particles for each bunches"""</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">"""Return an array with the bunch emittance of alive particles for each</span>
+<span class="sd"> bunches and each plane"""</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">"""Return an array with the average Courant-Snyder invariant for each </span>
+<span class="sd"> bunch"""</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">"""Switch on MPI parallelisation and initialise a Mpi object"""</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">"""Gather beam, all bunches of the different processors are sent to </span>
+<span class="sd"> all processors. Rather slow"""</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">"Error, mpi is not initialised."</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">"""Call mpi_gather and switch off MPI parallelisation"""</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">"""</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 {"bunch_current", "bunch_charge", "bunch_particle", </span>
+<span class="sd"> "bunch_mean", "bunch_std", "bunch_emit"}</span>
+<span class="sd"> Variable to be plotted.</span>
+<span class="sd"> option : str, optional</span>
+<span class="sd"> If var is "bunch_mean", "bunch_std", or "bunch_emit, option needs </span>
+<span class="sd"> to be specified.</span>
+<span class="sd"> For "bunch_mean" and "bunch_std", </span>
+<span class="sd"> option = {"x","xp","y","yp","tau","delta"}.</span>
+<span class="sd"> For "bunch_emit", option = {"x","y","s"}.</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"> """</span>
+
+ <span class="n">var_dict</span> <span class="o">=</span> <span class="p">{</span>
+ <span class="s2">"bunch_current"</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">"bunch_charge"</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">"bunch_particle"</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">"bunch_mean"</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">"bunch_std"</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">"bunch_emit"</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">"bunch_mean"</span> <span class="ow">or</span> <span class="n">var</span> <span class="o">==</span> <span class="s2">"bunch_std"</span><span class="p">:</span>
+ <span class="n">value_dict</span> <span class="o">=</span> <span class="p">{</span>
+ <span class="s2">"x"</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span>
+ <span class="s2">"xp"</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span>
+ <span class="s2">"y"</span><span class="p">:</span> <span class="mi">2</span><span class="p">,</span>
+ <span class="s2">"yp"</span><span class="p">:</span> <span class="mi">3</span><span class="p">,</span>
+ <span class="s2">"tau"</span><span class="p">:</span> <span class="mi">4</span><span class="p">,</span>
+ <span class="s2">"delta"</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">"x (um)"</span><span class="p">,</span> <span class="s2">"x' ($</span><span class="se">\\</span><span class="s2">mu$rad)"</span><span class="p">,</span> <span class="s2">"y (um)"</span><span class="p">,</span> <span class="s2">"y' ($</span><span class="se">\\</span><span class="s2">mu$rad)"</span><span class="p">,</span>
+ <span class="s2">"$</span><span class="se">\\</span><span class="s2">tau$ (ps)"</span><span class="p">,</span> <span class="s2">"$</span><span class="se">\\</span><span class="s2">delta$"</span>
+ <span class="p">]</span>
+ <span class="n">label_std</span> <span class="o">=</span> <span class="p">[</span>
+ <span class="s2">"std x (um)"</span><span class="p">,</span> <span class="s2">"std x' ($</span><span class="se">\\</span><span class="s2">mu$rad)"</span><span class="p">,</span> <span class="s2">"std y (um)"</span><span class="p">,</span>
+ <span class="s2">"std y' ($</span><span class="se">\\</span><span class="s2">mu$rad)"</span><span class="p">,</span> <span class="s2">"std $</span><span class="se">\\</span><span class="s2">tau$ (ps)"</span><span class="p">,</span> <span class="s2">"std $</span><span class="se">\\</span><span class="s2">delta$"</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">'bunch number'</span><span class="p">)</span>
+ <span class="k">if</span> <span class="n">var</span> <span class="o">==</span> <span class="s2">"bunch_mean"</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">"bunch_emit"</span><span class="p">:</span>
+ <span class="n">value_dict</span> <span class="o">=</span> <span class="p">{</span><span class="s2">"x"</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="s2">"y"</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span> <span class="s2">"s"</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">"x"</span><span class="p">:</span> <span class="n">label_y</span> <span class="o">=</span> <span class="s2">"hor. emittance (nm.rad)"</span>
+ <span class="k">elif</span> <span class="n">option</span> <span class="o">==</span> <span class="s2">"y"</span><span class="p">:</span> <span class="n">label_y</span> <span class="o">=</span> <span class="s2">"ver. emittance (nm.rad)"</span>
+ <span class="k">elif</span> <span class="n">option</span> <span class="o">==</span> <span class="s2">"s"</span><span class="p">:</span> <span class="n">label_y</span> <span class="o">=</span> <span class="s2">"long. emittance (fm.rad)"</span>
+
+ <span class="n">ax</span><span class="o">.</span><span class="n">set_xlabel</span><span class="p">(</span><span class="s1">'bunch number'</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">"bunch_current"</span> <span class="ow">or</span> <span class="n">var</span> <span class="o">==</span> <span class="s2">"bunch_charge"</span> <span class="ow">or</span> <span class="n">var</span> <span class="o">==</span> <span class="s2">"bunch_particle"</span><span class="p">:</span>
+ <span class="n">scale</span> <span class="o">=</span> <span class="p">{</span>
+ <span class="s2">"bunch_current"</span><span class="p">:</span> <span class="mf">1e3</span><span class="p">,</span>
+ <span class="s2">"bunch_charge"</span><span class="p">:</span> <span class="mf">1e9</span><span class="p">,</span>
+ <span class="s2">"bunch_particle"</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">'bunch number'</span><span class="p">)</span>
+
+ <span class="k">if</span> <span class="n">var</span> <span class="o">==</span> <span class="s2">"bunch_current"</span><span class="p">:</span> <span class="n">label_y</span> <span class="o">=</span> <span class="s2">"bunch current (mA)"</span>
+ <span class="k">elif</span> <span class="n">var</span> <span class="o">==</span> <span class="s2">"bunch_charge"</span><span class="p">:</span> <span class="n">label_y</span> <span class="o">=</span> <span class="s2">"bunch chagre (nC)"</span>
+ <span class="k">else</span><span class="p">:</span> <span class="n">label_y</span> <span class="o">=</span> <span class="s2">"number of particles"</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">"current"</span> <span class="ow">or</span> <span class="n">var</span> <span class="o">==</span> <span class="s2">"charge"</span> <span class="ow">or</span> <span class="n">var</span> <span class="o">==</span> <span class="s2">"particle_number"</span><span class="p">:</span>
+ <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span>
+ <span class="s2">"'</span><span class="si">{0}</span><span class="s2">'is a total value and cannot be plotted."</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">"""</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 "<file_name>.hdf5".</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"> """</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">".hdf5"</span><span class="p">,</span>
+ <span class="s2">"a"</span><span class="p">,</span>
+ <span class="n">libver</span><span class="o">=</span><span class="s1">'earliest'</span><span class="p">,</span>
+ <span class="n">driver</span><span class="o">=</span><span class="s1">'mpio'</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">"Bunch_"</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">"alive"</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">"phasespace"</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">"current"</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">"""</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"> """</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">"r"</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">"Bunch_"</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">'current'</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">
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+ >modules</a> |</li>
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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 0000000000000000000000000000000000000000..f341313d18852138fa40dd03a8b7087a032f1c1f
--- /dev/null
+++ b/docs/build/html/_modules/mbtrack2/tracking/rf.html
@@ -0,0 +1,1889 @@
+
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+
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+ <h1>Source code for mbtrack2.tracking.rf</h1><div class="highlight"><pre>
+<span></span><span class="c1"># -*- coding: utf-8 -*-</span>
+<span class="sd">"""</span>
+<span class="sd">This module handles radio-frequency (RF) cavitiy elements. </span>
+<span class="sd">"""</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">"""</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"> """</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">"""</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"> """</span>
+ <span class="n">bunch</span><span class="p">[</span><span class="s2">"delta"</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">"tau"</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">"""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 > 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. "Investigation </span>
+<span class="sd"> of Longitudinal Beam Dynamics With Harmonic Cavities by Using the Code </span>
+<span class="sd"> Mbtrack." IPAC’19, Melbourne, Australia, 2019.</span>
+<span class="sd"> """</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">"""</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"> """</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">"""</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"> """</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 -> 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 -> 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">"beam"</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">"tau"</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">"beam"</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">"beam"</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">"beam"</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">"beam"</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">"beam"</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">"delta"</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">"beam"</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">"""</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 "rf" 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"> """</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">"rf"</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">"rf"</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">"rf"</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">"rf"</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">"beam"</span><span class="p">):</span>
+<span class="w"> </span><span class="sd">"""</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 "beam" or "rf".</span>
+
+<span class="sd"> """</span>
+ <span class="k">if</span> <span class="n">ref_frame</span> <span class="o">==</span> <span class="s2">"beam"</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">"rf"</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">"beam"</span><span class="p">):</span>
+<span class="w"> </span><span class="sd">"""</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 "beam" or "rf".</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"> """</span>
+ <span class="k">if</span> <span class="n">ref_frame</span> <span class="o">==</span> <span class="s2">"beam"</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">"rf"</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">"""</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"> """</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">"rf"</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">"rf"</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">"""Generator phasor in [V]"""</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">"""Cavity total phasor in [V]"""</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">"""Last cavity phasor value of each bunch in [V]"""</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">"""Last current generator phasor of each bunch in [A]"""</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">"""Last direct feedback current generator phasor of each bunch in [A]"""</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">"""Cavity total voltage in [V]"""</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">"""Cavity total phase in [rad]"""</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">"""Beam loading voltage in [V]"""</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">"""Beam loading phase in [rad]"""</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">"""Cavity loss factor in [V/C]"""</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">"""Harmonic number of the cavity"""</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">"""Number of cavities"""</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">"""Shunt impedance of a single cavity in [Ohm], defined as </span>
+<span class="sd"> 0.5*Vc*Vc/Pc."""</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">"""Shunt impedance [ohm]"""</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">"""Loaded shunt impedance [ohm]"""</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">"""Quality factor"""</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">"""Loaded quality factor"""</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">"""Coupling coefficient"""</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">"""Cavity detuning [Hz] - defined as (fr - m*f1)"""</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">"""Resonance frequency of the cavity in [Hz]"""</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">"""Angular resonance frequency in [Hz.rad]"""</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">"""Tuning angle in [rad]"""</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">"""Cavity filling time in [s]"""</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">"""Power dissipated in the cavity walls in [W]"""</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">"""</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"> """</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">"""</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"> """</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">"""</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"> """</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">"""</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"> """</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">"""Cavity impedance in [Ohm] for a given frequency f in [Hz]"""</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">"""</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"> """</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">"""</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"> """</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">"""</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"> """</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">"""</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"> """</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">'black'</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">'red'</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">'blue'</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">'Vc'</span><span class="p">,</span> <span class="s1">'Vb'</span><span class="p">,</span> <span class="s1">'Vg'</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">"""</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"> """</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">></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">"""</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"> """</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">></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">"""</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"> """</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">"Detune [Hz]"</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">"Threshold current [A]"</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">"DC Robinson stability limit"</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">"""Total RF voltage taking into account form factor amplitude F and form factor phase PHI"""</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">"""Return derivative of total RF voltage taking into account form factor amplitude F and form factor phase PHI"""</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">"""Return the second derivative of total RF voltage taking into account form factor amplitude F and form factor phase PHI"""</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">"""Return the generator voltage minus beam loading voltage taking into account form factor amplitude F and form factor phase PHI"""</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">"""Force feedback update from current CavityResonator parameters."""</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">"""</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 > 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"> """</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">"beam"</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">"beam"</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">"beam"</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">"""</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"> """</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"><</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">"delay must be >= 1."</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">"""</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"> """</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">"""</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"> """</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">"""</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"> """</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">"""</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 > 1e6), the Pgain of ~100 </span>
+<span class="sd"> can be used.</span>
+<span class="sd"> In a "bad" 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 >> 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 "track" 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-->(rot)-->IIR-->(-)-->(V->I,fac)-->PI-->Ig --> 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"> ==> 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"> ==> 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., & 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"> """</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">></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">></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"><</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">"Bad parameter set : delay or every"</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">"""</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"> """</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">"""</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"> """</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">"""Initialize feedforward constant."""</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">"""</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"> """</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">"""</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"> """</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">"""</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"> """</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">"""</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"> """</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">></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">"""Return IIR filter output."""</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">"""Return IIR cutoff frequency in [Hz]."""</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">"""</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'23. doi:10.18429/JACoW-IPAC2023-WEPL161</span>
+
+<span class="sd"> """</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"><</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">"Bad parameter set : DFB_delay or DFB_every"</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">"""Return DFB phase shift."""</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">"""Set DFB_phase_shift and phase_shift"""</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">"""</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"> """</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">"""</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"> """</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">"""</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"> """</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">"""</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"> """</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">"""</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"> """</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">"""</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"> """</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">"""</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"> """</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">"""Return the generator voltage main and DFB components in [V]."""</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">"""Return the modified synchrotron frequency in [Hz]."""</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">></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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diff --git a/docs/build/html/_modules/mbtrack2/tracking/synchrotron.html b/docs/build/html/_modules/mbtrack2/tracking/synchrotron.html
new file mode 100644
index 0000000000000000000000000000000000000000..5460f30defaeb758ecab2addd7d4cf8b76bdc051
--- /dev/null
+++ b/docs/build/html/_modules/mbtrack2/tracking/synchrotron.html
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+<!DOCTYPE html>
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+ <head>
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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">"""</span>
+<span class="sd">Module where the Synchrotron class is defined.</span>
+<span class="sd">"""</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">"""</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'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'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"> """</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">'L'</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">'E0'</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">'ac'</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">'tune'</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">'chro'</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">'U0'</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">'L'</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">'E0'</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">'ac'</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">'tune'</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">'chro'</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">'U0'</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">'tau'</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">'sigma_delta'</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">'sigma_0'</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">'emit'</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">'adts'</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">'mcf_order'</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">"""Harmonic number"""</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">"""Ring circumference [m]"""</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">"""Revolution time [s]"""</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">""""Fundamental RF period [s]"""</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">"""Revolution frequency [Hz]"""</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">"""Angular revolution frequency [Hz rad]"""</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">"""Fundamental RF frequency [Hz]"""</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">"""Fundamental RF angular frequency[Hz rad]"""</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">"""Fundamental RF wave number [m**-1]"""</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">"""Relativistic gamma"""</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">"""Relativistic beta"""</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">"""Nominal (total) energy of the ring [eV]"""</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">"""Higher-orders momentum compaction factor"""</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">"""</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["delta"], 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"> """</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">"""</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"> """</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">"""</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"> """</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">"""</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"> """</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">"ADTS needs to be provided manualy as no AT"</span> <span class="o">+</span>
+ <span class="s2">" lattice file is loaded."</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">"""</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"> """</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">"ADTS needs to be provided manualy as no AT"</span> <span class="o">+</span>
+ <span class="s2">" lattice file is loaded."</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">'k.'</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">'r'</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">'Energy (%)'</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">'Momemtum compaction factor'</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">'Data'</span><span class="p">,</span> <span class="s1">'polyfit'</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">"""</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"> """</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">"You must provide array of the same length for"</span>
+ <span class="s2">" V, phase and harmonics"</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">"""</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"> """</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">"If sevral cavities are provided, "</span>
+ <span class="s2">"harmonic_number and TimeLag should be provided."</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>
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new file mode 100644
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+++ b/docs/build/html/_modules/mbtrack2/tracking/wakepotential.html
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+
+ <h1>Source code for mbtrack2.tracking.wakepotential</h1><div class="highlight"><pre>
+<span></span><span class="c1"># -*- coding: utf-8 -*-</span>
+<span class="sd">"""</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">"""</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">"""</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"> """</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">'ignore'</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">"""</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"> """</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">"constant"</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">"""</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, "x" or "y".</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"> """</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">"dipole_"</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">"""</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: "Wlong", "Wxdip", ...</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"> """</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">"real"</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"><</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">></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">></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">></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">></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">></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"><</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">"constant"</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">"tau0_"</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">"dtau0_"</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">"W0_"</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">"""</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: "Wlong", "Wxdip", ...</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"> """</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">"Wlong"</span> <span class="ow">or</span> <span class="n">wake_type</span> <span class="o">==</span> <span class="s2">"Wxquad"</span> <span class="ow">or</span> <span class="n">wake_type</span> <span class="o">==</span> <span class="s2">"Wyquad"</span> <span class="ow">or</span> <span class="n">wake_type</span> <span class="o">==</span> <span class="s2">"Wxcst"</span> <span class="ow">or</span> <span class="n">wake_type</span> <span class="o">==</span> <span class="s2">"Wycst"</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">'same'</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">"Wxdip"</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">"x"</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">'same'</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">"Wydip"</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">"y"</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">'same'</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">"This type of wake is not taken into account."</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">"profile0_"</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">"""</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"> """</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">"tau"</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">"Wlong"</span><span class="p">:</span>
+ <span class="n">bunch</span><span class="p">[</span><span class="s2">"delta"</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">"Wxdip"</span><span class="p">:</span>
+ <span class="n">bunch</span><span class="p">[</span><span class="s2">"xp"</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">"Wydip"</span><span class="p">:</span>
+ <span class="n">bunch</span><span class="p">[</span><span class="s2">"yp"</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">"Wxquad"</span><span class="p">:</span>
+ <span class="n">bunch</span><span class="p">[</span><span class="s2">"xp"</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">"x"</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">"Wyquad"</span><span class="p">:</span>
+ <span class="n">bunch</span><span class="p">[</span><span class="s2">"yp"</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">"y"</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">"Wxcst"</span><span class="p">:</span>
+ <span class="n">bunch</span><span class="p">[</span><span class="s2">"xp"</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">"Wycst"</span><span class="p">:</span>
+ <span class="n">bunch</span><span class="p">[</span><span class="s2">"yp"</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">"""</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: "Wlong", "Wxdip", ...</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"> """</span>
+
+ <span class="n">labels</span> <span class="o">=</span> <span class="p">{</span>
+ <span class="s2">"Wlong"</span><span class="p">:</span> <span class="sa">r</span><span class="s2">"$W_{p,long}$ (V/pC)"</span><span class="p">,</span>
+ <span class="s2">"Wxdip"</span><span class="p">:</span> <span class="sa">r</span><span class="s2">"$W_{p,x}^</span><span class="si">{D}</span><span class="s2"> (V/pC)$"</span><span class="p">,</span>
+ <span class="s2">"Wydip"</span><span class="p">:</span> <span class="sa">r</span><span class="s2">"$W_{p,y}^</span><span class="si">{D}</span><span class="s2"> (V/pC)$"</span><span class="p">,</span>
+ <span class="s2">"Wxquad"</span><span class="p">:</span> <span class="sa">r</span><span class="s2">"$W_{p,x}^</span><span class="si">{Q}</span><span class="s2"> (V/pC/m)$"</span><span class="p">,</span>
+ <span class="s2">"Wyquad"</span><span class="p">:</span> <span class="sa">r</span><span class="s2">"$W_{p,y}^</span><span class="si">{Q}</span><span class="s2"> (V/pC/m)$"</span><span class="p">,</span>
+ <span class="s2">"Wxcst"</span><span class="p">:</span> <span class="sa">r</span><span class="s2">"$W_{p,x}^</span><span class="si">{M}</span><span class="s2">$ (V/pC)"</span><span class="p">,</span>
+ <span class="s2">"Wycst"</span><span class="p">:</span> <span class="sa">r</span><span class="s2">"$W_{p,y}^</span><span class="si">{M}</span><span class="s2">$ (V/pC)"</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">"tau0_"</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">"$</span><span class="se">\\</span><span class="s2">tau$ (ps)"</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">"profile0_"</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">"$\rho$ interpolated (a.u.)"</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">"$\rho$ (a.u.)"</span><span class="p">,</span>
+ <span class="n">linestyle</span><span class="o">=</span><span class="s1">'dashed'</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">"W0_"</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">"$W_</span><span class="si">{function}</span><span class="s2">$ (a.u.)"</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">"dipole_"</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">"Dipole moment (a.u.)"</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">"""</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: "Wlong", "Wxdip", ...</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"> """</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">"Wlong"</span> <span class="ow">or</span> <span class="n">wake_type</span> <span class="o">==</span> <span class="s2">"Wxquad"</span> <span class="ow">or</span> <span class="n">wake_type</span> <span class="o">==</span> <span class="s2">"Wyquad"</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">'same'</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">"Wxdip"</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">'same'</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">"Wydip"</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">'same'</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">"This type of wake is not taken into account."</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">"""</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: "Wlong", "Wxdip", ...</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"> """</span>
+
+ <span class="n">labels</span> <span class="o">=</span> <span class="p">{</span>
+ <span class="s2">"Wlong"</span><span class="p">:</span> <span class="sa">r</span><span class="s2">"$W_{p,long}$ (V/pC)"</span><span class="p">,</span>
+ <span class="s2">"Wxdip"</span><span class="p">:</span> <span class="sa">r</span><span class="s2">"$W_{p,x}^</span><span class="si">{D}</span><span class="s2"> (V/pC)$"</span><span class="p">,</span>
+ <span class="s2">"Wydip"</span><span class="p">:</span> <span class="sa">r</span><span class="s2">"$W_{p,y}^</span><span class="si">{D}</span><span class="s2"> (V/pC)$"</span><span class="p">,</span>
+ <span class="s2">"Wxquad"</span><span class="p">:</span> <span class="sa">r</span><span class="s2">"$W_{p,x}^</span><span class="si">{Q}</span><span class="s2"> (V/pC/m)$"</span><span class="p">,</span>
+ <span class="s2">"Wyquad"</span><span class="p">:</span> <span class="sa">r</span><span class="s2">"$W_{p,y}^</span><span class="si">{Q}</span><span class="s2"> (V/pC/m)$"</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">"$</span><span class="se">\\</span><span class="s2">tau$ (ps)"</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">"$\rho$ (a.u.)"</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">"$W_</span><span class="si">{function}</span><span class="s2">$ (a.u.)"</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">"Dipole moment (a.u.)"</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">"""</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"> """</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">"profile0_"</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">"Wlong"</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">"Wxdip"</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">"x"</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">"Wydip"</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">"y"</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">"Z"</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">'tau'</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">"Wlong"</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">"Wlong [V/C]"</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">" [V/C/m]"</span><span class="p">)</span>
+
+ <span class="n">column</span> <span class="o">=</span> <span class="p">[</span><span class="s1">'TD factor'</span><span class="p">,</span> <span class="s1">'FD factor'</span><span class="p">,</span> <span class="s1">'Relative error [%]'</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">"""</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"> """</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">"The wake function must be uniformly sampled."</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">"""</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"> """</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">"""</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 ["Wlong","Wxdip","Wydip"].</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. "Simultaneous computation of intrabunch and </span>
+<span class="sd"> interbunch collective beam motions in storage rings." NIM.A (2016).</span>
+<span class="sd"> """</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">"Wlong"</span><span class="p">,</span> <span class="s2">"Wxdip"</span><span class="p">,</span> <span class="s2">"Wydip"</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">></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">"The approximated wake functions are not valid."</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">"""</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"> """</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">"""</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"> "x" or "y".</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"> """</span>
+ <span class="k">if</span> <span class="n">plane</span> <span class="o">==</span> <span class="s2">"x"</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">"y"</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">"""</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"> """</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">"""</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"> """</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"><=</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">"Wlong"</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">"Wxdip"</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">"x"</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">"Wydip"</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">"y"</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">"Wxquad"</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">"Wyquad"</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">"""</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"> """</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">"Wlong"</span><span class="p">:</span>
+ <span class="n">bunch</span><span class="p">[</span><span class="s2">"delta"</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">"Wxdip"</span><span class="p">:</span>
+ <span class="n">bunch</span><span class="p">[</span><span class="s2">"xp"</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">"Wydip"</span><span class="p">:</span>
+ <span class="n">bunch</span><span class="p">[</span><span class="s2">"yp"</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">"Wxquad"</span><span class="p">:</span>
+ <span class="n">bunch</span><span class="p">[</span><span class="s2">"xp"</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">"x"</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">"Wyquad"</span><span class="p">:</span>
+ <span class="n">bunch</span><span class="p">[</span><span class="s2">"yp"</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">"y"</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">"""</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"> """</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>
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+++ b/docs/build/html/_modules/mbtrack2/utilities/beamloading.html
@@ -0,0 +1,487 @@
+
+<!DOCTYPE html>
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+<html lang="en">
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+
+ <h1>Source code for mbtrack2.utilities.beamloading</h1><div class="highlight"><pre>
+<span></span><span class="c1"># -*- coding: utf-8 -*-</span>
+<span class="sd">"""</span>
+<span class="sd">Module where the BeamLoadingEquilibrium class is defined.</span>
+<span class="sd">"""</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">"""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"> """</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">"1.0"</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">"""Update potentials with cavity and ring data."""</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">"""Return energy balance for the synchronous particle</span>
+<span class="sd"> (z = 0 ,delta = 0)."""</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">"""Return center of mass position in [s]"""</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">"""Scaled potential u(z)"""</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">"""Partial derivative of the scaled potential u(z) by z"""</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">"""Return Integral[f*g]/Integral[f] between B1 and B2"""</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">"""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"> """</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">"""Return bunch equilibrium profile at postion z"""</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">"""Plot the bunch equilibrium profile between z1 and z2"""</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">"$\tau$ [ps]"</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">"Equilibrium bunch profile"</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">"""Return the RF system total voltage at position z"""</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">"""Return derivative of the RF system total voltage at position z"""</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">"""Return the second derivative of the RF system total voltage at position z"""</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">"""Return the generator voltage minus beam loading voltage of the total RF system at position z"""</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">"""Plot the derivative of RF system total voltage between z1 and z2"""</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">"z [m]"</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">"Total RF voltage (V)"</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">"""Plot the RF system total voltage between z1 and z2"""</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">"z [m]"</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">"Total RF voltage (V)"</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">"""Return the rms bunch equilibrium size in [m]"""</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">'hybr'</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">"""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"> """</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">"The initial center of mass offset is "</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">" ps"</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">"The initial energy balance is "</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">" eV"</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">"The final center of mass offset is "</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">" ps"</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">"The final energy balance is "</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">" eV"</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">"The algorithm has converged: "</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">"""</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"> """</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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diff --git a/docs/build/html/_modules/mbtrack2/utilities/misc.html b/docs/build/html/_modules/mbtrack2/utilities/misc.html
new file mode 100644
index 0000000000000000000000000000000000000000..79c29713a92c343286c36f0dab40ff3d416d76a1
--- /dev/null
+++ b/docs/build/html/_modules/mbtrack2/utilities/misc.html
@@ -0,0 +1,390 @@
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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">"""</span>
+<span class="sd">This module defines miscellaneous utilities functions.</span>
+<span class="sd">"""</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">"Hermite"</span><span class="p">):</span>
+<span class="w"> </span><span class="sd">"""</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"> -"Hermite" 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"> """</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">"</span><span class="si">{}</span><span class="s2"> should be an Impedance object."</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">></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">"Hermite"</span><span class="p">,</span> <span class="s2">"Legendre"</span><span class="p">,</span> <span class="s2">"Sinusoidal"</span><span class="p">,</span> <span class="s2">"Sacherer"</span><span class="p">,</span> <span class="s2">"Chebyshev"</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">"Not implemanted yet."</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">"long"</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">"xdip"</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">"ydip"</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">"xdip"</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">"ydip"</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">"Effective impedance is only defined for long, xdip"</span>
+ <span class="s2">" and ydip impedance type."</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">"Hermite"</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">"</span><span class="si">{}</span><span class="s2"> should be an Impedance object."</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">></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">"Hermite"</span><span class="p">,</span> <span class="s2">"Legendre"</span><span class="p">,</span> <span class="s2">"Sinusoidal"</span><span class="p">,</span> <span class="s2">"Sacherer"</span><span class="p">,</span> <span class="s2">"Chebyshev"</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">"Not implemanted yet."</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">"long"</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">"xdip"</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">"ydip"</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">"xdip"</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">"ydip"</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">"Effective impedance is only defined for long, xdip"</span>
+ <span class="s2">" and ydip impedance type."</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">"""</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"> """</span>
+ <span class="k">if</span> <span class="n">y_radius</span> <span class="o"><</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">"data"</span> <span class="o">/</span> <span class="s2">"Yokoya_elliptic_from_Elias_USPAS.csv"</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">"x"</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"><</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">"dipy"</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">"dipx"</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">"quady"</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">"quadx"</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">"dipy"</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">"dipx"</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">"quady"</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">"quadx"</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">"""</span>
+<span class="sd"> Compute "beam" 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 "long"</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"> """</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">>=</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">"""</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"> """</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">>=</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">"long"</span><span class="p">:</span>
+ <span class="n">negative_data</span><span class="p">[</span><span class="s2">"imag"</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">"imag"</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">"xdip"</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">"ydip"</span><span class="p">):</span>
+ <span class="n">negative_data</span><span class="p">[</span><span class="s2">"real"</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">"real"</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">"xquad"</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">"yquad"</span><span class="p">):</span>
+ <span class="n">negative_data</span><span class="p">[</span><span class="s2">"real"</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">"real"</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">"Wrong impedance type"</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>
+ </div>
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+ <h1>Source code for mbtrack2.utilities.optics</h1><div class="highlight"><pre>
+<span></span><span class="c1"># -*- coding: utf-8 -*-</span>
+<span class="sd">"""</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">"""</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">"""</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"> """</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">"""</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"> """</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">"n_points"</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">"periodicity"</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">></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">"""Setup interpolation of the optic functions."""</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">'linear'</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">'linear'</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">'linear'</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">'linear'</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">'linear'</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">'linear'</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">'linear'</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">'linear'</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">'linear'</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">'linear'</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">'linear'</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">'linear'</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">"""</span>
+<span class="sd"> Return beta function at the location defined by the lattice file.</span>
+
+<span class="sd"> """</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">"""</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"> """</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">"""</span>
+<span class="sd"> Return alpha function at the location defined by the lattice file.</span>
+
+<span class="sd"> """</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">"""</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"> """</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">"""</span>
+<span class="sd"> Return beta function at the location defined by the lattice file.</span>
+
+<span class="sd"> """</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">"""</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"> """</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">"""</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"> """</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">"""</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"> """</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">"""</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"> """</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">"""</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"> """</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">"""</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 : {"beta", "alpha", "gamma", "dispersion", "mu"}</span>
+<span class="sd"> Optical variable to be plotted.</span>
+<span class="sd"> option : str</span>
+<span class="sd"> If var = "beta", "alpha" and "gamma", option = {"x","y"} specifying</span>
+<span class="sd"> the axis of interest.</span>
+<span class="sd"> If var = "dispersion", option = {"x","px","y","py"} 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"> """</span>
+
+ <span class="n">var_dict</span> <span class="o">=</span> <span class="p">{</span>
+ <span class="s2">"beta"</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">"alpha"</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">"gamma"</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">"dispersion"</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">"mu"</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">"dispersion"</span><span class="p">:</span>
+ <span class="n">option_dict</span> <span class="o">=</span> <span class="p">{</span><span class="s2">"x"</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="s2">"px"</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span> <span class="s2">"y"</span><span class="p">:</span> <span class="mi">2</span><span class="p">,</span> <span class="s2">"py"</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">"D$_</span><span class="si">{x}</span><span class="s2">$ (m)"</span><span class="p">,</span> <span class="s2">"D'$_</span><span class="si">{x}</span><span class="s2">$"</span><span class="p">,</span> <span class="s2">"D$_</span><span class="si">{y}</span><span class="s2">$ (m)"</span><span class="p">,</span> <span class="s2">"D'$_</span><span class="si">{y}</span><span class="s2">$"</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">"beta"</span> <span class="ow">or</span> <span class="n">var</span> <span class="o">==</span> <span class="s2">"alpha"</span> <span class="ow">or</span> <span class="n">var</span> <span class="o">==</span> <span class="s2">"gamma"</span> <span class="ow">or</span> <span class="n">var</span> <span class="o">==</span> <span class="s2">"mu"</span><span class="p">:</span>
+ <span class="n">option_dict</span> <span class="o">=</span> <span class="p">{</span><span class="s2">"x"</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="s2">"y"</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">"beta"</span><span class="p">:</span> <span class="s2">"$</span><span class="se">\\</span><span class="s2">beta$"</span><span class="p">,</span>
+ <span class="s2">"alpha"</span><span class="p">:</span> <span class="s2">"$</span><span class="se">\\</span><span class="s2">alpha$"</span><span class="p">,</span>
+ <span class="s2">"gamma"</span><span class="p">:</span> <span class="s2">"$</span><span class="se">\\</span><span class="s2">gamma$"</span><span class="p">,</span>
+ <span class="s2">"mu"</span><span class="p">:</span> <span class="s2">"$</span><span class="se">\\</span><span class="s2">mu$"</span>
+ <span class="p">}</span>
+
+ <span class="k">if</span> <span class="n">option</span> <span class="o">==</span> <span class="s2">"x"</span><span class="p">:</span> <span class="n">label_sup</span> <span class="o">=</span> <span class="s2">"$_</span><span class="si">{x}</span><span class="s2">$"</span>
+ <span class="k">elif</span> <span class="n">option</span> <span class="o">==</span> <span class="s2">"y"</span><span class="p">:</span> <span class="n">label_sup</span> <span class="o">=</span> <span class="s2">"$_</span><span class="si">{y}</span><span class="s2">$"</span>
+
+ <span class="n">unit</span> <span class="o">=</span> <span class="p">{</span>
+ <span class="s2">"beta"</span><span class="p">:</span> <span class="s2">" (m)"</span><span class="p">,</span>
+ <span class="s2">"alpha"</span><span class="p">:</span> <span class="s2">""</span><span class="p">,</span>
+ <span class="s2">"gamma"</span><span class="p">:</span> <span class="s2">" (m$^{-1}$)"</span><span class="p">,</span>
+ <span class="s2">"mu"</span><span class="p">:</span> <span class="s2">""</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">"Variable name is not found."</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">"position (m)"</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">"""</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"> """</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">"""</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. "Simultaneous computation of intrabunch </span>
+<span class="sd"> and interbunch collective beam motions in storage rings." 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"> """</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">"""</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"> """</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">></span> <span class="n">start_position</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">position</span> <span class="o"><</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">></span> <span class="n">start_position</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">position</span><span class="p">[</span><span class="mi">1</span><span class="p">:]</span> <span class="o"><</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">"""</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"> """</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">></span> <span class="n">start_position</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">position</span> <span class="o"><</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">></span> <span class="n">start_position</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">position</span><span class="p">[</span><span class="mi">1</span><span class="p">:]</span> <span class="o"><</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">"""Plot horizontal and vertical apertures."""</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">"Longitudinal position [m]"</span><span class="p">,</span>
+ <span class="n">ylabel</span><span class="o">=</span><span class="s2">"Horizontal aperture [mm]"</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">"Right"</span><span class="p">,</span> <span class="s2">"Left"</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">"Longitudinal position [m]"</span><span class="p">,</span>
+ <span class="n">ylabel</span><span class="o">=</span><span class="s2">"Vertical aperture [mm]"</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">"Top"</span><span class="p">,</span> <span class="s2">"Bottom"</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">'linear'</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">'linear'</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">'linear'</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">'linear'</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">"""Plot resistivity along the ring."""</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">"Longitudinal position [m]"</span><span class="p">,</span>
+ <span class="n">ylabel</span><span class="o">=</span><span class="s2">"Resistivity [ohm.m]"</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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+++ b/docs/build/html/_modules/mbtrack2/utilities/read_impedance.html
@@ -0,0 +1,464 @@
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+<!DOCTYPE html>
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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">"""</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">"""</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">'long'</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">"""</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 'long'.</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"> """</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">"#"</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">"</span><span class="se">\t</span><span class="s2">"</span><span class="p">,</span>
+ <span class="n">names</span><span class="o">=</span><span class="p">[</span><span class="s2">"Frequency"</span><span class="p">,</span> <span class="s2">"Real"</span><span class="p">,</span> <span class="s2">"Imaginary"</span><span class="p">])</span>
+ <span class="n">df</span><span class="p">[</span><span class="s2">"Frequency"</span><span class="p">]</span> <span class="o">=</span> <span class="n">df</span><span class="p">[</span><span class="s2">"Frequency"</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">"Real"</span><span class="p">]</span> <span class="o">=</span> <span class="n">df</span><span class="p">[</span><span class="s2">"Real"</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">"Imaginary"</span><span class="p">]</span> <span class="o">=</span> <span class="n">df</span><span class="p">[</span><span class="s2">"Imaginary"</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">"long"</span><span class="p">:</span>
+ <span class="n">df</span><span class="p">[</span><span class="s2">"Real"</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">"Real"</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">"Frequency"</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">"Real"</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">"Imaginary"</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">"#"</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">"</span><span class="se">\t</span><span class="s2">"</span><span class="p">,</span>
+ <span class="n">names</span><span class="o">=</span><span class="p">[</span><span class="s2">"Distance"</span><span class="p">,</span> <span class="s2">"Wake"</span><span class="p">])</span>
+ <span class="n">df</span><span class="p">[</span><span class="s2">"Time"</span><span class="p">]</span> <span class="o">=</span> <span class="n">df</span><span class="p">[</span><span class="s2">"Distance"</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">"Wake"</span><span class="p">]</span> <span class="o">=</span> <span class="n">df</span><span class="p">[</span><span class="s2">"Wake"</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">"Wake"</span><span class="p">]</span> <span class="o">=</span> <span class="n">df</span><span class="p">[</span><span class="s2">"Wake"</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">"Time"</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">"Wake"</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">'Zlong'</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">"""</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"> """</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">"Z"</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">"Frequency"</span><span class="p">,</span> <span class="s2">"Real"</span><span class="p">,</span> <span class="s2">"Imaginary"</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">"Frequency"</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">"Real"</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">"Imaginary"</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">"Real"</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">"Imaginary"</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">"W"</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">"Distance"</span><span class="p">,</span> <span class="s2">"Wake"</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">"Time"</span><span class="p">]</span> <span class="o">=</span> <span class="n">df</span><span class="p">[</span><span class="s2">"Distance"</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">"Time"</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">"Nan values have been interpolated to:"</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">"Wake"</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">"file_type should begin by Z or W."</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">"WZ"</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">"""</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 "Zlong_test.dat" the</span>
+<span class="sd"> suffix should be "_test.dat".</span>
+<span class="sd"> select : str, optional</span>
+<span class="sd"> Select which object to load. "W" for WakeFunction, "Z" for Impedance</span>
+<span class="sd"> and "WZ" or "ZW" 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"> """</span>
+ <span class="k">if</span> <span class="p">(</span><span class="n">select</span> <span class="o">==</span> <span class="s2">"WZ"</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">"ZW"</span><span class="p">):</span>
+ <span class="n">types</span> <span class="o">=</span> <span class="p">{</span><span class="s2">"W"</span><span class="p">:</span> <span class="n">WakeFunction</span><span class="p">,</span> <span class="s2">"Z"</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">"W"</span><span class="p">):</span>
+ <span class="n">types</span> <span class="o">=</span> <span class="p">{</span><span class="s2">"W"</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">"Z"</span><span class="p">):</span>
+ <span class="n">types</span> <span class="o">=</span> <span class="p">{</span><span class="s2">"Z"</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">"select should be W, Z or WZ."</span><span class="p">)</span>
+
+ <span class="n">components</span> <span class="o">=</span> <span class="p">[</span><span class="s2">"long"</span><span class="p">,</span> <span class="s2">"xdip"</span><span class="p">,</span> <span class="s2">"ydip"</span><span class="p">,</span> <span class="s2">"xquad"</span><span class="p">,</span> <span class="s2">"yquad"</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">"""</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"> "AZIMUTHAL" data.</span>
+<span class="sd"> If False, it is loaded from the "TRANSVERSE" 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"> """</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">"AZIMUTHAL"</span>
+ <span class="k">else</span><span class="p">:</span>
+ <span class="n">source</span> <span class="o">=</span> <span class="s2">"TRANSVERSE"</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">"Z"</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">"Frequency"</span><span class="p">,</span> <span class="s2">"Real"</span><span class="p">])</span>
+ <span class="n">df</span><span class="p">[</span><span class="s2">"Real"</span><span class="p">]</span> <span class="o">=</span> <span class="n">df</span><span class="p">[</span><span class="s2">"Real"</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">"Frequency"</span><span class="p">]</span> <span class="o">=</span> <span class="n">df</span><span class="p">[</span><span class="s2">"Frequency"</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">"Frequency"</span><span class="p">,</span> <span class="s2">"Imaginary"</span><span class="p">])</span>
+ <span class="n">df2</span><span class="p">[</span><span class="s2">"Imaginary"</span><span class="p">]</span> <span class="o">=</span> <span class="n">df2</span><span class="p">[</span><span class="s2">"Imaginary"</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">"Frequency"</span><span class="p">]</span> <span class="o">=</span> <span class="n">df2</span><span class="p">[</span><span class="s2">"Frequency"</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">"Frequency"</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">"Frequency"</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">"Real"</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">"Imaginary"</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">"W"</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">"Time"</span><span class="p">,</span> <span class="s2">"Wake"</span><span class="p">])</span>
+ <span class="n">df</span><span class="p">[</span><span class="s2">"Time"</span><span class="p">]</span> <span class="o">=</span> <span class="n">df</span><span class="p">[</span><span class="s2">"Time"</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">"Wake"</span><span class="p">]</span> <span class="o">=</span> <span class="n">df</span><span class="p">[</span><span class="s2">"Wake"</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">"dip"</span><span class="p">):</span>
+ <span class="n">df</span><span class="p">[</span><span class="s2">"Wake"</span><span class="p">]</span> <span class="o">=</span> <span class="n">df</span><span class="p">[</span><span class="s2">"Wake"</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">"Time"</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">"Wake"</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">' TITLE: LONGITUDINAL WAKE POTENTIAL </span><span class="se">\n</span><span class="s1">'</span><span class="p">:</span>
+ <span class="s1">'Wlong'</span><span class="p">,</span>
+ <span class="s1">' TITLE: REAL PART OF LONGITUDINAL IMPEDANCE </span><span class="se">\n</span><span class="s1">'</span><span class="p">:</span>
+ <span class="s1">'Zlong_re'</span><span class="p">,</span>
+ <span class="s1">' TITLE: IMAGINARY PART OF LONGITUDINAL IMPEDANCE </span><span class="se">\n</span><span class="s1">'</span><span class="p">:</span>
+ <span class="s1">'Zlong_im'</span><span class="p">,</span>
+ <span class="sa">f</span><span class="s1">' 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">'</span><span class="p">:</span>
+ <span class="s1">'Wxdip'</span><span class="p">,</span>
+ <span class="sa">f</span><span class="s1">' 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">'</span><span class="p">:</span>
+ <span class="s1">'Zxdip_re'</span><span class="p">,</span>
+ <span class="sa">f</span><span class="s1">' 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">'</span><span class="p">:</span>
+ <span class="s1">'Zxdip_im'</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">''</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">" TITLE:"</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">''</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">'\s+'</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">"W"</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">"w+"</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">"long"</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">"long"</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 & Wlongydip not implemented yet</span>
+ <span class="c1"># comp = _read_temp(tmp.name, abci_dict[header[0]]+'dip')</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">"Wxdip"</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">"Wydip"</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">"Z"</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">"re"</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">"w+"</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">"Z"</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">"im"</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">"w+"</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">"long"</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">"Zlong"</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">"long"</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 & Zlongydip not implemented yet</span>
+ <span class="c1"># comp = _read_temp(tmp1.name, "Zlongdip", 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">"Zxdip"</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">"Zydip"</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">'long'</span><span class="p">):</span>
+<span class="w"> </span><span class="sd">"""</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 'long'.</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"> """</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">"Distance"</span><span class="p">,</span> <span class="s2">"Wake"</span><span class="p">])</span>
+ <span class="n">df</span><span class="p">[</span><span class="s2">"Time"</span><span class="p">]</span> <span class="o">=</span> <span class="n">df</span><span class="p">[</span><span class="s2">"Distance"</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">"Wake"</span><span class="p">]</span> <span class="o">=</span> <span class="n">df</span><span class="p">[</span><span class="s2">"Wake"</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">'long'</span><span class="p">:</span>
+ <span class="n">df</span><span class="p">[</span><span class="s2">"Wake"</span><span class="p">]</span> <span class="o">=</span> <span class="n">df</span><span class="p">[</span><span class="s2">"Wake"</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">"Time"</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">"Wake"</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>
+ </div>
+ <div class="sphinxsidebar" role="navigation" aria-label="main navigation">
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+ >modules</a> |</li>
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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
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--- /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 — mbtrack2 0.6.0 documentation</title>
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+ <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">"""</span>
+<span class="sd">Module where bunch and beam spectrums and profile are defined.</span>
+<span class="sd">"""</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">"Hermite"</span><span class="p">):</span>
+<span class="w"> </span><span class="sd">"""</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"> -"Hermite" modes for Gaussian bunches (typical for electrons)</span>
+<span class="sd"> -"Chebyshev" for airbag bunches</span>
+<span class="sd"> -"Legendre" for parabolic bunches (typical for protons)</span>
+<span class="sd"> -"Sacherer" or "Sinusoidal" 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"> """</span>
+
+ <span class="k">if</span> <span class="n">mode</span> <span class="o">==</span> <span class="s2">"Hermite"</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">"Chebyshev"</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">"Legendre"</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">"Sacherer"</span> <span class="ow">or</span> <span class="n">mode</span> <span class="o">==</span> <span class="s2">"Sinusoidal"</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">"Not implemanted yet."</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">"""</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"> """</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">"""</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"> """</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">"""</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"> """</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> »</li>
+ <li class="nav-item nav-item-1"><a href="../../index.html" >Module code</a> »</li>
+ <li class="nav-item nav-item-this"><a href="">mbtrack2.utilities.spectrum</a></li>
+ </ul>
+ </div>
+ <div class="footer" role="contentinfo">
+ © 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 0000000000000000000000000000000000000000..e4a144e71baa32d7db8a321dad04cfc7d987c926
--- /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 0000000000000000000000000000000000000000..2d40343a406285ee6e46dbd2564089030b7ea3cf
--- /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 0000000000000000000000000000000000000000..7b7e8f42ed3d2f9a6c6aaef50588153626829a70
--- /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 0000000000000000000000000000000000000000..7d99aebe497efa9d06f618ec0f9fc7797ec3f4e6
--- /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 0000000000000000000000000000000000000000..36cd62af870903ce7758b93a8b82dc6e3821b745
--- /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 0000000000000000000000000000000000000000..36df13cb70e54d50e6d3ed61a1a23a6deb0d81e6
--- /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 0000000000000000000000000000000000000000..e23f1f6963dce8fae82b56f772a419b03a8cc407
--- /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 0000000000000000000000000000000000000000..8549469dc29fac0cbf16d10355e3313897cb3752
--- /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 0000000000000000000000000000000000000000..088967717207949a5bf50138c5f253fd839b831f
--- /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 0000000000000000000000000000000000000000..c3db08d1c3896f616576ba6e6b96dc80fcfc50b9
--- /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 0000000000000000000000000000000000000000..00e2e111dd5c7be61945965c4f89280ac7d2c45a
--- /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
index 0000000000000000000000000000000000000000..a858a410e4faa62ce324d814e4b816fff83a6fb3
Binary files /dev/null and b/docs/build/html/_static/file.png differ
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 0000000000000000000000000000000000000000..fc6c299b73e792ef288e785c22393a5df9dded4b
--- /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 0000000000000000000000000000000000000000..c4c6022f2982e8dae64cebd6b9a2b59f2547faad
--- /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 0000000000000000000000000000000000000000..2e22b06ab13bec689de4d1530b8b625bc6d69ae8
--- /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;
+ }
+}
+
diff --git a/docs/build/html/_static/minus.png b/docs/build/html/_static/minus.png
new file mode 100644
index 0000000000000000000000000000000000000000..d96755fdaf8bb2214971e0db9c1fd3077d7c419d
Binary files /dev/null and b/docs/build/html/_static/minus.png differ
diff --git a/docs/build/html/_static/nature.css b/docs/build/html/_static/nature.css
new file mode 100644
index 0000000000000000000000000000000000000000..5e981bf6e41195f21d6dd875256b36021f3cebb7
--- /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
diff --git a/docs/build/html/_static/plus.png b/docs/build/html/_static/plus.png
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diff --git a/docs/build/html/_static/pygments.css b/docs/build/html/_static/pygments.css
new file mode 100644
index 0000000000000000000000000000000000000000..6110e9f1add5782e8b1ba15a6801e1cdf733a1e0
--- /dev/null
+++ b/docs/build/html/_static/pygments.css
@@ -0,0 +1,84 @@
+pre { line-height: 125%; }
+td.linenos .normal { color: inherit; background-color: transparent; padding-left: 5px; padding-right: 5px; }
+span.linenos { color: inherit; background-color: transparent; padding-left: 5px; padding-right: 5px; }
+td.linenos .special { color: #000000; background-color: #ffffc0; padding-left: 5px; padding-right: 5px; }
+span.linenos.special { color: #000000; background-color: #ffffc0; padding-left: 5px; padding-right: 5px; }
+.highlight .hll { background-color: #ffffcc }
+.highlight { background: #f8f8f8; }
+.highlight .c { color: #8f5902; font-style: italic } /* Comment */
+.highlight .err { color: #a40000; border: 1px solid #ef2929 } /* Error */
+.highlight .g { color: #000000 } /* Generic */
+.highlight .k { color: #204a87; font-weight: bold } /* Keyword */
+.highlight .l { color: #000000 } /* Literal */
+.highlight .n { color: #000000 } /* Name */
+.highlight .o { color: #ce5c00; font-weight: bold } /* Operator */
+.highlight .x { color: #000000 } /* Other */
+.highlight .p { color: #000000; font-weight: bold } /* Punctuation */
+.highlight .ch { color: #8f5902; font-style: italic } /* Comment.Hashbang */
+.highlight .cm { color: #8f5902; font-style: italic } /* Comment.Multiline */
+.highlight .cp { color: #8f5902; font-style: italic } /* Comment.Preproc */
+.highlight .cpf { color: #8f5902; font-style: italic } /* Comment.PreprocFile */
+.highlight .c1 { color: #8f5902; font-style: italic } /* Comment.Single */
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+.highlight .gd { color: #a40000 } /* Generic.Deleted */
+.highlight .ge { color: #000000; font-style: italic } /* Generic.Emph */
+.highlight .ges { color: #000000; font-weight: bold; font-style: italic } /* Generic.EmphStrong */
+.highlight .gr { color: #ef2929 } /* Generic.Error */
+.highlight .gh { color: #000080; font-weight: bold } /* Generic.Heading */
+.highlight .gi { color: #00A000 } /* Generic.Inserted */
+.highlight .go { color: #000000; font-style: italic } /* Generic.Output */
+.highlight .gp { color: #8f5902 } /* Generic.Prompt */
+.highlight .gs { color: #000000; font-weight: bold } /* Generic.Strong */
+.highlight .gu { color: #800080; font-weight: bold } /* Generic.Subheading */
+.highlight .gt { color: #a40000; font-weight: bold } /* Generic.Traceback */
+.highlight .kc { color: #204a87; font-weight: bold } /* Keyword.Constant */
+.highlight .kd { color: #204a87; font-weight: bold } /* Keyword.Declaration */
+.highlight .kn { color: #204a87; font-weight: bold } /* Keyword.Namespace */
+.highlight .kp { color: #204a87; font-weight: bold } /* Keyword.Pseudo */
+.highlight .kr { color: #204a87; font-weight: bold } /* Keyword.Reserved */
+.highlight .kt { color: #204a87; font-weight: bold } /* Keyword.Type */
+.highlight .ld { color: #000000 } /* Literal.Date */
+.highlight .m { color: #0000cf; font-weight: bold } /* Literal.Number */
+.highlight .s { color: #4e9a06 } /* Literal.String */
+.highlight .na { color: #c4a000 } /* Name.Attribute */
+.highlight .nb { color: #204a87 } /* Name.Builtin */
+.highlight .nc { color: #000000 } /* Name.Class */
+.highlight .no { color: #000000 } /* Name.Constant */
+.highlight .nd { color: #5c35cc; font-weight: bold } /* Name.Decorator */
+.highlight .ni { color: #ce5c00 } /* Name.Entity */
+.highlight .ne { color: #cc0000; font-weight: bold } /* Name.Exception */
+.highlight .nf { color: #000000 } /* Name.Function */
+.highlight .nl { color: #f57900 } /* Name.Label */
+.highlight .nn { color: #000000 } /* Name.Namespace */
+.highlight .nx { color: #000000 } /* Name.Other */
+.highlight .py { color: #000000 } /* Name.Property */
+.highlight .nt { color: #204a87; font-weight: bold } /* Name.Tag */
+.highlight .nv { color: #000000 } /* Name.Variable */
+.highlight .ow { color: #204a87; font-weight: bold } /* Operator.Word */
+.highlight .pm { color: #000000; font-weight: bold } /* Punctuation.Marker */
+.highlight .w { color: #f8f8f8 } /* Text.Whitespace */
+.highlight .mb { color: #0000cf; font-weight: bold } /* Literal.Number.Bin */
+.highlight .mf { color: #0000cf; font-weight: bold } /* Literal.Number.Float */
+.highlight .mh { color: #0000cf; font-weight: bold } /* Literal.Number.Hex */
+.highlight .mi { color: #0000cf; font-weight: bold } /* Literal.Number.Integer */
+.highlight .mo { color: #0000cf; font-weight: bold } /* Literal.Number.Oct */
+.highlight .sa { color: #4e9a06 } /* Literal.String.Affix */
+.highlight .sb { color: #4e9a06 } /* Literal.String.Backtick */
+.highlight .sc { color: #4e9a06 } /* Literal.String.Char */
+.highlight .dl { color: #4e9a06 } /* Literal.String.Delimiter */
+.highlight .sd { color: #8f5902; font-style: italic } /* Literal.String.Doc */
+.highlight .s2 { color: #4e9a06 } /* Literal.String.Double */
+.highlight .se { color: #4e9a06 } /* Literal.String.Escape */
+.highlight .sh { color: #4e9a06 } /* Literal.String.Heredoc */
+.highlight .si { color: #4e9a06 } /* Literal.String.Interpol */
+.highlight .sx { color: #4e9a06 } /* Literal.String.Other */
+.highlight .sr { color: #4e9a06 } /* Literal.String.Regex */
+.highlight .s1 { color: #4e9a06 } /* Literal.String.Single */
+.highlight .ss { color: #4e9a06 } /* Literal.String.Symbol */
+.highlight .bp { color: #3465a4 } /* Name.Builtin.Pseudo */
+.highlight .fm { color: #000000 } /* Name.Function.Magic */
+.highlight .vc { color: #000000 } /* Name.Variable.Class */
+.highlight .vg { color: #000000 } /* Name.Variable.Global */
+.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 0000000000000000000000000000000000000000..ac4d5861f95f5c6161b846522d572532725aa275
--- /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 0000000000000000000000000000000000000000..ffd77af9648a47d389f2d6976d4aa1c44d7ce7ce
--- /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 = {
+ '&': '&',
+ '<': '<',
+ '>': '>',
+ '"': '"',
+ "'": ''',
+ '`': '`'
+ };
+
+ // 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 0000000000000000000000000000000000000000..cf177d4285ab55fbc16406a5ec827b80e7eecd53
--- /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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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 0000000000000000000000000000000000000000..e1deb15d5a9432e596c666c9df9cb588e9457213
--- /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 — 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> »</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> »</li>
+ <li class="nav-item nav-item-this"><a href="">Index</a></li>
+ </ul>
+ </div>
+ <div class="footer" role="contentinfo">
+ © 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 0000000000000000000000000000000000000000..06506293b232e16a359c397731974e07eeb990a6
--- /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! — 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> »</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> »</li>
+ <li class="nav-item nav-item-this"><a href="">Welcome to mbtrack2’s documentation!</a></li>
+ </ul>
+ </div>
+ <div class="footer" role="contentinfo">
+ © 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 0000000000000000000000000000000000000000..4563121865dc45f838c344daec4c677aa9538233
--- /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 — 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> »</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>
+
+
+ <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>
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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., & 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 << (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>â€nameâ€<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=â€Zlongâ€, component=â€realâ€, 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 “imagâ€.</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
+Deviceâ€, 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.â€
+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.â€
+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: “longâ€, “xdipâ€, “xquadâ€, …</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 > n, the
+input is padded with zeros. If nout < 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<0.
+If False, the original result is preserved.
+If a float is given, the pseudo wake function is trimmed from
+time <= 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 “Zâ€, drop all impedance components.
+If “Wâ€â€, 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: “longâ€, “xdipâ€, “xquadâ€, …</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 / câ€.</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 > n, the
+input is padded with zeros. If nout < 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 > n, the
+input is padded with zeros. If nout < 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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+
+ <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 ringsâ€, SLAC-PUB-14561
+[2] : D. Zhou, “Coherent synchrotron radiation and microwave instability in
+electron storage ringsâ€, 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 ringâ€, 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 ringâ€, 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=â€linearâ€, the rise time is an assymptotic grow time
+(i.e. y ~ exp(sqrt(t/tau))) [1].
+If model=â€decoherenceâ€, the rise time is an e-folding time
+(i.e. y ~ exp(t/tau)) [2].
+If model=â€non-linearâ€, 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 << sigmax,sigmay</p>
+</dd>
+<dt>The decoherence model assumes that [2]:</dt><dd><p>Lsep << c / (2 * pi * ion_frequency)
+Lsep << c / (2 * pi * betatron_frequency)</p>
+</dd>
+<dt>The non-linear model assumes that [3]:</dt><dd><p>x,y >> 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 “linearâ€, use [1].
+If “decoherenceâ€, use [2].
+If “non-linearâ€, 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 “COâ€.</p>
+</dd>
+<dt>dim<span class="classifier">“y†o “xâ€, optional</span></dt><dd><p>Dimension to consider. The default is “yâ€.</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 simulationsâ€, Physical Review E 52 (1995).
+[2] : G. V. Stupakov, T. O. Raubenheimer, and F. Zimmermann, “Fast beam-ion
+instability. II. effect of ion decoherenceâ€, Physical Review E 52 (1995).
+[3] : Chao, A. W., & 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 revisitedâ€, Reviews of modern physics
+43 (1971).
+[2] : P. F. Tavares, “Bremsstrahlung detection of ions trapped in the EPA
+electron beamâ€, 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 “COâ€.</p>
+</dd>
+<dt>dim<span class="classifier">“y†o “xâ€, optional</span></dt><dd><p>Dimension to consider. The default is “yâ€.</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 simulationsâ€, Physical Review E 52 (1995).
+[2] : G. V. Stupakov, T. O. Raubenheimer, and F. Zimmermann, “Fast beam-ion
+instability. II. effect of ion decoherenceâ€, 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>
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+
+ <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
+@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
+@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
+@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
+@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 @parallel which handle the embarrassingly
+parallel case which happens when there is no bunch to bunch
+interaction in the tracking routine.</p>
+<p>Adding @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
+@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
+@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
+@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
+@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
+@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">{“xâ€,â€yâ€,â€sâ€}</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
+@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">{“xâ€,â€yâ€,â€sâ€}</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 “sâ€.
+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 “sâ€.
+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 “tauâ€.</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_currentâ€, “bunch_chargeâ€, “bunch_particleâ€, </span></dt><dd><blockquote>
+<div><p>“bunch_meanâ€, “bunch_stdâ€, “bunch_emitâ€}</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_meanâ€, “bunch_stdâ€, or “bunch_emit, option needs
+to be specified.
+For “bunch_mean†and “bunch_stdâ€,</p>
+<blockquote>
+<div><p>option = {“xâ€,â€xpâ€,â€yâ€,â€ypâ€,â€tauâ€,â€deltaâ€}.</p>
+</div></blockquote>
+<p>For “bunch_emitâ€, option = {“xâ€,â€yâ€,â€sâ€}.
+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 “<file_name>.hdf5â€.</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]. !!! -> 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=â€tauâ€, y_var=â€deltaâ€, plot_type=â€jâ€)</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 “tauâ€.</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, {“scatterâ€, “kdeâ€, “histâ€, “hexâ€, “regâ€, “residâ€}</span></dt><dd><p>Kind of plot to draw. See seeborn documentation.
+The defualt value is “scatterâ€.</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 “tauâ€.</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 “<file_name>.hdf5â€.</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 > 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 “rfâ€.</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 “rfâ€.</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 > 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 > 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 >> 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–>(rot)–>IIR–>(-)–>(V->I,fac)–>PI–>Ig –> 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
+==> 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>==> 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., & 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
+@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[“deltaâ€], 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 [“Wlongâ€,â€Wxdipâ€,â€Wydipâ€].</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 “yâ€.</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 “yâ€.</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: “Wlongâ€, “Wxdipâ€, …</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: “Wlongâ€, “Wxdipâ€, …</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: “Wlongâ€, “Wxdipâ€, …</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: “Wlongâ€, “Wxdipâ€, …</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: “Wlongâ€, “Wxdipâ€, …</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
+@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>
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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>
+ <li class="nav-item nav-item-0"><a href="index.html">mbtrack2 0.6.0 documentation</a> »</li>
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new file mode 100644
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@@ -0,0 +1,1259 @@
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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> »</li>
+ <li class="nav-item nav-item-this"><a href="">mbtrack2.tracking.monitors package</a></li>
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+
+ <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>“allâ€</p></li>
+<li><p>“tauâ€</p></li>
+<li><p>“xâ€</p></li>
+<li><p>“yâ€</p></li>
+<li><p>“xy†or “yxâ€</p></li>
+<li><p>“xtau†or “tauxâ€</p></li>
+<li><p>“ytau†or “tauyâ€</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>“allâ€</p></li>
+<li><p>“tauâ€</p></li>
+<li><p>“xâ€</p></li>
+<li><p>“yâ€</p></li>
+<li><p>“xy†or “yxâ€</p></li>
+<li><p>“xtau†or “tauxâ€</p></li>
+<li><p>“ytau†or “tauyâ€</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, “Wxdipâ€, …</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">{“currentâ€,â€emitâ€,â€meanâ€,â€stdâ€,â€cs_invariantâ€}</span></dt><dd><p>HDF5 file’s dataset to be plotted. The default is “meanâ€.</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 “emitâ€, dimension = {“xâ€,â€yâ€,â€sâ€},
+for “cs_invariantâ€, dimension = {“xâ€,â€yâ€,â€sâ€},
+for “mean†and “stdâ€, dimension = {“xâ€,â€xpâ€,â€yâ€,â€ypâ€,â€tauâ€,â€deltaâ€}.
+not used if “currentâ€.</p>
+</dd>
+</dl>
+</div></blockquote>
+<p>The default is “tauâ€.</p>
+</dd>
+<dt>stat_var<span class="classifier">{“meanâ€, “stdâ€}</span></dt><dd><p>Statistical value of the dimension.</p>
+</dd>
+<dt>x_var<span class="classifier">{“timeâ€, “indexâ€}</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 = “indexâ€.
+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">{“xâ€,â€yâ€,â€tauâ€}, optional</span></dt><dd><p>The dimension of the dataset to plot.
+The default is “tauâ€.</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">{“currentâ€, “emitâ€, “meanâ€, “stdâ€, “cs_invariantâ€}</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 “currentâ€,
+otherwise use the following :</p>
+<blockquote>
+<div><p>for “emitâ€, dimension = {“xâ€,â€yâ€,â€sâ€},
+for “cs_invariantâ€, dimension = {“xâ€,â€yâ€,â€sâ€},
+for “mean†and “stdâ€, dimension = {“xâ€,â€xpâ€,â€yâ€,â€ypâ€,â€tauâ€,â€deltaâ€},
+for “actionâ€, dimension = {“xâ€,â€yâ€}.</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_incoherentâ€, “coherentâ€, “incoherentâ€}</span></dt><dd><p>HDF5 file’s dataset to be plotted.
+The default is “incoherentâ€.</p>
+</dd>
+<dt>dim<span class="classifier">{“xâ€,â€yâ€,â€tauâ€}, optional</span></dt><dd><p>The dimension of the dataset to plot.
+The default is “tauâ€.</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 “beamâ€, “cavityâ€, “generator†or
+“igâ€.</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 {“xâ€, “xpâ€, “yâ€, “ypâ€, “tauâ€, “deltaâ€}</span></dt><dd><p>If dataset is “particlesâ€, 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 “tauâ€</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: “Wlongâ€, “Wxdipâ€, …</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">{“currentâ€,â€emitâ€,â€meanâ€,â€stdâ€,â€cs_invariantâ€}</span></dt><dd><p>HDF5 file’s dataset to be plotted. The default is “meanâ€.</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 “emitâ€, dimension = {“xâ€,â€yâ€,â€sâ€},
+for “cs_invariantâ€, dimension = {“xâ€,â€yâ€,â€sâ€},
+for “mean†and “stdâ€, dimension = {“xâ€,â€xpâ€,â€yâ€,â€ypâ€,â€tauâ€,â€deltaâ€}.
+not used if “currentâ€.</p>
+</dd>
+</dl>
+</div></blockquote>
+<p>The default is “tauâ€.</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">{“xâ€,â€yâ€,â€tauâ€}, optional</span></dt><dd><p>The dimension of the dataset to plot.
+The default is “tauâ€.</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">{“coherentâ€, “incoherentâ€}</span></dt><dd><p>HDF5 file’s dataset to be plotted.
+The default is “incoherentâ€.</p>
+</dd>
+<dt>dim<span class="classifier">{“xâ€,â€yâ€,â€tauâ€}, optional</span></dt><dd><p>The dimension of the dataset to plot.
+The default is “tauâ€.</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.hdf5â€</p></li>
+<li><p>“files_prefix_1.hdf5â€</p></li>
+</ul>
+<p>…
+- “files_prefix_files_number.hdf5â€</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>
+
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+ <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 “longâ€
+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">{“betaâ€, “alphaâ€, “gammaâ€, “dispersionâ€, “muâ€}</span></dt><dd><p>Optical variable to be plotted.</p>
+</dd>
+<dt>option<span class="classifier">str</span></dt><dd><p>If var = “betaâ€, “alpha†and “gammaâ€, option = {“xâ€,â€yâ€} specifying
+the axis of interest.
+If var = “dispersionâ€, option = {“xâ€,â€pxâ€,â€yâ€,â€pyâ€} 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.datâ€.</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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+ </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> »</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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+ <link rel="stylesheet" type="text/css" href="_static/pygments.css" />
+ <link rel="stylesheet" type="text/css" href="_static/nature.css" />
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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> »</li>
+ <li class="nav-item nav-item-this"><a href="">Python Module Index</a></li>
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+ <div class="body" role="main">
+
+
+ <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> </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>   
+ <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>   
+ <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>   
+ <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>   
+ <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>   
+ <a href="mbtrack2.impedance.html#module-mbtrack2.impedance.resonator"><code class="xref">mbtrack2.impedance.resonator</code></a></td><td>
+ <em></em></td></tr>
+ <tr class="cg-1">
+ <td></td>
+ <td>   
+ <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>   
+ <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>   
+ <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>   
+ <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>   
+ <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>   
+ <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>   
+ <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>   
+ <a href="mbtrack2.tracking.html#module-mbtrack2.tracking.element"><code class="xref">mbtrack2.tracking.element</code></a></td><td>
+ <em></em></td></tr>
+ <tr class="cg-1">
+ <td></td>
+ <td>   
+ <a href="mbtrack2.tracking.html#module-mbtrack2.tracking.feedback"><code class="xref">mbtrack2.tracking.feedback</code></a></td><td>
+ <em></em></td></tr>
+ <tr class="cg-1">
+ <td></td>
+ <td>   
+ <a href="mbtrack2.tracking.monitors.html#module-mbtrack2.tracking.monitors"><code class="xref">mbtrack2.tracking.monitors</code></a></td><td>
+ <em></em></td></tr>
+ <tr class="cg-1">
+ <td></td>
+ <td>   
+ <a href="mbtrack2.tracking.monitors.html#module-mbtrack2.tracking.monitors.monitors"><code class="xref">mbtrack2.tracking.monitors.monitors</code></a></td><td>
+ <em></em></td></tr>
+ <tr class="cg-1">
+ <td></td>
+ <td>   
+ <a href="mbtrack2.tracking.monitors.html#module-mbtrack2.tracking.monitors.plotting"><code class="xref">mbtrack2.tracking.monitors.plotting</code></a></td><td>
+ <em></em></td></tr>
+ <tr class="cg-1">
+ <td></td>
+ <td>   
+ <a href="mbtrack2.tracking.monitors.html#module-mbtrack2.tracking.monitors.tools"><code class="xref">mbtrack2.tracking.monitors.tools</code></a></td><td>
+ <em></em></td></tr>
+ <tr class="cg-1">
+ <td></td>
+ <td>   
+ <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>   
+ <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>   
+ <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>   
+ <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>   
+ <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>   
+ <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>   
+ <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>   
+ <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>   
+ <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>   
+ <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>   
+ <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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\ No newline at end of file
diff --git a/docs/build/html/search.html b/docs/build/html/search.html
new file mode 100644
index 0000000000000000000000000000000000000000..0ba1cc492831d0915f26c56ba7d92b06595fa70e
--- /dev/null
+++ b/docs/build/html/search.html
@@ -0,0 +1,103 @@
+
+<!DOCTYPE html>
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+ >modules</a> |</li>
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+ </form>
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+
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+ </div>
+ </div>
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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>
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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> »</li>
+ <li class="nav-item nav-item-this"><a href="">Search</a></li>
+ </ul>
+ </div>
+ <div class="footer" role="contentinfo">
+ © Copyright 2024, A. Gamelin et al.
+ Created using <a href="https://www.sphinx-doc.org/">Sphinx</a> 5.0.2.
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+</html>
\ No newline at end of file
diff --git a/docs/build/html/searchindex.js b/docs/build/html/searchindex.js
new file mode 100644
index 0000000000000000000000000000000000000000..cff3f41f523b398ef307170d8760a370a5d7940d
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@@ -0,0 +1 @@
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"monitors"], [5, 0, 0, "-", "plotting"], [5, 0, 0, "-", "tools"]], "mbtrack2.tracking.monitors.monitors": [[5, 1, 1, "", "BeamMonitor"], [5, 1, 1, "", "BeamSpectrumMonitor"], [5, 1, 1, "", "BunchMonitor"], [5, 1, 1, "", "BunchSpectrumMonitor"], [5, 1, 1, "", "CavityMonitor"], [5, 1, 1, "", "Monitor"], [5, 1, 1, "", "PhaseSpaceMonitor"], [5, 1, 1, "", "ProfileMonitor"], [5, 1, 1, "", "WakePotentialMonitor"]], "mbtrack2.tracking.monitors.monitors.BeamMonitor": [[5, 2, 1, "", "to_buffer"], [5, 2, 1, "", "to_buffer_no_mpi"], [5, 2, 1, "", "track"], [5, 2, 1, "", "write"], [5, 2, 1, "", "write_no_mpi"]], "mbtrack2.tracking.monitors.monitors.BeamSpectrumMonitor": [[5, 3, 1, "", "fft_resolution"], [5, 3, 1, "", "frequency_samples"], [5, 2, 1, "", "get_beam_spectrum"], [5, 3, 1, "", "signal_resolution"], [5, 2, 1, "", "to_buffer"], [5, 2, 1, "", "track"], [5, 2, 1, "", "write"]], "mbtrack2.tracking.monitors.monitors.BunchMonitor": [[5, 2, 1, "", "track"]], "mbtrack2.tracking.monitors.monitors.BunchSpectrumMonitor": [[5, 3, 1, "", "fft_resolution"], [5, 3, 1, "", "frequency_samples"], [5, 2, 1, "", "get_coherent_spectrum"], [5, 2, 1, "", "get_incoherent_spectrum"], [5, 3, 1, "", "signal_resolution"], [5, 2, 1, "", "to_buffer"], [5, 2, 1, "", "track"], [5, 2, 1, "", "write"]], "mbtrack2.tracking.monitors.monitors.CavityMonitor": [[5, 2, 1, "", "track"]], "mbtrack2.tracking.monitors.monitors.Monitor": [[5, 2, 1, "", "close"], [5, 3, 1, "", "file"], [5, 3, 1, "", "file_name"], [5, 2, 1, "", "monitor_init"], [5, 2, 1, "", "to_buffer"], [5, 2, 1, "", "track_bunch_data"], [5, 2, 1, "", "write"]], "mbtrack2.tracking.monitors.monitors.PhaseSpaceMonitor": [[5, 2, 1, "", "to_buffer"], [5, 2, 1, "", "track"]], "mbtrack2.tracking.monitors.monitors.ProfileMonitor": [[5, 2, 1, "", "to_buffer"], [5, 2, 1, "", "track"], [5, 2, 1, "", "write"]], "mbtrack2.tracking.monitors.monitors.WakePotentialMonitor": [[5, 2, 1, "", "to_buffer"], [5, 2, 1, "", "track"], [5, 2, 1, "", "write"]], "mbtrack2.tracking.monitors.plotting": [[5, 4, 1, "", "plot_beamdata"], [5, 4, 1, "", "plot_beamspectrum"], [5, 4, 1, "", "plot_bunchdata"], [5, 4, 1, "", "plot_bunchspectrum"], [5, 4, 1, "", "plot_cavitydata"], [5, 4, 1, "", "plot_phasespacedata"], [5, 4, 1, "", "plot_profiledata"], [5, 4, 1, "", "plot_wakedata"], [5, 4, 1, "", "streak_beamdata"], [5, 4, 1, "", "streak_beamspectrum"], [5, 4, 1, "", "streak_bunchspectrum"]], "mbtrack2.tracking.monitors.tools": [[5, 4, 1, "", "copy_files"], [5, 4, 1, "", "merge_files"]], "mbtrack2.tracking.parallel": [[4, 1, 1, "", "Mpi"]], "mbtrack2.tracking.parallel.Mpi": [[4, 3, 1, "", "bunch_num"], [4, 2, 1, "", "bunch_to_rank"], [4, 3, 1, "", "next_bunch"], [4, 3, 1, "", "previous_bunch"], [4, 2, 1, "", "rank_to_bunch"], [4, 2, 1, "", "share_distributions"], [4, 2, 1, "", "share_means"], [4, 2, 1, "", "share_stds"], [4, 2, 1, "", "write_table"]], "mbtrack2.tracking.particles": [[4, 1, 1, "", "Beam"], [4, 1, 1, "", "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 0000000000000000000000000000000000000000..747ffb7b3033659bdd2d1e6eae41ecb00358a45e
--- /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/requirements.txt b/docs/requirements.txt
new file mode 100644
index 0000000000000000000000000000000000000000..51841ddd3367519b3e333f401e98dd6546e9e43b
--- /dev/null
+++ b/docs/requirements.txt
@@ -0,0 +1,13 @@
+# Defining the exact version will make sure things don't break
+sphinx==5.3.0
+sphinx_rtd_theme==1.1.1
+readthedocs-sphinx-search==0.1.1
+numpy>=1.21
+pandas>=1.5.3
+scipy>=1.7
+h5py>=3.6
+matplotlib>=3.5
+seaborn>=0.12
+mpmath>=1.2.1
+accelerator-toolbox>=0.5.0
+myst_parser>=0.15
\ No newline at end of file
diff --git a/docs/source/Makefile b/docs/source/Makefile
new file mode 100644
index 0000000000000000000000000000000000000000..d4bb2cbb9eddb1bb1b4f366623044af8e4830919
--- /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 0000000000000000000000000000000000000000..928c0eddb28aa252dbdb3192e295d36e2a470be7
--- /dev/null
+++ b/docs/source/conf.py
@@ -0,0 +1,75 @@
+# 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('.'))
+sys.path.insert(0, os.path.abspath("../"))
+sys.path.insert(0, os.path.abspath("../../"))
+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.mathjax',
+ 'sphinx.ext.mathjax',
+ 'sphinx.ext.viewcode',
+ 'myst_parser',
+]
+
+autodoc_default_options = {
+ 'member-order': 'bysource', # Keep the order of members as they appear in the source code
+ 'undoc-members': True, # Do not show undocumented members
+ 'private-members': True, # Do not show private members
+ 'special-members': '__init__', # Document __init__ method
+ 'show-inheritance': False, # Do not show base classes
+}
+add_module_names = False
+# 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 = 'sphinx_rtd_theme'
+
+# 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 0000000000000000000000000000000000000000..665fe88b0713ad651f385acd529280ddcd02b400
--- /dev/null
+++ b/docs/source/index.rst
@@ -0,0 +1,26 @@
+.. mbtrack2 documentation master file, created by
+ sphinx-quickstart on Sun Apr 28 21:51:15 2024.
+ You can adapt this file completely to your liking, but it should at least
+ contain the root `toctree` directive.
+About mbtrack2
+====================================
+
+.. include:: ../../README.md
+ :parser: myst_parser.sphinx_
+
+mbtrack2 documentation
+====================================
+
+.. toctree::
+ :maxdepth: 6
+ :caption: Table of contents:
+
+ mbtrack2
+
+
+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 0000000000000000000000000000000000000000..32bb24529f92346af26219baed295b7488b77534
--- /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 0000000000000000000000000000000000000000..2d40343a406285ee6e46dbd2564089030b7ea3cf
--- /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 0000000000000000000000000000000000000000..7b7e8f42ed3d2f9a6c6aaef50588153626829a70
--- /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 0000000000000000000000000000000000000000..7d99aebe497efa9d06f618ec0f9fc7797ec3f4e6
--- /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 0000000000000000000000000000000000000000..36cd62af870903ce7758b93a8b82dc6e3821b745
--- /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 0000000000000000000000000000000000000000..e26114f1a72d37c950a51d30ccbc294787b4e042
--- /dev/null
+++ b/docs/source/mbtrack2.tracking.rst
@@ -0,0 +1,117 @@
+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.beam\_ion\_effects module
+-------------------------------------------
+
+.. automodule:: mbtrack2.tracking.beam_ion_effects
+ :members:
+ :undoc-members:
+ :show-inheritance:
+
+mbtrack2.tracking.element module
+--------------------------------
+
+.. automodule:: mbtrack2.tracking.element
+ :members:
+ :undoc-members:
+ :show-inheritance:
+
+mbtrack2.tracking.excite module
+-------------------------------
+
+.. automodule:: mbtrack2.tracking.excite
+ :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.particles\_electromagnetic\_fields module
+-----------------------------------------------------------
+
+.. automodule:: mbtrack2.tracking.particles_electromagnetic_fields
+ :members:
+ :undoc-members:
+ :show-inheritance:
+
+mbtrack2.tracking.rf module
+---------------------------
+
+.. automodule:: mbtrack2.tracking.rf
+ :members:
+ :undoc-members:
+ :show-inheritance:
+
+mbtrack2.tracking.spacecharge module
+------------------------------------
+
+.. automodule:: mbtrack2.tracking.spacecharge
+ :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 0000000000000000000000000000000000000000..e23f1f6963dce8fae82b56f772a419b03a8cc407
--- /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:
diff --git a/docs/source/modules.rst b/docs/source/modules.rst
new file mode 100644
index 0000000000000000000000000000000000000000..390494f92f178040fef20b8db12b478c50fe2acf
--- /dev/null
+++ b/docs/source/modules.rst
@@ -0,0 +1,7 @@
+mbtrack2
+========
+
+.. toctree::
+ :maxdepth: 4
+
+ mbtrack2
diff --git a/docs/source/readme_link.md b/docs/source/readme_link.md
new file mode 100644
index 0000000000000000000000000000000000000000..060259b6b72fd0fe4dc11244b40f75bef9cf381f
--- /dev/null
+++ b/docs/source/readme_link.md
@@ -0,0 +1,2 @@
+```{include} ../../README.md
+```
\ No newline at end of file
diff --git a/examples/mbtrack2_cavity_resonator.ipynb b/examples/mbtrack2_cavity_resonator.ipynb
index 94d9ac9373532f5211b841c314f598d8b5434422..e617cd08ce7d1afc2b08908d066e7ca508959f94 100644
--- a/examples/mbtrack2_cavity_resonator.ipynb
+++ b/examples/mbtrack2_cavity_resonator.ipynb
@@ -4,9 +4,7 @@
"metadata": {
"colab": {
"provenance": [],
- "toc_visible": true,
- "authorship_tag": "ABX9TyOm5fHBtug/d3SMEK1DtfNi",
- "include_colab_link": true
+ "toc_visible": true
},
"kernelspec": {
"name": "python3",
@@ -17,16 +15,6 @@
}
},
"cells": [
- {
- "cell_type": "markdown",
- "metadata": {
- "id": "view-in-github",
- "colab_type": "text"
- },
- "source": [
- "<a href=\"https://colab.research.google.com/github/GamelinAl/mbtrack2_examples/blob/main/mbtrack2_cavity_resonator.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
- ]
- },
{
"cell_type": "markdown",
"source": [
@@ -89,13 +77,13 @@
},
{
"cell_type": "code",
- "execution_count": null,
+ "execution_count": 1,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "BKGTZA_EvtF6",
- "outputId": "d2d1c5c2-8293-4ae6-9db0-3f57f4909268"
+ "outputId": "9e40ac0e-904e-4a75-dc37-862d6110f562"
},
"outputs": [
{
@@ -103,17 +91,17 @@
"name": "stdout",
"text": [
"Cloning into 'mbtrack2'...\n",
- "remote: Enumerating objects: 1629, done.\u001b[K\n",
- "remote: Counting objects: 100% (311/311), done.\u001b[K\n",
- "remote: Compressing objects: 100% (181/181), done.\u001b[K\n",
- "remote: Total 1629 (delta 182), reused 212 (delta 130), pack-reused 1318\u001b[K\n",
- "Receiving objects: 100% (1629/1629), 1.88 MiB | 2.24 MiB/s, done.\n",
- "Resolving deltas: 100% (1091/1091), done.\n"
+ "remote: Enumerating objects: 3169, done.\u001b[K\n",
+ "remote: Counting objects: 100% (159/159), done.\u001b[K\n",
+ "remote: Compressing objects: 100% (147/147), done.\u001b[K\n",
+ "remote: Total 3169 (delta 101), reused 15 (delta 12), pack-reused 3010 (from 1)\u001b[K\n",
+ "Receiving objects: 100% (3169/3169), 4.97 MiB | 4.89 MiB/s, done.\n",
+ "Resolving deltas: 100% (2163/2163), done.\n"
]
}
],
"source": [
- "! git clone https://gitlab.synchrotron-soleil.fr/PA/collective-effects/mbtrack2.git"
+ "! pip install mbtrack2"
]
},
{
@@ -126,9 +114,9 @@
"base_uri": "https://localhost:8080/"
},
"id": "aIwNdoXlVDus",
- "outputId": "6cfb7ede-b04e-46ad-856b-93b94deb22e9"
+ "outputId": "8f3aa306-1143-48e6-97b3-7edd7f669946"
},
- "execution_count": null,
+ "execution_count": 2,
"outputs": [
{
"output_type": "stream",
@@ -156,10 +144,28 @@
"from mbtrack2.utilities import Optics"
],
"metadata": {
- "id": "ewMLyHDOslSD"
+ "id": "ewMLyHDOslSD",
+ "outputId": "1eca8f4b-60c1-46cf-f9b8-9586c04cadfd",
+ "colab": {
+ "base_uri": "https://localhost:8080/"
+ }
},
- "execution_count": null,
- "outputs": []
+ "execution_count": 3,
+ "outputs": [
+ {
+ "output_type": "stream",
+ "name": "stdout",
+ "text": [
+ "mbtrack2 version 0.6.0.54\n",
+ "--------------------------------------------------\n",
+ "If used in a publication, please cite mbtrack2 paper and the zenodo archive for the corresponding code version (and other papers for more specific features).\n",
+ "[1] A. Gamelin, W. Foosang, N. Yamamoto, V. Gubaidulin and R. Nagaoka, “mbtrack2â€. Zenodo, Mar. 25, 2024. doi: 10.5281/zenodo.10871040.\n",
+ "[2] A. Gamelin, W. Foosang, and R. Nagaoka, “mbtrack2, a Collective Effect Library in Pythonâ€, presented at the 12th Int. Particle Accelerator Conf. (IPAC'21), Campinas, Brazil, May 2021, paper MOPAB070.\n",
+ "\n",
+ "\n"
+ ]
+ }
+ ]
},
{
"cell_type": "code",
@@ -180,7 +186,7 @@
"metadata": {
"id": "GH7V8wmmxH4i"
},
- "execution_count": null,
+ "execution_count": 4,
"outputs": []
},
{
@@ -195,7 +201,7 @@
"metadata": {
"id": "yY9Fh3JR1rQy"
},
- "execution_count": null,
+ "execution_count": 5,
"outputs": []
},
{
@@ -208,7 +214,7 @@
"metadata": {
"id": "WiPq6SDLvbjC"
},
- "execution_count": null,
+ "execution_count": 6,
"outputs": []
},
{
@@ -228,7 +234,7 @@
"metadata": {
"id": "Vcy-pUOYTwp4"
},
- "execution_count": null,
+ "execution_count": 7,
"outputs": []
},
{
@@ -248,9 +254,9 @@
"height": 466
},
"id": "T2Gu7M1XTzSc",
- "outputId": "cba53b56-05d1-477c-bbd2-36299129201d"
+ "outputId": "a9775d9e-0f73-43c3-98f1-d789bf24126f"
},
- "execution_count": null,
+ "execution_count": 8,
"outputs": [
{
"output_type": "stream",
@@ -297,7 +303,7 @@
"metadata": {
"id": "_Un3rKy7PFWT"
},
- "execution_count": null,
+ "execution_count": 9,
"outputs": []
},
{
@@ -311,7 +317,7 @@
"metadata": {
"id": "W3yPFAXfPJUr"
},
- "execution_count": null,
+ "execution_count": 10,
"outputs": []
},
{
@@ -337,17 +343,17 @@
"base_uri": "https://localhost:8080/"
},
"id": "NnUmubbnUyGJ",
- "outputId": "d956f844-891a-4da6-ff46-ecb92e696273"
+ "outputId": "93bde587-5e1e-43a4-d478-0e8a33c141be"
},
- "execution_count": null,
+ "execution_count": 11,
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
- "[ 6.30935783e-04 1.85770969e-05 1.04912102e-03 -1.62874235e-03\n",
- " 4.16169410e-04]\n",
- "[ 0.00076549 0.00014476 0.00118558 -0.00149344 0.00054759]\n"
+ "[-0.00070136 -0.00023309 -0.00118755 -0.00025426 -0.00131552]\n",
+ "[-5.77827373e-04 -9.63700266e-05 -1.05731502e-03 -1.24226321e-04\n",
+ " -1.18057734e-03]\n"
]
}
]
@@ -377,7 +383,7 @@
"metadata": {
"id": "f2hjNnrzoYi8"
},
- "execution_count": null,
+ "execution_count": 12,
"outputs": []
},
{
@@ -405,7 +411,7 @@
"metadata": {
"id": "ebAW1aY_rCR0"
},
- "execution_count": null,
+ "execution_count": 13,
"outputs": []
},
{
@@ -431,9 +437,9 @@
"base_uri": "https://localhost:8080/"
},
"id": "f_XRdEeutedr",
- "outputId": "51bb3ad7-865f-4354-c691-1692fea54e24"
+ "outputId": "11f536d3-80dd-4855-da42-5a7eb96b6fd4"
},
- "execution_count": null,
+ "execution_count": 14,
"outputs": [
{
"output_type": "stream",
@@ -479,7 +485,7 @@
"metadata": {
"id": "oCn2lTk6rUtr"
},
- "execution_count": null,
+ "execution_count": 15,
"outputs": []
},
{
@@ -509,9 +515,9 @@
"base_uri": "https://localhost:8080/"
},
"id": "jqbtSTJ6s4Ge",
- "outputId": "4ca6d5ba-1e3c-410c-e45a-5aaf7387c3cb"
+ "outputId": "e1592dc9-c98b-4920-ba84-5de02047f957"
},
- "execution_count": null,
+ "execution_count": 16,
"outputs": [
{
"output_type": "stream",
@@ -547,9 +553,9 @@
"height": 459
},
"id": "Ypdhc4McFwXa",
- "outputId": "1530c97c-6e2d-49e8-b1c9-a444beda9477"
+ "outputId": "680fc391-f18d-4066-a19f-614de50aa343"
},
- "execution_count": null,
+ "execution_count": 17,
"outputs": [
{
"output_type": "display_data",
@@ -584,9 +590,9 @@
"base_uri": "https://localhost:8080/"
},
"id": "ZQNoawSrIDyA",
- "outputId": "fa936c10-5a9b-4f36-d616-deb4f6a8daee"
+ "outputId": "b613eb60-0679-4c45-a25e-c432e8ab2203"
},
- "execution_count": null,
+ "execution_count": 18,
"outputs": [
{
"output_type": "stream",
@@ -624,9 +630,9 @@
"base_uri": "https://localhost:8080/"
},
"id": "VCeGDP9eJOWT",
- "outputId": "97d6bb4e-dee9-43ef-eda5-b77088ac133f"
+ "outputId": "4289ec18-a2ee-46f3-af0d-2b07305df0b6"
},
- "execution_count": null,
+ "execution_count": 19,
"outputs": [
{
"output_type": "stream",
@@ -657,9 +663,9 @@
"base_uri": "https://localhost:8080/"
},
"id": "PdZ8GmWxLrVi",
- "outputId": "207e8971-15d6-4b30-a1e5-7e22fa43e817"
+ "outputId": "4039457e-94b0-4f26-de20-144d8558e2f7"
},
- "execution_count": null,
+ "execution_count": 20,
"outputs": [
{
"output_type": "execute_result",
@@ -688,9 +694,9 @@
"height": 507
},
"id": "yOhFgjdFLrSi",
- "outputId": "b79d7e8e-c547-4b36-b913-3c920a876431"
+ "outputId": "1e625c40-4513-421b-de1c-0c12e55770b8"
},
- "execution_count": null,
+ "execution_count": 21,
"outputs": [
{
"output_type": "stream",
@@ -703,7 +709,7 @@
"output_type": "execute_result",
"data": {
"text/plain": [
- "<matplotlib.legend.Legend at 0x7f86cf0196f0>"
+ "<matplotlib.legend.Legend at 0x7b3a2858e080>"
]
},
"metadata": {},
@@ -777,9 +783,9 @@
"base_uri": "https://localhost:8080/"
},
"id": "BwnJdmllhV1h",
- "outputId": "9ace34d2-aba9-43e6-bb66-dc6ad6d3395c"
+ "outputId": "55b4b166-396d-42e8-d2cd-343e1b0605a7"
},
- "execution_count": null,
+ "execution_count": 22,
"outputs": [
{
"output_type": "stream",
@@ -818,18 +824,18 @@
"base_uri": "https://localhost:8080/"
},
"id": "PLyRKsWxhiWP",
- "outputId": "8272b139-b93d-4230-ac6c-93202f4a8968"
+ "outputId": "01567cff-20a4-46f8-d5d8-ab1670ed4cc8"
},
- "execution_count": null,
+ "execution_count": 23,
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
- "[-283883.46892953+933000.63156325j]\n",
- "[201830.81678459+979657.57904508j]\n",
- "[1000232.29841092]\n",
- "[1.36761734]\n"
+ "[-283883.53096983+933000.63147547j]\n",
+ "[201830.75474429+979657.5789573j]\n",
+ "[1000232.28580621]\n",
+ "[1.3676174]\n"
]
}
]
@@ -854,9 +860,9 @@
"base_uri": "https://localhost:8080/"
},
"id": "Y4IpK8W4mnPz",
- "outputId": "545a3716-612e-4abd-ae4f-404a10113743"
+ "outputId": "32ca6b4d-42da-4064-e16c-34640b75fbfd"
},
- "execution_count": null,
+ "execution_count": 24,
"outputs": [
{
"output_type": "stream",
@@ -891,18 +897,20 @@
"colab": {
"base_uri": "https://localhost:8080/"
},
- "outputId": "417891de-d6de-4d8b-a9ef-b0d235b83fe2"
+ "outputId": "ddcb37c7-4272-4572-a6a7-241b56b5fdeb"
},
- "execution_count": null,
+ "execution_count": 25,
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
- "[ 0.00076549 0.00014476 0.00118558 -0.00149344 0.00054759]\n",
- "[-283883.46892953+933000.63156325j]\n",
- "[ 0.00090082 0.00027107 0.0013232 -0.00135713 0.00067958]\n",
- "[-283883.56168717+932993.66729763j]\n"
+ "[-5.77827373e-04 -9.63700266e-05 -1.05731502e-03 -1.24226321e-04\n",
+ " -1.18057734e-03]\n",
+ "[-283883.53096983+933000.63147547j]\n",
+ "[-4.53984817e-04 4.14028612e-05 -9.26763183e-04 6.32551203e-06\n",
+ " -1.04467636e-03]\n",
+ "[-283883.59547312+932996.4387065j]\n"
]
}
]
@@ -928,24 +936,24 @@
"base_uri": "https://localhost:8080/"
},
"id": "FDPJPsHHWY94",
- "outputId": "7aedb0a7-f06a-43cb-d793-a4017d8f76a3"
+ "outputId": "3390774a-ca7b-4cce-d3ac-78e0845b1b18"
},
- "execution_count": null,
+ "execution_count": 26,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
- "array([200036.15208512+979657.38497534j, 200035.66739687+979655.84112697j,\n",
- " 200035.17760907+979653.80141957j, 200034.68246341+979652.31199819j,\n",
- " 200034.18718513+979650.29995926j, 198239.02581783+979647.78612658j,\n",
- " 196444.82944756+979648.55556845j, 196446.26204388+979652.3585456j ,\n",
- " 196447.70261996+979657.0909942j , 196449.15126411+979661.20675296j,\n",
- " 198245.27031205+979666.01342313j, 200040.42824809+979667.66040315j,\n",
- " 200039.95505622+979666.04782213j, 200039.48039337+979664.5148787j ,\n",
- " 200039.00555869+979662.21766757j, 200038.52380292+979659.4067355j ,\n",
- " 200038.03692367+979656.92114933j, 200037.54507254+979655.36000134j,\n",
- " 200037.05063212+979653.79945364j, 200036.55748377+979652.10889599j])"
+ "array([200036.09194052+979657.20893956j, 200035.60313321+979655.25039183j,\n",
+ " 200035.11019246+979653.61267534j, 200034.61732473+979651.42944194j,\n",
+ " 200034.12008955+979649.43032761j, 198238.96016133+979647.50721553j,\n",
+ " 196444.75883405+979648.24111963j, 196446.19226499+979652.47412264j,\n",
+ " 196447.63284473+979657.47676175j, 196449.08216472+979661.9412014j ,\n",
+ " 198245.20254092+979666.74759656j, 200040.36180403+979668.39429939j,\n",
+ " 200039.89056465+979666.79071288j, 200039.41751214+979665.73673562j,\n",
+ " 200038.94152303+979663.68354521j, 200038.46314288+979661.94427288j,\n",
+ " 200037.98301094+979659.86203178j, 200037.49683581+979658.2088997j ,\n",
+ " 200037.00845764+979656.52444428j, 200036.51880305+979654.88173367j])"
]
},
"metadata": {},
@@ -987,7 +995,7 @@
"metadata": {
"id": "_qCp81Zo1n-u"
},
- "execution_count": null,
+ "execution_count": 27,
"outputs": []
},
{
@@ -1009,9 +1017,9 @@
"base_uri": "https://localhost:8080/"
},
"id": "-nWBy0b42FpF",
- "outputId": "1500a99d-b6ee-4619-d573-973a614a649a"
+ "outputId": "63287191-1d49-4ca8-bde6-34f099599594"
},
- "execution_count": null,
+ "execution_count": 28,
"outputs": [
{
"output_type": "execute_result",
@@ -1043,7 +1051,7 @@
"metadata": {
"id": "QiSFXSAZ2B4u"
},
- "execution_count": null,
+ "execution_count": 29,
"outputs": []
},
{
@@ -1159,7 +1167,7 @@
"metadata": {
"id": "CHF_GzVC5KQD"
},
- "execution_count": null,
+ "execution_count": 30,
"outputs": []
},
{
@@ -1179,7 +1187,7 @@
"metadata": {
"id": "yN07pCXd5G6q"
},
- "execution_count": null,
+ "execution_count": 31,
"outputs": []
},
{
@@ -1207,7 +1215,7 @@
"metadata": {
"id": "tywlUGCoKguV"
},
- "execution_count": null,
+ "execution_count": 32,
"outputs": []
},
{
@@ -1230,9 +1238,9 @@
"height": 465
},
"id": "wL7jVkvMLVzL",
- "outputId": "9a8e8ff0-945c-4605-9343-9b85b1d465b3"
+ "outputId": "5689a6c8-ee61-4d41-d545-f95c21d6dae1"
},
- "execution_count": null,
+ "execution_count": 33,
"outputs": [
{
"output_type": "display_data",
@@ -1240,7 +1248,7 @@
"text/plain": [
"<Figure size 640x480 with 2 Axes>"
],
- "image/png": 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\n"
+ "image/png": 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\n"
},
"metadata": {}
}
@@ -1257,9 +1265,9 @@
"height": 465
},
"id": "fRGflKdSLuvk",
- "outputId": "dd824d08-3c06-414c-9fd2-54e7fbe2b2f7"
+ "outputId": "ba6f212b-47a4-4725-efe7-6700ff44ef83"
},
- "execution_count": null,
+ "execution_count": 34,
"outputs": [
{
"output_type": "display_data",
@@ -1267,7 +1275,7 @@
"text/plain": [
"<Figure size 640x480 with 2 Axes>"
],
- "image/png": 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\n"
+ "image/png": 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\n"
},
"metadata": {}
}
@@ -1283,10 +1291,10 @@
"base_uri": "https://localhost:8080/",
"height": 465
},
- "outputId": "15fd1864-b200-4591-d42d-ee76e40ee8ba",
+ "outputId": "c7b9cbad-786c-4c4f-a14e-f1ab2a9886aa",
"id": "srURo9xxMqqy"
},
- "execution_count": null,
+ "execution_count": 35,
"outputs": [
{
"output_type": "display_data",
@@ -1294,7 +1302,7 @@
"text/plain": [
"<Figure size 640x480 with 2 Axes>"
],
- "image/png": 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\n"
+ "image/png": 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\n"
},
"metadata": {}
}
@@ -1310,10 +1318,10 @@
"base_uri": "https://localhost:8080/",
"height": 449
},
- "outputId": "5d60b6f7-9380-43d4-9e5f-e91c8e8ab2aa",
+ "outputId": "cc6adca8-3589-4fa3-a367-3f8e37402baf",
"id": "vI20crgCMTkj"
},
- "execution_count": null,
+ "execution_count": 36,
"outputs": [
{
"output_type": "display_data",
@@ -1355,7 +1363,7 @@
"metadata": {
"id": "aYfAxnr3Pe9V"
},
- "execution_count": null,
+ "execution_count": 37,
"outputs": []
},
{
@@ -1384,7 +1392,7 @@
"metadata": {
"id": "hBQxYlQvN2f5"
},
- "execution_count": null,
+ "execution_count": 38,
"outputs": []
},
{
@@ -1405,49 +1413,28 @@
" HC.detune = det\n",
" V = BeamLoadingEquilibrium(ring, [MC,HC], I0, auto_set_MC_theta=False)\n",
" sol = V.beam_equilibrium(plot=False)\n",
- " fig = V.plot_rho(z1=-0.2, z2=0.2)\n",
+ " fig = V.plot_rho()\n",
"plt.legend(leg)"
],
"metadata": {
"id": "xAlbfHmoPk4G",
"colab": {
"base_uri": "https://localhost:8080/",
- "height": 754
+ "height": 493
},
- "outputId": "d6b113e7-40b3-4dea-a7b4-d04b3f1d50fc"
+ "outputId": "bf7737f2-a0e1-478b-d27c-43a8ea331ac6"
},
- "execution_count": null,
+ "execution_count": 40,
"outputs": [
- {
- "output_type": "stream",
- "name": "stdout",
- "text": [
- "The initial center of mass offset is -0.17202964722127753 ps\n",
- "The final center of mass offset is 0.7603234535161224 ps\n",
- "The algorithm has converged: True\n",
- "The initial center of mass offset is -0.7480023322567962 ps\n",
- "The final center of mass offset is 1.507668642882292 ps\n",
- "The algorithm has converged: True\n",
- "The initial center of mass offset is -21.12365937281321 ps\n",
- "The final center of mass offset is 6.987443148551981 ps\n",
- "The algorithm has converged: True\n",
- "The initial center of mass offset is -178.42158504142026 ps\n",
- "The final center of mass offset is 13.77731893548217 ps\n",
- "The algorithm has converged: True\n",
- "The initial center of mass offset is -325.2644871748486 ps\n",
- "The final center of mass offset is 17.165812866907483 ps\n",
- "The algorithm has converged: True\n"
- ]
- },
{
"output_type": "execute_result",
"data": {
"text/plain": [
- "<matplotlib.legend.Legend at 0x7f86ceb5e8c0>"
+ "<matplotlib.legend.Legend at 0x7b3a28309d20>"
]
},
"metadata": {},
- "execution_count": 39
+ "execution_count": 40
},
{
"output_type": "display_data",
@@ -1455,7 +1442,7 @@
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
],
- "image/png": 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\n"
+ "image/png": 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\n"
},
"metadata": {}
}
@@ -1492,24 +1479,23 @@
"# Plot the equilibrium bunch profile\n",
"V = BeamLoadingEquilibrium(ring, [MC,HC], I0, auto_set_MC_theta=False)\n",
"sol = V.beam_equilibrium(plot=False)\n",
- "z0 = np.linspace(-0.2, 0.2, 1000)\n",
- "plt.plot(z0, V.rho(z0)/np.max(V.rho(z0)))\n",
+ "plt.plot(V.tau0, V.rho0/np.max(V.rho0))\n",
"plt.xlabel(\"z [m]\")\n",
"plt.title(\"Equilibrium bunch profile\")\n",
"\n",
"# Plot the bunch profile of bunch 0 from tracking\n",
"bins, sorted_index, profile, center = mybeam[0].binning(\"tau\", 75)\n",
- "plt.plot(center*3e8, profile/max(profile))"
+ "plt.plot(center, profile/max(profile))"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
- "height": 888
+ "height": 837
},
"id": "xvg8zezzV4f_",
- "outputId": "85f9d757-1e1a-4ec0-83c3-5785a8521721"
+ "outputId": "c3850fb7-e40c-4490-fa92-279a6af9f760"
},
- "execution_count": null,
+ "execution_count": 41,
"outputs": [
{
"output_type": "stream",
@@ -1534,21 +1520,18 @@
"1600\n",
"1700\n",
"1800\n",
- "1900\n",
- "The initial center of mass offset is -178.42158504142026 ps\n",
- "The final center of mass offset is 13.77731893548217 ps\n",
- "The algorithm has converged: True\n"
+ "1900\n"
]
},
{
"output_type": "execute_result",
"data": {
"text/plain": [
- "[<matplotlib.lines.Line2D at 0x7f86cea53460>]"
+ "[<matplotlib.lines.Line2D at 0x7b3a28272170>]"
]
},
"metadata": {},
- "execution_count": 40
+ "execution_count": 41
},
{
"output_type": "display_data",
@@ -1556,11 +1539,20 @@
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
],
- "image/png": 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\n"
+ "image/png": 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\n"
},
"metadata": {}
}
]
+ },
+ {
+ "cell_type": "code",
+ "source": [],
+ "metadata": {
+ "id": "J7qkgaaeAPwK"
+ },
+ "execution_count": null,
+ "outputs": []
}
]
}
\ No newline at end of file
diff --git a/mbtrack2.yml b/mbtrack2.yml
index 059955435b085f9f8d09645d9abe96cc33353dbc..5d8716c4646eae3a9c3059312f3a9741480f98c4 100644
--- a/mbtrack2.yml
+++ b/mbtrack2.yml
@@ -8,7 +8,7 @@ dependencies:
- mpi4py>=3.1
- matplotlib>=3.5
- seaborn>=0.12
- - mpmath>=1.21
+ - mpmath>=1.2.1
- pip
- pip:
- accelerator-toolbox
\ No newline at end of file
diff --git a/mbtrack2/__init__.py b/mbtrack2/__init__.py
index d3383ef03200638c6247696f30aa04af63525fac..e478887b2fea2eeabdfbb44b0e5327efc3ade1c6 100644
--- a/mbtrack2/__init__.py
+++ b/mbtrack2/__init__.py
@@ -1,6 +1,48 @@
# -*- coding: utf-8 -*-
-__version__ = "0.6.0"
+__version__ = "0.7.0"
from mbtrack2.impedance import *
from mbtrack2.instability import *
from mbtrack2.tracking import *
from mbtrack2.utilities import *
+
+try:
+ DYNAMIC_VERSIONING = True
+ import os
+ import subprocess
+
+ worktree = os.path.dirname(os.path.dirname(os.path.abspath(__file__)))
+ gitdir = worktree + "/.git/"
+ with open(os.devnull, "w") as devnull:
+ __version__ = subprocess.check_output(
+ "git --git-dir=" + gitdir + " --work-tree=" + worktree +
+ " describe --long --dirty --abbrev=10 --tags",
+ shell=True,
+ stderr=devnull,
+ )
+ __version__ = __version__.decode("utf-8").rstrip() # remove trailing \n
+ # remove commit hash to conform to PEP440:
+ split_ = __version__.split("-")
+ __version__ = split_[0]
+ if split_[1] != "0":
+ __version__ += "." + split_[1]
+ dirty = "dirty" in split_[-1]
+except:
+ DYNAMIC_VERSIONING = False
+ from . import __version__
+
+ dirty = False
+
+print(("mbtrack2 version " + __version__))
+if dirty:
+ print("(dirty git work tree)")
+print(50 * '-')
+print(
+ "If used in a publication, please cite mbtrack2 paper and the zenodo archive for the corresponding code version (and other papers for more specific features)."
+)
+print(
+ "[1] A. Gamelin, W. Foosang, N. Yamamoto, V. Gubaidulin and R. Nagaoka, “mbtrack2â€. Zenodo, Mar. 25, 2024. doi: 10.5281/zenodo.10871040."
+)
+print(
+ "[2] A. Gamelin, W. Foosang, and R. Nagaoka, “mbtrack2, a Collective Effect Library in Pythonâ€, presented at the 12th Int. Particle Accelerator Conf. (IPAC'21), Campinas, Brazil, May 2021, paper MOPAB070."
+)
+print("\n")
diff --git a/mbtrack2/impedance/impedance_model.py b/mbtrack2/impedance/impedance_model.py
index 713fe464a7f336b543e3ba282748275c356433fa..badc6321bfff0bdefe5af296ea92cc0214b65f78 100644
--- a/mbtrack2/impedance/impedance_model.py
+++ b/mbtrack2/impedance/impedance_model.py
@@ -305,7 +305,7 @@ class ImpedanceModel():
Z_type : str, optional
Type of impedance to plot.
component : str, optional
- Component to plot, can be "real" or "imag".
+ Component to plot, can be "real" or "imag".
sigma : float, optional
RMS bunch length in [s] to use for the spectral density. If equal
to None, the spectral density is not plotted.
@@ -496,29 +496,51 @@ class ImpedanceModel():
return summary
- def energy_loss(self, sigma, M, bunch_spacing, I, n_points=10e6):
+ def energy_loss(self,
+ M,
+ bunch_spacing,
+ I,
+ sigma=None,
+ bunch_spectrum=None,
+ freq_spectrum=None,
+ n_points=10e6):
"""
- 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.
+ Compute the beam and bunch loss factor and energy losses for each type
+ of element in the model.
+
+ Assumtions:
+ - Constant spacing between bunches.
+ - All bunches have the same bunch distribution.
+ - Gaussian bunches if sigma is given.
Parameters
----------
- sigma : float
- RMS bunch length in [s].
M : int
Number of bunches in the beam.
bunch_spacing : float
Time between two bunches in [s].
I : float
Total beam current in [A].
+ sigma : float, optional
+ RMS bunch length in [s].
+ If None, freq_spectrum and bunch_spectrum must be given.
+ Default is None.
+ bunch_spectrum : array
+ Bunch spectrum to consider (i.e. FT of bunch profile).
+ Not used if sigma is not None.
+ Default is None.
+ freq_spectrum : array
+ Frequency points corresponding to bunch_spectrum in [Hz].
+ Not used if sigma is not None.
+ Default is None.
n_points : float, optional
Number of points used in the frequency spectrums.
+ Default is 10e6.
Returns
-------
summary : Dataframe
- Contains the beam and bunch loss factor and energy loss for the
+ Contains the beam and bunch loss factor and energy loss for the
full model and for each type of different component.
"""
@@ -532,9 +554,33 @@ class ImpedanceModel():
fmin = -1 * fmax
f = np.linspace(fmin, fmax, int(n_points))
- beam_spect = beam_spectrum(f, M, bunch_spacing, sigma=sigma)
-
- bunch_spect = gaussian_bunch_spectrum(f, sigma)
+ if sigma is None:
+ if bunch_spectrum is None:
+ raise ValueError(
+ "Either sigma or bunch_spectrum and freq_spectrum" +
+ "must be specified.")
+ else:
+ if freq_spectrum is None:
+ raise ValueError(
+ "freq_spectrum must be given if bunch_spectrum" +
+ " is specified.")
+ if freq_spectrum[0] >= 0:
+ freq_spectrum = np.concatenate(
+ (-1 * freq_spectrum[:0:-1], freq_spectrum))
+ bunch_spectrum = np.concatenate(
+ (bunch_spectrum[:0:-1], bunch_spectrum))
+ bunch_spectrum_interp = interp1d(freq_spectrum,
+ bunch_spectrum,
+ bounds_error=False,
+ fill_value=0)
+ bunch_spect = bunch_spectrum_interp(f)
+ beam_spect = beam_spectrum(f,
+ M,
+ bunch_spacing,
+ bunch_spectrum=bunch_spect)
+ else:
+ beam_spect = beam_spectrum(f, M, bunch_spacing, sigma=sigma)
+ bunch_spect = gaussian_bunch_spectrum(f, sigma)
attr_list = self.sum_names
@@ -566,42 +612,60 @@ class ImpedanceModel():
return summary
def power_loss_spectrum(self,
- sigma,
M,
bunch_spacing,
I,
+ sigma=None,
+ bunch_spectrum=None,
+ freq_spectrum=None,
n_points=10e6,
max_overlap=False,
plot=False):
"""
- Compute the power loss spectrum of the summed longitudinal impedance
+ Compute the power loss spectrum of the summed longitudinal impedance
as in Eq. (4) of [1].
- Assume Gaussian bunches and constant spacing between bunches.
+ Assumtions:
+ - Constant spacing between bunches.
+ - All bunches have the same bunch distribution.
+ - Gaussian bunches if sigma is given.
Parameters
----------
- sigma : float
- RMS bunch length in [s].
M : int
Number of bunches in the beam.
bunch_spacing : float
Time between two bunches in [s].
I : float
Total beam current in [A].
+ sigma : float, optional
+ RMS bunch length in [s].
+ If None, freq_spectrum and bunch_spectrum must be given.
+ Default is None.
+ bunch_spectrum : array
+ Bunch spectrum to consider (i.e. FT of bunch profile).
+ Not used if sigma is not None.
+ Default is None.
+ freq_spectrum : array
+ Frequency points corresponding to bunch_spectrum in [Hz].
+ Not used if sigma is not None.
+ Default is None.
n_points : float, optional
Number of points used in the frequency spectrum.
+ Default is 10e6.
max_overlap : bool, optional
- 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
+ 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.
+ Default is False.
plot : bool, optional
If True, plots:
- - the overlap between the real part of the longitudinal impedance
+ - the overlap between the real part of the longitudinal impedance
and the beam spectrum.
- the power loss spectrum.
+ Default is False.
Returns
-------
@@ -612,8 +676,8 @@ class ImpedanceModel():
References
----------
- [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
+ [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
"""
@@ -629,10 +693,38 @@ class ImpedanceModel():
double_sided_impedance(impedance)
frequency = np.linspace(fmin, fmax, int(n_points))
+
+ if sigma is None:
+ if bunch_spectrum is None:
+ raise ValueError(
+ "Either sigma or bunch_spectrum and freq_spectrum" +
+ "must be specified.")
+ else:
+ if freq_spectrum is None:
+ raise ValueError(
+ "freq_spectrum must be given if bunch_spectrum" +
+ " is specified.")
+ if freq_spectrum[0] >= 0:
+ freq_spectrum = np.concatenate(
+ (-1 * freq_spectrum[:0:-1], freq_spectrum))
+ bunch_spectrum = np.concatenate(
+ (bunch_spectrum[:0:-1], bunch_spectrum))
+ bunch_spectrum_interp = interp1d(freq_spectrum,
+ bunch_spectrum,
+ bounds_error=False,
+ fill_value=0)
+ bunch_spectrum = bunch_spectrum_interp(frequency)
+ else:
+ bunch_spectrum = None
+
if max_overlap is False:
- spectrum = beam_spectrum(frequency, M, bunch_spacing, sigma)
+ spectrum = beam_spectrum(frequency, M, bunch_spacing, sigma,
+ bunch_spectrum)
else:
- spectrum = gaussian_bunch_spectrum(frequency, sigma) * M
+ if bunch_spectrum is None:
+ spectrum = gaussian_bunch_spectrum(frequency, sigma) * M
+ else:
+ spectrum = bunch_spectrum * M
pmax = np.floor(fmax / self.ring.f0)
pmin = np.floor(fmin / self.ring.f0)
diff --git a/mbtrack2/impedance/resonator.py b/mbtrack2/impedance/resonator.py
index b89a818678bb0268c14a4ecda14b6752649dd4f2..33e8560b95d818ca7ab740b1ce856019ec623eb6 100644
--- a/mbtrack2/impedance/resonator.py
+++ b/mbtrack2/impedance/resonator.py
@@ -98,7 +98,7 @@ class Resonator(WakeField):
(2 * self.Q_p)))
if np.any(np.abs(t) < atol):
wl[np.abs(t) < atol] = wl[np.abs(t) < atol] / 2
- elif np.any(t < -atol):
+ if np.any(t < -atol):
wl[t < -atol] = 0
return wl
diff --git a/mbtrack2/impedance/wakefield.py b/mbtrack2/impedance/wakefield.py
index 6f221f2f80a7cd66ec8ddb9476fdc11f480527ab..9b751fd20129155f8d370a6feb17f0e91071dd7e 100644
--- a/mbtrack2/impedance/wakefield.py
+++ b/mbtrack2/impedance/wakefield.py
@@ -1,6 +1,6 @@
# -*- coding: utf-8 -*-
"""
-This module defines general classes to describes wakefields, impedances and
+This module defines general classes to describes wakefields, impedances and
wake functions.
"""
@@ -18,7 +18,7 @@ from scipy.interpolate import interp1d
class ComplexData:
"""
- Define a general data structure for a complex function based on a pandas
+ Define a general data structure for a complex function based on a pandas
DataFrame.
Parameters
@@ -49,29 +49,29 @@ class ComplexData:
"""
Method to add two structures. If the data don't have the same length,
different cases are handled.
-
+
Parameters
----------
structure_to_add : ComplexData object, int, float or complex.
structure to be added.
method : str, optional
- manage how the addition is done, possibilties are:
+ manage how the addition is done, possibilties are:
-common: the common range of the index (variable) from the two
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.
-extrapolate: extrapolate the value of both ComplexData.
- -zero: outside of the common range, the missing values are zero. In
+ -zero: outside of the common range, the missing values are zero. In
the common range, behave as "common" method.
interp_kind : str, optional
interpolation method which is passed to pandas and to
scipy.interpolate.interp1d.
index_name : str, optional
name of the dataframe index passed to the method
-
+
Returns
-------
- ComplexData
+ ComplexData
Contains the sum of the two inputs.
"""
@@ -178,17 +178,17 @@ class ComplexData:
"""
Interpolation of the data by calling the class to have a function-like
behaviour.
-
+
Parameters
----------
values : list or numpy array of complex, int or float
values to be interpolated.
interp_kind : str, optional
interpolation method which is passed to scipy.interpolate.interp1d.
-
+
Returns
-------
- numpy array
+ numpy array
Contains the interpolated data.
"""
real_func = interp1d(x=self.data.index,
@@ -338,7 +338,7 @@ class ComplexData:
class WakeFunction(ComplexData):
"""
Define a WakeFunction object based on a ComplexData object.
-
+
Parameters
----------
variable : array-like
@@ -347,12 +347,12 @@ class WakeFunction(ComplexData):
Wake function values in [V/C] for "long" and in [V/C/m] for others.
component_type : str, optinal
Type of the wake function: "long", "xdip", "xquad", ...
-
+
Attributes
----------
data : DataFrame
wake_type : str
-
+
Methods
-------
to_impedance()
@@ -432,9 +432,9 @@ class WakeFunction(ComplexData):
"""
Return an Impedance object from the WakeFunction data.
The WakeFunction data is assumed to be sampled equally.
-
+
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
+ Fourier transform of a Gaussian distribution. It then can be used to go
from wake potential data to impedance.
Parameters
@@ -496,11 +496,11 @@ class WakeFunction(ComplexData):
def deconvolution(self, freq_lim, sigma, mu, nout=None):
"""
Compute a wake function from wake potential data.
-
- The present data loaded into the WakeFunction object is assumed to be
- an uniformly sampled wake potential from a Gaussian bunch distribution
+
+ 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.
-
+
The offset mu depends on the code used to compute the wake potential:
- for CST, it is the first time sample, so self.data.index[0].
- for ABCI, it is "-1 * ISIG * SIG / c".
@@ -546,25 +546,25 @@ class WakeFunction(ComplexData):
def loss_factor(self, sigma):
"""
- Compute the loss factor or the kick factor for a Gaussian bunch.
+ 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].
-
+
Parameters
----------
sigma : float
RMS bunch length in [s]
-
+
Returns
-------
kloss: float
- Loss factor in [V/C] or kick factor in [V/C/m] depanding on the
+ Loss factor in [V/C] or kick factor in [V/C/m] depanding on the
impedance type.
-
+
References
----------
- [1] : Zotter, Bruno W., and Semyon A. Kheifets. Impedances and wakes
+ [1] : Zotter, Bruno W., and Semyon A. Kheifets. Impedances and wakes
in high-energy particle accelerators. World Scientific, 1998.
-
+
"""
time = self.data.index
S = 1 / (2 * np.sqrt(np.pi) * sigma) * np.exp(-1 * time**2 /
@@ -577,7 +577,7 @@ class WakeFunction(ComplexData):
class Impedance(ComplexData):
"""
Define an Impedance object based on a ComplexData object.
-
+
Parameters
----------
variable : array-like
@@ -586,12 +586,12 @@ class Impedance(ComplexData):
Impedance values in [Ohm].
component_type : str, optinal
Type of the impedance: "long", "xdip", "xquad", ...
-
+
Attributes
----------
data : DataFrame
impedance_type : str
-
+
Methods
-------
loss_factor(sigma)
@@ -671,20 +671,20 @@ class Impedance(ComplexData):
def loss_factor(self, sigma):
"""
- Compute the loss factor or the kick factor for a Gaussian bunch.
+ Compute the loss factor or the kick factor for a Gaussian bunch.
Formulas from Eq. (2) p239 and Eq.(7) p240 of [1].
-
+
Parameters
----------
sigma : float
RMS bunch length in [s]
-
+
Returns
-------
kloss: float
- Loss factor in [V/C] or kick factor in [V/C/m] depanding on the
+ Loss factor in [V/C] or kick factor in [V/C/m] depanding on the
impedance type.
-
+
References
----------
[1] : Handbook of accelerator physics and engineering, 3rd printing.
@@ -716,7 +716,7 @@ class Impedance(ComplexData):
"""
Return a WakeFunction object from the impedance data.
The impedance data is assumed to be sampled equally.
-
+
Parameters
----------
nout : int or float, optional
@@ -725,11 +725,11 @@ class Impedance(ComplexData):
input is padded with zeros. If nout < n, the input it cropped.
Note that, for any nout value, nout//2+1 input points are required.
trim : bool or float, optional
- If True, the pseudo wake function is trimmed at time=0 and is forced
- to zero where time<0.
+ If True, the pseudo wake function is trimmed at time=0 and is forced
+ to zero where time<0.
If False, the original result is preserved.
- If a float is given, the pseudo wake function is trimmed from
- time <= trim to 0.
+ If a float is given, the pseudo wake function is trimmed from
+ time <= trim to 0.
"""
Z0 = (self.data['real'] + self.data['imag'] * 1j)
@@ -784,16 +784,16 @@ class Impedance(ComplexData):
class WakeField:
"""
- Defines a WakeField which corresponds to a single physical element which
- produces different types of wakes, represented by their Impedance or
+ Defines a WakeField which corresponds to a single physical element which
+ produces different types of wakes, represented by their Impedance or
WakeFunction objects.
-
+
Parameters
----------
structure_list : list, optional
list of Impedance/WakeFunction objects to add to the WakeField.
name : str, optional
-
+
Attributes
----------
impedance_components : array of str
@@ -802,7 +802,7 @@ class WakeField:
WakeFunction components present for this element.
components : array of str
Impedance or WakeFunction components present for this element.
-
+
Methods
-------
append_to_model(structure_to_add)
@@ -819,6 +819,9 @@ class WakeField:
Save WakeField element to file.
load(file)
Load WakeField element from file.
+ save_to_pyheadtail(filename)
+ Save WakeField to PyHEADTAIL format.
+
"""
def __init__(self, structure_list=None, name=None):
@@ -949,7 +952,7 @@ class WakeField:
def save(self, file):
"""
Save WakeField element to file.
-
+
The same pandas version is needed on both saving and loading computer
for the pickle to work.
@@ -966,11 +969,31 @@ class WakeField:
with open(file, "wb") as f:
pickle.dump(self, f)
+ def save_to_pyheadtail(self, file):
+ """Saves wakefield model to pyheadtail format.
+
+ Parameters
+ ----------
+ file : str
+ filename to save the wakefield model
+
+ Returns
+ -------
+ None.
+ """
+ df_to_save = pd.concat(
+ [self.Wlong.data, self.Wxdip.data, self.Wydip.data], axis=1)
+ df_to_save = df_to_save.drop('imag', axis=1)
+ df_to_save.to_csv(file,
+ sep='\t',
+ header=[0.0, 0.0, 0.0],
+ index_label='0.0')
+
@staticmethod
def load(file):
"""
Load WakeField element from file.
-
+
The same pandas version is needed on both saving and loading computer
for the pickle to work.
@@ -1033,7 +1056,7 @@ class WakeField:
def add_several_wakefields(wakefields, beta):
"""
Add a list of WakeFields taking into account beta functions.
-
+
Parameters
----------
wakefields : list of WakeField
diff --git a/mbtrack2/instability/instabilities.py b/mbtrack2/instability/instabilities.py
index 692c465ecbddf93b82328b1380079e6603af30a0..0a198eb98c90e9f55f16dc5a0805faa948889837 100644
--- a/mbtrack2/instability/instabilities.py
+++ b/mbtrack2/instability/instabilities.py
@@ -103,10 +103,11 @@ def lcbi_growth_rate_mode(ring,
fr=None,
RL=None,
QL=None,
- Z=None):
+ Z=None,
+ bunch_length=None):
"""
Compute the longitudinal coupled bunch instability growth rate driven by
- an impedance for a given coupled bunch mode mu [1].
+ an impedance for a given coupled bunch mode mu [1-2].
Use either a list of resonators (fr, RL, QL) or an Impedance object (Z).
@@ -131,6 +132,10 @@ def lcbi_growth_rate_mode(ring,
Loaded quality factor of the resonator.
Z : Impedance, optional
Longitunial impedance to consider.
+ bunch_length : float, optional
+ Bunch length in [s].
+ Used to computed the form factor for a resonator impedance if given.
+ Default is None.
Returns
-------
@@ -142,9 +147,12 @@ def lcbi_growth_rate_mode(ring,
[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.
+
+ [2] : Tavares, P. F., et al. "Beam-based characterization of higher-order-mode
+ driven coupled-bunch instabilities in a fourth-generation storage ring."
+ NIM A (2022): 165945.
"""
-
if synchrotron_tune is None and Vrf is None:
raise ValueError("Either synchrotron_tune or Vrf is needed.")
if synchrotron_tune is None:
@@ -189,7 +197,15 @@ def lcbi_growth_rate_mode(ring,
omega_p = ring.omega0 * (n0*M + mu + nu_s)
omega_m = ring.omega0 * (n1*M - mu - nu_s)
- sum_val = np.sum(omega_p * Zr(omega_p)) - np.sum(omega_m * Zr(omega_m))
+ if bunch_length is None:
+ FFp = 1
+ FFm = 1
+ else:
+ FFp = np.exp(-(omega_p * bunch_length)**2)
+ FFm = np.exp(-(omega_m * bunch_length)**2)
+
+ sum_val = np.sum(omega_p * Zr(omega_p) * FFp) - np.sum(
+ omega_m * Zr(omega_m) * FFm)
return factor * sum_val
@@ -202,10 +218,11 @@ def lcbi_growth_rate(ring,
fr=None,
RL=None,
QL=None,
- Z=None):
+ Z=None,
+ bunch_length=None):
"""
Compute the maximum growth rate for longitudinal coupled bunch instability
- driven an impedance [1].
+ driven an impedance [1-2].
Use either a list of resonators (fr, RL, QL) or an Impedance object (Z).
@@ -228,6 +245,10 @@ def lcbi_growth_rate(ring,
Loaded quality factor of the HOM.
Z : Impedance, optional
Longitunial impedance to consider.
+ bunch_length : float, optional
+ Bunch length in [s].
+ Used to computed the form factor for a resonator impedance if given.
+ Default is None.
Returns
-------
@@ -245,6 +266,10 @@ def lcbi_growth_rate(ring,
[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.
+
+ [2] : Tavares, P. F., et al. "Beam-based characterization of higher-order-mode
+ driven coupled-bunch instabilities in a fourth-generation storage ring."
+ NIM A (2022): 165945.
"""
growth_rates = np.zeros(M)
@@ -259,7 +284,8 @@ def lcbi_growth_rate(ring,
fr=fr,
RL=RL,
QL=QL,
- Z=Z)
+ Z=Z,
+ bunch_length=bunch_length)
growth_rate = np.max(growth_rates)
mu = np.argmax(growth_rates)
diff --git a/mbtrack2/instability/ions.py b/mbtrack2/instability/ions.py
index 2ca737772d467d29b91208b443c615abe0bef25a..8ddd8f7eac65c80ca4f28dc71f263719b9b41a3f 100644
--- a/mbtrack2/instability/ions.py
+++ b/mbtrack2/instability/ions.py
@@ -17,6 +17,7 @@ from scipy.constants import (
physical_constants,
pi,
)
+from scipy.special import k0
rp = 1 / (4*pi*epsilon_0) * e**2 / (m_p * c**2)
re = physical_constants["classical electron radius"][0]
@@ -25,12 +26,12 @@ re = physical_constants["classical electron radius"][0]
def ion_cross_section(ring, ion):
"""
Compute the collisional ionization cross section.
-
+
Compute the inelastic collision cross section between a molecule or an atom
- by a relativistic electron using the relativistic Bethe asymptotic formula
+ by a relativistic electron using the relativistic Bethe asymptotic formula
[1].
-
- Values of M02 and C02 from [2].
+
+ Values of M02 and C02 from [2-4] (values of constants are independent of beam energy).
Parameters
----------
@@ -42,29 +43,42 @@ def ion_cross_section(ring, ion):
-------
sigma : float
Cross section in [m**2].
-
+
References
----------
- [1] : M. Inokuti, "Inelastic collisions of fast charged particles with
- atoms and molecules-the bethe theory revisited", Reviews of modern physics
+ [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
+ [2] : P. F. Tavares, "Bremsstrahlung detection of ions trapped in the EPA
electron beam", Part. Accel. 43 (1993).
+ [3] : A. G. Mathewson, S. Zhang, "Beam-gas ionisation cross sections at 7.0 TEV", CERN Tech. rep. Vacuum-Technical-Note-96-01. https://cds.cern.ch/record/1489148/
+ [4] : F. Rieke and W. Prepejchal, "Ionization Cross Sections of Gaseous
+ Atoms and Molecules for High-Energy Electrons and Positrons",
+ Phys. Rev. A 6, 1507 (1972).
"""
if ion == "CO":
M02 = 3.7
- C0 = 35.1
+ C0 = 35.14
elif ion == "H2":
- M02 = 0.7
- C0 = 8.1
+ M02 = 0.695
+ C0 = 8.115
+ elif ion == "CO2":
+ M02 = 5.75
+ C0 = 55.92
+ elif ion == "CH4":
+ M02 = 4.23
+ C0 = 42.85
+ elif ion == "H20":
+ M02 = 3.24
+ C0 = 32.26
else:
raise NotImplementedError
- sigma = 4 * pi * (hbar / m_e / c)**2 * (
- M02 * (1 / ring.beta**2 * np.log(ring.beta**2 /
- (1 - ring.beta**2)) - 1) +
- C0 / ring.beta**2)
+ sigma = (4 * pi * (hbar / m_e / c)**2 *
+ (M02 * (1 / ring.beta**2 * np.log(ring.beta**2 /
+ (1 - ring.beta**2)) - 1) +
+ C0 / ring.beta**2))
return sigma
@@ -94,36 +108,27 @@ def ion_frequency(N,
dim : "y" o "x", optional
Dimension to consider. The default is "y".
express : str, optional
- Expression to use to compute the ion oscillation frequency.
- The default is "coupling" corresponding to Gaussian electron and ion
+ 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
+ Also possible is "no_coupling" corresponding to Gaussian electron and
ion distributions without coupling [2].
Returns
-------
f : float or array
Ion oscillation frequencies in [Hz].
-
+
References
----------
- [1] : T. O. Raubenheimer and F. Zimmermann, "Fast beam-ion instability. I.
+ [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
+ [2] : G. V. Stupakov, T. O. Raubenheimer, and F. Zimmermann, "Fast beam-ion
instability. II. effect of ion decoherence", Physical Review E 52 (1995).
"""
- if ion == "CO":
- A = 28
- elif ion == "H2":
- A = 2
- elif ion == "CH4":
- A = 18
- elif ion == "H2O":
- A = 16
- elif ion == "CO2":
- A = 44
+ ion_mass = {"CO": 28, "H2": 2, "CH4": 18, "H20": 16, "CO2": 44}
if dim == "y":
pass
@@ -137,43 +142,45 @@ def ion_frequency(N,
elif express == "no_coupling":
k = 1
- f = c * np.sqrt(2 * rp * N / (A * k * Lsep * sigmay *
- (sigmax+sigmay))) / (2*pi)
+ f = (c * np.sqrt(2 * rp * N / (ion_mass[ion] * k * Lsep * sigmay *
+ (sigmax+sigmay))) / (2*pi))
return f
-def fast_beam_ion(ring,
- Nb,
- nb,
- Lsep,
- sigmax,
- sigmay,
- P,
- T,
- beta,
- model="linear",
- delta_omega=0,
- ion="CO",
- dim="y"):
+def fast_beam_ion(
+ ring,
+ Nb,
+ nb,
+ Lsep,
+ sigmax,
+ sigmay,
+ P,
+ T,
+ beta,
+ model="linear",
+ delta_omega=0,
+ ion="CO",
+ dim="y",
+):
"""
Compute fast beam ion instability rise time [1].
-
- Warning !
- If model="linear", the rise time is an assymptotic grow time
+
+ 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
+ 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].
-
+
The linear model assumes that [1]:
x,y << sigmax,sigmay
-
+
The decoherence model assumes that [2]:
- Lsep << c / (2 * pi * ion_frequency)
+ Lsep << c / (2 * pi * ion_frequency)
Lsep << c / (2 * pi * betatron_frequency)
-
+
The non-linear model assumes that [3]:
x,y >> sigmax,sigmay
@@ -212,16 +219,16 @@ def fast_beam_ion(ring,
-------
tau : float
Instability rise time in [s].
-
+
References
----------
- [1] : T. O. Raubenheimer and F. Zimmermann, "Fast beam-ion instability. I.
+ [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
+ [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., & Mess, K. H. (Eds.). (2013). Handbook of accelerator
+ [3] : Chao, A. W., & Mess, K. H. (Eds.). (2013). Handbook of accelerator
physics and engineering. World scientific. 3rd Printing. p417.
-
+
"""
if dim == "y":
pass
@@ -234,15 +241,19 @@ def fast_beam_ion(ring,
A = 28
elif ion == "H2":
A = 2
+ elif ion == "H2O":
+ A = 16
+ elif ion == "CO2":
+ A = 44
sigma_i = ion_cross_section(ring, ion)
d_gas = P / (Boltzmann*T)
- num = 4 * d_gas * sigma_i * beta * Nb**(3 / 2) * nb**2 * re * rp**(
- 1 / 2) * Lsep**(1 / 2) * c
- den = 3 * np.sqrt(3) * ring.gamma * sigmay**(3 / 2) * (sigmay + sigmax)**(
- 3 / 2) * A**(1 / 2)
+ num = (4 * d_gas * sigma_i * beta * Nb**(3 / 2) * nb**2 * re *
+ rp**(1 / 2) * Lsep**(1 / 2) * c)
+ den = (3 * np.sqrt(3) * ring.gamma * sigmay**(3 / 2) *
+ (sigmay + sigmax)**(3 / 2) * A**(1 / 2))
tau = den / num
@@ -276,11 +287,11 @@ def plot_critical_mass(ring, bunch_charge, bunch_spacing, n_points=1e4):
Returns
-------
fig : figure
-
+
References
----------
- [1] : Gamelin, A. (2018). Collective effects in a transient microbunching
- regime and ion cloud mitigation in ThomX (Doctoral dissertation,
+ [1] : Gamelin, A. (2018). Collective effects in a transient microbunching
+ regime and ion cloud mitigation in ThomX (Doctoral dissertation,
Université Paris-Saclay).
"""
@@ -310,3 +321,136 @@ def plot_critical_mass(ring, bunch_charge, bunch_spacing, n_points=1e4):
ax.set_xlabel("Longitudinal position [m]")
return fig
+
+
+def get_tavares_ion_distribution(x, sigma_x):
+ """
+ Get tranvserse ion distribution
+
+ Parameters
+ ----------
+ x: float, numpy array
+ an array defining the range of values in which to compute the distribution.
+ sigma_x: float
+ rms beam size of an electron bunch (assumed to have a Gaussian distribution) that focuses the ions.
+
+ Returns
+ -------
+ Transverse ion distribution density.
+
+ References
+ ----------
+ [1] Tavares, P. F. (1992). Transverse Distribution of Ions Trapped in an Electron Beam.
+ """
+ return (1 / (pi * np.sqrt(2 * pi) * sigma_x) *
+ k0(x**2 / (2 * sigma_x)**2) * np.exp(-(x**2) / (2 * sigma_x)**2))
+
+
+@np.vectorize
+def find_A_critical(sigma_x,
+ sigma_y,
+ bunch_intensity=int(1e9),
+ bunch_spacing=0.85):
+ """
+ Compute critical mass for ion trapping
+
+ Parameters
+ ----------
+ sigma_x: float, ndarray
+ horizontal rms electron bunch size in [m]
+ sigma_y: float, ndarray
+ vertical rms electron bunch size in [m]
+ bunch_intensity: float
+ number of particles per bunch
+ bunch_spacing: float
+ spacing between bunches in [m]
+
+ Returns
+ -------
+ A_x, A_y: tuple of ndarrays
+ critical ion trapping mass in horizontal and vertical planes
+ References
+ ----------
+
+ """
+ A = bunch_intensity * bunch_spacing * rp / (2 * (sigma_x+sigma_y))
+ A_x, A_y = A / sigma_x, A / sigma_y
+ return A_x, A_y
+
+
+@np.vectorize
+def get_omega_i(sigma_x,
+ sigma_y,
+ ion_mass=28,
+ bunch_intensity=int(1e9),
+ bunch_spacing=0.85):
+ """
+ Compute ion bounce frequency
+
+ Parameters
+ ----------
+ sigma_x: float, numpy array
+ horizontal rms electron bunch size in [m]
+ sigma_y: float, numpy array
+ vertical rms electron bunch size in [m]
+ ion_mass: int
+ Ion mass normalised in [u]
+ bunch_intensity: float
+ number of particles per bunch
+ bunch_spacing: float
+ spacing between bunches in [m]
+
+ Returns
+ -------
+ omega_x, omega_y: tuple of ndarrays
+ Ion bounce oscillation frequency (horizontal, vertical) in [Hz/rad]
+ References
+ ----------
+ """
+ omega_i_times_sqrt_sigma = c * np.sqrt(4 * bunch_intensity * rp /
+ (3 * bunch_spacing *
+ (sigma_y+sigma_x) * ion_mass))
+ omega_x, omega_y = omega_i_times_sqrt_sigma / np.sqrt(
+ sigma_x), omega_i_times_sqrt_sigma / np.sqrt(sigma_y)
+ return omega_x, omega_y
+
+
+@np.vectorize
+def get_omega_e(
+ sigma_x,
+ sigma_y,
+ ionisation_cross_section,
+ residual_gas_density,
+ bunch_intensity,
+ lorenzt_gamma,
+):
+ """
+ Compute electron-in-ions bounce frequency
+
+ Parameters
+ ----------
+ sigma_x: float, numpy array
+ horizontal rms electron bunch size in [m]
+ sigma_y: float, numpy array
+ vertical rms electron bunch size in [m]
+ ionisation_cross_section:
+ collisional ionisation cross section in [m**2]
+ residual_gas_density: float
+ Residual gas density in [m**-3]
+ bunch_intensity: float
+ number of particles per bunch
+ gamma_r:
+
+ Returns
+ -------
+ omega_x, omega_y: tuple of ndarrays
+ Electron-in-ions oscillation frequency (horizontal, vertical) in [Hz/rad]
+ References
+ ----------
+ """
+ omega_e_times_sqrt_sigma = c * np.sqrt(
+ 4 * ionisation_cross_section * residual_gas_density * bunch_intensity *
+ re / (lorenzt_gamma * (sigma_y+sigma_x)))
+ omega_x, omega_y = omega_e_times_sqrt_sigma / np.sqrt(
+ sigma_x), omega_e_times_sqrt_sigma / np.sqrt(sigma_y)
+ return omega_x, omega_y
diff --git a/mbtrack2/tracking/__init__.py b/mbtrack2/tracking/__init__.py
index 02843e280f5cd945178b040b903c468b095765cc..cef735267511672fb666bed6db12a187dd13ad3b 100644
--- a/mbtrack2/tracking/__init__.py
+++ b/mbtrack2/tracking/__init__.py
@@ -5,6 +5,12 @@ from mbtrack2.tracking.aperture import (
LongitudinalAperture,
RectangularAperture,
)
+from mbtrack2.tracking.beam_ion_effects import (
+ BeamIonElement,
+ IonAperture,
+ IonMonitor,
+ IonParticles,
+)
from mbtrack2.tracking.element import (
Element,
LongitudinalMap,
@@ -14,6 +20,7 @@ from mbtrack2.tracking.element import (
TransverseMapSector,
transverse_map_sector_generator,
)
+from mbtrack2.tracking.excite import Sweep
from mbtrack2.tracking.feedback import ExponentialDamper, FIRDamper
from mbtrack2.tracking.monitors import *
from mbtrack2.tracking.parallel import Mpi
@@ -26,6 +33,7 @@ from mbtrack2.tracking.rf import (
RFCavity,
TunerLoop,
)
+from mbtrack2.tracking.spacecharge import TransverseSpaceCharge
from mbtrack2.tracking.synchrotron import Synchrotron
from mbtrack2.tracking.wakepotential import (
LongRangeResistiveWall,
diff --git a/mbtrack2/tracking/aperture.py b/mbtrack2/tracking/aperture.py
index c9316d1727d501073644e86dc07f58d56a59009d..46e5ea980334472973903bd89d9f29c749e3b05e 100644
--- a/mbtrack2/tracking/aperture.py
+++ b/mbtrack2/tracking/aperture.py
@@ -10,9 +10,9 @@ from mbtrack2.tracking.element import Element
class CircularAperture(Element):
"""
- Circular aperture element. The particles which are outside of the circle
+ Circular aperture element. The particles which are outside of the circle
are 'lost' and not used in the tracking any more.
-
+
Parameters
----------
radius : float
@@ -29,21 +29,21 @@ class CircularAperture(Element):
Tracking method for the element.
No bunch to bunch interaction, so written for Bunch objects and
@Element.parallel is used to handle Beam objects.
-
+
Parameters
----------
bunch : Bunch or Beam object
"""
- alive = bunch.particles["x"]**2 + bunch.particles[
- "y"]**2 < self.radius_squared
+ alive = (bunch.particles["x"]**2 + bunch.particles["y"]**2
+ <= self.radius_squared)
bunch.alive[~alive] = False
class ElipticalAperture(Element):
"""
- Eliptical aperture element. The particles which are outside of the elipse
+ Eliptical aperture element. The particles which are outside of the elipse
are 'lost' and not used in the tracking any more.
-
+
Parameters
----------
X_radius : float
@@ -64,21 +64,21 @@ class ElipticalAperture(Element):
Tracking method for the element.
No bunch to bunch interaction, so written for Bunch objects and
@Element.parallel is used to handle Beam objects.
-
+
Parameters
----------
bunch : Bunch or Beam object
"""
alive = (bunch.particles["x"]**2 / self.X_radius_squared +
- bunch.particles["y"]**2 / self.Y_radius_squared < 1)
+ bunch.particles["y"]**2 / self.Y_radius_squared <= 1)
bunch.alive[~alive] = False
class RectangularAperture(Element):
"""
- Rectangular aperture element. The particles which are outside of the
+ Rectangular aperture element. The particles which are outside of the
rectangle are 'lost' and not used in the tracking any more.
-
+
Parameters
----------
X_right : float
@@ -103,23 +103,23 @@ class RectangularAperture(Element):
Tracking method for the element.
No bunch to bunch interaction, so written for Bunch objects and
@Element.parallel is used to handle Beam objects.
-
+
Parameters
----------
bunch : Bunch or Beam object
"""
- if (self.X_left is None):
- alive_X = np.abs(bunch.particles["x"]) < self.X_right
+ if self.X_left is None:
+ alive_X = np.abs(bunch.particles["x"]) <= self.X_right
else:
- alive_X = ((bunch.particles["x"] < self.X_right) &
- (bunch.particles["x"] > self.X_left))
+ alive_X = (bunch.particles["x"]
+ <= self.X_right) & (bunch.particles["x"] >= self.X_left)
- if (self.Y_bottom is None):
- alive_Y = np.abs(bunch.particles["y"]) < self.Y_top
+ if self.Y_bottom is None:
+ alive_Y = np.abs(bunch.particles["y"]) <= self.Y_top
else:
- alive_Y = ((bunch.particles["y"] < self.Y_top) &
- (bunch.particles["y"] > self.Y_bottom))
+ alive_Y = (bunch.particles["y"]
+ <= self.Y_top) & (bunch.particles["y"] >= self.Y_bottom)
alive = alive_X & alive_Y
bunch.alive[~alive] = False
@@ -127,9 +127,9 @@ class RectangularAperture(Element):
class LongitudinalAperture(Element):
"""
- Longitudinal aperture element. The particles which are outside of the
+ Longitudinal aperture element. The particles which are outside of the
longitudinal bounds are 'lost' and not used in the tracking any more.
-
+
Parameters
----------
ring : Synchrotron object
@@ -152,13 +152,13 @@ class LongitudinalAperture(Element):
Tracking method for the element.
No bunch to bunch interaction, so written for Bunch objects and
@Element.parallel is used to handle Beam objects.
-
+
Parameters
----------
bunch : Bunch or Beam object
"""
- alive = ((bunch.particles["tau"] < self.tau_up) &
- (bunch.particles["tau"] > self.tau_low))
+ alive = (bunch.particles["tau"]
+ <= self.tau_up) & (bunch.particles["tau"] >= self.tau_low)
bunch.alive[~alive] = False
diff --git a/mbtrack2/tracking/beam_ion_effects.py b/mbtrack2/tracking/beam_ion_effects.py
new file mode 100644
index 0000000000000000000000000000000000000000..458aa1705a855d98de4ff8aa514f467d67616244
--- /dev/null
+++ b/mbtrack2/tracking/beam_ion_effects.py
@@ -0,0 +1,694 @@
+"""
+Module implementing necessary functionalities for beam-ion interactions.
+Classes:
+BeamIonElement
+IonMonitor
+IonAperture
+IonParticles
+"""
+import warnings
+from abc import ABCMeta
+from functools import wraps
+from itertools import count
+
+import h5py as hp
+import numpy as np
+from numpy.random import choice, normal, uniform
+from scipy.constants import c, e
+
+from mbtrack2.tracking.aperture import ElipticalAperture
+from mbtrack2.tracking.element import Element
+from mbtrack2.tracking.monitors import Monitor
+from mbtrack2.tracking.particles import Beam, Bunch
+from mbtrack2.tracking.particles_electromagnetic_fields import (
+ _efieldn_mit,
+ get_displaced_efield,
+)
+
+
+class IonMonitor(Monitor, metaclass=ABCMeta):
+ """
+ A class representing an ion monitor.
+
+ Parameters
+ ----------
+ save_every : int
+ The number of steps between each save operation.
+ buffer_size : int
+ The size of the buffer to store intermediate data.
+ total_size : int
+ The total number of steps to be simulated.
+ file_name : str, optional
+ The name of the HDF5 file to store the data. If not provided, a new file will be created. Defaults to None.
+
+ Methods
+ -------
+ monitor_init(group_name, save_every, buffer_size, total_size, dict_buffer, dict_file, file_name=None, dict_dtype=None)
+ Initialize the monitor object.
+ track(bunch)
+ Tracking method for the element.
+ Raises
+ ------
+ ValueError
+ If total_size is not divisible by buffer_size.
+ """
+
+ _n_monitors = count(0)
+ file = None
+
+ def __init__(self, save_every, buffer_size, total_size, file_name=None):
+ group_name = "IonData_" + str(next(self._n_monitors))
+ dict_buffer = {
+ "mean": (6, buffer_size),
+ "std": (6, buffer_size),
+ "charge": (buffer_size, ),
+ "charge_per_mp": (buffer_size, ),
+ }
+ dict_file = {
+ "mean": (6, total_size),
+ "std": (6, total_size),
+ "charge": (total_size, ),
+ "charge_per_mp": (buffer_size, ),
+ }
+ self.monitor_init(group_name, save_every, buffer_size, total_size,
+ dict_buffer, dict_file, file_name)
+
+ self.dict_buffer = dict_buffer
+ self.dict_file = dict_file
+
+ def monitor_init(self,
+ group_name,
+ save_every,
+ buffer_size,
+ total_size,
+ dict_buffer,
+ dict_file,
+ file_name=None,
+ dict_dtype=None):
+ """
+ Initialize the monitor object.
+
+ Parameters
+ ----------
+ group_name : str
+ The name of the HDF5 group to store the data.
+ save_every : int
+ The number of steps between each save operation.
+ buffer_size : int
+ The size of the buffer to store intermediate data.
+ total_size : int
+ The total number of steps to be simulated.
+ dict_buffer : dict
+ A dictionary containing the names and sizes of the attribute buffers.
+ dict_file : dict
+ A dictionary containing the names and shapes of the datasets to be created.
+ file_name : str, optional
+ The name of the HDF5 file to store the data. If not provided, a new file will be created. Defaults to None.
+ dict_dtype : dict, optional
+ A dictionary containing the names and data types of the datasets. Defaults to None.
+
+ Raises
+ ------
+ ValueError
+ If total_size is not divisible by buffer_size.
+ """
+ if self.file == None:
+ self.file = hp.File(file_name, "a", libver='earliest')
+
+ self.group_name = group_name
+ self.save_every = int(save_every)
+ self.total_size = int(total_size)
+ self.buffer_size = int(buffer_size)
+ if total_size % buffer_size != 0:
+ raise ValueError("total_size must be divisible by buffer_size.")
+ self.buffer_count = 0
+ self.write_count = 0
+ self.track_count = 0
+
+ # setup attribute buffers from values given in dict_buffer
+ for key, value in dict_buffer.items():
+ if dict_dtype == None:
+ self.__setattr__(key, np.zeros(value))
+ else:
+ self.__setattr__(key, np.zeros(value, dtype=dict_dtype[key]))
+ self.time = np.zeros((self.buffer_size, ), dtype=int)
+ # create HDF5 groups and datasets to save data from group_name and
+ # dict_file
+ self.g = self.file.require_group(self.group_name)
+ self.g.require_dataset("time", (self.total_size, ), dtype=int)
+ for key, value in dict_file.items():
+ if dict_dtype == None:
+ self.g.require_dataset(key, value, dtype=float)
+ else:
+ self.g.require_dataset(key, value, dtype=dict_dtype[key])
+
+ # create a dictionary which handle slices
+ slice_dict = {}
+ for key, value in dict_file.items():
+ slice_dict[key] = []
+ for i in range(len(value) - 1):
+ slice_dict[key].append(slice(None))
+ self.slice_dict = slice_dict
+
+ def track(self, object_to_save):
+ if self.track_count % self.save_every == 0:
+ self.to_buffer(object_to_save)
+ self.track_count += 1
+
+
+class IonAperture(ElipticalAperture):
+ """
+ Class representing an ion aperture.
+
+ Inherits from ElipticalAperture. Unlike in ElipticalAperture, ions are removed from IonParticles instead of just being flagged as not "alive".
+ For beam-ion simulations there are too many lost particles and it is better to remove them.
+
+ Attributes
+ ----------
+ X_radius_squared : float
+ The squared radius of the aperture in the x-direction.
+ Y_radius_squared : float
+ The squared radius of the aperture in the y-direction.
+
+ Methods
+ -------
+ track(bunch)
+ Tracking method for the element.
+
+ """
+
+ @Element.parallel
+ def track(self, bunch):
+ """
+ Tracking method for the element.
+ No bunch to bunch interaction, so written for Bunch objects and
+ @Element.parallel is used to handle Beam objects.
+
+ Parameters
+ ----------
+ bunch : Bunch or Beam object
+ The bunch object to be tracked.
+
+ """
+ alive = (bunch.particles["x"]**2 / self.X_radius_squared +
+ bunch.particles["y"]**2 / self.Y_radius_squared <= 1)
+ for stat in ['x', 'xp', 'y', 'yp', 'tau', 'delta']:
+ bunch.particles[stat] = bunch.particles[stat][alive]
+ bunch.mp_number = len(bunch.particles['x'])
+ bunch.alive = np.ones((bunch.mp_number, ))
+
+
+class IonParticles(Bunch):
+ """
+ Class representing a collection of ion particles.
+
+ Parameters:
+ ----------
+ mp_number : int
+ The number of particles.
+ ion_element_length : float
+ The length of the ion segment.
+ ring : Synchrotron class object
+ The ring object representing the accelerator ring.
+ track_alive : bool, optional
+ Flag indicating whether to track the alive particles. Default is False.
+ alive : bool, optional
+ Flag indicating whether the particles are alive. Default is True.
+ Methods:
+ --------
+ generate_as_a_distribution(electron_bunch)
+ Generates the particle positions based on a normal distribution, taking distribution parameters from an electron bunch.
+ generate_from_random_samples(electron_bunch)
+ Generates the particle positions and times based on random samples from electron positions.
+ """
+
+ def __init__(self,
+ mp_number,
+ ion_element_length,
+ ring,
+ track_alive=False,
+ alive=True):
+ self.ring = ring
+ self._mp_number = int(mp_number)
+ self.alive = np.ones((self.mp_number, ), dtype=bool)
+ if not alive:
+ self.alive = np.zeros((self.mp_number, ), dtype=bool)
+ mp_number = 1
+ self.ion_element_length = ion_element_length
+ self.track_alive = track_alive
+ self.current = 0
+ self.particles = {
+ "x": np.zeros((mp_number, ), dtype=np.float64),
+ "xp": np.zeros((mp_number, ), dtype=np.float64),
+ "y": np.zeros((mp_number, ), dtype=np.float64),
+ "yp": np.zeros((mp_number, ), dtype=np.float64),
+ "tau": np.zeros((mp_number, ), dtype=np.float64),
+ "delta": np.zeros((mp_number, ), dtype=np.float64),
+ }
+ self.charge_per_mp = 0
+
+ @property
+ def mp_number(self):
+ """Macro-particle number"""
+ return self._mp_number
+
+ @mp_number.setter
+ def mp_number(self, value):
+ self._mp_number = int(value)
+
+ def generate_as_a_distribution(self, electron_bunch):
+ """
+ Generates the particle positions based on a normal distribution, taking distribution parameters from an electron bunch.
+
+ Parameters:
+ ----------
+ electron_bunch : Bunch
+ An instance of the Bunch class representing the electron bunch.
+ """
+ self["x"], self["y"] = (
+ normal(
+ loc=electron_bunch["x"].mean(),
+ scale=(electron_bunch["x"]).std(),
+ size=self.mp_number,
+ ),
+ normal(
+ loc=electron_bunch["y"].mean(),
+ scale=(electron_bunch["y"]).std(),
+ size=self.mp_number,
+ ),
+ )
+ self["xp"], self["yp"], self["delta"] = (
+ np.zeros((self.mp_number, )),
+ np.zeros((self.mp_number, )),
+ np.zeros((self.mp_number, )),
+ )
+
+ self["tau"] = uniform(
+ low=-self.ion_element_length / c,
+ high=self.ion_element_length / c,
+ size=self.mp_number,
+ )
+
+ def generate_from_random_samples(self, electron_bunch):
+ """
+ Generates the particle positions and times based on random samples from electron positions in the bunch.
+
+ Parameters:
+ ----------
+ electron_bunch : Bunch
+ An instance of the Bunch class representing the electron bunch.
+ """
+ self["x"], self["y"] = (
+ choice(electron_bunch["x"], size=self.mp_number),
+ choice(electron_bunch["y"], size=self.mp_number),
+ )
+ self["xp"], self["yp"], self["delta"] = (
+ np.zeros((self.mp_number, )),
+ np.zeros((self.mp_number, )),
+ np.zeros((self.mp_number, )),
+ )
+ self["tau"] = uniform(
+ low=-self.ion_element_length / c,
+ high=self.ion_element_length / c,
+ size=self.mp_number,
+ )
+
+ def __add__(self, new_particles):
+ self.mp_number += new_particles.mp_number
+ for t in ["x", "xp", "y", "yp", "tau", "delta"]:
+ self.particles[t] = np.append(self.particles[t],
+ new_particles.particles[t])
+ self.alive = np.append(
+ self.alive, np.ones((new_particles.mp_number, ), dtype=bool))
+ return self
+
+
+class BeamIonElement(Element):
+ """
+ Represents an element for simulating beam-ion interactions.
+
+ Parameters
+ ----------
+ ion_mass : float
+ The mass of the ions in kg.
+ ion_charge : float
+ The charge of the ions in Coulomb.
+ ionization_cross_section : float
+ The cross section of ionization in meters^2.
+ residual_gas_density : float
+ The residual gas density in meters^-3.
+ ring : instance of Synchrotron()
+ The ring.
+ ion_field_model : str
+ The ion field model, the options are 'weak' (acts on each macroparticle), 'strong' (acts on c.m.), 'PIC'.
+ For 'PIC' the PyPIC package is required.
+ electron_field_model : str
+ The electron field model, the options are 'weak', 'strong', 'PIC'.
+ bunch_spacing : float
+ The bunch spacing, the distance between bunches in meters. Used to propagate the ions in between bunches or in the gaps between the bunches.
+ ion_element_length : float
+ The length of the beam-ion interaction region. For example, if only a single interaction point is used this should be equal to ring.L.
+ x_radius : float
+ The x radius of the aperture.
+ y_radius : float
+ The y radius of the aperture.
+ n_steps : int
+ The number of records in the built-in ion beam monitor. Should be number of turns times number of bunches because the monitor records every turn after each bunch passage.
+ n_ion_macroparticles_per_bunch : int, optional
+ The number of ion macroparticles generated per electron bunch passed. Defaults to 30.
+ use_ion_phase_space_monitor : bool, optional
+ Whether to use the ion phase space monitor.
+ generate_method : str, optional
+ The method to generate the ion macroparticles, the options are 'distribution', 'samples'. Defaults to 'distribution'.
+ 'Distribution' generates a distribution statistically equivalent to the distribution of electrons.
+ 'Samples' generates ions from random samples of electron positions.
+
+ Methods
+ -------
+ __init__(self, ion_mass, ion_charge, ionization_cross_section, residual_gas_density, ring, ion_field_model, electron_field_model, bunch_spacing, ion_element_length, n_steps, x_radius, y_radius, ion_beam_monitor_name=None, use_ion_phase_space_monitor=False, n_ion_macroparticles_per_bunch=30, generate_method='distribution')
+ Initializes the BeamIonElement object.
+ parallel(track)
+ Defines the decorator @parallel to handle tracking of Beam() objects.
+ clear_ions(self)
+ Clear the ion particles in the ion beam.
+ track_ions_in_a_drift(self, drift_length)
+ Tracks the ions in a drift.
+ generate_new_ions(self, electron_bunch)
+ Generate new ions based on the given electron bunch.
+ track(self, electron_bunch)
+ Beam-ion interaction kicks.
+
+ Raises
+ ------
+ UserWarning
+ If the BeamIonMonitor object is used, the user should call the close() method at the end of tracking.
+ NotImplementedError
+ If the ion phase space monitor is used.
+ """
+
+ def __init__(self,
+ ion_mass,
+ ion_charge,
+ ionization_cross_section,
+ residual_gas_density,
+ ring,
+ ion_field_model,
+ electron_field_model,
+ bunch_spacing,
+ ion_element_length,
+ n_steps,
+ x_radius,
+ y_radius,
+ ion_beam_monitor_name=None,
+ use_ion_phase_space_monitor=False,
+ n_ion_macroparticles_per_bunch=30,
+ generate_method='distribution'):
+ if use_ion_phase_space_monitor:
+ raise NotImplementedError(
+ "Ion phase space monitor is not implemented.")
+ self.ring = ring
+ self.bunch_spacing = bunch_spacing
+ self.ion_mass = ion_mass
+ self.ionization_cross_section = ionization_cross_section
+ self.residual_gas_density = residual_gas_density
+ self.ion_charge = ion_charge
+ self.electron_field_model = electron_field_model
+ self.ion_field_model = ion_field_model
+ self.ion_element_length = ion_element_length
+ self.generate_method = generate_method
+ self.n_ion_macroparticles_per_bunch = 30
+ self.ion_beam_monitor_name = ion_beam_monitor_name
+ self.ion_beam = IonParticles(
+ mp_number=1,
+ ion_element_length=self.ion_element_length,
+ ring=self.ring)
+ self.ion_beam["x"] = 0
+ self.ion_beam["xp"] = 0
+ self.ion_beam["y"] = 0
+ self.ion_beam["yp"] = 0
+ self.ion_beam["tau"] = 0
+ self.ion_beam["delta"] = 0
+
+ if self.ion_beam_monitor_name:
+ warnings.warn(
+ 'BeamIonMonitor.ion_beam_monitor_name.close() should be called at the end of tracking',
+ UserWarning,
+ stacklevel=2)
+ self.beam_monitor = IonMonitor(
+ 1,
+ int(n_steps / 10),
+ n_steps,
+ file_name=self.ion_beam_monitor_name)
+
+ self.aperture = IonAperture(X_radius=x_radius, Y_radius=y_radius)
+
+ def parallel(track):
+ """
+ Defines the decorator @parallel which handle the embarrassingly
+ parallel case which happens when there is no bunch to bunch
+ interaction in the tracking routine.
+
+ Adding @Element.parallel allows to write the track method of the
+ Element subclass for a Bunch object instead of a Beam object.
+
+ Parameters
+ ----------
+ track : function, method of an Element subclass
+ track method of an Element subclass which takes a Bunch object as
+ input
+
+ Returns
+ -------
+ track_wrapper: function, method of an Element subclass
+ track method of an Element subclass which takes a Beam object or a
+ Bunch object as input
+ """
+
+ @wraps(track)
+ def track_wrapper(*args, **kwargs):
+ if isinstance(args[1], Beam):
+ if Beam.switch_mpi:
+ warnings.warn(
+ 'Tracking through beam-ion element is performed sequentially. Bunches are not parallelized.',
+ UserWarning,
+ stacklevel=2)
+ self = args[0]
+ beam = args[1]
+ for bunch in beam.bunch_list:
+ track(self, bunch, *args[2:], **kwargs)
+ else:
+ self = args[0]
+ bunch = args[1]
+ track(self, bunch, *args[2:], **kwargs)
+
+ return track_wrapper
+
+ def clear_ions(self):
+ """
+ Clear the ion particles in the ion beam.
+ """
+ self.ion_beam.particles = IonParticles(
+ mp_number=1, ion_element_length=self.ion_element_length)
+
+ def track_ions_in_a_drift(self, drift_length):
+ """
+ Tracks the ions in a drift.
+
+ Parameters
+ ----------
+ drift_length : float
+ The drift length in meters.
+ """
+ drifted_ions_x = self.ion_beam["x"] + drift_length * self.ion_beam["xp"]
+ drifted_ions_y = self.ion_beam["y"] + drift_length * self.ion_beam["yp"]
+
+ self.ion_beam["x"] = drifted_ions_x
+ self.ion_beam["y"] = drifted_ions_y
+
+ def _get_efields(self, first_beam, second_beam, field_model):
+ """
+ Calculates the electromagnetic field of the first beam acting on the second beam for a given field model.
+
+ Parameters
+ ----------
+ first_beam : IonParticles or Bunch
+ The first beam, represented as an instance of IonParticles() or Bunch().
+ second_beam : IonParticles or Bunch
+ The second beam, represented as an instance of IonParticles() or Bunch().
+ field_model : str, optional
+ The field model used for the interaction. Options are 'weak', 'strong', or 'PIC'.
+
+ Returns
+ -------
+ en_x : numpy.ndarray
+ The x component of the electric field.
+ en_y : numpy.ndarray
+ The y component of the electric field.
+ """
+ assert field_model in [
+ "weak",
+ "strong",
+ "PIC",
+ ], "The implementation for required beam-ion interaction model {:} is not implemented".format(
+ self.interaction_model)
+ sb_mx, sb_stdx = (
+ second_beam["x"].mean(),
+ second_beam["x"].std(),
+ )
+ sb_my, sb_stdy = (
+ second_beam["y"].mean(),
+ second_beam["y"].std(),
+ )
+ if field_model == "weak":
+ en_x, en_y = get_displaced_efield(
+ _efieldn_mit,
+ first_beam["x"],
+ first_beam["y"],
+ sb_stdx,
+ sb_stdy,
+ sb_mx,
+ sb_my,
+ )
+
+ elif field_model == "strong":
+ fb_mx, fb_my = (
+ first_beam["x"].mean(),
+ first_beam["y"].mean(),
+ )
+ en_x, en_y = get_displaced_efield(_efieldn_mit, fb_mx, fb_my,
+ sb_stdx, sb_stdy, sb_mx, sb_my)
+
+ elif field_model == "PIC":
+ from PyPIC import FFT_OpenBoundary
+ from PyPIC import geom_impact_ellip as ellipse
+ qe = e
+ Dx = 0.1 * sb_stdx
+ Dy = 0.1 * sb_stdy
+ x_aper = 10 * sb_stdx
+ y_aper = 10 * sb_stdy
+ chamber = ellipse.ellip_cham_geom_object(x_aper=x_aper,
+ y_aper=y_aper)
+ picFFT = FFT_OpenBoundary.FFT_OpenBoundary(
+ x_aper=chamber.x_aper,
+ y_aper=chamber.y_aper,
+ dx=Dx,
+ dy=Dy,
+ fftlib="pyfftw",
+ )
+ nel_part = 0 * second_beam["x"] + 1.0
+ picFFT.scatter(second_beam["x"], second_beam["y"], nel_part)
+ picFFT.solve()
+ en_x, en_y = picFFT.gather(first_beam["x"], first_beam["y"])
+ en_x /= qe * second_beam["x"].shape[0]
+ en_y /= qe * second_beam["x"].shape[0]
+ return en_x, en_y
+
+ def _get_new_beam_momentum(self,
+ first_beam,
+ second_beam,
+ prefactor,
+ field_model="strong"):
+ """
+ Calculates the new momentum of the first beam due to the interaction with the second beam.
+
+ Parameters
+ ----------
+ first_beam : IonParticles or Bunch
+ The first beam, represented as an instance of IonParticles() or Bunch().
+ second_beam : IonParticles or Bunch
+ The second beam, represented as an instance of IonParticles() or Bunch().
+ prefactor : float
+ A scaling factor applied to the calculation of the new momentum.
+ field_model : str
+ The field model used for the interaction. Options are 'weak', 'strong', or 'PIC'.
+ Default is "strong".
+
+ Returns
+ -------
+ new_xp : numpy.ndarray
+ The new x momentum of the first beam.
+ new_yp : numpy.ndarray
+ The new y momentum of the first beam.
+ """
+
+ en_x, en_y = BeamIonElement._get_efields(first_beam,
+ second_beam,
+ field_model=field_model)
+ kicks_x = prefactor * en_x
+ kicks_y = prefactor * en_y
+ new_xp = first_beam["xp"] + kicks_x
+ new_yp = first_beam["yp"] + kicks_y
+ return new_xp, new_yp
+
+ def _update_beam_momentum(self, beam, new_xp, new_yp):
+ beam["xp"] = new_xp
+ beam["yp"] = new_yp
+
+ def generate_new_ions(self, electron_bunch):
+ """
+ Generate new ions based on the given electron bunch.
+
+ Parameters
+ ----------
+ electron_bunch : ElectronBunch
+ The electron bunch used to generate new ions.
+
+ Returns
+ -------
+ None
+ """
+ new_ion_particles = IonParticles(
+ mp_number=self.n_ion_macroparticles_per_bunch,
+ ion_element_length=self.ion_element_length,
+ ring=self.ring,
+ )
+ if self.generate_method == 'distribution':
+ new_ion_particles.generate_as_a_distribution(
+ electron_bunch=electron_bunch)
+ elif self.generate_method == 'samples':
+ new_ion_particles.generate_from_random_samples(
+ electron_bunch=electron_bunch)
+ self.ion_beam += new_ion_particles
+ self.ion_beam.charge_per_mp = (electron_bunch.charge *
+ self.ionization_cross_section *
+ self.residual_gas_density *
+ self.ion_element_length /
+ self.n_ion_macroparticles_per_bunch)
+
+ @parallel
+ def track(self, electron_bunch):
+ """
+ Beam-ion interaction kicks.
+
+ Parameters
+ ----------
+ electron_bunch : Bunch() or Beam() class object
+ An electron bunch to be interacted with.
+ """
+
+ self.generate_new_ions(electron_bunch=electron_bunch)
+
+ self.aperture.track(self.ion_beam)
+
+ if self.ion_beam_monitor_name is not None:
+ self.beam_monitor.track(self.ion_beam)
+
+ prefactor_to_ion_field = -self.ion_beam.charge / (self.ring.E0)
+ prefactor_to_electron_field = -electron_bunch.charge * (
+ e / (self.ion_mass * c**2))
+ new_xp_ions, new_yp_ions = self._get_new_beam_momentum(
+ self.ion_beam,
+ electron_bunch,
+ prefactor_to_electron_field,
+ field_model=self.electron_field_model,
+ )
+ new_xp_electrons, new_yp_electrons = self._get_new_beam_momentum(
+ electron_bunch,
+ self.ion_beam,
+ prefactor_to_ion_field,
+ field_model=self.ion_field_model,
+ )
+ self._update_beam_momentum(self.ion_beam, new_xp_ions, new_yp_ions)
+ self._update_beam_momentum(electron_bunch, new_xp_electrons,
+ new_yp_electrons)
+ self.track_ions_in_a_drift(drift_length=self.bunch_spacing)
diff --git a/mbtrack2/tracking/element.py b/mbtrack2/tracking/element.py
index 47cc401cf796021e47a2995279821d58e265caa6..4385b57d2f44e87d82648d2ba97831c22051f581 100644
--- a/mbtrack2/tracking/element.py
+++ b/mbtrack2/tracking/element.py
@@ -16,7 +16,7 @@ from mbtrack2.tracking.particles import Beam
class Element(metaclass=ABCMeta):
"""
- Abstract Element class used for subclass inheritance to define all kinds
+ Abstract Element class used for subclass inheritance to define all kinds
of objects which intervene in the tracking.
"""
@@ -25,7 +25,7 @@ class Element(metaclass=ABCMeta):
"""
Track a beam object through this Element.
This method needs to be overloaded in each Element subclass.
-
+
Parameters
----------
beam : Beam object
@@ -35,19 +35,19 @@ class Element(metaclass=ABCMeta):
@staticmethod
def parallel(track):
"""
- Defines the decorator @parallel which handle the embarrassingly
- parallel case which happens when there is no bunch to bunch
+ Defines the decorator @parallel which handle the embarrassingly
+ parallel case which happens when there is no bunch to bunch
interaction in the tracking routine.
-
- Adding @Element.parallel allows to write the track method of the
+
+ Adding @Element.parallel allows to write the track method of the
Element subclass for a Bunch object instead of a Beam object.
-
+
Parameters
----------
track : function, method of an Element subclass
track method of an Element subclass which takes a Bunch object as
input
-
+
Returns
-------
track_wrapper: function, method of an Element subclass
@@ -60,7 +60,7 @@ class Element(metaclass=ABCMeta):
if isinstance(args[1], Beam):
self = args[0]
beam = args[1]
- if (beam.mpi_switch == True):
+ if beam.mpi_switch == True:
track(self, beam[beam.mpi.bunch_num], *args[2:], **kwargs)
else:
for bunch in beam.not_empty:
@@ -76,7 +76,7 @@ class Element(metaclass=ABCMeta):
class LongitudinalMap(Element):
"""
Longitudinal map for a single turn in the synchrotron.
-
+
Parameters
----------
ring : Synchrotron object
@@ -91,7 +91,7 @@ class LongitudinalMap(Element):
Tracking method for the element.
No bunch to bunch interaction, so written for Bunch objects and
@Element.parallel is used to handle Beam objects.
-
+
Parameters
----------
bunch : Bunch or Beam object
@@ -103,9 +103,9 @@ class LongitudinalMap(Element):
class SynchrotronRadiation(Element):
"""
- Element to handle synchrotron radiation, radiation damping and quantum
+ Element to handle synchrotron radiation, radiation damping and quantum
excitation, for a single turn in the synchrotron.
-
+
Parameters
----------
ring : Synchrotron object
@@ -123,37 +123,34 @@ class SynchrotronRadiation(Element):
Tracking method for the element.
No bunch to bunch interaction, so written for Bunch objects and
@Element.parallel is used to handle Beam objects.
-
+
Parameters
----------
bunch : Bunch or Beam object
"""
- if (self.switch[0] == True):
+ if self.switch[0] == True:
rand = np.random.normal(size=len(bunch))
- bunch["delta"] = (
- (1 - 2 * self.ring.T0 / self.ring.tau[2]) * bunch["delta"] +
- 2 * self.ring.sigma_delta *
- (self.ring.T0 / self.ring.tau[2])**0.5 * rand)
+ bunch["delta"] = (1 - 2 * self.ring.T0 / self.ring.tau[2]) * bunch[
+ "delta"] + 2 * self.ring.sigma_delta * (
+ self.ring.T0 / self.ring.tau[2])**0.5 * rand
- if (self.switch[1] == True):
+ if self.switch[1] == True:
rand = np.random.normal(size=len(bunch))
- bunch["xp"] = (
- (1 - 2 * self.ring.T0 / self.ring.tau[0]) * bunch["xp"] +
- 2 * self.ring.sigma()[1] *
- (self.ring.T0 / self.ring.tau[0])**0.5 * rand)
+ bunch["xp"] = (1 - 2 * self.ring.T0 / self.ring.tau[0]
+ ) * bunch["xp"] + 2 * self.ring.sigma()[1] * (
+ self.ring.T0 / self.ring.tau[0])**0.5 * rand
- if (self.switch[2] == True):
+ if self.switch[2] == True:
rand = np.random.normal(size=len(bunch))
- bunch["yp"] = (
- (1 - 2 * self.ring.T0 / self.ring.tau[1]) * bunch["yp"] +
- 2 * self.ring.sigma()[3] *
- (self.ring.T0 / self.ring.tau[1])**0.5 * rand)
+ bunch["yp"] = (1 - 2 * self.ring.T0 / self.ring.tau[1]
+ ) * bunch["yp"] + 2 * self.ring.sigma()[3] * (
+ self.ring.T0 / self.ring.tau[1])**0.5 * rand
class TransverseMap(Element):
"""
Transverse map for a single turn in the synchrotron.
-
+
Parameters
----------
ring : Synchrotron object
@@ -170,7 +167,7 @@ class TransverseMap(Element):
np.poly1d(self.ring.adts[0]),
np.poly1d(self.ring.adts[1]),
np.poly1d(self.ring.adts[2]),
- np.poly1d(self.ring.adts[3])
+ np.poly1d(self.ring.adts[3]),
]
@Element.parallel
@@ -179,7 +176,7 @@ class TransverseMap(Element):
Tracking method for the element.
No bunch to bunch interaction, so written for Bunch objects and
@Element.parallel is used to handle Beam objects.
-
+
Parameters
----------
bunch : Bunch or Beam object
@@ -187,23 +184,29 @@ class TransverseMap(Element):
# Compute phase advance which depends on energy via chromaticity and ADTS
if self.ring.adts is None:
- phase_advance_x = 2 * np.pi * (self.ring.tune[0] +
- self.ring.chro[0] * bunch["delta"])
- phase_advance_y = 2 * np.pi * (self.ring.tune[1] +
- self.ring.chro[1] * bunch["delta"])
+ phase_advance_x = (
+ 2 * np.pi *
+ (self.ring.tune[0] + self.ring.chro[0] * bunch["delta"]))
+ phase_advance_y = (
+ 2 * np.pi *
+ (self.ring.tune[1] + self.ring.chro[1] * bunch["delta"]))
else:
- Jx = (self.ring.optics.local_gamma[0] * bunch['x']**2) + \
- (2*self.ring.optics.local_alpha[0] * bunch['x']*bunch['xp']) + \
- (self.ring.optics.local_beta[0] * bunch['xp']**2)
- Jy = (self.ring.optics.local_gamma[1] * bunch['y']**2) + \
- (2*self.ring.optics.local_alpha[1] * bunch['y']*bunch['yp']) + \
- (self.ring.optics.local_beta[1] * bunch['yp']**2)
- phase_advance_x = 2 * np.pi * (
- self.ring.tune[0] + self.ring.chro[0] * bunch["delta"] +
- self.adts_poly[0](Jx) + self.adts_poly[2](Jy))
- phase_advance_y = 2 * np.pi * (
- self.ring.tune[1] + self.ring.chro[1] * bunch["delta"] +
- self.adts_poly[1](Jx) + self.adts_poly[3](Jy))
+ Jx = ((self.ring.optics.local_gamma[0] * bunch["x"]**2) +
+ (2 * self.ring.optics.local_alpha[0] * bunch["x"] *
+ bunch["xp"]) +
+ (self.ring.optics.local_beta[0] * bunch["xp"]**2))
+ Jy = ((self.ring.optics.local_gamma[1] * bunch["y"]**2) +
+ (2 * self.ring.optics.local_alpha[1] * bunch["y"] *
+ bunch["yp"]) +
+ (self.ring.optics.local_beta[1] * bunch["yp"]**2))
+ phase_advance_x = (
+ 2 * np.pi *
+ (self.ring.tune[0] + self.ring.chro[0] * bunch["delta"] +
+ self.adts_poly[0](Jx) + self.adts_poly[2](Jy)))
+ phase_advance_y = (
+ 2 * np.pi *
+ (self.ring.tune[1] + self.ring.chro[1] * bunch["delta"] +
+ self.adts_poly[1](Jx) + self.adts_poly[3](Jy)))
# 6x6 matrix corresponding to (x, xp, delta, y, yp, delta)
matrix = np.zeros((6, 6, len(bunch)), dtype=np.float64)
@@ -232,14 +235,14 @@ class TransverseMap(Element):
matrix[4, 5, :] = self.dispersion[3]
matrix[5, 5, :] = 1
- x = matrix[0, 0, :] * bunch["x"] + matrix[
- 0, 1, :] * bunch["xp"] + matrix[0, 2, :] * bunch["delta"]
- xp = matrix[1, 0, :] * bunch["x"] + matrix[
- 1, 1, :] * bunch["xp"] + matrix[1, 2, :] * bunch["delta"]
- y = matrix[3, 3, :] * bunch["y"] + matrix[
- 3, 4, :] * bunch["yp"] + matrix[3, 5, :] * bunch["delta"]
- yp = matrix[4, 3, :] * bunch["y"] + matrix[
- 4, 4, :] * bunch["yp"] + matrix[4, 5, :] * bunch["delta"]
+ x = (matrix[0, 0] * bunch["x"] + matrix[0, 1] * bunch["xp"] +
+ matrix[0, 2] * bunch["delta"])
+ xp = (matrix[1, 0] * bunch["x"] + matrix[1, 1] * bunch["xp"] +
+ matrix[1, 2] * bunch["delta"])
+ y = (matrix[3, 3] * bunch["y"] + matrix[3, 4] * bunch["yp"] +
+ matrix[3, 5] * bunch["delta"])
+ yp = (matrix[4, 3] * bunch["y"] + matrix[4, 4] * bunch["yp"] +
+ matrix[4, 5] * bunch["delta"])
bunch["x"] = x
bunch["xp"] = xp
@@ -249,14 +252,14 @@ class TransverseMap(Element):
class SkewQuadrupole:
"""
- Thin skew quadrupole element used to introduce betatron coupling (the
+ Thin skew quadrupole element used to introduce betatron coupling (the
length of the quadrupole is neglected).
-
+
Parameters
----------
strength : float
Integrated strength of the skew quadrupole [m].
-
+
"""
def __init__(self, strength):
@@ -268,19 +271,19 @@ class SkewQuadrupole:
Tracking method for the element.
No bunch to bunch interaction, so written for Bunch objects and
@Element.parallel is used to handle Beam objects.
-
+
Parameters
----------
bunch : Bunch or Beam object
"""
- bunch['xp'] = bunch['xp'] - self.strength * bunch['y']
- bunch['yp'] = bunch['yp'] - self.strength * bunch['x']
+ bunch["xp"] = bunch["xp"] - self.strength * bunch["y"]
+ bunch["yp"] = bunch["yp"] - self.strength * bunch["x"]
class TransverseMapSector(Element):
"""
- Transverse map for a sector of the synchrotron, from an initial
+ Transverse map for a sector of the synchrotron, from an initial
position s0 to a final position s1.
Parameters
@@ -293,20 +296,20 @@ class TransverseMapSector(Element):
Beta Twiss function at the initial location of the sector.
dispersion0 : array of shape (4,)
Dispersion function at the initial location of the sector.
- alpha1 : array of shape (2,)
+ alpha1: array of shape (2,)
Alpha Twiss function at the final location of the sector.
beta1 : array of shape (2,)
Beta Twiss function at the final location of the sector.
dispersion1 : array of shape (4,)
Dispersion function at the final location of the sector.
phase_diff : array of shape (2,)
- Phase difference between the initial and final location of the
+ Phase difference between the initial and final location of the
sector.
chro_diff : array of shape (2,)
- Chromaticity difference between the initial and final location of
+ Chromaticity difference between the initial and final location of
the sector.
adts : array of shape (4,), optional
- Amplitude-dependent tune shift of the sector, see Synchrotron class
+ Amplitude-dependent tune shift of the sector, see Synchrotron class
for details. The default is None.
"""
@@ -338,7 +341,7 @@ class TransverseMapSector(Element):
np.poly1d(adts[0]),
np.poly1d(adts[1]),
np.poly1d(adts[2]),
- np.poly1d(adts[3])
+ np.poly1d(adts[3]),
]
else:
self.adts_poly = None
@@ -349,7 +352,7 @@ class TransverseMapSector(Element):
Tracking method for the element.
No bunch to bunch interaction, so written for Bunch objects and
@Element.parallel is used to handle Beam objects.
-
+
Parameters
----------
bunch : Bunch or Beam object
@@ -357,23 +360,27 @@ class TransverseMapSector(Element):
# Compute phase advance which depends on energy via chromaticity and ADTS
if self.adts_poly is None:
- phase_advance_x = 2 * np.pi * (self.tune_diff[0] +
- self.chro_diff[0] * bunch["delta"])
- phase_advance_y = 2 * np.pi * (self.tune_diff[1] +
- self.chro_diff[1] * bunch["delta"])
+ phase_advance_x = (
+ 2 * np.pi *
+ (self.tune_diff[0] + self.chro_diff[0] * bunch["delta"]))
+ phase_advance_y = (
+ 2 * np.pi *
+ (self.tune_diff[1] + self.chro_diff[1] * bunch["delta"]))
else:
- Jx = (self.gamma0[0] * bunch['x']**2) + \
- (2*self.alpha0[0] * bunch['x']*self['xp']) + \
- (self.beta0[0] * bunch['xp']**2)
- Jy = (self.gamma0[1] * bunch['y']**2) + \
- (2*self.alpha0[1] * bunch['y']*bunch['yp']) + \
- (self.beta0[1] * bunch['yp']**2)
- phase_advance_x = 2 * np.pi * (
- self.tune_diff[0] + self.chro_diff[0] * bunch["delta"] +
- self.adts_poly[0](Jx) + self.adts_poly[2](Jy))
- phase_advance_y = 2 * np.pi * (
- self.tune_diff[1] + self.chro_diff[1] * bunch["delta"] +
- self.adts_poly[1](Jx) + self.adts_poly[3](Jy))
+ Jx = ((self.gamma0[0] * bunch["x"]**2) +
+ (2 * self.alpha0[0] * bunch["x"] * self["xp"]) +
+ (self.beta0[0] * bunch["xp"]**2))
+ Jy = ((self.gamma0[1] * bunch["y"]**2) +
+ (2 * self.alpha0[1] * bunch["y"] * bunch["yp"]) +
+ (self.beta0[1] * bunch["yp"]**2))
+ phase_advance_x = (
+ 2 * np.pi *
+ (self.tune_diff[0] + self.chro_diff[0] * bunch["delta"] +
+ self.adts_poly[0](Jx) + self.adts_poly[2](Jy)))
+ phase_advance_y = (
+ 2 * np.pi *
+ (self.tune_diff[1] + self.chro_diff[1] * bunch["delta"] +
+ self.adts_poly[1](Jx) + self.adts_poly[3](Jy)))
# 6x6 matrix corresponding to (x, xp, delta, y, yp, delta)
matrix = np.zeros((6, 6, len(bunch)))
@@ -383,18 +390,18 @@ class TransverseMapSector(Element):
np.cos(phase_advance_x) + self.alpha0[0] * np.sin(phase_advance_x))
matrix[0, 1, :] = np.sqrt(
self.beta0[0] * self.beta1[0]) * np.sin(phase_advance_x)
- matrix[0, 2, :] = self.dispersion1[0] - matrix[
- 0, 0, :] * self.dispersion0[0] - matrix[0,
- 1, :] * self.dispersion0[1]
+ matrix[0, 2, :] = (self.dispersion1[0] -
+ matrix[0, 0, :] * self.dispersion0[0] -
+ matrix[0, 1, :] * self.dispersion0[1])
matrix[1, 0, :] = (
(self.alpha0[0] - self.alpha1[0]) * np.cos(phase_advance_x) -
(1 + self.alpha0[0] * self.alpha1[0]) *
np.sin(phase_advance_x)) / np.sqrt(self.beta0[0] * self.beta1[0])
matrix[1, 1, :] = np.sqrt(self.beta0[0] / self.beta1[0]) * (
np.cos(phase_advance_x) - self.alpha1[0] * np.sin(phase_advance_x))
- matrix[1, 2, :] = self.dispersion1[1] - matrix[
- 1, 0, :] * self.dispersion0[0] - matrix[1,
- 1, :] * self.dispersion0[1]
+ matrix[1, 2, :] = (self.dispersion1[1] -
+ matrix[1, 0, :] * self.dispersion0[0] -
+ matrix[1, 1, :] * self.dispersion0[1])
matrix[2, 2, :] = 1
# Vertical
@@ -402,28 +409,28 @@ class TransverseMapSector(Element):
np.cos(phase_advance_y) + self.alpha0[1] * np.sin(phase_advance_y))
matrix[3, 4, :] = np.sqrt(
self.beta0[1] * self.beta1[1]) * np.sin(phase_advance_y)
- matrix[3, 5, :] = self.dispersion1[2] - matrix[
- 3, 3, :] * self.dispersion0[2] - matrix[3,
- 4, :] * self.dispersion0[3]
+ matrix[3, 5, :] = (self.dispersion1[2] -
+ matrix[3, 3, :] * self.dispersion0[2] -
+ matrix[3, 4, :] * self.dispersion0[3])
matrix[4, 3, :] = (
(self.alpha0[1] - self.alpha1[1]) * np.cos(phase_advance_y) -
(1 + self.alpha0[1] * self.alpha1[1]) *
np.sin(phase_advance_y)) / np.sqrt(self.beta0[1] * self.beta1[1])
matrix[4, 4, :] = np.sqrt(self.beta0[1] / self.beta1[1]) * (
np.cos(phase_advance_y) - self.alpha1[1] * np.sin(phase_advance_y))
- matrix[4, 5, :] = self.dispersion1[3] - matrix[
- 4, 3, :] * self.dispersion0[2] - matrix[4,
- 4, :] * self.dispersion0[3]
+ matrix[4, 5, :] = (self.dispersion1[3] -
+ matrix[4, 3, :] * self.dispersion0[2] -
+ matrix[4, 4, :] * self.dispersion0[3])
matrix[5, 5, :] = 1
- x = matrix[0, 0, :] * bunch["x"] + matrix[
- 0, 1, :] * bunch["xp"] + matrix[0, 2, :] * bunch["delta"]
- xp = matrix[1, 0, :] * bunch["x"] + matrix[
- 1, 1, :] * bunch["xp"] + matrix[1, 2, :] * bunch["delta"]
- y = matrix[3, 3, :] * bunch["y"] + matrix[
- 3, 4, :] * bunch["yp"] + matrix[3, 5, :] * bunch["delta"]
- yp = matrix[4, 3, :] * bunch["y"] + matrix[
- 4, 4, :] * bunch["yp"] + matrix[4, 5, :] * bunch["delta"]
+ x = (matrix[0, 0, :] * bunch["x"] + matrix[0, 1, :] * bunch["xp"] +
+ matrix[0, 2, :] * bunch["delta"])
+ xp = (matrix[1, 0, :] * bunch["x"] + matrix[1, 1, :] * bunch["xp"] +
+ matrix[1, 2, :] * bunch["delta"])
+ y = (matrix[3, 3, :] * bunch["y"] + matrix[3, 4, :] * bunch["yp"] +
+ matrix[3, 5, :] * bunch["delta"])
+ yp = (matrix[4, 3, :] * bunch["y"] + matrix[4, 4, :] * bunch["yp"] +
+ matrix[4, 5, :] * bunch["delta"])
bunch["x"] = x
bunch["xp"] = xp
@@ -434,19 +441,22 @@ class TransverseMapSector(Element):
def transverse_map_sector_generator(ring, positions):
"""
Convenience function which generate a list of TransverseMapSector elements
- from a ring with an AT lattice.
-
- Tracking through all the sectors is equivalent to a full turn (and thus to
+ from a ring:
+ - if an AT lattice is loaded, the optics functions and chromaticity is
+ computed at the given positions.
+ - if no AT lattice is loaded, the local optics are used everywhere.
+
+ Tracking through all the sectors is equivalent to a full turn (and thus to
the TransverseMap object).
Parameters
----------
ring : Synchrotron object
- Ring parameters, must .
+ Ring parameters.
positions : array
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
+ 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, ...]).
Returns
@@ -455,56 +465,76 @@ def transverse_map_sector_generator(ring, positions):
List of TransverseMapSector elements.
"""
- import at
-
- def _compute_chro(ring, pos, dp=1e-4):
- lat = deepcopy(ring.optics.lattice)
- lat.append(at.Marker("END"))
- N = len(lat)
- refpts = np.arange(N)
- *elem_neg_dp, = at.linopt2(lat, refpts=refpts, dp=-dp)
- *elem_pos_dp, = at.linopt2(lat, refpts=refpts, dp=dp)
-
- s = elem_neg_dp[2]["s_pos"]
- mux0 = elem_neg_dp[2]['mu'][:, 0]
- mux1 = elem_pos_dp[2]['mu'][:, 0]
- muy0 = elem_neg_dp[2]['mu'][:, 1]
- muy1 = elem_pos_dp[2]['mu'][:, 1]
-
- Chrox = (mux1-mux0) / (2*dp) / 2 / np.pi
- Chroy = (muy1-muy0) / (2*dp) / 2 / np.pi
- chrox = np.interp(pos, s, Chrox)
- chroy = np.interp(pos, s, Chroy)
-
- return np.array([chrox, chroy])
-
- if ring.optics.use_local_values:
- raise ValueError(
- "The Synchrotron object must be loaded from an AT lattice")
-
N_sec = len(positions)
sectors = []
- for i in range(N_sec):
- alpha0 = ring.optics.alpha(positions[i])
- beta0 = ring.optics.beta(positions[i])
- dispersion0 = ring.optics.dispersion(positions[i])
- mu0 = ring.optics.mu(positions[i])
- chro0 = _compute_chro(ring, positions[i])
- if i != (N_sec - 1):
- alpha1 = ring.optics.alpha(positions[i + 1])
- beta1 = ring.optics.beta(positions[i + 1])
- dispersion1 = ring.optics.dispersion(positions[i + 1])
- mu1 = ring.optics.mu(positions[i + 1])
- chro1 = _compute_chro(ring, positions[i + 1])
- else:
- alpha1 = ring.optics.alpha(positions[0])
- beta1 = ring.optics.beta(positions[0])
- dispersion1 = ring.optics.dispersion(positions[0])
- mu1 = ring.optics.mu(ring.L)
- chro1 = _compute_chro(ring, ring.L)
- phase_diff = mu1 - mu0
- chro_diff = chro1 - chro0
- sectors.append(
- TransverseMapSector(ring, alpha0, beta0, dispersion0, alpha1,
- beta1, dispersion1, phase_diff, chro_diff))
+ if ring.optics.use_local_values:
+ for i in range(N_sec):
+ sectors.append(
+ TransverseMapSector(
+ ring,
+ ring.optics.local_alpha,
+ ring.optics.local_beta,
+ ring.optics.local_dispersion,
+ ring.optics.local_alpha,
+ ring.optics.local_beta,
+ ring.optics.local_dispersion,
+ ring.tune / N_sec,
+ ring.chro / N_sec,
+ ))
+ else:
+ import at
+
+ def _compute_chro(ring, pos, dp=1e-4):
+ lat = deepcopy(ring.optics.lattice)
+ lat.append(at.Marker("END"))
+ N = len(lat)
+ refpts = np.arange(N)
+ (*elem_neg_dp, ) = at.linopt2(lat, refpts=refpts, dp=-dp)
+ (*elem_pos_dp, ) = at.linopt2(lat, refpts=refpts, dp=dp)
+
+ s = elem_neg_dp[2]["s_pos"]
+ mux0 = elem_neg_dp[2]["mu"][:, 0]
+ mux1 = elem_pos_dp[2]["mu"][:, 0]
+ muy0 = elem_neg_dp[2]["mu"][:, 1]
+ muy1 = elem_pos_dp[2]["mu"][:, 1]
+
+ Chrox = (mux1-mux0) / (2*dp) / 2 / np.pi
+ Chroy = (muy1-muy0) / (2*dp) / 2 / np.pi
+ chrox = np.interp(pos, s, Chrox)
+ chroy = np.interp(pos, s, Chroy)
+
+ return np.array([chrox, chroy])
+
+ for i in range(N_sec):
+ alpha0 = ring.optics.alpha(positions[i])
+ beta0 = ring.optics.beta(positions[i])
+ dispersion0 = ring.optics.dispersion(positions[i])
+ mu0 = ring.optics.mu(positions[i])
+ chro0 = _compute_chro(ring, positions[i])
+ if i != (N_sec - 1):
+ alpha1 = ring.optics.alpha(positions[i + 1])
+ beta1 = ring.optics.beta(positions[i + 1])
+ dispersion1 = ring.optics.dispersion(positions[i + 1])
+ mu1 = ring.optics.mu(positions[i + 1])
+ chro1 = _compute_chro(ring, positions[i + 1])
+ else:
+ alpha1 = ring.optics.alpha(positions[0])
+ beta1 = ring.optics.beta(positions[0])
+ dispersion1 = ring.optics.dispersion(positions[0])
+ mu1 = ring.optics.mu(ring.L)
+ chro1 = _compute_chro(ring, ring.L)
+ phase_diff = mu1 - mu0
+ chro_diff = chro1 - chro0
+ sectors.append(
+ TransverseMapSector(
+ ring,
+ alpha0,
+ beta0,
+ dispersion0,
+ alpha1,
+ beta1,
+ dispersion1,
+ phase_diff,
+ chro_diff,
+ ))
return sectors
diff --git a/mbtrack2/tracking/excite.py b/mbtrack2/tracking/excite.py
new file mode 100644
index 0000000000000000000000000000000000000000..818fceb8cc1702956c3b46b2ebe6a4753992d4d7
--- /dev/null
+++ b/mbtrack2/tracking/excite.py
@@ -0,0 +1,118 @@
+# -*- coding: utf-8 -*-
+"""
+Module to deal with different kinds of beam excitation.
+"""
+import matplotlib.pyplot as plt
+import numpy as np
+from scipy.signal import chirp
+
+from mbtrack2.tracking.element import Element
+from mbtrack2.tracking.particles import Beam, Bunch
+
+
+class Sweep(Element):
+ """
+ Element which excite the beam in between two frequencies, i.e. apply
+ frequency sweep (chirp) on all or a given bunch in the chosen plane.
+
+ If applied to a full beam, the excitation is the same (and at the same time)
+ for all bunches, so it drives a growth of coupled bunch mode 0.
+
+ Parameters
+ ----------
+ ring : Synchrotron
+ Synchrotron object.
+ f0 : float
+ Initial frequency of the sweep in [Hz].
+ f1 : float
+ Final frequency of the sweep in [Hz].
+ t1 : float
+ Time duration of the sweep in [s].
+ level : float
+ Kick level to apply in [V].
+ plane : "x", "y" or "tau"
+ Plane on which to apply the kick.
+ bunch_to_sweep : int, optional
+ Bunch number to which the sweeping is applied.
+ If None, the sweeping is applied for all bunches.
+ Default is None.
+
+ Methods
+ -------
+ track(bunch_or_beam)
+ Tracking method for the element.
+ plot()
+ Plot the sweep voltage applied.
+
+ """
+
+ def __init__(self, ring, f0, f1, t1, level, plane, bunch_to_sweep=None):
+ self.ring = ring
+ self.t = np.arange(0, t1, ring.T0)
+ self.N = len(self.t)
+ self.count = 0
+ self.level = level
+ self.sweep = chirp(self.t, f0, t1, f1)
+ if plane == "x":
+ self.apply = "xp"
+ elif plane == "y":
+ self.apply = "yp"
+ elif plane == "tau":
+ self.apply = "delta"
+ else:
+ raise ValueError("plane should be 'x', 'y' or 'tau'.")
+ self.bunch_to_sweep = bunch_to_sweep
+
+ def track(self, bunch_or_beam):
+ """
+ Tracking method for this element.
+
+ Parameters
+ ----------
+ bunch_or_beam : Bunch or Beam
+ """
+ if isinstance(bunch_or_beam, Bunch):
+ bunch = bunch_or_beam
+ self._track_bunch(bunch)
+ elif isinstance(bunch_or_beam, Beam):
+ beam = bunch_or_beam
+ if (beam.mpi_switch == True):
+ if self.bunch_to_sweep is not None:
+ if beam.mpi.bunch_num == self.bunch_to_sweep:
+ self._track_bunch(beam[beam.mpi.bunch_num])
+ else:
+ self._track_bunch(beam[beam.mpi.bunch_num])
+ else:
+ if self.bunch_to_sweep is not None:
+ self._track_bunch(beam[self.bunch_to_sweep])
+ else:
+ for bunch in beam.not_empty:
+ self._track_bunch(bunch, False)
+ self.count += 1
+ if self.count >= self.N:
+ self.count = 0
+ else:
+ raise TypeError("bunch_or_beam should be a Beam or Bunch object.")
+
+ def _track_bunch(self, bunch, count_step=True):
+ """
+ Tracking method for a bunch for this element.
+
+ Parameters
+ ----------
+ bunch : Bunch
+ """
+ sweep_val = self.sweep[self.count]
+ bunch[self.apply] += self.level / self.ring.E0 * sweep_val
+ if count_step:
+ self.count += 1
+ if self.count >= self.N:
+ self.count = 0
+
+ def plot(self):
+ """Plot the sweep voltage applied."""
+ fig, ax = plt.subplots()
+ ax.plot(self.t, self.sweep)
+ ax.xlabel("Time [s]")
+ ax.ylabel("Sweep voltage [V]")
+ return fig
diff --git a/mbtrack2/tracking/monitors/monitors.py b/mbtrack2/tracking/monitors/monitors.py
index 151fe2a3cedaf638a1045e230f4983df3488aec2..ee16f66703a994f8065a8d161252dc308bdee78d 100644
--- a/mbtrack2/tracking/monitors/monitors.py
+++ b/mbtrack2/tracking/monitors/monitors.py
@@ -352,9 +352,10 @@ class PhaseSpaceMonitor(Monitor):
----------
bunch_number : int
Bunch to monitor
- mp_number : int or float
+ sample_number : int or float
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.
+ total number of macroparticles, the total number must be specified in
+ optinal parameter mp_number and a random fraction of the bunch is saved.
save_every : int or float
Set the frequency of the save. The data is saved every save_every
call of the montior.
@@ -373,6 +374,10 @@ class PhaseSpaceMonitor(Monitor):
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.
+ mp_number : int or float, optional
+ Total number of macroparticle of the tracked bunch.
+ Mandatory if sample_number != mp_number.
+ Default is None.
Methods
-------
@@ -382,23 +387,28 @@ class PhaseSpaceMonitor(Monitor):
def __init__(self,
bunch_number,
- mp_number,
+ sample_number,
save_every,
buffer_size,
total_size,
file_name=None,
- mpi_mode=False):
+ mpi_mode=False,
+ mp_number=None):
self.bunch_number = bunch_number
- self.mp_number = int(mp_number)
+ self.sample_number = int(sample_number)
+ if mp_number is None:
+ self.mp_number = self.sample_number
+ else:
+ self.mp_number = int(mp_number)
group_name = "PhaseSpaceData_" + str(self.bunch_number)
dict_buffer = {
- "particles": (self.mp_number, 6, buffer_size),
- "alive": (self.mp_number, buffer_size)
+ "particles": (self.sample_number, 6, buffer_size),
+ "alive": (self.sample_number, buffer_size)
}
dict_file = {
- "particles": (self.mp_number, 6, total_size),
- "alive": (self.mp_number, total_size)
+ "particles": (self.sample_number, 6, total_size),
+ "alive": (self.sample_number, total_size)
}
self.monitor_init(group_name, save_every, buffer_size, total_size,
dict_buffer, dict_file, file_name, mpi_mode)
@@ -406,6 +416,13 @@ class PhaseSpaceMonitor(Monitor):
self.dict_buffer = dict_buffer
self.dict_file = dict_file
+ if self.sample_number != self.mp_number:
+ index = np.arange(self.mp_number)
+ samples_meta = random.sample(list(index), self.sample_number)
+ self.samples = sorted(samples_meta)
+ else:
+ self.samples = slice(None)
+
def track(self, object_to_save):
"""
Save data
@@ -426,17 +443,10 @@ class PhaseSpaceMonitor(Monitor):
"""
self.time[self.buffer_count] = self.track_count
- if len(bunch.alive) != self.mp_number:
- index = np.arange(len(bunch.alive))
- samples_meta = random.sample(list(index), self.mp_number)
- samples = sorted(samples_meta)
- else:
- samples = slice(None)
-
- self.alive[:, self.buffer_count] = bunch.alive[samples]
+ self.alive[:, self.buffer_count] = bunch.alive[self.samples]
for i, dim in enumerate(bunch):
- self.particles[:, i,
- self.buffer_count] = bunch.particles[dim][samples]
+ self.particles[:, i, self.buffer_count] = bunch.particles[dim][
+ self.samples]
self.buffer_count += 1
@@ -1012,6 +1022,10 @@ class BunchSpectrumMonitor(Monitor):
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.
+ higher_orders : bool, optional
+ If True, save coherent spectrums for higher order moments (FFT of the
+ std, skew and kurtosis components).
+ Default is False.
Attributes
----------
@@ -1040,13 +1054,16 @@ class BunchSpectrumMonitor(Monitor):
dim="all",
n_fft=None,
file_name=None,
- mpi_mode=False):
+ mpi_mode=False,
+ higher_orders=False):
if n_fft is None:
self.n_fft = int(save_every)
else:
self.n_fft = int(n_fft)
+ self.higher_orders = higher_orders
+
self.sample_size = int(sample_size)
self.store_dict = {"x": 0, "y": 1, "tau": 2}
@@ -1093,6 +1110,14 @@ class BunchSpectrumMonitor(Monitor):
"std_incoherent": (3, total_size)
}
+ if self.higher_orders:
+ dict_buffer["coherent_q"] = (3, self.n_fft // 2 + 1, buffer_size)
+ dict_buffer["coherent_s"] = (3, self.n_fft // 2 + 1, buffer_size)
+ dict_buffer["coherent_o"] = (3, self.n_fft // 2 + 1, buffer_size)
+ dict_file["coherent_q"] = (3, self.n_fft // 2 + 1, total_size)
+ dict_file["coherent_s"] = (3, self.n_fft // 2 + 1, total_size)
+ dict_file["coherent_o"] = (3, self.n_fft // 2 + 1, total_size)
+
self.monitor_init(group_name, save_every, buffer_size, total_size,
dict_buffer, dict_file, file_name, mpi_mode)
@@ -1104,6 +1129,10 @@ class BunchSpectrumMonitor(Monitor):
self.positions = np.zeros(
(self.size_list, self.sample_size, self.save_every + 1))
self.mean = np.zeros((self.size_list, self.save_every + 1))
+ if self.higher_orders:
+ self.std = np.zeros((self.size_list, self.save_every + 1))
+ self.skew = np.zeros((self.size_list, self.save_every + 1))
+ self.kurtosis = np.zeros((self.size_list, self.save_every + 1))
index = np.arange(0, int(mp_number))
self.index_sample = sorted(random.sample(list(index),
@@ -1111,6 +1140,13 @@ class BunchSpectrumMonitor(Monitor):
self.incoherent = np.zeros((3, self.n_fft // 2 + 1, self.buffer_size))
self.coherent = np.zeros((3, self.n_fft // 2 + 1, self.buffer_size))
+ if self.higher_orders:
+ self.coherent_q = np.zeros(
+ (3, self.n_fft // 2 + 1, self.buffer_size))
+ self.coherent_s = np.zeros(
+ (3, self.n_fft // 2 + 1, self.buffer_size))
+ self.coherent_o = np.zeros(
+ (3, self.n_fft // 2 + 1, self.buffer_size))
self.file[self.group_name].create_dataset("freq",
data=self.frequency_samples)
@@ -1172,6 +1208,11 @@ class BunchSpectrumMonitor(Monitor):
self.positions[value, :, self.save_count] = np.nan
self.mean[:, self.save_count] = bunch.mean[self.mean_index]
+ if self.higher_orders:
+ self.std[:, self.save_count] = bunch.std[self.mean_index]
+ self.skew[:, self.save_count] = bunch.skew[self.mean_index]
+ self.kurtosis[:, self.save_count] = bunch.kurtosis[
+ self.mean_index]
self.save_count += 1
@@ -1201,6 +1242,19 @@ class BunchSpectrumMonitor(Monitor):
self.coherent[self.store_dict[key], :,
self.buffer_count] = self.get_coherent_spectrum(
self.mean[value])
+ if self.higher_orders:
+ self.coherent_q[
+ self.store_dict[key], :,
+ self.buffer_count] = self.get_coherent_spectrum(
+ self.std[value])
+ self.coherent_s[
+ self.store_dict[key], :,
+ self.buffer_count] = self.get_coherent_spectrum(
+ self.skew[value])
+ self.coherent_o[
+ self.store_dict[key], :,
+ self.buffer_count] = self.get_coherent_spectrum(
+ self.kurtosis[value])
self.buffer_count += 1
@@ -1236,6 +1290,19 @@ class BunchSpectrumMonitor(Monitor):
self.buffer_size:(self.write_count +
1) *
self.buffer_size] = self.coherent
+ if self.higher_orders:
+ self.file[self.group_name][
+ "coherent_q"][:, :, self.write_count *
+ self.buffer_size:(self.write_count + 1) *
+ self.buffer_size] = self.coherent_q
+ self.file[self.group_name][
+ "coherent_s"][:, :, self.write_count *
+ self.buffer_size:(self.write_count + 1) *
+ self.buffer_size] = self.coherent_s
+ self.file[self.group_name][
+ "coherent_o"][:, :, self.write_count *
+ self.buffer_size:(self.write_count + 1) *
+ self.buffer_size] = self.coherent_o
self.file.flush()
self.write_count += 1
diff --git a/mbtrack2/tracking/monitors/plotting.py b/mbtrack2/tracking/monitors/plotting.py
index e407151aa17b7450205afcf80f6909c56ff5f970..9e1f56b03eef2694f75ca186a681017a095e5b6d 100644
--- a/mbtrack2/tracking/monitors/plotting.py
+++ b/mbtrack2/tracking/monitors/plotting.py
@@ -401,7 +401,7 @@ def plot_phasespacedata(filename,
turn,
only_alive=True,
plot_size=1,
- plot_kind='kde'):
+ plot_kind='scatter'):
"""
Plot data recorded by PhaseSpaceMonitor.
@@ -425,7 +425,7 @@ def plot_phasespacedata(filename,
of macro-particles recorded. This option helps reduce processing time
when the data is big.
plot_kind : {'scatter', 'kde', 'hex', 'reg', 'resid'}, optional
- The plot style. The default is 'kde'.
+ The plot style. The default is 'scatter'.
Return
------
@@ -473,8 +473,8 @@ def plot_phasespacedata(filename,
x_axis = path[samples, option_dict[x_var], turn_index[0][0]]
y_axis = path[samples, option_dict[y_var], turn_index[0][0]]
- fig = sns.jointplot(x_axis * scale[option_dict[x_var]],
- y_axis * scale[option_dict[y_var]],
+ fig = sns.jointplot(x=x_axis * scale[option_dict[x_var]],
+ y=y_axis * scale[option_dict[y_var]],
kind=plot_kind)
plt.xlabel(label[option_dict[x_var]])
@@ -780,7 +780,8 @@ def plot_bunchspectrum(filenames,
bunch_number : int or list of int
Bunch to plot. This has to be identical to 'bunch_number' parameter in
'BunchSpectrumMonitor' object.
- dataset : {"mean_incoherent", "coherent", "incoherent"}
+ dataset : {"mean_incoherent", "coherent", "incoherent", "coherent_q",
+ "coherent_s", "coherent_o"}
HDF5 file's dataset to be plotted.
The default is "incoherent".
dim : {"x","y","tau"}, optional
@@ -834,7 +835,7 @@ def plot_bunchspectrum(filenames,
ax.errorbar(time, y_var, y_err)
xlabel = "Turn number"
ylabel = "Mean incoherent frequency [Hz]"
- elif dataset == "incoherent" or dataset == "coherent":
+ else:
if turns is None:
turn_index = np.where(time == time)[0]
@@ -862,10 +863,6 @@ def plot_bunchspectrum(filenames,
ax.set_yscale('log')
ylabel = "FFT amplitude [a.u.]"
- if dataset == "incoherent":
- ax.set_title("Incoherent spectrum")
- elif dataset == "coherent":
- ax.set_title("Coherent spectrum")
ax.set_xlabel(xlabel)
ax.set_ylabel(ylabel)
@@ -897,7 +894,7 @@ def streak_bunchspectrum(filename,
bunch_number : int
Bunch to plot. This has to be identical to 'bunch_number' parameter in
'BunchSpectrumMonitor' object.
- dataset : {"coherent", "incoherent"}
+ dataset : {coherent", "incoherent", "coherent_q", "coherent_s", "coherent_o"}
HDF5 file's dataset to be plotted.
The default is "incoherent".
dim : {"x","y","tau"}, optional
@@ -921,13 +918,11 @@ def streak_bunchspectrum(filename,
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.
-
Returns
-------
fig : Figure
"""
-
file = hp.File(filename, "r")
group = file["BunchSpectrum_{0}".format(bunch_number)]
@@ -984,11 +979,6 @@ def streak_bunchspectrum(filename,
ylabel = ""
fig, ax = plt.subplots()
- if dataset == "incoherent":
- ax.set_title("Incoherent spectrum")
- elif dataset == "coherent":
- ax.set_title("Coherent spectrum")
-
cmap = mpl.cm.inferno # sequential
c = ax.imshow(data.T,
cmap=cmap,
diff --git a/mbtrack2/tracking/particles.py b/mbtrack2/tracking/particles.py
index 7ba97ff2bbcc6cc762ee127a0a3c3a9a19c19a0b..2b3edbb76dd4546e4f8fce9a2120dd4876b98eb7 100644
--- a/mbtrack2/tracking/particles.py
+++ b/mbtrack2/tracking/particles.py
@@ -9,6 +9,7 @@ import numpy as np
import pandas as pd
import seaborn as sns
from scipy.constants import c, e, m_e, m_p
+from scipy.stats import moment
class Particle:
@@ -48,10 +49,17 @@ class Proton(Particle):
super().__init__(m_p, e)
+class Ion(Particle):
+ """Define an ion"""
+
+ def __init__(self, ion_mass, ion_charge):
+ super().__init(ion_mass * m_p, ion_charge * e)
+
+
class Bunch:
"""
Define a bunch object.
-
+
Parameters
----------
ring : Synchrotron object
@@ -68,13 +76,13 @@ class Bunch:
load_from_file : str, optional
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
+ Otherwise, the bunch from the file is loaded and the other inputs are
ignored.
Default is None.
load_suffix : str or int, optional
Suffix to the group name used to load the data from the HDF5 file.
Default is None.
-
+
Attributes
----------
mp_number : int
@@ -94,10 +102,16 @@ class Bunch:
mean : array of shape (6,)
Mean position of alive particles for each coordinates.
std : array of shape (6,)
- Standard deviation of the position of alive particles for each
+ Standard deviation of the position of alive particles for each
coordinates.
emit : array of shape (3,)
- Bunch emittance for each plane [1]. !!! -> Correct for long ?
+ Bunch emittance for each plane [1].
+ skew : array of shape (6,)
+ Skew (3rd moment) of the position of alive particles for each
+ coordinates.
+ kurtosis : array of shape (6,)
+ Kurtosis (4th moment) of the position of alive particles for each
+ coordinates.
Methods
-------
@@ -106,14 +120,14 @@ class Bunch:
plot_phasespace(x_var="tau", y_var="delta", plot_type="j")
Plot phase space.
save(file_name)
- Save bunch object data (6D phase space, current, and state) in an HDF5
+ Save bunch object data (6D phase space, current, and state) in an HDF5
file format.
load(file_name)
Load data from a HDF5 file recorded by Bunch save method.
-
+
References
----------
- [1] Wiedemann, H. (2015). Particle accelerator physics. 4th edition.
+ [1] Wiedemann, H. (2015). Particle accelerator physics. 4th edition.
Springer, Eq.(8.39) of p224.
"""
@@ -239,27 +253,67 @@ class Bunch:
@property
def std(self):
"""
- Return the standard deviation of the position of alive
+ Return the standard deviation of the position of alive
particles for each coordinates.
"""
std = [[self[name].std()] for name in self]
return np.squeeze(np.array(std))
+ @property
+ def skew(self):
+ """
+ Return the skew (3rd moment) of the position of alive
+ particles for each coordinates.
+ """
+ skew = [[moment(self[name], 3)] for name in self]
+ return np.squeeze(np.array(skew))
+
+ @property
+ def kurtosis(self):
+ """
+ Return the kurtosis (4th moment) of the position of alive
+ particles for each coordinates.
+ """
+ kurtosis = [[moment(self[name], 4)] for name in self]
+ return np.squeeze(np.array(kurtosis))
+
@property
def emit(self):
"""
Return the bunch emittance for each plane.
"""
- cor = np.squeeze([[self[name] - self[name].mean()] for name in self])
- emitX = np.sqrt(
- np.mean(cor[0]**2) * np.mean(cor[1]**2) -
- np.mean(cor[0] * cor[1])**2)
- emitY = np.sqrt(
- np.mean(cor[2]**2) * np.mean(cor[3]**2) -
- np.mean(cor[2] * cor[3])**2)
- emitS = np.sqrt(
- np.mean(cor[4]**2) * np.mean(cor[5]**2) -
- np.mean(cor[4] * cor[5])**2)
+
+ cov_x = np.cov(self['x'], self['xp'])
+ cov_y = np.cov(self['y'], self['yp'])
+ cov_z = np.cov(self['tau'], self['delta'])
+
+ if (np.array(self.ring.optics.local_dispersion)
+ != np.array([0, 0, 0, 0])).any():
+ cov_xdelta = np.cov(self['x'], self['delta'])
+ cov_xpdelta = np.cov(self['xp'], self['delta'])
+ cov_ydelta = np.cov(self['y'], self['delta'])
+ cov_ypdelta = np.cov(self['yp'], self['delta'])
+
+ sig11 = cov_x[
+ 0, 0] - cov_xdelta[0, 1] * cov_xdelta[0, 1] / cov_z[1, 1]
+ sig12 = cov_x[
+ 0, 1] - cov_xdelta[0, 1] * cov_xpdelta[0, 1] / cov_z[1, 1]
+ sig22 = cov_x[
+ 1, 1] - cov_xpdelta[0, 1] * cov_xpdelta[0, 1] / cov_z[1, 1]
+ emitX = np.sqrt(sig11*sig22 - sig12*sig12)
+
+ sig11 = cov_y[
+ 0, 0] - cov_ydelta[0, 1] * cov_ydelta[0, 1] / cov_z[1, 1]
+ sig12 = cov_y[
+ 0, 1] - cov_ydelta[0, 1] * cov_ypdelta[0, 1] / cov_z[1, 1]
+ sig22 = cov_y[
+ 1, 1] - cov_ypdelta[0, 1] * cov_ypdelta[0, 1] / cov_z[1, 1]
+ emitY = np.sqrt(sig11*sig22 - sig12*sig12)
+ else:
+ emitX = np.sqrt(np.linalg.det(cov_x))
+ emitY = np.sqrt(np.linalg.det(cov_y))
+
+ emitS = np.sqrt(np.linalg.det(cov_z))
return np.array([emitX, emitY, emitS])
@property
@@ -267,13 +321,20 @@ class Bunch:
"""
Return the average Courant-Snyder invariant of each plane.
+ To get non-zero longitudinal Courant-Snyder invariant, the longitudinal
+ Twiss parameters need to be computed using the ring.get_longitudinal_twiss
+ method.
"""
- Jx = (self.ring.optics.local_gamma[0] * self['x']**2) + \
- (2*self.ring.optics.local_alpha[0] * self['x'])*self['xp'] + \
- (self.ring.optics.local_beta[0] * self['xp']**2)
- Jy = (self.ring.optics.local_gamma[1] * self['y']**2) + \
- (2*self.ring.optics.local_alpha[1] * self['y']*self['yp']) + \
- (self.ring.optics.local_beta[1] * self['yp']**2)
+ xb = self['x'] - self['delta'] * self.ring.optics.local_dispersion[0]
+ yb = self['y'] - self['delta'] * self.ring.optics.local_dispersion[2]
+ xpb = self['xp'] - self['delta'] * self.ring.optics.local_dispersion[1]
+ ypb = self['yp'] - self['delta'] * self.ring.optics.local_dispersion[3]
+ Jx = (self.ring.optics.local_gamma[0] * xb**2) + \
+ (2*self.ring.optics.local_alpha[0] *xb*xpb) + \
+ (self.ring.optics.local_beta[0] * xpb**2)
+ Jy = (self.ring.optics.local_gamma[1] * yb**2) + \
+ (2*self.ring.optics.local_alpha[1] * yb*ypb) + \
+ (self.ring.optics.local_beta[1] * ypb**2)
Js = (self.ring.long_gamma * self['tau']**2) + \
(2*self.ring.long_alpha * self['tau']*self['delta']) + \
(self.ring.long_beta * self['delta']**2)
@@ -284,17 +345,17 @@ class Bunch:
Initialize bunch particles with 6D gaussian phase space.
Covariance matrix is taken from [1] and dispersion is added following
the method explained in [2].
-
+
Parameters
----------
cov : (6,6) array, optional
Covariance matrix of the bunch distribution
mean : (6,) array, optional
Mean of the bunch distribution
-
+
References
----------
- [1] Wiedemann, H. (2015). Particle accelerator physics. 4th
+ [1] Wiedemann, H. (2015). Particle accelerator physics. 4th
edition. Springer, Eq.(8.38) of p223.
[2] http://www.pp.rhul.ac.uk/bdsim/manual-develop/dev_beamgeneration.html
@@ -308,10 +369,12 @@ class Bunch:
optics = kwargs.get("optics", self.ring.optics)
cov = np.zeros((6, 6))
- cov[0, 0] = self.ring.emit[0] * optics.local_beta[0] + (
- optics.local_dispersion[0] * self.ring.sigma_delta)**2
- cov[1, 1] = self.ring.emit[0] * optics.local_gamma[0] + (
- optics.local_dispersion[1] * self.ring.sigma_delta)**2
+ cov[0,
+ 0] = (self.ring.emit[0] * optics.local_beta[0] +
+ (optics.local_dispersion[0] * self.ring.sigma_delta)**2)
+ cov[1,
+ 1] = (self.ring.emit[0] * optics.local_gamma[0] +
+ (optics.local_dispersion[1] * self.ring.sigma_delta)**2)
cov[0, 1] = -1 * self.ring.emit[0] * optics.local_alpha[0] + (
optics.local_dispersion[0] * optics.local_dispersion[1] *
self.ring.sigma_delta**2)
@@ -322,10 +385,12 @@ class Bunch:
cov[5, 0] = optics.local_dispersion[0] * self.ring.sigma_delta**2
cov[1, 5] = optics.local_dispersion[1] * self.ring.sigma_delta**2
cov[5, 1] = optics.local_dispersion[1] * self.ring.sigma_delta**2
- cov[2, 2] = self.ring.emit[1] * optics.local_beta[1] + (
- optics.local_dispersion[2] * self.ring.sigma_delta)**2
- cov[3, 3] = self.ring.emit[1] * optics.local_gamma[1] + (
- optics.local_dispersion[3] * self.ring.sigma_delta)**2
+ cov[2,
+ 2] = (self.ring.emit[1] * optics.local_beta[1] +
+ (optics.local_dispersion[2] * self.ring.sigma_delta)**2)
+ cov[3,
+ 3] = (self.ring.emit[1] * optics.local_gamma[1] +
+ (optics.local_dispersion[3] * self.ring.sigma_delta)**2)
cov[2, 3] = -1 * self.ring.emit[1] * optics.local_alpha[1] + (
optics.local_dispersion[2] * optics.local_dispersion[3] *
self.ring.sigma_delta**2)
@@ -377,7 +442,7 @@ class Bunch:
bins = np.linspace(bin_min, bin_max, n_bin)
center = (bins[1:] + bins[:-1]) / 2
- sorted_index = np.searchsorted(bins, self[dimension], side='left')
+ sorted_index = np.searchsorted(bins, self[dimension], side="left")
sorted_index -= 1
profile = np.bincount(sorted_index, minlength=n_bin - 1)
@@ -447,9 +512,9 @@ class Bunch:
def save(self, file_name, suffix=None, mpi_comm=None):
"""
- Save bunch object data (6D phase space, current, and state) in an HDF5
+ Save bunch object data (6D phase space, current, and state) in an HDF5
file format.
-
+
The output file is named as "<file_name>.hdf5".
Parameters
@@ -467,11 +532,13 @@ class Bunch:
if mpi_comm is None:
f = hp.File(file_name + ".hdf5", "a", libver="earliest")
else:
- f = hp.File(file_name + ".hdf5",
- "a",
- libver='earliest',
- driver='mpio',
- comm=mpi_comm)
+ f = hp.File(
+ file_name + ".hdf5",
+ "a",
+ libver="earliest",
+ driver="mpio",
+ comm=mpi_comm,
+ )
if suffix is None:
group_name = "Bunch"
@@ -514,14 +581,14 @@ class Bunch:
else:
group_name = "Bunch_" + str(suffix)
- self.mp_number = len(f[group_name]['alive'][:])
+ self.mp_number = len(f[group_name]["alive"][:])
for i, dim in enumerate(self):
self.particles[dim] = f[group_name]["phasespace"][:, i]
- self.alive = f[group_name]['alive'][:]
- if f[group_name]['current'][:][0] != 0:
- self.current = f[group_name]['current'][:][0]
+ self.alive = f[group_name]["alive"][:]
+ if f[group_name]["current"][:][0] != 0:
+ self.current = f[group_name]["current"][:][0]
else:
self.charge_per_mp = 0
@@ -532,8 +599,8 @@ class Bunch:
class Beam:
"""
- Define a Beam object composed of several Bunch objects.
-
+ Define a Beam object composed of several Bunch objects.
+
Parameters
----------
ring : Synchrotron object
@@ -558,7 +625,7 @@ class Beam:
bunch_mean : array of shape (6, ring.h)
Mean position of alive particles for each bunch
bunch_std : array of shape (6, ring.h)
- Standard deviation of the position of alive particles for each bunch
+ Standard deviation of the position of alive particles for each bunch
bunch_emit : array of shape (6, ring.h)
Bunch emittance of alive particles for each bunch
mpi : Mpi object
@@ -567,17 +634,17 @@ class Beam:
mpi_init() and mpi_close()
bunch_index : array of shape (len(self,))
Return an array with the positions of the non-empty bunches
-
+
Methods
------
init_beam(filling_pattern, current_per_bunch=1e-3, mp_per_bunch=1e3)
- Initialize beam with a given filling pattern and marco-particle number
+ Initialize beam with a given filling pattern and marco-particle number
per bunch. Then initialize the different bunches with a 6D gaussian
phase space.
mpi_init()
Switch on MPI parallelisation and initialise a Mpi object
mpi_gather()
- Gather beam, all bunches of the different processors are sent to
+ Gather beam, all bunches of the different processors are sent to
all processors. Rather slow
mpi_share_distributions()
Compute the bunch profile and share it between the different bunches.
@@ -597,7 +664,7 @@ class Beam:
if bunch_list is None:
self.init_beam(np.zeros((self.ring.h, 1), dtype=bool))
else:
- if (len(bunch_list) != self.ring.h):
+ if len(bunch_list) != self.ring.h:
raise ValueError(("The length of the bunch list is {} ".format(
len(bunch_list)) + "but should be {}".format(self.ring.h)))
self.bunch_list = bunch_list
@@ -636,7 +703,7 @@ class Beam:
@property
def distance_between_bunches(self):
- """Return an array which contains the distance to the next bunch in
+ """Return an array which contains the distance to the next bunch in
units of the RF period (ring.T1)"""
return self._distance_between_bunches
@@ -671,25 +738,27 @@ class Beam:
self._distance_between_bunches = distance
- def init_beam(self,
- filling_pattern,
- current_per_bunch=1e-3,
- mp_per_bunch=1e3,
- track_alive=True,
- mpi=False):
+ def init_beam(
+ self,
+ filling_pattern,
+ current_per_bunch=1e-3,
+ mp_per_bunch=1e3,
+ track_alive=True,
+ mpi=False,
+ ):
"""
- Initialize beam with a given filling pattern and marco-particle number
+ Initialize beam with a given filling pattern and marco-particle number
per bunch. Then initialize the different bunches with a 6D gaussian
phase space.
-
- If the filling pattern is an array of bool then the current per bunch
+
+ 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.
-
+
Parameters
----------
filling_pattern : numpy array or list of length ring.h
- Filling pattern of the beam, can be a list or an array of bool,
+ 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.
current_per_bunch : float, optional
@@ -705,7 +774,7 @@ class Beam:
other bunches are initialized with a single marco-particle.
"""
- if (len(filling_pattern) != self.ring.h):
+ if len(filling_pattern) != self.ring.h:
raise ValueError(("The length of filling pattern is {} ".format(
len(filling_pattern)) +
"but should be {}".format(self.ring.h)))
@@ -814,7 +883,7 @@ class Beam:
@property
def bunch_std(self):
- """Return an array with the standard deviation of the position of alive
+ """Return an array with the standard deviation of the position of alive
particles for each bunches"""
bunch_std = np.zeros((6, self.ring.h))
for idx, bunch in enumerate(self.not_empty):
@@ -834,7 +903,7 @@ class Beam:
@property
def bunch_cs(self):
- """Return an array with the average Courant-Snyder invariant for each
+ """Return an array with the average Courant-Snyder invariant for each
bunch"""
bunch_cs = np.zeros((3, self.ring.h))
for idx, bunch in enumerate(self.not_empty):
@@ -845,14 +914,15 @@ class Beam:
def mpi_init(self):
"""Switch on MPI parallelisation and initialise a Mpi object"""
from mbtrack2.tracking.parallel import Mpi
+
self.mpi = Mpi(self.filling_pattern)
self.mpi_switch = True
def mpi_gather(self):
- """Gather beam, all bunches of the different processors are sent to
+ """Gather beam, all bunches of the different processors are sent to
all processors. Rather slow"""
- if (self.mpi_switch == False):
+ if self.mpi_switch == False:
print("Error, mpi is not initialised.")
bunch = self[self.mpi.bunch_num]
@@ -872,17 +942,17 @@ class Beam:
Parameters
----------
- var : str {"bunch_current", "bunch_charge", "bunch_particle",
+ var : str {"bunch_current", "bunch_charge", "bunch_particle",
"bunch_mean", "bunch_std", "bunch_emit"}
Variable to be plotted.
option : str, optional
- If var is "bunch_mean", "bunch_std", or "bunch_emit, option needs
+ If var is "bunch_mean", "bunch_std", or "bunch_emit, option needs
to be specified.
- For "bunch_mean" and "bunch_std",
+ For "bunch_mean" and "bunch_std",
option = {"x","xp","y","yp","tau","delta"}.
For "bunch_emit", option = {"x","y","s"}.
The default is None.
-
+
Return
------
fig : Figure
@@ -895,7 +965,7 @@ class Beam:
"bunch_particle": self.bunch_particle,
"bunch_mean": self.bunch_mean,
"bunch_std": self.bunch_std,
- "bunch_emit": self.bunch_emit
+ "bunch_emit": self.bunch_emit,
}
fig, ax = plt.subplots()
@@ -911,12 +981,20 @@ class Beam:
}
scale = [1e6, 1e6, 1e6, 1e6, 1e12, 1]
label_mean = [
- "x (um)", "x' ($\\mu$rad)", "y (um)", "y' ($\\mu$rad)",
- "$\\tau$ (ps)", "$\\delta$"
+ "x (um)",
+ "x' ($\\mu$rad)",
+ "y (um)",
+ "y' ($\\mu$rad)",
+ "$\\tau$ (ps)",
+ "$\\delta$",
]
label_std = [
- "std x (um)", "std x' ($\\mu$rad)", "std y (um)",
- "std y' ($\\mu$rad)", "std $\\tau$ (ps)", "std $\\delta$"
+ "std x (um)",
+ "std x' ($\\mu$rad)",
+ "std y (um)",
+ "std y' ($\\mu$rad)",
+ "std $\\tau$ (ps)",
+ "std $\\delta$",
]
y_axis = var_dict[var][value_dict[option]]
@@ -927,7 +1005,7 @@ class Beam:
ax.plot(np.arange(len(self.filling_pattern)),
y_axis * scale[value_dict[option]])
- ax.set_xlabel('bunch number')
+ ax.set_xlabel("bunch number")
if var == "bunch_mean":
ax.set_ylabel(label_mean[value_dict[option]])
else:
@@ -946,11 +1024,14 @@ class Beam:
ax.plot(np.arange(len(self.filling_pattern)),
y_axis * scale[value_dict[option]])
- if option == "x": label_y = "hor. emittance (nm.rad)"
- elif option == "y": label_y = "ver. emittance (nm.rad)"
- elif option == "s": label_y = "long. emittance (fm.rad)"
+ if option == "x":
+ label_y = "hor. emittance (nm.rad)"
+ elif option == "y":
+ label_y = "ver. emittance (nm.rad)"
+ elif option == "s":
+ label_y = "long. emittance (fm.rad)"
- ax.set_xlabel('bunch number')
+ ax.set_xlabel("bunch number")
ax.set_ylabel(label_y)
elif var == "bunch_current" or var == "bunch_charge" or var == "bunch_particle":
@@ -962,11 +1043,14 @@ class Beam:
ax.plot(np.arange(len(self.filling_pattern)),
var_dict[var] * scale[var])
- ax.set_xlabel('bunch number')
+ ax.set_xlabel("bunch number")
- if var == "bunch_current": label_y = "bunch current (mA)"
- elif var == "bunch_charge": label_y = "bunch chagre (nC)"
- else: label_y = "number of particles"
+ if var == "bunch_current":
+ label_y = "bunch current (mA)"
+ elif var == "bunch_charge":
+ label_y = "bunch chagre (nC)"
+ else:
+ label_y = "number of particles"
ax.set_ylabel(label_y)
@@ -979,7 +1063,7 @@ class Beam:
def save(self, file_name):
"""
Save beam object data in an HDF5 file format.
-
+
The output file is named as "<file_name>.hdf5".
Parameters
@@ -1000,11 +1084,13 @@ class Beam:
mp_number = None
mp_number = self.mpi.comm.bcast(
mp_number, root=self.mpi.bunch_to_rank(i))
- f = hp.File(file_name + ".hdf5",
- "a",
- libver='earliest',
- driver='mpio',
- comm=self.mpi.comm)
+ f = hp.File(
+ file_name + ".hdf5",
+ "a",
+ libver="earliest",
+ driver="mpio",
+ comm=self.mpi.comm,
+ )
group_name = "Bunch_" + str(i)
g = f.create_group(group_name)
g.create_dataset("alive", (mp_number, ), dtype=bool)
@@ -1040,7 +1126,7 @@ class Beam:
f = hp.File(file_name, "r")
filling_pattern = []
for i in range(self.ring.h):
- current = f["Bunch_" + str(i)]['current'][:][0]
+ current = f["Bunch_" + str(i)]["current"][:][0]
filling_pattern.append(current)
self.init_beam(filling_pattern,
diff --git a/mbtrack2/tracking/particles_electromagnetic_fields.py b/mbtrack2/tracking/particles_electromagnetic_fields.py
new file mode 100644
index 0000000000000000000000000000000000000000..ac9577b15b251745be03f0048f6e8e497b88d49a
--- /dev/null
+++ b/mbtrack2/tracking/particles_electromagnetic_fields.py
@@ -0,0 +1,209 @@
+"""
+A package dealing with particles electromagnetic fields.
+For example, it can be applied to space charge, beam-beam force, electron lenses or beam-ion instabilities.
+This is largely adapted from a fork of PyHEADTAIL https://github.com/gubaidulinvadim/PyHEADTAIL.
+Only the fastest Fadeeva implementation of the error function is used here.
+See Oeftiger, A., de Maria, R., Deniau, L., Li, K., McIntosh, E., Moneta, L., Hegglin, S., Aviral, A. (2016).
+Review of CPU and GPU Fadeeva Implementations. https://cds.cern.ch/record/2207430/files/wepoy044.pdf
+"""
+
+from functools import wraps
+
+import numpy as np
+from scipy.constants import epsilon_0, pi
+from scipy.special import wofz as _scipy_wofz
+
+
+def _wofz(x, y):
+ """
+ Compute the Faddeeva function w(z) = exp(-z^2) * erfc(-i*z).
+
+ Parameters
+ ----------
+ x : float
+ Real part of the argument.
+ y : float
+ Imaginary part of the argument.
+
+ Returns
+ -------
+ tuple
+ Real and imaginary parts of the Faddeeva function.
+ """
+ res = _scipy_wofz(x + 1j*y)
+ return res.real, res.imag
+
+
+def _sqrt_sig(sig_x, sig_y):
+ """
+ Compute the square root of the difference between the squared transverse rms and vertical rms.
+
+ Parameters
+ ----------
+ sig_x : float
+ Transverse rms of the distribution.
+ sig_y : float
+ Vertical rms of the distribution.
+
+ Returns
+ -------
+ float
+ Square root of the difference between the squared transverse rms and vertical rms.
+ """
+ return np.sqrt(2 * (sig_x*sig_x - sig_y*sig_y))
+
+
+def _efieldn_mit(x, y, sig_x, sig_y):
+ """
+ Returns electromagnetic fields as E_x/Q, E_y/Q in (V/m/Coulomb).
+
+ Parameters
+ ----------
+ x : np.ndarray
+ x coordinates in meters.
+ y : np.ndarray
+ y coordinates in meters.
+ sig_x : float
+ Transverse rms of the distribution in meters.
+ sig_y : float
+ Vertical rms of the distribution in meters.
+
+ Returns
+ -------
+ tuple
+ Normalized electromagnetic fields Ex/Q, Ey/Q in the units of (V/m/Coulomb).
+ """
+ sig_sqrt = _sqrt_sig(sig_x, sig_y)
+ w1re, w1im = _wofz(x / sig_sqrt, y / sig_sqrt)
+ ex = np.exp(-x * x / (2*sig_x*sig_x) - y * y / (2*sig_y*sig_y))
+ w2re, w2im = _wofz(x * sig_y / (sig_x*sig_sqrt),
+ y * sig_x / (sig_y*sig_sqrt))
+ denom = 2 * epsilon_0 * np.sqrt(pi) * sig_sqrt
+ return (w1im - ex*w2im) / denom, (w1re - ex*w2re) / denom
+
+
+def efieldn_gauss_round(x, y, sig_x, sig_y):
+ """
+ Computes the electromagnetic field of a round Gaussian distribution.
+
+ Parameters
+ ----------
+ x : np.ndarray
+ x coordinates in meters.
+ y : np.ndarray
+ y coordinates in meters.
+ sig_x : float
+ Transverse rms of the distribution in meters.
+ sig_y : float
+ Vertical rms of the distribution in meters.
+
+ Returns
+ -------
+ tuple
+ Normalized electromagnetic fields Ex/Q, Ey/Q in the units of (V/m/Coulomb).
+ """
+ r_squared = x*x + y*y
+ sig_r = sig_x
+ amplitude = (1 - np.exp(-r_squared /
+ (2*sig_r*sig_r))) / (2*pi*epsilon_0*r_squared)
+ return x * amplitude, y * amplitude
+
+
+def _efieldn_linearized(x, y, sig_x, sig_y):
+ """
+ Computes linearized electromagnetic field.
+
+ Parameters
+ ----------
+ x : np.ndarray
+ x coordinate in meters.
+ y : np.ndarray
+ y coordinate in meters.
+ sig_x : float
+ Vertical rms of the distribution in meters.
+ sig_y : float
+ Vertical rms of the distribution in meters.
+
+ Returns
+ -------
+ tuple
+ Normalized electromagnetic fields Ex/Q, Ey/Q in the units of (V/m/Coulomb).
+ """
+ a = np.sqrt(2) * sig_x
+ b = np.sqrt(2) * sig_y
+ amplitude = 1 / (pi * epsilon_0 * (a+b))
+ return x / a * amplitude, y / b * amplitude
+
+
+def add_sigma_check(efieldn):
+ """
+ Wrapper for a normalized electromagnetic field function.
+ Adds the following actions before calculating the field:
+ 1) Exchange x and y quantities if sig_x < sig_y.
+ 2) Apply round beam field formula when sig_x is close to sig_y.
+
+ Parameters
+ ----------
+ efieldn : function
+ Function to calculate normalized electromagnetic field.
+
+ Returns
+ -------
+ function
+ Wrapped function, including round beam and inverted sig_x/sig_y.
+ """
+ sigmas_ratio_threshold = 1e-3
+ absolute_threshold = 1e-10
+
+ @wraps(efieldn)
+ def efieldn_checked(x, y, sig_x, sig_y, *args, **kwargs):
+ tol_kwargs = dict(rtol=sigmas_ratio_threshold, atol=absolute_threshold)
+ if np.allclose(sig_x, sig_y, **tol_kwargs):
+ if np.allclose(sig_y, 0, **tol_kwargs):
+ en_x = en_y = np.zeros(x.shape, dtype=np.float64)
+ else:
+ en_x, en_y = efieldn_gauss_round(x, y, sig_x, sig_y, *args,
+ **kwargs)
+ elif np.all(sig_x < sig_y):
+ en_y, en_x = efieldn(y, x, sig_y, sig_x, *args, **kwargs)
+ else:
+ en_x, en_y = efieldn(x, y, sig_x, sig_y, *args, **kwargs)
+ return en_x, en_y
+
+ return efieldn_checked
+
+
+def get_displaced_efield(efieldn, xr, yr, sig_x, sig_y, mean_x, mean_y):
+ """
+ Compute the charge-normalized electric field components of a two-dimensional Gaussian charge distribution.
+
+ Parameters
+ ----------
+ efieldn : function
+ Calculates electromagnetic field of a given distribution of charges.
+ xr : np.array
+ x coordinates in meters.
+ yr : np.array
+ y coordinates in meters.
+ sig_x : float
+ Horizontal rms size in meters.
+ sig_y : float
+ Vertical rms size in meters.
+ mean_x : float
+ Horizontal mean of the distribution in meters.
+ mean_y : float
+ Vertical mean of the distribution in meters.
+
+ Returns
+ -------
+ tuple
+ Charge-normalized electromagnetic fields with a displaced center of the distribution.
+ """
+ x = xr - mean_x
+ y = yr - mean_y
+ efieldn = add_sigma_check(efieldn)
+ en_x, en_y = efieldn(np.abs(x), np.abs(y), sig_x, sig_y)
+ en_x = np.abs(en_x) * np.sign(x)
+ en_y = np.abs(en_y) * np.sign(y)
+
+ return en_x, en_y
diff --git a/mbtrack2/tracking/rf.py b/mbtrack2/tracking/rf.py
index a92c4b342c3c5a6e80d7b1cf9d99a573a388ed36..4de4aa28530c1f3942fa81d47a11f2fb19670ffa 100644
--- a/mbtrack2/tracking/rf.py
+++ b/mbtrack2/tracking/rf.py
@@ -1,8 +1,10 @@
# -*- coding: utf-8 -*-
"""
-This module handles radio-frequency (RF) cavitiy elements.
+This module handles radio-frequency (RF) cavitiy elements.
"""
+from functools import partial
+
import matplotlib.patches as mpatches
import matplotlib.pyplot as plt
import numpy as np
@@ -16,7 +18,7 @@ class RFCavity(Element):
"""
Perfect RF cavity class for main and harmonic RF cavities.
Use cosine definition.
-
+
Parameters
----------
ring : Synchrotron object
@@ -40,7 +42,7 @@ class RFCavity(Element):
Tracking method for the element.
No bunch to bunch interaction, so written for Bunch objects and
@Element.parallel is used to handle Beam objects.
-
+
Parameters
----------
bunch : Bunch or Beam object
@@ -56,15 +58,15 @@ class RFCavity(Element):
class CavityResonator():
"""Cavity resonator class for active or passive RF cavity with beam
loading or HOM, based on [1,2].
-
+
Use cosine definition.
-
- If used with mpi, beam.mpi.share_distributions must be called before the
+
+ If used with mpi, beam.mpi.share_distributions must be called before the
track method call.
-
+
Different kind of RF feeback and loops can be added using:
cavity_resonator.feedback.append(loop)
-
+
Parameters
----------
ring : Synchrotron object
@@ -87,11 +89,11 @@ class CavityResonator():
theta : float, optional
Total cavity phase objective value in [rad].
n_bin : int, optional
- Number of bins used for the beam loading computation.
- Only used if MPI is not used, otherwise n_bin must be specified in the
+ 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.
-
+
Attributes
----------
beam_phasor : complex
@@ -146,7 +148,7 @@ class CavityResonator():
distance : array
Distance between bunches.
valid_bunch_index : array
-
+
Methods
-------
Vbr(I0)
@@ -191,15 +193,15 @@ class CavityResonator():
Force feedback update from current CavityResonator parameters.
sample_voltage()
Sample the voltage seen by a zero charge particle during an RF period.
-
+
References
----------
- [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
+ [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.
-
- [2] Naoto Yamamoto, Alexis Gamelin, and Ryutaro Nagaoka. "Investigation
- of Longitudinal Beam Dynamics With Harmonic Cavities by Using the Code
+
+ [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.
"""
@@ -258,11 +260,11 @@ class CavityResonator():
def track(self, beam):
"""
Track a Beam object through the CavityResonator object.
-
+
Can be used with or without mpi.
If used with mpi, beam.mpi.share_distributions must be called before.
-
- The beam phasor is given at t=0 (synchronous particle) of the first
+
+ The beam phasor is given at t=0 (synchronous particle) of the first
non empty bunch.
Parameters
@@ -362,8 +364,8 @@ class CavityResonator():
"""
Initialize the beam phasor for a given beam distribution using a
tracking like method.
-
- Follow the same steps as the track method but in the "rf" reference
+
+ Follow the same steps as the track method but in the "rf" reference
frame and without any modifications on the beam.
Parameters
@@ -422,7 +424,7 @@ class CavityResonator():
def phasor_decay(self, time, ref_frame="beam"):
"""
- Compute the beam phasor decay during a given time span, assuming that
+ Compute the beam phasor decay during a given time span, assuming that
no particles are crossing the cavity during the time span.
Parameters
@@ -446,9 +448,9 @@ class CavityResonator():
charge_per_mp,
ref_frame="beam"):
"""
- Compute the beam phasor evolution during the crossing of a bunch using
+ Compute the beam phasor evolution during the crossing of a bunch using
an analytic formula [1].
-
+
Assume that the phasor decay happens before the beam loading.
Parameters
@@ -461,11 +463,11 @@ class CavityResonator():
Charge per macro-particle in [C].
ref_frame : string, optional
Reference frame to be used, can be "beam" or "rf".
-
+
References
----------
[1] mbtrack2 manual.
-
+
"""
if ref_frame == "beam":
delta = self.wr
@@ -490,13 +492,13 @@ class CavityResonator():
"""
Initialize the beam phasor for a given beam distribution using an
analytic formula [1].
-
+
No modifications on the Beam object.
Parameters
----------
beam : Beam object
-
+
References
----------
[1] mbtrack2 manual.
@@ -636,7 +638,7 @@ class CavityResonator():
@property
def Rs_per_cavity(self):
- """Shunt impedance of a single cavity in [Ohm], defined as
+ """Shunt impedance of a single cavity in [Ohm], defined as
0.5*Vc*Vc/Pc."""
return self._Rs_per_cavity
@@ -840,7 +842,7 @@ class CavityResonator():
def set_generator(self, I0):
"""
- Set generator parameters (Pg, Vgr, theta_gr, Vg and theta_g) for a
+ Set generator parameters (Pg, Vgr, theta_gr, Vg and theta_g) for a
given current and set of parameters.
Parameters
@@ -877,14 +879,14 @@ class CavityResonator():
def plot_phasor(self, I0):
"""
- Plot phasor diagram showing the vector addition of generator and beam
+ Plot phasor diagram showing the vector addition of generator and beam
loading voltage.
Parameters
----------
I0 : float
Beam current in [A].
-
+
Returns
-------
Figure.
@@ -948,12 +950,12 @@ class CavityResonator():
modes=None,
bool_return=False):
"""
- Check Coupled-Bunch-Instability stability,
+ Check Coupled-Bunch-Instability stability,
Effect of Direct RF feedback is not included.
- This method is a wraper around lcbi_growth_rate to caluclate the CBI
+ This method is a wraper around lcbi_growth_rate to caluclate the CBI
growth rate from the CavityResonator own impedance.
-
+
See lcbi_growth_rate for details.
Parameters
@@ -962,7 +964,7 @@ class CavityResonator():
Beam current in [A].
synchrotron_tune : float, optinal
Fractional number of longitudinal tune.
- If None, synchrotron_tune is computed using self.Vc as total
+ If None, synchrotron_tune is computed using self.Vc as total
voltage.
Default is None.
modes : float or list of float, optional
@@ -971,17 +973,17 @@ class CavityResonator():
Default is None.
bool_return : bool, optional
If True:
- - return True if the most unstable mode is stronger than
+ - return True if the most unstable mode is stronger than
longitudinal damping time.
- return False if it is not the case.
Default is False.
-
+
Returns
-------
growth_rate : float
Maximum coupled bunch instability growth rate in [s-1].
mu : int
- Coupled bunch mode number corresponding to the maximum coupled bunch
+ Coupled bunch mode number corresponding to the maximum coupled bunch
instability growth rate.
"""
@@ -1101,7 +1103,7 @@ class CavityResonator():
n_points : int or float, optional
Number of sample points. The default is 1e4.
index : int, optional
- RF bucket number to sample. Be carful if index > 0 as no new beam
+ RF bucket number to sample. Be carful if index > 0 as no new beam
loading is not taken into account here.
The default is 0.
@@ -1146,9 +1148,9 @@ class CavityResonator():
class ProportionalLoop():
"""
Proportional feedback loop to control a CavityResonator amplitude and phase.
-
+
Feedback setpoints are cav_res.Vc and cav_res.theta.
-
+
The loop must be added to the CavityResonator object using:
cav_res.feedback.append(loop)
@@ -1203,9 +1205,9 @@ class TunerLoop():
"""
Cavity tuner loop used to control a CavityResonator tuning (psi or detune)
in order to keep the phase between cavity and generator current constant.
-
+
Only a proportional controller is assumed.
-
+
The loop must be added to the CavityResonator object using:
cav_res.feedback.append(loop)
@@ -1218,7 +1220,7 @@ class TunerLoop():
Proportional gain of the tuner loop.
If not specified, 0.01 is used.
avering_period:
- Period during which the phase difference is monitored and averaged.
+ 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.
@@ -1226,7 +1228,7 @@ class TunerLoop():
too fast compared to the actual situation.
offset : float
Tuning offset in [rad].
-
+
"""
def __init__(self, ring, cav_res, gain=0.01, avering_period=0, offset=0):
@@ -1246,11 +1248,11 @@ class TunerLoop():
def track(self):
"""
Tracking method for the tuner loop.
-
+
Returns
-------
None.
-
+
"""
if self.count == self.avering_period:
diff = self.diff / self.avering_period - self.offset
@@ -1264,35 +1266,35 @@ class TunerLoop():
class ProportionalIntegralLoop():
"""
- Proportional Integral (PI) loop to control a CavityResonator amplitude and
+ Proportional Integral (PI) loop to control a CavityResonator amplitude and
phase via generator current (ig) [1,2].
-
+
Feedback reference targets (setpoints) are cav_res.Vc and cav_res.theta.
-
- The ProportionalIntegralLoop should be initialized only after generator
+
+ The ProportionalIntegralLoop should be initialized only after generator
parameters are set.
-
+
The loop must be added to the CavityResonator object using:
cav_res.feedback.append(loop)
-
- When the reference target is changed, it might be needed to re-initialize
+
+ When the reference target is changed, it might be needed to re-initialize
the feedforward constant by calling init_FFconst().
Parameters
----------
ring : Synchrotron object
cav_res : CavityResonator object
- CavityResonator in which the loop will be added.
+ CavityResonator in which the loop will be added.
gain : float list
- Proportional gain (Pgain) and integral gain (Igain) of the feedback
+ 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
+ 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 > 1e6), the Pgain of ~100
+ In case of super conducting cavity (QL > 1e6), the Pgain of ~100
can be used.
- In a "bad" parameter set, unstable oscillation of the cavity voltage
+ 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
+ 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.
sample_num : int
Number of bunch over which the mean cavity voltage is computed.
@@ -1302,7 +1304,7 @@ class ProportionalIntegralLoop():
Time interval between two cavity voltage monitoring and feedback.
Units are in bucket numbers.
delay : int
- Loop delay of the PI feedback system.
+ Loop delay of the PI feedback system.
Units are in bucket numbers.
IIR_cutoff : float, optinal
Cutoff frequency of the IIR filter in [Hz].
@@ -1310,12 +1312,12 @@ class ProportionalIntegralLoop():
Default is 0.
FF : bool, optional
Boolean switch to use feedforward constant.
- True is recommended to prevent a cavity voltage drop in the beginning
+ 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
+ In case of small Pgain (QL ~ 1e4), cavity voltage drop may cause
beam loss due to static Robinson.
Default is True.
-
+
Methods
-------
track()
@@ -1340,7 +1342,7 @@ class ProportionalIntegralLoop():
Notes
-----
Assumption : delay >> every ~ sample_num
-
+
Adjusting ig(Vg) parameter to keep the cavity voltage constant (to target values).
The "track" method is
1) Monitoring the cavity voltage phasor
@@ -1364,14 +1366,14 @@ class ProportionalIntegralLoop():
is one reasonable parameter set.
The practical clock period is 13ns.
==> Igain_PF = Igain_mbtrack * Trf / 13ns = Igain_mbtrack * 0.153
-
+
References
----------
[1] : https://en.wikipedia.org/wiki/PID_controller
- [2] : Yamamoto, N., Takahashi, T., & Sakanaka, S. (2018). Reduction and
- compensation of the transient beam loading effect in a double rf system
+ [2] : Yamamoto, N., Takahashi, T., & 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.
-
+
"""
def __init__(self,
@@ -1461,8 +1463,8 @@ class ProportionalIntegralLoop():
def init_Ig2Vg_matrix(self):
"""
Initialize matrix for Ig2Vg_matrix.
-
- Shoud be called before first use of Ig2Vg_matrix and after each cavity
+
+ Shoud be called before first use of Ig2Vg_matrix and after each cavity
parameter change.
"""
k = np.arange(0, self.ring.h)
@@ -1484,7 +1486,7 @@ class ProportionalIntegralLoop():
def Ig2Vg_matrix(self):
"""
Return Vg from Ig using matrix formalism.
- Warning: self.init_Ig2Vg should be called after each CavityResonator
+ Warning: self.init_Ig2Vg should be called after each CavityResonator
parameter change.
"""
generator_phasor_record = (
@@ -1496,7 +1498,7 @@ class ProportionalIntegralLoop():
def Ig2Vg(self):
"""
Go from Ig to Vg.
-
+
Apply new values to cav_res.generator_phasor_record, cav_res.Vg and
cav_res.theta_g from ig_phasor_record.
"""
@@ -1522,7 +1524,7 @@ class ProportionalIntegralLoop():
cutoff : float
Cutoff frequency of the IIR filter in [Hz].
If 0, cutoff frequency is infinity.
-
+
"""
if cutoff == 0:
self.IIRcoef = 1.0
@@ -1554,18 +1556,18 @@ class ProportionalIntegralLoop():
class DirectFeedback(ProportionalIntegralLoop):
"""
Direct RF FB (DFB) via generator current (ig) using PI controller [1,2].
-
- The DirectFeedback inherits from ProportionalIntegralLoop so all
+
+ The DirectFeedback inherits from ProportionalIntegralLoop so all
mandatory parameters from ProportionalIntegralLoop should be passed as
kwargs when initializing a DirectFeedback object.
-
+
To avoid cavity-beam unmatching (large synchrotron oscilation of beam),
- the CavityResonator generator parameters should be set before
+ the CavityResonator generator parameters should be set before
initialization.
-
+
The loop must be added to the CavityResonator object using:
cav_res.feedback.append(loop)
-
+
Parameters
----------
DFB_gain : float
@@ -1588,7 +1590,7 @@ class DirectFeedback(ProportionalIntegralLoop):
Units are in bucket numbers.
If None, value from the ProportionalIntegralLoop is used.
Default is None.
-
+
Attributes
----------
phase_shift : float
@@ -1601,7 +1603,7 @@ class DirectFeedback(ProportionalIntegralLoop):
Return the gain gamma of the DFB.
DFB_Rs : float
Return the shunt impedance of the DFB in [ohm].
-
+
Methods
-------
DFB_parameter_set(DFB_gain, DFB_phase_shift)
@@ -1612,14 +1614,14 @@ class DirectFeedback(ProportionalIntegralLoop):
Return the generator voltage main and DFB components in [V].
DFB_fs()
Return the modified synchrotron frequency in [Hz].
-
+
References
----------
- [1] : Akai, K. (2022). Stability analysis of rf accelerating mode with
- feedback loops under heavy beam loading in SuperKEKB. PRAB, 25(10),
+ [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
+ [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
"""
@@ -1686,7 +1688,7 @@ class DirectFeedback(ProportionalIntegralLoop):
def DFB_psi(self):
"""
Return detuning angle value with Direct RF feedback in [rad].
-
+
Fig.4 of ref [1].
"""
return (np.angle(np.mean(self.cav_res.cavity_phasor_record)) -
@@ -1696,7 +1698,7 @@ class DirectFeedback(ProportionalIntegralLoop):
def DFB_alpha(self):
"""
Return the amplitude ratio alpha of the DFB.
-
+
Near Eq. (13) of [1].
"""
fac = np.abs(
@@ -1707,7 +1709,7 @@ class DirectFeedback(ProportionalIntegralLoop):
def DFB_gamma(self):
"""
Return the gain gamma of the DFB.
-
+
Near Eq. (13) of [1].
"""
fac = np.abs(
@@ -1718,7 +1720,7 @@ class DirectFeedback(ProportionalIntegralLoop):
def DFB_Rs(self):
"""
Return the shunt impedance of the DFB in [ohm].
-
+
Eq. (15) of [1].
"""
return self.cav_res.Rs / (1 + self.DFB_gamma * np.cos(self.DFB_psi))
diff --git a/mbtrack2/tracking/spacecharge.py b/mbtrack2/tracking/spacecharge.py
new file mode 100644
index 0000000000000000000000000000000000000000..7eb70f6175baa9a4083c31966d2b71f1f43f662d
--- /dev/null
+++ b/mbtrack2/tracking/spacecharge.py
@@ -0,0 +1,100 @@
+"""
+Module for transverse space charge calculations.
+"""
+from scipy.constants import c
+
+from mbtrack2.tracking.element import Element
+from mbtrack2.tracking.particles_electromagnetic_fields import (
+ _efieldn_mit,
+ get_displaced_efield,
+)
+
+
+class TransverseSpaceCharge(Element):
+ """
+ Class representing a transverse space charge element.
+
+ Parameters
+ ----------
+ ring : Synchrotron
+ The synchrotron object representing the particle accelerator ring.
+ interaction_length : float
+ The interaction length of the space charge effect in meters.
+ n_bins : int, optional
+ The number of bins (longitudinal) used for space charge calculations. Default is 100.
+
+ Attributes
+ ----------
+ ratio_threshold : float
+ The ratio numerical threshold for the space charge element to decide if the beam is transversely round.
+ absolute_threshold : float
+ The absolute numerical threshold for the space charge element to decide if the beam is transversely round.
+ ring: Synchrotron
+ Ring object with information about the ring. This class uses ring.E0 and ring.gamma for calculations.
+ efieldn : function
+ The electric field function.
+
+ Methods
+ -------
+ track(bunch)
+ Perform the tracking of the bunch through the space charge element.
+
+ """
+
+ ratio_threshold = 1e-3
+ absolute_threshold = 1e-10
+
+ def __init__(self, ring, interaction_length, n_bins=100):
+ """
+ Initialize the SpaceCharge object.
+
+ Parameters
+ ----------
+ ring : Synchrotron
+ The synchrotron object representing the particle accelerator ring.
+ interaction_length : float
+ The interaction length of the space charge effect in meters.
+ n_bins : int, optional
+ The number of bins (longitudinal) used for space charge calculations. Default is 100.
+ """
+ self.ring = ring
+ self.n_bins = n_bins
+ self.interaction_length = interaction_length
+ self.efieldn = _efieldn_mit
+
+ @Element.parallel
+ def track(self, bunch):
+ """
+ Perform the tracking of the bunch through the space charge element.
+
+ Parameters
+ ----------
+ bunch : Bunch
+ The bunch of particles to be tracked.
+
+ """
+ prefactor = self.interaction_length / (self.ring.E0 *
+ self.ring.gamma**2)
+ (bins, sorted_index, profile,
+ center) = bunch.binning(n_bin=self.n_bins)
+ dz = (bins[1] - bins[0]) * c
+ charge_density = bunch.charge_per_mp * profile / dz
+ for bin_index in range(self.n_bins - 1):
+ particle_ids = (bin_index == sorted_index)
+ if len(particle_ids) == 0:
+ continue
+ x = bunch['x'][particle_ids]
+ y = bunch['y'][particle_ids]
+
+ mean_x, std_x = x.mean(), x.std()
+ mean_y, std_y = y.mean(), y.std()
+
+ en_x, en_y = get_displaced_efield(self.efieldn,
+ bunch['x'][particle_ids],
+ bunch['y'][particle_ids], std_x,
+ std_y, mean_x, mean_y)
+
+ kicks_x = prefactor * en_x * charge_density[bin_index]
+ kicks_y = prefactor * en_y * charge_density[bin_index]
+ bunch['xp'][particle_ids] += kicks_x
+ bunch['yp'][particle_ids] += kicks_y
diff --git a/mbtrack2/tracking/synchrotron.py b/mbtrack2/tracking/synchrotron.py
index b6e36fa2b06e579028a892c24aad1502ae961f88..15235ecd1b60f38a4984074ab71c87c1fba54a85 100644
--- a/mbtrack2/tracking/synchrotron.py
+++ b/mbtrack2/tracking/synchrotron.py
@@ -11,10 +11,10 @@ from scipy.constants import c, e
class Synchrotron:
"""
Synchrotron class to store main properties.
-
- Optional parameters are optional only if the Optics object passed to the
+
+ Optional parameters are optional only if the Optics object passed to the
class uses a loaded lattice.
-
+
Parameters
----------
h : int
@@ -44,25 +44,25 @@ class Synchrotron:
U0 : float, optional
Energy loss per turn in [eV].
adts : list of arrays or None, optional
- List that contains arrays of polynomial's coefficients, in decreasing
- powers, used to determine Amplitude-Dependent Tune Shifts (ADTS).
+ 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.
- 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
+ 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]).
-
+
Use None, to exclude the ADTS from calculation.
mcf_order : array, optional
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
+ The 1st order should be included in the array and be at the last
position.
-
+
Attributes
----------
T0 : float
@@ -92,8 +92,8 @@ class Synchrotron:
long_gamma : float
Longitudinal gamma Twiss parameter at the tracking location in [s-1].
Initialized at zero.
-
-
+
+
Methods
-------
synchrotron_tune(V)
@@ -104,18 +104,19 @@ class Synchrotron:
Momentum compaction taking into account higher orders if provided in
mcf_order.
mcf(delta)
- Momentum compaction factor taking into account higher orders if
+ Momentum compaction factor taking into account higher orders if
provided in mcf_order.
get_adts()
- Compute and add Amplitude-Dependent Tune Shifts (ADTS) sextupolar
+ Compute and add Amplitude-Dependent Tune Shifts (ADTS) sextupolar
componenet from AT lattice.
get_mcf_order()
Compute momentum compaction factor up to 3rd order from AT lattice.
get_longitudinal_twiss(V)
- Compute the longitudinal Twiss parameters and the synchrotron tune for
+ Compute the longitudinal Twiss parameters and the synchrotron tune for
single or multi-harmonic RF systems.
to_pyat(Vrf)
Return a pyAT simple_ring element from the Synchrotron element data.
+
"""
def __init__(self, h, optics, particle, **kwargs):
@@ -305,13 +306,13 @@ class Synchrotron:
Parameters
----------
position : float or array, optional
- Longitudinal position in [m] where the beam size is computed.
+ Longitudinal position in [m] where the beam size is computed.
If None, the local values are used.
Returns
-------
sigma : array
- RMS beam size in [m] at position location or at local positon if
+ RMS beam size in [m] at position location or at local positon if
position is None.
"""
@@ -352,7 +353,7 @@ class Synchrotron:
def synchrotron_tune(self, V):
"""
Compute the (unperturbed) synchrotron tune from main RF voltage.
-
+
Parameters
----------
V : float
@@ -362,7 +363,7 @@ class Synchrotron:
-------
tuneS : float
Synchrotron tune.
-
+
"""
Vsum = V * np.sin(np.arccos(self.U0 / V))
phi = np.arccos(1 - self.eta(0) * np.pi * self.h / self.E0 * Vsum)
@@ -371,7 +372,7 @@ class Synchrotron:
def get_adts(self):
"""
- Compute and add Amplitude-Dependent Tune Shifts (ADTS) sextupolar
+ Compute and add Amplitude-Dependent Tune Shifts (ADTS) sextupolar
componenet from AT lattice.
"""
import at
@@ -389,7 +390,7 @@ class Synchrotron:
def get_mcf_order(self, add=True, show_fit=False):
"""
Compute momentum compaction factor up to 3rd order from AT lattice.
-
+
Parameters
----------
add : bool, optional
@@ -399,7 +400,7 @@ class Synchrotron:
show_fit : bool, optional
If True, show a plot with the data and fit.
The default is False.
-
+
Return
------
pvalue : array, optional
@@ -439,13 +440,13 @@ class Synchrotron:
def get_longitudinal_twiss(self, V, phase=None, harmonics=None, add=True):
"""
- Compute the longitudinal Twiss parameters and the synchrotron tune for
+ Compute the longitudinal Twiss parameters and the synchrotron tune for
single or multi-harmonic RF systems.
-
+
Hypthesis:
- Use the linear approximation (tau ~ 0).
- For higher haromics only, cos(phi) ~ 0 must be true.
-
+
Parameters
----------
V : float or array-like of float
@@ -457,17 +458,18 @@ class Synchrotron:
Harmonics of the cavities to consider.
Default is None.
add : bool, optional
- If True,
-
+ If True, add the computed longitudinal Twiss parameters as class
+ arguements.
+
Usage
-----
- - If a single voltage value is given, assume a single RF system set at
+ - If a single voltage value is given, assume a single RF system set at
the synchronous phase.
- - If a single pair of voltage/phase value is given, assume a single RF
+ - 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
+ - Otherwise, compute the synchrotron tune for a multi-harmonic RF
system.
-
+
Returns
-------
tuneS : float
@@ -475,7 +477,7 @@ class Synchrotron:
long_alpha : float
Longitudinal alpha Twiss parameter at the tracking location.
long_beta : float
- Longitudinal beta Twiss parameter at the tracking location in [s].
+ Longitudinal beta Twiss parameter at the tracking location in [s].
long_gamma : float
Longitudinal gamma Twiss parameter at the tracking location in [s-1].
"""
@@ -513,7 +515,7 @@ class Synchrotron:
def to_pyat(self, Vrf, harmonic_number=None, TimeLag=False):
"""
Return a pyAT simple_ring element from the Synchrotron element data.
-
+
See pyAT documentation for informations about simple_ring.
Parameters
@@ -524,7 +526,7 @@ class Synchrotron:
harmonic_number : float or array-like of float, optional
Harmonic numbers of the RF cavities. The default is None.
TimeLag : float or array-like of float, optional
- Set the timelag of the cavities in pyAT definition.
+ Set the timelag of the cavities in pyAT definition.
The default is False.
Returns
diff --git a/mbtrack2/utilities/beamloading.py b/mbtrack2/utilities/beamloading.py
index 19e51e98749451baad6eb72e195f1a44d9995d4b..5e1de2691744db6cca761dba4e383259b678562f 100644
--- a/mbtrack2/utilities/beamloading.py
+++ b/mbtrack2/utilities/beamloading.py
@@ -6,18 +6,17 @@ Module where the BeamLoadingEquilibrium class is defined.
import matplotlib.pyplot as plt
import numpy as np
from scipy.constants import c
-from scipy.integrate import quad
+from scipy.fft import rfft, rfftfreq
+from scipy.integrate import trapz
from scipy.optimize import root
+from mbtrack2.utilities.spectrum import gaussian_bunch
-class BeamLoadingEquilibrium():
- """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].
- [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.
+class BeamLoadingEquilibrium():
+ """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 [1] which is an extension of [2].
Parameters
----------
@@ -30,6 +29,19 @@ class BeamLoadingEquilibrium():
PHI : list of form factor phase
B1 : lower intergration boundary
B2 : upper intergration boundary
+ N : int or float, optinal
+ Number of points used for longitudinal grid.
+ Default is 1000.
+
+ References
+ ----------
+ [1] Gamelin, A., & Yamamoto, N. (2021). Equilibrium bunch density
+ distribution with multiple active and passive RF cavities.
+ IPAC'21 (MOPAB069).
+ [2] 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.
+
"""
def __init__(self,
@@ -40,7 +52,8 @@ class BeamLoadingEquilibrium():
F=None,
PHI=None,
B1=-0.2,
- B2=0.2):
+ B2=0.2,
+ N=1000):
self.ring = ring
self.cavity_list = cavity_list
self.I0 = I0
@@ -57,7 +70,12 @@ class BeamLoadingEquilibrium():
self.B1 = B1
self.B2 = B2
self.mpi = False
- self.__version__ = "1.0"
+ self.N = N
+ self.z0 = np.linspace(self.B1, self.B2, self.N)
+ self.tau0 = self.z0 / c
+ self.rho0 = gaussian_bunch(self.tau0, self.ring.sigma_0) / c
+ self.sampling = self.tau0[1] - self.tau0[0]
+ self.freq0 = rfftfreq(self.N, self.sampling)
# Define constants for scaled potential u(z)
self.u0 = self.ring.U0 / (self.ring.ac * self.ring.sigma_delta**2 *
@@ -66,6 +84,11 @@ class BeamLoadingEquilibrium():
self.ub = np.zeros((self.n_cavity, ))
self.update_potentials()
+ def update_rho(self):
+ uexp_vals = self.uexp(self.z0)
+ A = trapz(uexp_vals, x=self.z0)
+ self.rho0 = uexp_vals / A
+
def update_potentials(self):
"""Update potentials with cavity and ring data."""
for i in range(self.n_cavity):
@@ -90,9 +113,7 @@ class BeamLoadingEquilibrium():
def center_of_mass(self):
"""Return center of mass position in [s]"""
- z0 = np.linspace(self.B1, self.B2, 1000)
- rho = self.rho(z0)
- CM = np.average(z0, weights=rho)
+ CM = np.average(self.z0, weights=self.rho0)
return CM / c
def u(self, z):
@@ -125,15 +146,15 @@ class BeamLoadingEquilibrium():
def integrate_func(self, f, g):
"""Return Integral[f*g]/Integral[f] between B1 and B2"""
- A = quad(lambda x: f(x) * g(x), self.B1, self.B2)
- B = quad(f, self.B1, self.B2)
- return A[0] / B[0]
+ A = trapz(f * g, x=self.z0)
+ B = trapz(f, x=self.z0)
+ return A / B
def to_solve(self, x, CM=True):
"""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
+ 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.
@@ -150,6 +171,7 @@ class BeamLoadingEquilibrium():
else:
self.F = x[::2]
self.PHI = x[1::2]
+ self.update_rho()
# Compute system
if self.auto_set_MC_theta:
@@ -158,12 +180,12 @@ class BeamLoadingEquilibrium():
cavity = self.cavity_list[i]
res[2 *
i] = self.F[i] * np.cos(self.PHI[i]) - self.integrate_func(
- lambda y: self.uexp(y),
- lambda y: np.cos(self.ring.k1 * cavity.m * y))
+ self.uexp(self.z0),
+ np.cos(self.ring.k1 * cavity.m * self.z0))
res[2*i +
1] = self.F[i] * np.sin(self.PHI[i]) - self.integrate_func(
- lambda y: self.uexp(y),
- lambda y: np.sin(self.ring.k1 * cavity.m * y))
+ self.uexp(self.z0),
+ np.sin(self.ring.k1 * cavity.m * self.z0))
# Factor 1e-8 or 1e12 for better convergence
if CM is True:
res[self.n_cavity * 2] = self.center_of_mass() * 1e12
@@ -175,27 +197,17 @@ class BeamLoadingEquilibrium():
cavity = self.cavity_list[i]
res[2 *
i] = self.F[i] * np.cos(self.PHI[i]) - self.integrate_func(
- lambda y: self.uexp(y),
- lambda y: np.cos(self.ring.k1 * cavity.m * y))
+ self.uexp(self.z0),
+ np.cos(self.ring.k1 * cavity.m * self.z0))
res[2*i +
1] = self.F[i] * np.sin(self.PHI[i]) - self.integrate_func(
- lambda y: self.uexp(y),
- lambda y: np.sin(self.ring.k1 * cavity.m * y))
+ self.uexp(self.z0),
+ np.sin(self.ring.k1 * cavity.m * self.z0))
return res
- def rho(self, z):
- """Return bunch equilibrium profile at postion z"""
- A = quad(lambda y: self.uexp(y), self.B1, self.B2)
- return self.uexp(z) / A[0]
-
- def plot_rho(self, z1=None, z2=None):
- """Plot the bunch equilibrium profile between z1 and z2"""
- if z1 is None:
- z1 = self.B1
- if z2 is None:
- z2 = self.B2
- z0 = np.linspace(z1, z2, 1000)
- plt.plot(z0 / c * 1e12, self.rho(z0))
+ def plot_rho(self):
+ """Plot the bunch equilibrium profile"""
+ plt.plot(self.tau0 * 1e12, self.rho0)
plt.xlabel(r"$\tau$ [ps]")
plt.title("Equilibrium bunch profile")
@@ -231,38 +243,22 @@ class BeamLoadingEquilibrium():
Vtot += cavity.deltaVRF(z, self.I0, self.F[i], self.PHI[i])
return Vtot
- def plot_dV(self, z1=None, z2=None):
- """Plot the derivative of RF system total voltage between z1 and z2"""
- if z1 is None:
- z1 = self.B1
- if z2 is None:
- z2 = self.B2
- z0 = np.linspace(z1, z2, 1000)
- plt.plot(z0, self.dV(z0))
+ def plot_dV(self):
+ """Plot the derivative of RF system total voltage"""
+ plt.plot(self.z0, self.dV(self.z0))
plt.xlabel("z [m]")
plt.ylabel("Total RF voltage (V)")
- def plot_voltage(self, z1=None, z2=None):
+ def plot_voltage(self):
"""Plot the RF system total voltage between z1 and z2"""
- if z1 is None:
- z1 = self.B1
- if z2 is None:
- z2 = self.B2
- z0 = np.linspace(z1, z2, 1000)
- plt.plot(z0, self.voltage(z0))
+ plt.plot(self.z0, self.voltage(self.z0))
plt.xlabel("z [m]")
plt.ylabel("Total RF voltage (V)")
- def std_rho(self, z1=None, z2=None):
+ def std_rho(self):
"""Return the rms bunch equilibrium size in [m]"""
- if z1 is None:
- z1 = self.B1
- if z2 is None:
- z2 = self.B2
- z0 = np.linspace(z1, z2, 1000)
- values = self.rho(z0)
- average = np.average(z0, weights=values)
- variance = np.average((z0 - average)**2, weights=values)
+ average = np.average(self.z0, weights=self.rho0)
+ variance = np.average((self.z0 - average)**2, weights=self.rho0)
return np.sqrt(variance)
def beam_equilibrium(self,
@@ -276,7 +272,7 @@ class BeamLoadingEquilibrium():
"""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.
-
+
Parameters
----------
x0 : initial guess
@@ -287,7 +283,7 @@ class BeamLoadingEquilibrium():
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.
-
+
Returns
-------
sol : OptimizeResult object representing the solution
@@ -333,19 +329,19 @@ class BeamLoadingEquilibrium():
print("The algorithm has converged: " + str(sol.success))
if plot:
- self.plot_rho(self.B1 / 4, self.B2 / 4)
+ self.plot_rho()
return sol
def PTBL_threshold(self, I0, m=None, MC_index=0, HC_index=1):
"""
- Compute the periodic transient beam loading (PTBL) instability
+ Compute the periodic transient beam loading (PTBL) instability
threshold based on [1].
-
- The beam_equilibrium method should be called before the PTBL_threshold
+
+ The beam_equilibrium method should be called before the PTBL_threshold
one.
-
- Eq. (22) and (23) have been modified for cosine voltage convention
+
+ Eq. (22) and (23) have been modified for cosine voltage convention
for the main cavity.
Parameters
@@ -353,7 +349,7 @@ class BeamLoadingEquilibrium():
I0 : float
Beam total current in [A].
m : int, optional
- Number of bunches in the beam.
+ Number of bunches in the beam.
The default is None. If None, uniform filling is assumed.
MC_index : int, optional
Index of the main cavity in cavity_list. The default is 0.
@@ -363,18 +359,18 @@ class BeamLoadingEquilibrium():
Returns
-------
eta : float
- Amplification factor, if bigger than 1 then the beam is possibly
+ Amplification factor, if bigger than 1 then the beam is possibly
in the PTBL regime, Eq. (22) of [1].
RQth : float
R/Q threshold, Eq. (24) of [1].
f : float
f function, Eq. (23) of [1].
-
+
Reference
---------
- [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),
+ [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.
"""
@@ -404,3 +400,32 @@ class BeamLoadingEquilibrium():
(2 * np.pi * HC.m**2 * self.F[1] * self.ring.h * I0 * f))
return (eta, RQth, f)
+
+ @property
+ def R_factor(self):
+ """
+ Touschek lifetime ratio as defined in [1].
+
+ Reference
+ ---------
+ [1] : Byrd, J. M., and M. Georgsson. "Lifetime increase using passive
+ harmonic cavities in synchrotron light sources." Physical Review
+ Special Topics-Accelerators and Beams 4.3 (2001): 030701.
+
+ """
+ rho0 = gaussian_bunch(self.tau0, self.ring.sigma_0) / c
+ R = trapz(rho0**2, self.tau0) / trapz(self.rho0**2, self.tau0)
+ return R
+
+ @property
+ def bunch_spectrum(self):
+ """Return the bunch equilibrium spectrum."""
+ dft_rho = rfft(self.rho0) * self.sampling / self.N
+ return np.abs(dft_rho) / np.max(np.abs(dft_rho))
+
+ def plot_bunch_spectrum(self):
+ """Plot the bunch equilibrium spectrum"""
+ plt.plot(self.freq0 * 1e-9, self.bunch_spectrum)
+ plt.xlabel(r"Frequency [GHz]")
+ plt.xlim([0, self.freq0.max() * 1e-9 / 3])
+ plt.title("Equilibrium bunch spectrum")
diff --git a/mbtrack2/utilities/misc.py b/mbtrack2/utilities/misc.py
index c31af03d547338323c8ca1d98e886eefd02fe853..f884b17f205bb24d61a16c7ab3ed630f44386aa7 100644
--- a/mbtrack2/utilities/misc.py
+++ b/mbtrack2/utilities/misc.py
@@ -8,6 +8,7 @@ from pathlib import Path
import numpy as np
import pandas as pd
from scipy.interpolate import interp1d
+from scipy.special import factorial, gamma, hyp2f1
from mbtrack2.impedance.wakefield import Impedance
from mbtrack2.utilities.spectrum import spectral_density
@@ -168,7 +169,6 @@ def tune_shift_from_effective_impedance(Zeff):
def yokoya_elliptic(x_radius, y_radius):
"""
Compute Yokoya factors for an elliptic beam pipe.
- Function adapted from N. Mounet IW2D.
Parameters
----------
@@ -189,37 +189,169 @@ def yokoya_elliptic(x_radius, y_radius):
Yokoya factor for the quadrupolar horizontal impedance.
yokyquad : float
Yokoya factor for the quadrupolar vertical impedance.
+
+ References
+ ----------
+ [1] : M. Migliorati, L. Palumbo, C. Zannini, N. Biancacci, and
+ V. G. Vaccaro, "Resistive wall impedance in elliptical multilayer vacuum
+ chambers." Phys. Rev. Accel. Beams 22, 121001 (2019).
+ [2] : R.L. Gluckstern, J. van Zeijts, and B. Zotter, "Coupling impedance
+ of beam pipes of general cross section." Phys. Rev. E 47, 656 (1993).
+
"""
- if y_radius < x_radius:
- small_semiaxis = y_radius
- large_semiaxis = x_radius
- else:
- small_semiaxis = x_radius
- large_semiaxis = y_radius
-
- path_to_file = Path(__file__).parent
- file = path_to_file / "data" / "Yokoya_elliptic_from_Elias_USPAS.csv"
-
- # read Yokoya factors interpolation file
- # BEWARE: columns are ratio, dipy, dipx, quady, quadx
- yokoya_file = pd.read_csv(file)
- ratio_col = yokoya_file["x"]
- # compute semi-axes ratio (first column of this file)
- ratio = (large_semiaxis-small_semiaxis) / (large_semiaxis+small_semiaxis)
-
- # interpolate Yokoya file at the correct ratio
- yoklong = 1
-
- if y_radius < x_radius:
- yokydip = np.interp(ratio, ratio_col, yokoya_file["dipy"])
- yokxdip = np.interp(ratio, ratio_col, yokoya_file["dipx"])
- yokyquad = np.interp(ratio, ratio_col, yokoya_file["quady"])
- yokxquad = np.interp(ratio, ratio_col, yokoya_file["quadx"])
+
+ if (x_radius <= 0) or (y_radius <= 0):
+ raise ValueError("Both radii must be non-zero positive values.")
+ elif (x_radius == np.inf) and (y_radius == np.inf):
+ raise ValueError("Both radii have infinite values.")
+ elif x_radius == np.inf:
+ yoklong = 1.0
+ yokxdip = np.pi**2 / 24
+ yokydip = np.pi**2 / 12
+ yokxquad = -np.pi**2 / 24
+ yokyquad = np.pi**2 / 24
+ elif y_radius == np.inf:
+ yoklong = 1.0
+ yokxdip = np.pi**2 / 12
+ yokydip = np.pi**2 / 24
+ yokxquad = np.pi**2 / 24
+ yokyquad = -np.pi**2 / 24
else:
- yokxdip = np.interp(ratio, ratio_col, yokoya_file["dipy"])
- yokydip = np.interp(ratio, ratio_col, yokoya_file["dipx"])
- yokxquad = np.interp(ratio, ratio_col, yokoya_file["quady"])
- yokyquad = np.interp(ratio, ratio_col, yokoya_file["quadx"])
+ if y_radius < x_radius:
+ small_semiaxis = y_radius
+ large_semiaxis = x_radius
+ else:
+ small_semiaxis = x_radius
+ large_semiaxis = y_radius
+
+ qr = (large_semiaxis-small_semiaxis) / (large_semiaxis+small_semiaxis)
+
+ if qr == 0:
+ yoklong = 1.0
+ yokxdip = 1.0
+ yokydip = 1.0
+ yokxquad = 0.0
+ yokyquad = 0.0
+
+ else:
+ # Define form factor functions
+ def function_ff(small_semiaxis, F, mu_b, ip, il):
+ coeff_fflong = 2 * np.sqrt(2) * small_semiaxis / (np.pi * F)
+ coeff_fftrans = np.sqrt(2) * small_semiaxis**3 / (np.pi * F**3)
+
+ fflong = (coeff_fflong * (-1)**ip / np.cosh(2 * ip * mu_b) *
+ (-1)**il / np.cosh(2 * il * mu_b))
+ ffdx = (coeff_fftrans * (-1)**ip * (2*ip + 1) / np.cosh(
+ (2*ip + 1) * mu_b) * (-1)**il * (2*il + 1) / np.cosh(
+ (2*il + 1) * mu_b))
+ ffdy = (coeff_fftrans * (-1)**ip * (2*ip + 1) / np.sinh(
+ (2*ip + 1) * mu_b) * (-1)**il * (2*il + 1) / np.sinh(
+ (2*il + 1) * mu_b))
+ ffquad = (coeff_fftrans * (-1)**ip * (2 * ip)**2 /
+ np.cosh(2 * ip * mu_b) * (-1)**il /
+ np.cosh(2 * il * mu_b))
+
+ return (fflong, ffdx, ffdy, ffquad)
+
+ def function_L(mu_b, ip, il):
+ common_L = (np.sqrt(2) * np.pi *
+ np.exp(-(2 * abs(ip - il) + 1) * mu_b) *
+ gamma(0.5 + abs(ip - il)) /
+ (gamma(0.5) * factorial(abs(ip - il))) *
+ hyp2f1(0.5,
+ abs(ip - il) + 0.5,
+ abs(ip - il) + 1, np.exp(-4 * mu_b)))
+ val_m = (
+ np.sqrt(2) * np.pi * np.exp(-(2*ip + 2*il + 1) * mu_b) *
+ gamma(0.5 + ip + il) / (gamma(0.5) * factorial(ip + il)) *
+ hyp2f1(0.5, ip + il + 0.5, ip + il + 1, np.exp(-4 * mu_b)))
+ val_d = (
+ np.sqrt(2) * np.pi * np.exp(-(2*ip + 2*il + 3) * mu_b) *
+ gamma(1.5 + ip + il) /
+ (gamma(0.5) * factorial(ip + il + 1)) *
+ hyp2f1(0.5, ip + il + 1.5, ip + il + 2, np.exp(-4 * mu_b)))
+
+ Lm = common_L + val_m
+ Ldx = common_L + val_d
+ Ldy = common_L - val_d
+
+ return (Lm, Ldx, Ldy)
+
+ ip_range = np.arange(51)
+ il_range = np.arange(51)
+ ip, il = np.meshgrid(ip_range, il_range, indexing="ij")
+
+ coeff_long = np.where((ip == 0) & (il == 0), 0.25,
+ np.where((ip == 0) | (il == 0), 0.5, 1.0))
+ coeff_quad = np.where(il == 0, 0.5, 1.0)
+
+ # Our equations are approximately valid only for qr (ratio) values
+ # less than or equal to 0.8.
+ qr_th = 0.8
+
+ if qr < qr_th:
+ F = np.sqrt(large_semiaxis**2 - small_semiaxis**2)
+ mu_b = np.arccosh(large_semiaxis / F)
+
+ ff_values = np.array(
+ function_ff(small_semiaxis, F, mu_b, ip, il))
+ L_values = np.array(function_L(mu_b, ip, il))
+
+ yoklong = np.sum(coeff_long * ff_values[0] * L_values[0])
+ yokxdip = np.sum(ff_values[1] * L_values[1])
+ yokydip = np.sum(ff_values[2] * L_values[2])
+ yokxquad = -np.sum(coeff_quad * ff_values[3] * L_values[0])
+ yokyquad = -yokxquad
+
+ if y_radius > x_radius:
+ yokxdip, yokydip = yokydip, yokxdip
+ yokxquad, yokyquad = yokyquad, yokxquad
+
+ # Beyond the threshold (qr >= qr_th), they may not be valid,
+ # but should converge to Yokoya form factors of parallel plates.
+ # Fortunately, beyond this threshold, they should show asymptotic behavior,
+ # so we perform linear interpolation.
+ else:
+ yoklong_pp = 1.0
+ yokxdip_pp = np.pi**2 / 24
+ yokydip_pp = np.pi**2 / 12
+ yokxquad_pp = -np.pi**2 / 24
+ yokyquad_pp = np.pi**2 / 24
+
+ small_semiaxis_th = large_semiaxis * (1-qr_th) / (1+qr_th)
+ F_th = np.sqrt(large_semiaxis**2 - small_semiaxis_th**2)
+ mu_b_th = np.arccosh(large_semiaxis / F_th)
+
+ ff_values_th = np.array(
+ function_ff(small_semiaxis_th, F_th, mu_b_th, ip, il))
+ L_values_th = np.array(function_L(mu_b_th, ip, il))
+
+ yoklong_th = np.sum(coeff_long * ff_values_th[0] *
+ L_values_th[0])
+ yokxdip_th = np.sum(ff_values_th[1] * L_values_th[1])
+ yokydip_th = np.sum(ff_values_th[2] * L_values_th[2])
+ yokxquad_th = -np.sum(
+ coeff_quad * ff_values_th[3] * L_values_th[0])
+ yokyquad_th = -yokxquad_th
+
+ if y_radius > x_radius:
+ yokxdip_th, yokydip_th = yokydip_th, yokxdip_th
+ yokxquad_th, yokyquad_th = yokyquad_th, yokxquad_th
+ yokxdip_pp, yokydip_pp = yokydip_pp, yokxdip_pp
+ yokxquad_pp, yokyquad_pp = yokyquad_pp, yokxquad_pp
+
+ qr_array = np.array([qr_th, 1.0])
+ yoklong_array = np.array([yoklong_th, yoklong_pp])
+ yokxdip_array = np.array([yokxdip_th, yokxdip_pp])
+ yokydip_array = np.array([yokydip_th, yokydip_pp])
+ yokxquad_array = np.array([yokxquad_th, yokxquad_pp])
+ yokyquad_array = np.array([yokyquad_th, yokyquad_pp])
+
+ yoklong = np.interp(qr, qr_array, yoklong_array)
+ yokxdip = np.interp(qr, qr_array, yokxdip_array)
+ yokydip = np.interp(qr, qr_array, yokydip_array)
+ yokxquad = np.interp(qr, qr_array, yokxquad_array)
+ yokyquad = np.interp(qr, qr_array, yokyquad_array)
return (yoklong, yokxdip, yokydip, yokxquad, yokyquad)
diff --git a/mbtrack2/utilities/optics.py b/mbtrack2/utilities/optics.py
index 3c7ff926d21c268e6d9187a82db7e39304302965..4e2f58bf3ec2624b7a796c2790a11ce507535154 100644
--- a/mbtrack2/utilities/optics.py
+++ b/mbtrack2/utilities/optics.py
@@ -119,9 +119,10 @@ class Optics:
self.periodicity = periodicity
if self.periodicity > 1:
- for i in range(self.periodicity - 1):
- pos = np.append(twiss.s_pos,
- twiss.s_pos + twiss.s_pos[-1] * (i+1))
+ periods = np.arange(0, self.periodicity)
+ shift = periods * twiss.s_pos[-1]
+ shift = np.repeat(shift, len(twiss.s_pos))
+ pos = np.tile(twiss.s_pos.T, self.periodicity) + shift
else:
pos = twiss.s_pos
diff --git a/pyproject.toml b/pyproject.toml
index 9d1b011a64e8ad3b256552747640c25461654733..5e2b88465bd69d95670f721ee64a30dbef2df0ec 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -1,6 +1,6 @@
[tool.poetry]
name = "mbtrack2"
-version = "0.6.0"
+version = "0.7.0"
description = "A coherent object-oriented framework to work on collective effects in synchrotrons."
authors = ["Alexis Gamelin <alexis.gamelin@synchrotron-soleil.fr>"]
license = "BSD-3-Clause"
@@ -31,7 +31,8 @@ build-backend = "poetry.core.masonry.api"
[tool.yapf]
based_on_style = "pep8"
arithmetic_precedence_indication = true
+blank_line_before_nested_class_or_def = true
[tool.isort]
multi_line_output = 3
-include_trailing_comma = true
\ No newline at end of file
+include_trailing_comma = true
diff --git a/readthedocs.yaml b/readthedocs.yaml
new file mode 100644
index 0000000000000000000000000000000000000000..952007cf21cf344c6712b15b85cdcd76b3ca80c4
--- /dev/null
+++ b/readthedocs.yaml
@@ -0,0 +1,17 @@
+version: 2
+
+build:
+ os: "ubuntu-22.04"
+ tools:
+ python: "3.9"
+
+python:
+ install:
+ - requirements: docs/requirements.txt
+
+sphinx:
+ configuration: docs/source/conf.py
+
+formats:
+ - pdf
+ - epub
\ No newline at end of file
diff --git a/tests/test_bunch.py b/tests/test_bunch.py
index 7c1499a6af032b73f44a5f375cfb669f6c3861ce..25189d3499db3dd97bf2505a31cfc5dd1448df6c 100644
--- a/tests/test_bunch.py
+++ b/tests/test_bunch.py
@@ -8,9 +8,9 @@ from mbtrack2 import Bunch
def test_bunch_values(demo_ring):
mp_number = 10
current = 20e-3
- mybunch = Bunch(demo_ring, mp_number=mp_number, current=current,
+ mybunch = Bunch(demo_ring, mp_number=mp_number, current=current,
track_alive=True)
-
+
assert mybunch.mp_number == mp_number
assert pytest.approx(mybunch.current) == current
assert len(mybunch) == mp_number
@@ -19,35 +19,35 @@ def test_bunch_values(demo_ring):
assert pytest.approx(mybunch.charge_per_mp) == current * demo_ring.T0 / mp_number
assert pytest.approx(mybunch.particle_number) == current * demo_ring.T0 / e
assert mybunch.is_empty == False
-
+
def test_bunch_magic(mybunch):
for label in mybunch:
np.testing.assert_allclose(mybunch[label], np.zeros(len(mybunch)))
mybunch[label] = np.ones(len(mybunch))
np.testing.assert_allclose(mybunch[label], np.ones(len(mybunch)))
-
+
def test_bunch_losses(mybunch):
charge_init = mybunch.charge
mybunch.alive[0] = False
assert len(mybunch) == mybunch.mp_number - 1
assert pytest.approx(mybunch.charge) == charge_init * len(mybunch) / mybunch.mp_number
-
+
def test_bunch_init_gauss(large_bunch):
large_bunch.init_gaussian(mean=np.ones((6,)))
np.testing.assert_allclose(large_bunch.mean, np.ones((6,)), rtol=1e-2)
-
+
def test_bunch_save_load(mybunch, demo_ring, tmp_path):
mybunch["x"] += 1
mybunch.save(str(tmp_path / "test"))
-
+
mybunch2 = Bunch(demo_ring, mp_number=1, current=1e-5)
mybunch2.load(str(tmp_path / "test.hdf5"))
-
+
assert mybunch.mp_number == mybunch2.mp_number
assert pytest.approx(mybunch.charge) == mybunch2.charge
for label in mybunch:
np.testing.assert_allclose(mybunch[label], mybunch2[label])
-
+
def test_bunch_stats(demo_ring, large_bunch):
large_bunch.init_gaussian()
np.testing.assert_array_almost_equal(large_bunch.mean, np.zeros((6,)), decimal=5)
@@ -55,7 +55,7 @@ def test_bunch_stats(demo_ring, large_bunch):
np.testing.assert_allclose(large_bunch.std, sig, rtol=1e-2)
np.testing.assert_allclose(large_bunch.emit[:2], demo_ring.emit, rtol=1e-2)
np.testing.assert_allclose(large_bunch.cs_invariant[:2], demo_ring.emit*2, rtol=1e-2)
-
+
def test_bunch_binning(mybunch):
mybunch.init_gaussian()
(bins, sorted_index, profile, center) = mybunch.binning()
@@ -64,10 +64,42 @@ def test_bunch_binning(mybunch):
assert bins[val] <= mybunch["tau"][i] <= bins[val+1]
profile0[val] += 1
np.testing.assert_allclose(profile0, profile)
-
+
def test_bunch_plots(mybunch):
mybunch.init_gaussian()
mybunch.plot_phasespace()
mybunch.plot_profile()
assert True
-
\ No newline at end of file
+def test_bunch_emittance(demo_ring):
+ mp_number = 1_000_000
+ current = 1.2e-3
+ mybunch = Bunch(demo_ring, mp_number=mp_number, current=current,
+ track_alive=False)
+ mybunch.init_gaussian()
+ np.testing.assert_allclose(mybunch.emit[0], demo_ring.emit[0], rtol=1e-2, atol=0,
+ err_msg=f'Emittances do not match. {demo_ring.emit[0]} initialised, {mybunch.emit[0]:} calculated')
+ np.testing.assert_allclose(mybunch.emit[1], demo_ring.emit[1], rtol=1e-2, atol=0,
+ err_msg=f'Emittances do not match. {demo_ring.emit[1]} initialised, {mybunch.emit[1]:} calculated')
+
+ np.testing.assert_allclose(mybunch.emit[0], mybunch.cs_invariant[0]/2, rtol=1e-2, atol=0,
+ err_msg=f'Emittances do not match. {mybunch.cs_invariant[0]/2} calculated with optics functions, {mybunch.emit[0]:} calculated with coordinates only')
+ np.testing.assert_allclose(mybunch.emit[1], mybunch.cs_invariant[1]/2, rtol=1e-2, atol=0,
+ err_msg=f'Emittances do not match. {mybunch.cs_invariant[1]/2} calculated with optics functions, {mybunch.emit[1]:} calculated with coordinates only')
+
+
+def test_bunch_emittance_with_dispersion(demo_ring):
+ mp_number = 1_000_000
+ current = 1.2e-3
+ demo_ring.optics.local_dispersion = np.array([1e-2, 1e-3, 1e-2, 1e-3])
+ mybunch = Bunch(demo_ring, mp_number=mp_number, current=current,
+ track_alive=False)
+ mybunch.init_gaussian()
+ np.testing.assert_allclose(mybunch.emit[0], demo_ring.emit[0], rtol=1e-2, atol=0,
+ err_msg=f'Emittances do not match. {demo_ring.emit[0]} initialised, {mybunch.emit[0]:} calculated')
+ np.testing.assert_allclose(mybunch.emit[1], demo_ring.emit[1], rtol=1e-2, atol=0,
+ err_msg=f'Emittances do not match. {demo_ring.emit[1]} initialised, {mybunch.emit[1]:} calculated')
+
+ np.testing.assert_allclose(mybunch.emit[0], mybunch.cs_invariant[0]/2, rtol=1e-2, atol=0,
+ err_msg=f'Emittances do not match. {mybunch.cs_invariant[0]/2} calculated with optics functions, {mybunch.emit[0]:} calculated with coordinates only')
+ np.testing.assert_allclose(mybunch.emit[1], mybunch.cs_invariant[1]/2, rtol=1e-2, atol=0,
+ err_msg=f'Emittances do not match. {mybunch.cs_invariant[1]/2} calculated with optics functions, {mybunch.emit[1]:} calculated with coordinates only')