From db11aea5d8ecf620d9ad0d814d436587268fe6a9 Mon Sep 17 00:00:00 2001
From: Gamelin Alexis <alexis.gamelin@synchrotron-soleil.fr>
Date: Wed, 6 Jul 2022 15:32:57 +0200
Subject: [PATCH] Add notebook on RF cavities

Add a new example notebook on RF cavities and longitudinal beam dynamics which explain the RFCavity, CavityResonator and BeamLoadingEquilibrium classes.
---
 examples/mbtrack2_cavity_resonator.ipynb | 1570 ++++++++++++++++++++++
 1 file changed, 1570 insertions(+)
 create mode 100644 examples/mbtrack2_cavity_resonator.ipynb

diff --git a/examples/mbtrack2_cavity_resonator.ipynb b/examples/mbtrack2_cavity_resonator.ipynb
new file mode 100644
index 0000000..e052168
--- /dev/null
+++ b/examples/mbtrack2_cavity_resonator.ipynb
@@ -0,0 +1,1570 @@
+{
+  "nbformat": 4,
+  "nbformat_minor": 0,
+  "metadata": {
+    "colab": {
+      "name": "mbtrack2_cavity_resonator.ipynb",
+      "provenance": [],
+      "collapsed_sections": [],
+      "toc_visible": true
+    },
+    "kernelspec": {
+      "name": "python3",
+      "display_name": "Python 3"
+    },
+    "language_info": {
+      "name": "python"
+    }
+  },
+  "cells": [
+    {
+      "cell_type": "markdown",
+      "source": [
+        "# Introduction\n",
+        "\n",
+        "This notebook introduces different classes for **mbtrack2** dealing with RF cavities and longitudinal beam dynamics:\n",
+        "\n",
+        "* The `RFCavity` class is a very simple class using in tracking to model RF cavities using a perfect cosine wave.\n",
+        "\n",
+        "* The `CavityResonator` class is the main class which can be used to model RF cavities self-consistenly considering beam loading. It can be used in tracking to model:\n",
+        "\n",
+        "  *   Active RF cavity\n",
+        "  *   Passive RF cavity\n",
+        "  *   Cavity HOM\n",
+        "\n",
+        "  The cavity physics is based on the phasor formalism developped in [1], details of the implementation and benchmark can be found in [2,3].\n",
+        "\n",
+        "* The `BeamLoadingEquilibrium` is used to compute analytically the 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.\n",
+        "\n",
+        "  The implementation is based on an extention of [4] which is detailed in [3].\n",
+        "\n",
+        "## Convention\n",
+        "mbtrack2 uses the cosine convention for RF voltage.\n",
+        "\n",
+        "## References\n",
+        "\n",
+        "[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.\n",
+        "\n",
+        "[2] 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.\n",
+        "\n",
+        "[3] Gamelin, Alexis, and Naoto Yamamoto. \"Equilibrium Bunch Density Distribution with Multiple Active and Passive RF Cavities.\" 12th International Particle Accelerator Conference. 2021.\n",
+        "\n",
+        "[4] 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.\n",
+        "\n"
+      ],
+      "metadata": {
+        "id": "IKih_9pcq9Ui"
+      }
+    },
+    {
+      "cell_type": "markdown",
+      "source": [
+        "# Initialization"
+      ],
+      "metadata": {
+        "id": "MvPLW4R_Td8L"
+      }
+    },
+    {
+      "cell_type": "markdown",
+      "source": [
+        "## mbtrack2 set-up"
+      ],
+      "metadata": {
+        "id": "O5fColz-q2EI"
+      }
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 1,
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "id": "BKGTZA_EvtF6",
+        "outputId": "46212648-9f92-4a45-a4c0-5c14fdaa74f8"
+      },
+      "outputs": [
+        {
+          "output_type": "stream",
+          "name": "stdout",
+          "text": [
+            "Cloning into 'mbtrack2'...\n",
+            "remote: Enumerating objects: 1249, done.\u001b[K\n",
+            "remote: Counting objects: 100% (224/224), done.\u001b[K\n",
+            "remote: Compressing objects: 100% (110/110), done.\u001b[K\n",
+            "remote: Total 1249 (delta 127), reused 205 (delta 111), pack-reused 1025\u001b[K\n",
+            "Receiving objects: 100% (1249/1249), 502.01 KiB | 1.45 MiB/s, done.\n",
+            "Resolving deltas: 100% (831/831), done.\n"
+          ]
+        }
+      ],
+      "source": [
+        "! git clone https://gitlab.synchrotron-soleil.fr/PA/collective-effects/mbtrack2.git"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "%cd mbtrack2"
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "id": "aIwNdoXlVDus",
+        "outputId": "6b55f033-48b0-42d0-cf23-f50534902dac"
+      },
+      "execution_count": 2,
+      "outputs": [
+        {
+          "output_type": "stream",
+          "name": "stdout",
+          "text": [
+            "/content/mbtrack2\n"
+          ]
+        }
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "source": [
+        "## Define a Synchrotron object"
+      ],
+      "metadata": {
+        "id": "-CHO7pYlsa76"
+      }
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "import numpy as np\n",
+        "from mbtrack2.tracking import Synchrotron, Electron\n",
+        "from mbtrack2.utilities import Optics"
+      ],
+      "metadata": {
+        "id": "ewMLyHDOslSD"
+      },
+      "execution_count": 3,
+      "outputs": []
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "h = 20 # Harmonic number of the accelerator.\n",
+        "L = 100 # Ring circumference in [m].\n",
+        "E0 = 1.5e9 # Nominal (total) energy of the ring in [eV].\n",
+        "particle = Electron() # Particle considered.\n",
+        "ac = 1e-3 # Momentum compaction factor.\n",
+        "U0 = 200e3 # Energy loss per turn in [eV].\n",
+        "tau = np.array([1e-3, 1e-3, 2e-3]) # Horizontal, vertical and longitudinal damping times in [s].\n",
+        "tune = np.array([12.2, 15.3]) # Horizontal and vertical tunes.\n",
+        "emit = np.array([10e-9, 10e-12]) # Horizontal and vertical equilibrium emittance in [m.rad].\n",
+        "sigma_0 = 15e-12 # Natural bunch length in [s].\n",
+        "sigma_delta = 1e-3 # Equilibrium energy spread.\n",
+        "chro = [2.0, 3.0] # Horizontal and vertical (non-normalized) chromaticities."
+      ],
+      "metadata": {
+        "id": "GH7V8wmmxH4i"
+      },
+      "execution_count": 4,
+      "outputs": []
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "local_beta = np.array([3, 2]) # Beta function at the tracking location.\n",
+        "local_alpha = np.array([0, 0]) # Alpha function at the tracking location.\n",
+        "local_dispersion = np.array([0, 0, 0, 0]) # Dispersion function and its derivative at the tracking location.\n",
+        "optics = Optics(local_beta=local_beta, local_alpha=local_alpha, \n",
+        "                  local_dispersion=local_dispersion)"
+      ],
+      "metadata": {
+        "id": "yY9Fh3JR1rQy"
+      },
+      "execution_count": 5,
+      "outputs": []
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "ring = Synchrotron(h=h, optics=optics, particle=particle, L=L, E0=E0, ac=ac, \n",
+        "                   U0=U0, tau=tau, emit=emit, tune=tune, \n",
+        "                   sigma_delta=sigma_delta, sigma_0=sigma_0, chro=chro)"
+      ],
+      "metadata": {
+        "id": "WiPq6SDLvbjC"
+      },
+      "execution_count": 6,
+      "outputs": []
+    },
+    {
+      "cell_type": "markdown",
+      "source": [
+        "## Define a Beam object"
+      ],
+      "metadata": {
+        "id": "xETy3HQMTql_"
+      }
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "from mbtrack2.tracking import Beam"
+      ],
+      "metadata": {
+        "id": "Vcy-pUOYTwp4"
+      },
+      "execution_count": 7,
+      "outputs": []
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "filling_pattern = np.ones(ring.h)*0.025\n",
+        "filling_pattern[5:7] = 0.05\n",
+        "filling_pattern[10:12] = 0\n",
+        "mybeam = Beam(ring)\n",
+        "mybeam.init_beam(filling_pattern, mp_per_bunch=1e3)\n",
+        "fig = mybeam.plot(\"bunch_current\")\n",
+        "print(mybeam.current)"
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 296
+        },
+        "id": "T2Gu7M1XTzSc",
+        "outputId": "7c4fc5aa-96d0-49b9-e344-89aacfed91a7"
+      },
+      "execution_count": 8,
+      "outputs": [
+        {
+          "output_type": "stream",
+          "name": "stdout",
+          "text": [
+            "0.5000000000000001\n"
+          ]
+        },
+        {
+          "output_type": "display_data",
+          "data": {
+            "text/plain": [
+              "<Figure size 432x288 with 1 Axes>"
+            ],
+            "image/png": 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\n"
+          },
+          "metadata": {
+            "needs_background": "light"
+          }
+        }
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "source": [
+        "# RFCavity class"
+      ],
+      "metadata": {
+        "id": "IvqUpee5OXBF"
+      }
+    },
+    {
+      "cell_type": "markdown",
+      "source": [
+        "The `RFCavity` class is a very simple class to model RF cavities using a perfect cosine wave."
+      ],
+      "metadata": {
+        "id": "EaCxRIgzOfZn"
+      }
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "from mbtrack2.tracking import RFCavity"
+      ],
+      "metadata": {
+        "id": "_Un3rKy7PFWT"
+      },
+      "execution_count": 9,
+      "outputs": []
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "m = 1 # Harmonic number of the cavity\n",
+        "Vc = 1e6 # Total cavity voltage in [V].\n",
+        "theta = np.arccos(ring.U0/Vc) # Total cavity phase in [rad].\n",
+        "RF = RFCavity(ring, m, Vc, theta)"
+      ],
+      "metadata": {
+        "id": "W3yPFAXfPJUr"
+      },
+      "execution_count": 10,
+      "outputs": []
+    },
+    {
+      "cell_type": "markdown",
+      "source": [
+        "The `track` method of the `RFCavity` class can be called for both `Bunch` and `Beam` elements and simply applies:\n",
+        "\n",
+        "$\\delta = \\delta +  \\frac{V_c}{E_0} \\cos(m \\omega_1 \\tau + \\theta)$"
+      ],
+      "metadata": {
+        "id": "DrGl4KxsSX9n"
+      }
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "print(mybeam[0][\"delta\"][:5])\n",
+        "RF.track(mybeam)\n",
+        "print(mybeam[0][\"delta\"][:5])"
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "id": "NnUmubbnUyGJ",
+        "outputId": "7e3c2a8b-9f31-42b1-8152-83ce6694ffa3"
+      },
+      "execution_count": 11,
+      "outputs": [
+        {
+          "output_type": "stream",
+          "name": "stdout",
+          "text": [
+            "[-0.00232786  0.0010207   0.00039116 -0.00193677 -0.0007547 ]\n",
+            "[-0.00219293  0.00115227  0.00052083 -0.00180337 -0.00061871]\n"
+          ]
+        }
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "source": [
+        "# CavityResonator class\n",
+        "The `CavityResonator` can be used to model:\n",
+        "\n",
+        "*   Active RF cavities\n",
+        "*   Passive RF cavities\n",
+        "*   Cavity HOMs\n",
+        "\n",
+        "The cavity physics is based on the phasor formalism developped in [1], details of the implementation and benchmark can be found in [2,3]."
+      ],
+      "metadata": {
+        "id": "ffXq_OnXoFXX"
+      }
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "import matplotlib.pyplot as plt\n",
+        "from mbtrack2.tracking import CavityResonator"
+      ],
+      "metadata": {
+        "id": "f2hjNnrzoYi8"
+      },
+      "execution_count": 12,
+      "outputs": []
+    },
+    {
+      "cell_type": "markdown",
+      "source": [
+        "Let us define a first `CavityResonator` element, for example to describe the fundamental RF cavity needed for our synchrotron."
+      ],
+      "metadata": {
+        "id": "OtAksc5Bqf6x"
+      }
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "m = 1 # Harmonic number of the cavity\n",
+        "Rs = 5e6 # Shunt impedance of the cavity in [Ohm], defined as 0.5*Vc*Vc/Pc.         \n",
+        "         # If Ncav = 1, used for the total shunt impedance.\n",
+        "         # If Ncav > 1, used for the shunt impedance per cavity.\n",
+        "Q = 35e3 # Quality factor of the cavity.\n",
+        "QL = 5e3 # Loaded quality factor of the cavity.\n",
+        "detune = -100e3 # Detuing of the cavity in [Hz], defined as (fr - m*ring.f1).\n",
+        "Ncav = 4 # Number of cavities.\n",
+        "MC = CavityResonator(ring, m, Rs, Q, QL, detune, Ncav=Ncav)"
+      ],
+      "metadata": {
+        "id": "ebAW1aY_rCR0"
+      },
+      "execution_count": 13,
+      "outputs": []
+    },
+    {
+      "cell_type": "markdown",
+      "source": [
+        "From this first input, usual quantities are computed:"
+      ],
+      "metadata": {
+        "id": "EFCTmCKVtmsG"
+      }
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "print(MC.beta) # Coupling coefficient of the cavity.\n",
+        "print(MC.fr) # Resonance frequency of the cavity in [Hz].\n",
+        "print(MC.psi) # Tuning angle in [rad].\n",
+        "print(MC.filling_time) # Cavity filling time in [s].\n",
+        "print(MC.loss_factor) # Cavity loss factor in [V/C]."
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "id": "f_XRdEeutedr",
+        "outputId": "c79a074d-52a9-4a7e-c2ba-307ac5a21ed5"
+      },
+      "execution_count": 14,
+      "outputs": [
+        {
+          "output_type": "stream",
+          "name": "stdout",
+          "text": [
+            "6.0\n",
+            "59858491.6\n",
+            "-1.5109593939048\n",
+            "2.6588532192798413e-05\n",
+            "107457712837.44363\n"
+          ]
+        }
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "source": [
+        "The full list of parameter, attribute and method are listed in the class docstring and can be accessed by calling:\n",
+        "\n",
+        "```\n",
+        "help(CavityResonator)\n",
+        "```"
+      ],
+      "metadata": {
+        "id": "OgBGRud4sNbS"
+      }
+    },
+    {
+      "cell_type": "markdown",
+      "source": [
+        "As this cavity is intented to be an active one, the total voltage and phase must be declared:"
+      ],
+      "metadata": {
+        "id": "7C-P4zzYuPBE"
+      }
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "MC.Vc = 1e6 # Total cavity voltage in [V].\n",
+        "MC.theta = np.arccos(ring.U0/MC.Vc) # Total cavity phase in [rad]."
+      ],
+      "metadata": {
+        "id": "oCn2lTk6rUtr"
+      },
+      "execution_count": 15,
+      "outputs": []
+    },
+    {
+      "cell_type": "markdown",
+      "source": [
+        "Then class methods can be used to set the optimal tuning point and computing the generator parameters for a given beam current $I_0$:"
+      ],
+      "metadata": {
+        "id": "2fwKN1vDuOJe"
+      }
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "I0 = 0.5 # Total multi-bunch current in [A].\n",
+        "MC.set_optimal_detune(I0) # Set detuning to optimal conditions.\n",
+        "print(MC.detune) # Cavity detuning in [Hz] at optimal condition.\n",
+        "MC.set_generator(I0) # Set generator parameters (Pg, Vgr, theta_gr, Vg and theta_g) for a given current and set of parameters.\n",
+        "print(MC.Pg) # Generator power in [W].\n",
+        "print(MC.Vgr) # Generator voltage at resonance in [V].\n",
+        "print(MC.theta_gr) # Generator phase at resonance in [rad].\n",
+        "print(MC.Vg) # Generator voltage in [V].\n",
+        "print(MC.theta_g) # Generator phase in [rad]."
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "id": "jqbtSTJ6s4Ge",
+        "outputId": "e259484a-caff-4886-ee6b-81e933a8640d"
+      },
+      "execution_count": 16,
+      "outputs": [
+        {
+          "output_type": "stream",
+          "name": "stdout",
+          "text": [
+            "-16782.53176803142\n",
+            "126041.66666666666\n",
+            "1571428.5714285714\n",
+            "1.369438406005134\n",
+            "528626.2644652845\n",
+            "0.14173199913728252\n"
+          ]
+        }
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "source": [
+        "The phasor diagram showing the phasor addition of the beam voltage $V_b$ and generator voltage $V_g$ giving the total cavity voltage $V_c$ can be plotted:"
+      ],
+      "metadata": {
+        "id": "DihPkQmzFymv"
+      }
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "fig = MC.plot_phasor(I0)"
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 286
+        },
+        "id": "Ypdhc4McFwXa",
+        "outputId": "26f1bfa3-5154-4804-b3c4-31acfaa73f6c"
+      },
+      "execution_count": 17,
+      "outputs": [
+        {
+          "output_type": "display_data",
+          "data": {
+            "text/plain": [
+              "<Figure size 432x288 with 1 Axes>"
+            ],
+            "image/png": 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\n"
+          },
+          "metadata": {
+            "needs_background": "light"
+          }
+        }
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "source": [
+        "The power dissipated in the walls, transmitted to the beam and reflected can be computed: "
+      ],
+      "metadata": {
+        "id": "3pvaDaiSIDgH"
+      }
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "print(MC.Pc) # Power dissipated in the cavity walls in [W].\n",
+        "print(MC.Pb(I0)) # Return power transmitted to the beam in [W].\n",
+        "print(MC.Pr(I0)) # Return power reflected back to the generator in [W]."
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "id": "ZQNoawSrIDyA",
+        "outputId": "4b350628-d3fa-451c-d301-c8c361e88fa0"
+      },
+      "execution_count": 18,
+      "outputs": [
+        {
+          "output_type": "stream",
+          "name": "stdout",
+          "text": [
+            "25000.0\n",
+            "99999.99999999997\n",
+            "1041.666666666686\n"
+          ]
+        }
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "source": [
+        "The reflected power can be minimized if the cavity coupling is set to the optimal value using the `set_optimal_coupling` method:\n",
+        "\n",
+        "\n"
+      ],
+      "metadata": {
+        "id": "Z8D6mvrdJPYS"
+      }
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "MC.set_optimal_coupling(I0) # Set coupling to optimal value.\n",
+        "print(MC.beta) # Coupling coefficient of the cavity.\n",
+        "MC.set_optimal_detune(I0)\n",
+        "MC.set_generator(I0)\n",
+        "print(MC.Pr(I0)) # Return power reflected back to the generator in [W]."
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "id": "VCeGDP9eJOWT",
+        "outputId": "66cbc458-12b6-4d1d-ec61-dbfdd60755ce"
+      },
+      "execution_count": 19,
+      "outputs": [
+        {
+          "output_type": "stream",
+          "name": "stdout",
+          "text": [
+            "4.999999999999998\n",
+            "-1.4551915228366852e-11\n"
+          ]
+        }
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "source": [
+        "The DC Robinson stability (for single RF system) can be checked using the methods `is_DC_Robinson_stable` or `plot_DC_Robinson_stability`:"
+      ],
+      "metadata": {
+        "id": "Ahr1lJIuLazM"
+      }
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "MC.is_DC_Robinson_stable(I0)"
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "id": "PdZ8GmWxLrVi",
+        "outputId": "c8e888b8-7fc1-4d46-d2c2-2c6320304637"
+      },
+      "execution_count": 20,
+      "outputs": [
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "True"
+            ]
+          },
+          "metadata": {},
+          "execution_count": 20
+        }
+      ]
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "fig = MC.plot_DC_Robinson_stability([-50e3,-5e3])\n",
+        "plt.scatter(MC.detune,I0,c=\"g\")\n",
+        "print(MC.is_DC_Robinson_stable(0.6))\n",
+        "plt.scatter(MC.detune,0.6,c=\"r\")\n",
+        "plt.legend([\"Threshold\",\"stable\",\"unstable\"])"
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 330
+        },
+        "id": "yOhFgjdFLrSi",
+        "outputId": "4da2cd69-7f10-4a20-d8f4-5bac3587561a"
+      },
+      "execution_count": 21,
+      "outputs": [
+        {
+          "output_type": "stream",
+          "name": "stdout",
+          "text": [
+            "False\n"
+          ]
+        },
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "<matplotlib.legend.Legend at 0x7f58a66e6ad0>"
+            ]
+          },
+          "metadata": {},
+          "execution_count": 21
+        },
+        {
+          "output_type": "display_data",
+          "data": {
+            "text/plain": [
+              "<Figure size 432x288 with 1 Axes>"
+            ],
+            "image/png": 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\n"
+          },
+          "metadata": {
+            "needs_background": "light"
+          }
+        }
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "source": [
+        "## Tracking"
+      ],
+      "metadata": {
+        "id": "bT_CpT4F_0tv"
+      }
+    },
+    {
+      "cell_type": "markdown",
+      "source": [
+        "Tracking using the `CavityResonator` class is based on the `cavity_phasor` which is the phasor sum of: \n",
+        "+ the `generator_phasor` which is fixed by the generator voltage `Vg` and phase `theta_g` attributes:\n",
+        "\n",
+        "$$\\tilde{V}_{g} = V_{g} e^{j(m \\omega_{1} \\tau + \\theta_{g})}$$\n",
+        "\n",
+        "+ the `beam_phasor` which evolves dynamically at each call of the `track` method depending on the macro-particle positions and charges. \n",
+        "\n",
+        "The beam phasor $\\tilde{V}_b$ is built up by the successive passages of the different particles inside the cavity. Each bunch is binned longitudinally and when a bin of charged particle goes through the RF cavity, it induces a voltage \n",
+        "\n",
+        "$$\\tilde{V}_0 = -2 k_l q_{mp} N_{mp}$$\n",
+        "\n",
+        "Where $k_l$ is the cavity loss factor, $q_{mp}$ is the macroparticle charge, and $N_{mp}$ is the number of macropartiles in the bin.\n",
+        "\n",
+        "The voltage induced by the different particles crossing the cavity between time $t$ and time $t + \\Delta t$ is added to the voltage $\\tilde{V}_{b} (t)$ already present in the cavity at time $t$: \n",
+        "\n",
+        "$$\n",
+        "\\tilde{V}_{b} (t + \\Delta t) = \\tilde{V}_{b} (t) e^{-\\frac{\\Delta t}{\\tau_l}}  e^{j\\delta_l \\Delta t} + \\tilde{V}_0 = \\tilde{V}_{b} (t) e^{-\\frac{\\Delta t}{\\tau_l}}  e^{j\\delta_l \\Delta t} -2 k_l q_M\n",
+        "$$\n",
+        "\n",
+        "Where $\\tau_l$ is the cavity filling time and $\\delta_l$ is the phase slippage factor.\n",
+        "\n",
+        "As a particle see only half of its wake, the energy change felt by the particles in the bin is:\n",
+        "\n",
+        "$$\\delta = \\delta + \\frac{q}{E_0} \\left [ Re[\\tilde{V}_{g}] + Re[\\tilde{V}_{b}] - q_M k_l \\right]$$\n",
+        "\n",
+        "At the initialization of the `CavityResonator`, the `beam_phasor` attribute is set to zero:"
+      ],
+      "metadata": {
+        "id": "KeXH-A3WWGyH"
+      }
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "print(MC.beam_phasor) # Beam phasor for tracking in [V]\n",
+        "print(MC.cavity_phasor) # Cavity phasor for tracking in [V]\n",
+        "print(MC.cavity_voltage) # Cavity voltage for tracking in [V]\n",
+        "print(MC.cavity_phase) # Cavity phase for tracking in [rad]"
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "id": "BwnJdmllhV1h",
+        "outputId": "d58b9919-69d2-471c-d492-1d688e09ab25"
+      },
+      "execution_count": 22,
+      "outputs": [
+        {
+          "output_type": "stream",
+          "name": "stdout",
+          "text": [
+            "[0.+0.j]\n",
+            "[485714.28571412+46656.94748183j]\n",
+            "[487950.03647412]\n",
+            "[0.0957646]\n"
+          ]
+        }
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "source": [
+        "Depending on the cavity parameters, it can take a long time (especially for super conducting cavities) to fill the cavity and reach the equilibrium beam loading.\n",
+        "\n",
+        "To speed-up the cavity filling, one should use the `init_phasor` method before starting the tracking."
+      ],
+      "metadata": {
+        "id": "Y5kCnNBjhjZN"
+      }
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "MC.init_phasor(mybeam)\n",
+        "print(MC.beam_phasor) # Beam phasor for tracking in [V]\n",
+        "print(MC.cavity_phasor) # Cavity phasor for tracking in [V]\n",
+        "print(MC.cavity_voltage) # Cavity voltage for tracking in [V]\n",
+        "print(MC.cavity_phase) # Cavity phase for tracking in [rad]"
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "id": "PLyRKsWxhiWP",
+        "outputId": "b10820b4-27ec-443c-ae3c-43a44875edcc"
+      },
+      "execution_count": 23,
+      "outputs": [
+        {
+          "output_type": "stream",
+          "name": "stdout",
+          "text": [
+            "[-283882.59602631+933000.63002653j]\n",
+            "[201831.68968781+979657.57750836j]\n",
+            "[1000232.47304403]\n",
+            "[1.36761648]\n"
+          ]
+        }
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "source": [
+        "After the `beam_phasor` initialization, the cavity is filled and the `cavity_voltage` and `cavity_phase` attributes match the objective values `Vc` and `theta` which were set previously."
+      ],
+      "metadata": {
+        "id": "AGi1mcHSlPul"
+      }
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "print(MC.Vc) # Total cavity voltage in [V]. Objective value used in calculations but not in tracking.\n",
+        "print(MC.theta) # Total cavity phase in [rad]. Objective value used in calculations but not in tracking."
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "id": "Y4IpK8W4mnPz",
+        "outputId": "104d4b05-54d7-43c0-8b8a-ddea1b72efea"
+      },
+      "execution_count": 24,
+      "outputs": [
+        {
+          "output_type": "stream",
+          "name": "stdout",
+          "text": [
+            "1000000.0\n",
+            "1.369438406004566\n"
+          ]
+        }
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "source": [
+        "Once the `beam_phasor` initialization is done, just call the `track` method to update both the beam particle energy deviation $\\delta$ and the `beam_phasor`:"
+      ],
+      "metadata": {
+        "id": "Skr9SAQRnA1b"
+      }
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "print(mybeam[0][\"delta\"][:5])\n",
+        "print(MC.beam_phasor)\n",
+        "MC.track(mybeam)\n",
+        "print(mybeam[0][\"delta\"][:5])\n",
+        "print(MC.beam_phasor)"
+      ],
+      "metadata": {
+        "id": "uFca7rCTpVWU",
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "outputId": "82c7a558-573a-4d5e-e187-1ebab616f834"
+      },
+      "execution_count": 25,
+      "outputs": [
+        {
+          "output_type": "stream",
+          "name": "stdout",
+          "text": [
+            "[-0.00219293  0.00115227  0.00052083 -0.00180337 -0.00061871]\n",
+            "[-283882.59602631+933000.63002653j]\n",
+            "[-0.00205699  0.00128446  0.00065101 -0.00166916 -0.00048177]\n",
+            "[-283882.71212199+932993.63076803j]\n"
+          ]
+        }
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "source": [
+        "The value stored in `beam_phasor` corresponds to the last value of the beam phasor at t=0 (synchronous particle) of the first non empty bunch.\n",
+        "\n",
+        "The last value of the beam phasor at t=0 (synchronous particle) of each bunch in stored in the `cavity_phasor_record` attribute."
+      ],
+      "metadata": {
+        "id": "-qa6lLrKojo6"
+      }
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "MC.cavity_phasor_record"
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "id": "FDPJPsHHWY94",
+        "outputId": "d1633eaf-7223-4941-9a75-bd76d120d15f"
+      },
+      "execution_count": 26,
+      "outputs": [
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "array([200037.02401695+979657.34988496j, 200036.53611279+979655.45608534j,\n",
+              "       200036.04712366+979653.28391847j, 200035.5523303 +979651.2983488j ,\n",
+              "       200035.05262454+979649.44196298j, 198239.88409674+979646.89121197j,\n",
+              "       196445.68625732+979648.32586931j, 196447.11998679+979652.54663041j,\n",
+              "       196448.5611901 +979657.27992109j, 196450.01073998+979661.54239132j,\n",
+              "       198246.12991393+979666.34736958j, 200041.28797294+979667.99265838j,\n",
+              "       200040.81466583+979665.63314484j, 200040.3380717 +979664.17294936j,\n",
+              "       200039.8590515 +979661.85309936j, 200039.37691663+979659.53672756j,\n",
+              "       200038.88956584+979657.64069376j, 200038.3996667 +979655.0885858j ,\n",
+              "       200037.9050291 +979653.69751251j, 200037.40756945+979652.07384169j])"
+            ]
+          },
+          "metadata": {},
+          "execution_count": 26
+        }
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "source": [
+        "## Passive cavity or HOM\n",
+        "\n"
+      ],
+      "metadata": {
+        "id": "VTTme9ogyDrF"
+      }
+    },
+    {
+      "cell_type": "markdown",
+      "source": [
+        "A passive (harmonic) cavity or a cavity HOM can be defined in the same way as an active cavity:"
+      ],
+      "metadata": {
+        "id": "I889WwKa3Aak"
+      }
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "m = 4 # Harmonic number of the cavity\n",
+        "Rs = 4.5e9 # Shunt impedance of the cavity in [Ohm], defined as 0.5*Vc*Vc/Pc.         \n",
+        "           # If Ncav = 1, used for the total shunt impedance.\n",
+        "           # If Ncav > 1, used for the shunt impedance per cavity.\n",
+        "Q = 1e8 # Quality factor of the cavity.\n",
+        "QL = 1e8 # Loaded quality factor of the cavity.\n",
+        "detune = 25e3 # Detuing of the cavity in [Hz], defined as (fr - m*ring.f1).\n",
+        "HC = CavityResonator(ring, m, Rs, Q, QL, detune)"
+      ],
+      "metadata": {
+        "id": "_qCp81Zo1n-u"
+      },
+      "execution_count": 27,
+      "outputs": []
+    },
+    {
+      "cell_type": "markdown",
+      "source": [
+        "The induced voltage can be estimated:"
+      ],
+      "metadata": {
+        "id": "ohllR8eG3Jj8"
+      }
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "HC.Vb(I0) # Beam voltage in [V]."
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "id": "-nWBy0b42FpF",
+        "outputId": "7abe3b54-ab96-46ce-f9f0-114f479d9daa"
+      },
+      "execution_count": 28,
+      "outputs": [
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "215861.81892505847"
+            ]
+          },
+          "metadata": {},
+          "execution_count": 28
+        }
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "source": [
+        "If the `CavityResonator` is passive, the **generator voltage** `Vg` and **phase** `theta_g` should **explicitly be set to zero before tracking**:"
+      ],
+      "metadata": {
+        "id": "CSITLGxv3Tf0"
+      }
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "HC.Vg = 0\n",
+        "HC.theta_g = 0"
+      ],
+      "metadata": {
+        "id": "QiSFXSAZ2B4u"
+      },
+      "execution_count": 29,
+      "outputs": []
+    },
+    {
+      "cell_type": "markdown",
+      "source": [
+        "## Tracking using MPI"
+      ],
+      "metadata": {
+        "id": "YqJtFL_OIvSq"
+      }
+    },
+    {
+      "cell_type": "markdown",
+      "source": [
+        "MPI can be used to speed up the tracking when using a `Beam` object by distributing the different `Bunch` objects in different cores.\n",
+        "\n",
+        "To be able to use this feature, **the python code must be run with as many core as there is of `Bunch` objects in the `Beam`.**"
+      ],
+      "metadata": {
+        "id": "KmnutEIbrZgf"
+      }
+    },
+    {
+      "cell_type": "markdown",
+      "source": [
+        "MPI parallelisation can be enabled during ``Beam`` initialization by setting the ``mpi`` option to ``True``:"
+      ],
+      "metadata": {
+        "id": "dQLd4_Rym5oz"
+      }
+    },
+    {
+      "cell_type": "markdown",
+      "source": [
+        "\n",
+        "\n",
+        "```\n",
+        "mybeam = Beam(ring)\n",
+        "mybeam.init_beam(filling_pattern, mp_per_bunch=1e3, mpi=True)\n",
+        "```\n",
+        "\n"
+      ],
+      "metadata": {
+        "id": "Le0RaqmJIeaO"
+      }
+    },
+    {
+      "cell_type": "markdown",
+      "source": [
+        "Compared to the tracking without using MPI, the method `Beam.mpi.share_distributions` must be called before each call of `CavityResonator.track` to compute the bunch profiles and share it between the different cores using MPI."
+      ],
+      "metadata": {
+        "id": "Ha14JRYIssAI"
+      }
+    },
+    {
+      "cell_type": "markdown",
+      "source": [
+        "A typical tracking loop using MPI would then be:\n",
+        "\n",
+        "\n",
+        "\n",
+        "```\n",
+        "MC.init_phasor(beam)\n",
+        "HC.init_phasor(beam)\n",
+        "\n",
+        "for i in range(turns):\n",
+        "    \n",
+        "    long.track(beam) # Longitudinal map\n",
+        "    rad.track(beam) # Synchrotron radiation element\n",
+        "    beam.mpi.share_distributions(beam) # Using MPI, this line is needed\n",
+        "    MC.track(beam) # CavityResonator element\n",
+        "    HC.track(beam) # CavityResonator element\n",
+        "```\n",
+        "\n"
+      ],
+      "metadata": {
+        "id": "sUO8Nj4wzLCM"
+      }
+    },
+    {
+      "cell_type": "markdown",
+      "source": [
+        "## CavityMonitor"
+      ],
+      "metadata": {
+        "id": "a_B5YgHFHaIA"
+      }
+    },
+    {
+      "cell_type": "markdown",
+      "source": [
+        "The `CavityMonitor` can be used to save data from a `CavityResonator` during the tracking.\n",
+        "\n",
+        "The follwing attributes are saved:\n",
+        "\n",
+        "\n",
+        "*   Cavity and Beam phasor for at each bunch\n",
+        "*   Cavity detuning and angle\n",
+        "*   Generator voltage, phase and power\n",
+        "*   Shunt impedance, loaded and unload quality factor\n",
+        "\n"
+      ],
+      "metadata": {
+        "id": "vXI4RF7thfdw"
+      }
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "from mbtrack2.tracking.monitors import CavityMonitor, plot_cavitydata"
+      ],
+      "metadata": {
+        "id": "CHF_GzVC5KQD"
+      },
+      "execution_count": 30,
+      "outputs": []
+    },
+    {
+      "cell_type": "markdown",
+      "source": [
+        "Like the other monitors, the `CavityMonitor` must be initialized before the tracking:"
+      ],
+      "metadata": {
+        "id": "pz6oiLwWKx59"
+      }
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "MCmon = CavityMonitor(\"MC\", ring, file_name=\"tracking_test\", save_every=1, buffer_size=10, total_size=100, mpi_mode=False)"
+      ],
+      "metadata": {
+        "id": "yN07pCXd5G6q"
+      },
+      "execution_count": 31,
+      "outputs": []
+    },
+    {
+      "cell_type": "markdown",
+      "source": [
+        "The `track` method of `CavityMonitor` takes the `Beam` object as first agrument and the saved `CavityResonator` as second agrument."
+      ],
+      "metadata": {
+        "id": "QfvJPLzhLEfu"
+      }
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "from mbtrack2.tracking import LongitudinalMap, SynchrotronRadiation\n",
+        "long = LongitudinalMap(ring)\n",
+        "rad = SynchrotronRadiation(ring)\n",
+        "\n",
+        "for i in range(100):\n",
+        "    long.track(mybeam)\n",
+        "    rad.track(mybeam)\n",
+        "    MC.track(mybeam)\n",
+        "    MCmon.track(mybeam, MC)"
+      ],
+      "metadata": {
+        "id": "tywlUGCoKguV"
+      },
+      "execution_count": 32,
+      "outputs": []
+    },
+    {
+      "cell_type": "markdown",
+      "source": [
+        "The saved data can be plotted using the `plot_cavitydata` function:"
+      ],
+      "metadata": {
+        "id": "tYptR7efLVar"
+      }
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "fig = plot_cavitydata(\"tracking_test.hdf5\",\"MC\")"
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 290
+        },
+        "id": "wL7jVkvMLVzL",
+        "outputId": "8e3b303f-c7ea-49dc-bbb3-2f307f36a5a5"
+      },
+      "execution_count": 33,
+      "outputs": [
+        {
+          "output_type": "display_data",
+          "data": {
+            "text/plain": [
+              "<Figure size 432x288 with 2 Axes>"
+            ],
+            "image/png": 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\n"
+          },
+          "metadata": {
+            "needs_background": "light"
+          }
+        }
+      ]
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "fig = plot_cavitydata(\"tracking_test.hdf5\",\"MC\",plot_type=\"turn\",turn=50)"
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 290
+        },
+        "id": "fRGflKdSLuvk",
+        "outputId": "1d1f3904-3a44-4b7c-b4f6-93f923455c6e"
+      },
+      "execution_count": 34,
+      "outputs": [
+        {
+          "output_type": "display_data",
+          "data": {
+            "text/plain": [
+              "<Figure size 432x288 with 2 Axes>"
+            ],
+            "image/png": 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\n"
+          },
+          "metadata": {
+            "needs_background": "light"
+          }
+        }
+      ]
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "fig = plot_cavitydata(\"tracking_test.hdf5\",\"MC\",plot_type=\"streak_volt\")"
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 290
+        },
+        "outputId": "407827b0-6370-446a-8b55-7454c842ade5",
+        "id": "srURo9xxMqqy"
+      },
+      "execution_count": 35,
+      "outputs": [
+        {
+          "output_type": "display_data",
+          "data": {
+            "text/plain": [
+              "<Figure size 432x288 with 2 Axes>"
+            ],
+            "image/png": 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VeLUbVUzLfhcJCVEackhwmHqiyHMgcoupKvDZlJI8oj12fvBd05Tg+4RBkIvYbiJYB2YD+Un2WFGZXx/IL75DZZ04LTn3RJK3IJSso0UD/c1OObcdT6aFzhjlvC/FHC/pJol7zH0OpFSzi10fSEdUMAb0+8EgyGXfiiirgfwg91IuQ6XlUsZdsmJAJVNtAWVhsQQplQ6B9nXGuxcP3RlGXo23FBIwsQUnf07cVmZWnqua8xjObzbJveOuvif7dO2NcBgfKFbHMMjlkHDYg8pMzEXVAHV15cSCmV1hpWmM+047jjHPcgp2R5DcL/qTWmnFBtVU5KJfcbZd9D2biDwTTO3Q/+8RW+KhGIsoe8FgyGVTf/a2PLGk8ZaZAspYsDKbVAL37rdJ9HSfxltcrGUdsi5m6pwUMA9TxER5JeZCUUjpjyvEpOTjLEUqcu4slcmkkIhR5C6LLZitGNT2AEMZtMdssdWxHSPpQlQDset8bQvm3YRFP9Mn9zDAelQKDsOy1DW24LUM2rTbpe3YspmZLCx2jcXnrEhwSGRzIqw60KU1M0PA7Kymm30NASHm0tfxSDpF0sckXSHpzJrfj5b0Rv/7eyXdNfrtWX75xyQ9rEObL5f0r0udgJ4wCMvFPYgP48LsC9WYS5wx5iwTTQ4S6yVUopcBbmKrpcZ6aeXq2obTbrPTM1dFLMvjVEhFxgfpIyuvlOCvxlzcq7u1NZTBMsYQ+7x5zHE/d21JmgC/CzwEuBK4TNJFZvaRaLUnA182s7tJOg14EfB4SfcATgPuCdwJeIeku/ttGtuUdDJw614OYAWslVwk/SpwBmDAh4AnAccDFwC3Bd4P/IyZ3bjOfrTFtt14swRTTtkbrVQSS7wsEatc1hLpWl3fJebSRY4/7b+RZMoVG2RA7mahTNULmLU2gkvMVsxY2LZrZ6jYFu/BzH22PO4DXGFmn/TtXgCcCsTkcirwXP/5zcAr5DpwKnCBmd0AfErSFb49mtr0ZPZbwBOAR/d1EMtgbeQi6QTgl4F7mNk3JF2IY+GHA79tZhdIehWOtV85v7Htunk3cQPMmuB+n0WdS6jKn01FtsglVNEUk7NW8hXdXo19xlYWw4QqQc2oIVfqXUoFgkK8MsRbyAsrzs1SWT6NVi2W5PyOGKFO9/jtJF0efT/XzM6Nvp8AfC76fiVw36SNYh0zOyLpq7iH7xOAS5NtT/Cfm9r8ReAiM7u6R4JcCut2ix0Ax0r6JnBT4GrggThWBTgfx9jzyWXHK2briDPOboplXoBSaj9KNS5iDoqJpVpACZTSL7YcucwL1vcl/TJDUHJxF5cx1mClhePP4+VW/oY7b2kBZUA2UeP8K/vmkt17SKh9QP9LZnbyOrvTFpLuBDwWuP8hdwVYI7mY2VWS/h/gs8A3gP+Fc4N9xcyO+NViJq5A0lOBpwLc6abHbJXlsgmkaciVZYUVEwWtswbCCaKVlFpibWIuTe6tvqX1W7VrIZBfKgsUVfpQur9CMWU0n0sRdylUDUp3WGzBWD4dSaQG+3bfBfR43FcBd4m+39kvq1vnSkkHwC2BaxZsW7f8e4G7AVd4q+Wmkq4ws7v1cyjdsE632K1xfsATga8AbwJOabu9Ny3PBbjXbW9p+3iRl2SSFFBCSSxZFNR3G0UB7mrgO5Z9CYN5U43JEvHt5uNIiGqp2E/c94pLzJNnJjTFEQw4grGScKXI/VXrFtu/66srdtl7EEOomJqhB1wGnCTpRBwBnEbpuQm4CDgdeA/wGOAvzcwkXQS8QdJLcAH9k4D34dJsZto0sw8DdyyOQ/rXwyIWWK9b7MHAp8zsXwAkvQX4IeBWkg689VLH4oPAum+0tMal8J8G11dsoRQb+YF25saIrZdyEJ1XvNhGEibGPHmYLnGY9gkBVQUCpUkMyqptVeRzyrTltLhyxAinN9XPw4aPofwicDEwAc4zsw9LOhu43MwuAl4D/IEP2F+LIwv8ehfigv9HgKeb2RSgrs1eOtwj1kkunwXuJ+mmOLfYg4DLgb/CsfMFOLZ+a5vGNnXzb8sTbNVt41NoJ5MyZqCIZOIiSk8+lk0qAe9ck7J4MsRcerROpqgfrT/TLFGppnamIgETnYvJxFksuS+mLCw7H9w/mDgrRmUGXnYwIT8yqiJvOzZ5b/Y53pjZ24C3JcueE32+Hhcrqdv2hcAL27RZs87Nl+lvX1hnzOW9kt4MfADHun+Pc3P9OXCBpBf4Za9Z2NgeyjHMvbiDplhqocwIV9ZLvrSt0O8sv99y9UUklFpNmY+55OlcLiSForFwZbGz6JzMxLD265pqg/GcOIznYXWsNVvMzM4CzkoWf5IyV7s19unPTutbsoOJk6MIFktUOMlkUk1BTlxmblAuJwjLLXxe7K4K5LOMXtjcdqPm2hBYLpEFi6uwXErrJVhqZFM/o2QGEzDLZ6X2QyFlXYFqR6QPAE2qypvE6N7rAXKSQSNWwyAq9DeBbbwp0/qLRuHKuLaF8DSf1IeomwpyZdu1xEx82w3WU0o6TfUusxvWF1GW1ks6bXR/dS7beA3tAg7lwXL8L1fGYMily427C1ZOKfcSxQzCk3dclS95iyUUSpZ1H0ZG7mMvLtPKWS1TyyILpl/rpC/hypg4MvKqBTYj/xK/wr6jIsrJAZbdSJg0rJoptrz8y4huGMp9qTC53IiVMAhy2dXJexaJU6rQwUpENZOalnKjkIKcld+pDtSxFdL0ubFPLQmoa6pxu8nCylkt45kt4yLRyoAQiCY+x1n1vKQTsFk+vx/LXoOL2u1jHyN6xmi5rIxBkAvsTkC/rQVWTUVOhSuT2EuUFVZ+rqtxURlvoe3M9hESAurt9lv015qLuxQV+lHcpYwxlcKdygOJ5IXUfqh1iScNoxJv8e60pi6uMNj0VzIxYlPYlfHmMDEMctH++bNrL+4ogF2xWqLgdqkjFuo+Susljz6HdOS5fVhgqSwTvq77FxdaTXIhFFOki5bW+BTrZliWo2AtxNI4kepBaRWqsFr27Rrrgr0abCPJoBHLYxjkwp5d3ERusVi6JIoRBJTTGSsin5JoKlZLNL1xIIY6F1ahRNyzCCUsR0gTqpI1wXohkeAPmWHgCcYiN1h0boI1CPF5HmMuXbDr9+OYLbY6BkIuu+MW64Q4XVZBBTmq2UgJxaMiVBlIxmYJpk5fTLLe1JL7Ukk2SmsrdC1VRS6SGBQcflHMJa7ej8h6iBNZbSt2yuoTvVXo7zMGQi6bwTbdIEH2pZDWT2pcKsKUkYuokETxmWFQrW6vzOpYM/CvQgZ9aIjVBfc9VRRtxorOlpwDhSJKn0UXNKKKcwiVGFapkLw9//2Iw8Zuq7BvCoMgF60QcxnqE2mcKhtSaItgfhTIr8zGCEUwvyL7ImGWFZIvoZiy95I/08pBfkOzsZ403uKD+WVqsnONuXM0cQRp5tpJEh9UWC1lYH+UfxkONnY/j6nIK2MQ5ALDJYlFaCTNEHiWKk/dfiNX5xJcYx6FNVN8D5ZLnLobxVtaWildamC6EFYTEdXN5xIT44z8C9ms5VJsG5ZTne8mfN8z7Op91CvEmIrcA4ZBLtoyM3UDN6iUFZIvcUqyk3tJ6lwq2WKlaGWagpyTFVliOe21wBZnlS13jDENzCOwzESuVLwyKyyWcNwKgX1whARI06q15wVAC0kYlRI7TfItW3XtjdgARvmXPjAMcoG9e8qsfcIsigCTIslKllj8W/mUX4m1RIH8edlibdFEUl1IZy6ByWZSp5vlXxzxyCKiiBQM4iwx9+5IxvLpSCJLYCctITGmIveAwZBLj5P3bB0apzn2T9SaTCKLxccQgnWSlZaMNRRPViyWKPYytaZzmhRLLikNs8gyaktiTs7fW1+WMbUsOs5JaallExdrIXcEoxybTNDUk+8ksQQnk+I87+Qg2RIjqabQ3j3MrgODIZcu2JWBIr3pZ2Rgyh8qQpWVTLGQRZZminXI5Mo7ZJB1IaK2opVN21a2jxMayFxkqU64MnyOssRcVt5Y5zLCQez2w+wiSHp5i9WuM7Nnz1thEOQiiexgv/7sMKlVIViZlTEWyw78ADmJ4g5ZEW8pM8VKccog+5IDUxN5CJD34BaLMY2IaPmEm+qGE3KmJhd7qRRTZpUXQU/MWy7IigyyEMzXxH0O6cjBaumjHmefsVOD8VjncirwnAXrnAkMn1w2ga10DcRzkBTuMG+RZOWT+ozlMmPJ1BdNNlkOfdWndJ3psomMKsKVCSGWWmM+HTluLA7w4/5jI463lJaglGFWDejv1IA5ogOqRcl7iN82s/PnrSDp1osaGQy5LD34D/QJJJ7IqpB/iXWyoqf1akV+Vfol18TVuKQWTM/THLv6lBXbsHqSynFWS0W+xk/bXJ3yOBBMOBdWTFFg2YEjC79ukTGmMt4ixgyhER49ZotJOgV4GU7J6NVmdk7y+9HA64B7A9cAjzezT/vfngU8GZdc+ctmdvG8NiW9HjgZ+CbwPuDnzeybHbv8t4tWMLOXLlpnGOSyYTN1G6yYuL6lSEOekXwpA/ilvH5WibOk73F1e5dYyjyEOMsqZBWIqdZqMisslmp1flVbrLDifLVNSSwq61wCWVO1YCBvlMbflRjeiJboUbhS0gT4XeAhwJXAZZIuMrOPRKs9Gfiymd1N0mnAi4DHS7oHcBpwT+BOwDsk3d1v09Tm64Gf9uu8ATgDeGXHbp8r6ebABcAfJn1tjWGQywDkGHqfXCiuzI8C0H5n1TiDR/EEH4s6UsYpwMVcinhLD2QAq5FUK2KSqpZXXOsyx3KBqRe0rKoauB3HoqDCxf/bH8e867Hv6Y63/drfSfT3QHEf4Aoz+ySApAtwMY14wD4VeK7//GbgFXIDyqnABWZ2A/ApSVdQThFf26aZvS00Kul9wJ27dtjMvlfSt+OI7c2Svgn8oe/Lp9u2MxByWcPg3QaHeFMX0i9h8AuB6clkxnJBIpf7K2vncPEupWlwLRVuseXPaSCDVWewnNpid1qGkReFn6EINHKJFUQarDY/uGcTlE+r1l4lBTmS2DkAFk3q1XLAUdbgUmlqf7SMtg/9xVxOAD4Xfb8SuG/TOmZ2RNJXgdv65Zcm257gP89tU9JRwM8Az1im02b2MeB5wPMkfTeOaN4p6fNm9kNt2hgGuYi9kmNI53SfSUGOqvMr85oUkvORyygRrCzdS4ulWtqc8S4E1UREiywoF3OxQlkgL7LF2hVRlnL8cZFpnIrsIz3rHuR3gET2xopq/zB7O0mXR9/PNbNz19Cjrvg94K/N7G9WaUQuq+X2wB2AmwFfbLttJ3LxGQJ3MbN/7NTDHrDtfu/ebzrJpSNHci/KPJlkpQsoDKaVIH42qVotRLpc8ecFg3qdlONKBmQNEbU7azbT74I0NSHPJuT5BGVOwkXkmCbIDMsmJbEUMavSgilSvfvMbtggxrne14AgEtsOXzKzk+f8fhVwl+j7nf2yunWulHQA3BIX2J+3bWObks4CvgX4+bYHkULSfwR+EngU8CFc/OVXzeyrbdtYSC6S3gU80q/7fuCLkv7WzH5tmU4vgyK4vUdoKpase/quaItFxZNODTkK5keB/HnilfNcXW3H4LZjXlvraSYFmXq3niNakOVJanIUvI9TkEPsJR8H6Y1hCPdyk2uzOy4DTpJ0Io4ATgOekKxzEXA68B7gMcBfmplJugh4g6SX4AL6J+EywNTUpqQzgIcBD7I0t74lJH0O+AyOUJ5rZq2tlRhtLJdbmtl1vtOvM7OzJG3cclk5z3WL0IYoC3mSSST/ErKdCnFKF2tJ04+tSNN1cYhS8kVM8zKYP20aUJNBexmjcaH0S8tYzRQQQj5OlFt0PCqtl1BAKssxcwSDnOVi2QGW3Qg16ciFttieV+hvu2dgo+hmucyFj6H8InAxLm34PDP7sKSzgcvN7CLgNcAf+ID9tTiywK93IS74fwR4uplNXRdn2/S7fBWOGN7jrdq3mNnZHbv9w2b2meWP2qENuRxIOh54HPAbq+5wWeyb5VKLJDusXF6VoYeq7Et4j62VwqIpAvPNu10U547RdoyaF6tpQzxx4SREx6sM2bTQFisbjc5PlI5cZOWNg+uIGD0+zPoMrrcly54TfZoOGR8AACAASURBVL4eeGzDti8EXtimTb+8jzj678xzt5rZI9s00qYjZ+MY8n+b2WWS/j3wiVZd7Av7cvPHQXxFtS2JcKVlEyf9kkWijT5jKvcWTRCszFHFcgkusdwgjyyXOktjmUywaW07HRtJiGeSGXku8kxeuiaeSiDoqMkXckYWTJjnJYh7hnPpA/yV6aMHGnM5FOyQF6ER+12h/wO4bLQ/BN4LS0h20IJczOxNwJui758EfmKZna0Vu2jZNGWJJShTcme/Bwshnb+lzVjaNVV52WywahsN/UinUI5jSXHWnPMa+M9WG3cpzKu4fkhqZ8aN2ANo36+BO+IKNH8SF8v5c1wx5YfnbpWgTUD/W4CnAHeN1zezn+uyo1Wxb5P3FLUY4cm6qNDPfAxh4mpbkip1U2nJhCf8InUXb7nkwYppsliW7HRERssamml/JPNim5DlwjKKdORCep+gVODiL5K5VOQ40SFkjWW+TigWsDyYOI/2iI1hmz0RJrA9G29i+LjOXwB/4aVpfhJ4l6Tnmdkr2rbTxi32VuBvgHdQn526fvQYYBsUwpN1koYcoyJ/Epb5wZaopiUQiyugpJFYYHkPUbVqf7k20jHHWShlY2VRaPQ9cguGS9SCQnIs5RHXA4EP5IesMRXyL9s88I3YBPqTfxkqPKk8AkcsdwVeDvxxlzbakMtNzeyZnXvXI8Qe5vP7ynxFFkv5Kivz4yp1iIsnU7HKpE7Ev4J0y7ITgsUwW92bUJc7mRU1Lq5SvyIBY9Vz4NxhpbZYQb7FNAXeEpwcYLqxiLtYlu37eDIixh5fDJJeB3wnLmHgeWb2T8u004Zc/kzSw2PNmkPBnlkuFfmXUAAY0pBjiZd4UIXqwBsRTE6ZMVaVgHH7ayPD0gbZCnPBQD1BhQSEKkF6t18Q76QkklAdY1gR1HeuMV+MWpzPcG4z1LMe2Ihho1b9YX/w08DXcdIxvxw92AswMzuuTSNtyOUZwK9LugEn49xpB4eJQbs3Iv2w2HKxeHmkihyn5FZ0xSr6YvOD+n0IWS4rYhlbTnX9CHI1cUo1UNTyVN2Dud+mPEeukxFRQyH7EiwX5hHMnj3c7DV6VEUeIswa5z/vhLnk4nVlTjGzhfr+a4UveNsn6GBSZoulhFLMQBkNqiEVOZrnZBqlIMdildOcopgyjY30EYhf5qFvmpBS3EaG+WOwwnLJLSOnhkQ1wT//YLLyHMXpyEVAP3Pn2XI4Mu11Do8RPWPT5L7flksvmEsuZpZLegXwvRvqz+FiyyydUmwxibkAaX1HJaCf3Bhl8WSVTOqC7l0D8XWnrI8ZKOM2XK2OFXU66W9xOjKF4kWwVsq00kJ+f96OuyAd8NbhWhstpkOA9jpbTNIHzOz7Vl2njVvsnZJ+Aicj0GnYkHQr4NW44JABPwd8DHgjLgPh08DjzOzL8xvyT/L7BP9kXQSgo9knw1N4HlswFcslK57sg8x+acU4q2Waz5INdOfXfoomF/ch9DVkvk3jY1JpueShQNKMPJuQ2bRquYR05GzissUmE8iDZvSK6E+PakQdNuWq0gb3tZ34DwskvoQT15yLNuTy88CvAUckXU+3mMvLgL8ws8dIuglwU+DXgXea2TmSzgTOBA41G20uDtM8jiyWiqw+sdzJbP/S2Rwrgo+R+2kZy6UN+axaNDlDeJTZbcF6KfYVye/HRZSV34P8ZVqEum8DyL4d7wpI5ZT2DN/RYp2FZSltKvRv0ao7CSTdEvhPwBN9OzcCN0o6Fbi/X+184F0sJBftnT+8nOY4Kp6clJZKkTUWhBsjDTEX9J6UGVV+QJ6GGpecwnLpGiups1Sq/e54oC2slnj2zBzzVkxWkd6vzErpFZEzwDStxKnCedTEiVlqMoHpdMUctxG7hf2u0O9DtBLaVej/p4YO/PWCTU8E/gX4fT+T2ftxmWd3MLOr/Tqfx01CU7ffpwJPBbjLbRdaYBvH2utusijGEmU4lVli1RRkiAoqI6KBau3IKtlibQ65b6sFSssldotBbLWUopUuQ6ycLKxSYOrTkWfkYPZ0IBnFYJux55ZLL2jjFvs/o8/H4OZwfj/wwBZtfx/wS2b2Xkkvw7nACvg5C2qHIz+b27kA33fiCbZv2WJlZlN4hbhBNcYya7lkZYwlEq10cZYQc3HWS+cq+n5mAS6bm5F6qV8v6KLFRaBFvU5hqWWu2LKwXCa+zcjKC0SdTF9Alrmz16sWzojBIsTlRqyENm6xH4u/S7oL8NIWbV8JXGlm7/Xf34wjly9IOt7MrvZS/ktNRLMxHNLgokj2pcgYwz+Jz9R1EP0WWS6JrD5U61CWqWuZdzpWzTSb159gteRRSvXMFM7SjOVSWHdRKrdbHJ9fV++yN0QyWixzYex9EWUBSd8KnGRm75B0LHBgZl9rs+0y2v9XAv9h0Upm9nlJn5P07Wb2MeBBuElvPoKbde0c//7WVntd8s8erOkfXGGV90lBNGmGlBVV6Y58gtz+NAhW5kGwcrG22Dw0bbNcbUu77Uu3WFzrUlbqOwWCjCxKRw6WS6a8jMX431UhG6+C0PJkdHWHdkmw3DuJo23G6BZD0lNwoYnbAN+Gm075VbixfCHaxFx+h9IhkgHfA3ygZf9+CXi9zxT7JPAk38aFkp6MmzHtcQtb0QZIYtsupohY4oHRIhdPmYackQb0Y3HHYK0UMYvICuijm7C62OVcq4W476XVEtSR00LK4r+0aVVrLbZevNViQXl6TQP7WgljqA9OA0CacbmneDouDPJeADP7hKTbt924jeVyefT5CE7Xv1XFvpl9EDi55qdWzFdig3IM21JImRRPWqQr5kbkmkEVn6o7QzRl3KJCMCvW/ClbnaDa/qsxIZbZY4oyxkIcSmDu7IQAv8VWSpwgEbnGOpZwbSdGy6cnVN3Ne4wbzOzG8IAk6YCFkdcSbcjlVmb2sniBpGeky9aOroP+0C+OrGYelyQ4XZF+STKo8iKwX7rFKgN0H5ZLlOm+LCeHJub9XTPZYlHWWKXOJdS0eFeY69e0eq5i91iU5o3aMe0yFrS1qNwfrPt2VzH08aMfvFvSrwPHSnoI8DTgT9tu3OYMnl6z7Iltd9Ab4qfONq9NIAxO63jNHFNZPFlMjhUXCBKyp6ouMre87HIeWS2WDtZzXouQW7dXCsubX/kMsZSkMtNOek68RE514rBZK0Zex23Raxmsq91e0fX+2ubXijCvftHm1erUSqdI+pikK3zhePr70ZLe6H9/r6S7Rr89yy//mKSHLWpT0om+jSt8mzdZ4VSciSsn+RCumP5twLPbbtxouUgKU1yeKOmi6KdbANcu1dVlIdo9Gu/S04ZiovEDYzYpM8XiVGSbjbkEaZQ89wWUkVhlSEfu4gnqowYmRlqMOTegn+NmoPRB/dwH9Z17LMjcZC4Z2We2GxMQRZA/tvqc/Es1/sKEfuQJRuwGenIxSpoAv4ubNvhK4DJJF5nZR6LVngx82czuJuk04EXA4yXdAzgNuCdwJ+Adku7ut2lq80XAb5vZBZJe5dt+5TJ9N7Mc+B/+1Rnz3GJ/B1wN3A54cbT8a8A83Zk1YIMxl3Wh48UaUpCL2oxo+zJIXbrDAJ8lVj7Rx4KVRJ/DGJq3ZJesRd/bElVTU3O316wlFWIuM+3486HINRwXllZSkaEM6k8ZyWMehn7/dUSPMZf7AFeY2ScBJF0AnIrLmg04FXiu//xm4BVygY5TgQvM7AbgU5Ku8O1R16akj+LqD5/g1znft7sUuUj6ELMxlq/i4vAvMLNr5m3fSC5eAuAzwA8s07He0WKA2wr3Ql9IAvouqD8p5fYj11hOVEQZYiyJYGUQq8y9S2yaW+uAfhtxlNb3YkNT8whsmrv200JKMwoBy4kycibIzJFRUCeIUpFzHTDx51GSK6Y8krW3XFxHWx7oiOGi+tC2ALeTFCc9nesLwANOAD4Xfb8SuG/SRrGOmR2R9FXgtn75pcm2J/jPdW3eFviKmR2pWX8ZvB332PUG//00nD7k54HXAj9Wv5nDMnUuG4c2kYq8SbQZieNU5JCOXDZQptfGQpRp5liD/EtpubTrRhvMI6o2hzvPippIldgLlCQ60w98tlg8+ZjiydSqlkvhHjNG4miDPbFgOlguXzKzuozYXcCDE1n9DwWpfUk/vWjjQZDL0m6xIQ8WSbpsIbEfWy4hvhKRTJEtFglWms2KVVrLmMsioUpoYVQu0E9d9DdNMTdbZBQvCunIuWXF+7SIueSYCcl8gaki2f3YEjxAOsLSqciLJqJZFmNK8eFC9PkfXAXcJfp+Z7+sbp0rfbrvLYFrFmxbt/wa4FaSDrz1UrevLphIuo+ZvQ9A0vfjbHxwZSlzMS+g/04ze5CkF5nZ4UviD5koUrQhyrimpU7mpSCYamZUXOdSxlwi6yZKR24zoLYpAlw12L/Igpowm7XWlMXmrJkMUaYjB5FP9zkQjRewLFyPPU30tQfEsFNehBoEvb6ecBlwkqQTcQP9aZQxkYCLcFm57wEeA/yl1128CHiDpJfgAvonAe/DXcwzbfpt/sq3cQFdFFDqcQZwnqSb+31eB5wh6WbAby7aeJ7lcrykHwQe6QNGlbvGzNpW6feDdZrj2zggxE/YRQrtpDKNcSH/kmaL+VhEOb2xyxTLi9ReK6yZxZg/8rcZZ+aRTxvymk7ds0XurRaX9Ray4oL1krmJwgq6ddaIO19HCsulJOysjLlkQv1MG3542BN31abQV0Dfx1B+EbgY95x0npl9WNLZwOVmdhHwGuAPfMD+WhxZ4Ne7EBf8PwI83cxNWFTXpt/lM4ELJL0A+Hvf9rJ9vwy4l58+BTP7avTzhYu2n0cuzwH+G860ekm6XxarIveHWHBwCOjjwqzUu1TdgkVBYGSlQFT/EdW3zEwLXLjEbOUML+g+s29KRm2tp9wMSwpBay0XE7l84WVkuZSxlljlAM9aGdSLc48I2CXPQQv0Kf9iZm/D1YjEy54Tfb4eeGzDti8EXtimTb/8k5QZZStD0iNwqdDHhAdBMzu7zbbzssXeDLxZ0n8zs+f30dGVcJhPZodwYxWV5EV1vhekzCaFO6yoTvfWC4RMqkg1OMquqigL5+0Gdteme+9DJ2s6DW112crIpJliyjw61pCCHeRfcoG8gGcp8FlaLk7Asnzft8GzwGjx1GCUfwHwdTI3BR6Am67+MTi3XCu0kdx/vqRH4maVBHiXmf3ZEn1dDYc1wB8WIoulJJoJZabYLMFANWMsDL55hVCiwbmz1dHn0337/zPPnXFRtVoiKwb/W1zPEr5HUyAHgq5L895by2VIHoENYpTcB+AHzey7JP2jmT1P0otx6cmt0EYV+TdxZtbr/aJnSPpBM/v15frbHTbUJ4lV+lxxialysacxl0qNi8XWS3WiLQjxlvBqeRh+113JqHI4S7jDyv2rQooQEUxEroUkTOgvcskAkSROcS4DqQT3Y01B5ogEQ7wHl4Cp14D+kPEN//5vku6Ey0Y7vu3GbVKRHwF8j5cCQNL5uEDRxsjFpQau+cLeNrdIFMwvXl7PqJB9idKOYyXkHArByjh9dzr1Af1iJsqWA/wShY8ppg3pyO2aMLJI/iWkVOf4RIWsnH1TMtdfhfjLBCOIV05KK1AZNpmgaZjjZYcsl227lgeIUXIfgD+TdCvgt3DTrBjOPdYKbetcbkWpJ3Y4E9rv6g3TRJpRADpNaCjna0nkX6yadhy+x7NPdpHcX8Tni8ipD9mY2GqK+zuTmpwUjga3WPp7abnE5zdzAmYjOmOQHoUW2NXj6oj/20vP/JGkP8NNc399243bkMtvAn/v86eFi73MKHuuF0sWUXbaxZaRl3+yji2YXD4VWVVX0DQimRDczz2p5LHlUsRcrHCPzYMtKH6E+UH+XmRjPEEqpCJPg9Wlgjin0eeM0i0WCkwnXuyzsPoiS1BBBWHoqcgB46DYC0bLBXB1N98H4EnmBkkfCMsWoU1A/w8lvQv4fr/omWb2+eX6ugK2bfBfJxLp8CIQHb5Tzj5ZtVTS73XFhxbVuzR3obXsSwNBtc0sa7Ke0jHS7ad6bHH/c7w8GCKL3GIx0USdiyyXPQ/obwoD8jwMNsbbEyTdEadJdqyk76W88Y7DZY+1Qiu3mJldjasiPRxsIuZS2d/hX1iWqRCqjOVfKkWUPgU3LqIM8ZZKmm5hvViUMWbYHHZpMlrUnnUWrjKvqdhqMvlal9zIc1VkbEIdT+kmNHI5gjGFeFRWBGnzKO5CNnGV+vmepSJvwfW97dhzy+VhuDm70hrHr9Eh1r7b2mJDRo3cS/E9BPNRYpWUlks53wnF94DcrLEIsdh9w701j5DKrre7MZuaarN5JR05yZoDZ8EotnRSyy8VsNy362tbsSUeirz1BNy7BzM7Hzhf0k+Y2R8t285AyMU9yW8l1jUoSf7JOpIsCYWAafptYcV44slnM8VCZX7upfYtN/IO8xxnHc6/LVC7XDR+pFbTZBKy3cR0asWkZ4FgqsWUWXFWwrQEbkqCI+7cZJNK/ZAroDyAfKEO3/5hbwm36obeN0j6tbrPAWaWKrbUYi65+FnUPmxm39G5h31jzy70is+3KAKMqvDjjLFALInlEp7soRpjCTUuXeIlfRJRV6HL3Gbn4y7UBoisNMr1Qkp2iLvEfvRCDiZU6MPeXV9bjUP+L4y9d4vdoo9G5pKLmU39PM3/zsw+28cOl8LQtMVaYm7QUGqcHKyowC/eS8JxMZesyBTLTT67ylsx01Ctb3OKIsvRfxkB3Km3XPqQi8m8YmU+hWlmzkpJlAZioq1aLuYtl+i8aVIha0m+3mXlru4VttaT0BP2mVzM7Hl9tNPGLXZr4MOS3gd8PerAI/voQFvsXfaG0hhBRDB+rpZqIFs1lkuZVRVbKpaXVfqNu/fEsExVfiCkpeZIoUpKeW4VS6iqkaboPARrxXxVftVlmFouZf2QX7bjg+XWYCD38T6TS4CkOwO/A/yQX/Q3wDPM7Mo227chl/+2ZN/6xQ5aLvNQuMEKocWgKZYl1kv55B5LvcQSMPjloSo/fG4KzivT0sQAkOer/VephllZ1xJceqrMpplH5FqkIBNZNLHFF+uPxXEXMuc7HMjgt7PYivtcI7k4/D5uiuOg2PzTftlD2mzcps7l3ZK+FTjJzN4h6aaUs5FtCPuVLVadJKx04aTusNqYS0Q6sWBlQSpTF8g3nzFWi6mtlJlrWPuU5brdT6vWS5aZ6/eBS0WOhTfjlOQckGVu/zIUnyuykmSUkeuATDc6t1g2QfkURj2ppbFLngWDQmV8z/EtZvb70ffXSvqVthu3Ea58CvBU4DbAt+GKa14FPKhjR1fCLl28rREF8YGCYFIUgWviJ3y/TRTQL9xiUY1LWJbGRzrE7wvEfNImZTlGSkax5ZTnYjKhiLXkUUGlVVxjKoohHdESLY/ci2kaMu7capEeDnt6He4hRssFgGsk/TTwh/77T+LEK1uhjVvs6ThV5PcCmNknJN2+ay9XgtgSc3kzsMgVVgT2o+LJ3DIftHevSr1HFIsIgfwyiO+C7WF5Pi0HU0ukWpaxPOIM5M7B/GjjmV1nFNaW+UnDgpxNHjLG/LFPTUyCHllIR/YyMKVrLMxKGVkt5C7YP6J/DJCQR3IB4OdwMZffxhl0fwc8qe3GbcjlBjO7MQwWkg6AJZ5rtwuDeAKts1xqpOEDscTf0+LJVAZmEbpYHnVE1DZmU5v2nGyaRW68QIzlfqpZY+BiMqpYMFEMJjmf4b2N1bJVGML1O1io9j7bQ/zbKolbbcjl3ZJ+Hacz8xDgacCfLrvD5SA/Udb+oHiyZjYNOQhTTuPCSataLa54Mi42tCjukruXWa22V+dxq2J1dLsp21hMOSoSEIrC0GmcBRdEOkVmIpfh5mfJMFnpOitiLhMq2WISlh3UEswgHkJ2GYfgsTCoTB++Lki6DfBG4K7Ap4HHmdmXa9Y7HXi2//oCX0GPpHsDrwWOxU15/Awzs6Z2Jf0U8EycL+hrwH8xs3+Y08W/lfRp39YfmdlXuhxfmzvnTOBfgA8BP+8P4tlzt9glVGYr3OCL2D0WE0z1Lysr1Mtl6RBZKaSMHvubHtYtr3+1Qe5JbNGrCZbb7Cu4w6yc7Cw+rvRY06fOSgJEfG6hIq1TUUxOrMadQzyVwza/DgNG4XJe9FoRZwLvNLOTgHdSozbvieIs4L648MRZkm7tf34l8BTgJP86ZUG7nwJ+xMzuBTwfOHde58zs7rix/p7AByT9mY/BtEKbbLHcTxD2Xhypf8xWyVNdFi1u9J2amjQmlro05GQysEK4MrFagsjjdEoxSE9zYzr1rqakjmQe5knwd42xpHL88/7eLJKrCZOdldI28oKcIs/kLCefrkwGmYlJiEcl6cguY+zIUgNZW+JZ5G7baQIbMDYUczkVuL//fD7wLpxlEeNhwCVmdi2ApEuAU7xS/XFmdqlf/jrgUbhpiGvbNbO/i9q9FCdMORdm9j7gfZL+O07E8nzgf7Y5uDbZYo/AZYf9fzhz6kRJP29mredSXhXGwIijhwGjeKKOLJfit4RgiuVWfXIva0HizCuiz1Z5b0Ib8mlTkDl3+3lj8KR07ZX7q89oy01uhuiIvCo1MFE6MrjvknOfrQM7QR5Duvd6QaeYy+0kXR59P9fM5loEEe7gFecBPg/coWadE4DPRd+v9MtO8J/T5W3bfTKOiBoh6Tjg0cBpuEzhP8ZZT63QJubyYuABZnaF3+G3AX++qGO9IqqkXje2hcQKS0UZhNoMXJZYXNuSR/EGCG6y6tO9+SyxYK0UrqaWQfvpnGLLlkdTu7StxTSdgjKX5Tb1FkxuIZbijxkfj8HP6aJAQBlmua/9mVTTkSPLsA+pmq3ALpDZIcPoZLl8ycxObvpR0juAO9b89BuVfbpYSe9POHXtSnoAjlx+eMHm/wD8CXC2mb2n677bkMvXArF4fBIXDNootmXQ7wsLn2jD4Mes5ZLHemJJ5lSo0oeoiDJexw/MIbV3EeYNuovIaRH5tBHDDARkSX/LmpeqHIwEmHnJ/ar1Et6Lc1oUq46ThbXFrt2HTegrW8zMHtz0m6QvSDrezK6WdDzwxZrVrqJ0cYFzZb3LL79zsvwq/7mxXUnfBbwa+M9mtqhm5d+vEgJpJBdJP+4/Xi7pbcCFOFJ/LHDZsjtcFjvhXgho4yaqBJajoD7l03qhp2XJsijIn4o8Bun9tpL7ywhXFscwtZUtgmluTA4y32/z/a6SSnnsznohxF1U1V3LiV1iVctl/1w/S2CX7sEF2FBi+kXA6cA5/v2tNetcDPz3KIj/UOBZZnatpOsk3Q8XD/9ZXE1KY7uS/h3wFuBnzOzjizq3amx9nuXyY9HnLwA/4j//Cy71rRW8bP/lwFVm9qOSTgQuAG4LvB93oDcuaGWnb/464gxZYRVdrHQOlzigH0nAQEImVrVW4tc8hNkfl0W2okZZKZ5ZklSlriWPrZbSJZhhIJUFloFYKunIWcX1uAaPxE5jly2YkO6/AZwDXCjpycBngMcBSDoZ+AUzO8OTyPMpH+jPDsF9XFnIa3Hj8dspQxW17QLPwY27v+fvpyPzXHqropFczKx1JeYCPAP4KG7+ZYAXAb9tZhdIehXO9/fKRY3slOXSBjVP0zN6YnGchTo3UTUNOQz0eWS11Lm2gjtrGWJIFY27oqqAHPx7FEH9EG8p1wkZcladz8XHX8K5gcg1FoL5cTKEhGqOd5cH0W3DNt3jmyii9G6pGRktM7scOCP6fh5wXsN639mh3TPidhdB0m1buM4a0SZb7ETgl3AFOcX6bSo3vWTzI4AXAr8mN/I8EHiCX+V84LksIBcXYNueC28TiN1ixdzvFotXlqm4pRpyJOoYPeGHNOSiENFbMNOmGSNXEK5cXbRy1pWWZVQtriBjY1XLraiF8aThvWOlm7Aiv1/KwGBH/PXlaGibBrlBYYeIeJR/AeBSSR/EKSG/vaubrE1A/0+A1+Cq8ru6Il8K/F+UM5vdFviKmYU5ZeP0uQokPRUnmMmdj6/LpOsJW3xDuAt8NgV5Zj2rPmlZZLGEp/zYPdYGXYyOlEv6lo7Ji+mZPUFGRZSpW8z9ZMXfGp+z4BYrlqu0ZGTT7SSVLb4+dxYNae57iLsDD8ZpjL1c0oXAa9vEa6AduVxvZi/v2itJPwp80czeL+n+Xbf3ueLnAnzPPb/DFt1kWzkwrIJYat8H8/PELVaZgdHfDNM8pCaXcYki/TgPT/25S0vO8woRLGtxhNpKLTVtpdv/3F1nZZZb0BibSVIILkFc4WTgp0zJ+cJZgnG2mJEhtXtu2rnrbCDYpOeiYyryzsJbKpcAl/j05f8JPE3SPwBnLkpPbkMuL5N0FvC/gBuiHX9gwXY/BDxS0sOBY3Axl5cBt5J04K2XOH1uLgZ/Uy9RAW6qaooFxJOCxUNiEV+JUpGhWjhZTeetPp7NmzysVZ8bpq1sQzrznhQnBIKM9lVYYUlcyiBXVdco6K9R9+4nC9s3t2sTxvPgMApXupgLboKwn8Eldf0SLhPte4A3ASfO274NudzLN/5AiGKj7nsjzOxZwLN8J+8P/B9m9lOS3gQ8Bpcx1pR+N4sNuwcOm8zi+pbCcrGMafQUXkq91GSJ5dVsqunUigJEN1DnrV1kNMRm2opUWl6vG9OWtKa4bK4QJ8qnVhyfWfoSYORypSt5JQEim0lHLj6vlnV5+BjdZz3CicKO4D3AHwCPsurUxpf7ZKy5aEMuj8UV0yxIF26NZwIXSHoB8Pe4eM4C6NAH+00jPd5KTCWpbQmIs8PqvhfbR6KQdWg76DeRU3vSac5UW7htZJ0VUx37eEv4PUjwz2wbWS3FeQ7R/0pnxgFmFQz1ng1ZhiN4tpldGC+Q9Fgze5OZvWjRxm3I5Z+AW1FfPdoKZvYuXFUpZvZJOujTFG3suA90CRuO/wAAIABJREFUhkzkgvkuWyyLYgalpL4VsRVFcQclBYZV2Rcnte/VhRvIJSxfPgazwva18v05+bScMCykI08T6yX3Vpzk5F9yRRL9Sa2Li7uomDDMzZG81OHuF/aEcIduyPaEM3HF8zGehXOJLUQbcrkV8P9KuoxqzGXpSWQOA0N8ipoRrLR6Qb3UQqlki+Xle7A00kB+4/5XzfpquX0TCYX+Zr7OJU6jLtepusXi5RkUKcgQWzO+f9vGJnsycA8BW3dtbBCS/jPwcOAESXEy13HAkfqtZtGGXM7q2Le1YFlyGGoR3KzUflLjgiqB/TiYnw64cX1IHrnEukruz8Ua9TLyLFUaiLLgZiy10hVWWjSpqkFapX+4wpVDfPDZaYypyP+MU1V5JE5FJeBrwK+2baTNfC7v7ty1nmHaTpJY76BQI/VSSUUuB9MwgEJitUQ1Lu635Km/peR+wDwS6lrNHw/m7ayonDzPIlIx6pLTnMUinwDgiCaOTRUSMMX+A4Hv1miyz0/eq8KAPN/f8+dnp/wHSa+PahI7o02F/tcoo6I3AY4Cvm5mxzVv1Td2KaDfMmBdU+NS/BZlQVUUj5Oaj7TGBajUi7QlhFjjqyuaCKkLGQktdIeFcyILMjAqZPmh1BgLtS7l9NFZIXC579ide2x1bGKa422FpAvN7HHA39dNA2Bm39WmnTaWS6iux8u3nArcr0Nfe8Lu/tm1wpVxJXlcLBmWVYhEySBLkYYc5nUpdbmIZnVcPMBrBfHJPoQvwfc3q85DU7j1ItdYxWrDpyJD1RUWv2LX4yhcuRDb6D1YF/Y8oP8M//6jqzTSJuZSwFds/okvqpyZ73nbMPQnsdS1EbKdZtarSTkuXWHhvWq9FBIqkW+prthxlaB+J+ukZuAKxBR3KxBk2T9miMXtO7gMLToHs0Kgy2KfBtrDwmHdv9Zwn+0LolksfwK4wMz+eZl22rjFfjz6mgEnA9cvs7NV0PVCG/rNn7psCnn9osZl1lqBUFAZLy+tlFA8WT79Vwsps4YK+/ZYYTCYs2meQxZZXYVAZR67/8p6l4wy1hTPbVOR369MwqZO18vQH1q2H4d8744B/YBb4KRfrgXeCLzJzL7QduM2lks8r8sR4NM419gG0e3m33a0eWIuJwcrs8SK3+KBMhGsrL5b5R2qlkhaBLl6UeQsObXVG5tnIWmiggwDXM1LTTsWpjmu/hjOX1zrAmVsqwwr7iN2597qC3vuFgPAzJ4HPM/PXvl44N2Srpw3u2aMNjGXJ63Yx14wtOyXVZ9uK/IvREWUkRWTztsy8x4kYPLSgiktmXa1LuCKIpeW0Z9WpV/aElUM83Efy43pNE/iLbOzUoIjEZn5WFNi7aUxGAntiRtktLoWw2CUf6nii8DngWuA27fdaN40x8+Zs52Z2fPb9+3wsQs3VTzxVXX5rBmfJ1ZLPFlYLL3fthq/bfB/EZaxjiw3p15Z00aodQnnYFIsr77D7ANKX9bwLlxb24bD9lSMlgtIehpuFstvwVXlP8XMPtJ2+3mWy9drlt0MN3PkbYGNkYux3A08NGsnRmm11NW5QBxziSv0C0mUPP4tybJKCimBXua7XwX5nL838zUuRQp1XrXK0thTaGqai0kGeVTrUj2fPtXb2qe6H/agN3QM5Z4cyQWAuwC/YmYfXGbjedMcvzh8lnQLXHrak3Bqxi9u2m5dGMpF2QXzBrRitkTKAHRAPF9LWufifg/fq9bJzOfkDqrL7upCOCsJUc7V3C/dYsX6DXU6IR41M4FZPGFYRCal+3F/R5NdvLdWQVyUvM/wyvZIuj1u2pSw/LNttp8bc5F0G+DXgJ/CTUn8fWb25aV7uyy0S0WUs6idXTIMfvHkYDMZYjX1LdHnMK1xpcbFynhL3iI7LFtmAjAPSZ1SmWvbyFwxpBJry3KLCLac8rjQFCNI7kfnBOprXUx7P8Du8v21DDZhufjx9Y3AXXGJUo+rG18lnQ482399gZmd75ffG3gtcCzwNuAZZmaL2pX0/Tg5/dPM7M1z+vdjwEuAO+HiLt8KfBS4Z5vja7yiJP0WcBlOT+ZeZvbcQyGWDaDW/bTBV3O/qn9PPOlVZb2amMtM5liUbZVHT/3zpPcB8jxv9artf3BjLXjNQ9q/QJSVfURz19Qdfyz9Umn7kAilor6wJa9twrrupy6Y5u1eK+JM4J1mdhLwTmpqBz1RnAXcF6cmf5akW/ufXwk8BTjJv05Z1K6kCfAi3OSPi/ACXMH8x83sROBBwKVtD26e5fJfcSrIzwZ+I3KPCBfQ36D8y3aZ7pu4GdMbJqTQ5okVE2dKQVVqv1JAGZ72m1xkS1oYwe3VxgpKEayihcWWOVF9Tl5aLTV9jt1iFSsujlVRyukMxS22Tdf/rsOYfRBZE04F7u8/n4+bluSZyToPAy4xs2sBJF0CnCLpXcBxZnapX/464FHA2xe0+0vAHwHf36J/3zSzayRlkjIz+ytJL217cPNiLlv1OLNtT1d9Y14mU0g9DsiZU5UeSevHBZTlOla4xNpU0C+KucytT1kQb+nilgvHUuw3KaRskn8p1y+Xl3EXVYpU9xW7fm91RnJfLcDtJF0efT/XzM5tue0domr4zwN3qFnnBOBz0fcr/bIT/Od0eWO7kk4AHg08gHbk8hVJNwf+Gni9pC9Sn+hVi07yL0PGEAePkNFU+V5z0VcG1fCeh9880eTV9ONSCmaB/EuHuywlolXngwFHQHHcJxWwjGNOM0RbWCz+WFMCNy1VPzgOxu0wxHsuoMOl+yUzO7npR0nvAO5Y89NvxF98rKR38zlp96XAM80sb5mocyrwDZzM/k8BtwTObrvvQZBLn77U1vs87Dz7qDK/roCyLoBfbBvSc6MCyhl1ZKtWvLvtlnMiq617q27bUCk/L+5DTpZnlPO5lC6+Mn5UzuuSUc67VaZtly7FvOJyzLbKLTbkAXkdOAwid26xntqaU80u6QuSjjezqyUdT/1sv1dRurgA7oxzc13lP8fLr/Kfm9o9GTfFPMDtgIdLOmJmf5L062446+dv/aIcOF/SD+Mmj7xmwWEDK4lBbRaFC2NDr8NGRe7FE0vxPalxKZbn6dO7FcvLdUp3WB4G6JpXp77m+cyr9bYdA/wBuc1aMNV2q+cmT34rPkexl/C+jckdh419SzRILeKm14q4CDjdfz4deGvNOhcDD5V0ax/IfyhwsXd7XSfpfl6t/mej7WvbNbMTzeyuZnZX4M3A01Ji8XgpcF3N8q/631phEJbLMkgzrYaI8JQdEGaeDAHqwgVWxFpii6ZMPYaqKyxfQALKsqWl8kuZ/OWtoBmCycv+z7jFYussF5aVRKKEgM1S8ihrXVBWZeEIoxusim0mwV5gvWSCtcE5wIWSngx8BlcNj6STgV8wszPM7FpJz8dl7gKcHYL7wNMoU5Hf7l+N7XbAHczsQ+lCM/uQpLu2bWQw5LILZJFifhpy4gprWLcpBlP9Xi5okl+prJ8QQ1vxSaCWlLpMo1wrfjmZzLjxAqnMbO93Hxuf8VNmJS1Z/jzL6ZDtMonsPCH0CKP+2up9P2bX4NJ70+WXA2dE388DzmtY7zvbtpus88Q5P99qzm/Hzms3xoDIZX9ujpRM4iLKtHDSZqyWYJ2UT/vVAspyWdtssVVjMatOGGbmsttyq1ov5as8B7LS11u1WspzWisDsyUxl01jG1zA24i+Yi4DxeWSnmJm/yNeKOkM4P1tGxkMuWw71kF+IahffG/w8+bJ8rjGpViW50sN8vMIaHGa8nxSamMR5bmRkcOkTBrochhVq4Va4c9tx0gAJTblwdhzcvkV4I8l/RQlmZyMm+b+0W0bGQi5bHewc1nMdYtFT9c5SgLSDQH9KEMsfE+LDSuThrUcpZvShNsG35tIqLVFlE1mK/WDBVbEl1Qef+YlYIqYlCKV6NnC1G1J4ugLu+hC3iTS+2rfYG5CsB+U9ABKt9ufm9lfdmlnIOSyeWwjmaVZY8XyGotmVnK/OrVxl7ThVeX2F+1rkQWU50Y2KT9XYy9WUUae2TbOGEvlX5asc+kT+0IE23g/zcMyafW7BjP7K+Cvlt1+EORiDO/ibEJbWYnKk7VVtwv1HCFLrFxuFRdZcIPVEYz73t5JtMiFtUrB5ELyIYoXxXGjBjLJvPUSSsdS11iIXxUB/aRYdWjYlXtjm5DMcTdiCQyCXNaNDekIrYx87mRhVnyGknSK9OM4YyxOS04G9qZJu9oQ0apTGje63/Kcymxh8W9FYoP5AsqQCg2mNBbl3sORpLVEWhDUHwfxErt8LnqqYdl7DIZchkIAbdDmxqxMbTyTPVa+0iJK93vVYiksmETBuC4teV6q8qIpittaQk0k1Eg6E0XClWVVftv5XGLLL5zHUrgyw3zN/tAGzKH1d0jY55hLXxgMuayKXbgR08rg4kncLEpHLoklFBdCGtRfXERZhzY1MrAaCbXVNwuEGSRg8lyOXLPQ17KIsmynKr3fxnLZhetmVezjORgtl9UxGHLZxQt8np+/Uodhs4H8PCGYym/J2F2Nsyy+a2oLGbsUUvZs/SibeFmafCaYP7O9XxTvJsSn3GdV1gvnVxqe5RIw1H5vM1ad5G7EgMhlVQw5YBsQBsJ41kWgWkTpx96yaDKsE6kimxUFiU2YCbr3FPxfZP3UkY/lVgm5VDLf/DGG8xFWiwsri32H36JiylxiQr3lsu+D9i65orvAbGPyLzuNgZDLsLN5uiKezKr83rBuzVg9W0AZWS4t7f14m0XzssxuO1/Gfx7qyGdCcOXZwnVzMzI0R/7Fv9e4xIZOJvtKBuvAKqoSIxwGQi7rxzYOLLNqyPWBxlJ6P5p9MhF5tMhSiac8buMCWynNuAeLx/KyQj+1uFyNSwjwz56rumyx2piLd401Yd8H7m28P9YFY4y59IGdI5dduQlmJfZrssXydkH2akZZXvu5sm+/vKvV4bbtx+JJ959mhzmCrGsD8sxm3Gsz1lwU3DdliOleEMiu3B9rxZiK3AvWRi6S7gK8DjfFpuGm/3yZpNsAbwTuCnwaeJyZfXlRe4d5U+SHtO8ZyX0fa5ldr+ruyiMLJs6qimefjCcNg/oq+VWtjlVnogz7z7OsFKNMC0F9fUuwYELJfXCPVWJTyXTGq15T+zxQ77ab2lpnRo5oxjqvkCPAfzWzewD3A54u6R7AmcA7zewk4J3++6EhL7S7ml/bhjIFubq8HGDrf59tpzpId52wq9LWEhOFVbefn2CQos2qTYdR0Wlj1kUW/zbEib2Wgav3af/adVje7jWiGWuzXPxMaVf7z1+T9FHgBNy8zPf3q52Pm7LzmXPb4vCshz7Rxe1SpiGXk4TFbcSZYqGmpdg2TUUOBYjWfpbJtnL8tduuUExZTzB5EScK0wU09THIvyiqd3HWiyoW3WxAfzsskV0duLfh3LaFGUyno+WyKjYSc/Gzl30v8F7cLGdX+58+j3Ob1W3zVOCpAMff6YT1d7IB2+SH72JQ5FHwfuY3qw/od42xpIP7IgHKme1X2HfZRkhccJZbaCbIv8zddknhyl0lgDYYEkmsglG4cnWsnVwk3Rz4I+BXzOy6eAAyM1NDio6ZnQucC3DPe313p396mwhhWcxMFlaJvZRB/VRyv2LBNFTn132u+w7dBv26G7It4cyv2p/MzEfTND9NnfxLWA4hblUmSIS0b+0AYezLwL9uGKP8Sx9Y6x0l6SgcsbzezN7iF39B0vH+9+OBL7ZpK56NcdFrW7HIh5/68+t8+7WpyHmacjsbNzFf4d65z1Espe61cPsklrNMXCet05k5tqSGpbpt8+/b5mrtcn1sYwyoTfxyE6+VYZFFvOC1CiTdRtIlkj7h32/dsN7pfp1PSDo9Wn5vSR+SdIWkl8s/yc1rV9L9JX1Q0oclvXulA1iAtZGLP9DXAB81s5dEP10EhBN0OvDWdfVhVax6s/d98y9DnLXijtF8LrmPYeR5+3jMTFtLBvNXTSKAWNYlLbBsTtOuJaEW/0/f18O2kUMdNjqobxFiHb95rxWxMLnJZ9eeBdwXuA9wVkQWrwSeApzkX6fMa1fSrYDfAx5pZvcEHrvyEczBOi2XHwJ+BnigZ8oPSno4cA7wEEmfAB7sv/eOod/slboWVJnoqukCT6c3rpPVr2ST1cVjtohsYtKJ40RuP/VPjnVTPLvl1fdCCiZxkW3r9bAIW2sF9IAuXou+PBfpfdD0WhGn4pKa8O+PqlnnYcAlZnatL9m4BDjFe32OM7NLzd0kr4u2b2r3CcBbzOyzAGbWymu0LNaZLfa/aQ6XPqhze1tyofeNece17M3SdM0vY8bHN1DWsSjS7bOb8nJzGxPfn/bTMwcM0X++LQN7X9hmd3UKMyNvny12O0mXR9/P9fHiNmiT3HQC8Lno+5V+2Qn+c7p8Xrt3B46S9C7gFsDLzOx1LfvaGTtXob8pHAbZxSnJlb4kRZQQCVhGhZPF+g3yL4sG/EVPal3IZ141fheE9OqQkh2eZ0oFg3jdak1LtHpr7NqgvwhDIoU+0aGI8ktmdnLTj5LeAdyx5qffiL/MS25aBUm7B8C9cQ/3xwLvkXSpmX287/2GnY1IMFQrKZ6/BRbfIE3ZYssO9IF8VrFw2u677wrqHJFR4yYc6LXQBvtKHG3QVyqymT246TdJX5B0vJldPSe56SrKukCAO+NqA6/yn+PlV/nPTe1eCVxjZl8Hvi7pr4HvBtZCLsPPv2zAUGMtATOpyNG1HuYnya0+EJ66jaqpyItvmlXiJrBa3KYpIy1OQijWrSuizGeXpxIwlffoP9/WmEOKrjGIbc6q3MbECJfSv5GYS5vkpouBh0q6tQ/kPxS42Lu9rpN0P5889bPR9k3tvhX4YUkHkm6KSxL46KoH0YSdsFy2hRBWRd0N3+exLfs01pdFE6OTC21GsHL3dTe2ZfBfBUO+LzdUQ3kOcKGkJwOfAR4HIOlk4BfM7Awzu1bS84HL/DZnm9m1/vPTgNfiXFxv96/Gds3so5L+AvhHnJf91Wb2T+s6uIGQy/ZYFIvQ56CQPjk3pT+m8i9hWfxeyRhrKEBchK7TE8/DqokCZZ/KrLI8V1mh7wMqqcVX2bZX4h7G9bkshnL/9QEzY7qB2cLM7BpqkpvM7HLgjOj7ecB5Det9Z9t2/W+/BfzW8r1uj4GQy/Zi6INKbBV0lW+ptJPnhxKrmdtuA3/mS/5nQ/+v52GfyKMNxmmOV8dILjXY9kGkqNmYsVaqyxapts6LYSxDNJtMCLCOPu8mN0eZOeYmC9v2/74NdpkoNnVsI7msjpFc2H4yqYMVqcZt1q26xFq1b7a0JdNnjCYQTVu5jVTAcqbtsF6cMIGf5niA1wHsHpkc+vFYs9U7oj32glyGOGjEN1hOtxuur2DkvInEWm2/IsmAI5pJtPlSc80MeKA49IG2BwztGIzRcukDO0kuQySTGOu6GZeeyKsnkonRuUJ/Mim+L1vjsu0kM7xBeFj9bY/lte5GlNgZchkyoSySgNkWrDp/S6WtFRIAUgTumqcpts0Y2iA9tP52hrGRbLFdxyDIxaXg7tYF3UqFt2ZgrMt0SiX3YX4hZV/YCrdZkWq9xP7XeE3t0gC8S8fSBqNbrB8Mglx2Ddtws+56IeK8oP66sA3/a5/YteNpDRvJpQ+M5LJBrHqzLjWfS4MsfZ9YJbMM+nWRVdpd0/iwa4Purh3P6rDetev2ESO5jBixxxiJpR6j5bI6RnLZIISNN/PAMf5/uw+jf+t+HzGSy4CwhukeRnTE+ICwBzCYHtntmOQmMJLLhiE/Z8imBijVSKmsEh9ZB9YRbwFY12Fu+j9cJ0ayrMNY59IHBkEuUrun9iGlKy87QGVaYvrEuv1nGTadrtwObB9ZbQrhPwwY6iA9EkwVTqNvtFxWxSDIpS1SAhoC2aQDFJSDVFtSzbLZWpfUYqmzYFZFH6TSl9WSHt6m05Bh/n+57ajrOwyn/32jh4nA9h47RS4phkg2sL4nyT4G8j6tlD76k6mcw6Vr1zYRwxr6oL1LLsAuGN1iq2OnySXFosFkW8kno3mQqkPfXqptI5RO+1P958PG0KycuL/b3M8+YGbkY0B/ZewVuSzCNlk6XchknViFWPoikrgdSWQd+7RNpDIPQ4nh7APR5IsmQxqxEIfgmR4OJFv4Opx+gTL3ajN+x/GWtgO+pEMnlixTZeKwPuJGQ7rg3eTe9a9twRD62BlWzh+06LUKJN1G0iWSPuHfb92w3ul+nU9IOj1afm9JH5J0haSXy9+wTe1KuqWkP5X0D5I+LOlJKx3AAgzpXttKtCGgTRFRIJ3i+4J/NyWPQCjLkoqyrHgtg0AmKam4tme/181YKdUTbnpIYfCLB8JteoBYhCEM6POIZ5v7b7Qjlh6q+M8E3mlmJwHv9N8rkHQb4CzgvsB9gLMiEnol8BTgJP86ZUG7Twc+YmbfDdwfeLGkm6x6EE0YCLkM7wKtw6oD1zJjfh1RpG6mVa2UtM1l0GZq476Q1Zz3ef/FthNNjCHeFzG2pc9m1uq1Ik4FzvefzwceVbPOw4BLzOxaM/sycAlwiqTjgePM7FJzHXldtH1Tuwbcwls4NweuBY6sehBN2MmYy7IX5WH4j5sGLDORhZssWqeOAySRZVaZ8jgliywhkCwTXaas6DsQ3xeZKCvJMe6ii80s2HaJ62RVghlaHO+wYyqHQjAG+WbqXO5gZlf7z58H7lCzzgnA56LvV/plJ/jP6fJ57b4CuAj4Z+AWwOPN1hdc2klyWRbbFFBN+9LFsOi7puWwrZIZ912H/sSbbtA4asQ8ctrGbMVtuic2BcPI2xcY307S5dH3c83s3PBF0juAO9Zs9xuVfZqZ1mAaJ+0+DPgg8EDg24BLJP2NmV3X935hJJe56POpqc+bMlN4yQ+erp9ZFgYo/92PrGoIiivLZiqRD51IGvavLHMWStz/GsbNsrpYUkks4T6rWIPhfEX/d75FVuwibJKUhmj9dEa3+Vy+ZGYnNzZl9uCm3yR9QdLxZna1d3N9sWa1q3DxkYA7A+/yy++cLL/Kf25q90nAOd6NdoWkTwHfAbxv3gEui4HEXLoHB7cNffSzrz8rJZhVA/Ewm9nVvU/d9t81Hblxvw3/QYZVXtuMbU9AGOJ9u6GA/kVAyP46HXhrzToXAw+VdGsfyH8ocLF3e10n6X4+hvKz0fZN7X4WeBCApDsA3w58ctWDaMLOWi6rXqibetpq7Kco4i3CiiB0fczFt2TBYikzpsKA7wbvJCU5b2f69x1s7zN+42ItcqnZiq0an6pdd76YPZeLCGRdBLMOC6lPgtm0q247CMY2VedyDnChpCcDnwEeByDpZOAXzOwMM7tW0vOBy/w2Z5vZtf7z04DXAscCb/evxnaB5wOvlfQhQMAzzexL6zq4nSWXVdH1It+k6e80x8rXIiz7lL+qJdIX4rayhCTbIHWJbROaSOsw3HJ1mJdwsquwDU1zbGbX4C2JZPnlwBnR9/OA8xrW+84O7f4zzvLZCAZDLqsMDJu4Efp44koJajaob3OD0i5rKoolZLMpxi5u4QbrPi2SVclkUSp0FvXb7U+1JKMiDpUur75nxfLSOlyETT5ALGspbYqU+iDqbSaoURV5dQyGXFbBthNTQN0AF7vGmpCqItfVrbiiw2p9S5ez0rcrqy9kCgH7KqkUCQ9zCiq7DuDreIDoG6u47zZtLW2jJQmAdcoWG9GAvSCXVbCNT2hhQA1ZUOEZK61OD4N4V/mXdVshrdvx/Qj9z7LlCj5jq6WugHKT2GZ3a1di2hbXXd8wRsn9PnAo5CLpFOBlwAR4tZmdM3d91hdQTbEtAVYzeaslduGEtmZdXWkRZRnIV7FO8dv/3975x9hRVXH8891SgRQsra24KEFrSLWiYCGVNlirlQINKaJVqyYUUQmRJmJCTBMUQSWKRmP4EQhoKRhS669i09SURYxNlFag9jelP7CotbQqpAUxlpbjH/e+3eF1Zne67857s+35JJOdnXtm3tkzc9/Z+2O+V+LVri7U4hvG7VzPpdlOXV3F8i9xML9IETk7q0pxNphI0w1iiSdgVjHAnSphVV0nO5a8fLGwJLQ9uUgaBtwJXEh4q/RxSUvNbHO7fcmjLv+99fcS5Wve2+iC5u/FIk2xwSSDTsvC5F2jWcwyjC3la4pl809zLqqiW2awSSp1UuqPOreesnRuCniSacbHPJ1ouUwCtpvZMwCSfkrQwuk3ubRjiuJgKlFVFeAQYXC+K9O66JLlvnHemIrc1WW9L1E2ElCYptv3X37jd3UJvZq2+2rw5w/shzJ+Q6NrMOclSvUl17zusEZLsFm48kieryq+bFO1nGBotJ6g3i9XVqiKcszQieSSp5XzvmYjSVcDVwN0n/bm5uJKaFSiuj30dR34TNMqqSbWqV6yzKPoy7Yuz01Rompn66gMdY1jWCzMB/RbpbYD+lGf5x4ASf+ccOZbni0wHQNU9iJQSdyHPurgRx18gHr4UQcfoL1+nNHKyf/Zt3XFH5ZNG1PSvA6xrSWdSC67gNMzv2c1cXIxs7FFZZKe6E/bpx24D/Xyow4+1MWPOvhQJz/KYGYXD2zlDEQn2smPA2dKeltcqGYOQQvHcRzHOUpoe8vFzA5KmkcQZBsGLDCzTe32w3Ecx6mOjoy5mNlyYHmiy90zsEnluA991MGPOvgA9fCjDj5Affxw2oQSLNXpOI7jOK+hXnMTHcdxnKMCTy6O4zhOcoZEcpF0saSnJW2XND+n/HhJi2P5aklvrcCH0yX9TtJmSZskfSnHZpqkfZLWxu3GCvzYKWlDvP4TOeWSdFuMxXpJEyvwYXzmb1wrab+k65psKomFpAWS9kramDk2WlKPpG3x56iCc+dGm22S5ubZtODD9yRtiTFfIumUgnP7vX8t+nCTpF2ZmM8sOLff+pTAj8UZH3ZcNNDYAAAGO0lEQVRKWltwbpJYODXFzGq9EWaU7QDGAa8D1gETmmy+CNwd9+cAiyvwoxuYGPdPBrbm+DENWFZxPHYCY/opn0lYkU7A+cDqNtyf54Az2hELYCowEdiYOfZdYH7cnw/cmnPeaMKSrqOBUXF/VEIfZgDHxf1b83woc/9a9OEm4PoS96vf+tSqH03l3wdurDIWvtVzGwotl14tMjM7ADS0yLJcBtwf938BTFfKRUMAM9ttZmvi/ovAUwQpm7pxGfCABVYBp0jqrvDzpgM7zKxIQSEpZrYSeL7pcPb+3w98JOfUi4AeM3vezF4AeoBBvSyX54OZPWxmB+OvqwgvB1dGQRzKUKY+JfEj1sFPAIsGe31n6DIUkkueFlnzl3qvTazg+4A3VOVQ7HZ7L7A6p3iypHWSfiPpXRV8vAEPS3oy6q81UyZeKZlD8ZdH1bFocKqZ7Y77zwGn5ti0My5X0beeeTMD3b9WmRe75hYUdA+2Mw7vB/aY2baC8qpj4XSQoZBcaoWkk4BfAteZ2f6m4jWE7qGzgduBhypw4QIzmwhcAlwraWoFn1GKqLAwC/h5TnE7YnEYZmbQMa12JN0AHAQeLDCp8v7dBbwdOAfYTeiS6iSfov9WS22eZSc9QyG5lNEi67WRdBwwEvh3akckDScklgfN7FfN5Wa238xeivvLgeGSygrglcLMdsWfe4ElhG6OLEes3dYClwBrzGxPjp+VxyLDnkbXX/y5N8em8rhIuhK4FPhMTHKHUeL+DRoz22Nmhyzoxd9bcO22PB+xHn4UWFxkU2UsnM4zFJJLGS2ypUBj9s9s4NGiyj1YYv/xj4GnzOwHBTZvaoz1SJpEiG+yJCdphKSTG/uEQeSNTWZLgSvirLHzgX2ZLqPUFP5nWnUsmsje/7nAr3NsVgAzJI2K3UUz4rEkKKyu+hVglpm9XGBT5v614kN2bO3ygmu3S9vvw8AWM/t7XmHVsXBqQKdnFJTZCDOgthJmudwQj32DUJEBTiB0zWwH/gSMq8CHCwjdLeuBtXGbCVwDXBNt5gGbCDNwVgFTEvswLl57XfycRiyyPoiw0ucOYANwXkX3ZAQhWYzMHKs8FoRktht4hTBe8DnC+NpvgW3AI8DoaHseYRntxrlXxWdkO/DZxD5sJ4xlNJ6NxuzF04Dl/d2/hD78JN7z9YSE0d3sQ1F9SulHPL6w8SxkbCuJhW/13Fz+xXEcx0nOUOgWcxzHcYYYnlwcx3Gc5HhycRzHcZLjycVxHMdJjicXx3EcJzmeXJyWkXQoKtuuk7RG0pQKPuOlEjazjlTlV9JCSbMH75njOHl0ZJlj56jjv2Z2DoCki4BvAx9otxNmtpRqXgh0HOcI8ZaLk5rXAy9A75ouyxoFku6IEimNtTxuji2dDZLeEY+fJOm+eGy9pI9lzr8lto5WSTpMnFLSlZLuiPsLFda1+aOkZxqtk6hccEdcz+QR4I2Z88+V9PsopLhCUrekkdF2fLRZJOkLFcTNcY4qPLk4KTgxdottAX4EfLPkef+yIFx4F3B9PPY1gmTNu83sPcCj8fgIYJUFIcyVQJkv+G6CssKlwHfiscuB8cAE4ApgCvTqxt0OzDazc4EFwC1mto+gNrBQ0hzCGjD3lvz7HOeYxbvFnBRku8UmAw9IOqvEeQ3xzycJIocQNKnmNAwsrL0CcABYlrG/sMT1H7Ig4rg509KZCiwys0PAPyQ1ktd44CygJ0qiDSPImmBmPZI+TpDVObvE5zrOMY8nFycpZvZYVD8eS5Cez7aOT2gy/1/8eYiBn8VXrE+rqIx99voQNNf6Q8AmM5t8WIHUBbwTeJmwimWuGKPjOH14t5iTlDh2MowgavksMEHS8Qpryk8vcYke4NrM9fIWvGqFlcAnJQ2LKsIfjMefBsbGlheShqtvgbMvE1Ye/TRwX+xCcxynH7zl4qTgRElr476AubHb6W+SfkaQUv8L8OcS1/oWcKekjYQWys30dZ+lYAnwIWAz8FfgMQAzOxAH/W+TNJJQN34o6SDweWCSmb0oaSXwVeDrCX1ynKMOV0V2HMdxkuPdYo7jOE5yPLk4juM4yfHk4jiO4yTHk4vjOI6THE8ujuM4TnI8uTiO4zjJ8eTiOI7jJOf/Inz2sUFFeEkAAAAASUVORK5CYII=\n"
+          },
+          "metadata": {
+            "needs_background": "light"
+          }
+        }
+      ]
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "fig = plot_cavitydata(\"tracking_test.hdf5\",\"MC\",plot_type=\"psi\")"
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 279
+        },
+        "outputId": "43daec2f-4b6c-4ce6-ee3f-cbde41532d40",
+        "id": "vI20crgCMTkj"
+      },
+      "execution_count": 36,
+      "outputs": [
+        {
+          "output_type": "display_data",
+          "data": {
+            "text/plain": [
+              "<Figure size 432x288 with 1 Axes>"
+            ],
+            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZQAAAEGCAYAAABCa2PoAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjIsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+WH4yJAAAYJUlEQVR4nO3dfbRddX3n8fdHQFEejEoEeXCCCiqDEpgrA4P1IWIbUxWh0qlDGXVUxLEOKI5jyyyQdjlLS8HW0epEcdS1qI4LSOMQCgUnFR1r4AYDBgLV8amRKHFVnrSiId/5Y++rx8t9Osk+9+m8X2uddc/e+3f2+W52uJ+7n36/VBWSJO2uR811AZKkxcFAkSR1wkCRJHXCQJEkdcJAkSR1Ys+5LmAuHXDAAbVs2bK5LkOSFpSNGzf+qKqWjp8/1IGybNkyRkdH57oMSVpQknx3ovme8pIkdcJAkSR1wkCRJHXCQJEkdcJAkSR1wkCRJHXCQJEkdcJAkSR1wkCRJHXCQJEkdcJAkSR1wkCRJHXCQJEkdcJAkSR1wkCRJHXCQJEkdcJAkSR1wkCRJHXCQJEkdcJAkSR1wkCRJHViXgRKktOT3J5kZ5KRSdoclmR9kjvatuf0LLs4yZ1JbkuyJsmS2atekgTzJFCAzcBpwI1TtNkBnFdVRwEnAG9NclS77Hrg6Kp6LvAPwB8OslhJ0iPNi0Cpqi1Vddc0bbZV1S3t+weALcAh7fTfVtWOtulXgUMHWa8k6ZHmRaD0K8ky4FhgwwSL/wPwN1N89qwko0lGt2/fPpgCJWkI7TlbX5TkBuCgCRadX1Vr+1jPvsCVwLlVdf+4ZefTnBq7fLLPV9VqYDXAyMhIzfR7JUlTm7VAqaqTd3cdSfaiCZPLq+qqccteB7wceElVGRSSNMtmLVB2V5IAlwFbqurScctWAu8CXlhVP52L+iRp2M2LayhJTk2yFTgRWJfkunb+wUmuaZudBJwJrEiyqX2tapd9CNgPuL6d/9HZ3gZJGnbz4gilqtYAayaYfzewqn3/ZSCTfP4ZAy1QkjSteXGEIkla+AwUSVInDBRJUicMFElSJwwUSVInDBRJUicMFElSJwwUSVInDBRJUicMFElSJwwUSVInDBRJUicMFElSJwwUSVInDBRJUicMFElSJwwUSVInDBRJUicMFElSJwwUSVInDBRJUicMFElSJ+ZFoCQ5PcntSXYmGZmkzWFJ1ie5o217zgRtzktSSQ4YfNWSpF7zIlCAzcBpwI1TtNkBnFdVRwEnAG9NctTYwiSHAb8JfG+QhUqSJjYvAqWqtlTVXdO02VZVt7TvHwC2AIf0NPkA8C6gBlaoJGlS8yJQ+pVkGXAssKGdPgX4flXdOoPPnpVkNMno9u3bB1qnJA2TPWfri5LcABw0waLzq2ptH+vZF7gSOLeq7k/yOOCPaE53TauqVgOrAUZGRjyakaSOzFqgVNXJu7uOJHvRhMnlVXVVO/vpwOHArUkADgVuSXJ8Vf1gd79TkjQzsxYouytNWlwGbKmqS8fmV9XXgSf3tPsOMFJVP5r1IiVpiM2LayhJTk2yFTgRWJfkunb+wUmuaZudBJwJrEiyqX2tmqOSJUnjzIsjlKpaA6yZYP7dwKr2/ZeBzGBdy7quT5I0vXlxhCJJWvgMFElSJwwUSVInDBRJUicMFElSJwwUSVInDBRJUicMFElSJwwUSVInDBRJUicMFElSJ2bcl1eSzwCbgNuAm+3NV5LUq58jlI8APwV+B7ghyZok+w2mLEnSQtNPoCwDvgicXVXLgSuAiwZRlCRp4emn+/ojgFcDRyV5gObU1wuTrANuqyoHaJekIdZPoPz3qroHIMkTgBHgZcAZwPuA53VfniRpoegnUK5tg+RO4C7gWcBnquqcgVQmSVpQZhwoVXVckj1oguSZwA3AtYMqTJK0sPQ1BHBVPQzc3r4kSfolH2yUJHXCQJEkdWLGgZLG7ye5oJ1+apLjB1eaJGkh6ecI5S+BE4HXtNMPAB/uoogkpye5PcnOJCOTtDksyfokd7Rtzxm3/G1J7myX/WkXdUmSZq6fi/L/ur3T62sAVfXjJI/uqI7NwGnA/5iizQ7gvKq6pe3yZWOS66vqjiQvBk4Bjqmqh5I8uaO6JEkz1E+g/KK9bbgAkiwFdnZRRFVtadc5VZttwLb2/QNJtgCHAHcAbwHeV1UPtcvv6aIuSdLM9XPK64PAGuDJSd4LfBn4bwOpahpJlgHHAhvaWUcCv5FkQ5IvJpn0qf0kZyUZTTK6fbu9xUhSV/p5sPHyJBuBlwABXjV2ZDETSW4ADppg0flVtbaP9ewLXAmcW1X3t7P3BJ4InEDTBcznkjytqmqC7VgNrAYYGRl5xHJJ0q7p98HGO2m6XulbVZ28K5/rlWQvmjC5vKqu6lm0FbiqDZCbkuwEDgA8BJGkWTJtoLQ9C0/0l3yAqqr9O69q4joCXAZsqapLxy3+a+DFwPokRwKPBhwATJJm0bTXUKpqv6raf4LXfl2FSZJTk2yluS15XZLr2vkHJ7mmbXYScCawIsmm9rWqXfYJ4GlJNgOfBV470ekuSdLgZJh/746MjNTo6OhclyFJC0qSjVX1iGcG+xlT/h0TzL4P2FhVm3anOEnSwtfPbcMjwNk0z34cArwZWAl8LMm7BlCbJGkB6ecur0OB46rqQYAkFwLrgBcAGwG7O5GkIdbPEcqTgYd6pn8BHFhV/zxuviRpCPVzhHI5sCHJWppbhl8B/FWSfWi6P5EkDbF+npT/kyR/Q3P7bgFvrqqxW6TOGERxkqSFo5/xUB5D02fWPsASYNXY2CiSJPVzymst7W3CeM1EkjROX3d5VdXKgVUiSVrQ+rnL6ytJnjOwSiRJC1o/RyjPB16X5Ns0p7zGOod87kAqkyQtKP0EyssGVoUkacHr57bh7yZ5AnAEsHfPou92XpUkacHpp3PINwLn0HTBsolmdMS/B1YMpjRJ0kLSzymvc2iG1/1qVb04ybOYozHl59pF//t27rj7/ukbStI8ddTB+3PhK/5lp+vs5y6vn1XVz6B5yLEdDviZnVYjSVqw+jlC2ZpkCc1wu9cn+TFDev2k61SXpMWgn4vyp7Zv35NkPfB44NqBVCVJWnD6OUL5par6YteFSJIWtn6uoUiSNCkDRZLUCQNFktSJfh5sfMcEs+8DNlbVpt0pIsnpwHuAZwPH9wzc1dvmMODTwIE0A3ytrqq/aJctBz5K8wT/DuA/VtVNu1OTJKk//RyhjABnA4e0rzcDK4GPJXnXbtaxGTgNuHGKNjuA86rqKJqn9N+a5Kh22Z8CF1XVcuCCdlqSNIv6Gg8FOK6qHgRIciGwDngBzaBbu/xLvKq2tOucqs02YFv7/oEkW2iC7Q6aI5b926aPB+7e1VokSbumn0B5Mr8+UuMvgAOr6p+TzOoIjkmWAccCG9pZ5wLXJfkzmqOufzPFZ88CzgJ46lOfOtA6JWmY9BMolwMbkqylGQvlFcBfJdmH5ihhSkluAA6aYNH5VbV2pkUk2Re4Eji3qsY61HoL8PaqujLJ7wKXASdP9PmqWg2sBhgZGamZfq8kaWqpmvnv1CQjwEk0p5i+MtHF890qJvk74J2TrTfJXsDVwHVVdWnP/PuAJVVVac6b3VdV+0+0jl4jIyM1OtrpJkjSopdkY1WNjJ8/44vySR4DHAnsAywBViW5oLsSp/3+0Bx5bOkNk9bdwAvb9yuAb8xWXZKkRj93ea0FTqG52+onPa/dluTUJFuBE4F1Sa5r5x+c5Jq22UnAmcCKJJva16p22ZuAS5LcStOl/lld1CVJmrkZn/JKsrmqjh5wPbPKU16S1L/dPuUFfCXJczqsSZK0iPRzl9fzgdcl+TbN7cMBqqqeO5DKJEkLSj+B8rKBVSFJWvD6GWBrKEdnlCTNzLTXUJJ8uf35QJL7259jr/un+7wkaThMe4RSVc9vf+43+HIkSQtVP93XPwb4HWBZ7+eq6o+7L0uStND0c1F+Le34J/x6J5GSJPXXfX1VrRxYJZKkBc0HGyVJnej3wcbXJ/kWPtgoSRrHBxslSZ3oJ1BeO8l87/KSJPUVKL1d1e8NvBzY0m05kqSFqp+uVy7pnW7Hb7+u84okSQtSP3d5jfc44NCuCpEkLWz9PCn/dZqx5AH2AJbi9RNJUmvaQEmyZ1XtoLlmMmYH8MN2viRJMzpCuQk4zu7rJUlTmck1lAy8CknSgjeTI5SlSd4x2cKqurTDeiRJC9RMAmUPYF88UpEkTWEmgbJtNsY8SXI68B7g2cDxVTU6QZu9gRuBx9DUfkVVXdguOxz4LPAkmi72z6yqnw+6bklSYz5dQ9kMnEYTGJN5CFhRVccAy4GVSU5ol70f+EBVPQP4MfCGQRYrSfp1MwmUlwy8CqCqtlTVXdO0qap6sJ3cq31VkgArgCvaZZ8CXjWwYiVJjzBtoFTVP81GITOVZI8km4B7gOuragPNaa57e56L2QocMsnnz0oymmR0+/bts1O0JA2B3el6pW9JbkiyeYLXKTNdR1U9XFXLabp9OT7J0f3UUFWrq2qkqkaWLl3a7yZIkibRT2/Du62qTu5wXfcmWQ+sBC4BlvQ81X8o8P2uvkuSNL1ZPULZXUmWJlnSvn8s8FLgzqoqYD3w6rbpa4G1c1OlJA2neRMoSU5NshU4EViX5Lp2/sFJrmmbPQVYn+Q24GaaayhXt8v+C/COJN+kuaZy2exugSQNtzR/3A+nkZGRGh19xOMukqQpJNlYVSPj58+bIxRJ0sJmoEiSOmGgSJI6YaBIkjphoEiSOmGgSJI6YaBIkjphoEiSOmGgSJI6YaBIkjphoEiSOmGgSJI6YaBIkjphoEiSOmGgSJI6YaBIkjphoEiSOmGgSJI6YaBIkjphoEiSOmGgSJI6YaBIkjoxLwIlyelJbk+yM8nIJG32TnJTklvbthf1LLs8yV1JNif5RJK9Zq96SRLMk0ABNgOnATdO0eYhYEVVHQMsB1YmOaFddjnwLOA5wGOBNw6wVknSBPac6wIAqmoLQJKp2hTwYDu5V/uqdtk1Y+2S3AQcOqhaJUkTmy9HKDOSZI8km4B7gOurasO45XsBZwLXTrGOs5KMJhndvn37YAuWpCEya4GS5Ib2Gsf41ykzXUdVPVxVy2mOQI5PcvS4Jn8J3FhVX5piHauraqSqRpYuXbprGyNJeoRZO+VVVSd3uK57k6wHVtJcfyHJhcBS4M1dfY8kaeYWzCmvJEuTLGnfPxZ4KXBnO/1G4LeA11TVzrmrUpKG17wIlCSnJtkKnAisS3JdO//gJGMX3J8CrE9yG3AzzTWUq9tlHwUOBP4+yaYkF8zyJkjS0Jsvd3mtAdZMMP9uYFX7/jbg2Ek+Py+2Q5KG2bw4QpEkLXwGiiSpEwaKJKkTBookqRMGiiSpEwaKJKkTBookqRMGiiSpEwaKJKkTBookqRMGiiSpEwaKJKkTBookqRMGiiSpEwaKJKkTBookqRMGiiSpEwaKJKkTBookqRMGiiSpEwaKJKkTBookqRPzJlCSnJ7k9iQ7k4xM0mbvJDclubVte9EEbT6Y5MHBVyxJ6jVvAgXYDJwG3DhFm4eAFVV1DLAcWJnkhLGFbRA9YaBVSpImNG8Cpaq2VNVd07Spqho7+tirfRVAkj2Ai4F3DbRQSdKE5k2gzFSSPZJsAu4Brq+qDe2iPwA+X1Xbpvn8WUlGk4xu37590OVK0tDYcza/LMkNwEETLDq/qtbOZB1V9TCwPMkSYE2So4F/Ak4HXjSDz68GVgOMjIzUDEuXJE1jVgOlqk7ucF33JlkPrAS2AM8AvpkE4HFJvllVz+jq+yRJU1tQp7ySLG2PTEjyWOClwJ1Vta6qDqqqZVW1DPipYSJJs2veBEqSU5NsBU4E1iW5rp1/cJJr2mZPAdYnuQ24meYaytVzU7EkqdesnvKaSlWtAdZMMP9uYFX7/jbg2Bmsa9/OC5QkTSlVw3tdOsl24Lu7+PEDgB91WM5CMYzbPYzbDMO53cO4zdD/dv+Lqlo6fuZQB8ruSDJaVRM+0b+YDeN2D+M2w3Bu9zBuM3S33fPmGookaWEzUCRJnTBQdt3quS5gjgzjdg/jNsNwbvcwbjN0tN1eQ5EkdcIjFElSJwwUSVInDJRdkGRlkruSfDPJu+e6nkFIcliS9UnuaAczO6ed/8Qk1yf5Rvtz0Y0/0/Zo/bUkV7fThyfZ0O7v/5Xk0XNdY9eSLElyRZI7k2xJcuJi39dJ3t7+296c5DPtAH6Lbl8n+USSe5Js7pk34b5N44Pt9t+W5Lh+vstA6VM77sqHgZcBRwGvSXLU3FY1EDuA86rqKOAE4K3tdr4b+EJVHQF8oZ1ebM6h6XB0zPuBD7T9w/0YeMOcVDVYfwFcW1XPAo6h2f5Fu6+THAL8J2Ckqo4G9gB+j8W5rz9J04lur8n27cuAI9rXWcBH+vkiA6V/xwPfrKpvVdXPgc8Cp8xxTZ2rqm1VdUv7/gGaXzCH0Gzrp9pmnwJeNTcVDkaSQ4HfBj7eTgdYAVzRNlmM2/x44AXAZQBV9fOqupdFvq9pup56bJI9gccB21iE+7qqbqQZ4qPXZPv2FODT7WCGXwWWJHnKTL/LQOnfIcA/9kxvbectWkmW0fShtgE4sGcQsx8AB85RWYPy5zSjfu5sp58E3FtVO9rpxbi/Dwe2A/+zPdX38ST7sIj3dVV9H/gz4Hs0QXIfsJHFv6/HTLZvd+v3m4GiKSXZF7gSOLeq7u9dVs0954vmvvMkLwfuqaqNc13LLNsTOA74SFUdC/yEcae3FuG+fgLNX+OHAwcD+/DI00JDoct9a6D07/vAYT3Th7bzFp0ke9GEyeVVdVU7+4djh8Dtz3vmqr4BOAl4ZZLv0JzKXEFzbWFJe1oEFuf+3gps7RlO+wqagFnM+/pk4NtVtb2qfgFcRbP/F/u+HjPZvt2t328GSv9uBo5o7wZ5NM2FvM/PcU2da68dXAZsqapLexZ9Hnht+/61wIyGbl4IquoPq+rQdpC23wP+T1WdAawHXt02W1TbDFBVPwD+Mckz21kvAe5gEe9rmlNdJyR5XPtvfWybF/W+7jHZvv088O/bu71OAO7rOTU2LZ+U3wVJVtGca98D+ERVvXeOS+pckucDXwK+zq+uJ/wRzXWUzwFPpen6/3eravwFvwUvyYuAd1bVy5M8jeaI5YnA14Dfr6qH5rK+riVZTnMjwqOBbwGvp/mDc9Hu6yQXAf+W5o7GrwFvpLlesKj2dZLPAC+i6aL+h8CFwF8zwb5tw/VDNKf/fgq8vqpGZ/xdBookqQue8pIkdcJAkSR1wkCRJHXCQJEkdcJAkSR1wkDRUEpSSS7pmX5nkvd0tO5PJnn19C13+3tOb3sGXj9u/rIk/27Q3y+NZ6BoWD0EnJbkgLkupFfPU9oz8QbgTVX14nHzlwF9B0rbk7a0ywwUDasdNONov338gvFHGEkebH++KMkXk6xN8q0k70tyRpKbknw9ydN7VnNyktEk/9D2ETY2zsrFSW5ux5p4c896v5Tk8zRPa4+v5zXt+jcneX877wLg+cBlSS4e95H3Ab+RZFM75sfrknyoZ31Xtw9ukuTBJJckuRU4sZ1+b5Jbk3w1yYFtu9Pb7781yY39/sfWcDBQNMw+DJzRdt8+U8cAZwPPBs4Ejqyq42meMn9bT7tlNEMd/Dbw0SR70xxR3FdVzwOeB7wpyeFt++OAc6rqyN4vS3IwzRgdK4DlwPOSvKqq/hgYBc6oqv88rsZ3A1+qquVV9YFptmcfYENVHVNVX26nv1pVxwA3Am9q210A/FY7/5XTrFNDykDR0Gp7T/40zUBLM3VzO1bMQ8D/A/62nf91mhAZ87mq2llV36DpyuRZwG/S9JO0iaYLmyfRDGQEcFNVfXuC73se8HdtJ4Y7gMtpxi7pysM0HYCO+Tlwdft+I7/apv8LfDLJm2i6HJIewUDRsPtzmiOHfXrm7aD9fyPJo2j6txrT26/Tzp7pnTTdwI8Z36dRAQHe1h45LK+qw6tqLJB+sltbMbVfbk9r7573P6uqh3umf1G/6o/pYdptqqqzgf9K0xPtxiRPGmC9WqAMFA21trPDz/HrQ71+B/hX7ftXAnvtwqpPT/Ko9rrK04C7gOuAt7TDApDkyHYgq6ncBLwwyQHtRfPXAF+c5jMPAPv1TH8HWN7WcxjNqbi+JHl6VW2oqgtoBuM6bLrPaPj0c0eJtFhdAvxBz/THgLXthepr2bWjh+/RhMH+wNlV9bMkH6c5hXRL26vrdqYZYraqtiV5N0236gHWVdV0XarfBjzc1v9JmqOwb9Nc8N8C3LIL23NxkiPaGr4A3LoL69AiZ2/DkqROeMpLktQJA0WS1AkDRZLUCQNFktQJA0WS1AkDRZLUCQNFktSJ/w/l0EXMS1NE5QAAAABJRU5ErkJggg==\n"
+          },
+          "metadata": {
+            "needs_background": "light"
+          }
+        }
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "source": [
+        "# BeamLoadingEquilibrium"
+      ],
+      "metadata": {
+        "id": "FCcSoOCRxtGo"
+      }
+    },
+    {
+      "cell_type": "markdown",
+      "source": [
+        "The `BeamLoadingEquilibrium` class is used to compute beam equilibrium profile for a given storage ring and a list of RF cavities of any harmonic. \n",
+        "\n",
+        "The class assumes an uniform filling of the storage ring and is based on [3,4]."
+      ],
+      "metadata": {
+        "id": "994_v-dON3Kn"
+      }
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "from mbtrack2.utilities import BeamLoadingEquilibrium"
+      ],
+      "metadata": {
+        "id": "aYfAxnr3Pe9V"
+      },
+      "execution_count": 37,
+      "outputs": []
+    },
+    {
+      "cell_type": "markdown",
+      "source": [
+        "For example, we can define a $4^{th}$ harmonic passive cavity and compute the resulting bunch profile from the addition of this new cavity with the active fundamental cavity which was defined earlier from tracking.\n",
+        "\n",
+        "To do that, we reuse the same `CavityResonator` class which was used for tracking:"
+      ],
+      "metadata": {
+        "id": "U0vGsmpj0u_p"
+      }
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "m = 4\n",
+        "Rs = 90e8\n",
+        "Q = 1e8\n",
+        "QL = 1e8\n",
+        "detune = 60e3\n",
+        "HC = CavityResonator(ring, m, Rs, Q, QL,detune)\n",
+        "HC.Vg = 0\n",
+        "HC.theta_g = 0"
+      ],
+      "metadata": {
+        "id": "hBQxYlQvN2f5"
+      },
+      "execution_count": 38,
+      "outputs": []
+    },
+    {
+      "cell_type": "markdown",
+      "source": [
+        "Then it is possible to define a `BeamLoadingEquilibrium` object to solve using the `beam_equilibrium` method for different harmonic cavity detuning:"
+      ],
+      "metadata": {
+        "id": "VfWbDnTp2Jwn"
+      }
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "values = np.array([100e3, 60e3, 45e3, 42e3, 41e3])\n",
+        "leg = [\"Detune = \" + str(val*1e-3) + \" kHz\" for val in values]\n",
+        "for det in values:\n",
+        "  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",
+        "plt.legend(leg)"
+      ],
+      "metadata": {
+        "id": "xAlbfHmoPk4G",
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 573
+        },
+        "outputId": "2bfd5bd8-abd4-4bfa-b229-75d065735279"
+      },
+      "execution_count": 39,
+      "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 1.5076686428822734 ps\n",
+            "The algorithm has converged: True\n",
+            "The initial center of mass offset is -21.123659372813226 ps\n",
+            "The final center of mass offset is 6.987443148552072 ps\n",
+            "The algorithm has converged: True\n",
+            "The initial center of mass offset is -178.42158504142017 ps\n",
+            "The final center of mass offset is 13.777318935482338 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 17.165960774475234 ps\n",
+            "The algorithm has converged: True\n"
+          ]
+        },
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "<matplotlib.legend.Legend at 0x7f58a1f1c510>"
+            ]
+          },
+          "metadata": {},
+          "execution_count": 39
+        },
+        {
+          "output_type": "display_data",
+          "data": {
+            "text/plain": [
+              "<Figure size 432x288 with 1 Axes>"
+            ],
+            "image/png": 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MoOaw6Li4OAYPHtxOr6x5mh3AhRBOwBfA/0kp84E3gd5AFKYW+iv1nSelXC2lHCmlHOnt7V3fIYrSqU6lFzbY/10lzMuB2Myiev9DWzprSie7Zs0aEhMTOX78OMeOHeOGG24AGk4ne767776bd955p/rY+jITdmfNCuBCCBtMwfsjKeWXAFLKNCllpZTSCLwDXNBx1VSU9lFRaSQ2s4je3o0H8F5eTuSXVpBt5allLT2d7JtvvslTTz1VPS29KmdJQ+lka0pJSSE/P58xY8YghGDevHlNpo198sknmT9/PpWVlY0et2DBguq0sd7e3k1+QLZWk33gwpSV5l3gmJTy1Rrb/c394wBXAYc7pIaK0o6Sc0swVBqbEcAdAIjLKsLTybZjKrNpMaQeat9r+g2BGS1bfMCS08mePn2aTz/9lK+++gpvb29WrlxJnz59GkwbW5UiFkwpZ4OCguoc05CHH36YgoIC3n///epkXTfddBP29vYAGAyG6g+S//73vwDEx8dz6aWXMn/+/Aav2xbNyUY4DrgFOCSEqMo+8xhwoxAiCpBAHLCwQ2qoKO0owbxkWoinQ6PHhXmabnDGZhYzwpwfpSewtHSyZWVl2NnZER0dzZdffsntt9/Ozp07m31+cz333HOMHj2a1atX19r+0UcfVWchjIuLq37dYMrQOGfOHF5//fU6Kwa1l+aMQvkVqC+vpho2qFicxOwSAII9Gg/gwR4OaDWiY29ktrCl3FEsOZ1sUFAQV199NQBXXXUVt912G9BwOtmaAgMDSUpKavSYKqNGjWLv3r1kZ2dXJ79qyqJFi7j66quZMmVKs45vDTUTU+lREnOKsdEK/FwaDiIANloNQe72xGZZ50iUKpaeTvbKK6/k559/BmDHjh307dsXaDidbE3+/v64uLiwa9cupJR88MEHDaaNvfTSS1m8eDGzZs2q9T405D//+Q8FBQWNZjFsD2pBB6VHScguJtDNHq2m6cUaQjwcrHKV+qp0suXl5eh0Om655Zbqpb0WLFhAXFwcw4cPR0qJt7c3X3/9da10svPnz+f//u//qtPJDhgwoNnpZO+55x4iIyOpqKhg/PjxbU4pu3jxYm666SZWrFiBk5NTdd/zzJkz2bhxIxERETg4OPD+++9XnxMVFVX94fHGG28wf/58SkpKmDFjBjNmzGiwrDlz5lBQUMDs2bPZuLHxDojly5djY2NDVFQUcG4ptfam0skqPcoVq37Fxd6GD+8Y3eSxj355kM1H0tj75NR2K1+lk1WaotLJKkoDEnNKmuz/rhLk7kBWkYESQ+NDxhSlq6gArvQYhWWmcd3B7s0L4IFupuFhybnW142iWAcVwJUeo6o/O9jDvlnHB7qbjkvKKemwOilKW6gArvQY1QG8xS1wFcCV7kkFcKXHOGsOxFUt66b4utih0wiSVQtc6aZUAFd6jJS8UvRaDZ6OzZtVqNUI/N3sVAtc6bZUAFd6jJS8Uvxc7apnCTZHoJu91bXArSmdbJX777+/1pT8NWvW4O3tXZ1Qqmp8+Pl6TDpZRbF0KXkl+Ls2PgPzfIFuDlZ3E9Oa0skCREdHk5OTU2f79ddfXz2Lc8GCBfWe2yPSySqKNUjJKyXArXn931UC3exILyilorLxFqqlsvR0slX1ffnll1t8bo9IJ6so1sBolKTlm7pQWsLP1R6jhIzCMvxdWxb8m7Lsz2Uczz7ertfs79Gff17wzxadY8npZFetWsXs2bPr5DkB+OKLL/jll1/o27cvK1asqJVeFnpOOllFsXiZhWWUV0oCWhzATbnAU/NK2z2Ad0eWlE727NmzfP7553UyJQJcfvnl3Hjjjdja2vL2229z66238tNPPzX7NZzPYtPJKoo1SMkzpTv1a2EQ9jVnLUzNK23iyJZraUu5o1hqOtn9+/dz6tQpIiIiACguLiYiIoJTp07h6elZfdyCBQt45JFH6lxPpZNVFAuRkme6EdnSm5hVaWdT89s/gHcHlpxOdtasWaSmphIXF0dcXBwODg6cOnUKoNbyad9++229CcRUOllFsRBVLfCWBnAPRz16rcaqArg1pZNtrKxvv/0WnU6Hh4dHrT57lU62lVQ6WaWrvLjxGGt+j+PEc5e2aBw4wMUv/8TwEHf+fcOwNtdDpZNVmqLSySrKeVLySvFv4SSeKn4udh3SB64obaUCuNIjpOS2fBJPFT9Xe9KsqAtFsR4qgCs9QkobhgH6udiSklda7zRrRelKKoArVk9KSUZBGT4utq0639fFjrIKI3kl5e1cM0VpGxXAFauXW1yOodKIj3PrulCqWu7WNBJFsQ4qgCtWL72gDAAf59a1wKtmY6aoG5lKN6MCuGL10gtMgbe1AbxqNmaalQTwnpBO9tVXX2XgwIFERkYyefJk4uPj6z1PpZNVlG4uPd/cAndpXRdKVdeLtXSh9IR0ssOGDSM6OpqDBw9y7bXX1juVHlQ6WUXp9trahaLXafBw1Fdfx5pYazrZiRMn4uBgWvt0zJgxtXKeVFHpZBXFAqQXlOKo1+Jo2/o/dx9nWzLaOYCnvvgiZcfaN52s7YD++D32WIvOsdZ0slXefffdeqfI94h0skKIYOADwBeQwGop5b+FEB7Ap0AYEAdcJ6WsuyyGonSx9IKy6n7s1vJ2trXKFvj5rCWdbJV169YRHR3Njh07ml3/+lhyOtkK4CEp5T4hhDOwVwixBZgPbJNSLhVCLAYWA90jP6ai1JCRX4Z3K7tPqng723I6vbCdamTS0pZyR7HGdLJg+sB44YUX2LFjB7a2df/9e0Q6WSllipRyn/l5AXAMCASuANaaD1sLXNlRlVSUtkgrKG31DcwqPs52ZBSWWd1sTGtNJ7t//34WLlzIt99+i4+PT7316XHpZIUQYcAwYDfgK6WsSrqbiqmLpb5z7gLuAggJCWltPRWlVaSUpOeXtfoGZhUfZ1vKKyW5xeW4Oza/O6E76gnpZB9++GEKCwuZM2cOYIo93377LdBD08kKIZyAHcALUsovhRC5Ukq3GvtzpJTujV1DpZNVOltBaTlDlmzm0Rn9WXhJ71Zf57u/znLfx/v58f/G08/PudXXUelklaa0ezpZIYQN8AXwkZTyS/PmNCGEv3m/P5DeplorSgeoHkLYyjwoVapa8FWTghSlO2gygAvT3Yh3gWNSyldr7PoWuNX8/Fbgm/avnqK0TfUknlbmQalS1Yfe3kMJFaUtmtMHPg64BTgkhKi66/AYsBT4TAhxBxAPXNcxVVSU1qtqMfu2sQXuXd0CVwFc6T6aDOBSyl+BhpYxmdy+1VGU9lXVYvZuYwvcyVaHg15b3aJXlO5ATaVXrFp6QRm2Og0udm2fdOzjbKv6wJVuRU2lV6xaWn4pPi62ja+FWZoPcb+CnQuEXAia+ts13h0wnV5R2kK1wBWrZhoD3kj3SexO+PdQ+ORGWDML/jsJ8lPqPdTH2c4qAnhPSCf7yy+/MHz4cHQ6Xb2pYKuodLKK0o2lF5Q2PIkn5SCsuwYcveHW7+DKNyEzBtbPgbK60+atJR9KT0gnGxISwpo1a5g7d26j56p0sorSjaUXNDALs6IMNtwODh5w20boNR6i5sKctZB6GH5+sc4pPi62FJZVUGyo6ISadw5rTScbFhZGZGRkdXbA+qh0sorSjZWWV1JQWlF/HpQ9/4WsGLhpAzh6ndveZwqMmA+734Lh88Cnf/UubyfTB0FGQRmhnm3/r7Pzs5NkJrZvgiyvYCcuvq5vi86x9nSyDekR6WQVxVKdm8RzXgu8vAR2vgLhE6HP1LonTn4KDn5mOuaad6o3V30QpBeUEerp2GH17krWlk62vVhyOllFsUjVa2Ge3wI/tAGKs+Dih+o/0cEDRt4Gu96AyU+CmykJW/V0+nYaC97SlnJHsdZ0sk3pEelkFcVS1buUmpSw+23wGQRhFzV88gV3mY7d/1H1pqrZmBlWNBbcWtPJNoc1pJNVAVyxWmn59axGn7wP0g7BBXdCY2PD3UMhfALsXwdG0w0rDwc9Oo2w+JEoVelkBw0axJQpU5g2bRpPP/00YLr5NnDgQIYPH87gwYNZuHAhFRUVtdLJrlixgnHjxlWnk73//vubnU42OjqayMhIBg4c2GGpZAH27NlDUFAQn3/+OQsXLmTQoEHV+6pSvIIpneyCBQuIiIigd+/eTaaTvfPOO5k9ezYlJSWNlr98+XIOHTpUfSOzo15rs9PJtgeVTlbpTMt+OM47v5zh5PMz0GjMwfqHR003MP8RA/ZujV/g8Jew4Ta4+UuIMGWNGPPiNi7q48XyOUNbVSeVTlZpSrunk1UUS5RRYFpKrTp4Gyvh8BfQZ1rTwRug30zQO8HRc0PLrGUsuGIdVABXrFadMeDxv0FhGgy5tnkXsLGDvtPh+P+qu1E6YnV6RWktFcAVq1XVAq92YhNobU0t8OYacLlpxEr874BpMk9bb2Ja27qaSvtp6d+GCuCK1aoTwE/+AL0uBn0LxnBHTAWdnakVjmkyT1aRgYrKxnOHNMTOzo6srCwVxJU6pJRkZWU1OszyfGocuGKVKiqNZBWVncsDnnkKss/A6LtbdiFbJwgdB6e3AeDtYoeUkFVkwLcVK90HBQWRlJRERkZGi89VrJ+dnV2t2aFNUQFcsUrZRQakPDd2m5gfTY99W9B9UqX3JNj8OOQm1prM05oAbmNjQ69evVpeB0Wph+pCUaxS1UiRqvwlnPwRvPqBe1jLL9Z7kunxzM/nJvMUWs9kHsVyqQCuWKWMmqvRl5dCwi6IaOWUZp8B4OwPp39q9+n0itIWKoArVimjZgs8ORoqy0w3MFtDCFMr/PTPeDnoal1fUbqSCuCKVcoorFrM2Na0XBoCQsa2/oLhE6A0F7vsY7ja26jJPEq3oAK4YpUyCspwsdNhZ6M1BXD/yObNvmxI6IWmx/g/1NqYSrehArhildILSk2t7/JSSPwTwlrZfVLFNQhcQyDhd7U6vdJtqACuWKXqSTxV/d+NpY5trtCxEP8HPk766i4aRelKKoArVskUwO3ap/+7SshYKEqnnz6d9PwyNZtS6XIqgCtWqTqRVdyv4Dekbf3fVcz94IPKj1BWYaSgzHoWN1YskwrgitUpKqug2FCJj5POtIBD8Oj2ubBXX3DwJKzoIKDGgitdr8kALoR4TwiRLoQ4XGPbEiFEshDigPlnZsdWU1Gar2qESLhMhPIiCL6gfS4sTF0xPjn7ANSNTKXLNacFvga4tJ7tK6SUUeafje1bLUVpvaox2mElR0wbguosZNJ6wRdgV5iAB/lqKKHS5ZoM4FLKX4DsTqiLorSL6lmYeQfBwQvc2zF5VOAIAIZqTqsArnS5tvSB3yuEOGjuYnFv6CAhxF1CiGghRLRKoal0hqoFF5wz9kPQqMYXL24p/yik0DBCd0YFcKXLtTaAvwn0BqKAFOCVhg6UUq6WUo6UUo709vZuZXGK0nwZhWV4aorQZp+C4FHte3FbJ4T3AEbqzqjp9EqXa1UAl1KmSSkrpZRG4B2gne4SKUrbpeeXMd4h3vRLUDsHcIDA4QySMWTkq5uYStdqVQAXQvjX+PUq4HBDxypKZ8soLOMCm9MgNBAwvP0LCBqJsyxElxfb/tdWlBZockUeIcTHwATASwiRBDwNTBBCRAESiAMWdmAdFaVFMgrKGCJPgs8g05Jo7c18IzOg6Gj7X1tRWqDJAC6lvLGeze92QF0UpV2k55cSLk9C4NUdU4D3AMo1dvQxnMBQYUSvU/PhlK6h/vIUq1JplDgUJeJQWQABwzqmEK2OHNeBRGlOk6mSWildSAVwxapkFxkYJMx90wFRHVZOsc8wBoo4MnILOqwMRWmKCuCKVUkvKGWIJhajsAGfgR1WjggYhq2ooDhJ3b9Xuo4K4IpVySgoY7CIpcSjH+hsO6wch1DTjUyReqDDylCUpqgArliVjHxTC1z6De3QctyC+pIv7bHPVC1wpeuoAK5YldLMWNxEEfrgER1ajo1Ox0nRC/f8Yx1ajqI0RgVwxarYpptydeuDO2gESg0Jtn3wKzkFlWphB6VrqACuWBW33COUowPfQR1eVppjP/TSAJknO7wsRamPCuCKVfErOk6iLrRDb2BWyXc3f0ikqNIhIXwAACAASURBVBuZStdQAVyxHlISZoghxaF/55Tn2YdiaYs8qwK40jVUAFesR248LhSS49Zx479r8nJx4KgMpSJZBXCla6gArliNkgTTWpVl3pGdUp6Psy2HjWFo0w6B0dgpZSpKTSqAK1ajNH4v5VKLzr/jb2CCKYAfkWFoKooh+3SnlKkoNakArlgNkXKAEzIYb3fXTinP29mWQ8Zw0y+qH1zpAiqAK9ZBShwyD3HI2AtfF7tOKdLHxY5TMoAKjV6NRFG6hArginXITUBfnsdh2XkB3FGvxcbGljS73pDyV6eUqSg1qQCuWAdzC/i0LgIn2ybXKWkXQgh8XGyJtYmAlIMgZaeUqyhVVABXrMPZA1SiJce5T6cW6+1ky1HCoSwPcuI6tWxFUQFcsQ4pB4jXheLp6tKpxfq42LKvPKS6DorSmVQAVyyflHD2AEdkeKf1f1fxcbbjz2I/0OhUP7jS6VQAVyxfXiKUZBNtCOn0AO7tbEt2qcDoPUAFcKXTqQCuWD5z4DxQEYavS8cnsarJ29lUXrHnYFM91I1MpROpAK5YvrMHkELLcdn5LfCq8rJcBkBxFuQnd2r5Ss+mArhi+VL+osi1D2XoOz2A+5nLS7DtU10XReksKoArlk1KSDlAupMphWxnd6H4uZoCeAyhIDRqSr3SqVQAVyxb/lkoyiBeb2oB+zh3bgvcxU6Hg15LcpEAr36qBa50KhXAFctmDpjHRW88HfXodZ37Jy2EwM/VjtS8UvAfqgK40qlUAFcsW8oBEBoOlgfh08n931X8Xe1IySuBgCgoTIWC1C6ph9LzNBnAhRDvCSHShRCHa2zzEEJsEULEmB/dO7aaitKAswfAqx8JheDXyf3fVXxdarTAwZQXRVE6QXNa4GuAS8/bthjYJqXsA2wz/64onS/lLwiIIi2/rNNHoFTxd7UjvaCMSp/B5jqpG5lK52gygEspfwGyz9t8BbDW/HwtcGU710tRmlaQCoWpVPpGklXUdQHcz9WeCqMkq1wPnhGqH1zpNK3tA/eVUqaYn6cCvg0dKIS4SwgRLYSIzsjIaGVxilIPc6DMdh2IlHRdC9xcboq6kal0sjbfxJRSSqDB+cNSytVSypFSypHe3t5tLU5Rzjl7ABAk6nsDEODWVS3wmgE8ypSbpSirS+qi9CytDeBpQgh/APNjevtVSVGaKeUAePUhscj0ZxzoZt8l1agK4Kl5JeduZKaqVrjS8VobwL8FbjU/vxX4pn2qoygtkPIX+A/lbG4pAP5dFMA9HPTotRpS88vAP9K0Uc3IVDpBc4YRfgz8AfQTQiQJIe4AlgJThRAxwBTz74rSeQozTImj/KM4m1uCq71Npy2ldj6NRuDramtqgdu7g1uo6gdXOkWTf/FSyhsb2DW5neuiKM1XFSADojh7soSALmp9V/F3sTf1gYO6kal0GjUTU7FMKftNj35DSM4tIbCLbmBW8XO1IzXfHMADoiAnFkpyu7ROivVTAVyxTGcPgEdvsHPlbG7Xt8Cr8qFIKWvcyDzUpXVSrJ8K4IplOrsfAqIoLKsgv7SiywN4gKsdZRVGsooM4Fc1pV7dyFQ6lgrgiuXJTzHdwAwcSUpuCUCXB/AgdwcAknJKwMkbXAJVP7jS4brmtr2itMXZfabHwBEkmwN4a/vApZQkFiRyIOMAZ3LPkFCQQFpxGsXlxZRWlGKrtcXRxhEPOw/CXMMIdw0nyieKMJcwhBDV1wl0N32AJOeUEBXspm5kKp1CBXDF8iTvBY0O/CM5u8+UnsHftfkt8PLKcnal7GJL/BZ+SfqFrFLTrEmdRkeQUxB+jn5423tjq7Wl3FhOUXkRSYVJ/H72dwxGAwA+9j5cFHQRs3rNYqTfyOoAnpRTbCrEPwpObIKyQrB1ascXryjnqACuWJ7kveA7CGzsOZtbglYj8HFuOpVsYn4in5z4hK9PfU2+IR9HG0fGB45npN9IhvkMo5drL3Sahv9LVBorSShIYG/aXnan7OaH2B/4MuZL/Bz9mNt/Li4OHqYuFDDfyJSmG5mhY9vphStKbSqAK5bFaITk/TDkGgDO5pbg52KHTtvw7ZyjWUd586832ZG4A63QMjl0MpeHX87YgLHotfpmF63VaOnl2oterr24tu+1lFSUsCNxBxtObuDVva8iQuzYnTuV4vIncAgYZjopea8K4EqHUQFcsSxZp6AsDwJHAJCcW9JgEqtTOad4ff/r/JT4Ey56FxYOXcicvnPwcfBpl6rY6+y5tNelXNrrUo5mHeXu7/9FCt8x66s/uH/Y/VzhGoImObpdylKU+qgArliW5L2mR3MAP5tXwvCQ2gtCFRgKePOvN1l/bD32Onv+FvU3bhlwC076juuLHug5kMkeD/PJwZ0EDtvJU78/xfdeziw5u5fgDitV6enUMELFsiTvBb0TePWlotJISm5pdRZCKSWbYjdx+VeXs+7oOq7qcxUbr97I3UPv7tDgXSXQ3Z7igiD+Pf5dloxdwlHKuMbFyIaD75km+ChKO1MtcMWyJO+FgGGg0ZKSXUyFURLq6UB2aTbP73qeLfFbGOw5mP9M/g+DvAZ1atWCzCNRzuaWck3faxiHPU/9dD/P7F/B3rwYnhzzJA42Dp1aJ8W6qRa4YjkqykyjOszdJwnZpiF72XI/V31zFT8n/swDwx9g3cx1nR684VwArxpK6NdrIm+l53Cv8yA2xm7kxv/dSHx+fKfXS7FeKoArliPlIBjLqwN4bFY+tj7f88axJ/C29+aTWZ+wYMgCtBptl1Sv1mxMABt7NL6DWFhQxDtT3yGnNIebNt5EdKq6sam0DxXAFcuRuMv0GDyatKI03jv9CHrPX7mx31zWz1pPP49+XVo9V3sbnG115ybzAASOhOT9XOA7go9mfoS7rTt3brmT705/13UVVayGCuCK5UjYBe5h7C6M47rvryO7PB7n/Pk8NubRFo3n7kiB7vbV0/sBCBoFhgLIPEmwSzDrZq5juM9wHvv1MdYdXdd1FVWsggrgimWQEhJ385lvGAu3LMTd1h3fwn8S4XhxV9esliB3BxKzawbwkabHJFO3iautK29OeZPJIZNZtmcZ7xx8pwtqqVgLFcAVi1CZFcMy23KeKzvD2ICxrJu5jtRMF0I8ujYL4flCPR2Izy7CaDQPGzTnLKfGhB69Vs/yS5ZzWfhlrNy/ktf2vqaGGSqtooYRKt1eoaGQf/7yCL+4unBz6AweGv8iRaWSvJJyQj0cu7p6tYR5OVJabiStoNSUYEujMXWjJOyudZxOo+OFi17AXmfPu4ffRavRct+w+7qo1oqlUgFc6dYySzK5e+vdxBSc5om8Eq4fvxQ0GhJz8gAI9uhe46p7eZo+UGIzi85lSAwZAz89D8XZ4OBRfaxGaHhyzJMYpZHVB1djp7Xjzsg7u6LaioVSXShKt5VYkMi8TfOIz4/n9WI913tEmVq0QHyWaaRHSDcL4GFepvrEZdYYiRJyoekxYVed44UQPDnmSWaFz2Ll/pV8ePTDzqimYiVUAFe6pRPZJ5i3aR75hnzeGf8KF6edgpDR1fvjsooACPHsXgE8wNUevU5TXT/ANG5dq4eE3+s9R6vR8vy455kaOpWX97zMVzFfdVJtFUunArjS7USnRjP/h/lohZa1l65laHGhaUfwmOpjzmQU4etii5Nt9+oF1GgEoR4OxGbWCOA2dqYgHv9Hg+fpNDqWXbyMCwMu5Jk/nmFn0s5OqK1i6VQAV7qVHYk7WLR1EV72Xnw440N6u/WGuF9Ba3tuSB5wOqOQ3t7dc6WbMC9H4moGcICQsaZFjg1F9Z8E2GhteHXCq/R178tDOx7icObhDq6pYulUAFe6ja3xW/m/n/+PCLcIPpjxAf5O/qYdsTsg+AKwOZd1sDsH8F5ejsRnF58bSggQeiEYK6rHgzfE0caRN6a8gYedB/dsu4fE/MQOrq1iybrX90+lx/oh9gcW71zMYK/BvDnlTZz1zqYdxdmQehgmPlZ9bEZhGQWlFfT27l5DCKv0crHBNT+LxN//xKOskIqMTCrSkjHud8GY/CpG1+8xFhcjDQYQAjQCgUDY2qJ1dUHj4sLrthN5O2UDL6bcyrNzVuMV0LvWIsqKAiqAK93Ad6e/44nfniDKO4o3pryBo02NwBz3KyCh1/jqTafTTd0QvX26pgUuKyooT02jPCkRQ2Ii5YlJ5udJlCcmEpWbywdA8WaoMRYFoXNCk3gajVcpGgcHhF5vmmEqJRiNGA1lGPPyqczLQxoM3AFAIZlvXU62izP2gwdjN2gw9lFDcRg9Gq1T9/wGonSeNgVwIUQcUABUAhVSypGNn6EotX0V8xVP//40o/xG8fqk1+vmy47bCTYOEDC8etPpDNNNzY7sQjEWFWFITMSQkEB5ojlQJyRiSEqi/OxZqKg4d7BOh01AAPqgIOymTaPM3YuXdmcwc/wgpo0fjM7bC52HB2LbUxD9Hvwz2nRjs7HyS0ooT0lh156v+d/Od7nQ4MnQrHyy1qyB8nLQ6bCPGorT+EtwmTkTfVBgh70XSvfVHi3wiVLKzHa4jtLDfH7yc57941kuDLiQ1ya+hr2unmnxsTtNNwB155JVnc4oxEGvxc+l8SDYGCkllVlZGBISKU9MwJCQiCExwRSkExOpzMqqdbzW1RWbkBDsBw/C5dJLsQkOQh8cjE1QMDZ+vgidrta1dz27BS9/f64YXCMvefgE2PWGKati+IRG66ext8c2PJyLwx7kWKArK//6kutDruJit/EUxsRTeiae0rgEyr88gWbDEewCfHAaOgjPi0biGuCKs4cdenv1BdvaqX9hpUusP7ael/58ifFB43l1wqvYam3rHlSYDhnHYOj1tTafzigi3NsRjabxPmFZUUF5Ssq5VnSNYF2emIixuEYHhxDo/PzQBwfjNHEC+uAQ9CHB2JgftS4uzX5tQgj6+jpxMq2g9o7QC0GjgzPb6wTwsuJyspILyUwqIi+9mLyMEvIySsjPLMFY2YtreIiKQ/AzMeYz/MHJH2p+CTkBnDhR/auDqx6fEGe8Q10I6ueGb7grWq0at2BN2hrAJbBZCCGBt6WUq88/QAhxF3AXQEhISBuLU6zB2iNrWR69nEnBk1h+yXJstDb1H3hqm+kxfGKtzWcyChkRalrI2FhcbO57rtuKPr+rQ+j12AQHow8OxmH0BbWCtE1QIBp9+6Wk7evrzHd/nUVKee7mo60zMnAUBUf3kemVQWZiAZlJhWQmFVKQVVp9ro2tFlcfezwDHQmP8sbFyw4bZw0rDv+L46VHeO3S5QzyHYhGq0GjEVRWGDGUVlCw7xCpG74n+0AMpfaeGAaMITclmLjDWez5HmzstAQP8KDPSF/CIj3R2XTNwhdK+xFtyYImhAiUUiYLIXyALcB9UspfGjp+5MiRMjparUbSk713+D1W7F3BtNBpLB2/FBtNA8EbYMPtELuTyruiTUE6IZ6C07F88e0uRtkU4VmQQWVG7d47jasr+uDgWq1nm+Bg9CEh6Hx8EJrOaYF+8EccT319hJ//dhHG7DLS4wvISCgg/VQ6ZQZzu0mAu68DnkFOeAU54RXkjFeQEw6u+npHnGSVZHHTxpswVBpYP2s9fo5+9ZZdnpxM1rvvkvP5BoQQON1wC6UT5pAYW0LcX5kU5xuwddDRZ5QvQycF4+bbvWazKnUJIfbWd4+xTQH8vAKWAIVSyuUNHaMCeM/230P/5d/7/s2MsBm8ePGL6DQ1+o0rKzEkJFB26hSGU6cwxMZh+OMrDMV2VBaV17pOpp0rzr3D8Onfu25Xh6trZ78sU/2lpCjXQHp8PhkJBZw8lkVKXD6O0hSINRqBR6AjPp6leJ9Zhdf0m/G8aBY2ti1rBcfkxHDLplsIcQ5hzaVrGl0k2ZCUTOYbb5D39ddo3d3xeeghnGfPJvlkLid2pXJqXzrGSknYEC9GzAjFr1fXvHdK09o9gAshHAGNlLLA/HwL8KyU8oeGzlEBvOdafXA1r+9/nZm9ZvLs0MVUHD1O6ZEjlMXEUBoTg+H0GWRZWfXxOi939JpU9EPGoR92CTYhIehDw/giVfL4plP8tngSgW5dkwu8ssJITmoxWcmF5p8iMhILKMk3ACA0Aldfe37Jymf4UB+unBSOZ5CjqcuisgKWhcHgq2H2ylaV/0vSL9z3031MCJrAiokr0IjGv1WUHj1K6rPPUXLgAPZRUfi/8Dy2vXtTnG/g0PYkDu9IprSonPAob0ZfEY6Hf/ccX9+TdUQADweqsu7ogPVSyhcaO0cF8J5HGo189O3z/LXtUy4pCKB/mg3lsbHV+3W+vthGRGDbp4/pp28fbMPD0exeATtfgUfOgL179fGPf3WI7/46y19PT+vwiS2G0gry0kvITS8mL72Y7BRT0M5NPTfLUqMTuPs54hXkhE+oCz6hzngGOWGj1zLy+a1M7OfNv+YMrX3hT282zcj8+zHTRJ5WWHd0Hcv2LOP2wbfz4IgHmzxeGo3kff0N6S+/jLG4GO8HH8Rj3i0IrRZDaQV/bUtk/+YEKgyVDJkQxOjZ4WoUSzfSUABv9b+QlPIMMLTJA5UeRUpJ2ckYinfvoujPP8n541dGFJUxAtB6lWIb2Re32ZdjN3gIdoMHoXN3r/9CMZsh6IJawRvgWEo+A/xd2hy8pZSUFpZTmFNGUW4Zhbnmx+xS8jJLyE0vqW5RV3HysMUr0ImwSC+8Ap3wCHTEzdehwZEd9Y5EAeg3E459Z8qNEjCsVfW/acBNxObF8t7h9+jl2osrI65s9Hih0eB29VU4XXwRKU8vIX3ZMgq2biVg2VL0QUGMmtWLweMD2f1dLAe3J3F6XzoX39CX8ChvNQO0G1MfsUqbGQ0GinfvpuCnnyj8eTsVqalIoNjHjd29QT/8Iq6e/RhaTx+MlSCRlEkoKwaKCzn3JdD0RBakQ0I+jLoeGZ9vnqwoMRolOYmFTO7nw9lTuSCleRKjpMJgpMJQee6x3PRYXlpJaVF59U9ZcQWlhabnxsra3z6FAAdXW1y87Agb7Imrjz1uPg64+jjg6m3f4v7q/n4ufLQ7nopKI7qaQb7PNEDAiR9aHcCFECwevZj4gnie+eMZgpyCGOnX9Dw6nbc3Qf9ZRd4335D2wovEXnU1/i88j8u0adg765kwtx/9x/ix/aMT/PD2YXoP92HCTf2wc2zkZrPSZdrtJmZzqC4Uy2c0SgqySshLLSRr90Gy9seQn5qHQdhTYetEpbMX5TaOlFUAsuvHHGttNNg56LBzssHWwQY7JxvsHHTYOtrg6GaLk7ut6dHNDgcXGzTtOE766/3J/N+nB9j0wMUM8D9vHPm706G8GBa1LW1sXlkeN2+8mdyyXNbPXE+wS3CzzzUkJZH84N8pPXQI91tuwefhf1QPpTRWGtm3OYE938Vi76JnyvwBBPX3aOKKSkfp8FEozaECuGWprDCSkVhA2pl8MpMLyUoqJDu5gMrKGgdJI3bachxcbbH3dsXOSU9MyXEO5O+jn3cEU8Ino7PRobPRoNUJNDpNna/kQgDmTQIB256D8kLEzGUgRHU38a7YLN7acYbnrhxMmJcjCNNpGq1Ap9eis9Gi02tMz/UadDaadg3ILXU6o5DJr+zg5WsiuW7UeYH119dg69Pw4FFwbds0+IT8BOZunIuHnQfrZq7DRd/8SUfSYCBt+XJyPvgQuyFDCFr5b2z8/av3p8fns+W9o+SmFzN8WgijZ4d36XvaU7V7H7hifaRRkp5QQPyhTJJP5pIel09FuREAO5tKHAuSCMg4hVN5Fh6DwvCdOhbviePQ2ZtmUUopWbF3Be8feZ85F8zhH2Nua3KERB0FafDNB3DJP2God61da+PSSHMQjL0wsHaXRDfVy9MRZ1sdB5Nz6wbwfjNMAfzERrigbetghriEsGLCCu7achf/2P4P3pjyRq0hmo0Rej1+jz2Gw8iRpDz6GLFzriNo5b9xGG7KPeMT6sJ1j43i1w0x7PsxgbS4fKbdMRgHl/ab9KS0ngrgPZyx0kjisRxO70sn7nCW6cadAO9gZ/oNccDp1C5stn+BPj8du8hI3O+4AZfp09A41h5qZpRGXtj1Ap+d/Iwb+t3Ao6MfbXnwBjj+PSBh4BV1dh1IzGVIoKtFBG8wjf0eHOjKoaS8uju9+pp+jnzd5gAOMMpvFE+NeYqnfn+KpX8u5YkxT7TofJdp07ANDyfxnnuIv3U+/k8/hdu11wKmmaETb+qPf7gr29ef4POX9jD9rsFq3Hg3oAJ4DySlJCOhgBO7UomJTqOkoBy9vY6QQR6EDfHCuyKRog/fo/CD7Qg7O1wvvwy3G27AftCgeq9XYazgyd+e5Psz33PH4Dt4YPgDrR+5cPQb8IwAnwG1NhsqjBw5m8/8C8Nad90uEhnkyvu/xWGoMKLX1fjgEQIGXwvbX4K85DZ3owBc1ecqYvNief/I+4S7hjN3wNwWnW8bEUGvTz8l+e9/J+WJJyk9fgLfxf+sTtTVf6w/noFObHr7EF+9so8Jc/sx4MKANtdbaT0VwHuQynIjMXvTOPhTEhkJBWh1GsIiPel7gR8hgzwo+W0nWf9+ibR9+9C6ueF1/314zJ2L1s2twWsaKg088ssjbEvYxgPDH2DBkAWtr2BeEsT+Apc8Umd89LGUfAwVRoYGNVyX7mhosBuGSiNHzuYxLOS8IZNDroXtL8KRL+HC+9qlvAeGP0BsfizL9iwjyDmI8UHjmz6pBq2bG8GrV5P+r3+RvfYDDGdOE7hiRfUMV+8QZ657dBQ//vcwP31wnJzUYsZe2RvRRGIxpWNYxndRpU1KCgzs/vYMax/7jW1rjlFhqGT8DX257eVxXHrXEHxLTpF481ySFt1NRWoqvk88QcTPP+H9t781GryLy4u5d9u9bEvYxqMXPNq24A1w8FNAwtAb6uzal5ADQFSIZQXwUWGmkRt/xmbX3enZG/yj4NCGditPq9Gy7OJl9Pfoz0PbH+JA+oEWX0PodPg++ij+L7xA0Z5o4q6/gbIak6/snGy47L6hDLo4gP2bE/hh9WHKyyobuaLSUVQAt2LF+QZ+++IUHzz+O9Gb4vDt5crsB6K48enRDJkQROWJw8TfOp+E226nIj0D/+efo/ePP+Bx801o7Bufpp5bmsvCLQvZnbqb58Y91+Kv63VICQc+hpALwSO8zu5dZ7IIcrfvsunzreXtbEu4lyN74uoJ4ABD5pgm9GSearcyHWwceGPyG/g4+HDPtns4nXu6Vddxu+ZqQt9/j8q8POKuv4GiP/6o3qfVarhkbj8umtOHM39l8NUr+yjKLWvkakpHUAHcChXnG/j1sxg+ePx3/tqaQO9hPsx9ejSz/hZJ8AAPDKdPk7jobuJvnEvZqVP4PvYYvX/8Abdrr0XYND1hI6kgiVs23cLRrKMsv2R5k7MAmyUpGrJiIOrGOruMRsnu2GzGhnu2vZwuMCrMgz1xObUXOa4y+BoQGjiwrl3L9LT35O2pb6PX6lm4ZSGpRamtuo7DyJGEff4ZNr4+JCy4k5xPPq3eJ4Rg6ORgZt0dSW5aMZ8vjSYjoZ6Zp0qHUQHcilRWGDmwNYGPnvqDg9uT6DPKl7nPjGHKbQNx93OkIieH1Oee58wVV1K8dy/eDz5IxJbNeMy7pdm5sI9mHeXmjTeTXZrN6mmrmRo6tX0qv+e/oHeCgXU/DI6l5pNbXM7Y3pYZwC/o5UFeSTkn0+sJbi7+0HcG7F8HFYa6+9sgyDmIN6e8SVF5EQu3LCSvrJ7RMM2gDwoi9OOPcbxoHKlLlpD6wovIGnnWwyK9uPrhEQgBXy7fS+xfGe31EpQmqABuJeIPZ/HJc3/y24ZT+Ee4ceNTFzB53gDcfByQBgPZa9dyevql5Hz8Me7XX0fvzT/itfAuNA7NzwX9W/Jv3PbDbdhqbflwxoeM8B3RPpUvTIfDX0DUXLCrOwnlj9Om5c0sNYCPMdf715gGVh4ceRsUZZiHULav/h79WTlpJUkFSSzasoh8Q36rrqN1ciL4jTfwuPVWcj78kMRFd1OZf+5aXkFOXLt4JB7+jmx86xAHtibQmZMEeyoVwC1cblox36/6i+9X/QXArHsiuezeobj7OSKlpODnnzkz+wrSXlqK/eDB9Pr6K/yeeqrhJFL1kFKy/th67tl2DyEuIaybuY5wt7r91K22dw0Yy+GCu+rdvTMmk15ejvi7Wlb/d5VAN3v6+Dix42QDLdPek8A1xLTgcQcY5TeKVya8wvGc49y95W4KDYWtuo7QavF9dDF+zz1L0a5dxN1wI4b4+Or9jq62XPnQcHpHefPbhlPsWH+Cykpje70MpR4qgFuospIKftsQw8fP7CblVC7jro3ghicvIGyIl2l/TAyJdywg6e6/ARD01psEv/tf7Pr2bVE5hkoDS/5Ywkt/vsTFQRez5tI1eDt4N31ic5WXmLpPek8Crz51dheWVfDH6Swm9/dpvzK7wMT+Puw+k01RWUXdnRotXLAA4nbC2f0dUv6E4Am8cskrHM06yqKti1odxAHc58wh5N13qczKIu666yn688/qfTZ6LdPvHMzw6aEc2XmW/636i7Li8kauprSFCuAWRholR387y0dP/cGBbYn0H+vHTc+OJWpKCFqdhsq8PFKff4EzV15FyeHD+D72KOHffYvzhAktnlyTWZLJHT/ewZcxX3JX5F38e+K/cbRp52T/+z6EwjS4qP6c1jtPZmCoNDJloG/7ltvJJvT1xlBp5PfTWfUfMOI2sHU15UjpIJNCJvGvS/7F4czDLNra+u4UAMfRFxD22adoPT1JuP0OcjecGwopNIKxV/Vm0rz+JJ/I5YuX95KfWdIeL0E5jwrgFiTlVC6fL43m5w+P4+bjwJzFI5l4ywAcXPTIykpyPvnU1M+9fj1u180xDQmcN69ZI0vOty9tHzd8fwMnck6w/JLl3DfsvtZNjW9MRRn8MgW8CgAAGNpJREFU9hqEjIWwi+s9ZMuxNNwcbBgZ2vwun+5oZJgHTrY6Nh9pYDSInQuMugOOfQtZrRv21xxTQqfwr0v+xZGsI9z2w21kFLf+hqM+NJSwTz7GcfRoUp54krSXliJrZDobcGEAlz8QRXG+gQ3Lokk53bqbqErDVAC3AIU5pWx+9whfLt9HSYGBqXcM5Kp/DMcn1HTDr3jPHmKvnUPqkiWm6dBffoH/00+3qJ+7ilEaeefgO9z+4+3otXo+mPEB08Omt/dLMtm7BvKTYfzD9a5MU1peydajaUzq72Mx+U8aotdpmD7Ijx+OpFJa3sCklzF3g9YWfn6xQ+syNXQq/5n8HxILEpm3aR6J+YmtvpbWxYXgt9/C/eabyV67lsS//Y3KwnPdM0H93LnmkRHY2On4ZsV+Tu5p3XBGpX6W/b/CylUYKtnzv1g+enoXZw5kMHJWGHOXjKHvKD+EEJSnpJD8978Tf8s8KnNzCVzxKiEffoBd//6tKi+zJJOFWxaycv9KpoVO47PLPqO/R+uu1aTibFOg6nWJqf+7HluOppFfWsHVw4I6pg6d7IqoAApKK9h+ooFWr5MPXHgvHN4Ayfs6tC4XBlzIu9PepbC8kFs23dKqGZtVhE6H3xOP47fkaYp+/Y34G2/EkHjuQ8Hdz5Fr/zkCnzBntrx7lN82xKibm+1EBfBuSErJqb3prF+ymz+/iyV0sBdznx7N6MvDsbHVYiwqIuP1VZyeMZOCbT/hdc899N74P1xmzGhVEikpJZtiN3HVN1dxIP0AS8YuYdn4ZTjpnTrg1ZltfwnK8uHSlxpcF/KLfUkEuNpZ7PDB813Y2xMvJz1f7///9s49Pory3OPfZ2/ZzRUSQgiXkJACEuQqKKjIRVuogFj1WHoqUu3Rauux6lGLiufUnk9b9bS11mNr1dNWaxHUtopWQQQRyt3IJaAC4U4SQu63zWZ3Z9/zx0zCEpOY6yaB9/v5zGffmXnfmd++886z777zzvPktZDpbohOgvcfhS6ehjcmeQwvff0lop3R3Lr6Vt7KfatDx+u7cCFpL75AoPA0R667nspVZ+Kbe2JdLPjhBC6cPohdH5zgrad2UlOh39zsKNqA9zAKj1by9198wuoX9uLyOLj23gnMuf1C4vt5UIEAZcuXkzt7DsXPPkvsjBlkvvsPkv/9ri999b05imuLuXf9vTy44UGGxA1hxbwVXD/i+q6Ng3h8G2x/ASbdCilNezg8WeZlw4EivjFxEPZzxFGSw27juomDWfNZIfnlzTzUc8fDrKVw7J+w6y9drmlYwjBenfsqE1MmsnTTUp7c8SSBUPtnjcRMnUrGG6/jysgg7557KXj0UUJeL2BGR5r+rZF89dYsio5XseKnOzi5v6yzvsp5iY7I00OoLvOx5c1DHNhWiCfexZRrhnHBpanYbGLO5/7gA4p++Sv8R4/imXQRKfffj2f8+HafLxgK8saBN3hm5zP4gj7umnAXi7IWtToQQLvxe+G5y8EIwPc3Q1Rck9l+vHIfr2w9xsYfzey187+b4mSZlyue/JDbr8hkydebGZ4KheCleVC4F36wHeIGdLmuQCjAL3b8gmWfL2NMvzE8ccUTDIlrfXi2xqhAgKLfPEPJiy/iyshg4BOP4xkzpmF/SX41q36/l/LTXsZfOYRLFgzD4WxbzNHzCR1SrYfiqw6wc81x9qw7gVIw7qohXDRnKC63A6UU1R99RPFvf4dvzx5cmZn0/4/7iJ05s0M95B2ndvD49sc5UHaASwZcwsNTHmZYQie+mNMcSsGb34fdy+DmlTBsepPZymr8XPr4Oq4ek8ovbxzX9boizJ2vZLP5UAkbHpxJgqeZGULFufDcZTB4Mix6E+yR8fy8+uhqHtv8GCFCPHzJw8wfNr9Dba1myxbylzxEsKiIxEU3kXz33Q3BQAJ1Bpv/msveDXn0TY3hq7dkkZzW9A/6+Y424D2MOm+AXWtPsHvtCQJ1BsMnpTBlwTBzqEQpqteto/jZ3+L79FOcgwbR7847SLj22gbn+u3h89LPeXbXs6w/sZ7UmFQemPwAV6Vd1bXDJeFs/R2sWgLTl8DMh5rN9tjb+3hp81FW3XMFI1LOvRt6b14F8575J3fOyORHc1p4SLxrGbx5J1x2D3z1sYjpy6/OZ8nGJew8vZNLB17K0ilLO9QbN6qqOP2rX1H+6nKcAweS8uhSYsPeSzi+r4R1L39GbVWAsbMGM3leBi63DlUQjjbgPQRvpZ+c9SfJWX+SOm+QzAnJTJ6XQdKgWEK1tVS88w5lL/+ZuoMHcaal0e973yPhmvntmstdz/7S/fx+z+9Zc2wNca44Fmct5ubRN+NxRHBoYs9r8Lfb4YK5cOOfwdb045eDhVXMeXoj35w8hJ99Y0yTec4F7l2xi3dzCvjgvukMSWzBH83b90D2H+HqX3RK6LXWYoQMVuxfwW92/gYjZHDrhbeyePRiop2t953TGG92NgWP/if+w4eJnjqFlAcfxD3KjLzkqwmw5W+5fLqpgJgEF5fe8BWGT0qJXOeih6MNeDdTml/DrrXHObCtEMMIkTG2H5PnZpCcFkcgL4+y5cspf+11jIoKokaOJPGW75Awb167e9xGyOCjkx/xl8/+wvZT24lxxrAoaxGLsha1KWp5p7BrGbz1Axh6Gfzra+Bq2gj4gyFueG4zx0q8rPuP6STFRkVWZwTJK69l9lMbyBoYz6u3TWn+Qa0RgNduNoMfz3vKfPAbQU7VnOLJHU+y5tgaEt2J3DHuDq4ffj0ue/uCGiu/n7LlKyj+7W8xKiqInzuXpNtva3DxcOpIBRtePUDR8Sr6DYnlkvnDGDom6bw35NqAdwN+X5Dc7NN8vrmAgkMVOJw2LpiayrgrhxAXE6Jq9ftUrFyJd9s2sNmIu+oqEhfdhGfSpHY32GOVx3jn8Du8feht8qrzGBAzgIUjF3LDiBtIiIpwEFojAOv+GzY9DRlXwMJXIarpqYlKKf5r5T5e3nKM526ayJwLUyOrtRt4/eMTPPDGHn4wM5MHZrcwlBLwwWuL4OD75nDKrEcjNiZez+6i3TyV/RTZhdkkuZP49qhvc+PIG9vdpozKSkqef57SZa+ivF5iZ84k6dZb8EyahFJwYPspdrxzhMpiH/3T4xl/1RCGTUjG3stf6Gov2oBHCL8vyPF9pRzeeZojOSUE6wz6DojmgktTGZHlIbh9E9UfrqN64z9RPh/OoWkkLFhAnwULcA5qe2BbpRS55blszNvI2mNr2VO8B0G4OPVibhxxI7PSZnX9zJKmKNgNK+82o81cdAtc/T9gb3oYSCnFL98/wP9+mMtt0zJ4ZG5WhMV2D0opHvpbDst3nGDp3FH827QWHiQbQXjvAdNj4eDJsOBZSB4ZObGYercWbOWlfS+xKX8TUfYoZg2ZxfzM+UwdOLVd7SxYVkbZsmWU/fkVjPJyXOnpJFx/HQnXLMDWrx/7t5wie9VRKot9RCe4GH35QEZOGUBCcvuHcnoj2oB3ESEjRNGJavIOlJG3v5y8/WUYwRCeOCfpWX1Ijy8l5kg2tTu2U7tnDyiFIyWFuCtnET9/Pp7x49vU21ZKcaLqBLuLdpNdmM2m/E0N0VZGJY5i7rC5zEmfQ0pMNzl/yt8Fm58x3yaMToJ5v4asa5rNXuENsPStvby9O5+F1ri37RyZ990agkaIu5btZNW+U9w0JY2Hrx5FtKsFQ5jzBvzjPqirhok3w2V3NxmCrqs5UHaA1/e/zntH36OiroJEdyKXD7qcaYOnMTV1apt75iGvl8rV71P+1zeo/TgbAPe4scTNupLoK6ZT6E9k74Y8ju8zQ9Mlp8XxlYv6kzY6iaSBMed8UOUuMeAiMgd4GrADLyqlHm8pf2834IE6g4qiWkryqik6UUXxiWqKjlXi95m+LRLiIcVdQf+qz4jN3Yb/UK45p9fhwD06i9hpVxA7cwburKwvNdpKKaoCVRyvPE5ueS6Hyg+RW57LpyWfUuozG3GsM5ZLUi9h2qBpXD7o8u4x2kpB4T7I/QD2/d3scTs8pl+Py34InqaDEJd7/SzfcYIXNhymzOvn/tkjuXN65nk51mmEFI+/9xkvbDzCoD4e7piRyfUTBzVvyGuK4aMn4eP/g1DQdEUwaj4Mnw0Jbf8X1xECRoANeRtYfXQ1m/I2UemvRBAy+2QyNnksY/qNYXjf4aTHp7faqNcdOULVqlVUrfsQX04OALb4eKInTCB04cUUODM4fjqKonwfYAZZHjSiLynp8fQbEkvykDjcse1/6N8T6XQDLiJ24ADwVeAksAP4llLq0+bK9BQDrpTCCIQI+kMEAwZBf4iA3yDgDVBbXoO33EdthY/ayjq8VQGqSuuoqjTw1Z0xLjYM4owy4qqPk1Cwhz6l+4my3HM6UlNxjxhB1IWjcU0cD6NHEIyyU2fUmUuwjupANRV1FVT6Kxs+y3xlnPKeorCmkIKaAmoCNQ3nc9qcZCRkcEHiBYzvP55xyePITMjEbuvClx+MAPirwV9jLt4SqMyHqgIoPw6n9povm9RZbkkHjIEJN8PYfwFPX5RS1PgNyr1+ymoCHC6uJvd0NduOlJJ9rAwjpLg0M4lH5o5i9MAIj8/3QLYdLuFn733O7hPluBw2LstMYmJaX0YOiGNw32j6xbpIjHGdcexVmQ+fvGy+sVl+3NwWP8iMdJ88EvoMgYQhpo+VqHhwJ5gvTjUzlNVRjJBBTnEOWwq2sKdoDznFOWeFcUt0JzI0fij9o/uT7EkmOTqZZE8y8a54YpwxxLpiiXHGEOOMwW1347Q5UUUleLdupTb7E7zZ2fgPH244nj8hlcrMKZQmDKfUloLXcDfsc7uFuAQHcUlu4pOjiU6IwpPgxh3vxhPnIsrjwOGy4XDZcTht2J22Ht156AoDPhX4sVJqtrX+EIBS6ufNlWmvAf/DbUsxAlmWzwxzUdbnmW2Y2xpcngoqPH9D2kaolU/Q7UYdTn8VHl8J7tpiPL4SPL5iXL58QqqQ0vgQxQlCcQIUx0NhX+F4CnjdQgAItOFvnV0p4g1FsqHoHwyREgyRHFQMDBqkB0IMDIRwcuZaNT6yEH4dm853dp6Wy7gI4KKJ4AMW1Xg4SBr7GcpevsJmNZYiEs86mi9gEGwUyNcmcMGAeGaMTGb+uIGMSo3wjJgejlKKj4+V8W5OAR/tL+Jwcc0X8rjsNlwOc4ly2LALZHCCi43dXBDKZUToEIPUKRw07fUwiJ0gdgwcBMVOEAcGdgzs1n0V1hrCjJoKv8/C85gZv7BPAQUOOOGEPCecdECBE0rtUGaH2lbeH3alcChwAPG1isFFMLBEMbAYkssUfaugTzU4jRiqYwdTFTsEr6c/Pk8SPncSvqhEVCs6OhLyYwsFgRAoZd0fYWkVsr6h9e2+1HaevT9pbD7X3fdAq77zF7Q1Y8A78nRrEBDuh/IkcEkTJ74duB0gLS2tXSeyx4RQpQWAAqlvGuYiKKuaQghYa03sDysnAT+oAEIAlB8hQMhmLXYvIbsXw+HF7w5QmyAUu4Q6j41aj406tw3DKYDpYEkaTKSQCKYJ84MDwakEJzYcytaQdirBKTailZ1o5SAmZCdG2YnC3nAsVX/TOMylzg1HzlRoQ72osLM3Xq+/kcyPs834WYSthpcP2lz4bdEE7B78NnOpdcRT6Uym0tWfOlsMiCACTmB6w+HOHNDjspHgcVqLi4x+MaT3iybKoV+Zbg4RYXJ6IpPTE2G+GZHoYGEVpyp8FNf4Ka324wsa1AVC+A0DfzBE0FAokjikxnEIeAcgZBAfLKVvsJDYYBluoxpPqAa3UYNT1WFXlhlXhplWQWyWwQ9vYQ26GoyVapQnvCOgGq2DGxgODA8CQcB3plythKiwGdRKKGxR1EqIgCgMUQRRBAUMzLRhg2CKoiwFSgEl5nkVYA8oomvyifLnEeVTRNWZiyMANiMKmxGDLRSNqBhEebApB+ACnChxYrZkB/UdvfrO39lpc101vo++eCW/sMUT3/kvpXX59ASl1PPA82D2wNtzjMW/7lr/yBpNTyU2ysGEtN4dzELTdXRkUmUeEP5+7WBrm0aj0WgiQEcM+A5guIhkiIgLWAis7BxZGo1Go/ky2j2EopQKishdwGrMaYR/UErt6zRlGo1Go2mRDo2BK6XeBd7tJC0ajUajaQPnp2MBjUajOQfQBlyj0Wh6KdqAazQaTS9FG3CNRqPppUTUG6GIFAHH2lm8H1DciXI6C62rbWhdbUPrahs9VRd0TNtQpVRy440RNeAdQUQ+bsoXQHejdbUNrattaF1to6fqgq7RpodQNBqNppeiDbhGo9H0UnqTAX++uwU0g9bVNrSutqF1tY2eqgu6QFuvGQPXaDQazdn0ph64RqPRaMLQBlyj0Wh6KT3KgItIooisEZGD1ucXPNmLyHgR2SIi+0Rkj4h8M2xfhohsE5FcEVlhubmNiC4r3yoRKReRdxpt/5OIHBGRXdYyvofo6u76WmzlOSgii8O2rxeR/WH11b+DeuZYx8sVkSVN7I+yvn+uVR/pYfsesrbvF5HZHdHRWbpEJF1EasPq57kI67pCRD4RkaCI3NBoX5PXtAfoMsLqq1PdXrdC130i8qllr9aKyNCwfR2rL6VUj1mAJ4ElVnoJ8EQTeUYAw630QKAA6GOtvwYstNLPAXdGSpe170pgPvBOo+1/Am7ojvr6El3dVl+Y0ecOW599rXRfa996YFInabEDh4BhmPGzdgNZjfJ8H3jOSi8EVljpLCt/FJBhHcfeA3SlA3s7uz21QVc6MBZ4Obxdt3RNu1OXta+6G+trJhBtpe8Mu44drq8e1QMHFgAvWemXgGsbZ1BKHVBKHbTS+cBpIFlEBJgFvNFS+a7SZelZC1R10jlbQ7t19YD6mg2sUUqVKqXKgDXAnE46fzgXA7lKqcNKKT+w3NLXnN43gCut+lkALFdK1SmljgC51vG6W1dX8qW6lFJHlVJ7gFCjsl15TTuiqytpja4PlVJea3UrZvQy6IT66mkGPEUpVWClTwEpLWUWkYsxf/UOYUYZLldK1YdSP4kZeDniuprhp9ZfqKdEJKoH6Oru+moqKHb4+f9o/d19tING68vOc1Yeqz4qMOunNWW7QxdAhojsFJGPRGRaJ2lqra6uKNvVx3aLyMcislVEOquj0h5d3wXea2fZL9DlQY0bIyIfAAOa2PVI+IpSSolIs3McRSQV+DOwWCkV6mjHpLN0NcNDmIbMhTkX9EfAT3qArnbTxbq+rZTKE5E44K/AIsy/xRqTAiBNKVUiIhcBb4rIaKVUZXcL68EMtdrUMGCdiOQopQ5FUoCI3ARMAqZ31jEjbsCVUlc1t09ECkUkVSlVYBno083kiwf+ATyilNpqbS4B+oiIw+qttCnIcmfoauHY9b3ROhH5I3B/D9DV3fWVB8wIWx+MOfaNUirP+qwSkWWYf1Pba8BbE3y7Ps9JEXEACZj105WBu9utS5kDqHUASqlsETmE+Wzo4wjpaqnsjEZl13eCpvpjt/tahLWpwyKyHpiA+c89IrpE5CrMzs10pVRdWNkZjcqub8vJe9oQykqg/knsYuCtxhnEnCnxd+BlpVT9+C1Wo/4QuKGl8l2lqyUsI1Y/7nwtsLe7dfWA+loNfE1E+oo5S+VrwGoRcYhIPwARcQLz6Fh9tSb4drjeG4B1Vv2sBBZas0EygOHA9g5o6RRdIpIsInYAq0c5HPMBWKR0NUeT17S7dVl6oqx0P+Ay4NNI6RKRCcDvgWuUUuGdmY7XV1c8mW3vgjm+txY4CHwAJFrbJwEvWumbgACwK2wZb+0bhnmD5QKvA1GR0mWtbwSKgFrM8azZ1vZ1QA6mIXoFiO0hurq7vm61zp0L3GJtiwGygT3APuBpOjjzA7gaOIDZ43rE2vYTzBsKwG19/1yrPoaFlX3EKrcf+Hont/d26QKut+pmF/AJMD/CuiZb7agG85/KvpauaXfrAi617r/d1ud3I6zrA6CQM/ZqZWfVl36VXqPRaHopPW0IRaPRaDStRBtwjUaj6aVoA67RaDS9FG3ANRqNppeiDbhGo9H0UrQB12g0ml6KNuCa8xIROSoiOSLS6ijhIpJp+Wep7kptGk1r0fPANeclInIU02VtcTvKViulYjtflUbTNnQPXHPOISJ3hDnvPyIiH7aizFER+blV5mMRmSgiq0XkkIjcEQndGk1b0QZcc86hlHpOKTWeM69W/6qVRY9b5TZiBeEApgCPdYVOjaajRNwboUYTQZ7GdAD1divz1zshysH0V1MFVIlInYj0UUqVd4lKjaadaAOuOScRke8AQ4G72lCs3s1nKCxdv67vFU2PQzdKzTmHFeTgfmCaUiqS4bU0moiix8A15yJ3YQaK/dB6KPlidwvSaLoCPY1Qc16ipxFqzgV0D1xzvlIErG3PizyYzvk1mm5H98A1Go2ml6J74BqNRtNL0QZco9FoeinagGs0Gk0vRRtwjUaj6aX8P9aAKZeTETgFAAAAAElFTkSuQmCC\n"
+          },
+          "metadata": {
+            "needs_background": "light"
+          }
+        }
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "source": [
+        "The equilibrium bunch profile computed analytically using `BeamLoadingEquilibrium` can be compared to the tracking results:"
+      ],
+      "metadata": {
+        "id": "cjL-np8paYEq"
+      }
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "HC.detune = 42e3\n",
+        "\n",
+        "# Tracking using a uniform beam filling pattern\n",
+        "filling_pattern = np.ones(ring.h)*I0/ring.h\n",
+        "mybeam = Beam(ring)\n",
+        "mybeam.init_beam(filling_pattern, mp_per_bunch=1e4, track_alive=False)\n",
+        "\n",
+        "for i in range(2000):\n",
+        "    if i%100 == 0:\n",
+        "      print(i)\n",
+        "    long.track(mybeam)\n",
+        "    rad.track(mybeam)\n",
+        "    MC.track(mybeam)\n",
+        "    HC.track(mybeam)\n",
+        "\n",
+        "\n",
+        "# 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.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))"
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 712
+        },
+        "id": "xvg8zezzV4f_",
+        "outputId": "55589a59-d678-4531-8a1d-a8adc5520801"
+      },
+      "execution_count": 40,
+      "outputs": [
+        {
+          "output_type": "stream",
+          "name": "stdout",
+          "text": [
+            "0\n",
+            "100\n",
+            "200\n",
+            "300\n",
+            "400\n",
+            "500\n",
+            "600\n",
+            "700\n",
+            "800\n",
+            "900\n",
+            "1000\n",
+            "1100\n",
+            "1200\n",
+            "1300\n",
+            "1400\n",
+            "1500\n",
+            "1600\n",
+            "1700\n",
+            "1800\n",
+            "1900\n",
+            "The initial center of mass offset is -178.42158504142017 ps\n",
+            "The final center of mass offset is 13.777318935482338 ps\n",
+            "The algorithm has converged: True\n"
+          ]
+        },
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "[<matplotlib.lines.Line2D at 0x7f58a1e95e90>]"
+            ]
+          },
+          "metadata": {},
+          "execution_count": 40
+        },
+        {
+          "output_type": "display_data",
+          "data": {
+            "text/plain": [
+              "<Figure size 432x288 with 1 Axes>"
+            ],
+            "image/png": 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\n"
+          },
+          "metadata": {
+            "needs_background": "light"
+          }
+        }
+      ]
+    }
+  ]
+}
\ No newline at end of file
-- 
GitLab