howto_notebooks/DetunersTest.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# general imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from __future__ import division, print_function\n",
    "\n",
    "import numpy as np\n",
    "np.random.seed(42)\n",
    "\n",
    "from scipy.constants import m_p, c, e\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# sets the PyHEADTAIL directory etc.\n",
    "try:\n",
    "    from settings import *\n",
    "except:\n",
    "    pass"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# PySussix imports\n",
    "\n",
    "Sussix is a tune analysis tool: https://cds.cern.ch/record/702438/files/sl-note-98-017.pdf .\n",
    "If you do not have PySussix, its python interface, find it under https://github.com/PyCOMPLETE/PySussix ."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "try:\n",
    "    from PySussix import Sussix\n",
    "except ImportError:\n",
    "    print ('ERROR: This interactive test needs the PySussix module. Trying PySUSSIX')\n",
    "    from PySUSSIX import Sussix\n",
    "    print('PySUSSIX found')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# PyHEADTAIL imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PyHEADTAIL v1.10.5.269\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "from PyHEADTAIL.trackers.transverse_tracking import TransverseMap\n",
    "from PyHEADTAIL.trackers.detuners import Chromaticity, AmplitudeDetuning\n",
    "import PyHEADTAIL.particles.generators as generators"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Setting up the machine and functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Basic parameters.\n",
    "n_turns = 1024\n",
    "n_segments = 1\n",
    "n_macroparticles = 500\n",
    "\n",
    "Q_x = 64.28\n",
    "Q_y = 59.31\n",
    "Q_s = 0.0020443\n",
    "\n",
    "C = 26658.883\n",
    "R = C / (2.*np.pi)\n",
    "\n",
    "alpha_x_inj = 0.\n",
    "alpha_y_inj = 0.\n",
    "beta_x_inj = 66.0064\n",
    "beta_y_inj = 71.5376\n",
    "alpha_0 = 0.0003225\n",
    "\n",
    "# Parameters for transverse map.\n",
    "s = np.arange(0, n_segments + 1) * C / n_segments\n",
    "\n",
    "alpha_x = alpha_x_inj * np.ones(n_segments)\n",
    "beta_x = beta_x_inj * np.ones(n_segments)\n",
    "D_x = np.zeros(n_segments)\n",
    "\n",
    "alpha_y = alpha_y_inj * np.ones(n_segments)\n",
    "beta_y = beta_y_inj * np.ones(n_segments)\n",
    "D_y = np.zeros(n_segments)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def calc_sussix_spec(x, xp, y, yp, p_idx, turn, window_width, q_x, q_y, n_lines=10):\n",
    "    # Initialise Sussix object\n",
    "    SX = Sussix()\n",
    "    SX.sussix_inp(nt1=1, nt2=window_width, idam=2, ir=0, tunex=q_x, tuney=q_y)\n",
    "\n",
    "    tunes_x = np.empty(n_lines)\n",
    "    tunes_y = np.empty(n_lines)\n",
    "\n",
    "    SX.sussix(x[p_idx,turn:turn+window_width], xp[p_idx,turn:turn+window_width],\n",
    "              y[p_idx,turn:turn+window_width], yp[p_idx,turn:turn+window_width],\n",
    "              x[p_idx,turn:turn+window_width], xp[p_idx,turn:turn+window_width]) # this line is not used by sussix!\n",
    "\n",
    "    return SX.ox[:n_lines], SX.oy[:n_lines]\n",
    "\n",
    "def track_n_save(bunch, map_):\n",
    "    n_particles = bunch.macroparticlenumber\n",
    "    x_i = np.empty((n_particles, n_turns))\n",
    "    xp_i = np.empty((n_particles, n_turns))\n",
    "    y_i = np.empty((n_particles, n_turns))\n",
    "    yp_i = np.empty((n_particles, n_turns))\n",
    "\n",
    "    for i in xrange(n_turns):\n",
    "        x_i[:,i] = bunch.x[:]\n",
    "        xp_i[:,i] = bunch.xp[:]\n",
    "        y_i[:,i] = bunch.y[:]\n",
    "        yp_i[:,i] = bunch.yp[:]\n",
    "   \n",
    "        for m_ in map_:\n",
    "            m_.track(bunch)\n",
    "\n",
    "    return x_i, xp_i, y_i, yp_i\n",
    "\n",
    "def analyse_n_plot(bunch, x_i, xp_i, y_i, yp_i):\n",
    "    ox = np.empty(bunch.macroparticlenumber)\n",
    "    oy = np.empty(bunch.macroparticlenumber)\n",
    "    print ('analysing particle spectra ... this may take some time.')\n",
    "    for p_idx in range(bunch.macroparticlenumber):\n",
    "        ox[p_idx], oy[p_idx] = calc_sussix_spec(x_i, xp_i, y_i, yp_i, p_idx,\n",
    "                                   turn=0, window_width=512, q_x=Q_x%1, q_y=Q_y%1, n_lines=1)\n",
    "        if (p_idx)%100 == 0:\n",
    "            print ('particle', p_idx)\n",
    "\n",
    "    fig = plt.figure(figsize=(20,20))\n",
    "    ax1 = fig.add_subplot(311)\n",
    "    ax2 = fig.add_subplot(312, sharex=ax1)\n",
    "    ax3 = fig.add_subplot(313)\n",
    "\n",
    "    ax1.scatter(ox, oy)\n",
    "    ax1.set_ylabel(r'$Q_y$', fontsize=20)\n",
    "    ax1.set_xlabel(r'$Q_x$', fontsize=20)\n",
    "    ax2.hist(ox, bins=50, color='blue')\n",
    "    ax2.set_xlabel(r'$Q_x$', fontsize=20)\n",
    "    ax3.hist(oy, bins=50, color='red')\n",
    "    ax3.set_xlabel(r'$Q_y$', fontsize=20)\n",
    "    \n",
    "    print ('std dev. Qx', np.std(ox))\n",
    "    print ('std dev. Qy', np.std(oy))\n",
    "    plt.show()\n",
    "    \n",
    "    os.remove('sussix.inp')\n",
    "\n",
    "def generate_bunch(n_macroparticles, alpha_x, alpha_y, beta_x, beta_y, alpha_0, Q_s, R):\n",
    "    intensity = 1.05e11\n",
    "    sigma_z = 0.059958\n",
    "    gamma = 3730.26\n",
    "    eta = alpha_0 - 1. / gamma**2\n",
    "    gamma_t = 1. / np.sqrt(alpha_0)\n",
    "    p0 = np.sqrt(gamma**2 - 1) * m_p * c\n",
    "\n",
    "    beta_z = eta * R / Q_s\n",
    "\n",
    "    epsn_x = 3.75e-6 # [m rad]\n",
    "    epsn_y = 3.75e-6 # [m rad]\n",
    "    epsn_z = 4 * np.pi * sigma_z**2 * p0 / (beta_z * e)\n",
    "    \n",
    "    bunch = generators.generate_Gaussian6DTwiss(\n",
    "        macroparticlenumber=n_macroparticles, intensity=intensity, charge=e,\n",
    "        gamma=gamma, mass=m_p, circumference=C,\n",
    "        alpha_x=alpha_x, beta_x=beta_x, epsn_x=epsn_x,\n",
    "        alpha_y=alpha_y, beta_y=beta_y, epsn_y=epsn_y,\n",
    "        beta_z=beta_z, epsn_z=epsn_z)\n",
    "\n",
    "    return bunch"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Let's go"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Amplitude detuning\n",
    "\n",
    "Amplitude detuning (such as from octupole magnets) can be modelled with the `AmplitudeDetuning` detuner class. Check out this LHC example with currents of $I=400~A$ where we expect $\\approx 5\\times 10^{-4}$ detuning in both transverse planes:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "analysing particle spectra ... this may take some time.\n",
      "particle 0\n",
      "particle 100\n",
      "particle 200\n",
      "particle 300\n",
      "particle 400\n",
      "std dev. Qx 0.000493943454511\n",
      "std dev. Qy 0.000504673628496\n"
     ]
    },
    {
     "data": {
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HPvL+vPOd783Y2DuT3JPkiIyNbc4rX/nanHXWn2TDhpEkH0pyRJIfphly/8EkK7Nhw+1Z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\nziR/p7v/6BTb+Kk89rKoJHlPkhfN1n9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4BQAAAMCwhFsAAAAADEu4BQAAAMCwljrcqqqz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\nGJZwCwAAAIBhCbcAAAAAGNb/B+e3HTJcMcSeAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f525687ef50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "bunch = generate_bunch(\n",
    "    n_macroparticles, alpha_x_inj, alpha_y_inj, beta_x_inj, beta_y_inj,\n",
    "    alpha_0, Q_s, R)\n",
    "\n",
    "ampl_det = AmplitudeDetuning.from_octupole_currents_LHC(i_focusing=400, i_defocusing=-400)\n",
    "trans_map = TransverseMap(\n",
    "    s, alpha_x, beta_x, D_x, alpha_y, beta_y, D_y, Q_x, Q_y, [ampl_det])\n",
    "\n",
    "map_ = [m for m in trans_map]\n",
    "\n",
    "x_i, xp_i, y_i, yp_i = track_n_save(bunch, map_)\n",
    "analyse_n_plot(bunch, x_i, xp_i, y_i, yp_i)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Chromatic detuning\n",
    "\n",
    "Chromaticity can be modelled with the `Chromaticity` detuner class. First-order chromaticity for values of $Q'_x=6$ and $Q'_y=3$ with LHC tunes yields:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "analysing particle spectra ... this may take some time.\n",
      "particle 0\n",
      "particle 100\n",
      "particle 200\n",
      "particle 300\n",
      "particle 400\n",
      "std dev. Qx 0.000561082708596\n",
      "std dev. Qy 0.00028045654874\n"
     ]
    },
    {
     "data": {
      "image/png": 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nJ0uWLOGggw5i0aJFrFmzhve85z2MHTuWp556iokTJ3Lvvffyhz/8gW3btvGq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\nv2OX0t/U9dZ9e815AIAVqap0dy2rviO6AAAAABiCoAsAAACAIQi6AAA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k3d23nPO4zdox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\nAAAAQxB0AQAAADAEQRcAAAAAQ/j/80e/E1wXA0kAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f523070e490>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "bunch = generate_bunch(\n",
    "    n_macroparticles, alpha_x_inj, alpha_y_inj, beta_x_inj, beta_y_inj,\n",
    "    alpha_0, Q_s, R)\n",
    "\n",
    "chroma = Chromaticity(Qp_x=[6], Qp_y=[3]) # note the lists!\n",
    "trans_map = TransverseMap(\n",
    "    s, alpha_x, beta_x, D_x, alpha_y, beta_y, D_y, Q_x, Q_y, [chroma])\n",
    "\n",
    "map_ = [m for m in trans_map]\n",
    "\n",
    "x_i, xp_i, y_i, yp_i = track_n_save(bunch, map_)\n",
    "analyse_n_plot(bunch, x_i, xp_i, y_i, yp_i)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Higher-order Chromatic Detuning\n",
    "\n",
    "The `Chromaticity` detuner class supports higher orders in chromatic detuning. Check out this LHC example with horizontal chromaticities of $Q'_x=6, Q''_x = 4\\times10^4$ and vertical chromaticities of $Q'_y=3, Q''_y=0, Q'''_y=2\\times10^8$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "analysing particle spectra ... this may take some time.\n",
      "particle 0\n",
      "particle 100\n",
      "particle 200\n",
      "particle 300\n",
      "particle 400\n",
      "std dev. Qx 0.000568932172386\n",
      "std dev. Qy 0.000322448107092\n"
     ]
    },
    {
     "data": {
      "image/png": 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PVtXr5/ueV1X/ar79t6vqP172eQFP6fr+1nP2\nvbGq/k1V/euq+sWq+or59qNVdWdVPVBVd1TVkWWeE7BhQdf3m6vqw1V1X1X9SlU9Y5nnBGxYxPV9\nzv4fraozVfUXl3EuwJda1PVdVT88fw+/v6puezI1CboYSlVdkuTvJ/nOJM9J8j1V9c3nNfuDJH+t\nu5+X5H9J8jNJ0t0f7e7nd/cLknxbks8leff8mDcnubW7n5/k1iT/x8JPBvgST/H6fsv82L+U5IeT\nvKC7vzUbt+5/9/yYk0nu6u6rktyd5JZFnwvwpRZ4fd+Z5DndfXWS34/rG5Zugdd3qurKJC9J8uCi\nzwP4cou6vqvqO5L8F0me293PTfK3n0xdgi5Gc02S3+/uB7v78ST/MMmN5zbo7g9096Pzhx9I8g0X\n6Oe6JB/r7ofmj88k+eIoj7+Q5I92vXJgKzu9vi9N8vSqOpTk8vyH6/jGJKfm66eS3LSg+oGL2+3r\n+9/Pj7mru8+cc8yVCzwH4MIWcn3P/WSSH1tY5cBWFnV9vzbJbd39hXkfn3oyRQm6GM03JPnEOY8f\nyoWDrC/6m0n+nwts/64k/+Ccx29M8rer6g+zMbrLX4Rh+Z7y9d3d/z7J/5nkD7MRcP1Zd/+Tebsr\nunt93u50kit2uW5ga7t9fd91gWNenQu/5wOLtZDru6puSPKJ7r5/EUUD27Ko9+9nJ/lrVfWBqvqn\nT3bqIEEXB9Z8OOQPJrn5vO1PS3JDknees/lvJXlDd39jNkKvty2rTuDJO//6rqq/kI2/Lj0zyV9K\n8lVV9cqLHO5bWmAPeyrXd1X9j0ke7+5fWnK5wJOw3eu7qi5L8uPZmFLk7OFLLhd4Ep7k+/ehJEe7\n+9uT/A9J3vFknkvQxWj+KMk3nvP4ylzgNsP5BHhvSXJDd//pebtfmuRD3f3Jc7Z9f3f/WpJ097uy\nMUQTWK6dXN/XJfmD7n6ku5/Ixvx7/+l833pVHZsfO0ny8ILqBy5uUdd3quoHkrwsycXCbWCxFnF9\n/0dJjif53ar6d/M+P1RVRmXDci3q/fuh+eN09weTnKmqr9luUYIuRvPBJH+5qp45/8aG707ynnMb\nVNU3JvmVJN/X3R+7QB/fky+9bTFJ/qiqXjw//tokH931yoGt7OT6/sMk315VX1lVleTaJB+e73tP\nkh+Yr39/kl9f3CkAF7GQ67uqrs/G/D03dPdjSzgP4Mvt+vXd3f+muyfd/azu/qZs/E/x87vbH6tg\nuRb1+fzXkvz1+fHPTvK07v6T7RZ16KmeDexF3f1EVb0uG9+ydEmSn+3uD1fVazZ291uS/E9J/mKS\nn55fUI939zVJUlWXZyNZ/m/P6/qHkvzdqro0yZ9fYD+wYDu5vrv7t6vqXUnuTfL4/Odb5l3fnuQd\nVfXqbHxr0yuWe2bAAq/vv5fkK5K8b+OQfKC7/7ulnhwccAu8vr/kaeLWRVi6BV7fb0vytqq6P8lj\nSV71ZOqqblORAAAAALD/uXURAAAAgCEIugAAAAAYgqALAAAAgCEIugAAAAAYgqALAAAAgCEIugAA\nAAAYgqALAAAAgCEIugAAAAAYwqFVFwAAwPZU1X+W5L9JcmmSzyf52iRPJLmtu+9dZW0AAHuBoAsA\nYI+rqq9K8rYkVyZ5dXd/5Jx9L0vyz6rqb3T3r6+qRgCAvaC6e9U1AABwEVV1PMk/SvJgkv+yu/+/\nC7T5u0leleRZ3f3IUgsEANhDzNEFALBHVdVlSd6b5LIk332hkGvu3UmekeT7l1UbAMBe5NZFAIC9\n6+8l+StJ/qvu/swm7f5o/vPbF18SAMDeZUQXAMAeVFXPS/KDSR7o7l/bovkzzvsJAHAgCboAAPam\n18x//vw22v7l+c9PLqgWAIB9QdAFALA3/fX5z3+8jbbTJJ3kAwurBgBgH/CtiwAAe1BV/XmSSnJ5\ndz+xSbunJXkoyZEkx7v79JJKBADYc0xGDwCwN30uyZ9vFnLNfW+Sr0vyFiEXAHDQGdEFALAHVdVd\nSZ7X3V+3SZtnJPlIkifmbR9ZVn0AAHuREV0AAHvTTyV5V1Ud6+71qvqmJK/Kxu2MfyfJp5O8I8nT\nk1x7bshVVX81ybck+dZszNt1JMn1Sd7Y3R9f6lkAACyRyegBAPag7v7VbIRdr62qS5K8vLvflOT2\nJP9rkjuTPCcbIdfvfPG4qvrqJFd199uS3JXkDd39fyf5bJL/d8mnAQCwVG5dBADYw6rqpiR/muS2\nJPdk49sVvzfJzyV5U3c/WlXT7p7N2x9O8kR3f6Gq/uckn+nuN6+megCA5RJ0AQDsM1X1we5+4Xz9\nsiQnu/vWC7T77SR/q7s/VFXP6O5PL7tWAIBlcusiAMA+UlVfkeTbqurlVfUtSd6dZHbO/hNV9caq\nemaS5ya5d77r+5deLADAkhnRBQCwz1TVZ7IxCX2S3NHdLz1n3w8keUGSB5JcluRMks8leXd3f3LJ\npQIALJWgCwBgn6mqk0luycY3Kv7XbkkEANgg6AIAAABgCOboAgAAAGAIgi4AAAAAhiDoAgAAAGAI\ngi4AAAAAhiDoAgAAAGAIgi4AAAAAhiDoAgAAAGAIgi4AAAAAhiDoAgAAAGAIgi4AAAAAhiDoAgAA\nAGAIgi4AAAAAhiDoAgAAAGAIgi4AAAAAhiDoAgAAAGAIgi4AAAAAhiDoAgAAAGAIgi4AAAAAhiDo\nAgAAAGAIgi4AAAAAhiDoAgAAAGAIQwddVXVJVd1bVe+ZP761qh6qqnvmy/WrrhEAAACA3XFo1QUs\n2BuS/F6SZ5yz7Se6+ydWVA8AAAAACzLsiK6qujLJy5K89fxdKygHAAAAgAUbNuhK8pNJfixJn7f9\ndVV1X1W9taqOrKAuAAAAABZgyKCrql6eZL2778uXjuD66STP6u6rk5xO4hZGAAAAgEFU9/kDnva/\nqvrfkvyNJF9IclmSr07y7u5+1Tltnpnkvd39rRfpY7wXBgAAAGDFunth00oNGXSdq6penORHu/uG\nqpp09+n59jcmeWF3v/Iix/Xorw1709raWtbW1lZdBgeQ3z1Wye8fq+J3j1Xy+8eq+N1jlapqoUHX\n6N+6eL43V9XVSc4k+XiS16y2HAAAAAB2y/BBV3e/P8n75+uv2qI5AAAAAPvUkJPRw342nU5XXQIH\nlN89VsnvH6vid49V8vvHqvjdY2TDz9H1VJmjCwAAAGB3LXqOLiO6AAAAABiCoAsA2FOOTyapqh0t\nxyeTVZ8GAAAr4NbFi3DrIgCsRlVlp+/AlcT7OADA3uPWRQAAAADYBkEXAAAAAEMQdAEAAAAwBEEX\nAAAAAEMQdAEAAAAwBEEXAAAAAEMQdAEASZLjk0mqakfL8clk1acBAMABVt296hr2pKpqrw0AB0lV\nZafvfJVkp++fe6UOAAB2X1Wlu2tR/RvRBQAAAMAQBF0AAAAADEHQBQAAAMAQBF0AAAAADEHQBQAA\nAMAQBF0AAAAADEHQBQAAAMAQBF0AAAAADEHQBQAAAMAQBF0AAAAADEHQBQAAAMAQBF0AAAAADEHQ\nBQAAAMAQBF0AAAAADGHooKuqLqmqe6rqPfPHR6vqzqp6oKruqKojq64RAAAAgN0xdNCV5A1J/u05\nj08muau7r0pyd5JbVlIVAAAAALtu2KCrqq5M8rIkbz1n841JTs3XTyW5adl1AQAAALAYwwZdSX4y\nyY8l6XO2Hevu9STp7tNJrlhFYQAAAADsviGDrqp6eZL17r4vSW3StDfZBwAAAMA+cmjVBSzIi5Lc\nUFUvS3JZkq+uql9IcrqqjnX3elVNkjy8WSdra2tn16fTaabT6eIqBgAAABjMbDbLbDZb2vNV99iD\nmqrqxUl+tLtvqKo3J/mT7r69qm5OcrS7T17kuB79tQGAc1XVjoc6V5Kdvn/ulToAANh9VZXu3uzu\nux0Z8tbFTdyW5CVV9UCSa+ePAQAAABjA8CO6niojugA4aPbKSKq9UgcAALvPiC4AAAAA2AZBFwAA\nAABDEHQBAAAAMARBFwAAAABDEHQBAAAAMARBFwAAAABDEHQBAAAAMARBFwAAAABDEHQBAAAAMARB\nFwAAAABDEHQBAAAAMARBFwCwaw4nqaodLXvF8clkx+dyfDJZ9WkAABwo1d2rrmFPqqr22gBwkFRV\ndvrOV8ne6WOH7+O79nr4PAEAcFZVpbsX9tdNI7oAAAAAGIKgCwAAAIAhCLoAAAAAGIKgCwAAAIAh\nCLoAAAAAGMKhVRcAALDbDmfjG30AADhYBF0AwHAeS9I77ENMBgCw/7h1EQAAAIAhCLoAAAAAGIKg\nCwAAAIAhCLoAAAAAGIKgCwAAAIAhCLoAAAAAGIKgCwAAAIAhCLoAAAAAGMKwQVdVHa6q36qqe6vq\n/qq6db791qp6qKrumS/Xr7pWAAAAAHauunvVNSxMVV3e3Z+vqkuT/Iskr0/y0iSf6e6f2OLYHvm1\nAYDzVVV2+s5XiT7O78PnCQCAs6oq3V2L6n/YEV1J0t2fn68eTnIo/+Hz6sJeUAAAAABWY+igq6ou\nqap7k5xO8r7u/uB81+uq6r6qemtVHVlhiQAAAADskqGDru4+093PT3Jlkmuq6q8k+ekkz+ruq7MR\ngG16CyMAAAAA+8OhVRewDN396aqaJbn+vLm5fibJey923Nra2tn16XSa6XS6oAoBAAAAxjObzTKb\nzZb2fMNORl9VX5vk8e5+tKouS3JHktuS3NPdp+dt3pjkhd39ygscbzJ6AA4Uk9EvqA+fJwAAzlr0\nZPQjj+j6+iSnquqSbNyi+cvd/ZtV9fNVdXWSM0k+nuQ1K6wRAAAAgF0y7IiunTKiC4CDxoiuBfXh\n8wQAwFmLHtE19GT0AAAAABwcgi4AAAAAhiDoAgAAAGAIgi4AGMDxySRVtaMFAAD2O5PRX4TJ6AHY\nT0wkv4f78HkCAOAsk9EDAAAAwDYIugAAAAAYgqALAAAAgCEIugAAAAAYgqALAAAAgCEIugAAAAAY\ngqALAAAAgCEIugAAAAAYgqALAAAAgCEIugAAAAAYgqALAAAAgCEIugAAAAAYgqALAAAAgCEIugAA\nAAAYgqALAAAAgCEIugAAAAAYgqALAAAAgCEIugAAAAAYgqALAAAAgCEIugAAAAAYgqALAGBBDiep\nqh0txyeTVZ8GAMC+Ud296hr2pKpqrw0A+0VVZafvWpXoY6/24TMJADCIqkp316L6H3ZEV1Udrqrf\nqqp7q+r+qrp1vv1oVd1ZVQ9U1R1VdWTVtQIAAACwc8MGXd39WJLv6O7nJ7k6yUur6pokJ5Pc1d1X\nJbk7yS0rLBMAAACAXTJs0JUk3f35+erhJIeycffAjUlOzbefSnLTCkoDAAAAYJcNHXRV1SVVdW+S\n00ne190fTHKsu9eTpLtPJ7lilTUCAAAAsDuGDrq6+8z81sUrk1xTVc/Jl88Ja3ZXAAAAgAEcWnUB\ny9Ddn66qWZLrk6xX1bHuXq+qSZKHL3bc2tra2fXpdJrpdLrgSgEAAADGMZvNMpvNlvZ8NerXVVfV\n1yZ5vLsfrarLktyR5LYkL07ySHffXlU3Jzna3ScvcHyP+toAMJ6q2vEQ5crOhznrY0F9+EwCAAyi\nqtLdtaj+Rx7R9fVJTlXVJdm4RfOXu/s3q+oDSd5RVa9O8mCSV6yySAAAAAB2x7AjunbKiC4A9hMj\nugbvw2cSAGAQix7RNfRk9AAAAAAcHIIuAAAAAIYg6AIAAABgCIIuAAAAAIYg6AIAAABgCIIuAAAA\nAIYg6AIAAABgCIIuAAAAAIYg6AIAAABgCIIuAAAAAIYg6AIAAABgCIIuAAAAAIYg6AIAAABgCIIu\nAAAAAIYg6AIAAABgCIIuAAAAAIYg6AIAAABgCIIuAAAAAIYg6AIAAABgCIIuAAAAAIYg6AIAAABg\nCIIuAAAAAIYg6AIAAABgCIIuAAAAAIYg6AIAAABgCIIuAAAAAIYg6AIAAABgCIIuAAAAAIYwbNBV\nVVdW1d1V9XtVdX9V/fB8+61V9VBV3TNfrl91rQAAAADsXHX3qmtYiKqaJJl0931V9VVJPpTkxiTf\nleQz3f0TWxzfo742AIynqrLTd61K9LFX+/CZBAAYRFWlu2tR/R9aVMer1t2nk5yer3+2qj6c5Bvm\nuxf2ggIAAACwGsPeuniuqjqe5OokvzXf9Lqquq+q3lpVR1ZWGAAAAAC7Zviga37b4ruSvKG7P5vk\np5M8q7uvzsaIr01vYQQAAABgfxj21sUkqapD2Qi5fqG7fz1JuvuT5zT5mSTvvdjxa2trZ9en02mm\n0+lC6gQAAAAY0Ww2y2w2W9rzDTsZfZJU1c8n+VR3/8g52ybz+btSVW9M8sLufuUFjjUZPQD7hsno\nB+/DZxIAYBCLnox+2KCrql6U5J8luT8bnzE7yY8neWU25us6k+TjSV7T3esXOF7QBcC+IegavA+f\nSQCAQQi6VkTQBcB+IugavA+fSQCAQSw66Bp+MnoAAAAADgZBFwAAAABDEHQBAP9/e3cfY9ld3gf8\n+ywbuxgEdQDvVWPwQGl4EwWRgtKC2mmJgkkk7IiUQFJBSpSSBtQoqSimL/ISNSqOKv4ILYqSONSp\nShFNeTOqwoJgilCLTAWUJNgG0noTKDsQ2SSAeXHsp3/MtT2Md9e7e1/ndz8f6WrO3HvOc59z9fNv\njr977jkAADAEQRcArNjWZJKqmukBAAC4GP0ZuRg9AMviQvJqPGgNxyQAwCBcjB4AAAAAzoGgCwAA\nAIAhCLoAAAAAGIKgCwAAAIAhCLoAAAAAGIKgC4BDaWsySVXN9NiaTFa9GwAAwByV21WfXlW1zwZg\nfVVVZp2lK8k6zPVz2xc1xq2xBuMUAGAeqirdXYuq74wuAAAAAIYg6AIAAABgCIIuAAAAAIYg6AIA\nAABgCIIuAAAAAIYg6AIAAABgCIIuAIA1dnH2bsM9y2NrMln1bgAALEV196p7WEtV1T4bgPVVVZl1\nlq4k6zDXz21f1FDjbDXWYKwDAFRVursWVd8ZXQAAAAAMQdAFAAAAwBAEXQAAAAAMQdAFAAAAwBAE\nXQAAAAAMQdAFAAAAwBAEXQAAAAAMYdigq6our6oPVdUfVtXvV9U/mT5/aVWdqKpbq+r9VfXIVfcK\nAAAAwOyGDbqS/EWSX+rupyX5m0leXVVPTnJNkg9295OSfCjJ61fYIwAAAABzMmzQ1d2nuvtT0+Wv\nJ7k5yeVJrkpyw3S1G5JcvZoOAQAAAJinYYOu/apqK8kzk3wsybHu3k32wrAkl62uMwAAAADmZfig\nq6oenuR3k/zC9MyuPrDKwd8BAAAAOISOrrqBRaqqo9kLuf5jd79n+vRuVR3r7t2qmiT58pm2P378\n+H3L29vb2d7eXmC3ABxGW5NJTu7urroNAABYSzs7O9nZ2Vna+1X3uCc0VdXvJPnT7v6lfc9dl+T2\n7r6uql6X5NLuvuY02/bInw3AYVdVM5+SW0lmnevn1ocaaiy6huMaAGANVFW6uxZWf9SDnqp6bpKP\nJPn97B0fdpJ/nuSmJO9I8tgkJ5O8pLu/eprtBV0Aa0zQpYYa51nDcQ0AsAYEXSsi6AJYb4IuNdQ4\nzxqOawCANbDooGv4i9EDAAAAsBkEXQAAAAAMQdAFAAAAwBAEXQAAAAAMQdAFAAAAwBAEXQAAAAAM\nQdAFAAAAwBAEXQAAAAAMQdAFAAAAwBAEXQAAAAAMQdAFAAAAwBAEXQAAAAAMQdAFAAAAwBAEXQAA\nAAAMQdAFAAAAwBAEXQAAAAAMQdAFAAAAwBAEXQAAAAAMQdAFAMCD2ppMUlUzPbYmk1XvBgAwuOru\nVfewlqqqfTYA66uqMussXUlmnevn1ocaaiy6xrqMdcdXALDRqirdXYuq74wuAAAAAIYg6AIAAABg\nCIIuAAAAAIYg6AIAAABgCIIuAAAAAIYg6AIAAABgCIIuAAAAAIYg6AIAAABgCMMGXVV1fVXtVtWn\n9z13bVV9oao+MX1cucoeAQAAAJifYYOuJG9N8oLTPP+m7n7W9PF7y24KAAAAgMUYNujq7o8mueM0\nL9WyewEAAABg8YYNus7iNVX1qar6rap65KqbAQAAAGA+Ni3oekuSJ3T3M5OcSvKmFfcDAAAAwJwc\nXXUDy9TdX9n3628mufFs6x8/fvy+5e3t7Wxvby+kLwAAAIAR7ezsZGdnZ2nvV929tDdbtqraSnJj\ndz99+vuku09Nl38xybO7+yfPsG2P/NkAHHZVlVln6Uoy61w/tz7UUGPRNdZlrDu+AoCNVlXp7oVd\nP33YM7qq6m1JtpM8qqr+OMm1Sf5uVT0zyT1JbkvyqpU1CAAAAMBcDX1G1yyc0QWw3tbl7BJndKlx\naGqsy1h3fAUAG23RZ3Rt2sXoAQAAABiUoAsAAACAIQi6AAAAABiCoAsAAACAIQi6AAAAABiCoAsA\nAACAIQi6AAAAABiCoAsAAACAIQi6AAAAABiCoAsAAACAIQi6ADhvW5NJqmqmx9ZksurdyMXJzPsB\nAACsj+ruVfewlqqqfTYAp1dVmXWGrCSzzLNz60ENNTalxozHNevw3z0AcPhVVbp7Yf9i7IwuUpmx\nDgAAEIxJREFUAAAAAIYg6AIAAABgCIIuAAAAAIYg6AIAAABgCIIuAAAAAIYg6AIAAABgCIIuAAAA\nAIYg6AIAAABgCIIuAAAAAIYg6AIAAABgCIIuAAAAAIYg6AIAAABgCIIuAAAAAIZwdNUNAACwWBcn\nqapVtzGXPq44diy3nTo1n4YAgOFUd6+6h7VUVe2zATi9qsqsM2QlmWWenVsPaqihxuGr4RgNAA6t\nqkp3L+xf4Ib96mJVXV9Vu1X16X3PXVpVJ6rq1qp6f1U9cpU9AgAAADA/wwZdSd6a5AUHnrsmyQe7\n+0lJPpTk9UvvCgAAAICFGDbo6u6PJrnjwNNXJblhunxDkquX2hQAAAAACzNs0HUGl3X3bpJ096kk\nl624HwAAAADmZNOCroNcyRQAAABgEEdX3cCS7VbVse7erapJki+fbeXjx4/ft7y9vZ3t7e3FdgcA\nwMJtTSY5ubt7wdtfcexYbjt1ao4dAcC4dnZ2srOzs7T3q5Fvz1xVW0lu7O6nT3+/Lsnt3X1dVb0u\nyaXdfc0Ztu2RPxuAWVTVzKfEVpJZ5tm59aCGGmocvhozHqPNOn/MowcA2FRVle6uhdUf9Y90Vb0t\nyXaSRyXZTXJtkncn+S9JHpvkZJKXdPdXz7C9oAvgDARdaqihxkprCLoA4NASdK2IoAvgzARdaqih\nxkprCLoA4NBadNC16RejBwAAAGAQgi4AAAAAhiDoAgAAAGAIgi4AAAAAhnB01Q0AAMC5ujh7F7EF\nADgdQRcAAIfGtzOfOzcCAGPy1UUAAAAAhiDoAgAAAGAIgi4AAAAAhiDoAgAAAGAIgi4AAAAAhiDo\nAgAAAGAIgi4AAAAAhiDoAgAAAGAIgi4AAAAAhiDoAgAAAGAIgi4AAAAAhiDoAgAAAGAIgi6AQ2Rr\nMklVzfTYmkxWvRsAAAALUd296h7WUlW1zwZYN1WVWWemSjLr/LYOfcytBzXUUEONC9necSIAXJCq\nSnfXouo7owsAAACAIQi6AAAAABiCoAsAAACAIQi6AAAAABiCoAsAAACAIRxddQMAbKaLs3fHFYDD\nZh7z1xXHjuW2U6fm0xAAcB9BFwAr8e0kPcP2IjJgVWadv5Kkdnfn0QoAcICvLgIAAAAwhI08o6uq\nbkvyZ0nuSXJXdz9ntR0BAAAAMKuNDLqyF3Btd/cdq24EAAAAgPnY1K8uVjZ33wEAAACGtKlhTyf5\nQFV9vKp+dtXNAAAAADC7Tf3q4nO7+0tV9ZjsBV43d/dHV90UAAAAABduI4Ou7v7S9OdXqupdSZ6T\n5AFB1/Hjx+9b3t7ezvb29pI6BFici5NU1arbAGBGW5NJTu7uzlTjimPHctupU3PqCAAeaGdnJzs7\nO0t7v+rupb3ZOqiqS5Ic6e6vV9XDkpxI8obuPnFgvd60zwZYf1WVWWemSoaosQ49qKGGGptZY249\nzHisObe/CY55AViiqkp3L+xf3jfxjK5jSd5VVZ29/f9PB0MuAAAAAA6fjTuj61w5owtYR87oWq8e\n1FBDjc2s4YwuALhwiz6ja1PvuggAAADAYARdAAAAAAxB0AUAAADAEDbxYvQA520et3C/5MiR3HnP\nPXPqCIDD7OLsXaMEAJgvF6M/AxejB/ZzEfj1q7EOPaihhhqbWWMdephrDce8ACyRi9EDAAAAwDkQ\ndAEAAAAwBEEXAAAAAEMQdAEAAAAwBEEXAAAAAEMQdAELszWZpKpmemxNJmvRBwAAAOuv3E749Kqq\nfTYwm6pai9uez60PNdaqxjr0oIYaamxmjXXoYa41HPMCsERVle5e2NkEzugCAAAAYAiCLgAAAACG\nIOgCAAAAYAiCLgAAAACGIOgCAAAAYAiCLgAAAACGIOgCTmtrMklVzfQAAMY3j2OGrclkmD4AWK3q\n7lX3sJaqqn02bLKqyqz/BVQynxoz/re4VvuixtxqrEMPaqihxmbWWIce5lpjXf7ODtIHAGdXVenu\nhZ0Z4YwuAAAAAIYg6AIAAABgCIIuAAAAAIYg6AIAAABgCEdX3QCM4hvf+Eb+1Wtfmzu//vWZ6rzw\nqqty1YtfPKeuAAAAYHO46+IZuOsi5+umm27KS7a3c803v3nBNT6T5JZnPzsnbrpppl62JpOc3N2d\nqUayHneD+ktJvj1jjcyhj7W6O5Yaa9ODGmqosZk11qGHedVYl7+zI/VxxbFjue3UqZlqzONY7pIj\nR3LnPffMVGMe+8KY5jFGja/Ntei7LjqjC+bososuys/NEHSdSHLLHPo4ubs7l4PndfDtzOd/BACA\nB1qXv7ND9TGHf2ycy7HcPfesxb4wprmMUeOLBdnIa3RV1ZVVdUtVfbaqXrfqfgAAAACY3cYFXVV1\nJMm/S/KCJE9L8rKqevJqu4L73f7nf77qFthQO6tugI22s+oG2Fg7q26Ajbazs7PqFthQxh4j27ig\nK8lzknyuu092911J3p7kqhX3BPe542tfW3ULbKidVTfARttZdQNsrJ1VN8BGEzawKsYeI9vEoOv7\nkvzJvt+/MH0OAAAAgEPMxehhju64667cOMP2n5xbJwAAALB5qnvWeyUcLlX1g0mOd/eV09+vSdLd\nfd2B9TbrgwEAAABYgu6ex81yT2sTg66HJLk1yfOTfCnJTUle1t03r7QxAAAAAGaycV9d7O67q+o1\nSU5k7xpl1wu5AAAAAA6/jTujCwAAAIAxDXvXxaq6sqpuqarPVtXrTvP6i6rqf1fVJ6vqpqp67oNt\nW1XPqKr/uW+bvzF9/oqqurOqPjF9vGU5e8k6WtDY++tV9T+m272nqh6+77XXV9Xnqurmqvrhxe8h\n62qZY8+8x0Ezjr/rq2q3qj59YJtLq+pEVd1aVe+vqkfue83cR5Lljj1zHwctaPz9eFX9QVXdXVXP\nOvCauY8kyx175j4OWtD4+9Xp3PapqvqvVfWIfa+d39zX3cM9shfgfT7JFUm+J8mnkjz5wDqX7Ft+\nepKbH2zbJO9P8sPT5Rcm+fB0+Yokn171fnus/rHAsXdTkudNl386yS9Pl5+avZs1Hk2yNd2+Vv05\neGzE2DPvedz3mGX8TX9/XpJnHhxTSa5L8s+my69L8sbpsrnP494xsuyxZ+7zuO+xwPH3pCR/LcmH\nkjxr3/NPMfd5TMfCsseeuc/jvscCx98PJTkyXX5jkn8zXT7v475Rz+h6TpLPdffJ7r4ryduTXLV/\nhe6+c9+vD09yzzlse0+Se/81+S8n+eK+Ggu7YwCHyqLG3vd390enyx9M8uLp8ouSvL27/6K7b0vy\nuWkdNs+yx15i3uN+s4y/TMfYHaepe1WSG6bLNyS5erps7uNeyx57ibmP+y1k/HX3rd39uTxwrF0V\ncx97lj32cobn2EyLGn8f7O571/tYksuny+d93Ddq0PV9Sf5k3+9fmD73Xarq6qq6OcmNSV55Dtv+\nYpJ/W1V/nORXk7x+33pb09M4P1xVz5vPbnAILWrs/UFVvWi6/JLc/x/9wW2+eLr3YyMse+wl5j3u\nN8v4O5vLuns3Sbr7VJLLzvB+5r7Nteyxl5j7uN+ixt+5vp+5b3Mte+wl5j7ut4zx98ok/+0M7/eg\nc9+oQdc56e53d/dTsvevdP/6HDb5x0l+obsfl73Q67enz38pyeO6+1lJ/mmSt9W+ayjBQRcw9n4m\nyaur6uNJHpbkO4vsj3HNceyZ9zhvFzD+HlBizi2xIeY49sx9nLc5jD+4IHMce/8v5j7O04WOv6r6\nF0nu6u7/fKHvPWrQ9cUkj9v3++X57q8ZfpfpqXNPqKrvfZBtX9Hd755u87uZni7X3d/p7jumy59I\n8kdJvn8+u8Ihs5CxNz2N+AXd/ezsnRr6R/ve77Hn+n4Mbaljz7zHAbOMv7PZrapjSVJVkyRf3vd+\n5j6SJY89cx8HLGr8ne39zH0kSx573X2XuY99Fjb+quqnk/xIkp888H7nNfeNGnR9PMkTp3eHuCjJ\nS5O8d/8KVfVX9y0/K8lF3X37GbZ9z3TVL1bV35lu8/wkn50uP7qqjkyXn5DkiUn+zyJ3kLU177H3\n3ul6j5n+PJLkXyb59WmJ9yZ5aVVdVFWPz97Yu2mRO8jaWurYM+9xwCzj776n88Drf7w3ezdBSJJX\n5P6/x+Y+7rXUsWfu44BFjb8ceP1e5j7utdSxZ+7jgIWMv6q6Mslrk7you7+976XznvuOnv8+rb/u\nvruqXpPkRPbCvOu7++aqetXey/0bSV5cVS/P3tdwvpm9a8+cadtbpqV/NsmvVdVDknwryT+aPv+3\nk/xyVX0nexdZe1V3f3UpO8taWcDYu3la+mVV9ersfXXind39H6bbfKaq3pHkM0nuSvLz3e2rPRto\n2WMv5j32mWX8JUlVvS3JdpJH1d51MK/t7rdm785376iqVyY5mfvHrLmPJMsfezH3sc+ixl9VXZ3k\nzUkeneR9VfWp7n6huY97LXvsxdzHPgv82/vmJBcl+UBVJcnHuvvnL2TuK3MjAAAAACMY9auLAAAA\nAGwYQRcAAAAAQxB0AQAAADAEQRcAAAAAQxB0AQAAADAEQRcAAAAAQxB0AQAAADAEQRcAAAAAQzi6\n6gYAADg3VfW8JD+T5CFJ7kzy6CR3J3ljd39ylb0BAKwDQRcAwJqrqocn+e0klyd5ZXffsu+1H0ny\nkar6B939nlX1CACwDqq7V90DAABnUFVbSd6X5GSSH+vu75xmnV9L8vIkT+ju25faIADAGnGNLgCA\nNVVVD01yY5KHJnnp6UKuqXcmeUSSVyyrNwCAdeSriwAA6+vNSZ6a5MXd/bWzrPfF6c8fXHxLAADr\nyxldAABrqKqekeQfJrm1u9/9IKs/4sBPAICNJOgCAFhPr5r+/J1zWPeJ059fWVAvAACHgqALAGA9\n/b3pz987h3W3k3SSjy2sGwCAQ8BdFwEA1lBVfStJJbmku+8+y3rfk+QLSR6ZZKu7Ty2pRQCAteNi\n9AAA6+kbSb51tpBr6qeSPCbJbwi5AIBN54wuAIA1VFUfTPKM7n7MWdZ5RJJbktw9Xff2ZfUHALCO\nXKMLAGA9/fsk31tVx5Kkqh5fVddW1fGqurSqHpLkHUkeluTH7g25qupIVb26qq6vqh+YPjepqv++\nqh0BAFgWQRcAwBrq7ndlL+z6uao6kuRHu/sNSa5L8itJTiR5WpLnd/f/2rfp1UnenuTiJI+fPvdD\nSXaX1TsAwKr46iIAwBqrqquT3JHkjUk+kb27K/5UkrcmeUN3/1lVbXf3znT9R0zX+Xz2Lk7/zar6\nrSSf6O63rGIfAACWRdAFAHDIVNXHu/vZ0+WHJrmmu6/d9/pPJPnx7v77098/n+RF3f2ZlTQMALAk\nvroIAHCIVNVFSX6gqn60qp6S5J1Jdg6s9leyd0ZXqupJSR4u5AIANoGgCwDgEOnu7yT5RpIbk/zh\n9LkPH1jt3UkeX1Uvzd41vT6y1CYBAFZE0AUAcPj8SpKvJflAkp84+GJ3/9/ufml3vz3JJUnet+T+\nAABWwjW6AAAGUlVPTXKiuy+vqucmeVOSv9Xdd6+4NQCAhTu66gYAAJirP03ym1X18iRPTfJCIRcA\nsCmc0QUAAADAEFyjCwAAAIAhCLoAAAAAGIKgCwAAAIAhCLoAAAAAGIKgCwAAAIAhCLoAAAAAGIKg\nCwAAAIAhCLoAAAAAGIKgCwAAAIAh/H8R91CrWK3ZZAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f525687efd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "bunch = generate_bunch(\n",
    "    n_macroparticles, alpha_x_inj, alpha_y_inj, beta_x_inj, beta_y_inj,\n",
    "    alpha_0, Q_s, R)\n",
    "\n",
    "chroma = Chromaticity(Qp_x=[6., 4e4], Qp_y=[3., 0., 2e8]) \n",
    "# here the lists are extended beyond first order! ^^^\n",
    "trans_map = TransverseMap(\n",
    "    s, alpha_x, beta_x, D_x, alpha_y, beta_y, D_y, Q_x, Q_y, [chroma])\n",
    "\n",
    "map_ = [m for m in trans_map]\n",
    "\n",
    "x_i, xp_i, y_i, yp_i = track_n_save(bunch, map_)\n",
    "analyse_n_plot(bunch, x_i, xp_i, y_i, yp_i)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The corresponding detuning curves versus $\\delta = \\frac{p-p_0}{p_0}$ show a parabola in the horizontal and a cubic polynomial in the vertical:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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atvTbW8pV0uZTHtx8KpisWbOGsmXLkpiYSLp0F/6O+ffff5MvXz6WLFlC8eLFL/paypuI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\nR1MPAAAAeO7/ASg399dTnxFsAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f5233fd83d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(12,8))\n",
    "\n",
    "chroma = Chromaticity(Qp_x=[6., 4e4], Qp_y=[3., 0., 2e8])\n",
    "chroma.generate_segment_detuner(dmu_x=1, dmu_y=1)\n",
    "\n",
    "dp = np.linspace(-5e-4, 5e-4, 500)\n",
    "\n",
    "dQx = chroma.segment_detuners[0].calc_detuning_x(dp)\n",
    "dQy = chroma.segment_detuners[0].calc_detuning_y(dp)\n",
    "\n",
    "plt.plot(dp, dQx, label='Detuning x')\n",
    "plt.plot(dp, dQy, label='Detuning y')\n",
    "plt.grid('on')\n",
    "plt.xlabel('dp')\n",
    "plt.ylabel('Detuning')\n",
    "plt.legend(loc='upper left')\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}