3_space_charge.ipynb

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   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "*This notebook was created by [Sergey Tomin](http://www.xfel.eu/organization/staff/tomin_sergey/) for Workshop: [Designing future X-ray FELs](http://www.xrayfels.co.uk/). Source and license info is on [GitHub](https://github.com/iagapov/ocelot/tree/dev/docs). August 2016.*"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Tutorial N3. Space Charge.\n",
      "*Second order tracking with space charge effect of the 200k particles.*\n",
      "\n",
      "As an example, we will use lattice file (converted to Ocelot format) of the European XFEL Injector. \n",
      "\n",
      "The space charge forces are calculated by solving the Poisson equation in the bunch frame. \n",
      "Then the Lorentz transformed electromagnetic field is applied as a kick in the laboratory frame.\n",
      "For the solution of the Poisson equation we use an integral representation of the electrostatic potential by convolution of the free-space Green's function with the charge distribution. The convolution equation is solved with the help of the Fast Fourier Transform (FFT). The same algorithm for solution of the 3D Poisson equation is used, for example, in [ASTRA](http://www.desy.de/~mpyflo/).\n",
      "\n",
      "#### This example will cover the following topics:\n",
      "* Initialization of the Space Charge objects and the places of their applying\n",
      "* tracking of second order with space charge effect.\n",
      "\n",
      "#### Requirements \n",
      "* injector_lattice.py - input file, the The European XFEL Injector lattice.\n",
      "* beam_6MeV.ast    - input file, initial beam distribution in ASTRA format (was obtained from s2e simulation performed with ASTRA)."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Import of modules"
     ]
    },
    {
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     "input": [
      "# the output of plotting commands is displayed inline within frontends, \n",
      "# directly below the code cell that produced it\n",
      "%matplotlib inline\n",
      "\n",
      "from time import time \n",
      "\n",
      "# this python library provides generic shallow (copy) and deep copy (deepcopy) operations \n",
      "from copy import deepcopy\n",
      "\n",
      "# import from Ocelot main modules and functions\n",
      "from ocelot import *\n",
      "\n",
      "# import from Ocelot graphical modules\n",
      "from ocelot.gui.accelerator import *\n",
      "\n",
      "# import injector lattice\n",
      "from ocelot.test.workshop.injector_lattice import *\n",
      "\n",
      "# load beam distribution\n",
      "# this function convert Astra beam distribution to Ocelot format - ParticleArray. ParticleArray is designed for tracking.\n",
      "# in order to work with converters we have to import specific module from ocelot.adaptors\n",
      "from ocelot.adaptors.astra2ocelot import *"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "initializing ocelot...\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Change RF parameters for the comparison with ASTRA"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "phi1=18.7268\n",
      "V1=18.50662e-3/np.cos(phi1*pi/180)\n",
      "\n",
      "C_A1_1_1_I1.v = V1; C_A1_1_1_I1.phi = phi1\n",
      "C_A1_1_2_I1.v = V1; C_A1_1_2_I1.phi = phi1\n",
      "C_A1_1_3_I1.v = V1; C_A1_1_3_I1.phi = phi1\n",
      "C_A1_1_4_I1.v = V1; C_A1_1_4_I1.phi = phi1\n",
      "C_A1_1_5_I1.v = V1; C_A1_1_5_I1.phi = phi1\n",
      "C_A1_1_6_I1.v = V1; C_A1_1_6_I1.phi = phi1\n",
      "C_A1_1_7_I1.v = V1; C_A1_1_7_I1.phi = phi1\n",
      "C_A1_1_8_I1.v = V1; C_A1_1_8_I1.phi = phi1\n",
      "\n",
      "phi13=180\n",
      "V13=-20.2E-3/8/np.cos(phi13*pi/180)\n",
      "\n",
      "C3_AH1_1_1_I1.v=V13; C3_AH1_1_1_I1.phi=phi13\n",
      "C3_AH1_1_2_I1.v=V13; C3_AH1_1_2_I1.phi=phi13\n",
      "C3_AH1_1_3_I1.v=V13; C3_AH1_1_3_I1.phi=phi13\n",
      "C3_AH1_1_4_I1.v=V13; C3_AH1_1_4_I1.phi=phi13\n",
      "C3_AH1_1_5_I1.v=V13; C3_AH1_1_5_I1.phi=phi13\n",
      "C3_AH1_1_6_I1.v=V13; C3_AH1_1_6_I1.phi=phi13\n",
      "C3_AH1_1_7_I1.v=V13; C3_AH1_1_7_I1.phi=phi13\n",
      "C3_AH1_1_8_I1.v=V13; C3_AH1_1_8_I1.phi=phi13"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
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     "collapsed": false,
     "input": [
      "p_array_init = astraBeam2particleArray(filename='beam_6MeV.ast')\n",
      "bins_start, hist_start = get_current(p_array_init, charge=p_array_init.q_array[0], num_bins=200)\n",
      "\n",
      "plt.title(\"current: end\")\n",
      "plt.plot(bins_start*1000, hist_start)\n",
      "plt.xlabel(\"s, mm\")\n",
      "plt.ylabel(\"I, A\")\n",
      "plt.grid(True)\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "('Astra to Ocelot: charge = ', 2.5000000000000012e-10)\n",
        "('Astra to Ocelot: particles number = ', 200000)\n",
        "('Astra to Ocelot: energy = ', 0.0065579389982232342)"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "('Astra to Ocelot: s pos = ', 3.2000000000000002)\n",
        "('Imax = ', 13.227182625297699)"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
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2kZJR0RcRqSLq6YuIVBEVfRGRKqKiLyJSRVT0RUSqiIq+iEgVUdEX\nEakiKvoiIlXk/wNDEbA2KiQAPQAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0xbd8f0d0>"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": true,
     "input": [
      "# initialization of tracking method\n",
      "method = MethodTM()\n",
      "\n",
      "# for second order tracking we have to choose SecondTM \n",
      "method.global_method = SecondTM\n",
      "\n",
      "# for first order tracking uncomment next line\n",
      "# method.global_method = TransferMap\n",
      "\n",
      "# we will start simulation from point 3.2 from the gun. For this purpose  marker was created (start_sim=Marker()) \n",
      "# and placed in 3.2 m after gun \n",
      "# Q_38_I1 is quadrupole between RF cavities 1.3 GHz and 3.9 GHz\n",
      "# C3_AH1_1_8_I1 is the last section of the 3.9 GHz cavity\n",
      "lat = MagneticLattice(cell, start=start_sim, stop=Q_38_I1, method=method)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Initializing SpaceCharge"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sc1 = SpaceCharge()\n",
      "sc1.nmesh_xyz = [63, 63, 63]\n",
      "sc1.low_order_kick = False\n",
      "sc1.step = 1\n",
      "\n",
      "sc5 = SpaceCharge()\n",
      "sc5.nmesh_xyz = [63, 63, 63]\n",
      "sc5.step = 5\n",
      "sc5.low_order_kick = False"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "navi = Navigator(lat)\n",
      "\n",
      "# add physics processes from the first element to the last of the lattice\n",
      "navi.add_physics_proc(sc1, lat.sequence[0], C_A1_1_2_I1)\n",
      "navi.add_physics_proc(sc5, C_A1_1_2_I1, lat.sequence[-1])\n",
      "\n",
      "# definiing of unit step in [m]\n",
      "navi.unit_step = 0.02\n",
      "\n",
      "# deep copy of the initial beam distribution \n",
      "p_array = deepcopy(p_array_init)\n",
      "start = time()\n",
      "tws_track, p_array = track(lat, p_array, navi)\n",
      "\n",
      "print(\"time exec: \", time() - start, \"sec\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 0.02 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 0.04 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 0.06 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 0.08 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 0.1 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 0.12 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 0.14 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 0.16 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 0.18 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 0.2 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 0.22 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 0.24 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 0.26 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 0.28 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 0.3 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 0.32 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 0.34 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 0.36 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 0.38 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 0.4 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 0.42 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 0.44 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 0.46 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 0.48 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 0.5 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 0.52 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 0.54 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 0.56 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 0.58 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 0.6 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 0.62 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 0.64 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 0.66 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 0.68 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 0.7 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 0.72 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 0.74 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 0.76 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 0.78 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 0.8 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 0.82 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 0.84 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 0.86 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 0.88 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 0.9 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 0.92 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 0.94 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 0.96 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 0.98 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 1.0 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 1.02 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 1.04 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 1.06 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 1.08 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 1.1 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 1.12 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 1.14 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 1.16 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 1.18 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 1.2 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 1.22 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 1.24 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 1.26 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 1.28 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 1.3 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 1.32 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 1.34 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 1.36 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 1.38 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 1.4 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 1.42 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 1.44 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 1.46 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 1.48 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 1.5 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 1.52 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 1.54 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 1.56 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 1.58 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 1.6 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 1.62 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 1.64 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 1.66 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 1.68 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 1.7 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 1.72 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 1.82 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 1.92 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 2.02 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 2.12 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 2.22 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 2.32 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 2.42 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 2.52 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 2.62 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 2.72 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 2.82 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 2.92 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 3.02 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 3.12 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 3.22 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 3.32 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 3.42 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 3.52 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 3.62 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 3.72 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 3.82 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 3.92 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 4.02 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 4.12 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 4.22 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 4.32 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 4.42 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 4.52 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 4.62 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 4.72 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 4.82 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 4.92 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 5.02 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 5.12 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 5.22 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 5.32 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 5.42 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 5.52 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 5.62 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 5.72 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 5.82 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 5.92 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 6.02 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 6.12 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 6.22 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 6.32 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 6.42 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 6.52 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 6.62 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 6.72 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 6.82 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 6.92 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 7.02 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 7.12 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 7.22 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 7.32 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 7.42 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 7.52 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 7.62 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 7.72 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 7.82 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 7.92 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 8.02 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 8.12 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 8.22 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 8.32 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 8.42 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 8.52 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 8.62 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 8.72 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 8.82 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 8.92 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 9.02 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 9.12 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 9.22 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 9.32 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 9.42 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 9.52 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 9.62 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 9.72 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 9.82 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 9.92 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 10.02 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 10.12 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 10.22 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 10.32 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 10.42 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 10.52 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 10.62 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 10.72 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 10.82 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 10.92 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 11.02 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 11.12 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 11.22 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 11.32 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 11.42 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 11.52 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 11.62 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 11.72 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 11.82 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 11.92 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 12.02 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 12.12 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 12.22 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 12.32 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 12.42 / 12.6974 : applied: SpaceCharge"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "z = 12.6974 / 12.6974 : applied: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "('time exec: ', 224.88700008392334, 'sec')\n"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# you can change top_plot argument, for example top_plot=[\"alpha_x\", \"alpha_y\"]\n",
      "plot_opt_func(lat, tws_track, top_plot=[\"E\"], fig_name=0, legend=False)\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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vpl+/fsTHx/Pss88SERHBqlVDqK6GKVNg5Ejv12c9KGOM6aPuu+8+j/a77bbb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\nKc1n0OF8UmvyGcoBhnZxnGr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JShZQxhhjgpIFlDHGmKBkAWWMMSYoWUAZY4wJShZQxhhj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\nNMebBDRekBYAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x11fe0f70>"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Comparison with ASTRA\n",
      "Beam tracking with ASTRA was performed by Igor Zagorodnov (DESY). "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sa, bx_sc, by_sc, bx_wo_sc, by_wo_sc = np.loadtxt(\"astra_sim.txt\", usecols=(0, 1, 2, 3, 4), unpack=True)\n",
      "\n",
      "s = [tw.s for tw in tws_track]\n",
      "bx = [tw.beta_x for tw in tws_track]\n",
      "by = [tw.beta_y for tw in tws_track]\n",
      "ax = plot_API(lat, legend=False)\n",
      "ax.plot(s, bx, \"r\", label=\"Ocelot, bx\")\n",
      "ax.plot(sa-3.2, bx_sc, \"b-\",label=\"ASTRA, bx\")\n",
      "ax.plot(s, by, \"r\", label=\"Ocelot, by\")\n",
      "ax.plot(sa-3.2, by_sc, \"b-\",label=\"ASTRA, by\")\n",
      "ax.legend()\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x12137e30>"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}