{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# general imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from __future__ import division, print_function\n",
    "\n",
    "import numpy as np\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": [
    "# works only if PyCUDA is available for GPU usage\n",
    "try:\n",
    "    import pycuda.autoinit\n",
    "    has_pycuda = True\n",
    "except ImportError:\n",
    "    has_pycuda = False"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# sets the PyHEADTAIL directory etc.\n",
    "try:\n",
    "    from settings import *\n",
    "except:\n",
    "    pass"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# PyHEADTAIL imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PyHEADTAIL v1.12.4.7\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "from PyHEADTAIL.particles.generators import generate_Gaussian6DTwiss\n",
    "from PyHEADTAIL.trackers.longitudinal_tracking import RFSystems\n",
    "import PyHEADTAIL.aperture.aperture as aperture"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Setting up the machine and functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# machine parameters\n",
    "circumference = 157.\n",
    "inj_alpha_x = 0\n",
    "inj_alpha_y = 0\n",
    "inj_beta_x = 5.9 # in [m]\n",
    "inj_beta_y = 5.7 # in [m]\n",
    "Qx = 5.1\n",
    "Qy = 6.1\n",
    "gamma_tr = 4.05\n",
    "alpha_c_array = [gamma_tr**-2]\n",
    "V_rf = 8e3 # in [V]\n",
    "harmonic = 1\n",
    "phi_offset = 0 # measured from aligned focusing phase (0 or pi)\n",
    "pipe_radius = 5e-2\n",
    "\n",
    "# beam parameters\n",
    "Ekin = 1.4e9 # in [eV]\n",
    "intensity = 1.684e12\n",
    "epsn_x = 2.5e-6 # in [m*rad]\n",
    "epsn_y = 2.5e-6 # in [m*rad]\n",
    "epsn_z = 1.2 # 4pi*sig_z*sig_dp (*p0/e) in [eVs]\n",
    "\n",
    "# calculations\n",
    "gamma = 1 + e * Ekin / (m_p * c**2)\n",
    "beta = np.sqrt(1 - gamma**-2)\n",
    "eta = alpha_c_array[0] - gamma**-2\n",
    "if eta < 0:\n",
    "    phi_offset = np.pi - phi_offset\n",
    "Etot = gamma * m_p * c**2 / e\n",
    "p0 = np.sqrt(gamma**2 - 1) * m_p * c\n",
    "Qs = np.sqrt(np.abs(eta) * V_rf / (2 * np.pi * beta**2 * Etot))\n",
    "beta_z = np.abs(eta) * circumference / (2 * np.pi * Qs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_phase_space(bunch, ax0, ax1, ax2, col):\n",
    "    # phase spaces\n",
    "    ax0.scatter(bunch.x, bunch.xp, color=col)\n",
    "    ax1.scatter(bunch.y, bunch.yp, color=col)\n",
    "    ax2.scatter(bunch.z, bunch.dp, color=col)\n",
    "    ax0.set_xlabel('$x$')\n",
    "    ax0.set_ylabel('$x\\'$')\n",
    "    ax1.set_xlabel('$y$')\n",
    "    ax1.set_ylabel('$y\\'$')\n",
    "    ax2.set_xlabel('$z$')\n",
    "    ax2.set_ylabel('$z\\'$')\n",
    "    # statistical quantities\n",
    "    ax0.scatter(bunch.mean_x(), bunch.mean_xp(), color='red')\n",
    "    ax1.scatter(bunch.mean_y(), bunch.mean_yp(), color='red')\n",
    "    ax2.scatter(bunch.mean_z(), bunch.mean_dp(), color='red')\n",
    "\n",
    "def generate_bunch(n_particles):\n",
    "    np.random.seed(0)\n",
    "    bunch = generate_Gaussian6DTwiss(\n",
    "        n_particles, intensity, e, m_p, circumference, gamma=gamma,\n",
    "        alpha_x=inj_alpha_x, beta_x=inj_beta_x, epsn_x=epsn_x,\n",
    "        alpha_y=inj_alpha_y, beta_y=inj_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": [
    "The `RectangularAperture<X,Y,Z>` classes provide an aperture as an interval in the horizontal, vertical or longitudinal direction, respectively.\n",
    "\n",
    "The blue particles will get lost while the green ones are within the aperture boundaries:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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O9LQ92lV/9XQ/Byzr0aXycdcfEQuAZ2Xm/8rKt/jTDcbvJecD2zNzR2YeBG6h8jeo1ui9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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f300addaa50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# (I) RectangularApertureX\n",
    "fig, (ax0, ax1, ax2) = plt.subplots(3, 1, figsize=(7, 7))\n",
    "\n",
    "bunch = generate_bunch(1000)\n",
    "plot_phase_space(bunch, ax0, ax1, ax2, col='b')\n",
    "\n",
    "apt_x = aperture.RectangularApertureX(x_low=-0.004, x_high=0.005)\n",
    "apt_x.track(bunch)\n",
    "\n",
    "plot_phase_space(bunch, ax0, ax1, ax2, col='g')\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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vgKuy11cB1+fUmQXsyJ5PzV6fmo17PTAXOFAyzbuALzS7f+PU1zXAF7PXy4Fv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\nFiBNMwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3002ea9b50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# (II) RectangularApertureY\n",
    "fig, (ax0, ax1, ax2) = plt.subplots(3, 1, figsize=(7, 7))\n",
    "\n",
    "bunch = generate_bunch(1000)\n",
    "plot_phase_space(bunch, ax0, ax1, ax2, col='b')\n",
    "\n",
    "apt_y = aperture.RectangularApertureY(y_low=-0.005, y_high=0.005)\n",
    "apt_y.track(bunch)\n",
    "\n",
    "plot_phase_space(bunch, ax0, ax1, ax2, col='g')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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yui+S9Ehe37UF0yu+HpKuy8c/IunCWpfZDA3q5/b8tX1AUs/I9GRwQ+2npFmS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\nMzNL5PA0MzNL5PA0MzNL9P8D+ne6R/5hnMUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3002cb4410>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# (III) RectangularApertureZ\n",
    "fig, (ax0, ax1, ax2) = plt.subplots(3, 1, figsize=(7, 7))\n",
    "\n",
    "bunch = generate_bunch(1000)\n",
    "plot_phase_space(bunch, ax0, ax1, ax2, col='b')\n",
    "\n",
    "apt_z = aperture.RectangularApertureZ(z_low=-15, z_high=25)\n",
    "apt_z.track(bunch)\n",
    "\n",
    "plot_phase_space(bunch, ax0, ax1, ax2, col='g')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `CircularApertureXY` keeps particles within a transverse circle of a given radius while the outer ones are lost:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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G53iTNFDP/4Sb7NzPQ8tU6SdMnb66n+PDh23NzMwSOTzNzMwSOTzHT1+zGzBB\n3M9Dy1TpJ0ydvrqf48DnPM3MzBJ5z9PMzCyRw9PMzCyRwzOBpDmSbpX0YP54ZJV6i/M6D0paXFa+\nQtLDkp6rqP8uSdsl3Z3//fl496WWcezrLElflbRR0k8ldY9vT0bWgH6+VtK9eX8+L0l5+RWSHil7\nT8+ZqD5VtPssSQ/k7bu0YHzV90PSZXn5A5LOrHeezTBO/dycv7d3SxqYmJ6MbLT9lNQp6QeSnpP0\nhYppCtfhZhunvt6Rz7P0uXzZqBsYEf6r8w/4NHBp/vxS4KqCOnOATfnjkfnzI/NxrwOOBp6rmOZd\nwBea3b8J6usy4Jr8+fnAVyd5P+8EXg8I+B5wdl5+BfChJvetDXgIOB6YCfwCWFDP+wEsyOvPAo7L\n59NWzzwPhX7m4zYDRzWzbw3sZwfwx8BFld811dbhQ7SvdwA9jWij9zzTLAJW589XA28uqHMmcGtE\n7IiIp4BbgbMAIuInEfHYhLR07Marr+Xz/TqwsMlbuqPup6SjgZdGxI8j+2ReX2X6ZjkF2BgRmyJi\nL3ATWX/LVXs/FgE3RcSeiPhPYGM+v3rmOdHGo5+taNT9jIhdEfFD4IXyyi28Dje8r43m8Ezz8lIg\n5I9Fu/zHAA+XDW/Ly2p5m6R7JH1d0rFjb+qYjVdfD0wTEfuAnUDnmFs7emPp5zH588rykovz9/S6\naoeDx1k970+192OkPo9m/R5P49FPgAD+XdJ6SUvGod2pxtLPkeY50jrcLOPR15Kv5IdsPzaWDffp\no53wUCXpNuAVBaOW1zuLgrJavwf6NnBjROyRdBHZ1tSpdS5v1JrU19FMMybj2M+R+rIK+EQ+/Ang\nfwLvqXN5jVLPa53at6IN7mb/3m08+gnwhoh4ND8vdqukX0XEf4yhnWM1ln6OZZ7NMB59BeiNiEck\n/Rbwr8A7yfa2kzk8K0TEadXGSXpc0tER8Vh+uOM3BdW2AW8sG55Hdpx9pGU+WTb4JeCquhs8Bs3o\naz7NscA2SdOB2cCOlHanGsd+bsufl5c/mi/z8bJlfAn4zmjbPwal17rkQPsK6lS+HyNNW2ueE21c\n+hkRpcffSPom2aHEZobnWPo50jwL1+EmG4++EhGP5I/PSvoXsvd0VOHpw7Zp1gKlKy0XA98qqHML\ncIakI/NDdWfkZVXlX9ol5wH3N6CtYzUufa2Y79uB2/NzLc0y6n7mh3mflfS6/PDPhaXpK97TtwC/\nHK8OjOAu4ERJx0maSXZRxdqKOtXej7XA+fkVjccBJ5JdWFLPPCdaw/spqSPfO0FSB9l73oz3sNxY\n+llopHW4yRreV0nTJR2VP58wpR4YAAAZyElEQVQBvImxvKfNuppqMv6RHU9fBzyYP87Jy3uAL5fV\new/ZhQcbgXeXlX+abGtpMH+8Ii//O2AD2RVlPwBedQj39TDgf+X17wSOn+T97Mk/gA8BX2Dorl03\nAPcC95B9yI9uUv/OAX6dt295XnYlcF6t94PssPZDwAOUXYFZNM9m/zW6n2RXef4i/9twiPRzM9me\n2XP5Z3LBSOtws/8a3Veyq3DX55/JDcDV5FdWj+bPt+czMzNL5MO2ZmZmiRyeZmZmiRyeZmZmiRye\nZmZmiRyeZmZmiRyeZmZmiabsHYaOOuqo6O7ubnYzzMyshaxfv/6JiJhbq96UDc/u7m4GBlriX/SZ\nmVmLkLSlnno+bGtmZpbI4WlmZpbI4WlmZpbI4WlmZpbI4WlmZpbI4WlmZpbI4WlmZpbI4WlmZpbI\n4WlmZpbI4WlmZpbI4WlmZpbI4WlmZpbI4WlmZpbI4WlmZpbI4WlmZpbI4WlmZpbI4WlmZpaopcJT\n0lmSHpC0UdKlBeNnSfpqPv6nkrrz8tMlrZd0b/546kS33czMpo6WCU9JbcA/AWcDC4ALJC2oqPZe\n4KmIOAH4LHBVXv4EcG5EnAQsBm6YmFabmdlU1DLhCZwCbIyITRGxF7gJWFRRZxGwOn/+dWChJEXE\nzyPi0bx8A3CYpFkT0mozM5tyWik8jwEeLhvelpcV1omIfcBOoLOiztuAn0fEnsoFSFoiaUDSwPbt\n2xvWcDMzm1paKTxVUBYpdSS9muxQ7vuLFhARfRHRExE9c+fOHXVDzcxsamul8NwGHFs2PA94tFod\nSdOB2cCOfHge8E3gwoh4aNxba2ZmU1YrheddwImSjpM0EzgfWFtRZy3ZBUEAbwduj4iQdARwM3BZ\nRPxowlpsZmZTUsuEZ34O82LgFuB+4GsRsUHSlZLOy6tdC3RK2gh8ECj9nOVi4ATgY5Luzv9eNsFd\nMDOzKUIRlacVp4aenp4YGBhodjPMzKyFSFofET216rXMnqeZmdlk4fA0MzNL5PA0MzNL5PA0MzNL\n5PA0MzNL5PA0MzNL5PA0MzNL5PA0MzNL5PA0MzNL5PA0MzNL5PA0MzNL5PA0MzNL5PA0MzNL5PA0\nMzNL5PA0MzNL5PA0MzNL5PA0MzNL5PA0MzNL5PA0MzNL5PA0s0PeslX9TP9wN7piGtM/3M2yVf3j\nurz+fujuhmnTssf+8V2cNYHD01raaL70JvqLsh7j8WVa1M+x9j2lnY3s03iGzbJV/ax6ZAn7X7IF\nFOx/yRZWPbLkwGvT6GX398OSJbBlC0Rkj0uWVJ9vK66vVpsiotltaIqenp4YGBhodjNa3rJV/fRt\nWs7+jq207ZrPkuNXsHJpb83x/f2wfDls3Qrz58OKFdDbS9XykvLx7X/Uz65Tl8DM3UMVXmxn6TF9\nw9pQPt2Wl/bDufVNU5rukkvgySez4c5OuPrq4W0q7+uqzZfA4VllvdDJRV1XAxx4DXh+Tlb58B2w\ncz4dP1nBha/pZfVq2F3WJCn7Yu3qghPe2s/tMy8hDssbsbsTvn81Xc/0csJb+7mjbfjrCwy1Q2UN\n3DcTCJj+Yl19L3otliwZ3s4ZM+ClL4UdOw5+Hyvrlr9+P3pm5PWm1nLb26Gvr/h9KFdr/QTQR46C\n9icPmnbaM11c/983s/jv+9n/xuUweyvsnE/bHStY/aHeYcuuZzkl3d1ZYFbq6oLNmyvntwUQqOx7\nuMb6OtLnx8ZO0vqI6KlZz+F56Ovvh/d/oZ9dr8u+IKY9O5/3n1D9ww8VQVH+Bf1iOwt397HxG71V\ng2rh7j5+/MXeg74MFy/moBAp/5Ls74f3vAf27s1HfqAbjij4Fnq6C129+cCXB5R9+X74KOg4+IuS\n3Z20Db6E/R1Z/w///1aw6ycV/T+pHxYOfYmybgVdz/SyYkUWBqsefffwYALYPx1CB5eX7G2Hb/fB\nvWXLOrCcLdm0iuGvMcCg4MUOmPnc8HGlj2tl/ZGUphlsg4EldN238sCXbuUGAZCF9y//FH73u1kb\nB9tg2v6ytrXB+iXw3ZXFyzupYL0ovQ5w0GtcWHZvb5WwqZiucjmhrMM7u1ioFdz/3I949JWril+v\ngFk3r2HPGQe3teP2Pp77ce+BZa96ZAnMOHg5bbu6WHL8Ct7w0t5s461gdS2RYHCwyvwqtD3Xxb7P\nbB7W72nPzke3r2D/3UPrUr0bGVY/h2cNjQzPlK3SidbfDxd+pp/B//vgL4il84q3bmt+uJ/ugs9t\nrh5uAezsOvAlWNLWBvvLvoOHhdXufI+t/cnhX9ZVvvRAB75EOzb1smtXPr+3/ln1aYaFkOChU+Go\njUPLn/XM8BAMwZ0X0f7/ruT593cTs0f4ZhxJ+esBB3/hT6TSx31/G7TVeI1HCugAHl8A12zIhs9e\nBn94zdAeVNG0uzphxvMVYcfB9YMDe99xT++I4TViG/fNgLYXq9eJfD7TCr4Dn+6i65ub2bJgGZxS\nJXwr+1DaECpY92Foz3P6h7uzQ8gjCWj72VL2//61MH3vUPm+mfCt64bNu3T0Yl0MbYAs1Apu+4fe\nqt9Nw/Z8889baUOg2lGdqbK3OynDU9JZwNVAG/DliPhUxfhZwPXAa4EngXdExOZ83GXAe4H9wF9G\nxC0jLatR4Vn4wS477NLMFW/ZMli1irr34ErtqvnhDsHfDMLl04Yfbqq0bwbseSm07xi2RwEU752M\nxt52+Pniob2k1D2yWvXzAK35BVqPve3w4uHFe8aTUQB3Ls2e1/P61PN6V9YvGetrnyqAhxbCb68b\n3bIrjjjMnAnvfS9c//N+dp1ZZQOvqA3VNkI+88TQcJU9/cOffD3Pv6Ki/fun8cr/ej+Pzl1d/Nmr\nOGTc309dh7Un2njusEy68JTUBvwaOB3YBtwFXBAR95XVWQacHBEXSTofeEtEvEPSAuBG4BTglcBt\nwO9ExP7K5ZQ0KjyrBU3bc12s/oPNoz6XM1YHghOqh1zZHlH7Q70H2qUraoRirT3PasYSdCNJ/VJO\nnr9Gfj2S5sXEB0GiC+6BT66D+Tth62z46EK48eQqlUdzGHmyGOt79XS+B3rWJcPPuY71tQrgb8rW\nx5GOABUta7DK3naudMgY4CWvL7juoOKwNqTtnVa7dqDe8CvcYck3VkqnWcby/VpveNZ1ta2kN0v6\nR0m/M/om1XQKsDEiNkXEXuAmYFFFnUXA6vz514GFkpSX3xQReyLiP4GN+fzG3f6OrVXLly8/+IKK\n3buzlWy8rfphf/ahunxafoirgMg+dOcuYfdv9/Nnf5Zd7KBn5lef8d72ocOPT5wwfO+glpm74ZRr\nsmU28st2vL+4GxWc0PIhc8E98KVvQ/fO7Muhe2c2fME9VSYQLd+nURtrv2ZvyU4jdDw59DqNx2s1\nu/g7qOqyaqzP+zu2HLjqd9frlh+8hzpzd1aeK7q6+J3vzM7xVl69vGxVfu1A+9BrEoc/yapH31P3\nVcZ9m5YffEpp5m5YuLzmlc2NVFd4RsS/AZ8F3iHpfePUlmOAh8uGt+VlhXUiYh+wE+isc9px0bar\nOGjads1na5V1ulp5vWpdWr9sVX4Y54js0nymDY48w3zFg/wDsL0gFAPY8xIWPt9H+0O92aGi3749\n/cugkUFkDffJddBRce1Tx4tZuSUar7Dc05F9/kobx4MN/sWhyH7O8/g7sw2AIrO3HvgOWrz44J2E\n0gHNyjDr27S8+OK66Xv54sb69iqq7bCUNiImagel7lc9IjYBHyXb22srlUt6d4PaUvXSkDrq1DMt\nkpZIGpA0sH379lE08WBLjl8BL7YPL3yxnSXHr2B+lR24auX1qPYbsmXLhgJ11a8LthZrKW29VgtF\nAc93cts/ZId3WbjcQXgImr8zrdyaYMYeWPTuoY3jtv3FG7vVRI3xJSN9vnfOP/AdtL/qybFMKcz6\n+8l/mlNs8Le21rXHWG2HhZ1D5WPdQalH6ibLr4A7gH+VNCMv+x8Nass24Niy4XnAo9XqSJoOzAZ2\n1DktEdEXET0R0TN37tyGNHrl0l6WHtNH23NdEKLtua4DJ9xXrMjOcZZrbx/6ecVoVDsUfM01Q4Fa\n9TDOSHbOz4LzzYurf2jy+fb2jnIZjZaa3c76mrbOTiu3Jmjbd/Dem8iuoA5l51qrCeCupdneaz3E\nwad9yk/d1Km0kc9gW/VKO+fXtcdYuMNS0aax7KDUKzU8IyKuAb4BrJV0OI07MHEXcKKk4yTNBM4H\n1lbUWQsszp+/Hbg9siue1gLnS5ol6TjgRODOBrWrppVLe9n3mc3EFYPs+8zmAye+e3uzi4O6urLj\n/11dY79YqNoW1bDrvnYmrjl72+GBc7JDvW3VNyOnPTs036pbf7WkbCHXooTp97ZnV086QEf00YWw\na8bwsl0zsnJrcdMGs6vgP7c5uxCwyJ4OlnavpOOOL+Y31ahHDNs5OOh3y3Voa8s3+qdV+X4JYN2K\nuvYYK3dYeHp4m8a6g1Kv1PB8CiAirgeuBW4G2kecok75OcyLgVuA+4GvRcQGSVdKOi+vdi3QKWkj\n8EHg0nzaDcDXgPuA7wN/MdKVthOptzf7bdfgYPY41qts69qiWrciC4tq9s3ILncvX/F+97sjH+oN\n8f4ThtbIJcevqH4h0kh2d2bLLC37zqXZFvOwZVX8jUR11NvflvVxzW3Z8q2qG0+G950Lm2fDINnj\n+84d4WpbG66ZG2flG81F3wF721m454usXAnP/biXpa+87kAA6fnOqm1v29U1bOeg65niL7G2/GOs\niq+F9vayQ7vVQn13J9zbW/ceY/kOy5qerE2N2kGp15h+qiLpTcA/R8RRjWvSxJisdxgqupVZ6VZv\nw5TdgEAvzMnGH77jwG+irvmL3uHTjPSbzRALnr+IDVcNv6OMrlD14w5Ft4oruttORVsLfw9afql/\n4dnt/LeYf/hF0ODwOmXL7OqCF1/Vz6Ovrbj0fv+0bKs9dVtgpB/ZlwyW/cylcv6N+NnKRP70ZRL8\nzGaYRvyMJqXP+2ZC297R3XQiRb2frZP6aTuz/t9Cvvojy7jv8GuodavAWrdTLPrZyoG7L41w96ny\nn8s1U0N/qlJNRHxnMgbnZFZ0KPiiiwrOrT7Uy5qebMts8FNPEFc9Meyw8kFbeNUO9e5vY+nLbzgo\nOCHbIq02zcJd16G1Xxm+l/ntPqZtKPhk3NubHWr6m0G6vrmZNR/pHerfM72s+f0niCui+vJ2zofv\nrYQr98M31hxY5rRnulg6r4+4J9tQ2LwZHvl+Lws29Q1v179dn01XuQdcj2/eUH0vf98M+OYN6MrI\n5r+rc2gveXfn6PaCy/fId3Vme+5Pd9W3l17vhSJF05WOEox0RKPqMlX7SEKpPyF4oaP+do40z51d\nsG9W/dOVyganDfV570uKpy/V2d82VPdb11XfsxrpXF+19g0b1rDltH3nK0x7pviwZUnXM8Wnk6rZ\ncNVKlr78hsLrN8rVOh1VdLTtwPUf9/Zmba34Xuh6pjWCM0XL3CRhok3WPc9qUu9kdNDWY9EWYY2b\nio/m7kpA1XuA1rqBxEg/jm67r5cjjjj4Bua1DHsdUu96VLpZRPm9aku3FszvrXrbP9S4f/C2Kssb\n4Sbv372qt/geqmfXuJXc013Zue2evqyNMQ32Hg6zdlWfZm87027uY/AXZUcCDrql4g7Y037wfIr2\nhs5ZBn9Y0cb9bXTcuprdP8026s45B/oeWcb+11TsBVXuvZXmf+yPht8asHwcwKL3HHSLu6WvvA6g\n6l1qhv2jgSrTF63jJ7y1n3XtB38mFry4mPtmrB7xfrbl98v93Wnn8MDgdw+07Y37V7DxG72Fn++x\n3Fh/Ik2W2/xNujsMTbRDLTxHo+iDX/kfPGptrY7lNlmj+TCNx225Kv+Ty/P/x3IGfys/3D3jmeLf\npZXdIH8sXwanfbB0T9Lhwcu6FUybBizM2lL5H2uqfVl+8p5l3Hd4QYDum8HSV36l/nsZx9CdX0o3\nPd+6FebMgWeegRcLXpLyYC3984HyaUuvUb3/caXyvS4PlKIb91eb51jXmdTpR7qf7DVb8v+eU/7+\nlL3Wo12XJ0swTQb1hicRMSX/Xvva14ZZLUtXrom2D3UFlxN8rC24nGj7UFcsXbmmYctYsyaiqysC\nItrasseurqy81jTSwXWXrlwT+khn1ubLCf6fzprtHeqnavavctlLl1Zvix0s5bW2iQcMRB0Z4j1P\nMzOz3IRcMGRmZjYVOTzNzMwSOTzNzMwSOTzNzMwSOTzNzMwSOTzNzMwSOTzNzMwSOTzNzMwSOTzN\nzMwSOTzNzMwSOTzNzMwSOTzNzMwSOTzNzMwSOTzNzMwSOTzNzMwSOTzNzMwSOTzNzMwSOTzNzMwS\nOTzNzMwSOTzNzMwStUR4Spoj6VZJD+aPR1aptziv86CkxXlZu6SbJf1K0gZJn5rY1puZ2VTTEuEJ\nXAqsi4gTgXX58DCS5gCXA38EnAJcXhayfx8RrwJeA7xB0tkT02wzM5uKWiU8FwGr8+ergTcX1DkT\nuDUidkTEU8CtwFkRsTsifgAQEXuBnwHzJqDNZmY2RbVKeL48Ih4DyB9fVlDnGODhsuFtedkBko4A\nziXbezUzMxsX0ydqQZJuA15RMGp5vbMoKIuy+U8HbgQ+HxGbqrRhCbAEYP78+XUu1szMbLgJC8+I\nOK3aOEmPSzo6Ih6TdDTwm4Jq24A3lg3PA+4oG+4DHoyIz43Qhr68Hj09PVGtnpmZ2Uha5bDtWmBx\n/nwx8K2COrcAZ0g6Mr9Q6Iy8DEl/C8wGPjABbTUzsymuVcLzU8Dpkh4ETs+HkdQj6csAEbED+ARw\nV/53ZUTskDSP7NDvAuBnku6W9OfN6ISZmU0NipiaRy97enpiYGCg2c0wM7MWIml9RPTUqtcqe55m\nZmaThsPTzMwskcPTzMwskcPTzMwskcPTzMwskcPTzMwskcPTzMwskcPTzMwskcPTzMwskcPTzMws\nkcPTzMwskcPTzMwskcPTzMwskcPTzMwskcPTzMwskcPTzMwskcPTzMwskSKi2W1oCknbgS3NbkeC\no4Anmt2IBjmU+gKHVn/cl9Z1KPWnlfvSFRFza1WasuE52UgaiIieZrejEQ6lvsCh1R/3pXUdSv05\nFPriw7ZmZmaJHJ5mZmaJHJ6TR1+zG9BAh1Jf4NDqj/vSug6l/kz6vvicp5mZWSLveZqZmSVyeLY4\nSZ+QdI+kuyX9u6RX5uWS9HlJG/Px/73Zba1F0mck/Spv7zclHVE27rK8Lw9IOrOZ7ayHpD+RtEHS\noKSeinGTqi8Aks7K27tR0qXNbk8qSddJ+o2kX5aVzZF0q6QH88cjm9nGekk6VtIPJN2fr2OX5OWT\ntT+HSbpT0i/y/vxNXn6cpJ/m/fmqpJnNbmsKh2fr+0xEnBwRfwB8B/h4Xn42cGL+twRY1aT2pbgV\n+G8RcTLwa+AyAEkLgPOBVwNnASsltTWtlfX5JfBW4D/KCydjX/L2/RPZOrUAuCDvx2Tyz2Svd7lL\ngXURcSKwLh+eDPYBfx0Rvwe8DviL/P2YrP3ZA5waEb8P/AFwlqTXAVcBn8378xTw3ia2MZnDs8VF\nxDNlgx1A6ST1IuD6yPwEOELS0RPewAQR8e8RsS8f/AkwL3++CLgpIvZExH8CG4FTmtHGekXE/RHx\nQMGoSdcXsvZtjIhNEbEXuImsH5NGRPwHsKOieBGwOn++GnjzhDZqlCLisYj4Wf78WeB+4Bgmb38i\nIp7LB2fkfwGcCnw9L580/SlxeE4CklZIehjoZWjP8xjg4bJq2/KyyeI9wPfy55O9L+UmY18mY5vr\n8fKIeAyyQAJe1uT2JJPUDbwG+CmTuD+S2iTdDfyG7AjUQ8DTZRvTk26dc3i2AEm3Sfplwd8igIhY\nHhHHAv3AxaXJCmbV9Euna/Ulr7Oc7NBUf6moYFaToi9FkxWUNb0vNUzGNh/yJL0E+FfgAxVHoCad\niNifn3qaR3ak4/eKqk1sq8ZmerMbYBARp9VZ9V+Am4HLybbUji0bNw94tMFNS1arL5IWA28CFsbQ\n76QmZV+qaMm+1DAZ21yPxyUdHRGP5ac0ftPsBtVL0gyy4OyPiG/kxZO2PyUR8bSkO8jO5R4haXq+\n9znp1jnvebY4SSeWDZ4H/Cp/vha4ML/q9nXAztIhnVYl6SzgI8B5EbG7bNRa4HxJsyQdR3YR1J3N\naGMDTMa+3AWcmF/9OJPsgqe1TW5TI6wFFufPFwPfamJb6iZJwLXA/RHxD2WjJmt/5paurJd0OHAa\n2XncHwBvz6tNmv6U+CYJLU7SvwK/CwyS/ReYiyLikfwD9gWyKwx3A++OiIHmtbQ2SRuBWcCTedFP\nIuKifNxysvOg+8gOU32veC6tQdJbgH8E5gJPA3dHxJn5uEnVFwBJ5wCfA9qA6yJiRZOblETSjcAb\nyf5bx+NkR2f+DfgaMB/YCvxJRFReVNRyJP0x8L+Be8k+9wAfJTvvORn7czLZBUFtZDtsX4uIKyUd\nT3Zx2hzg58CfRcSe5rU0jcPTzMwskQ/bmpmZJXJ4mpmZJXJ4mpmZJXJ4mpmZJXJ4mpmZJXJ4mpmZ\nJXJ4mpmZJXJ4mk1hkm5X9r9i75b0gqQ/aXabzCYD3yTBzJC0FPi/gAsiYn+z22PW6nxjeLMpTtKF\nZP8I+20OTrP6ODzNprD8MG0vsCgiXmx2e8wmC4en2RQl6U3AMuBNEfFCs9tjNpn4nKfZFCXpSWAH\nsCsv+seIuLaJTTKbNByeZmZmifxTFTMzs0QOTzMzs0QOTzMzs0QOTzMzs0QOTzMzs0QOTzMzs0QO\nTzMzs0QOTzMzs0T/P0yBk8RYlyo1AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3002afb310>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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UxopOCPeejVVmkTC9eTzssxUEQPTa9Zl8yPox2csvRrUSdG01GMTVfAy4PStZ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\na2HdCsg4qygAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3002b72710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# (IV) CircularApertureXY\n",
    "fig, (ax0, ax1, ax2) = plt.subplots(3, 1, figsize=(7, 7))\n",
    "\n",
    "bunch = generate_bunch(1000)\n",
    "plot_phase_space(bunch, ax0, ax1, ax2, col='b')\n",
    "fig2, axy = plt.subplots(1, 1, figsize=(7, 7))\n",
    "axy.plot(bunch.x, bunch.y, 'ob')\n",
    "\n",
    "apt_xy = aperture.CircularApertureXY(radius=0.003)\n",
    "apt_xy.track(bunch)\n",
    "\n",
    "plot_phase_space(bunch, ax0, ax1, ax2, col='g')\n",
    "\n",
    "axy.plot(bunch.x, bunch.y, 'og')\n",
    "axy.axis('equal')\n",
    "plt.xlabel('$x$')\n",
    "plt.ylabel('$y$');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `EllipticalApertureXY` class allows to define an elliptical vacuum chamber boundary:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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WhnbbioiIBFJ4ioiIBFJ4ls5ApRtQJurn9FIv/YT66av6WQI65ikiIhJIW54i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\n8WD5/NsAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f30028fd7d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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GWN8Kj8+A9a3m9VTDDEa+tLWkCWFxDD/EFyyAW24pvr+NjcarYBPVev4NCtFM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\nAwUirq1SyZ0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f30029d3510>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# (V) EllipticalApertureXY\n",
    "\n",
    "fig, (ax0, ax1, ax2) = plt.subplots(3, 1, figsize=(7, 7))\n",
    "\n",
    "bunch = generate_bunch(1000)\n",
    "plot_phase_space(bunch, ax0, ax1, ax2, col='b')\n",
    "fig2, axy = plt.subplots(1, 1, figsize=(7, 7))\n",
    "axy.plot(bunch.x, bunch.y, 'ob')\n",
    "\n",
    "x_aper = 5e-3\n",
    "y_aper = 2e-3\n",
    "\n",
    "apt_xy = aperture.EllipticalApertureXY(x_aper=x_aper, y_aper=y_aper)\n",
    "apt_xy.track(bunch)\n",
    "\n",
    "plot_phase_space(bunch, ax0, ax1, ax2, col='g')\n",
    "\n",
    "axy.plot(bunch.x, bunch.y, 'og')\n",
    "ttt = np.linspace(0,2*np.pi)\n",
    "axy.plot(x_aper*np.cos(ttt), y_aper*np.sin(ttt), 'r')\n",
    "\n",
    "axy.axis('equal')\n",
    "plt.xlabel('$x$')\n",
    "plt.ylabel('$y$');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Performance"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The performance can be significantly increased if the cython module is used for the CPU version.\n",
    "\n",
    "If a GPU is available via PyCUDA then we can achieve even further speed up:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "from PyHEADTAIL.aperture import aperture_cython\n",
    "from PyHEADTAIL.general.contextmanager import GPU"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (I) RectangularApertureX (same as Y, and Z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<TimeitResult : 100 loops, best of 3: 2.79 ms per loop>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# a. python version\n",
    "bunch = generate_bunch(int(1e6))\n",
    "apt_x = aperture.RectangularApertureX(x_low=-0.006, x_high=0.008)\n",
    "res = %timeit -q -o apt_x.track(bunch)\n",
    "res"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<TimeitResult : 1000 loops, best of 3: 1.33 ms per loop>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# b. cython version\n",
    "bunch = generate_bunch(int(1e6))\n",
    "apt_x = aperture_cython.RectangularApertureX(x_low=-0.006, x_high=0.008)\n",
    "res = %timeit -q -o apt_x.track(bunch)\n",
    "res"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<TimeitResult : 100 loops, best of 3: 401 µs per loop>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# c. PyCUDA (GPU) version\n",
    "bunch = generate_bunch(int(1e6))\n",
    "apt_x = aperture.RectangularApertureX(x_low=-0.006, x_high=0.008)\n",
    "with GPU(bunch) as contextmanager:\n",
    "    res = %timeit -q -o -n 100 apt_x.track(bunch)\n",
    "res"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### (II) CircularApertureXY"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<TimeitResult : 100 loops, best of 3: 4.47 ms per loop>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# a. python version\n",
    "bunch = generate_bunch(int(1e6))\n",
    "apt_xy = aperture.CircularApertureXY(radius=0.0076)\n",
    "res = %timeit -q -o apt_xy.track(bunch)\n",
    "res"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<TimeitResult : 1000 loops, best of 3: 1.66 ms per loop>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# b. cython version\n",
    "bunch = generate_bunch(int(1e6))\n",
    "apt_xy = aperture_cython.CircularApertureXY(radius=0.0076)\n",
    "res = %timeit -q -o apt_xy.track(bunch)\n",
    "res"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<TimeitResult : 100 loops, best of 3: 1.29 ms per loop>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# c. PyCUDA (GPU) version\n",
    "bunch = generate_bunch(int(1e6))\n",
    "apt_xy = aperture.CircularApertureXY(radius=0.0076)\n",
    "with GPU(bunch) as contextmanager:\n",
    "    res = %timeit -q -o -n 100 apt_xy.track(bunch)\n",
    "res"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
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