{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Gyromation of a charged particle in a constant magnetic field\n",
    "\n",
    "### Christian Hill, 11/09/2018\n",
    "\n",
    "More details at https://scipython.com/blog/gyromotion-of-a-charged-particle-in-a-magnetic-field/"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy.integrate import odeint\n",
    "from matplotlib import animation, rc\n",
    "rc('animation', html='html5')\n",
    "import matplotlib.pyplot as plt\n",
    "from mpl_toolkits.mplot3d import Axes3D"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Magnetic field, electric field\n",
    "B = np.array((0,0,1))\n",
    "E = np.array((0,0.01,0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def lorentz(X, t, q_over_m):\n",
    "        \"\"\"\n",
    "        The equations of motion for the Lorentz force on a particle with\n",
    "        q/m given by q_over_m. X=[x,y,z,vx,vy,vz] defines the particle's\n",
    "        position and velocity at time t: F = ma = (q/m)[E + v×B].\n",
    "        \n",
    "        \"\"\"\n",
    "        \n",
    "        v = X[3:]\n",
    "        drdt = v\n",
    "        dvdt = q_over_m * (E + np.cross(v, B))\n",
    "        return np.hstack((drdt, dvdt))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def larmor(q, m, v0):\n",
    "    \"\"\"Calculate the Larmor (cyclotron) radius.\n",
    "\n",
    "    rho = m.v_perp / (|q|B) where m is the particle's mass,\n",
    "    q is its charge, B is the magnetic field strength and\n",
    "    v_perp is its instantaneous speed perpendicular to the\n",
    "    magnetic field, **B**.\n",
    "\n",
    "    \"\"\"\n",
    "\n",
    "    B_sq = B @ B\n",
    "    v0_par = (v0 @ B) * B / B_sq\n",
    "    v0_perp = v0 - v0_par\n",
    "    v0_perp_abs = np.sqrt( v0_perp @ v0_perp)\n",
    "    return m * v0_perp_abs / np.abs(q) / np.sqrt(B_sq)\n",
    "\n",
    "def calc_trajectory(q, m, r0=None, v0 = np.array((1,0,1))):\n",
    "    \"\"\"Calculate the particle's trajectory.\n",
    "    \n",
    "    q, m are the particle charge and mass;\n",
    "    r0 and v0 are its initial position and velocity vectors.\n",
    "    If r0 is not specified, it is calculated to be the Larmor\n",
    "    radius of the particle, and particles with different q, m\n",
    "    are placed so as have a common guiding centre (for E=0).\n",
    "    \n",
    "    \"\"\"\n",
    "    if r0 is None:\n",
    "        rho = larmor(q, m, v0)\n",
    "        vp = np.array((v0[1],-v0[0],0))\n",
    "        r0 = -np.sign(q) * vp * rho\n",
    "    # Final time, number of time steps, time grid.\n",
    "    tf = 50\n",
    "    N = 10 * tf\n",
    "    t = np.linspace(0, tf, N)\n",
    "    # Initial positon and velocity components.\n",
    "    X0 = np.hstack((r0, v0))\n",
    "    # Do the numerical integration of the equation of motion.\n",
    "    X = odeint(lorentz, X0, t, args=(q/m,))\n",
    "    return X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def setup_axes(ax):\n",
    "    \"\"\"Style the 3D axes the way we want them.\"\"\"\n",
    "    \n",
    "    # Gotta love Matplotlib: this is how to indicate a right-handed\n",
    "    # coordinate system with the x, y, and z axes meeting at a point.\n",
    "    ax.yaxis._axinfo['juggled'] = (1,1,2)\n",
    "    ax.zaxis._axinfo['juggled'] = (1,2,0)\n",
    "    # Remove axes ticks and labels, the grey panels and the gridlines.\n",
    "    for axis in ax.w_xaxis, ax.w_yaxis, ax.w_zaxis:\n",
    "        for e in axis.get_ticklines() + axis.get_ticklabels():\n",
    "            e.set_visible(False) \n",
    "        axis.pane.set_visible(False)\n",
    "        axis.gridlines.set_visible(False)\n",
    "    # Label the x and z axes only.\n",
    "    ax.set_xlabel('x', labelpad=-10, size=16)\n",
    "    ax.set_zlabel('z', labelpad=-10, size=16)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def plot_trajectories(trajectories):\n",
    "    \"\"\"Produce a static plot of the trajectories.\n",
    "    \n",
    "    trajectories should be a sequence of (n,3) arrays representing\n",
    "    the n timepoints over which the (x,y,z) coordinates of the\n",
    "    particle are given.\n",
    "    \n",
    "    \"\"\"\n",
    "    \n",
    "    fig = plt.figure()\n",
    "    ax = fig.add_subplot(111, projection='3d')\n",
    "    for X in trajectories:\n",
    "        ax.plot(*X.T[:3])\n",
    "    setup_axes(ax)\n",
    "    # Plot a vertical line through the origin parallel to the\n",
    "    # magnetic field.\n",
    "    zmax = np.max(np.max([X.T[2] for X in trajectories]))\n",
    "    ax.plot([0,0],[0,0],[0,zmax],lw=2,c='gray')\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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EQz9CyteQvhrsFhG+uLEw/FaInwwhCWI+dYZm8S3YBfm7IH8nFOwG8zE5d89A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\nnhdXSNw4aYnvPknW0lgDP82W+RXdJ0n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OTspA27aNxcVFXLx4UUY6EAhg7969qkclou3D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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11903bda0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Test the static plot.\n",
    "\n",
    "# Electron mass and charge\n",
    "me, qe = 1, -1\n",
    "v0 = np.array((0,0,0))\n",
    "X = calc_trajectory(qe, me, r0=(0,0,0), v0=(0.1,0,0))\n",
    "X2 = calc_trajectory(-2*qe, me, r0=(0,0,0), v0=(0.1,0,0))\n",
    "X3 = calc_trajectory(-qe, me, r0=(0,0,0), v0=(0.1,0,0))\n",
    "plot_trajectories([X, X3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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+8XewY56PRk2gj5eiFoPeZMV3HB37fDQqjAqW37aXl4hwcFIMdIJg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\nKRe0dfs70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      "text/plain": [
       "<matplotlib.figure.Figure at 0x119ac1710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(X[:,0], X[:,1])\n",
    "plt.plot(X3[:,0], X3[:,1])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 285,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# charges and masses of the electron (e) and ion (i)\n",
    "qe, me = -1, 1\n",
    "qi, mi = 1, 3\n",
    "# Calculate the trajectories for the particles (which don't interact) by\n",
    "# numerical integration of their equations of motion.\n",
    "Xe = calc_trajectory(qe, me)\n",
    "Xi = calc_trajectory(qi, mi)\n",
    "\n",
    "def init():\n",
    "    \"\"\"Initialize the trajectory animation.\"\"\"\n",
    "    \n",
    "    fig = plt.figure()\n",
    "    ax = fig.add_subplot(111, projection='3d')\n",
    "    # The axis of the magentic field\n",
    "    ax.plot([0,0],[0,0],[0,50],lw=2,c='gray')\n",
    "    # Electron motion, ion motion\n",
    "    lne, = ax.plot(*Xe.T[:3])\n",
    "    lni, = ax.plot(*Xi.T[:3])\n",
    "    # The particles instantaneous positions are indicated by circles from \n",
    "    # a scatter plot, scaled according to particle mass. depthshade=0\n",
    "    # ensures that the colour doesn't fade as the the particle's distance\n",
    "    # from the observer increases.\n",
    "    SCALE = 40\n",
    "    particles = ax.scatter(*np.vstack((Xe[0][:3], Xi[0][:3])).T,\n",
    "                           s=(me*SCALE, mi*SCALE),\n",
    "                           c=('tab:blue', 'tab:orange'), depthshade=0)\n",
    "    # Some tidying up and labelling of the axes.\n",
    "    setup_axes(ax)\n",
    "    return fig, ax, lne, lni, particles\n",
    "\n",
    "def animate(i):\n",
    "    \"\"\"The main animation function, called for each frame.\"\"\"\n",
    "    \n",
    "    def animate_particle(X, ln, i):\n",
    "        \"\"\"Plot the trajectory of a particle up to step i.\"\"\"\n",
    "        \n",
    "        ln.set_data(X[:i,0], X[:i,1])\n",
    "        ln.set_3d_properties(X[:i,2])\n",
    "        particles._offsets3d = np.vstack((Xe[i][:3], Xi[i][:3])).T\n",
    "    animate_particle(Xe, lne, i)\n",
    "    animate_particle(Xi, lni, i)\n",
    "\n",
    "fig, ax, lne, lni, particles = init()\n",
    "anim = animation.FuncAnimation(fig, animate, frames=500, interval=10, blit=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 286,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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       "AF0AAAAVAAAAqgAAAEEAAAAUAAAAHQAAALMAAAAxAAAAIgAAAF8AAAC7AAAAKgAAAHwAAAAgAAAA\n",
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       "AAAiAAAAjwAAACgAAAAZAAAAVgAAACMAAABJAAAAjAAAACoAAABzAAAAHwAAAJUAAAA3AAAAHAAA\n",
       "ABYAAAB0AAAAMQAAABcAAAAbAAAAXAAAADQAAAAgAAAAEgAAAF8AAAAyAAAAGgAAABMAAABHAAAA\n",
       "SQAAACIAAAAUc3RjbwAAAAAAAAABAAAALAAAAGJ1ZHRhAAAAWm1ldGEAAAAAAAAAIWhkbHIAAAAA\n",
       "AAAAAG1kaXJhcHBsAAAAAAAAAAAAAAAALWlsc3QAAAAlqXRvbwAAAB1kYXRhAAAAAQAAAABMYXZm\n",
       "NTcuODMuMTAw\n",
       "\">\n",
       "  Your browser does not support the video tag.\n",
       "</video>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 286,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.display import HTML\n",
    "HTML(anim.to_html5_video())"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python [conda env:py35]",
   "language": "python",
   "name": "conda-env-py35-py"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}