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   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "Particle stepper\n",
    "================\n",
    "\n",
    "An example of PlasmaPy's particle stepper class, currently in need of a rewrite\n",
    "for speed.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "from astropy import units as u\n",
    "\n",
    "from plasmapy.formulary import ExB_drift, gyrofrequency\n",
    "from plasmapy.plasma import Plasma\n",
    "from plasmapy.simulation import ParticleTracker"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {
    "raw_mimetype": "text/restructuredtext"
   },
   "source": [
    "Take a look at the docs to :func:`~plasmapy.formulary.parameters.gyrofrequency` and :class:`~plasmapy.simulation.particletracker.ParticleTracker` for more information"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Initialize a plasma. This will be a source of electric and magnetic\n",
    "fields for our particles to move in.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "plasma = Plasma(\n",
    "    domain_x=np.linspace(-1, 1, 10) * u.m,\n",
    "    domain_y=np.linspace(-1, 1, 10) * u.m,\n",
    "    domain_z=np.linspace(-1, 1, 10) * u.m,\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Initialize the fields. We'll take B in the x direction\n",
    "and E in the y direction, which gets us an E cross B drift\n",
    "in the negative z direction.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "B0 = 4 * u.T\n",
    "plasma.magnetic_field[0, ...] = B0\n",
    "\n",
    "E0 = 2 * u.V / u.m\n",
    "plasma.electric_field[1, ...] = E0\n",
    "\n",
    "ExB_drift(plasma.electric_field[:, 0, 0, 0], plasma.magnetic_field[:, 0, 0, 0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Calculate the timestep. We'll take one proton `p`, take its gyrofrequency, invert that\n",
    "to get to the gyroperiod, and resolve that into 10 steps for higher accuracy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "freq = gyrofrequency(B0, \"p\").to(u.Hz, equivalencies=u.dimensionless_angles())\n",
    "gyroperiod = (1 / freq).to(u.s)\n",
    "steps_to_gyroperiod = 50\n",
    "timestep = 20 * gyroperiod / steps_to_gyroperiod"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Initialize the trajectory calculation.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "number_steps = steps_to_gyroperiod * int(2 * np.pi)\n",
    "trajectory = ParticleTracker(plasma, \"p\", 1, 1, timestep, number_steps)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We still have to initialize the particle's velocity. We'll limit ourselves to\n",
    "one in the x direction, parallel to the magnetic field B -\n",
    "that way, it won't turn in the z direction.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "trajectory.v[0][0] = 1 * (u.m / u.s)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Run the pusher and plot the trajectory versus time.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
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     "nbsphinx-thumbnail"
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   },
   "outputs": [],
   "source": [
    "trajectory.run()\n",
    "trajectory.plot_time_trajectories()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also take a look at the trajectory in the z direction:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "trajectory.plot_time_trajectories(\"z\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "or plot the shape of the trajectory in 3D:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "trajectory.plot_trajectories()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As a test, we calculate the mean velocity in the z direction from the\n",
    "velocity:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "vmean = trajectory.velocity_history[:, :, 2].mean()\n",
    "print(\n",
    "    f\"The calculated drift velocity is {vmean:.4f} to compare with the \"\n",
    "    f\"expected E0/B0 = {-E0/B0:.4f}\"\n",
    ")"
   ]
  }
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