{
 "cells": [
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   "execution_count": null,
   "metadata": {
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    "jupyter": {
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    }
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "Magnetostatic Fields\n",
    "=====================\n",
    "\n",
    "An example of using PlasmaPy's `Magnetostatic` class in `physics` subpackage.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "jupyter": {
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    }
   },
   "outputs": [],
   "source": [
    "import astropy.units as u\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "from plasmapy.formulary import magnetostatics\n",
    "from plasmapy.plasma.sources import Plasma3D"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Some common magnetostatic fields can be generated and added to a plasma object.\n",
    "A dipole\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "dipole = magnetostatics.MagneticDipole(\n",
    "    np.array([0, 0, 1]) * u.A * u.m * u.m, np.array([0, 0, 0]) * u.m\n",
    ")\n",
    "print(dipole)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "initialize a a plasma, where the magnetic field will be calculated on\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "plasma = Plasma3D(\n",
    "    domain_x=np.linspace(-2, 2, 30) * u.m,\n",
    "    domain_y=np.linspace(0, 0, 1) * u.m,\n",
    "    domain_z=np.linspace(-2, 2, 20) * u.m,\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "add the dipole field to it\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "plasma.add_magnetostatic(dipole)\n",
    "\n",
    "X, Z = plasma.grid[0, :, 0, :], plasma.grid[2, :, 0, :]\n",
    "U = plasma.magnetic_field[0, :, 0, :].value.T  # because grid uses 'ij' indexing\n",
    "W = plasma.magnetic_field[2, :, 0, :].value.T  # because grid uses 'ij' indexing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "tags": [
     "nbsphinx-thumbnail"
    ]
   },
   "outputs": [],
   "source": [
    "plt.figure()\n",
    "plt.axis(\"square\")\n",
    "plt.xlim(-2, 2)\n",
    "plt.ylim(-2, 2)\n",
    "plt.title(\n",
    "    \"Dipole field in x-z plane, generated by a dipole pointing in the z direction\"\n",
    ")\n",
    "plt.streamplot(plasma.x.value, plasma.z.value, U, W)"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {
    "raw_mimetype": "text/restructuredtext"
   },
   "source": [
    "A circular current-carring wire (:class:`~plasmapy.formulary.magnetostatics.CircularWire`)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "cw = magnetostatics.CircularWire(\n",
    "    np.array([0, 0, 1]), np.array([0, 0, 0]) * u.m, 1 * u.m, 1 * u.A\n",
    ")\n",
    "print(cw)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "initialize a a plasma, where the magnetic field will be calculated on\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "plasma = Plasma3D(\n",
    "    domain_x=np.linspace(-2, 2, 30) * u.m,\n",
    "    domain_y=np.linspace(0, 0, 1) * u.m,\n",
    "    domain_z=np.linspace(-2, 2, 20) * u.m,\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "add the circular coil field to it\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "plasma.add_magnetostatic(cw)\n",
    "\n",
    "X, Z = plasma.grid[0, :, 0, :], plasma.grid[2, :, 0, :]\n",
    "U = plasma.magnetic_field[0, :, 0, :].value.T  # because grid uses 'ij' indexing\n",
    "W = plasma.magnetic_field[2, :, 0, :].value.T  # because grid uses 'ij' indexing\n",
    "\n",
    "plt.figure()\n",
    "plt.axis(\"square\")\n",
    "plt.xlim(-2, 2)\n",
    "plt.ylim(-2, 2)\n",
    "plt.title(\n",
    "    \"Circular coil field in x-z plane, generated by a circular coil in the x-y plane\"\n",
    ")\n",
    "plt.streamplot(plasma.x.value, plasma.z.value, U, W)"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {
    "raw_mimetype": "text/restructuredtext"
   },
   "source": [
    "a circular wire can be described as parametric equation and converted to :class:`~plasmapy.formulary.magnetostatics.GeneralWire`\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "gw_cw = cw.to_GeneralWire()\n",
    "\n",
    "# the calculated magnetic field is close\n",
    "print(gw_cw.magnetic_field([0, 0, 0]) - cw.magnetic_field([0, 0, 0]))"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {
    "raw_mimetype": "text/restructuredtext"
   },
   "source": [
    "A infinite straight wire (:class:`~plasmapy.formulary.magnetostatics.InfiniteStraightWire`)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "iw = magnetostatics.InfiniteStraightWire(\n",
    "    np.array([0, 1, 0]), np.array([0, 0, 0]) * u.m, 1 * u.A\n",
    ")\n",
    "print(iw)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "initialize a a plasma, where the magnetic field will be calculated on\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "plasma = Plasma3D(\n",
    "    domain_x=np.linspace(-2, 2, 30) * u.m,\n",
    "    domain_y=np.linspace(0, 0, 1) * u.m,\n",
    "    domain_z=np.linspace(-2, 2, 20) * u.m,\n",
    ")\n",
    "\n",
    "# add the infinite straight wire field to it\n",
    "plasma.add_magnetostatic(iw)\n",
    "\n",
    "X, Z = plasma.grid[0, :, 0, :], plasma.grid[2, :, 0, :]\n",
    "U = plasma.magnetic_field[0, :, 0, :].value.T  # because grid uses 'ij' indexing\n",
    "W = plasma.magnetic_field[2, :, 0, :].value.T  # because grid uses 'ij' indexing\n",
    "\n",
    "plt.figure()\n",
    "plt.title(\n",
    "    \"Dipole field in x-z plane, generated by a infinite straight wire \"\n",
    "    \"pointing in the y direction\"\n",
    ")\n",
    "plt.axis(\"square\")\n",
    "plt.xlim(-2, 2)\n",
    "plt.ylim(-2, 2)\n",
    "plt.streamplot(plasma.x.value, plasma.z.value, U, W)"
   ]
  }
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