{
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   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "Cold Magnetized Plasma Waves Tensor Elements (S, D, P in Stix's notation)\n",
    "=========================================================================\n",
    "\n",
    "This example shows how to calculate the values of the cold plasma tensor\n",
    "elements for various electromagnetic wave frequencies.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
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   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "from astropy import units as u\n",
    "\n",
    "from plasmapy.formulary import (\n",
    "    cold_plasma_permittivity_LRP,\n",
    "    cold_plasma_permittivity_SDP,\n",
    ")"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {
    "raw_mimetype": "text/restructuredtext"
   },
   "source": [
    "Take a look at the docs to :func:`~plasmapy.formulary.dielectric.cold_plasma_permittivity_SDP` and :func:`~plasmapy.formulary.dielectric.cold_plasma_permittivity_LRP` for more information on these."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's define some parameters, such as the magnetic field magnitude,\n",
    "the plasma species and densities and the frequency band of interest\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
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   "source": [
    "B = 2 * u.T\n",
    "species = [\"e\", \"D+\"]\n",
    "n = [1e18 * u.m ** -3, 1e18 * u.m ** -3]\n",
    "\n",
    "f = np.logspace(start=6, stop=11.3, num=3001)  # 1 MHz to 200 GHz\n",
    "omega_RF = f * (2 * np.pi) * (u.rad / u.s)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
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    }
   },
   "outputs": [],
   "source": [
    "help(cold_plasma_permittivity_SDP)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
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   },
   "outputs": [],
   "source": [
    "S, D, P = cold_plasma_permittivity_SDP(B, species, n, omega_RF)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Filter positive and negative values, for display purposes only.\n",
    "Still for display purposes, replace 0 by NaN to NOT plot 0 values\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
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   "outputs": [],
   "source": [
    "S_pos = S * (S > 0)\n",
    "D_pos = D * (D > 0)\n",
    "P_pos = P * (P > 0)\n",
    "S_neg = S * (S < 0)\n",
    "D_neg = D * (D < 0)\n",
    "P_neg = P * (P < 0)\n",
    "S_pos[S_pos == 0] = np.NaN\n",
    "D_pos[D_pos == 0] = np.NaN\n",
    "P_pos[P_pos == 0] = np.NaN\n",
    "S_neg[S_neg == 0] = np.NaN\n",
    "D_neg[D_neg == 0] = np.NaN\n",
    "P_neg[P_neg == 0] = np.NaN"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "tags": [
     "nbsphinx-thumbnail"
    ]
   },
   "outputs": [],
   "source": [
    "plt.figure(figsize=(12, 6))\n",
    "plt.semilogx(f, abs(S_pos), f, abs(D_pos), f, abs(P_pos), lw=2)\n",
    "plt.semilogx(\n",
    "    f,\n",
    "    abs(S_neg),\n",
    "    \"#1f77b4\",\n",
    "    f,\n",
    "    abs(D_neg),\n",
    "    \"#ff7f0e\",\n",
    "    f,\n",
    "    abs(P_neg),\n",
    "    \"#2ca02c\",\n",
    "    lw=2,\n",
    "    ls=\"--\",\n",
    ")\n",
    "plt.yscale(\"log\")\n",
    "plt.grid(True, which=\"major\")\n",
    "plt.grid(True, which=\"minor\")\n",
    "plt.ylim(1e-4, 1e8)\n",
    "plt.xlim(1e6, 200e9)\n",
    "plt.legend((\"S > 0\", \"D > 0\", \"P > 0\", \"S < 0\", \"D < 0\", \"P < 0\"), fontsize=16, ncol=2)\n",
    "plt.xlabel(\"RF Frequency [Hz]\", size=16)\n",
    "plt.ylabel(\"Absolute value\", size=16)\n",
    "plt.tick_params(labelsize=14)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Cold Plasma tensor elements in the rotating basis\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "jupyter": {
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    }
   },
   "outputs": [],
   "source": [
    "L, R, P = cold_plasma_permittivity_LRP(B, species, n, omega_RF)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
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   "outputs": [],
   "source": [
    "L_pos = L * (L > 0)\n",
    "R_pos = R * (R > 0)\n",
    "L_neg = L * (L < 0)\n",
    "R_neg = R * (R < 0)\n",
    "L_pos[L_pos == 0] = np.NaN\n",
    "R_pos[R_pos == 0] = np.NaN\n",
    "L_neg[L_neg == 0] = np.NaN\n",
    "R_neg[R_neg == 0] = np.NaN\n",
    "\n",
    "plt.figure(figsize=(12, 6))\n",
    "plt.semilogx(f, abs(L_pos), f, abs(R_pos), f, abs(P_pos), lw=2)\n",
    "plt.semilogx(\n",
    "    f,\n",
    "    abs(L_neg),\n",
    "    \"#1f77b4\",\n",
    "    f,\n",
    "    abs(R_neg),\n",
    "    \"#ff7f0e\",\n",
    "    f,\n",
    "    abs(P_neg),\n",
    "    \"#2ca02c\",\n",
    "    lw=2,\n",
    "    ls=\"--\",\n",
    ")\n",
    "plt.yscale(\"log\")\n",
    "plt.grid(True, which=\"major\")\n",
    "plt.grid(True, which=\"minor\")\n",
    "plt.xlim(1e6, 200e9)\n",
    "plt.legend((\"L > 0\", \"R > 0\", \"P > 0\", \"L < 0\", \"R < 0\", \"P < 0\"), fontsize=16, ncol=2)\n",
    "plt.xlabel(\"RF Frequency [Hz]\", size=16)\n",
    "plt.ylabel(\"Absolute value\", size=16)\n",
    "plt.tick_params(labelsize=14)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Checks if the values obtained are coherent. They should satisfy\n",
    "S = (R+L)/2 and D = (R-L)/2\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "try:\n",
    "    np.testing.assert_allclose(S, (R + L) / 2)\n",
    "    np.testing.assert_allclose(D, (R - L) / 2)\n",
    "except AssertionError as e:\n",
    "    print(e)\n",
    "# Checks for R=S+D and L=S-D\n",
    "try:\n",
    "    np.testing.assert_allclose(R, S + D)\n",
    "    np.testing.assert_allclose(L, S - D)\n",
    "except AssertionError as e:\n",
    "    print(e)"
   ]
  }
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