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   "source": [
    "\n",
    "Analysing ITER parameters\n",
    "======================\n",
    "\n",
    "[ITER]: https://www.iter.org/\n",
    "[plasmapy.formulary]: https://docs.plasmapy.org/en/stable/formulary/index.html\n",
    "\n",
    "Let's try to look at [ITER] plasma conditions using [plasmapy.formulary]."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "jupyter": {
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    }
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "from astropy import units as u\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "\n",
    "from plasmapy import formulary"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {
    "raw_mimetype": "text/restructuredtext"
   },
   "source": [
    "The radius of electric field shielding clouds, also known as the :func:`~plasmapy.formulary.lengths.Debye_length`,\n",
    "would be"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "electron_temperature = 8.8 * u.keV\n",
    "electron_concentration = 10.1e19 / u.m**3\n",
    "print(formulary.Debye_length(electron_temperature, electron_concentration))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[Quantity]: https://docs.astropy.org/en/stable/api/astropy.units.Quantity.html#astropy.units.Quantity\n",
    "\n",
    "Note that we can also neglect the unit for the concentration, as m$^{-3}$ is the a standard unit for this kind of [Quantity]:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "print(formulary.Debye_length(electron_temperature, 10.1e19))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Assuming the magnetic field as 5.3 T (which is the value at the major radius):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "B = 5.3 * u.T\n",
    "\n",
    "print(formulary.gyrofrequency(B, particle=\"e\"))\n",
    "\n",
    "print(formulary.gyroradius(B, T=electron_temperature, particle=\"e\"))"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {
    "raw_mimetype": "text/restructuredtext"
   },
   "source": [
    "The electron :func:`~plasmapy.formulary.lengths.inertial_length` would be"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "print(formulary.inertial_length(electron_concentration, particle=\"e\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In these conditions, they should reach thermal velocities of about\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "print(formulary.thermal_speed(T=electron_temperature, particle=\"e\"))"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {
    "raw_mimetype": "text/restructuredtext"
   },
   "source": [
    "The Langmuir wave :func:`~plasmapy.formulary.frequencies.plasma_frequency` should be on the order of"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "print(formulary.plasma_frequency(electron_concentration, particle=\"e-\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's try to recreate some plots and get a feel for some of these quantities.\n",
    "We will also compare our data to real-world plasma situations.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "jupyter": {
     "outputs_hidden": false
    },
    "scrolled": true,
    "tags": [
     "nbsphinx-thumbnail"
    ]
   },
   "outputs": [],
   "source": [
    "n_e = np.logspace(4, 30, 100) / u.m**3\n",
    "plt.plot(n_e, formulary.plasma_frequency(n_e, particle=\"e-\"))\n",
    "plt.scatter(\n",
    "    electron_concentration,\n",
    "    formulary.plasma_frequency(electron_concentration, particle=\"e-\"),\n",
    "    label=\"Our Data\",\n",
    ")\n",
    "\n",
    "# IRT1 Tokamak Data\n",
    "# http://article.sapub.org/pdf/10.5923.j.jnpp.20110101.03.pdf\n",
    "n_e = 1.2e19 / u.m**3\n",
    "T_e = 136.8323 * u.eV\n",
    "B = 0.82 * u.T\n",
    "plt.scatter(n_e, formulary.plasma_frequency(n_e, particle=\"e-\"), label=\"IRT1 Tokamak\")\n",
    "\n",
    "# Wendelstein 7-X Stellarator Data\n",
    "# https://nucleus.iaea.org/sites/fusionportal/Shared%20Documents/FEC%202016/fec2016-preprints/preprint0541.pdf\n",
    "n_e = 3e19 / u.m**3\n",
    "T_e = 6 * u.keV\n",
    "B = 3 * u.T\n",
    "plt.scatter(\n",
    "    n_e, formulary.plasma_frequency(n_e, particle=\"e-\"), label=\"W7-X Stellerator\"\n",
    ")\n",
    "\n",
    "# Solar Corona\n",
    "n_e = 1e15 / u.m**3\n",
    "T_e = 1 * u.MK\n",
    "B = 0.005 * u.T\n",
    "T_e.to(u.eV, equivalencies=u.temperature_energy())\n",
    "plt.scatter(n_e, formulary.plasma_frequency(n_e, particle=\"e-\"), label=\"Solar Corona\")\n",
    "\n",
    "# Interstellar (warm neutral) Medium\n",
    "n_e = 1e6 / u.m**3\n",
    "T_e = 5e3 * u.K\n",
    "B = 0.005 * u.T\n",
    "T_e.to(u.eV, equivalencies=u.temperature_energy())\n",
    "plt.scatter(\n",
    "    n_e, formulary.plasma_frequency(n_e, particle=\"e-\"), label=\"Interstellar Medium\"\n",
    ")\n",
    "\n",
    "# Solar Wind at 1 AU\n",
    "n_e = 7e6 / u.m**3\n",
    "T_e = 1e5 * u.K\n",
    "B = 5e-9 * u.T\n",
    "T_e.to(u.eV, equivalencies=u.temperature_energy())\n",
    "plt.scatter(\n",
    "    n_e, formulary.plasma_frequency(n_e, particle=\"e-\"), label=\"Solar Wind (1AU)\"\n",
    ")\n",
    "\n",
    "plt.xlabel(\"Electron Concentration (m^-3)\")\n",
    "plt.ylabel(\"Langmuir Wave Plasma Frequency (rad/s)\")\n",
    "plt.grid()\n",
    "plt.xscale(\"log\")\n",
    "plt.yscale(\"log\")\n",
    "plt.legend()\n",
    "plt.title(\"Log-scale plot of plasma frequencies\")\n",
    "plt.show()"
   ]
  }
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