{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Typical plasma parameters\n",
    "==="
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using the experimental result measured by the langmuir probe, electron density and temperature has been specified at 2 points. Considering both experimental and equilibrium data calculated by TSC (Tokamak Simulation Code) has enabled us to obtain their 2-D profiles."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "from matplotlib.ticker import ScalarFormatter\n",
    "from raysect.optical import World\n",
    "\n",
    "from cherab.core.math import sample3d\n",
    "from cherab.phix.plasma import import_plasma\n",
    "from cherab.phix.plasma.species import PHiXSpecies\n",
    "from cherab.phix.tools.raytransfer import import_phix_rtc\n",
    "from cherab.phix.tools.visualize import show_phix_profiles\n",
    "\n",
    "plt.rcParams[\"figure.dpi\"] = 150\n",
    "world = World()\n",
    "plasma, eq = import_plasma(world)\n",
    "species = PHiXSpecies(equilibrium=eq)\n",
    "rtc = import_phix_rtc(world, equilibrium=eq)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "dr = rtc.material.dr\n",
    "dz = rtc.material.dz\n",
    "nr = rtc.material.grid_shape[0]\n",
    "nz = rtc.material.grid_shape[2]\n",
    "rmin = rtc.material.rmin\n",
    "zmin = rtc.transform[2, 3]\n",
    "rmax = rmin + dr * nr\n",
    "zmax = zmin + dz * nz"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plotting the plasma parameters distribution in 1D vs $\\psi_\\text{normalized}$ and 2D $r-z$ space\n",
    "---"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plasma parameters ($n_\\text{e}, T_\\text{e}$) is assumed to distribute as quadratic function along to $\\psi$.\n",
    "For instance, $n_\\text{e}$ represents as follows:\n",
    "\n",
    "$$\n",
    "n_e = (n_{\\min} - n_{\\max}) \\psi^2 + n_{\\min}\n",
    "$$\n",
    "\n",
    "The values of $n_{\\min}$ and $n_{\\max}$ are used as an experimental data measured by the langmuir probe which locates both near magnetic axis and LCFS."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "jupyter": {
     "source_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "x = np.linspace(0, 1, 100)\n",
    "y = [species.temp1d(i) for i in x]\n",
    "plt.plot(x, y)\n",
    "plt.xlabel(\"Normalized Psi\")\n",
    "plt.ylabel(\"$T_e$ [eV]\")\n",
    "plt.xlim([0, 1])\n",
    "plt.annotate(f\"{y[0]}eV\", (x[0], y[0]), (0.1, 35), arrowprops=dict())\n",
    "plt.annotate(f\"{y[-1]}eV\", (x[-1], y[-1]), (0.7, 20), arrowprops=dict());"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.linspace(0, 1, 100)\n",
    "y = [species.dens1d(i) for i in x]\n",
    "fig, ax = plt.subplots()\n",
    "ax.plot(x, y)\n",
    "ax.yaxis.set_major_formatter(ScalarFormatter(useMathText=True))\n",
    "ax.set_xlabel(\"Normalized Psi\")\n",
    "ax.set_ylabel(\"$n_e$ [m$^{-3}$]\")\n",
    "ax.set_xlim([0, 1])\n",
    "plt.annotate(f\"{y[0]}\", (x[0], y[0]), (0.1, 4e18), arrowprops=dict())\n",
    "plt.annotate(f\"{y[-1]}\", (x[-1], y[-1]), (0.7, 1e18), arrowprops=dict());"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "tags": [
     "nbsphinx-thumbnail"
    ]
   },
   "outputs": [],
   "source": [
    "r, _, z, ne_samples = sample3d(\n",
    "    plasma.electron_distribution.density, (rmin, rmax, nr), (0, 0, 1), (zmin, zmax, nz)\n",
    ")\n",
    "show_phix_profiles(\n",
    "    ne_samples.squeeze(),\n",
    "    clabel=\"$n_e$ [m$^{-3}$]\",\n",
    "    cmap=\"viridis\",\n",
    "    scientific_notation=True,\n",
    "    rtc=rtc,\n",
    ");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "r, _, z, te_samples = sample3d(\n",
    "    plasma.electron_distribution.effective_temperature,\n",
    "    (rmin, rmax, nr),\n",
    "    (0, 0, 1),\n",
    "    (zmin, zmax, nz),\n",
    ")\n",
    "show_phix_profiles(te_samples.squeeze(), clabel=\"$T_e$ [eV]\", cmap=\"viridis\", rtc=rtc);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Density Profile along R axis on the equatorial plane.\n",
    "---"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "r, _, z, t_samples = sample3d(\n",
    "    plasma.electron_distribution.density,\n",
    "    (rmin, rmax, nr),\n",
    "    (0, 0, 1),\n",
    "    (eq.magnetic_axis.y, eq.magnetic_axis.y, 1),\n",
    ")\n",
    "fig, ax = plt.subplots()\n",
    "ax.plot(r, t_samples.ravel())\n",
    "ax.yaxis.set_major_formatter(ScalarFormatter(useMathText=True))\n",
    "plt.xlabel(\"$R$[m]\")\n",
    "plt.ylabel(\"$n_e$ [m$^{-3}$]\")\n",
    "plt.xlim([0.2, 0.5])\n",
    "plt.ylim([0, 5e18]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Q profile as a function of $\\psi_\\text{normalized}$\n",
    "---"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.linspace(0, 0.96, 100)\n",
    "y = [eq.q(i) for i in x]\n",
    "plt.plot(x, y)\n",
    "plt.xlabel(\"Normalized Psi\")\n",
    "plt.ylabel(\"$q$\")\n",
    "plt.xlim([0, 1]);"
   ]
  }
 ],
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