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 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Plasma Coupling Using COMSOL Results"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this example, we use a COMSOL front-face coupling calculation provided by ORNL, exported as a standard Touchstone file.\n",
    "\n",
    "The Touchstone file is first import as a [scikit-rf](https://scikit-rf.org/) [Network](https://scikit-rf.readthedocs.io/en/latest/tutorials/Networks.html), which is then modified to fit the WEST ICRH antenna electrical model requirements."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Importing the S-parameters in the electric model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import skrf as rf\n",
    "\n",
    "# WEST ICRH Antenna package\n",
    "import sys; sys.path.append('..')\n",
    "from west_ic_antenna import WestIcrhAntenna"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "front_face_conventional = rf.Network(\n",
    "    '../west_ic_antenna/data/Sparameters/front_faces/COMSOL/ORNL_front_face_conventional.s4p')\n",
    "print(front_face_conventional)  # 50 Ohm S-param component at a single frequency of 55 MHz"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The ports have been defined as:\n",
    "<img src=\"COMSOL_WEST_port_index.png\" />\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So before to use the S-parameters directly to feed the electrical model, we need to:\n",
    "- deembed the ports by 0.3m.\n",
    "- renomalize port reference impedance to the front-face coax characteristic impedances. \n",
    "- reverse ports 2 and 3 to match the expected definition by the electrical model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# creating a 50 Ohm dummy coax line to be removed from the front face \n",
    "media_coax = rf.DefinedGammaZ0(frequency=front_face_conventional.frequency) # 50 Ohm TEM media\n",
    "extra_line = media_coax.line(d=0.3, unit='m')\n",
    "# deembed all the 4 ports\n",
    "for port_idx in range(4):\n",
    "    front_face_conventional = rf.connect(front_face_conventional, port_idx, extra_line.inv, 0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The COMSOL S-parameters have been exported using a 50 Ohm reference impedance. However, we expect the port reference impedance equals to the characteristic impedance, that is, about 46.64 ohm, so we renormalize the Network to fit this need:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "front_face_conventional.renormalize(46.64)  # done inplace"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And finally, for historical reasons (may change one day...), the S-matrix port ordering should be adjusted:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "front_face_conventional.renumber([1, 2], [2, 1]) # done inplace"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "OK, so now we can create the WEST antenna object:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "ant = WestIcrhAntenna(front_face=front_face_conventional,\n",
    "                     frequency=front_face_conventional.frequency) # restrict to single frequ"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's match the antenna for this coupling:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Cs = ant.match_both_sides(f_match=55e6)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The coupling resistance of the antenna for this coupling in a nominal dipole excitation is:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "power = [1, 1]\n",
    "phase = [0, np.pi]\n",
    "\n",
    "# Coupling resistance\n",
    "ant.Rc(power, phase)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The total voltages and currents at the capacitors are:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "power = [1.6/2, 1.6/2]  # MW, to adjust to fit with experiment\n",
    "phase = [0, np.pi]  # rad\n",
    "\n",
    "abs(ant.voltages(power, phase))  # results in kV"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "abs(ant.currents(power, phase))  # results in kA"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exporting voltage excitations\n",
    "Now that the electrical model has been created and the antenna matched, one can export the voltage values at the front-face port into COMSOL to visualize the electric field and currents in the antenna front face and in the plasma."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Depending of the needs, the total voltages at the front-face port can be splitted into forward and reflected voltages:\n",
    "$$\n",
    "V = V_{fwd} + V_{ref} \n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "V_fwd, V_ref = ant.front_face_voltage_waves(power, phase, Cs=Cs)\n",
    "print(V_fwd)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Of course, we find the same total voltage:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Vtot = V_fwd + V_ref\n",
    "V = ant.voltages(power, phase, Cs=Cs)\n",
    "# pay attention that the voltage index differ from the front-face port indexes...\n",
    "np.allclose(Vtot[:,[0,2,1,3]], V, rtol=1e-5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is also possible to deduce the forward powers and phases to setup on the four ports (assuming the reference impedance is real):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "powers, phases = ant.front_face_powers_phases(power, phase, Cs=Cs)\n",
    "print(powers) # in Watt\n",
    "print(phases) # in degrees"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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