{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Techron report - Parameters of the tokamak GOLEM" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On the GOLEM tokamak, plasma current generation, known as \"Current Drive\" (commonly abbreviated as \"CD\"), is facilitated by a transformer battery, which discharges into the primary winding wound around a metallic transformer core. A simplified diagram of this setup can be seen in the following image.\n", "\n", "\n", "
\n", " \"Popis\n", "
\n", "\n", "This primary circuit is characterized by the following parameters:\n", "\n", "$$\n", "R_{CD} = 45 m\\Omega \\quad L_{CD} = 10 mH \\quad C_{CD} = 48 mF \\quad N_{CD} = 48 turns \\quad U_{CD} = \\langle 0,700 \\rangle V,\n", "$$\n", "\n", "where $R_{CD}$ is the resistance, $L_{CD}$ is the inductance, $C_{CD}$ is the capacitance, $N_{CD}$ is the number of turns, and $U_{CD}$ is the operating voltage range on the capacitor during the operation of the GOLEM tokamak (currently around 300 to 400 volts [Example of discharge](http://golem.fjfi.cvut.cz/shots/46737/) for plasma discharges).\n", "\n", "During a discharge on the GOLEM tokamak, the secondary winding consists of two parts: the tokamak chamber, which acts as a resistor and can be approximated as a single short-circuited turn, and the plasma itself, which also forms a single short-circuited turn. A simplified diagram of this setup can be seen in the following image.\n", "\n", "
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\n", "\n", "For the secondary winding in the form of the tokamak chamber, the parameters are:\n", "\n", "$$\n", "R_{ch} = 9,7 m\\Omega \\quad L_{ch} = 1 \\mu H \\quad N_{ch} = 1 turn,\n", "$$\n", "\n", "where $R_{ch}$ is the resistance of the chamber and $L_{ch}$ is the inductance of the chamber. Operation with plasma is much more complex, as both resistance and inductance vary over time. However, for a rough approximation, the tokamak plasma exhibits the following approximate parameters:\n", "\n", "$$\n", "R_{p} \\approx 10 \\mu \\Omega \\quad L_{p} \\approx 1 \\mu H \\quad N_{p} = 1 turn,\n", "$$\n", "\n", "where $R_{p}$ is the resistance of the plasma, and $L_{p}$ is the inductance of the plasma. For reference, the following graph shows the waveforms of the plasma current and chamber current for a charging voltage of $U_{CD} = 350 V$ during the discharge. [#46737](http://golem.fjfi.cvut.cz/shots/46737/).\n", "\n", "
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Plasma current $I_p$ a current during chamber $I_{ch}$

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The voltage per turn $U_{loop}$

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\n", "\n", "Due to the complexity of operating with plasma, for an initial approximation, we will limit ourselves to the secondary winding in the form of the tokamak chamber, on which the first stabilization tests will be conducted. This reduced schematic can be seen in the following diagram.\n", "\n", "
\n", " \"Popis\n", "
\n", "\n", "Such operation is referred to as a vacuum discharge, or a discharge without tokamak plasma, where the current and voltage are induced solely in the chamber. As an example of such a vacuum discharge, we can refer to discharge number. [#46560](http://golem.fjfi.cvut.cz/shots/46560/) when the capacitor was charged to $U_{CD} = 500 V$.\n", "\n", "
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Plasma current $I_p$ a current during chamber $I_{ch}$

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The voltage per turn $U_{loop}$

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\n", "\n", "Our goal is to influence the waveform of the resulting current in the plasma, or for now, in the chamber, which will suffice for our purposes. This will be achieved using an additional primary winding powered by a current amplifier. A simplified schematic with the implemented amplifier is shown in the following diagram.\n", "\n", "
\n", " \"Popis\n", "
\n", "\n", "The estimated parameters for this stabilization winding (abbreviated as \"CST\" for current stabilization) are:\n", "\n", "$$\n", "R_{CST} = 0.3 \\Omega \\quad L_{CST} = 10.85 mH \\quad N_{CST} = 50 turns.\n", "$$\n", "\n", "A more detailed technological schematic is shown in the following image.\n", "\n", "
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" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# A concise summary of all the required parameters\n", "\n", "
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\n", "\n", "## Current drive as a primary winding\n", "$$\n", "R_{CD} = 45 m\\Omega \\quad L_{CD} = 10 mH \\quad C_{CD} = 48 mF \\quad N_{CD} = 48 turns \\quad U_{CD} = \\langle 0,700 \\rangle V,\n", "$$\n", "\n", "## Current stabilization as a extra primary winding\n", "$$\n", "R_{CST} = 0.3 \\Omega \\quad L_{CST} = 10.85 mH \\quad N_{CST} = 50 turns.\n", "$$\n", "\n", "## Chamber as a secondary winding\n", "$$\n", "R_{ch} = 9,7 m\\Omega \\quad L_{ch} = 1 \\mu H \\quad N_{ch} = 1 turn,\n", "$$" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [ { "ename": "", "evalue": "", "output_type": "error", "traceback": [ "\u001b[1;31mRunning cells with 'Python 3.10.11' requires the ipykernel package.\n", "\u001b[1;31mRun the following command to install 'ipykernel' into the Python environment. \n", "\u001b[1;31mCommand: '\"c:/Users/Jan Buryanec/AppData/Local/Microsoft/WindowsApps/PythonSoftwareFoundation.Python.3.10_qbz5n2kfra8p0/python.exe\" -m pip install ipykernel -U --user --force-reinstall'" ] } ], "source": [ "import numpy as np\n", "\n", "L = 10 * 1e-3 \n", "N = 48\n", "\n", "L_0 = L / N ** 2\n", "L_0\n", "\n", "N_CST = 50\n", "L_CST = L_0 * N_CST ** 2" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "name": "python", "version": "3.10.11" } }, "nbformat": 4, "nbformat_minor": 2 }