LIHEDP Notebooks

hack/LIHEDP_notebooks/Inverse_Bremsstrahlung.ipynb

@@ -0,0 +1,100 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "from scipy import constants as sc"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "equation (5.15), page 104\n",
+    "\n",
+    "\\begin{equation} \n",
+    "K_{ff} = 8 \\sqrt{\\pi} \\left( \\frac{e^2}{4 \\pi \\epsilon_0} \\right)^3 \\frac{4}{3 c^3} \\frac{Z_i^2}{m_0^2} n_e n_{Z_i} \\left( \\frac{m_0}{2 k_B T} \\right)^{1/2} \\frac{\\pi^2 c^2}{\\hbar \\omega^3} \\left( 1 - \\exp \\left( - \\frac{\\hbar \\omega}{k_B T} \\right) \\right) \n",
+    "\\end{equation}"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "exercise 5.8, page 112\n",
+    "\n",
+    "\\begin{equation}\n",
+    "K_{ff} = 2.7 \\times 10^{-50} \\frac{\\lambda^2 n_e n_{Z_i} Z_i^2}{(k_B T)^{3/2}} \\text{ m}^{-1}\n",
+    "\\end{equation}"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "equation (5.15), with $h \\nu \\ll k_B T$, becomes:"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "\\begin{equation}\n",
+    "k_{ff} = \\frac{8 \\sqrt{\\pi}}{3 \\sqrt{2}} \\left( \\frac{e^2}{4 \\pi \\epsilon_0} \\right)^3 \\frac{1}{m_0^{3/2} c^{3}} \\frac{\\lambda^2 n_e n_{Z_i} Z_i^2}{(k_B T)^{3/2}}\n",
+    "\\end{equation}"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "2.731832444805521e-47"
+      ]
+     },
+     "execution_count": 6,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "8*np.sqrt(np.pi)/(3*np.sqrt(2)) * (sc.e**2/(4*np.pi*sc.epsilon_0))**3 * (1/((sc.m_e**(3/2)*sc.c**3))) * (1e-12 / (sc.e**(3/2)))\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.8.10"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}