energy-dist-post-collision.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy.stats import maxwell\n",
    "from math import sqrt\n",
    "from random import gauss\n",
    "from matplotlib import pyplot as plt\n",
    "from matplotlib.ticker import FormatStrFormatter\n",
    "\n",
    "T = 87          # K\n",
    "M_a = 6.63e-26  # kg\n",
    "m_e = 9.1e-31   # kg\n",
    "k_b = 1.38e-23  # J/K\n",
    "\n",
    "def J_to_eV(J):\n",
    "    return 6.242e18 * J\n",
    "\n",
    "def eV_to_J(eV):\n",
    "    return 1.60218e-19 * eV\n",
    "\n",
    "def v_to_E(v):\n",
    "    return 0.5 * m_e * np.dot(v, v)\n",
    "\n",
    "def E_to_v(E):\n",
    "    return sqrt(2 * E / m_e)\n",
    "\n",
    "def rand_unit_vec():\n",
    "    vec = [gauss(0, 1) for i in range(3)]\n",
    "    mag = sum(x**2 for x in vec)**.5\n",
    "    return np.array([x / mag for x in vec])\n",
    "\n",
    "def random_velocity(eV):\n",
    "    mag = E_to_v(eV_to_J(eV))\n",
    "    return rand_unit_vec() * mag"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The below simulates $steps$ number of collisions occuring at initial electron energies $en\\_list$. It then plots the distribution of the final energies."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "en_list = [0.0001, 1, 10, 200] # Initial electron energies\n",
    "\n",
    "steps = 1000                   # Number of collisions to simulate\n",
    "\n",
    "for e in en_list:\n",
    "    energies = []\n",
    "    for i in range(steps):\n",
    "        v = random_velocity(e)\n",
    "\n",
    "        vm = rand_unit_vec() * maxwell.rvs(size=1, scale=134.568)\n",
    "        u = np.dot(v - vm, v - vm)**0.5\n",
    "        n = rand_unit_vec()\n",
    "\n",
    "        a = (M_a * u) * n\n",
    "        b = (m_e) * v\n",
    "        c = (M_a) * vm\n",
    "\n",
    "        v1 = (a + b + c) / (m_e + M_a)\n",
    "\n",
    "        v = v1\n",
    "        \n",
    "        energy = J_to_eV(v_to_E(v))\n",
    "\n",
    "        if (energy < 0):\n",
    "            print(energy)\n",
    "        \n",
    "        energies.append(energy)\n",
    "        \n",
    "    # plt.rcParams['font.size'] = 14\n",
    "    # plt.rcParams['font.family'] = 'serif'\n",
    "    # fig = plt.figure(figsize=(6, 6))\n",
    "    \n",
    "    plt.hist(energies, label=str(e), color='C0', histtype='stepfilled')\n",
    "\n",
    "    plt.xlabel('Energy [eV]')\n",
    "    plt.ylabel('Outgoing Electrons')\n",
    "\n",
    "    plt.title('Energy Distribution Post-Scatter')\n",
    "    plt.xticks(np.linspace(min(energies), max(energies), 3))\n",
    "    plt.gca().xaxis.set_major_formatter(FormatStrFormatter('%.3E'))\n",
    "\n",
    "    plt.grid()\n",
    "    plt.tight_layout()\n",
    "    plt.show()\n",
    "    \n",
    "    # plt.savefig(f'post_scattering_energy_dists_{e}.pdf', bbox_inches='tight')"
   ]
  },
  {
   "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": "3.6.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}