Velocity_Generator.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import random\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy\n",
    "from scipy import constants\n",
    "import math"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "550.0"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.read_csv(\"Na_22.csv\",sep=\";\",decimal=\",\",header=None)\n",
    "df[1] = df[1]/max(df[1])\n",
    "max(df[0])#Endpunktenergie"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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GljbeWLuHS0fFMCAi0Oo4ygWFB/ry/KzxVDS0cM+b2bTrG5zUKaDlfpLe21BMbXMbs88a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\nUkrZ0P8DaNtGfmME3y0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4aee86a6d8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(df[0],df[1])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "lower_endpoint = min(df[0])\n",
    "higher_endpoint = max(df[0])\n",
    "uniform_vals = [random.uniform(lower_endpoint, higher_endpoint) for i in range(1000000)]\n",
    "keeping_probability = np.interp(uniform_vals,df[0],df[1]) # 1-rejection_probability\n",
    "\n",
    "resulting_vals = []\n",
    "for energy_probability in zip(uniform_vals,keeping_probability):\n",
    "       if random.random() < energy_probability[1]:\n",
    "            resulting_vals.append(energy_probability[0])\n",
    "        \n",
    "        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "570105"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(resulting_vals)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Jl+omBCRpPT1ODRkCkkS/swWGgCSt0lMgGAKS1LHBX0Cup0SXNDm9XHDOkYAkrWPIC8aG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\nktQxQ0CSOmYISFLHDAFJ6tj/B7kfRgjSGQF7AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4aebfa2358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(resulting_vals,bins=200)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-189253653.84420285, 77077556.51029293, -147165624.4582218)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# p = sqrt(E_kin*(E_kin+2m_0c^2)/c^2)\n",
    "def momentum_components_from_energy(energy_in_kev):\n",
    "    energy = energy_in_kev*1000*scipy.constants.e\n",
    "    p = math.sqrt(energy*(energy+2*scipy.constants.m_e*scipy.constants.c**2)/scipy.constants.c**2)\n",
    "    \n",
    "    phi = random.uniform(0,2*scipy.constants.pi)\n",
    "    costheta = random.uniform(-1,1)\n",
    "    theta = math.acos( costheta )    \n",
    "    \n",
    "    x = p*math.sin( theta) * math.cos( phi )\n",
    "    y = p*math.sin( theta) * math.sin( phi )\n",
    "    z = p*math.cos( theta )\n",
    "    \n",
    "    return (energy,x,y,z)\n",
    "\n",
    "def velocity_from_momentum(energy,x,y,z):\n",
    "    mass = (energy/(scipy.constants.c**2))+scipy.constants.m_e\n",
    "    velocity = (x/mass,y/mass,z/mass)\n",
    "    for i in velocity:\n",
    "        if abs(i)>scipy.constants.c:\n",
    "            raise ValueError\n",
    "    return velocity\n",
    "\n",
    "velocity_from_momentum(*momentum_components_from_energy(random.random()*1000))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "velocity_list = [velocity_from_momentum(*momentum_components_from_energy(e)) for e in resulting_vals]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "with open(\"Na-22-Spectrum.csv\",\"w\") as f:\n",
    "    for (counter,velocity_tuple) in enumerate(velocity_list):\n",
    "        f.write(\"{};{};{};{}\\n\".format(counter,velocity_tuple[0],velocity_tuple[1],velocity_tuple[2]))\n",
    "    f.close()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-247.72547356270445"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum(velocity_list[:][0])/len(velocity_list)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "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": "3.6.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}