{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "brutal-hartford",
   "metadata": {},
   "outputs": [],
   "source": [
    "# This tutorial will use Monte Carlo methods to simulate the output of a\n",
    "# Photomultiplier Tube (PMT) once triggered by the detection of one or more\n",
    "# photons."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "literary-blink",
   "metadata": {},
   "outputs": [],
   "source": [
    "# This example follows notes posted online which you can find at the following\n",
    "# url: http://superk.physics.sunysb.edu/~mcgrew/phy310/lectures/phy310-lecture-06-2007.pdf\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import statistics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "constant-performance",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7961852081589491"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# In all Monte Carlo simulations it is necessary to generate random or\n",
    "# pseudo-random numbers.  The Python command 'np.random.uniform()'\n",
    "# from the NumPy module generates random numbers uniformly distributed \n",
    "# between zero and one. \n",
    "np.random.uniform()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "patent-american",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "546"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# First, suppose N photons hit the photocathode.  Determine the number of\n",
    "# photoelectrons (pe) that are generated.  Assume that the incoming light is\n",
    "# 400 nm and that the quantum efficiency of the photocathode is 0.23.\n",
    "#(Following  http://superk.physics.sunysb.edu/~mcgrew/phy310/lectures/phy310-lecture-06-2007.pdf)\n",
    "N = 2363\n",
    "QE = 0.23\n",
    "pe = 0\n",
    "for i in range(N):\n",
    "    if np.random.uniform() < QE:\n",
    "        pe += 1\n",
    "pe"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "listed-permit",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mean: 1998.539\n",
      "variance: 1942.5470260260263\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# When an electron with energy E hits a Dynode the average number of\n",
    "# secondary electrons liberated is alpha*E (i.e. number of secondary electrons\n",
    "# is proportional to the energy of the incoming electron) where alpha is a\n",
    "# contant.  Since we are counting electrons, the distribution of liberated\n",
    "# electrons follows the Poisson distribution.  In Python random numbers\n",
    "# drawn from a Poisson distribution with mean mu are generated using\n",
    "# poissrnd(mu). As an example, below we generate random integers drawn from\n",
    "# a Poisson parent distribtuion with mean 2000.\n",
    "mu = 2000\n",
    "Ydist = []\n",
    "for i in range(1000):\n",
    "    Ydist = Ydist + [np.random.poisson(mu)]\n",
    "print('mean:', statistics.mean(Ydist))\n",
    "print('variance:', statistics.stdev(Ydist)**2)\n",
    "nbins = 25\n",
    "plt.hist(Ydist, nbins, color = 'c', edgecolor = 'k')\n",
    "plt.xlabel('Y')\n",
    "plt.ylabel('counts');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "satisfied-helicopter",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2021-03-11 11:22:05.176837\n",
      "2021-03-11 11:22:05.230722\n"
     ]
    }
   ],
   "source": [
    "# A photomultiplier tube (PMT) consists of a photocathode followed by a\n",
    "# series of dynodes maintained at different electric potentials and then\n",
    "# finally an anode.  When a single photon is incident on the photocathode\n",
    "# it either produces a photoelectron or it doesn't.  The probability that\n",
    "# it produces a photoelectron is determined by the quantum efficiency\n",
    "# QE of the photocathode.  For this exercise we will assume that QE = 0.23.\n",
    "# If a photoelectron is produced, it is accelerated towards the first dynode by\n",
    "# means of a potential difference.  We assume that all electrons, whether\n",
    "# produced at the photocathode or one of the dynodes, start with zero kinetic\n",
    "# energy.  Therefore, the energy an electron gains is simply its charge times\n",
    "# the potential difference between its starting and final positions.  When\n",
    "# an electron collides with a dynode, secondary electrons are produced.  The\n",
    "# average number of secondary electrons produced is proportional to the energy\n",
    "# of the incoming electron.  In this problem, we assume that an electron\n",
    "# accelerated through 20 V will, on average, produce one secondary electron\n",
    "# upon colliding with the dynode.  Because we are \"counting\" electrons, the\n",
    "# distribution of secondary electrons generated will follow a Poisson\n",
    "# distribution.  \n",
    "\n",
    "QE = 0.23; # Set the quantum efficeincy of the photocathode\n",
    "maxi = int(1e4) # Set the number of Monte Carlo iterations\n",
    "dynode = [0, 150, 300, 450, 600, 750, 850] # Set the number of dynodes and\n",
    "# their voltages\n",
    "dist = []\n",
    "from datetime import datetime\n",
    "print(datetime.now()) # Print the time at the simulation was started\n",
    "for i in range(maxi): # This loop runs the Monte Carlo simulation maxi times\n",
    "    # (10,000 in this case)\n",
    "    if np.random.uniform() < QE: # Generate a random number between [0, 1] and check to see\n",
    "        # if it's greater than the quantum efficiency\n",
    "        electrons = 1 # If true, then a photoelectron is produced\n",
    "        for j in range(len(dynode)-1): # This loop will examine the secondary\n",
    "            # electrons produced at each of the dynodes\n",
    "            mu = electrons*(dynode[j+1]-dynode[j])/20 # Mean number of\n",
    "            # electrons generated at a dynode determined from the number of\n",
    "            # incoming electons and the energy of the incoming electrons.\n",
    "            # One electron accelerated through 20 V will on anverage produce\n",
    "            # one electron\n",
    "            electrons = electrons + np.random.poisson(mu)\n",
    "        dist = dist + [electrons] # Add the total number of electrons detected at\n",
    "        # the anode for this trial to a 'dist' list.  \n",
    "print(datetime.now()) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "returning-jefferson",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The fraction of trials that produced photoelectrons is 0.2286\n"
     ]
    }
   ],
   "source": [
    "print('The fraction of trials that produced photoelectrons is', len(dist)/maxi)\n",
    "# Determines what fraction of maxi trials actually\n",
    "# produced electrons at the PMT anode.  It should come out to be close the\n",
    "# QE = 0.23."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "smart-fleece",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The mean of the distribution was 268264.28783902014\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import statistics\n",
    "print('The mean of the distribution was', statistics.mean(dist))\n",
    "# Calculate the mean of the distribution\n",
    "xbins = np.linspace(0, 2e6, 101) # Set bin ranges for the histogram.\n",
    "# 100 equally-sized bins fron 0 to 2e6.\n",
    "plt.hist(dist, xbins, color = 'c', edgecolor = 'k') # Plot the histgram of the \n",
    "# simulated number of anode electrons\n",
    "plt.xlim((0, 2e6))\n",
    "plt.ylim((0, 500))\n",
    "plt.xlabel('Number of Anode Electons')\n",
    "plt.ylabel('Counts');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "dental-mission",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  0,   1,   5,  16,  21,  43,  76,  97, 146, 140, 185, 198, 202,\n",
       "       200, 169, 166, 147, 103,  92,  80,  51,  48,  30,  20,  22,  11,\n",
       "         6,   2,   4,   3,   1,   1,   0,   0,   0,   0,   0,   0,   0,\n",
       "         0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,\n",
       "         0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,\n",
       "         0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,\n",
       "         0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,\n",
       "         0,   0,   0,   0,   0,   0,   0,   0,   0], dtype=int64)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "counts, edges = np.histogram(dist, xbins) # Here we use 'np.histogram' to have \n",
    "# Python tell us how many counts there are in each of our 100 bins.\n",
    "counts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "critical-poultry",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  10000.,   30000.,   50000.,   70000.,   90000.,  110000.,\n",
       "        130000.,  150000.,  170000.,  190000.,  210000.,  230000.,\n",
       "        250000.,  270000.,  290000.,  310000.,  330000.,  350000.,\n",
       "        370000.,  390000.,  410000.,  430000.,  450000.,  470000.,\n",
       "        490000.,  510000.,  530000.,  550000.,  570000.,  590000.,\n",
       "        610000.,  630000.,  650000.,  670000.,  690000.,  710000.,\n",
       "        730000.,  750000.,  770000.,  790000.,  810000.,  830000.,\n",
       "        850000.,  870000.,  890000.,  910000.,  930000.,  950000.,\n",
       "        970000.,  990000., 1010000., 1030000., 1050000., 1070000.,\n",
       "       1090000., 1110000., 1130000., 1150000., 1170000., 1190000.,\n",
       "       1210000., 1230000., 1250000., 1270000., 1290000., 1310000.,\n",
       "       1330000., 1350000., 1370000., 1390000., 1410000., 1430000.,\n",
       "       1450000., 1470000., 1490000., 1510000., 1530000., 1550000.,\n",
       "       1570000., 1590000., 1610000., 1630000., 1650000., 1670000.,\n",
       "       1690000., 1710000., 1730000., 1750000., 1770000., 1790000.,\n",
       "       1810000., 1830000., 1850000., 1870000., 1890000., 1910000.,\n",
       "       1930000., 1950000., 1970000., 1990000.])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Calculate the centre positions of the bins from the edge locations.\n",
    "spacing = (edges[1] - edges[0])/2\n",
    "centres = edges[1:] - spacing\n",
    "centres"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "imperial-grass",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Counts')"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.semilogy(centres, counts, 'bo', fillstyle = 'none') # Make a semi-log plot \n",
    "# of the counts versus the number of detected anode electrons\n",
    "plt.xlim((0, 2e6))\n",
    "plt.ylim((.8, 500))\n",
    "plt.xlabel('Number of Anode Electrons')\n",
    "plt.ylabel('Counts')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "understanding-pricing",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2021-03-11 11:24:58.852798\n",
      "2021-03-11 11:24:59.142357\n",
      "The fraction of trials that produced photoelectrons is 0.8761\n",
      "The mean of the distribution was 560754.4641022715\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# This next block of code is very similar to the code presented above.  This time,\n",
    "# however, we imagine that there are 8 photons incident on the photocathode\n",
    "# instead of one. Now there can be 0, 1, 2, ..., or 8 photoelectrons\n",
    "# generated and then accelerated towards the first dynode.  How does the\n",
    "# distribution of electrons arriving at the anode change?  We only require\n",
    "# a relatively minor change to the code to study this problem.  Plot the\n",
    "# histograms using the same scale and the same binwidths to make comparisons\n",
    "# with the previous results easy.\n",
    "QE = 0.23 # Set the quantum efficeincy of the photocathode\n",
    "maxi = int(1e4) # Set the number of Monte Carlo iterations\n",
    "dynode = [0, 150, 300, 450, 600, 750, 850] # Set the number of dynodes and\n",
    "# their voltages\n",
    "numPhotons = 8 # Set the number of photons incident on the photocathode.\n",
    "dist = []\n",
    "print(datetime.now()) # Print the time at the simulation was started\n",
    "for i in range(maxi): # This loop runs the Monte Carlo simulation maxi times\n",
    "    # (10,000 in this case)\n",
    "    pe = 0 # Set the initial number of photoelectrons to zero.\n",
    "    for k in range(numPhotons): # This loop individually steps through each of the\n",
    "        # photons incident on the photocathode\n",
    "        if np.random.uniform() < QE: # Generate a random number between [0, 1] and check to see\n",
    "        # if it's greater than the quantum efficiency\n",
    "            pe += 1 # Increment pe by one every time a photoelectron is\n",
    "            # produced\n",
    "    if pe > 0: # If there are any photoelectrons, then do something.  If there\n",
    "        # are not photoelectrons then do nothing\n",
    "        electrons = pe # Set the initial number of electrons equal to the\n",
    "        # number of photoelectrons\n",
    "        for j in range(len(dynode)-1): # This loop will examine the secondary\n",
    "            # electrons produced at each of the dynodes\n",
    "            mu = electrons*(dynode[j+1]-dynode[j])/20; # Mean number of\n",
    "            # electrons generated at a dynode determined from the number of\n",
    "            # incoming electons and the energy of the incoming electrons.\n",
    "            # One electron accelerated through 20 V will on anverage produce\n",
    "            # one electron\n",
    "            electrons = electrons + np.random.poisson(mu)\n",
    "        dist = dist + [electrons] # Add the total number of electrons detected at\n",
    "        # the anode for this trial to a 'dist' list.\n",
    "print(datetime.now()) # Print the time at the simulation completed.  \n",
    "print('The fraction of trials that produced photoelectrons is', len(dist)/maxi)\n",
    " # Determines what fraction of maxi trials actually\n",
    "# produced electrons at the PMT anode.  \n",
    "print('The mean of the distribution was', statistics.mean(dist))\n",
    "# Calculate the mean of the distribution\n",
    "plt.figure() # Generate a new figure\n",
    "xbins = np.linspace(0, 2e6, 101) # Set bin ranges for the histogram.\n",
    "# 100 equally-sized bins fron 0 to 2e6.\n",
    "plt.hist(dist, xbins, color = 'c', edgecolor = 'k') # Plot the histgram of the \n",
    "# simulated number of anode electrons\n",
    "plt.xlim((0, 2e6))\n",
    "plt.ylim((0, 500))\n",
    "plt.xlabel('Number of Anode Electons')\n",
    "plt.ylabel('Counts')\n",
    "counts, edges = np.histogram(dist, xbins) # Here we use 'np.histogram' to have \n",
    "# Python tell us how many counts there are in each of our 100 bins.\n",
    "# Calculate the centre positions of the bins from the edge locations.\n",
    "spacing = (edges[1] - edges[0])/2\n",
    "centres = edges[1:] - spacing\n",
    "plt.figure() # Start a new figure.\n",
    "plt.semilogy(centres, counts, 'bo', fillstyle = 'none') # Make a semi-log plot \n",
    "# of the counts versus the number of detected anode electrons\n",
    "plt.xlim((0, 2e6))\n",
    "plt.ylim((.8, 500))\n",
    "plt.xlabel('Number of Anode Electrons')\n",
    "plt.ylabel('Counts');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "governing-dodge",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2021-03-11 11:25:35.795103\n",
      "Iteration 0\n",
      "The fraction of trials that produced photoelectrons is 0.2217\n",
      "The mean of the distribution was 262444.55435272894\n",
      "2021-03-11 11:25:35.842940\n",
      "Iteration 1\n",
      "The fraction of trials that produced photoelectrons is 0.4072\n",
      "The mean of the distribution was 302301.53806483303\n",
      "2021-03-11 11:25:36.061257\n",
      "Iteration 2\n",
      "The fraction of trials that produced photoelectrons is 0.6407\n",
      "The mean of the distribution was 378459.22553457157\n",
      "2021-03-11 11:25:36.291688\n",
      "Iteration 3\n",
      "The fraction of trials that produced photoelectrons is 0.8822\n",
      "The mean of the distribution was 560186.1229879846\n",
      "2021-03-11 11:25:36.651354\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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cfV6rG9KIRqrx6uobmUj8T0atoosiMr60OZB31Vru7jdn3qIGqBqvZEWXeks3aXc13tcn7s8ETgUeAXINICJZGRhQwBBpVNpTWEPJx2Y2C/i7lrRIRERKodk50f8DOCHLhoiISLmkCiBmdqeZ/VN0+wrwJPCl1jZNJB/1RqVrxLpIRdocyP9K3B8FnnX3kfFWFimreqPSQSPWRZJSXYUFYGYvp5JM/5a7P9eyVqWkq7Aka/VGpYNGrEtnyOoqrLSX8b4d+DhwP2DAHwIfdPfbJtuAyVAAkazVK30DKosjnaHdpUzWAq9393Pd/V3AG4C/muzORYqm3qh0jVgXGSttAJlSdcrqFw1sK1Ia9UrfqCyOyFhpk+j3mNm9QHzNyZ8Dd7WmSSL5SVP6RmVxRIK6ORAz6wVe7u5fN7O3AUsJOZBfAre4+/fb08zalAORPKn8iZRVu0qZfAq4AsDdbwduj3beHz23fLINECkjTUIlMnEeY667f6d6obvvBOa2pEUiJZCc6bKnpzLTpSr4SjeZKIDMrPPc72TZEJEy0SRUIhMHkB1mdmH1QjMbJEwqJdKVdEmvyMQB5P3A+WZ2v5l9Iro9ALwbuKTlrRMpqMlc0qt6WtIp6ibR3f1fgZPNbBnQFy3+irtvbXnLRAqs2ZkulXyXTpK6FlYR6TJeKZt6tbZUT0vapd2lTFrOzF5lZpvMLNf6WiLVsjzlpOS7dJKWBhAzu9HMnjOzXVXLTzezJ83sKTNbA+DuT7v7YO1XEslHfMppw4ZQSHHDhvC42SCi5Lt0klb3QDYDpycXmNlU4NPAGcAiYMDMFrW4HSJNyXq8h+ppSSdJWwurKe7+VTObW7X4DcBT7v40gJl9HjgTeDzNa5rZamA1wJw5c7JrrEgNWZ9yajb5LlJEeeRAjgF+lHg8AhxjZi8zsxuAk8zsQ+Nt7O4b3b3f3ftnz57d6rZKl2vklFMyV3LcceFWfb8vupZx164wh8iuXQoeUl55BBCrsczd/RfufpG7H+/uH2t7q0RqSHvKKZkr2bw5BIfRUXjPeyr3N2+efA5FpEhaegprHCPAcYnHxwI/yaEdIhNKe8opmSvp64NbbgnLzzgD7r678hq7doX1hobU85Dya/k4kCgH8mV374seTwO+B5wK/BjYAZzj7rsbeM3lwPLe3t4L9+7dm32jRRqUnAo3vg8wfTocOBDux1PfahpcyVspxoGY2TDwEHCimY2Y2aC7jwIXA/cCe4BbGwkeAO5+p7uvnjVrVvaNFmlCMlcS39++HWbMqNyP8ya6bFc6RauvwqrZSXf3u9CMhtJB4lzJpk1w+eWwahW4wwUXVO5fd10lh6Ky79IJ8siBiHSc6lzJ0UeHx3/7t5X7552ny3als5SyFpZyICIizStFDqRVlAMREclfKQOISKfQ3CBSZsqBiOREc4NI2akHIpKTrAs1irRbKQOImS03s4379u3LuykiTdPcIFJ2pQwgSqJLJ9DcIFJ2pQwgE1FiUspAc4NI2XVcEl2JSSkLzQ0iZVfKgYSx/v5+37lz55hlfX2hZPayZZVl27ZVKqGKiHS7rh5IWC+JrsSkiEh7lDKA1EuiKzEpItIepQwg9SgxKSLSHh2XRFdiUkSkPTougEAIFgoYIiKt1XGnsEREpD1KGUBUykREJH+lDCAqZSIikr9SBhAREcmfAoiIiDRFAUSkIFQEVMqmIy/jFSkbFQGVMlIPRKQANDuhlFEpA4gu45VOoyKgUkalDCC6jFc6jYqAShmVMoCIdBoVAZUyUhJdpABUBFTKSAFEpCBUBFTKRqewRESkKQogIiLSlI4JIBrFK91kvOO93udAnxHJWkfkQDSKV7rJeMf7gw/CV75S+3MA+oxIC7h7aW9Llixxd/fFi923bvUxtm4Ny0U6zXjH+4wZ438O9BmRJGCnZ/AdbOG1ysXMlgPLe3t7L9y7dy9Tp8L+/aEEROzgQZg5Ew4dyq2ZIi0x3vE+fTocOFD7cwD6jEiFmT3s7v2TfZ1S5kC8aiS6RvFKNxnveJ8xY/zPgT4j0gqlDCDVNIpXusl4x/uFF47/OdBnRFqhI5LoGsUr3aTe8X7yyfU/B/qMSJZKmQOJ9ff3+86dO/NuhohIqXR1DkRERPKnACIiIk1RABERkaYogIiISFMUQEREpCkKICIi0hQFEJGCSls9V1V2JS8dMZBQpNOkrTCtStSSJw0kFCmgvj7YsAGWLass27YtjCTftavx9USSshpIWMoAUl2NV6TTpK0wrUrU0oyuHoleXY1XpNOkrZ6rKruSp1IGEJFOl7Z6rqrsSp6URBcpoLQVplWJWvJUyhxITEl0EZHGdXUORERE8qcAIiIiTVEAERGRpiiAiIhIUxRARESkKQogIiLSFAUQERFpigKIiIg0RQFERESaogAiIiJNUQAREZGmKICIiEhTFEBERKQpCiAiItIUBRAREWlKYQKImb3IzG4ys8+a2aq82yNSJMPD0NcX5kDv6wuPW7ldo9tPdj9SUu7eshtwI/AcsKtq+enAk8BTwJpo2TuB5dH9L6R5/SVLlrhIp9uyxX3ePPetW90PHAg/580Ly1uxXaPbT3Y/0n7ATs/iOz6LFxn3xeG/A69LBhBgKvB94FXAdODbwCLgQ8Bro3W2pHl9BRDpBosXhy/lpK1bw/JWbNfo9pPdj7RfVgGk5VPamtlc4Mvu3hc9fiPwEXd/c/T4Q9GqI8Av3f3LZvZ5dz97nNdbDawGmDNnzpJnn322pe0XydvUqbB/P/T0VJYdPAgzZ8KhQ9lv1+j2k92PtF+Zp7Q9BvhR4vFItOx24H+Y2f8G7hxvY3ff6O797t4/e/bs1rZUpAAWLoTt28cu2749LG/Fdo1uP9n9SHnlEUCsxjJ399+4+/nu/hfufkvbWyVSUGvXwuAgbNsW/rPfti08Xru2Nds1uv1k9yPlNS2HfY4AxyUeHwv8JId2iJTCwED4OTQEe/aE/+zXrassz3q7Rref7H6kvPLIgUwDvgecCvwY2AGc4+67G3jN5cDy3t7eC/fu3Zt9o0VEOlgpciBmNgw8BJxoZiNmNujuo8DFwL3AHuDWRoIHgLvf6e6rZ82alX2jRUQklZaewnL3mp1Yd78LuKuV+xYRkdYqzEh0EREplzyS6JMW50CA/WbW0OmvnBwJ/DzvRqSgdmanDG0EtTNrZWnniVm8SMuT6K1kZjuzSAS1mtqZrTK0swxtBLUza93WTp3CEhGRpiiAiIhIU8oeQDbm3YCU1M5slaGdZWgjqJ1Z66p2ljoHIiIi+Sl7D0RERHKiACIiIk0pZAAxs9PN7Ekze8rM1tR43szsb6Lnv2Nmr0u7bZvbuSpq33fM7EEze03iuWfM7Ltm9piZ7cy5naeY2b6oLY+Z2YfTbtvmdn4w0cZdZnbIzF4aPdeW99PMbjSz58xs1zjPF+XYnKidRTk2J2pnUY7NidpZhGPzODPbZmZ7zGy3mV1SY51sj88sZqXK8sY4MxZWrfMW4G5Cafj/Bnwz7bZtbufJwO9F98+I2xk9fgY4siDv5ymEgpcNb9vOdlatvxzYmsP7+YJZNot2bKZsZ+7HZsp25n5spmlnQY7NVwCvi+4fQSha29LvziL2QN4APOXuT7v7AeDzwJlV65wJ3OzBN4DfNbNXpNy2be109wfd/ZfRw28QSte322Tek0K9n1UGgOEWtWVc7v5V4P/VWaUIx+aE7SzIsZnm/RxPod7PKnkdmz9190ei+/9OKFZ7TNVqmR6fRQwg481YmGadNNtmpdF9DRIif8yB+8zsYQvT9LZK2na+0cy+bWZ3m9niBrfNQup9mdl/AU4H/jGxuF3v50SKcGw2Kq9jM628j83UinJsWphG4yTgm1VPZXp8FrEWVs0ZC1Ouk2bbrKTel5ktI3xIlyYW/4G7/8TMfh/4P2b2RPRfTh7tfAR4pbv/2szeAtwBnJBy26w0sq/lwNfdPfkfYbvez4kU4dhMLedjM40iHJuNyP3YNLMXEwLY+939V9VP19ik6eOziD2QNDMWjrdOO2c7TLUvM3s18DngTHf/Rbzc3X8S/XwO+CKhC5lLO939V+7+6+j+XUCPmR2ZZtt2tjPhbKpOEbTx/ZxIEY7NVApwbE6oIMdmI3I9Ns2shxA8bnH322usku3x2erEThOJoGnA08A8KsmcxVXrvJWxiaBvpd22ze2cAzwFnFy1/EXAEYn7DwKn59jOo6gMKn0D8MPovS3U+xmtN4twLvpFebyf0T7mMn7SN/djM2U7cz82U7Yz92MzTTuLcGxG78vNwKfqrJPp8Vm4U1juPmpm8YyFU4Eb3X23mV0UPX8DYTKqtxA+AP8BnF9v2xzb+WHgZcBnzAxg1EMFzJcDX4yWTQO2uPs9ObZzJfAXZjYK/CdwtoejqmjvJ8CfAfe5+28Sm7ft/bQwy+YpwJFmNgJcBfQk2pj7sZmynbkfmynbmfuxmbKdkPOxCfwB8E7gu2b2WLTsCsI/Cy05PlXKREREmlLEHIiIiJSAAoiIiDRFAURERJqiACIiIk1RABERKYmJijrWWP/tZvZ4VFxxS9btUQCRzJiZm9knEo8vNbOPZPTam81sZRavNcF+zoqqmW4b5/m/NLP9ZjYrw32eZ2bXN7B+dYXax8zstOi5XzfZhhVmtqiZbaWtNhNKpUzIzE4APkQYCb8YeH/WjVEAkSw9D7wtGilcGGY2tYHVB4H3uvuycZ4fAHYQrvnP09fc/bWJ2/+d5OutAGoGEDMr3HixbuU1ijqa2fFmdk9Ua+trZrYgeupC4NMeFc30MBI+UwogkqVRwlzLf1n9RHUPIv5POfpv+gEzu9XMvmdm6y3MVfEtC3MoHJ94mdOiD8j3zOxPou2nmtnHzWyHhfkN3pN43W1Rt/27NdozEL3+LjO7Nlr2YUJNqBvM7OM1tjkeeDFwJSGQxMvPM7Pbow/xXjO7rt5+ouXnR7/HA4QBYPHy2Wb2j9Hvs8PMfvtcoyzMURG/L1cnlr8rWvZtM/s7MzsZ+FPg41Fv5ngzu9/Mronad4mZnWpmj0a/y41mNiN6rWfM7GozeyR6bkG0/I8SvaNHzeyIZn8PmdBGYMjdlwCXAp+Jls8H5pvZ183sG2aWqufSkFYO/detu27Ar4GXEOY/mBUdzB+JntsMrEyuG/08Bfg3wlwGM4AfA1dHz11CVJYh2v4ewj89JxBq98wEVgNXRuvMAHYSyjGcAvwGmFejnUcTSmLMJowO3gqsiJ67H+gf5/e7EvirqA3PAL8fLT+PUAZiVtSmZwl1hWruJ/pd4+XTga8D10evtQVYGt2fA+yp0Y5TgH3AY4nb8VXv65sIXywWtffLhDktFgNPEs1PAbx0nL/P/cBnovszCZVa50ePbyYU6iN6H4ai++8FPhfdv5Nw6gRC0J2W9/HZKTcSJVWi9/Y/q46FPdFzXybU3uqJPhMjwO9m2RZ1TSVT7v4rM7sZeB/hwE5jh7v/FMDMvg/cFy3/LpA8lXSrux8G9prZ08ACwhflqxO9m1mEAHOAUOfnBzX293rgfnf/WbTPWwhfrndM0M6zgT9z98NmdjtwFvDp6Ll/dvd90es9DrySUCqk1n6oWv4Fwn+LAKcBi8x+Wxz1JWZ2hIf5HZK+5u5/Uqetb4puj0aPX0x4X14D3ObuPwfwsVVjq30h+nki8AN3/170+CbgfwKfih7HRfseBt4W3f868Mnod77d3Ufq7EeaNwX4N3d/bY3nRoBvuPtB4Adm9iThGNiR5c5FsvYpQi7hRYllo0THm4Vvx+mJ555P3D+ceHyYsVMOVNfdictQD3klFzDP3eMA9Btqq1W6ui4LlWtPIJTjfoYQTAYSqyR/h0NRu+vtZ7waQlOANyZ+n2NqBI9UTQY+lnidXnffFC1PW78ofv8mer/i3z3+vXH39cC7gd8BvpE4Ly8Z8lCu/Qdmdhb8dsra10RP30H0D1iUl5xP6ClnRgFEMhf9V3srIYjEngGWRPfPJCpE16CzzGxKlIt4FeFUzL2EYns9AGY238xeVO9FCJPs/JGZHRkl2AeABybYZoBwOm5udDsaOMbMXtnEfr4JnGJmL4vafVZim/uAi+MHZvbaCdo1nnuBCyzMDYGZHWNhPop/Bt5uZi+Llr80Wv/fCdOg1vIEMNfMeqPH72SC98vMjnf377r7tYTTigogGbBQ1PEh4EQzGzGzQWAVMGhm3wZ2U5lJ8F7gF1GPeBvwQU+U7c+CTmFJq3yCxBch8FngS2b2LcKX2Hi9g3qeJHxxvRy4yN33m9nnCOeEH4l6Nj8j5BnG5e4/NbMPET5UBtzl7l+aYN9nE+YOT/pitPxfG92PhcubHwJ+Spg0Kb5S7H3Ap83sO4TP51eBi2q8/B9apeIqwEfd/bbEvu8zs4XAQ9HpsF8D7/BQ4Xgd8ICZHSKc4jqPMIXpZ83sfYQKuMnfY7+ZnQ/8g4UrsnYAN1Df+y1MVnUIeJyxMx5Kk9x9YJynXpAg95AI+UB0awlV4xURkaboFJaIiDRFAURERJqiACIiIk1RABERkaYogIiISFMUQEREpCkKICIi0pT/Dzz7zfO53rWiAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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a+CO+pLVpUxgn69Ch0D/k6qvDsvFxBRFpT9ok+gbgRmCXu99qZs8DNBm5SBdkvTSlMbOk01Il0c3sle5+y1TLuk1JdJHmNGaWNJNXEj3tJaxNKZeJSEnUj5O1a9fk3Ima+Eq7Wl7CMrMTgVcAc8ws2eLqGcCMThZMRNqTnJt9/Xo488zamFlxHkW91KUdU+VAjgCeHm13ZGL574DTOlUoEWlfszGzVq9WE1/JR9ocyHPd/aEulGdalAMREZm+bo/GO9PMNgMLkvu4+39ttwAiIlJNaQPIPwGXA1cCarMhIiKpW2EddPe/d/fvu/tt8a2jJRORQqQZ+VcE0tdArjOzdwFfAZ6MF7r7bzpSKhEphKZ9lulIWwM5B/gA8G3gtuim7LVIRTWrZSR7r081KZVqKpKqBuLuCztdkOnQaLwi2bWqZaQd+Vc1FYH0zXjPbrTc3bfmXqJpUDNekelrNb8IpJt7JO0cJVJO3W7G+7LE41nAq4HbgUIDiIhMX6taxuc/X+u9Xj8pVdpjSP9IewlrLPnczGYD/9iREolIRzWa+nbDhpDzOOus0GP97LPh0Ueb91jX9LkC6ZPo9f4deH6eBRGR7qifX+TCC+GSS+D97w8j9m7dGoLJ5z8fLkc1ymlknaNEekvaKW2vA+JkyQxgMXBNpwolIp1TP0bW0FAYbPHii8PyuOVVnBPZuLE2D8ny5SFYxGNrTVVTkd6WNon+qsTTg8BD7r63Y6VKSUl0kfYl5w2JHTgAM2fCggW1fMiGDaGmsn49XHTR5PyIAke1dHU+EHe/GfgxYUTeZwL7231hESmHZnOuH3HE5D4h27eHALJ9+9R9RKQ/pAogZvZm4PvA6YR50b9nZhrOXaQHNMtn7N8/uaXVnj1w3nmTW1qp5VV/S5tEHwde5u7nuPvZwMuBv+1csfKlHrMizY2OhlrE2FiY4nZsLDwfHp5cM1m8GC6/fHJLq2Ytr/Q/1yfcfcobcGfd84H6ZUXcli5d6lOZmHBfuNB9xw73/fvD/cKFYbmINFf/vzM+7j44GO5b/S/pf678gN2ew3dw2gDyceBGYHV0+xpwSR4FaOeWJoCMjIQTOGnHjrBcRFqbmAj/KwMD4X7dusnPGwUF/c+VX14BpGUrLDNbBDzH3W8xszcBJwEG/Bb4grv/pDP1onTStMJq1sJk1iw4pJlNRHKn/7ny61YrrE8Avwdw92vd/X3u/l7ghmhd6TVrYaIesyKdof+5/jFVAFng7j+qX+juuwnT25aeesyKdF4yab5vH6xa1fh/Tsn13jJVT/RZLdb9WZ4F6ZT6XrfqMSuSr0ZDu69adXgvddAQ8L1mqhzINmCHu19Rt3wN8Bp3X9Xh8rWknugixUs7tLuGgC+PvHIgUwWQ5xCmsd1PmIUQYBlwBPBGd3+s3QK0QwFEpHhpk+ZKrpdHV5Lo7v6v7v4KYAPwYHTb4O4nFh08RKQc0ibNlVzvPWnHwtrp7pui245OF0pEqiNtQxU1aOk9aWck7Dgzex5hyJTZ7q5xtkQqIm1Dlam227Zt8tDx4+NKrpddquHcMx/c7Crg9cAv3X1JYvmpwCcJc4tc6e4fS6z7ctoAohyISG9o1JJLQ8V3TleHc2/D1cCpyQVmNgP4NPDXwDAwambDHS6HiJTYxo2Th47XUPHV0NEA4u7fBH5Tt/jlwAPu/lN33w98EXhD2mOa2Voz221mux9//PEcSysiRdmzZ/LQ8aCh4qug0zWQRo4FHk483wsca2bPNrPLgb80swua7ezum919mbsvmzNnTqfLKiJtStP7fDottNSbvTyKSKJbg2Xu7r8Gzut2YUSkc5rlNmBybiNuodUoB5LleNIleQzp2+pGGDPrrsTzE4EbE88vAC7Icuw0w7mLSHGmM7R7/dDxGiq+c+jGcO55MLMFwPUetcIys0HgPuDVwCPArcAZ7n73NI65AlixaNGic++///78Cy0iuci797l6s+ejEq2worG0vgO8wMz2mtkadz8IrCNMULUHuGY6wQPA3a9z97WzZ8/Ov9Aikpu8e5+rN3u5dLoV1qi7H+3uQ+4+z923RMtvcPcT3P14d1dDPZEelXfvc/VmL5fS9EQXkd6T93QKmp6hXDqeA+kE5UBERLKrRA6kU5QDEREpXiUDiIj0hrSdAtV5sJyUAxGRQqTtFKjOg+VVyRxITKPxilSXpsItTlemtC0rJdFFqk9T4RZHSXQl0UUqTVPhVl8lA4iIVF+rToHJpPm+fbBq1dTbLVkSLmsp2d49SqKLSCGadQqEw5Pmq1bB2WfDo482327DBrjkEli/Hn7wAyXbu6GSOZCYkugivSdrcn3JEnj72+Gqq2rbKdnemJLoSqKL9KSsyfUZM+D3v4cjj6xtp2R7Y0qiK4ku0pOyJtcXL4bLL5+8nZLtnVXJACIivSvtiLv1261cGfIfK1dqpN5uUQARkVIZHQ1J8rGxcPlpbKzxiLv1223fDuedF+5nzQpJ9wMH4Kyz8mmRpeFUDqdWWCJSOqOj6VpONdsu7+FPNJxKY5VMosfUCktEGsl7+JNeG05FrbDUCktEmtBc7K2pFZZaYYlIE5qLvTsqGUBERFrRXOzdoSS6iPQczcXeHT1ZA1FzOxEZHQ0J7kOHwn3aL/tm3x9pj9dP3z89VwNRczsRyard74+++/5x98reli5d6vVGRtx37Ji8bMeOsFxEpJV2vz+q8v0D7PYcvoN7rhlvrzW3E5Huaff7oyrfP2rG26QZr5rbiUhW7X5/9Nv3TyUDSCtqbiciWbX7/dFv3z89l0RXczsRyard749++/6pZA4kprGwRESmr69zICIiUjwFEBERyUQBRET6QrKH+Pz54daN3uK93DO955LoIiL1kj3E9+4NU9+6w9VXw7x5nest3us905VEF5Gel5wQKn4MtQmhOjU5VFknotKEUppQSkRSSvYQjx9DrYd4p3qLl7Vnel+3wmrVE11EpF6yh3j8ONlDvFO9xXu9Z3olA4iIyHQke4ivXw9nnglnnBEed7K3eK/3TFcSXUR6Xn0P8WOOCc9Xr+5sb/Fe75leyRxITEl0EZHp6+sciIiIFE8BREREMlEAERGRTBRAREQkEwUQERHJRAFEREQyUQAREWmi1Ui67Y7um/bYrY5X9Ei/6kgoItJAq5F0ob3RfdMeu9UIvqUY6dfdK3tbunSpi4h0wsiI+44dk5ft2BGWJ9fFj+N1ye3aPXb9urTHmAqw23P4Dq5kT3SNxisindZqJF1ob3TftMeuX5c8Xjsj/fZ1T3TXaLwi0mGtRtJtd3TftMeuX5f2GF2TRzWmqJsuYYlIp0xMuC9cGC4L7d8f7hcuDMuT67ZudT/6aPe5c8Pj5HbtHrt+XdpjTIWcLmEVHgTauSmAiEgnTUyEnMLAQLhPfjkn182bF26Ntmv32K2Ol3a7enkFkErmQGIajVdEZPr6OgciIiLFUwAREZFMFEBERCQTBRAREclEAURERDJRABERkUwUQEREJBMFEBERyUQBREREMlEAERGRTBRAREQkEwUQERHJRAFEREQyUQAREZFMFEBERCST0gQQM3uamX3OzK4wszOLLo+I9Idt22DJkjDH+JIl4XkRr5W2HFnKW78PHPWsPN5PR2cMBK4CfgncVbf8VOBe4AHgQ9GytwIrosdfSnN8zUgoIu1oZ1rYPF+rk9PYNtoHXvSkl31KW+CvgJcmAwgwA/gJ8DzgCOCHwDBwAfCSaJuJNMdXABGRdoyMhC/UpB07wvJuvlbacmQpb6N9YPa9XoUpbc1sAXC9uy+Jnp8IfMTdXxs9vyDadC/wW3e/3sy+6O5vaXK8tcBagOOOO27pQw891NHyi0jvmjEDnngChoZqyw4cgFmz4NCh7r0WpCtHlvI22sds4Hb3p5a2+56KyIEcCzyceL43WnYt8N/N7O+B65rt7O6b3X2Zuy+bM2dOZ0sqIj1t8WLYtWvysl27wvJuvlbacmQpb6N94BlPn07Zm8qjGtPqBixg8iWs04ErE8/fCmzKcmxdwhKRdigH0t5tMJcoND17gfmJ5/OARwsoh4j0udHRcD82Bnv2hF/rGzfWlnf7taYqR5byNtoHHn0kj/dURA5kELgPeDXwCHArcIa73z2NY64AVixatOjc+++/P/9Ci4j0MDO7zd2XtXucjuZAzGwb8B3gBWa218zWuPtBYB1wI7AHuGY6wQPA3a9z97WzZ8/Ov9AiIpJKRy9huXvDipW73wDc0MnXFhGRzipNT3QREamWIpLobYtzIMATZjaty18FOQr4VdGFSEHlzE8VyggqZ96qUs4X5HGQjifRO8nMdueRCOo0lTNfVShnFcoIKmfe+q2cuoQlIiKZKICIiEgmVQ8gm4suQEoqZ76qUM4qlBFUzrz1VTkrnQMREZHiVL0GIiIiBVEAERGRTEoZQMzsVDO718weMLMPNVhvZvZ30fofmdlL0+7b5XKeGZXvR2b2bTN7cWLdg2Z2p5ndYWa7Cy7nyWa2LyrLHWb24bT7drmcH0iU8S4zO2Rmz4rWdeXzNLOrzOyXZnZXk/VlOTenKmdZzs2pylmWc3Oqcpbh3JxvZjvNbI+Z3W1m5zfYJt/zM48hffO80WTGwrptXgd8DTDgPwPfS7tvl8v5CuCZ0eO/jssZPX8QOKokn+fJhAEvp71vN8tZt/0KYEcBn+dhs2yW7dxMWc7Cz82U5Sz83ExTzpKcm0cDL40eH0kYtLaj351lrIG8HHjA3X/q7vuBLwJvqNvmDcBWD74L/LmZHZ1y366V092/7e6/jZ5+lzB0fbe185mU6vOsMwps61BZmnL3bwK/abFJGc7NKctZknMzzefZTKk+zzpFnZu/cPfbo8e/JwxWe2zdZrmen2UMIM1mLEyzTZp98zLd11pDiPwxB24ys9ssTNPbKWnLeaKZ/dDMvmZmI9PcNw+pX8vM/hNwKvDPicXd+jynUoZzc7qKOjfTKvrcTK0s56aFaTT+Evhe3apcz88yjoVlDZbVtzVutk2affOS+rXMbDnhn/SkxOJXuvujZvYXwP81sx9Hv3KKKOftwHPd/Q9m9jpgO/D8lPvmZTqvtQK4xd2Tvwi79XlOpQznZmoFn5tplOHcnI7Cz00zezohgL3H3X9Xv7rBLpnPzzLWQNLMWNhsm27OdpjqtczsRcCVwBvc/dfxcnd/NLr/JfAVQhWykHK6++/c/Q/R4xuAITM7Ks2+3Sxnwluou0TQxc9zKmU4N1Mpwbk5pZKcm9NR6LlpZkOE4PEFd7+2wSb5np+dTuxkSAQNAj8FFlJL5ozUbfPfmJwI+n7afbtczuOAB4BX1C1/GnBk4vG3gVMLLOdcap1KXw78PPpsS/V5RtvNJlyLfloRn2f0GgtonvQt/NxMWc7Cz82U5Sz83ExTzjKcm9HnshX4RIttcj0/S3cJy90Pmlk8Y+EM4Cp3v9vMzovWX06YjOp1hH+Afwfe1mrfAsv5YeDZwGfMDOCghxEwnwN8JVo2CEy4+9cLLOdpwDvN7CDwH8BbPJxVZfs8Ad4I3OTuf0zs3rXP08IsmycDR5nZXuAiYChRxsLPzZTlLPzcTFnOws/NlOWEgs9N4JXAW4E7zeyOaNn/IvxY6Mj5qaFMREQkkzLmQEREpAIUQEREJBMFEBERyUQBREREMlEAERGpiKkGdWyw/ZvN7J5ocMWJvMujACK5MTM3s8sSz99vZh/J6dhXm9lpeRxritc5PRrNdGeT9e81syfMbHaOr7nazD41je3rR6i9w8xOidb9IWMZVprZcJZ9pauuJgyVMiUzez5wAaEn/AjwnrwLowAieXoSeFPUU7g0zGzGNDZfA7zL3Zc3WT8K3Epo81+kb7n7SxK3/9fm8VYCDQOImZWuv1i/8gaDOprZ8Wb29WisrW+Z2QujVecCn/Zo0EwPPeFzpQAieTpImGv5vfUr6msQ8S/l6Nf0zWZ2jZndZ2YfszBXxfctzKFwfOIwp0T/IPeZ2euj/WeY2cfN7FYL8xu8I3HcnVG1/c4G5RmNjn+XmV0SLfswYUyoy83s4w32OR54OnAhIZDEy1eb2bXRP/H9ZnZpq9eJlr8teh83EzqAxcvnmNk/R+/nVjP707rpsjBHRfy5bEgsPzta9kMz+0czewXwN8DHo9rM8Wb2DTP7aFS+883s1Wb2g+i9XGVmM6NjPWhmG8zs9mjdC6Plr0rUjn5gZkdmfR8ypc3AmLsvBd4PfCZafgJwgpndYmbfNbNUNZdp6WTXf9366wb8AXgGYf6D2dHJ/JFo3dXAaclto/uTgX8jzGUwE3gE2BCtO59oWIZo/68TfvQ8nzB2zyxgLXBhtM1MYDdhOIaTgT8CCxuU8xjCkBhzCL2DdwAro3XfAJY1eX8XAn8bleFB4C+i5asJw0DMjsr0EGFcoYavE73XePkRwC3Ap6JjTQAnRY+PA/Y0KMfJwD7gjsTt+LrP9TWELxaLyns9YU6LEeBeovkpgGc1+ft8A/hM9HgWYaTWE6LnWwkD9RF9DmPR43cBV0aPryNcOoEQdAeLPj975UZiSJXos/2PunNhT7TuesLYW0PR/8Re4M/zLIuqppIrd/+dmW0F3k04sdO41d1/AWBmPwFuipbfCSQvJV3j7k8B95vZT4EXEr4oX5So3cwmBJj9hHF+ftbg9V4GfMPdH49e8wuEL9ftU5TzLcAb3f0pM7sWOB34dLTuX9x9X3S8e4DnEoYKafQ61C3/EuHXIsApwLDZnwZHfYaZHelhfoekb7n761uU9TXR7QfR86cTPpcXA192918B+ORRY+t9Kbp/AfAzd78vev454H8Cn4iex4P23Qa8KXp8C/B/ovd8rbvvbfE6kt0A8G/u/pIG6/YC33X3A8DPzOxewjlwa54vLpK3TxByCU9LLDtIdL5Z+HY8IrHuycTjpxLPn2LylAP14+7Ew1CPeS0XsNDd4wD0RxprNHR1SxZGrn0+YTjuBwnBZDSxSfI9HIrK3ep1mo0hNACcmHg/xzYIHqmKDPzvxHEWufuWaHna8Yviz2+qzyt+7/H7xt0/BvwP4M+A7yauy0uOPAzX/jMzOx3+NGXti6PV24l+gEV5yRMINeXcKIBI7qJftdcQgkjsQWBp9PgNRAPRTdPpZjYQ5SKeR7gUcyNhsL0hADM7wcye1uoghEl2XmVmR0UJ9lHg5in2GSVcjlsQ3Y4BjjWz52Z4ne8BJ5vZs6Nyn57Y5yZgXfzEzF4yRbmauRF4u4W5ITCzYy3MR/EvwJvN7NnR8mdF2/+eMA1qIz8GFpjZouj5W5ni8zKz4939Tne/hHBZUQEkBxYGdfwO8AIz22tma4AzgTVm9kPgbmozCd4I/DqqEe8EPuCJYfvzoEtY0imXkfgiBK4Avmpm3yd8iTWrHbRyL+GL6znAee7+hJldSbgmfHtUs3mckGdoyt1/YWYXEP6pDLjB3b86xWu/hTB3eNJXouX/Ot3XsdC8+TvALwiTJsUtxd4NfNrMfkT4//wmcF6Dw/8Xq424CnCxu3858do3mdli4DvR5bA/AGd5GOF4I3CzmR0iXOJaTZjC9AozezdhBNzk+3jCzN4G/JOFFlm3ApfT2nssTFZ1CLiHyTMeSkbuPtpk1WEJcg+JkPdFt47QaLwiIpKJLmGJiEgmCiAiIpKJAoiIiGSiACIiIpkogIiISCYKICIikokCiIiIZPL/Aa0IL+pRUP59AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Finally, this last block of code runs the same PMT simulation above four\n",
    "# times, each time using a different number of incoming photons [1, 2, 4, 8].\n",
    "# This chunk of code doesn't rely on anything that came before it.  These 44 lines\n",
    "# of code will simulate the expected distributions of anode electrons for 4\n",
    "# difference sets of incoming photons.  There real virtue of the Monte Carlo\n",
    "# simulation is that we can now vary properties of the PMT with trivial\n",
    "# modifications to the code below and systematically study the effects.\n",
    "# For example, what if there were mode dynodes?  All we have to do is modify\n",
    "# the line dynode:=[0,150,300,450,600,750,800].  Alternatively, we could\n",
    "# keep the number of dynodes fixed and modify the potential applied to the\n",
    "# dynodes.  Of course, after making this relatively simple simulation work,\n",
    "# we could make modifications to make it more sophisticated.  What if 8\n",
    "# photons are directed towards the photocathode, but they arrive at slightly\n",
    "# different times.  What does the current pulse at the anode look like?\n",
    "# That's not a problem that we'll tackle here, but it does demonstrate the\n",
    "# versitility of the Monte Carlo method.\n",
    "QE = 0.23 # Set the quantum efficeincy of the photocathode\n",
    "maxi = int(1e4) # Set the number of Monte Carlo iterations\n",
    "dynode = [0, 150, 300, 450, 600, 750, 850] # Set the number of dynodes and\n",
    "# their voltages\n",
    "numPhotons = [1, 2, 4, 8] # Set the number of photons incident on the\n",
    "# photocathode.  We will repeat the simulation for 4 different numners of\n",
    "# incoming photons\n",
    "print(datetime.now()) # Print the time at the simulation was started\n",
    "eventsList = []\n",
    "distList = []\n",
    "for m in range (len(numPhotons)):\n",
    "    dist = []\n",
    "    plt.figure() # Generate a new figure\n",
    "    for i in range(maxi): # This loop runs the Monte Carlo simulation maxi times\n",
    "    # (10,000 in this case)\n",
    "        pe = 0 # Set the initial number of photoelectrons to zero.\n",
    "        for k in range (numPhotons[m]): # This loop individually steps through each of the\n",
    "        # photons incident on the photocathode\n",
    "            if np.random.uniform() < QE: # Generate a random number between [0, 1]\n",
    "            # and check to see if it's greater than the quantum efficiency\n",
    "                pe += 1 # Increment pe by one every time a photoelectron is\n",
    "                # produced\n",
    "        if pe > 0: # If there are any photoelectrons, then do something.  If there\n",
    "        # are not photoelectrons then do nothing\n",
    "            electrons = pe # Set the initial number of electrons equal to the\n",
    "            # number of photoelectrons\n",
    "            for j in range(len(dynode)-1): # This loop will examine the secondary\n",
    "            # electrons produced at each of the dynodes\n",
    "                mu = electrons*(dynode[j+1]-dynode[j])/20 # Mean number of\n",
    "                # electrons generated at a dynode determined from the number of\n",
    "                # incoming electons and the energy of the incoming electrons.\n",
    "                # One electron accelerated through 20 V will on anverage produce\n",
    "                # one electron\n",
    "                electrons = electrons + np.random.poisson(mu)\n",
    "            dist = dist + [electrons] # Add the total number of electrons detected at\n",
    "            # the anode for this trial to a 'dist' list.\n",
    "    # This code can take some time to execute, so provide some intermediate\n",
    "    # outputs to track progress\n",
    "    print('Iteration', m)\n",
    "    print('The fraction of trials that produced photoelectrons is', len(dist)/maxi)\n",
    "    # Determines what fraction of maxi trials actually\n",
    "    # produced electrons at the PMT anode.\n",
    "    print('The mean of the distribution was', statistics.mean(dist))\n",
    "    # Calculate the mean of the distribution\n",
    "    print(datetime.now()) # Print the time that this iteration of  the simulation completed\n",
    "    eventsList = eventsList + [[numPhotons[m], len(dist)/maxi]] # Keep track of\n",
    "    # how many sets of incident photons actually resulted in a signal at\n",
    "    # the anode.\n",
    "    distList = distList + [dist] # Store the distributions recorded into a set\n",
    "    xbins = xbins = np.linspace(0, 2e6, 101) # Set bin ranges for the histogram.\n",
    "    # 100 equally-sized bins fron 0 to 2e6.\n",
    "    plt.hist(dist, xbins, color = 'c', edgecolor = 'k') \n",
    "    #Plot the histgram of the simulated number of anode electrons\n",
    "    plt.xlim((0, 2e6))\n",
    "    plt.ylim((0, 500))\n",
    "    plt.xlabel('Number of Anode Electons')\n",
    "    plt.ylabel('Counts')\n",
    "    counts, edges = np.histogram(dist, xbins) # Here we use 'np.histogram' to have \n",
    "    # Python tell us how many counts there are in each of our 100 bins.\n",
    "    # Calculate the centre positions of the bins from the edge locations.\n",
    "    spacing = (edges[1] - edges[0])/2\n",
    "    centres = edges[1:] - spacing\n",
    "    plt.figure() # Start a new figure.\n",
    "    plt.semilogy(centres, counts, 'bo', fillstyle = 'none') # Make a semi-log plot \n",
    "    # of the counts versus the number of detected anode electrons    \n",
    "    plt.xlim((0, 2e6))\n",
    "    plt.ylim((0.8, 500))\n",
    "    plt.xlabel('Number of Anode Electrons')\n",
    "    plt.ylabel('Counts');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "greatest-kelly",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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zroiIqEnTRGDbwHeHWfd2wF0N2yvLsr72l3SjpB9I+othXisiIoapSh/BzyTtM4y6+1vgvu9ax9cDO5bPKXyFAZKOpDmSeiT1rF69ehihRETEQKokghkUyeA3km6SdLOkmyqctxJobFbaHljVeIDtB2w/VL6/HJggadu+Fdk+03aX7a7Ozs4Kl46IiKqqdBYfMsy6lwBTJU0B7gaOBo5pPEDSC4A/2rakfSkS05+Geb2IiBiGKs8R/E7SdGCq7XMldQLPqnDeWkknAFcAHcA5tm+RdHy5/wzgLcB7Ja0FHgWOLvslIiKiRTTY566kjwNdwK62d5H0IuBi2we0IsC+urq63NPT045LR0SMWZKW2u7qb1+VPoIjgcOBhwFsrwK2HLnwIiKinaokgjVlc40BJG1Rb0gREdFKVRLBRZK+Bmwt6T3AfwFn1RtWRES0SpXO4i9KOgh4ANgF+JjtH9UeWUREtETVuYZuBjajaB66ub5wIiKi1QZtGpL0N8B1wJsohnv+TNK76w4sIiJao+rCNC+z/ScASc8F/gc4p87AIiKiNap0Fq8EHmzYfpD1J5OLiIgxbMA7AkkfLt/eDfxc0vco+giOoGgqioiIjUCzpqHeh8Z+U/70+l594URERKsNmAhsf7KVgURERHsM2lksqQuYB+zYeLztl9YYV0REtEiVUUMXUIwcuhl4st5wIiKi1aokgtW2F9YeSUREtEWVRPBxSWcDVwGP9xbavrS2qCIiomWqJILjgN2ACTzVNGQgiSAiYiNQJRHsafsltUcSERFtUeXJ4p9J2r32SCIioi2q3BFMB94p6Q6KPgIBzvDRiIiNQ5U7gpnAVOBg4DDg0PI16tLdDXvsAR0dxWt3d7sjioiNWJU7guar28fI6u6GefNgwQKYPh0WL4bZs4t9s2a1N7aI2ChVuSP4PnBZ+XoVsAL4QZXKJc2UdLuk5ZJOanLcPpLWSXpLlXo3avPnF0lgxgyYMKF4XbCgKI+IqEGVpSrXGzEkaW/gbwc7T1IHcBpwEMVU1kskLbR9az/HfQ64Yghxb7yWLSvuBBpNn16UR0TUoModwXpsXw/sU+HQfYHltlfYXgNcSDGFdV9zgUuAe4Yay0Zp2rSiOajR4sVFeUREDapMOvfhhs1nAHsDqyvUvR3rL2CzEtivT93bAUcCB1ItuWz85s0r+gT69hGkaSgialKls3jLhvdrKfoKLqlwnvop69vx/GXgo7bXSf0dXlYkzQHmAEyaNKnCpcew3g7huXOL5qBp04okkI7iiKiJ7HoGBUnaH/iE7deV2ycD2P5swzF38FTC2BZ4BJhj+7sD1dvV1eWenp5aYo6I2FhJWmq7q799zZaqPJeBh47a9uxBrrsEmCppCsVyl0cDx/SpZErD9c4DLmuWBCIiYuQ1axq6rJ+yScAHgY7BKra9VtIJFKOBOoBzbN8i6fhy/xlDDzciIkZapaYhSTsB/wi8Cvh/wIJyJFDLpWkoImLomjUNNR0+KmmapG8C/wksBna3fXq7kkBERIy8Zn0EFwNdwBeBDwHrgK16R/fY/nMrAoyIiHo16yPYh6Kz+CPA35dlvSN8DOxUY1wREdEiAyYC25NbGEdERLTJkKeYiIiIjUsSQUTEOJdEEBExzlVKBJKmSzqufN9ZPi0cEREbgUETgaSPAx8FTi6LJgDfrDOoiIhonSp3BEcChwMPA9hexfozkkZExBhWJRGscTEPhQEkbVFvSBER0UpVEsFFkr4GbC3pPcB/AWfVG1ZERLRKlTWLvyjpIOABYFfgY7Z/VHtkERHRElVWKKP84M+Hf0TERqjKmsUP8vQFau4HeoC/t72ijsAiIqI1qtwRfAlYBfwHxaRzRwMvAG4HzgFeU1dwERFRvyqdxTNtf832g7YfsH0m8Hrb3wKeU3N8ERFRsyqJ4ElJfy3pGeXPXzfsG3x5s4iIGNWqJIK3AW8H7gH+WL4/VtJmwAk1xhYRES1QZfjoCuCwAXYvHtlwIiKi1aqMGpoIzAb+ApjYW2773TXGFRERLVKlaegbFKOEXgdcA2wPPFilckkzJd0uabmkk/rZf4SkmyTdIKlH0vShBB8RERuuSiJ4se1/Bh62fT7wBuAlg50kqQM4DTgE2B2YJWn3PoddBexpey/g3cDZQ4g9IiJGQJVE8ET5+r+S9gCeDUyucN6+wHLbK2yvAS4Ejmg8wPZD5YR2AFuQUUgRES1XJRGcKek5wD8BC4Fbgc9VOG874K6G7ZVl2XokHSnpNuD7FHcFTyNpTtl01LN69eoKl46IiKqaJgJJzwAesH2f7Wtt72T7eba/VqFu9VP2tG/8tr9jezfgjcCn+6vI9pm2u2x3dXZ2Vrh0RERU1TQR2H6S4T8rsBLYoWF7e4qpKga61rXAzpK2Heb1IiJiGKo0Df1I0kck7SBpm96fCuctAaZKmiJpU4o5ihY2HiDpxZJUvt8b2BT40xB/h4iI2ABVJp3rbbd/X0OZgZ2anWR7raQTgCuADuAc27dIOr7cfwbwZuAdkp4AHgWOaug8joiIFtBY+9zt6upyT09Pu8OIiBhTJC213dXfvkGbhiRtLumfJJ1Zbk+VdOhIBxkREe1RpY/gXGAN8IpyeyXwL7VFFBERLVUlEexs+/OUD5bZfpT+h4ZGRMQYVCURrCmnnDaApJ2Bx2uNKiIiWqbKqKFPAD8EdpB0AXAA8K4aY4qIiBaqsh7BlZKWAn9J0ST0Adv31h5ZRES0RJX1CBYC3cBC2w/XH1JERLRSlT6CfwVeCdwq6WJJbykXq4mIiI1Alaaha4BryvUFDgTeA5wDbFVzbBER0QJVOospRw0dBhwF7A2cX2dQERHROlX6CL4F7Ecxcug04OpyVtKIiNgIVLkjOBc4xvY6AEkHSDrG9vsGOS8iIsaAKn0EP5S0l6RZFE1DdwCX1h5ZRES0xICJQNIuFGsIzKJYI+BbFLOVzmhRbBER0QLN7ghuA34MHGZ7OYCkD7UkqoiIaJlmzxG8GfgDsEjSWZJey1idbK67G/bYAzo6itfu7nZHFBExagyYCMpF5Y8CdgOuBj4EPF/S6ZIOblF8G667G+bNg698BR57rHidNy/JICKiNOiTxbYftn2B7UMpFqC/ATip7sBGzPz5sGABzJgBEyYUrwsWFOURETEOlqrs6CjuBCZMeKrsiSdg4kRYt27kA4yIGIU2aKnKMW/aNFi8eP2yxYuL8oiIGAeJYN48mD0bFi0q7gQWLSq2581rd2QREaNCpbmGhkvSTOBUoAM42/Ypffa/DfhoufkQ8F7bN45oELNmFa9z58KyZcWdwPz5T5VHRIxztSWCcrbS04CDKBa8XyJpoe1bGw67A3i17fskHQKcSTGv0ciaNSsf/BERA6izaWhfYLntFbbXABcCRzQeYPt/bN9Xbv6MYlRSRES0UJ2JYDvgrobtlWXZQGYDP+hvh6Q5knok9axevXoEQ4yIiDoTQX9PIfc7VlXSDIpE8NH+9ts+03aX7a7Ozs4RDDEiIursLF4J7NCwvT2wqu9Bkl4KnA0cYvtPNcYTERH9qPOOYAkwVdIUSZtSzGS6sPEASZMoprR+u+1f1RhLREQMoNYniyW9HvgyxfDRc2zPl3Q8gO0zJJ1NMbnd78pT1g705FtDnasbjh+qbYF7h3luO4yleMdSrDC24h1LscLYincsxQobFu+OtvttWx9zU0xsCEk9gyWa0WQsxTuWYoWxFe9YihXGVrxjKVaoL96N/8niiIhoKokgImKcG2+J4Mx2BzBEYynesRQrjK14x1KsMLbiHUuxQk3xjqs+goiIeLrxdkcQERF9JBFERIxz4yIRSDpH0j2SftnuWAYjaQdJiyQtk3SLpA+0O6ZmJE2UdJ2kG8t4P9numAYjqUPSLyRd1u5YBiPpt5JulnSDpCEszdd6kraW9G1Jt5X/fvdvd0wDkbRr+Tft/XlA0gfbHddAJH2o/P/1S0ndkiaOaP3joY9A0qso1jv4uu092h1PM5JeCLzQ9vWStgSWAm/sM333qCFJwBa2H5I0AVgMfMD2z9oc2oAkfRjoArYq1+IetST9FuiyPeofepJ0PvBj22eXswlsbvt/2xzWoMop8+8G9rM93IdVayNpO4r/V7vbflTSRcDlts8bqWuMizsC29cCf253HFXY/r3t68v3DwLLaD5ra1u58FC5OaH8GbXfLiRtD7yBYn6rGCGStgJeBSwAsL1mLCSB0muB34zGJNBgE2AzSZsAm9PPvG0bYlwkgrFK0mTgZcDP2xxKU2VTyw3APcCPbI/meL8M/APwZJvjqMrAlZKWSprT7mCa2AlYDZxbNrudLWmLdgdV0dFAd7uDGIjtu4EvAncCvwfut33lSF4jiWCUkvQs4BLgg7YfaHc8zdheZ3svihlm95U0KpvfJB0K3GN7abtjGYIDbO8NHAK8r2zmHI02AfYGTrf9MuBh4KT2hjS4sgnrcODidscyEEnPoVjUawrwImALSceO5DWSCEahsq39EuAC25e2O56qyqaAq4GZ7Y1kQAcAh5ft7hcCB0r6ZntDas72qvL1HuA7FCv/jUYrgZUNd4PfpkgMo90hwPW2/9juQJr4K+AO26ttP0ExY/MrRvICSQSjTNn5ugBYZvtL7Y5nMJI6JW1dvt+M4h/tbW0NagC2T7a9ve3JFM0B/217RL9ZjSRJW5QDBiibWQ4GRuXIN9t/AO6StGtZ9FpgVA5w6GMWo7hZqHQn8JeSNi8/H15L0Xc4YsZFIpDUDfwU2FXSSkmz2x1TEwcAb6f4tto7tO317Q6qiRcCiyTdRLEGxY9sj/phmWPE84HFkm4ErgO+b/uHbY6pmbnABeW/hb2Az7Q3nOYkbQ4cRPENe9Qq77K+DVwP3EzxuT2iU02Mi+GjERExsHFxRxAREQNLIoiIGOeSCCIixrkkgoiIcS6JICJinEsiiGGTZEn/2rD9EUmfGKG6z5P0lpGoa5DrvLWcKXNRn/LJw52tVtLhkvp9qlbSQ/2VV6z3XZJeNMC+8yTdUQ43vr535k9JV0uqvNi5pL1G+XDlqEESQWyIx4E3Sdq23YE0KmeTrGo28He2Z4zU9W0vtH3KSNXX4F0UUwwM5MRyqo+TgK8N8xp7AUkE40wSQWyItRQPtnyo746+3+h7vwlLeo2kayRdJOlXkk6R9LZyTYObJe3cUM1fSfpxedyh5fkdkr4gaYmkmyT9bUO9iyT9B8VDN33jmVXW/0tJnyvLPgZMB86Q9IWBfsnym/ilkn4o6deSPt+wb2b5DfxGSVc1HP/v5fspkn5axvvpPvWe2PB7fLIsm1zeoZylYv75KyVtVv4tuyge2LqhfIp7INcCL27Yfmv59/2VpFeW15ko6dzyb/ILSTPKeXc+BRxVXuMoSdtI+m4Z488kvbQ8/xMq1vm4WtIKSe8vy7eQ9P3y7/FLSUc1iTNGiU3aHUCMeacBNzV+OFawJzCNYmrwFcDZtvdVsQjPXOCD5XGTgVcDO1M8vfxi4B0Usy/uI+mZwE8k9c7EuC+wh+07Gi9WNqd8Dng5cB/FbJ5vtP0pSQcCH7E92KIve1HMBPs4cLukrwCPAWcBr7J9h6Rt+jnvVIqJ2L4u6X0NMR0MTC1jFrBQxYRyd5bls2y/R8Xc82+2/U1JJ1SM9TDWT4ablH/f1wMfp5gG5H0Atl8iaTfgSmAX4GMU6x+cUMb5FeAXtt9Y/q2+Xv4tAHYDZgBbln+T0ynmmVpl+w3l+c8eJNYYBXJHEBuknBn168D7h3DaknLdhceB31B8CEHx4TW54biLbD9p+9cUCWM3ivl23qFi2uufA8+l+OAEuK5vEijtA1xdTtq1FriAYu78objK9v22H6OYQ2dH4C+Ba3uvabu/NS8O4Km5bL7RUH5w+fMLiqkDdmv4Pe6wfUP5finr/02a+UL5d5lD0eTVq3cKhca6pvfGY/s24HcUiaCvxuP+G3huw4f7920/Xi6acw/FlBg3U9zJfU7SK23fXzH2aKPcEcRI+DLFh9m5DWVrKb9oSBKwacO+xxveP9mw/STr/5vsO/+JKb49z7V9ReMOSa+hmPq4Pxok/ioaY15HEaf6ibE//R0j4LO212vLV7EGRd9rNWsGanSi7W/3U95bX2/cvdevor/jen+fp/1NbP9K0ssp+hk+K+lK25+qeK1ok9wRxAYrvwlfxPrfQn9L0RQDxVzqE4ZR9VslPaPsN9gJuB24Aniviqm6kbSLBl8A5efAqyVtW3YkzwKuGUY8ff20rHdKGUt/TUM/oZjpFOBtDeVXAO9Wse4EkraT9LxBrvcgRTPMSLi2Nx5JuwCTKP6+fa/ReNxrgHubrY9RNsM9YvubFIupjIWpqMe93BHESPlX4ISG7bOA70m6DriKgb+tN3M7xQf284HjbT8m6WyK5o3ryzuN1cAbm1Vi+/eSTgYWUXzDvdz294YRT996V6tYNexSSc+gaB45qM9hHwD+o+z/uKTh3CslTQN+WvwaPAQcS/HNeiDnUXRsPwrsb/vRDQj/q2VdN1Pcvb3L9uMqhtGeVDYxfRb4BMWqYzcBjwDvHKTel1A0UT0JPAG8dwNijBbJ7KMREeNcmoYiIsa5JIKIiHEuiSAiYpxLIoiIGOeSCCIixrkkgoiIcS6JICJinPs/9hlUPRr9Yw0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Using the data stored in 'eventsSet', generate a plot of the average number\n",
    "# of electrons detected at the anode versus the number of photons incident\n",
    "# on the photocathode.\n",
    "y = []\n",
    "for i in range(len(eventsList)):\n",
    "    y = y + [eventsList[i][1]]\n",
    "plt.plot(numPhotons, y, 'ro', linewidth = 2, fillstyle = 'none')\n",
    "plt.xlabel('Number of Incident Photons')\n",
    "plt.ylabel('Average Number of Electrons at Anode');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "drawn-economics",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Finally, using the distributions stored in the set 'distSet', plot the\n",
    "# simulated distributions for the different numbers of incident photons all on\n",
    "# the same semi-log plot.\n",
    "plt.figure(figsize=(12,10))\n",
    "colours = ['ko', 'bo', 'ro', 'go']\n",
    "for i in range(len(numPhotons)):\n",
    "     counts, edges = np.histogram(distList[i], xbins) \n",
    "     spacing = (edges[1] - edges[0])/2\n",
    "     centres = edges[1:] - spacing\n",
    "     plt.semilogy(centres, counts, colours[i], fillstyle = 'none', linewidth = 2)\n",
    "plt.xlim((0, 2e6))\n",
    "plt.ylim((0.8, 500))\n",
    "plt.xlabel('Number of Anode Electrons')\n",
    "plt.ylabel('Counts')\n",
    "plt.legend(('1 photon', '2 photons', '4 photons', '8 photons'));"
   ]
  }
 ],
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