neutron_flux.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Μέτρηση της ροής της κατανομής νετρονίων σε υποκρίσιμο πυρηνικό αντιδραστήρα\n",
    "\n",
    "## Θεωρητική εισαγωγή"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Αντιδραστήρας\n",
    "Στο πείραμα αυτό μελετάται η κατανομή των νετρονίων σε υποκρίσιμο πυρηνικό αντιδραστήρα ($k_{eff} \\approx 0.8$). Ο αντιδραστήρας αποτελείται από ράβδους φυσικού ουρανίου $U_3O_8(UO_2 . 2UO_3)$, επιβραδυντή (και ανακλαστή) ελαφρύ ύδωρ $H_2O$. Το ουράνιο βρίσκεται σε σωλήνες αλουμινίου για την αποφυγή διαρροής ραδιενεργού υλικού. \n",
    "\n",
    "Στο κέντρο του αντιδραστήρα τοποθετείται πηγή νετρονίων 5Ci $\\ ^{241}AmBe$. \n",
    "\n",
    "Τα νετρόνια της πηγής θερμοποιούνται καθώς συγκρούνται με τους πυρήνες υδρογόνου στο νερό, και εν συνεχεία μέρος τους αντιδρά με το $\\ ^{235}U$ προκαλώντας σχάση και απελευθέρωση επιπλέον νετρονίων. Το νερό δρα και ως ανακλαστής, ώστε μέρος των νετρονίων που κανονικά θα διέφευγαν του αντιδραστήρα να ανακλώνται πίσω. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Διάχυση νετρονίων\n",
    "Θεωρώντας ότι τα νετρόνια είναι μονοενεργειακά μπορούμε να χρησιμοποιήσουμε την μέθοδο διάχυσης μιας ομάδας. Σύμφωνα με τη μέθοδο αυτή, όταν ο αντιδραστήρας λειτουργεί σε σταθερές συνθήκες, για τα νετρόνια ισχύει: \n",
    "\n",
    "$$ created - escaped - absorbed = 0 $$\n",
    "\n",
    "ή \n",
    "\n",
    "$$ D\\nabla^2\\Phi - \\Sigma_a\\Phi + S = 0$$\n",
    "\n",
    "όπου Φ η ροή των θερμικών νετρονίων, D ο συντελεστής διάχυσης, $\\Sigma_a$ η μακροσκοπική ενεργός διατομή απορρόφησης, και S ο αριθμός n ανά μονάδα όγκου ανά μονάδα χρόνου.\n",
    "\n",
    "Επιλύοντας την παραπάνω εξίσωση καταλήγουμε στην: \n",
    "\n",
    "$$ \\Phi(r,z)=A\\cdot J_0\\cdot (2.405/R_{ex}r)\\cdot e^{-\\gamma z} $$\n",
    "\n",
    "ή \n",
    "\n",
    "$$ln\\Phi(r,z) = ln[A\\cdot J_0\\cdot (2.405/R_{ex}r)] -\\gamma z \\qquad (1)$$\n",
    "\n",
    "\n",
    "Για δεδομένο $r=r_0$ η συνάρτηση του $ln\\Phi$ ως προς το ύψος $z$ είναι ευθεία με κλίση $\\gamma$. Επομένως το ύψος από το σημείο $r_0$ στο οποίο η ροή μειώνεται στο $1/e$ της αρχικής, είναι $l=1/\\gamma$ και ονομάζεται _μήκος χαλάρωσης_. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Ιδιαιτερότητες πειράματος\n",
    "\n",
    "Λόγω συντήρησης των ράβδων καυσίμου ο αντιδραστήρας περιείχε μόνο την πηγή $\\ ^{241}AmBe$ και το νερό, χωρίς καμία ράβδο καυσίμου. Επίσης, θεωρήθηκε ότι η ενεργοποίηση του $In$ οφείλεται αποκλειστικά σε θερμικά νετρόνια.\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Πείραμα\n",
    "\n",
    "Φύλλα $In$ τοποθετήθηκαν στον αντιδραστήρα σε συγκεκριμένη θέση, αλλά σε διαφορετικό ύψος ο καθένας. Στο φυσικό $In$ υπάρχει 95.7(1)% $\\ ^{115}In$. Μετά από ακτινοβόληση 4-5 ωρών (περίπου 5 ημιζωές του $\\ ^{116}In$ ώστε η ενεργότητα να φτάσει περίπου το 99(1)% της μέγιστης), τα φύλλα αφαιρέθηκαν. \n",
    "\n",
    "\n",
    "Ο ρυθμός υποβάθρου χωρίς $In$ ήταν $8\\ cpm$ και με **μη** ενεργοποιημένο $In$ ήταν $9\\ cpm$, και αφαιρείται από τον αληθή ρυθμό.  \n",
    "\n",
    "Η ομάδα μας μέτρησε τους ψευδείς ρυθμούς R' από τις πηγές 3,6,9. Οι R' μετατράπηκαν σε αληθείς μέσω της σχέσης: \n",
    "\n",
    "$$ R = \\frac{R'}{1-\\tau R'} $$\n",
    "\n",
    "όπου $\\tau=50\\ \\mu s$ o νεκρός χρόνος του ανιχνευτή Geiger. \n",
    "\n",
    "\n",
    "Η απόδοση του Geiger στις συγκεκριμένες ενέργειες των $\\beta^-$ είναι $\\varepsilon=100\\%$ και ο παράγοντας γεωμετρίας $g = 0.4$. H ενεργότητα $A'$ δίνεται από την σχέση: \n",
    "\n",
    "$$ A' = \\frac{R}{\\varepsilon\\cdot g} $$\n",
    "\n",
    "\n",
    "\n",
    "Η ενεργότητα ανά gr $A$ δίνεται από την σχέση: \n",
    "\n",
    "$$A = \\frac{A'}{m}$$\n",
    "\n",
    "όπου $m$ η μάζα του $In$ σε gr.\n",
    "\n",
    "Θεωρούμε ότι οι αντίστοιχες ενεργότητες που υπολογίσαμε αντιστοιχούν στο μέσο της διάρκειας μέτρησης. Πχ. αν $t_{exit}=18\\ min$ o χρόνος από την έξοδο από τον αντιδραστήρα και $t_0=60\\ s$ η διάρκεια μέτρησης, τότε η ενεργότητα αντιστοιχεί στην χρονική στιγμή $t=18.5\\ min$. \n",
    "\n",
    "H ροή των θερμικών νετρονίων δίνεται από την σχέση: \n",
    "\n",
    "$$ \\Phi_\\theta = \\frac {A_\\theta} {\\sigma \\cdot M (1-e^{-\\lambda t_{irr} }) }$$\n",
    "\n",
    "όπου:  \n",
    " - $t_{irr}$ ο χρόνος ακτινοβόλησης στον αντιδραστήρα\n",
    " - $\\sigma = 162\\ barn$ \n",
    " - $M = N_A\\cdot m/A$, με $A=115$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import numpy\n",
    "import matplotlib as mpl\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "import scipy.optimize\n",
    "import scipy.constants\n",
    "import sympy\n",
    "sympy.init_printing() \n",
    "\n",
    "# Used for latex-labels in plots .\n",
    "# (if you don't have the dependencies from http://stackoverflow.com/a/37218925/4230591 installed, \n",
    "# it will raise an error during plotting)\n",
    "from matplotlib import rc\n",
    "rc('text', usetex=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# ====================================================================================================\n",
    "# CONSTANTS AND MISC DATA\n",
    "#\n",
    "# One-letter variables should not be used to store data, \n",
    "# since they'll be needed for `sympy.symbols()` to display functions.\n",
    "# ====================================================================================================\n",
    "\n",
    "\n",
    "t_count = 60    # secs\n",
    "t_count_in_mins = t_count / 60.\n",
    "t_exit_reactor = 18 * 60.\n",
    "t_end = 66 * 60.\n",
    "t_between_measurements = 2 * 60.\n",
    "\n",
    "R_background = 8 /60.\n",
    "R_background_In = 9 /60.\n",
    "m_In = 1 /1000    # 1gr\n",
    "indium_115_ratio = .957\n",
    "\n",
    "M_constant = scipy.constants.N_A * m_In * indium_115_ratio / 115\n",
    "\n",
    "irradiation_start = '3:00'\n",
    "irradiation_t = 4.5 * 3600    # 4-5h\n",
    "g_times_e = 0.4\n",
    "τ_constant=50 * 10**-6\n",
    "\n",
    "half_life = 54.29 * 60.  #sec\n",
    "decay_constant = numpy.log(2) / half_life\n",
    "\n",
    "σ_In = 162 * 10e-28\n",
    "\n",
    "\n",
    "# =========================================================\n",
    "# IRRELEVANT DATA (not used in calculations)\n",
    "# =========================================================\n",
    "#\n",
    "# ~40μSv/h near reactor\n",
    "# AmBe ~10e+6 n/s\n",
    "# k_eff = ~.8\n",
    "# v_geiger = 500V"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Ο αληθής ρυθμός R δίνεται από την σχέση:\n"
     ]
    },
    {
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      "text/latex": [
       "$$R = \\frac{R'}{- R' \\tau + 1}$$"
      ],
      "text/plain": [
       "        R'   \n",
       "R = ─────────\n",
       "    -R'⋅τ + 1"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# =========================================================\n",
    "# R \n",
    "# =========================================================\n",
    "\n",
    "R_αληθής, σ_R_αληθής, R_ψευδής, τ, σ_R_ψευδής, t = sympy.symbols(\"R, \\sigma_R, R' tau, \\sigma_R', t\")\n",
    "_R_αληθής_f = lambda R_ψευδής, τ: R_ψευδής/(1-R_ψευδής*τ)\n",
    "R_αληθής_f = sympy.lambdify((R_ψευδής, τ), _R_αληθής_f(R_ψευδής, τ), (sympy, numpy))\n",
    "\n",
    "print('\\nΟ αληθής ρυθμός R δίνεται από την σχέση:')\n",
    "sympy.Eq(R_αληθής, R_αληθής_f(R_ψευδής, τ))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Το σφάλμα στον ψευδή ρυθμό δίνεται από την σχέση:\n"
     ]
    },
    {
     "data": {
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      "text/latex": [
       "$$\\sigma_R' = \\frac{\\sqrt{R'}}{t}$$"
      ],
      "text/plain": [
       "              ____\n",
       "            ╲╱ R' \n",
       "\\sigma_R' = ──────\n",
       "              t   "
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# =========================================================\n",
    "# R' error\n",
    "# =========================================================\n",
    "_σ_R_ψευδής_f = lambda R_ψευδής, t: sympy.sqrt(R_ψευδής) / t\n",
    "# (Currently `lambdify` can't handle both arrays *and* sympy functions,)\n",
    "# (therefor one function is used for pretty printing and a different one for calculations.)\n",
    "σ_R_ψευδής_f = sympy.lambdify((R_ψευδής, t), _σ_R_ψευδής_f(R_ψευδής, t), modules=['numpy'])\n",
    "\n",
    "print('\\nΤο σφάλμα στον ψευδή ρυθμό δίνεται από την σχέση:')\n",
    "sympy.Eq(σ_R_ψευδής, _σ_R_ψευδής_f(R_ψευδής, t))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Το σφάλμα στον αληθή ρυθμό δίνεται από την σχέση:\n"
     ]
    },
    {
     "data": {
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      "text/latex": [
       "$$\\sigma_R = \\sqrt{\\sigma_R'^{2} \\left(\\frac{R' \\tau}{\\left(- R' \\tau + 1\\right)^{2}} + \\frac{1}{- R' \\tau + 1}\\right)^{2}}$$"
      ],
      "text/plain": [
       "                 ________________________________________\n",
       "                ╱                                      2 \n",
       "               ╱           2 ⎛    R'⋅τ           1    ⎞  \n",
       "\\sigma_R =    ╱   \\sigma_R' ⋅⎜──────────── + ─────────⎟  \n",
       "             ╱               ⎜           2   -R'⋅τ + 1⎟  \n",
       "           ╲╱                ⎝(-R'⋅τ + 1)             ⎠  "
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# =========================================================\n",
    "# R error \n",
    "# =========================================================\n",
    "\n",
    "_err_R_αληθής_sq = sympy.diff(R_αληθής_f(R_ψευδής, τ), R_ψευδής)**2 * σ_R_ψευδής**2\n",
    "_err_R_αληθής = sympy.sqrt(_err_R_αληθής_sq)\n",
    "err_R_αληθής_f = sympy.lambdify((R_ψευδής, σ_R_ψευδής, τ), _err_R_αληθής, modules=['numpy'])\n",
    "\n",
    "print('\\nΤο σφάλμα στον αληθή ρυθμό δίνεται από την σχέση:')\n",
    "sympy.Eq(σ_R_αληθής, _err_R_αληθής)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "======================================================================\n",
      "Πηγή 9:\n",
      "\n",
      "   t (min)  R'(cpm)   t (s)   R'(cps)    R(cps)  error σR'(cps)  \\\n",
      "0     22.5       94  1350.0  1.566667  1.416789        0.161589   \n",
      "1     28.5       79  1710.0  1.316667  1.166753        0.148137   \n",
      "2     34.5       89  2070.0  1.483333  1.333443        0.157233   \n",
      "3     40.5       74  2430.0  1.233333  1.083409        0.143372   \n",
      "4     46.5       69  2790.0  1.150000  1.000066        0.138444   \n",
      "5     52.5       80  3150.0  1.333333  1.183422        0.149071   \n",
      "6     58.5       59  3510.0  0.983333  0.833382        0.128019   \n",
      "7     64.5       54  3870.0  0.900000  0.750041        0.122474   \n",
      "\n",
      "   error σR(cps)  relative σR %  \n",
      "0       0.161612      11.406934  \n",
      "1       0.148154      12.697959  \n",
      "2       0.157254      11.793076  \n",
      "3       0.143388      13.234851  \n",
      "4       0.138458      13.844842  \n",
      "5       0.149089      12.598111  \n",
      "6       0.128030      15.362681  \n",
      "7       0.122484      16.330275  \n",
      "\n",
      "======================================================================\n",
      "Πηγή 3:\n",
      "\n",
      "   t (min)  R'(cpm)   t (s)     R'(cps)      R(cps)  error σR'(cps)  \\\n",
      "0     18.5     9090  1110.0  151.500000  152.506372        1.589025   \n",
      "1     24.5     8364  1470.0  139.400000  140.228438        1.524248   \n",
      "2     30.5     7756  1830.0  129.266667  129.957595        1.467803   \n",
      "3     36.5     7290  2190.0  121.500000  122.092624        1.423025   \n",
      "4     42.5     6353  2550.0  105.883333  106.296881        1.328428   \n",
      "5     48.5     6084  2910.0  101.400000  101.766718        1.300000   \n",
      "6     54.5     5568  3270.0   92.800000   93.082599        1.243651   \n",
      "7     60.5     5353  3630.0   89.216667   89.466431        1.219403   \n",
      "\n",
      "   error σR(cps)  relative σR %  \n",
      "0       1.613539       1.058014  \n",
      "1       1.545850       1.102380  \n",
      "2       1.487065       1.144270  \n",
      "3       1.440559       1.179891  \n",
      "4       1.342663       1.263125  \n",
      "5       1.313331       1.290531  \n",
      "6       1.255308       1.348596  \n",
      "7       1.230387       1.375249  \n",
      "\n",
      "======================================================================\n",
      "Πηγή 6:\n",
      "\n",
      "   t (min)  R'(cpm)   t (s)    R'(cps)     R(cps)  error σR'(cps)  \\\n",
      "0     20.5     3899  1230.0  64.983333  65.045163        1.040700   \n",
      "1     26.5     3654  1590.0  60.900000  60.936007        1.007472   \n",
      "2     32.5     3331  1950.0  55.516667  55.521201        0.961914   \n",
      "3     38.5     3195  2310.0  53.250000  53.242157        0.942072   \n",
      "4     44.5     2875  2670.0  47.916667  47.881743        0.893650   \n",
      "5     50.5     2484  3030.0  41.400000  41.335876        0.830662   \n",
      "6     56.5     2337  3390.0  38.950000  38.876003        0.805709   \n",
      "7     62.5     2195  3750.0  36.583333  36.500373        0.780847   \n",
      "\n",
      "   error σR(cps)  relative σR %  \n",
      "0       1.047502       1.610423  \n",
      "1       1.013639       1.663449  \n",
      "2       0.967277       1.742175  \n",
      "3       0.947108       1.778869  \n",
      "4       0.897945       1.875339  \n",
      "5       0.834107       2.017876  \n",
      "6       0.808850       2.080590  \n",
      "7       0.783705       2.147115  \n"
     ]
    },
    {
     "data": {
      "image/png": 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0/PxxtcViGGaQ4q0RMm+eo5Fw881EDQ2Bu26+2bH8efMuv22RkZGk1+uptLSU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\njDMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f13509a9e48>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# ====================================================================================================\n",
    "# DATA (sources 3, 6, 9)\n",
    "# ====================================================================================================\n",
    "\n",
    "\n",
    "df3 = pd.read_csv('source3', names=['t (min)', \"R'(cpm)\"])\n",
    "df6 = pd.read_csv('source6', names=['t (min)', \"R'(cpm)\"])\n",
    "df9 = pd.read_csv('source9', names=['t (min)', \"R'(cpm)\"])\n",
    "\n",
    "dfs_3_6_9 = {3: df3, 6: df6, 9: df9}\n",
    "\n",
    "\n",
    "for source_n, _df in dfs_3_6_9.items():\n",
    "    # the measured rate is considered to have occured exactly in the middle of the measurement's duration\n",
    "    _df['t (min)'] += t_count_in_mins / 2\n",
    "    _df['t (s)'] = _df['t (min)'] * 60\n",
    "\n",
    "    _df[\"R'(cps)\"] = _df[\"R'(cpm)\"] / 60 \n",
    "    _df[\"R(cps)\"] = R_αληθής_f(_df[\"R'(cps)\"], τ_constant) - R_background_In\n",
    "    \n",
    "    # errors\n",
    "    _df[\"error σR'(cps)\"] = σ_R_ψευδής_f(_df[\"R'(cpm)\"], 60)\n",
    "    _df[\"error σR(cps)\"] = err_R_αληθής_f(_df[\"R(cps)\"], _df[\"error σR'(cps)\"], τ_constant)\n",
    "    _df[\"relative σR %\"] = _df[\"error σR(cps)\"] / _df[\"R(cps)\"] * 100\n",
    "    \n",
    "    \n",
    "    print('\\n' + '='*70)\n",
    "    print('Πηγή {}:\\n'.format(source_n))\n",
    "    print(_df)\n",
    "\n",
    "    source_label = r'source: {}'.format(source_n)\n",
    "    plt.plot(_df['t (s)'], _df[\"R(cps)\"], marker='.', label=source_label)\n",
    "    plt.ylim(ymin=0, ymax=160)\n",
    "\n",
    "\n",
    "plt.xlabel('t(s)')\n",
    "plt.ylabel('R(cps)')\n",
    "plt.legend(loc='upper right')\n",
    "plt.title('FIGURE 1:\\nRates vs time of sources 3,6 and 9. \\n(Errorbars were omitted since they are too small.)')\n",
    "plt.grid('on')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Υπολογισμός ρυθμού R κατά την έξοδο του In από τον αντιδραστήρα\n",
    "\n",
    "[Θεωρώντας ότι το σφάλμα στους ρυθμούς](http://www.mathworks.com/help/stats/examples/pitfalls-in-fitting-nonlinear-models-by-transforming-to-linearity.html) είναι πολλαπλασιαστικό και όχι προσθετικό, χρησιμοποιούμε μέθοδο ελαχίστων τετραγώνων, αφού μετατρέψουμε την εκθετική συνάρτηση σε γραμμική."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a = 5.26188, b = -0.00021825\n",
      "Ro = 192.8\n",
      "λ/b = 97.5%\n",
      "σφάλμα στο Ro: 2.819\n"
     ]
    }
   ],
   "source": [
    "# ====================================================================================================\n",
    "# Linear fit\n",
    "# ====================================================================================================\n",
    "\n",
    "\n",
    "_f = lambda x, a, b: a+x*b\n",
    "lin_popt, lin_pcov = scipy.optimize.curve_fit(_f, df3['t (s)'], scipy.log(df3['R(cps)']), \n",
    "                                              sigma=_df[\"error σR(cps)\"], absolute_sigma=True)\n",
    "lin_perr = numpy.sqrt(numpy.diag(lin_pcov))\n",
    "\n",
    "print('a = {:.6}, b = {:.6}'.format(*lin_popt))\n",
    "print('Ro = {:.4}'.format(scipy.e**lin_popt[0]))\n",
    "print('λ/b = {:.1%}'.format(-decay_constant/lin_popt[1]))\n",
    "print('σφάλμα στο Ro: {:.4}'.format(scipy.e**lin_perr[0]))\n",
    "# (using python variables in markdown is not supported yet, therefor it has to be done manually)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ο ρυθμός κατά το τέλος της ακτινοβόλησης είναι $R_0 = 193(3) cps$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a = 194.294, b = -0.000221309\n",
      "λ/b = 0.961513\n"
     ]
    }
   ],
   "source": [
    "# ====================================================================================================\n",
    "# Non linear fit (not used in further calculations; displayed just for comparison)\n",
    "# ====================================================================================================\n",
    "\n",
    "\n",
    "def exp_f(x, a,b):\n",
    "    return a * scipy.e**(b*x)\n",
    "\n",
    "exp_popt, _ = scipy.optimize.curve_fit(exp_f, df3['t (s)'], df3['R(cps)'],sigma=_df[\"error σR(cps)\"], p0=(300, -decay_constant))\n",
    "print('a = {:.6}, b = {:.6}'.format(*exp_popt))\n",
    "print('λ/b = {:.6}'.format(-decay_constant/exp_popt[1]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Κατανομή ροής νετρονίων συναρτήσει του ύψους z\n",
    "\n",
    "Αρχικά υπολογίζουμε την ενεργότητα της εκάστοτε πηγής στο τέλος της ακτινοβόλησης, λαμβάνοντας υπόψιν τον παράγοντα γεωμετρίας $g=0.4$ και την απόδοση $\\varepsilon=1$ του Geiger στις συγκεκριμένες ενέργειες των $\\beta^-$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# ============================================================================================\n",
    "# DATA (all sources' R at the end of irradiation)\n",
    "# ============================================================================================\n",
    "\n",
    "\n",
    "df_all = pd.read_csv('all_sources', names=['z (cm)', \"R(cps)\"])\n",
    "df_all['A(Bq)'] = df_all[\"R(cps)\"] / g_times_e"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Στην παρακάτω γραφική παράσταση παρουσιάζεται η ροή των νετρονίων συναρτήσει του ύψους. Το $z=0$ αντιστοιχεί στο ύψος της πηγής $\\ ^{241}AmBe$.\n",
    "\n",
    "Παρατηρείται ότι η μέγιστη ροή βρίσκεται στο ύψος της πηγής $\\ ^{241}AmBe$. Η ροή δεν είναι συμμετρική, λόγω της κατασκευής του αντιδραστήρα. Η επάνω επιφάνεια του αντιδραστήρα είναι ανοιχτή (αέρας), ενώ στην κάτω βρίσκεται ο μεταλλικός του πάτος καθώς και το τσιμέντο. Ως αποτέλεσμα αυτού, από την επάνω επιφάνεια τα νετρόνια διαφεύγουν ελεύθερα του αντιδραστήρα μόλις εξέλθουν του νερού, ενώ στην κάτω επιφάνεια μέρος των νετρονίων οπισθοσκεδάζεται από τα υλικά που προαναφέρθηκαν. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAMQAAAAvBAMAAABOC3gZAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nJWus/wCNwBuoiOxmqQAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$\\Phi = \\frac{A_{th}}{M \\sigma \\left(1 - e^{- \\lambda t_{irr}}\\right)}$$"
      ],
      "text/plain": [
       "                    Aₜₕ             \n",
       "\\Phi = ─────────────────────────────\n",
       "                ⎛     -\\lambda⋅tᵢᵣᵣ⎞\n",
       "       M⋅\\sigma⋅⎝1 - ℯ             ⎠"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# ============================================================================================\n",
    "# Neutron flux formula\n",
    "# ============================================================================================\n",
    "\n",
    "\n",
    "A_θ, t , λ, σ, t_irr, M, Φ = sympy.symbols('A_th, t, \\lambda, \\sigma, t_irr, M, \\Phi')\n",
    "_flux_f = lambda A_θ, λ, t_irr, M, σ: A_θ / (σ * M * (1-sympy.E**(-λ * t_irr)))\n",
    "flux_f = sympy.lambdify((A_θ, λ, t_irr, M, σ), _flux_f(A_θ, λ, t_irr, M, σ))\n",
    "\n",
    "sympy.Eq(Φ, _flux_f(A_θ, λ, t_irr, M, σ))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   z (cm)  R(cps)    A(Bq)           Φ\n",
      "0      40    1.90    4.750    2.417262\n",
      "1      30    0.30    0.750    0.381673\n",
      "2      20   45.86  114.650   58.345070\n",
      "3      10   89.13  222.825  113.395030\n",
      "4       5  177.60  444.000  225.950379\n",
      "5       0  349.90  874.750  445.157870\n",
      "6      -5  193.70  484.250  246.433494\n",
      "7     -10   58.50  146.250   74.426223\n",
      "8     -20   38.70   96.750   49.235809\n"
     ]
    },
    {
     "data": {
      "image/png": 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kVU0WISENx4iIiGRVTRYhIfWEzJkzJ+0mxCakLKA8PgspCyiPz0LKkoSaLEJC6glpbIxl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\nISIiIpIKFSEiIiKSiv8Ph9YhMnWeuAYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1380e41160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# ============================================================================================\n",
    "# FLUX CALCULATION\n",
    "# ============================================================================================\n",
    "\n",
    "\n",
    "# flux unit: n per cm^3 per sec\n",
    "df_all['Φ'] = flux_f(df_all[\"R(cps)\"], decay_constant, irradiation_t, M_constant, σ_In)/ (100**3)\n",
    "df_all['Φ'] = df_all['Φ'].astype(scipy.float64, copy=False)\n",
    "print(df_all)\n",
    "\n",
    "# --------------------------------------------------------------------\n",
    "plt.plot(df_all['Φ'],df_all['z (cm)'])\n",
    "\n",
    "plt.xlabel('flux$(n/cm^3/s)$')\n",
    "plt.ylabel('height (cm)')\n",
    "plt.title('FIGURE 2: \\nThermal neutron flux')\n",
    "plt.grid('on')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Μήκος χαλάρωσης\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a = 18.2358, b = -8.33343\n",
      "μήκος χαλάρωσης: 12.0 cm\n"
     ]
    }
   ],
   "source": [
    "# ====================================================================================================\n",
    "# Least squares\n",
    "# ====================================================================================================\n",
    "\n",
    "\n",
    "_f = lambda x, a, b: a+x*b\n",
    "# Converting flux to n/m^3/s first, and z to meters.\n",
    "# (No errors were given for Φ)\n",
    "lin_popt, _ = scipy.optimize.curve_fit(_f, df_all['z (cm)']/100, scipy.log(df_all['Φ']*(100**3)))\n",
    "print('a = {:.6}, b = {:.6}'.format(*lin_popt))\n",
    "relaxation_length = -1/lin_popt[1]\n",
    "print('μήκος χαλάρωσης: {:.5} cm'.format(relaxation_length * 100))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Το μήκος χαλάρωσης προκύπτει 12.0cm. \n",
    "\n",
    "(Λόγω του ότι δεν μας δόθηκαν τα σφάλματα από τις υπόλοιπες πηγές, δεν τα λαμβάνουμε υπόψιν στoυς υπολογισμούς και δεν μπορούμε να υπολογίσουμε το σφάλμα στο μήκος χαλάρωσης.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Πιθανές πηγές σφαλμάτων"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Οπισθοσκέδαση σωματιδίων $\\beta^-$ από το υλικό κάτω από την πηγή. \n",
    "\n",
    "Η οπισθοσκέδαση των $\\beta^-$ από την βάση τοποθέτησης, τον πάγκο και τα υλικά γύρω από τον ανιχνευτή, συμπεριλαμβανομένου και της θέσης της ερευνήτριας κατά τις μετρήσεις, πιθανόν προκάλεσε υπερεκτίμηση των ρυθμών."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Επιλογή χρόνου μέτρησης στο μέσο της διάρκειας μέτρησης\n",
    "\n",
    "Ο εκάστοτε ρυθμός αποδόθηκε στο μέσο της διάρκειας μέτρησης $t_0$ (δηλ. $t_0 = t_1 + \\frac{t_2-t_1}{2}$). Ωστόσο, λόγω της εκθετικής πτώσης της ενεργότητας, η υπολογιζόμενη ενεργότητα στην πραγματικότητα αντιστοιχεί σε χρόνο πριν του μέσου. \n",
    "\n",
    "![actual time for measured rate](actual_count_time.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Υπερεκτίμηση παράγοντα γεωμετρίας λόγω εγγύτητας πηγής-ανιχνευτή\n",
    "\n",
    "Σε επαρκώς μεγάλες αποστάσεις ο παράγοντας γεωμετρίας μπορεί να αγνοεί τις διαστάσεις του ανιχνευτή, και να χρησιμοποιείται ως έχει για τον υπολογισμό των σωματιδίων που διέρχονται από μέσα του. \n",
    "\n",
    "Για πολύ κοντινές αποστάσεις όμως, σε μεγάλες γωνίες πρόσπτωσης (δέσμη 2 στην παρακάτω εικόνα) τα σωματίδια διέρχονται από λιγότερο υλικό του ανιχνευτή, σε αντίθεση με σωματίδια που προσπίπτουν κάθετα στην επιφάνειά του (δέσμη 1). \n",
    "\n",
    "![beam differences](large_geometry_factor_distortion.png)\n",
    "\n",
    "Ως αποτέλεσμα, κάποια σωματίδια σε μεγάλες γωνίες δεν προκαλούν επαρκή ιονισμό ώστε να καταχωρηθούν από τον ανιχνευτή. Το φαινόμενο αυτό ίσως να μην είναι τόσο σημαντικό για άμεσα ιονίζουσες ακτινοβολίες, όπως τα $\\beta^-$ του πειράματος, αλλά ωστόσο όχι αμελητέο."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Ταυτόχρονη μετακίνηση/μέτρηση άλλων πηγών σε διπλανούς Geiger\n",
    "\n",
    "Ταυτόχρονα με την μέτρησή μας διεξάγονταν και άλλες μετρήσεις σε απόσταση μικρότερη των 2 μέτρων, πιθανόν αυξάνοντας σημαντικά το υπόβαθρο. Ενδέχεται αυτό το σφάλμα να επηρέασε ιδιαίτερα τις μετρήσεις πηγών με μικρές ενεργότητες (πχ. πηγή 9).\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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WGkjOjJG8+R8pPEShRnZvx4qu3/BPmUxufrMVi77cbnZIXvdjxmEaxfXjoa9b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\nTuuygUit9XaXbaVxqRBCCGFAsA+ZvjWfdWHYeri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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f134e879748>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(df9['t (s)'], df9[\"R(cps)\"], marker='.', label='Source 9')\n",
    "plt.errorbar(df9['t (s)'], df9[\"R(cps)\"], df9[\"error σR(cps)\"], label=None)\n",
    "plt.ylim(ymin=0)\n",
    "plt.xlabel('t(s)')\n",
    "plt.ylabel('R(cps)')\n",
    "plt.legend(loc='upper right')\n",
    "plt.title('FIGURE 3: \\nRate of source 9.')\n",
    "plt.grid('on')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Μη θερμικά νετρόνια \n",
    "\n",
    "Λόγω της μη χρήσης $Cd$, ταυτόχρονα και μη θερμικά νετρόνια απορροφόνται από το $\\ ^{115}In$. Ως αποτέλεσμα αυξάνει ο μετρούμενος ρυθμός, λόγω του ότι πολλά από αυτά τα νετρόνια αυτά θα διέφευγαν ή θα απορροφόνταν πριν θερμοποιηθούν,  επομένως δεν θα ήταν διαθέσιμα ως θερμικά. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Αναφορές\n",
    "\n",
    "Για την συγγραφή της εργασίας χρησιμοποιήθηκαν οι παρακάτω αναφορές:\n",
    "\n",
    "1. Η ΠΥΡΗΝΙΚΗ ΦΥΣΙΚΗ ΣΤΟ ΕΡΓΑΣΤΗΡΙΟ - ΦΟΙΤΗΤΙΚΕΣ ΑΣΚΗΣΕΙΣ, X. ΕΛΕΥΘΕΡΙΑΔΗΣ, Μ. ΖΑΜΑΝΗ, Α. ΛΙΟΛΙΟΣ, Μ. ΜΑΝΩΛΟΠΟΥΛΟΥ, X. ΠΕΤΡΙΔΟΥ, Η. ΣΑΒΒΙΔΗΣ, Εκδόσεις: COPY CITY\n",
    "\n",
    "2. https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.curve_fit.html \n",
    "\n"
   ]
  }
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