SimpleWPGen_Strip.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# SimpleWPGen_Strip\n",
    "# Ren Cooper, LBNL\n",
    "# Gamma-Ray Tracking School, ORNL, October 2018\n",
    "#\n",
    "# very simple Weighting Potential solver for a single strip of a HPGe detector via SOR method\n",
    "#  - Disclaimer: for demonstration/example purposes only!\n",
    "#\n",
    "# also includes a very crude example of signal generation\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "%reset -f"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from matplotlib import pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# set some detector parameters\n",
    "strip_width_mm = 2.8\n",
    "strip_gap_mm = 0.2\n",
    "detector_thickness_mm = 16.0\n",
    "pixel_size_mm = 0.1\n",
    "\n",
    "# set detector width to n*pitch where n is an odd number\n",
    "detector_width_mm = (9*strip_width_mm+strip_gap_mm)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# build some grids\n",
    "x_range = np.arange(-detector_width_mm/2 + pixel_size_mm, detector_width_mm/2 + pixel_size_mm, pixel_size_mm)\n",
    "y_range = np.arange(-pixel_size_mm, detector_thickness_mm + pixel_size_mm, pixel_size_mm)\n",
    "\n",
    "# initialize grid for solving for V\n",
    "N_xelements = np.shape(x_range)[0]\n",
    "N_yelements = np.shape(y_range)[0]\n",
    "V = np.zeros((N_xelements, N_yelements), dtype=float)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# build a little map of geometry for later, designating pixels based on their nature\n",
    "# Ge = 0 strip = 1 rest of strip surface = 2, back contact = 3, gap = 4\n",
    "geom_map = np.zeros((N_xelements, N_yelements), dtype=int)\n",
    "\n",
    "# continous contact\n",
    "geom_map[:,0] = 3\n",
    "\n",
    "# strip surface\n",
    "geom_map[:,-1] = 2\n",
    "\n",
    "# strip \n",
    "ix = np.where((x_range>=-strip_width_mm/2) & (x_range<=strip_width_mm/2))\n",
    "geom_map[ix,-1] = 1\n",
    "\n",
    "# gap\n",
    "ix = np.where((x_range>strip_width_mm/2) & (x_range<=(strip_width_mm/2 + strip_gap_mm)))\n",
    "geom_map[ix,-1] = 4\n",
    "ix = np.where((x_range<-strip_width_mm/2) & (x_range>=-(strip_width_mm/2 + strip_gap_mm)))\n",
    "geom_map[ix,-1] = 4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# set boundary conditions \n",
    "\n",
    "# non-strip contacts\n",
    "[ix,iy] = np.where(geom_map == 2)\n",
    "V[ix,iy] = 0\n",
    "\n",
    "# back face\n",
    "[ix,iy] = np.where(geom_map == 3)\n",
    "V[ix,iy] = 0\n",
    "\n",
    "# strip\n",
    "[ix,iy] = np.where(geom_map == 1)\n",
    "V[ix,iy] = 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# do the relaxation\n",
    "# set maximum number of iterations\n",
    "max_iters = 1000\n",
    "\n",
    "# \"over-relaxation\" factor to speed up convergence\n",
    "t = np.cos(3.14/N_xelements) + np.cos(3.14/N_yelements)\n",
    "w = (8 - np.sqrt(64 - 16*t*t)) / (t*t)\n",
    "\n",
    "# initialise arrays which will store the residuals\n",
    "R = np.zeros((N_xelements, N_yelements), dtype=float)\n",
    "resid_store = np.zeros(max_iters)\n",
    "\n",
    "# perform relaxation...\n",
    "resid = 1e6\n",
    "iterr = 1\n",
    "min_resid = 0.01\n",
    "\n",
    "while (iterr < max_iters and resid > min_resid):    \n",
    "    \n",
    "    # loop over detector grid points\n",
    "    for y in range(1, N_yelements-1):\n",
    "        for x in range(0, N_xelements-1):\n",
    "                        \n",
    "            # skip pixels with boundary conditions\n",
    "            if ((geom_map[x,y] == 1) or (geom_map[x,y] == 2) or (geom_map[x,y] == 3)):\n",
    "                continue\n",
    "                \n",
    "            # should deal with some boundary conditions...\n",
    "                                   \n",
    "            V_local_sum = (V[x+1,y] + V[x,y+1] + V[x-1,y] + V[x,y-1])\n",
    "            \n",
    "            # update the solution\n",
    "            R[x,y] = 0.25*V_local_sum - V[x,y]\n",
    "            V[x,y] = V[x,y] + w*R[x,y]\n",
    "            \n",
    "    # calculate the residual and store as a function of iteration number\n",
    "    resid = abs(np.sum(R))\n",
    "    resid_store[iterr] = resid\n",
    "    \n",
    "    # update iteration counter\n",
    "    iterr+=1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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2XfPvVbNsNks2m2XJkiXMmTMH0jTrx8wuMrOp3Wyfama/WPuyktHQ0EBjY6Oa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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x113e73780>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Final Difference:\n",
      "0.000272582469532\n"
     ]
    }
   ],
   "source": [
    "# visualise the weighting potential\n",
    "# plot difference vs. iteration number\n",
    "resid_store = resid_store[1:iterr]\n",
    "plt.plot(np.arange(1,iterr), resid_store)\n",
    "plt.grid(\"on\")\n",
    "plt.xlabel(\"Iteration Number\")\n",
    "plt.ylabel(\"Difference\")\n",
    "plt.yscale(\"log\")\n",
    "plt.show()\n",
    "\n",
    "# also print the final difference \n",
    "print(\"Final Difference:\")\n",
    "print(resid_store[-1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x119c9fcf8>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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AVwLHAx9vs955wJdJwvc1DY8dCvwwIv45/fl2Sf8POLibjjmoK8lVda4cuAXl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\nNMu8dIoAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x113e5ce80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X, Y = np.meshgrid(y_range, x_range)\n",
    "plt.contourf(Y,X, V, 30)\n",
    "plt.xlim(-detector_width_mm/2, detector_width_mm/2)\n",
    "plt.colorbar()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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lcc5l/sAP8Lyi5LkBLwCTW3mtAXu0ePwMeBwYDmzUxjb2B9zixYtdyD7xiU9k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\nmgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x117d865c0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# take a slice through the WP\n",
    "x_slice = 125\n",
    "Vslice = V[x_slice,:]\n",
    "\n",
    "\n",
    "plt.plot(y_range, Vslice, 'b-',linewidth=2)\n",
    "plt.grid(\"on\")\n",
    "plt.xlabel(\"Depth (mm)\")\n",
    "plt.ylabel(\"W\")\n",
    "plt.xlim(0, 16.1)\n",
    "plt.ylim(0, 1)\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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DPJ/TH9hQsU27V+T6EDi/jrcNw/1Qs2lKqT1KqZ+VUk8rpZo09OebYM2aNVaX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\n3KjZuFEv3LOn1uOszm0VyW0WyW0Wq3K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      "text/plain": [
       "<matplotlib.figure.Figure at 0x116d43080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# simple signal calculation assuming fixed velocity of one pixel per ns for both electrons and holes\n",
    "# holes into wp, electrons out\n",
    "# could easily vectorize to be faster and more pythonic\n",
    "\n",
    "# assume an interaction position at a given depth\n",
    "depth_mm = 10\n",
    "\n",
    "z0 = np.int(np.floor(depth_mm / pixel_size_mm))\n",
    "\n",
    "# number of time steps in signal\n",
    "Nt = 150\n",
    "\n",
    "# arrays which will store the induced charge signals\n",
    "Qh = np.zeros(Nt, dtype=float)\n",
    "Qe = np.zeros(Nt, dtype=float)\n",
    "\n",
    "# starting positions for electrons and holes\n",
    "zh = z0\n",
    "ze = z0\n",
    "\n",
    "# holes into wp\n",
    "t = 0\n",
    "for t in range(1, Nt):\n",
    "    if (zh<=N_yelements-1):\n",
    "        dw = Vslice[zh] - Vslice[zh-1]\n",
    "        Qh[t] = 1.0*dw    \n",
    "    elif (zh>N_yelements-1):\n",
    "        continue\n",
    "    zh = zh+1\n",
    "\n",
    "# electrons out of wp\n",
    "t = 0\n",
    "for t in range(1, Nt):\n",
    "    if (ze>=0):\n",
    "        dw = Vslice[ze] - Vslice[ze+1]\n",
    "        Qe[t] = -1.0*dw\n",
    "    elif (ze<0):\n",
    "        continue\n",
    "    ze = ze-1\n",
    "\n",
    "# take cumulative sums\n",
    "Qsignal_h = np.cumsum(Qh)\n",
    "Qsignal_e = np.cumsum(Qe)\n",
    "Qsignal = np.cumsum(Qe + Qh)\n",
    "\n",
    "# plot\n",
    "plt.plot(Qsignal_e, 'm', linewidth=1.5)\n",
    "plt.plot(Qsignal_h, 'c', linewidth=1.5)\n",
    "plt.plot(Qsignal, 'k', linewidth=2)\n",
    "plt.grid(\"on\")\n",
    "#plt.ylim(0,1)\n",
    "plt.xlim(0, Nt)\n",
    "plt.tick_params(labelbottom=\"off\")\n",
    "plt.xlabel(\"Time\")\n",
    "plt.ylabel(\"Charge (au)\")\n",
    "#plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python [default]",
   "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": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}