LennartNaeve_code/spilling_code/diagonalisation/dysprosium3.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "from helpers import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "initial_power = 700 * si.uW \n",
    "\n",
    "trap: PancakeTrap = PancakeTrap(\n",
    "    power=0,  # Set pancake laser power to 0, no 2D trap\n",
    "    grad_z= 3 * si.G / si.cm,\n",
    "    grad_r=0,\n",
    "    power_tweezer=initial_power,\n",
    "    waist_tweezer=1.838 * si.um,\n",
    "    a=184.4*(4 * np.pi * const.epsilon_0 * const.value(\"Bohr radius\")**3)/(2 * const.epsilon_0 * const.c),\n",
    "\n",
    "    wvl = 1064 * si.nm,    \n",
    ")\n",
    "\n",
    "zr = float(trap.subs(trap.get_tweezer_rayleigh()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-1.9457041266476965e-29\n"
     ]
    },
    {
     "data": {
      "image/png": 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Zme6GKFVl0sMvy5Ytg4eHB+bNm6e7QUHXrl317r5+6tQpKBQKNGvWDEePHtULb6FQCH9/fyQlJT0z1B8NuYhEIov5RbWkfakLdLyqh45X9RlyzAwZDjbpD0o9PDye+XxqaiqGDh2KuLg42NvbQy6XV7g7uVQqhUKhqM0yCSHEZJh0qD/L6dOn0alTJ0RGRmLmzJkAygO8pKREbz2FQgFbW9sq9alSqXSLRqMxes11QSAQIDY2tvofrtRTdLyqh45X9VX1mGk0Gr0MMli1R+F5EBsbq/uglDHG9u3bx+zt7dnatWv11tu9ezdr3bq17rFarWYNGjRgSUlJz+xfqVRW+IAiNjbWmLtACCHP9OhuUo8vSqWy2v2Y3dttSkoKhg0bhvXr12PixIl6z4WFhSEzMxMbN26EUqnEwoUL4e/vjxYtWlSpb7lcDqVSCaVSiZiYmNoonxBCKhUTE6PLn8dvel5dZhfqq1evhlwux7hx42Bra6tbjh07BhsbG+zevRsrV66Es7MzDh48iO3bt1e570cfZIhEIgiFwlrcC0II0ScUCvUyyFAmfUljXVGpVBCLxVAqlfSJPiGEdzXJJLM7UyeEEPJ0FOqEEGJBKNQJIcSCUKgTQogFoVAnhBALQqFOCCEWhEKdEEIsCIU6IYRYEAp1QgixIBTqhBBiQSjUCSHEglCoE0KIBaFQN5AyMws5u/bxXQYhhOgx6XuUmrLrU2ag+MwFiD3cYdc2mO9yCCEEAJ2pG8wvLgYQCnA9ajpUuXl8l0NIpS6E9ceFsP58l0HqEIW6gWQtA+Az410o7z1A6vSPwLRavksihBAK9Zpweb03nHu+ivxDR3Dvu/V8l0MIIRTqNcFxHBrPeAfWPt64vWg5Ck+f5bskQkg9R6FeQ0Iba/jPnw2ByAopb8+AKieX75IIIfUYhboR2Pj5oPH7U6F8kImUd2fR+DohhDcU6kbi0vs1uPTtiYIjx3H36zV8l0MIqaco1I3Ie1oUbPx8kbH4KxT8fZrvcggh9RCFuhEJra3RZP7HEEjESJnyAZTZD/kuiRBSz5hFqC9btgwRERG6x4mJiWjTpg1kMhlCQ0Nx48aNKj1XF2x8vOHzwbtQZWUjdRpdv04IqVsmHeplZWWIiYlBdHS0rq20tBSDBw9GdHQ08vLy0KNHD13gP+u5uuTcI0w3vn5/TXydb58QUn+ZdKhHRETg/PnziIyM1LUdPnwYTk5OCA8Ph1gsxpw5c3D58mUkJyc/87m65v1eFKwbe+H2omUo/vdynW+fEFI/mXSoL1u2DLt27YK7u7uuLTk5GYGBgbrHQqEQ/v7+SEpKeuZzdU1oY40mMR8C4JDy9gxoiovrvAZCSP1j0qHu4eFRoU0ul0Mqleq1SaVSKBSKZz5XFSqVSrdoNBrDC3+07eb+8Ioaj9L020ib+0mN+yOEWC6NRqOXQYYy6VCvjFQqRUlJiV6bQqGAra3tM5+rCplMBrFYDLFYjLi4OKPU6zp0IBp0fAnZP/+B7N92GqVPQojliYuL0+WPTCYzuB+zC/XAwEBcv35d91ij0SA1NRUBAQHPfK4q5HI5lEollEolYmJijFIvx3Hw/WgGRE6OSPt4HkrTbxulX0KIZYmJidHlj1wuN7gfswv1sLAwZGZmYuPGjVAqlVi4cCH8/f3RokWLZz5XFSKRSLcIhUKj1SxyaAC/udHQyBW4PnUmtDX404oQYpmEQqFeBhnK7ELdxsYGu3fvxsqVK+Hs7IyDBw9i+/btz32Ob/Ztg+EePgzyC/8iY8lXfJdDCLFQHGOM8V0E31QqFcRiMZRKZbXeIdW374AplVVeX6tW49o70ZAnX0eLH7+HwyudDCmXkCp7dNej4MO7eK6EVIehmQSY4Zm6ORNYWaHJf2ZBYGOD1OkfQZWXz3dJhBALQ6FexySNPNB4WhRUmVm4+dE80B9KhBBjolDngXOv7nDs2hm5u/bhIV3mSAgxIgp1Hjy6DZ7IyRFpcxag7M5dvksihFgICnWeiBwawPej96EpKkYKzeZICDESCnUeNejQDg0H90fRqX9wf80PfJdDCLEAFOo884qaUD6b4+dfQp50je9yCCFmjkKdZ0Jra/jNmQlotEh9Nxra0jK+SyKEmDEKdRMgC2wOj3FvQJF8Hbe/+JLvcgghZoxC3UR4jB4JWctA3F8Tj4ITp/guhxBipijUTQRnJYTf3GgIrCVInTGbbqpBCDEIhboJsfb0gNfkCVDeuYdbcYv5LocQYoYo1E1Mw4F9YdemNTI3b0P+0RN8l0MIMTMU6iaGEwjg++H7ENjY4MYHc6AuomEYQkjVUaibIImHG7ynvAXlvQe4teBzvsshhJgRCnUT5fJ6H9i1DUbWjz8jP+EY3+UQQswEhbqJ4jgOvh9Oh0AqxY0P5kJdUMh3SYQQM0ChbsIkbq7wnjoRygeZSJ+/iO9yCCFmgELdxLn06wX79m2Rve035B06wnc5hBATR6Fu4jiOg2/0NAhlUtyIjoE6v4DvkgghJoxC3QyIXV3gPXUSVJlZuPUJfSmJEPJ0FOpmwrlvj/KrYX76BQXHaW4YQkjlzDbUjxw5gtatW8Pe3h4vvfQSEhMTAQCJiYlo06YNZDIZQkNDcePGDZ4rNQ6O4+A7810IrCW4ER0DTUkJ3yURQkyQWYa6RqPB0KFDsXTpUhQUFGD8+PEYOXIkSktLMXjwYERHRyMvLw89evRAREQE3+UajaSRBxq9NRZltzOQsWQl3+UQQkyQWYZ6Xl4ecnJyoFKpwBiDUCiEjY0NDh8+DCcnJ4SHh0MsFmPOnDm4fPkykpOT+S7ZaNyGDoCsRXPcXxOP4ouX+C6HEGJizDLUXVxcMHHiRPTr1w9isRgzZ87Ehg0bkJycjMDAQN16QqEQ/v7+SEpK4rFa4+KEQvhETwPHcbjxwVxoVSq+SyKEmBCzDHWNRgN7e3vs378fcrkcn3zyCYYPH46ioiJIpVK9daVSKRQKBU+V1g6pvx/cR4+A4uo13Pv2e77LIYSYELMM9V9//RXJycno2bMnJBIJpk2bBmtrawBAyRMfICoUCtja2lapX5VKpVs0Go3R6zYmjzdHwdrHG3eWr0JJ6k2+yyGE1JBGo9HLIEOZZajfuXMHSqVSr00kEqFt27a4fv26rk2j0SA1NRUBAQFV6lcmk0EsFkMsFiMuLs6oNRubQCyC76xpYCoVbkTHgGm1fJdECKmBuLg4Xf7IZDKD+zHLUO/evTuOHz+O33//HVqtFj/88ANycnLQpUsXZGZmYuPGjVAqlVi4cCH8/f3RokWLKvUrl8uhVCqhVCoRExNTy3tRc7atWsJ1UH8UnT6LzI1b+S6HEFIDMTExuvyRy+UG92OWof7iiy9i8+bNmDt3LhwdHbF27Vrs2bMHDRo0wO7du7Fy5Uo4Ozvj4MGD2L59e5X7FYlEukUoFNbiHhiP56RxELu54vZnS1F2P5PvcgghBhIKhXoZZCiOMcaMWJdZUqlUEIvFUCqV1TqY6tt3wJ4YBuJD/olEpM6eD6f+vRGw+ku+yyEm5EJYfwBA8OFdPFdCqsPQTALM9Eyd6HPo3AEOoZ2Qu2sf8v7vKN/lEEJ4RKFuIRq/FwWBjQ3SZi+gKQQIqcco1C2E2NUFjSaMQVnGHdz98lu+yyGE8IRC3YK4DRkAm6ZNcO+79VBcS+G7HEIIDyjULQhnJYTPzHfBNBrc/HgeXbtOSD1EoW5hbFsEoOHAvihKPIvsn3/nuxxCSB2jULdAnhPHQeTkiFtxi6HKzeO7HEJIHaJQt0BWdrbwfmcS1Hn5dPs7QuoZCnUL5fjqK7Bv1wbZ235D4al/+C6HEFJHKNQtFMdxaPz+VHBiEW7OXkDzrhNST1CoWzBrr0Zwf2M4Sq6lIDP+R77LIYTUAQp1C+cePgxid1dkLF0JZVY23+UQQmoZhbqFE1pbw/udSdAUFeP2wiV8l0MIqWUU6vWAQ5eOsG/fFtm/7EDhP+f4LocQUoso1OsBjuPQ+L3J4KyskDZ7PpiJ36qPEGI4CvV6wtrbC24jh0CRdA2Zm+guSYRYKgr1esTjzVEQNXTB7c9XQJWTy3c5hJBaQKFejwhtrOE9NRKawkLc/mwZ3+UQQmoBhXo949itC+xCXkTWT7+g6NxFvsshhBgZhXo9w3EcGk97G5xQiLQ5C+hDU0IsDIV6PWTj2xiuwwdB/u8VZG39le9yCCFGRKFeTzUa9wZETo64/fmXUBcW8V0OIcRIKNTrKaFUCs/IcVDn5OLOl6v4LocQYiRmG+o3btxA9+7dYWtri4CAAOzduxcAkJiYiDZt2kAmkyE0NBQ3btzguVLT5dz7NUgDmuHB+k0ouZnOdzmEECMwy1DXarUYNGgQXn31VRQWFuKrr77CiBEjUFxcjMGDByM6Ohp5eXno0aMHIiIi+C7XZHECAbzfnQSmUuPWgs/5LocQYgRmGep///03SkpKMHv2bAgEAvTq1QvHjh3DsWPH4OTkhPDwcIjFYsyZMweXL19GcnIy3yWbLLsXguD0alfkHTyM/CPH+S6HEFJDZhnqFy5cQMuWLTF16lS4uroiJCQExcXFSE5ORmBgoG49oVAIf39/JCUl8Vit6fOMGg+BRIL0eZ+BqdV8l0MIqQGzDPW8vDzs2bMHL774Iu7cuYNZs2Zh4MCBKCoqglQq1VtXKpVCoVBUqV+VSqVbNPXo+m2JmyvcRg1FyfUbeEDzwhDCC41Go5dBhjJ6qKvVami1WmN3q0csFsPHxweTJ0+GWCzGqFGj4OnpCQAoKSnRW1ehUMDW1rZK/cpkMojFYojFYsTFxRm9blPm/sYwiBq64M6SlVDl5fNdDiH1TlxcnC5/ZDKZwf3UONTlcjm++eYb9OnTBy4uLpBIJBCLxXBzc0P//v3x3XffoajIuNdBN2/eHIWFhXptGo0GwcHBuH79ul5bamoqAgICqrwvSqUSSqUSMTExRq3Z1AltrOE1eTzU+QW4s+xrvsshpN6JiYnR5Y9cLje4H4NDXa1WY+HChfDy8sLatWsRHByMFStWYO/evdi5cyeWLFmCgIAArFu3Dj4+PliwYEGN/qR4XI8ePSAUCvHZZ59Bq9Vi8+bNePDgAcLCwpCZmYmNGzdCqVRi4cKF8Pf3R4sWLarUr0gk0i1CodAotZoTp9e6QRbUAg82/ATF9VS+yyGkXhEKhXoZZCiOMcYMeWFISAheeeUVvPfee2jSpMkz17169Sq++eYbHD9+HBcuXDBkc5X2+fbbb+P8+fNo3LgxVq1ahdDQUJw9exZRUVFITk5GcHAw4uPj4e/v/8y+VCoVxGIxlEpltQ6m+vYdMKWyprtiUuRXr+Nq1HQ06NoZLbasA8dxfJdEauBCWH8AQPDhXTxXQqrD0EwCahDq6enp8PX1rfXX1AUKdX1pny5Fzv5DCIz/Fo49wvguh9QAhbp5qkmoGzz88ng4Z2RkVLpOaWkpNm7cWOlriOnynBQBgY010uO+gNZIQ2aEkLphlKtffH19MWbMGJSWluq1FxQUYPz48cbYBKlDYhdnuI8ahtIbacjasp3vcggh1WCUUGeM4fTp0+jYsSPS09ON0SXhmdvIIRC5OCNj6dc0iyMhZsQooc5xHPbv3w9/f3+0a9cOBw4cMEa3hEdCG2t4ThwLdW4e7q5czXc5hJAqMtqZukwmwy+//IIpU6agf//+WLRoUb28LNCSOPd8FTZNm+D+uo0ozbjDdzmEkCow2pn6IwsWLMDmzZsRFxeHt956yxjdE55wQiG8p0wEUypxe9FyvsshhFSB0c7UHzdixAgcO3YM586dM0b3hEf2bYPRoONLyPljN4rO/8t3OYSQ5zBKqGu1Wri6uuq1hYSE4MyZM1i/fr0xNkF45BX1FiAU4NaCzyu8gRNCTIuVoS/899+qnbW1adPG0E0QE2Hj2xgN+/VG9p97kLv3IJz79uS7JELIUxgc6sHBweA4Tu/M7dHY+pNt9WkaW0vVaMIY5PyVgNsLl8DxtW4QiMV8l0QIqYTBoZ6Wlqb3mDGGVq1aYc+ePfDx8alxYcS0iBwd4DF6OO6u3YDMDT/BI3Ic3yURQiphcKhXFtwcx8HLy4tC3UK5DR+E7B17kLH8GzQcPghWDg34LokQ8gSzvPMR4YdAIoFn5DhoCgpxZ8W3fJdDCKkEhTqpFqfXukEa0AwPftiM0vTbfJdDCHkChTqpFk4gKP9CkkqN258t47scQsgTDB5T/+qrryq0qdVqxMfHw8XFRa/9vffeM3QzxATZBb8Ahy4vI2fXPhT9cw52L4XwXRIh5L8MvkmGn59f1TbAcbh586Yhm6gzdJOM6ivNuIMr496GLPgFtNrxE90hyUTRTTLMU01ukmG0SxpJ/WLt7QWXAX2Q/fsu5O7eD+f+vfkuiRACI42pnz17ttL2goICTJ482RibICaoUcRoCKRS3Fq4FNp6+hcLIabGKKH+2muvITExUa9t+/btCAwMxK5d9GefpRI5NIDHmBEou52BzA0/8V0OIQRGCvUZM2agZ8+eOH78OG7fvo1+/fph9OjRGD58OK5evWqMTRAT5TZsIMSuDZGx/Buo8wv4LoeQes/gMfXHxcTEwNHREX369AEABAUF4fTp0zSZVz0gkEjgOXEs0j5dijsrV8M3ZhbfJRFSrxntOvV33nkHq1atgkqlQmxsbJ0FelJSEqytrXX3Rk1MTESbNm0gk8kQGhqKGzdu1Ekd9ZlTjzBIm/njwfpNKL1Nd0gihE8Gh7qjoyOcnJz0lmnTpkGj0WDgwIF67bVFrVZj/PjxKCsrAwCUlpZi8ODBiI6ORl5eHnr06IGIiIha2z4pxwkE8JryFphShduL6AtJhPDJ4OGX5cuX835t8meffYYuXbrg9OnTAIDDhw/DyckJ4eHhAIA5c+Zg+fLlSE5ORmBgIJ+lWjz7kGA06NgeOTv2oCgyAnZtWvNdEiH1ksGhzvcZ8MWLF7Ft2zb8888/WLas/OzwyfAWCoXw9/dHUlIShXod8IqagILTZ3Ar7nME/bqZ9zd9Quojg4dfunTpgoSEhCqvf+DAAXTq1MnQzelRKpUYP348Vq9eDRsbG127XC6HVCrVW1cqlUKhUBhlu+TZyu+Q1AtFiWeRt/8Q3+UQUi8ZfKa+atUqTJo0CSUlJRg2bBj69OmDoKAgXcgWFxfj4sWLSEhIwKZNm2Bra4t169YZpegFCxagW7du6Ny5s167VCpFSUmJXptCoYCtrW2V+lWpVLqfBQIBhEJhzYutZxpFjEbOXwm49cliOHTvCkE1v+JMSH2l0Wig1WoB6GdRdRl8pt66dWv8/fffWLBgARISEtCxY0fY2tpCJpNBKpWiQYMG6N69O44cOYLPP/8cZ86cQXBwsMGFPu6XX37B999/DwcHBzg4OOjqcXd3x/Xr13XraTQapKamIiAgoEr9ymQyiMViiMVixMXFGaXW+kbk7AT3N4ahNO0WMjdv47scQsxGXFycLn9kMpnB/Rg8odeTiouLce7cOWRmZkIgEMDDwwOtW7eu8llyTXAch7S0NLi5ucHPzw9ffPEFRo0ahUWLFmHHjh1PncbgkUeT58jlct3kOVU5U6/PE3o9i6a0FJdHR4JpNGhz8iCs7O34Lqneogm9zMeTZ+oymaxuJ/R6kq2tLV555RVjdWcQGxsb7N69G1FRUZg6dSqCg4Oxffv2Kr9eJBJV+wCSioTW1vCcOBbpi5bj7jdr4PPxB3yXRIjJEwqFRhnyNVqo8+nxPzbatm2Lf/75h8dqCAA493wVmT//gftrN8B97BuQeDbiuyRC6gW68xGpFZxQCK+33wIrU+L2oi/5LoeQeoNCndSaBi+FwL59Ozz87U8U/3uZ73IIqRco1Emt8n57AiAQ4NaCL2Ckz+QJIc9glDH13NxcxMbG4vz58ygpKanwj/fcuXPG2AwxQzZNfOHS5zU83H0A+X8lwLFHGN8lEWLRjBLqEyZMQGJiIkaOHAlHR0djdEksSKMJbyL30FGkf7IYDmGh4Kws4vN5QkySUf51HTx4EAcPHjTaNADEsohdnOE2agjux/+IzB9/gfvYUXyXRIjFMsqYupOTk+6bnYRUxn3kUIicnXBn6Upoiov5LocQi2WUUI+OjsbMmTORlZVljO6IBRJKbdBowhioHubg7qrv+S6HEItl8PCLo6Oj3tSq+fn58PDwgK2tbYVvReXm5hpeIbEYLn16IPOXHbi/+ge4jRkJSSN3vksixOIYHOpffvmlEcsg9QEnFMI7agJSPoxFxuIVaLr8M75LIsTiGBzq48aNM2YdpJ6w79AOdu3aIPvnP+AxcRxkQXTzEkKMib58ROoUx3HwjpoAALgVR19IIsTYKNRJnZM284dzr+4oOHYS+QnH+S6HEItCoU544fnWWAgkEtyK+xxMrea7HEIshsGhPnv2bCQkJNTotkuk/hK7usBtxCCUXEtF1vbf+S6HEIthcKjLZDLExsbCzc0N/fv3x1dffYVr164ZszZi4dzDh8PK0QEZi1dAI5fzXQ4hFsHgUJ8zZw6OHDmC27dvY9KkSbh27Rr69+8PHx8fREZG4ueff0ZeXp4xayUWRiiVotH40VBlPcS91T/wXQ4hFqHGY+q2trYYMGAAvvnmG6SkpCAhIQFt27bFjz/+CH9/f3To0MEYdRIL1bBfb1j7eOPequ+hzKRvJBNSU0b/oNTPzw9RUVH4/fffkZ2djaVLlxp7E8SCcFZCeE2eAG1JCTKWrOS7HELMXq1e/SIUCtGlS5fa3ASxAA06tYddcGtkbf0V8qv0uQwhNUGXNBLecRwHrylvAVotbi34nL6QREgNUKgTkyALaAbn3q+h4OhJ5O0/xHc5hJgtCnViMrwmRUAokyJ93mfQlJTyXQ4hZsngUJ80aRKKn7jZwdmzZ/W+jJSTk4PmzZsbXt0z7NixA0FBQbC3t0e7du1w4sQJAEBiYiLatGkDmUyG0NBQ3Lhxo1a2T4xP5OwEj4jRKMu4i3vfruO7HELMksGh/v3330OhUOi1hYWFISMjQ/dYrVbXSqimpaVh7NixWLVqFfLz8/H+++9jwIABKCoqwuDBgxEdHY28vDz06NEDERERRt8+qT2uQ16HtW9j3P16LUoz7vBdDiFmx+BQr+zDrLr6gOv27duIjIxE165dIRAIMHr0aADAV199BScnJ4SHh0MsFmPOnDm4fPkykpOT66QuUnMCKys0fi8KrKwMt+Z/znc5hJgdsxxT79q1K5YsWaJ7fOrUKSgUCqjVagQG/m9+bqFQCH9/fyQlJfFRJjGQfdtgOHbtgty9B5F/hGZxJKQ6zDLUH5eamoqhQ4ciLi4OQqEQUqlU73mpVFphmOhpVCqVbtFoNLVRLqkir6kTIZBIkBazEFqlku9yCKl1Go1GL4MMZdahfvr0aXTq1AmRkZGYOXMmpFIpSkpK9NZRKBSwtbWtUn8ymQxisRhisRhxcXG1UTKpIombK9zHjEDpjTQ8WL+J73IIqXVxcXG6/JHJZAb3Y/Dt7ABg3bp1eoGpVqsRHx8PFxcXAEBRUVFNun+m/fv3Y8SIEVi6dCkmTpwIAAgMDMSGDRt062g0GqSmpiIgIKBKfcrlcohEIgCAQGDW73cWwX3kUOTs/QsZy76B84B+dKNqYtFiYmIwZ84cAOWjBoYGO8cM/HTT19cXHMdVad20tDRDNvFUKSkpCAkJQXx8PIYOHaprLykpgZ+fH7744guMGjUKixYtwo4dO3D27Nln9qdSqSAWi6FUKnWhXhXq23fAaGigVuWf+gepH8bCqU8PBKyjuWGq60JYfwBA8OFdPFdCqsPQTAJqcKaenp5u6EtrbPXq1ZDL5Rg3bpzeDbD37t2L3bt3IyoqClOnTkVwcDC2b9/OW52k5hxefgmO3co/NM3dfwhOvbrzXVKtOHDgAC5fvoy3334bNjY2fJdDzJjBZ+qWhM7UTZsyJxdX3pwEob09ghN2QVjFz0jMxalTp9CxY0cAQHh4OLZs2WK0vulM3TzV5EydBo6JyRM7O8Fz0ngo7z9AxmLLG4KJi4uDQCBAs2bN8OOPP+Lq1at8l0TMGIU6MQsNB/SBrGUg7q/fhOJ/L/NdjtHk5eXhwIED6NmzJ9auXQsA2Lx5M89VEXNGoU7MAicQwGfmu+A4Djdn/QdMrea7JKPYuXMn1Go1hg8fji5duqBhw4bYuXMn32URM0ahTsyG1N8PbqOGQH4pCffXbeS7HKM4evQoAKB3794QCoXo168fLl26hFu3bvFcGTFXFOrErHiMfQMSz0a4/cUKlKTe5LucGjt9+jS8vLzQqFEjAEDPnj0B/C/sCakuCnViVoTW1vD96H0wpRKp738MZsbTORQXF+PKlSt6N2d/dPvH48fL57xJSkrC6tWrqzzVBSEU6sTs2LUOgtvwQSg+dxH31sTzXY7Bzp49C61Wi/bt2+vavL290bhxYxw/fhz3799HaGgooqKiMHnyZB4rJeaEQp2YJc+JYyHx9kTGFyuguJ7KdzkGOX36NADohTpQfraelJSEr7/+Grm5uQDKr4i5fv16nddIzA+FOjFLAokEfh9/AKZWI3X6x2Z1NYxWq8WGDRuwe/duCAQCtGvXTu/5R0MwP/30E1xcXHDw4EEAwA8//ICsrCy8/vrrCA8Pr9W5lYj5qtGEXoTwyTYoEO4jh+DBT7/g7so18Hp/Ct8lVcnnn3+O2bNnAwCaNWtWYRbRzp07AyifM2nkyJF49dVX4ebmhp07dyIrKwu7dpV/O1QqlWLdOrrtH9FHZ+rErDUaPwY2TXyRsfwbFJ05z3c5z6VUKvHll1/qHlc2z0tQUJCuvUuXLhAIBOjXrx+uXLmCTZs2oUuXLnjllVfwww8/6N0+khCAQp2YOYFEjCaxH4ETCpHyzkyoC017SOLo0aPIysrCG2+8AQDIzs6usI5QKISnpycAoE2bNgCA/v3L53BRqVR488038cEHH0Cr1WLjRsu4Xp8YD4U6MXs2vo3h/U4kyjLu4uaHsXV2r1xDPBo6kUgkAID79+8jJyenwnqPnlf+d8K4V199VTfVde/evdGnTx+4ublhw4YNJr2/pO5RqBOL0HBAXziEdkLOn3uQvf03vsup1KZNm7BixQoIBAKkp6frZt9LTEyssO6jD0HPny8fUmrQoIHupglubm4QiUQYOXIkUlJSdOsQAlCoEwvBcRx8Z02DyNUFaXM+gfzqNb5L0qPVavHRRx/pfk5MTETLli0BoMJNXEpKSnDnzh0AwIkTJwCUD7uUlpYCAE6ePAkAGDlyJABg27Zttb8DxGxQqBOLYWVvB//Yj8CUSlyf+C7UBYV8l6Rz9uxZ3Lt3T/e4pKQEYWFhEAqFujPto0ePwsvLC1OmTIFWq4W7uztOnDgBxhiSk5Oh/u9lm/v27QMAvPzyy/D29sb27dtpCIboUKgTi2LbqiW835mE0vTbSJ32IZhWy3dJAIAdO3bofn50D9/Q0FAEBgbqQn3BggW4e/cu4uPjAQDBwcHIzMzEzZs3devY29tj//79AMrvoztixAikp6frvshECIU6sTgNB/eHU48w5B08jLsrvuO7HADAH3/8ASsrK9jb28PR0REA4O/vj+DgYKSnpyMlJQWHDh3Su+9v9+7lt+47duwYzp07BwDo1q0bLl68iPv37wP43xDM1q1b63J3iAmjUCcWh+M4+Mx8FzZNmyBj6Urk7j/Eaz2pqam4cuUKNBoNwsLCUFxcDAC4deuW7pLFn3/+GUD5F5OA8n0YNWoUOI7Dnj17cP78edjb22PIkCEAyu9pCgDt2rVDkyZN8PPPP0NrIn+VEH5RqBOLJLS2RtNP5sKqgT1Sps5E8cVLvNXyaOiFMYZ27drpzrITExMRHBwMAEhISABQfnYuFoshEAjg6emJDh06YN++fbhw4QKCg4PRu3dvANANwXAchxEjRuDu3bu6D1VJ/UahTiyWxMMdTT+NBdNokDzubZTductLHY+GXoDyLxYBgEgkwpkzZ3Rn6pcvX4a1tTWaNm0KpVIJjUaDW7duoX///igqKkJhYSFCQkLg5uaGNm3aYP/+/VCpVACAUaNGAaAhGFKOQp1YNNugQPjNmQlV9kNcHTu5zr9xmp2djZMnT0IqlcLV1RWXLpX/xdC6dWucOXMGjo6O8Pb2RmZmJtq2bYubN/9344+TJ09i4MCBuseP3gCGDx+O3Nxc/Pnnn7q+goKCsHnzZuTn59fdzhGTRKFOLJ5Tty7wipqAkmupSB47GZo6vOHEo7HuwsJC9O7dGzt37kS7du3QsWNH5ObmIj09HU2bNoVWq0Xbtm2RlJSke21iYiJatWoFNzc3AEBAQAAAYPz48bCyssKaNWsAlA/BREdHo7CwEKtWraqzfSOmySJDPTExEW3atIFMJkNoaChu3LjBd0mEZ26jhsJt1FAU/XMO1yZMhba0rE62++OPP+q+OdqoUSMUFxfjzTff1E23e/bsWdjb2wMAPDw8cPHiRQCAg4MDTp06BaD826TA/8bd3d3dMXDgQBw4cEB3qWN4eDh8fX3xxRdf6L64ROoniwv10tJSDB48GNHR0cjLy0OPHj0QERHBd1mEZxzHwStqAhoO6IuCY3/jetR0aP87r0ptOXv2LE6cOAGhUAgPDw/s3bsX1tbWGDVqlC7Uz5w5o/umqEAgwOnTp2Fra4tOnTrh/PnzkMvluHv3LiQSCb744gtkZmYCAGJiYsBxHKZNmwaNRgORSISvv/4aBQUFmDBhgm68ndQ/Fhfqhw8fhpOTE8LDwyEWizFnzhxcvnwZycnJfJdGeMZxHBq/PwXOPV9F3sHDuDbxXWhKSmtlW4wx3ZzppaWl6Ny5My5evIgpU6bA1dUVgYGBkEqlOHPmjG763NTUVJw5cwZt27ZFp06doFKpsGHDBsjlcvTq1Qu5ubl44403oFAo8OKLL2LKlCk4duwYZsyYAcYY+vXrh8jISBw8eBAjRoyg8fV6yuJCPTk5GYGBgbrHQqEQ/v7+emOVpP7iBAL4fvg+nHu/hvxDR3B19ESoi4qNuo3s7Gy89dZbOHDgADiOg4uLC/744w/4+vpizpw5AMp/Lzt06IBDhw4hKSkJIpEIa9euRXFxMXr06IGwsDAAwNSpUwEA7777LqZOnYrDhw+jQ4cO2Lp1K2bNmoUuXbrgq6++wiuvvII//vgDsbGxGDVqFP744w8EBAQgKysTcrkcmZmZNJVAfcEsTFxcHHvzzTf12kJDQ9mmTZue+hqlUskAMLlczpRKJVMqlUytVj9zO25ubozjuOov+N8CgBaeFg5g0+1d2clGAex7Fx/mKBDW6vb8/PzY5cuX9X6H1q1bp3u+R48eup+Tk5OZVqtlfn5+DABzdXVlKpWKaTQaFhcXx8RisW5dqVTKpFJpxf3jyn+/Njf0ZZsb+lb6/KOlSserkt/l6qxb35esrKznZpdardblj1wuZwCYUql87uueZHG3s5NKpSgpKdFrUygUFW4ZVplHU5sCQGxsLObNm/fUdRlj1T7z4TgO4B57/PgDM2Rw9Rz/+80BWFn8EMXQYoKtM9Y39MHH+feRoq75OLtAIIBEIoGrqyteeuklhIWFYcyYMXq/XwAwevRoJCQkQCaTYfbs2Xj77bfRpUsX3VUua9aswcKFCzFjxgzdde5z587FpEmT8Ouvv+Ls2bO4c+cOCgoKkJ+fj4KCApSWlkKlUkGj0UCj0fx32gEGgUDw1N9XzsD/H4a+7lme92+qsm1W999hdTzaXk23UZXXx8XFYf78+TXaDgBwrDaPCA/27NmDjz/+WHcVgUajgbOzM/7++2+0aNGi0teoVCqIxWLI5XLdlQoCgUD3RZGnUd++A1bLH7aR2vdw31+4tWQlOCsrNF2xCM79evFdktFcCCu/Y1Lw4V08V0KeR6PR6KZ6UKlUkMlkUCqVukyqKosbUw8LC0NmZiY2btwIpVKJhQsXwt/f/6mB/jiRSKRbnhfoxHK49H4NAV9+BoG1BNcnTUN67GfQltGbNalbQqFQL4MMZXGhbmNjg927d2PlypVwdnbGwYMHsX37dr7LIibOtlVLtFj9JWStWuL+ug241H8EFCn0/QZifixu+MUQj4ZfqvunDg2/WB6m1uDepp9wf+NWcFZCeL4XBc8pkRBIxHyXZhAafjFPhmYSYIFn6oTUBGclhOf4MQhc+QUkjTxwZ8lKXOwxEHmHj9ElgcQsUKgTUgnbVi3Rct1KeEaOQ1nGXSSPicSVYWNRdPYC36UR8kwU6oQ8hUAkgseYkXhhy1q49OuJotNncXnAKFweMho5ew+CaTR8l0hIBTSmDhpTJ1VTcisDD378Gbl/JYCp1RA3cofLoP5wGfI6ZC0C+C6vUjSmbp5qMqZOoQ4KdVI9ypxcZP+xGzn7D0GZmQUAsG7iC4eundHglc6w79AOVg3sea6yHIW6eaJQryEKdWIIptWi+FIScv9KQP6p01BlPdQ9J/Hxhu0LQbAJbAZrby9IGntB4uUJK0cHCG2sq78txsBUKmhLy6AtLYW2rOx/P5eWgT328+PP3125GuAAz3cmA0IBOIEQnFAAgY0NhLay8sXOFkJbW1g5OsDKoUGtfFOUVA+Feg1RqJOaYoyh9PYdFP5zDvLk61BcS0Vpxh2gkn9enFgMgZ0thLYyQCgEJxQCAgE4oQBMowFTqsDKyqBVqsCUSjCVCqxMCdTBjaU5sRgiVxeIXRtC7OYKiWcjWPs1hrWfD6z9fCHx9Civl9QqCvUaolAntUGjUKD0zj0o7tzDzBkz4CYUwV4ggJ1ACDuBEFJOAAEAIQAhx0EAQANAxRjKGIMKDCqmhZIxKP/bVsa0KEP5z0qm/W9befvKTz+DyMYGAokEnFgEgUSCtE+XAAzwmzMT0GrL3zS02vKzeUUJNAoFNIoSaORyqPMLocrNhephLlQ5uVDlF1R4I+HEItg09YcsKBCyVi0hDQqELKgFrOzteDjClotCvYYo1EltYoxBrVZX+G9VWVlZVRgSqWrb5XFRAIBWG76rft1qDZTZ2Si9cw9ld+6h9O49lGXcheJGGlTZD/XWtWnuD/v27WDXvi3s2odA4uVJwzg1UJNQt7hZGgkxNRzH6f5hisXm881UzkoIiYc7JB7uwEshes+p8gtQciMNitSbUFxLQfGlJGRu3obMzdsAAGJ3NzQI7QiHsFA0CO0EkZMjH7tQL1GoE0KqTeTQAKK2wbBvG6xrK8vMQvG/V1B8KQlFFy8h++c/kP3zH4BAANvgF+AQFgqnnq9CGtSCzuJrEYU6IcQoJG6ukPRwhXOP8rs2KbOyUXD6LApPn0XhmfMoPncRd5Z+DUljbzj36wmnfr1gG/wCBbyR0Zg6aEydWK6ajKkbk1athvzKVeQdPYm8Iyd0Y/JiTw849++NhsMGQdbSNL/AxQf6oLSGKNSJpTKVUH8c02ohv3odeUdPIC/hOJQPMgEA0qAWcB0+CC6D+0Pk4sxzlfyiUK8hCnViqUwx1B/HGEPx5STk7DuEvMNHoZErwFlZweHVV+A2ZiQcunWpl9fF09UvhBCzxHEc7F4Igt0LQWj83mTkHz+Fh/v+Qt5fCcg78H+QNPaC25uj4DpqKF1BU0V0pg46UyeWy9TP1J+mLDMLD3fuRfau/VDn5YMTi+Dcvw/cx4+GXciLfJdX62j4pYYo1ImlMtdQf0SrUiH/6Elk7diN4ouXAQB27duiUdQEOPYIAyewzNnDafiFEGKRBCIRnLp3hVP3rii5mY4H239H7sHDuDZhKqyb+KLRpAi4DBtk0CRplsoy3+YIIRbHpokv/D56Hy9sj4f76BFQZT3EzY/m4Vz7MNz58luoC4v4LtEkUKgTQsyK2NkJXpMi0PrnDfB+dzIEYjEyFq/AuQ7dkbHsa6gLCvkukVcU6oQQsySU2sBt2EC02rIWvh+9Dys7Ge4s/RrnOryK24u/giovn+8SeWGWoX7lyhWEhYXBwcEBTZo0wdq1a3XPZWdno2/fvrCzs0OzZs2wb98+HislhNQ2gZUVXPr0QKuNa+A3+wNYOTTA3S9XlYf7ouX17szdLEN9yJAh6NevH3JycvD777/j448/xokTJwAAkyZNQpMmTZCTk4OVK1ciPDwc+fn5/BZMCKl1nJUQzr26o9WG7+AXMwtiF2fcXbka5zq+hrur1kFTUsJ3iXXC7EI9JycH/v7+mDFjBoRCIV588UV07doVp06dQnFxMXbu3InY2FiIxWL07t0bnTt3xtatW/kumxBSRzihEM6vdUPQD6vgN/sDCG1scHvhEpzv3AuZm7dBq1LxXWKtMrtQd3Z2xp49eyD47/WpBQUFOH78OF544QWkpKTAwcEBDRs21K0fEBCApKQkvsolhPCEE/73zH3TGni/FwVWVoabH8biYrd+eLhjD1gd3B6QDyYb6vv27QPHcRWWiIgI3ToKhQKDBw9G+/bt0aNHD8jlckilUr1+pFIpFApFHVdPCDEVArEIbkMH4IWfvkejCWOgzHqIlCkzcKn/CBSePst3eUZnsl8+6tWrF1SV/Jn06Aw9KysL/fv3h4uLC7Zv3w6O4yCVSlHyxLiZQqGAra1tlbb5+PYEAgGE9XAiIUIslVAqRaNx4Wg4sB/ub96G7N924srg0XDq3xs+c2bCurEXr/VpNBpo//vXQ2XZV1Ume6bOcRysrKwqLAKBALdu3cLLL7+MF198EX/++SdsbGwAAE2bNkV+fj5yc3N1/Vy7dg0BAVWbp1kmk0EsFkMsFiMuLq5W9osQwi+RQwM0fmcSgjZ+B4cuLyN31z5c6NoXtz5bCnVRMW91xcXF6fJHJpMZ3I/Zzf2iUqnQpk0bdO/eHStWrKjw/IABA+Dp6Ynly5fjyJEjGDlyJJKTk+Hu7v7MPsViMeRyuW6ehaqcqdPcL8TUmfvcL3Wh8NwFZHyzDiWpNyFycYb3rGlwHTW0zqf8ffJMXSaTGTT3i8meqT/N/v37ceXKFaxbtw62tra65dNPPwUArFu3Dvfv34e7uzvee+89bN269ZmB/jiRSKRbaOiFkPrBPiQYLdesgE/0e2BaLW7O+g/+7T0URf+cq9M6hEKhXgYZyuzO1GsDzdJILBWdqVePRqHA/c3bkLntdzC1Gg1HDIbPnJl1fiemmszSaHZn6oQQUluEUim8Jo1HUPwq2Ldrg+ztv+N8aG88iN8CptHwXV6VUKgTQsgTrL290GzJJ/BfMBsCiQRpc+Lwb99hKDp7ge/SnotCnRBCKsFxHBy7dkGrjavhHj4cJVev4/KAUbgxcy5UuXl8l/dUFOqEEPIMQqkNvCaPR8v138Au5EVk/fQLLrzSB9m/7IApfiRJoU4IIVVg49sYzZd9Cr+YWQCA1Gkf4mr4Wyi9lcFzZfoo1AkhpIo4joPza93QauNquPTtiYKjJ3Hx1ddxd9U6MLWa7/IAUKgTQki1WdnbwffD6Wi+/DOIXJxxe+ES/Nt3GIovXuK7NAp1QggxlH3Iiwha/w083hyJkuQUXOo/EunzPoNGLuetJgp1QgipAYFEDM+J49By3UrIApvj/toNuPDq68g/eoKfenjZKiGEWBibJr4I/HoxGk97G+qcXFx94y2kfjCnzm+nZ7JT75oFKytwpndFEyH/w3Hl/xGJeS6kfuBEgNvIoXB4pTPSFy1H9tZfkX/4GFr98WOdTe1Lc7+gZvMsEEJIZRhjyN72G3L3H0LA91+DE1R9YKQmmUShDgp1QohpoQm9CCGEAKBQJ4QQi0KhTgghFoRCnRBCLAiFOiGEWBAKdUIIsSAU6oQQYkEo1AkhxIJQqBNCiAWhUCeEEAti1qFeUlKCgIAAxMfH69qys7PRt29f2NnZoVmzZti3bx9/BRJCSB0z61D/+OOPkZqaqtc2adIkNGnSBDk5OVi5ciXCw8ORn5/PT4GEEFLHzDbUjx49ilOnTqFTp066tuLiYuzcuROxsbEQi8Xo3bs3OnfujK1bt/JYKSGE1B2zDPXi4mJERUVh/fr1EAqFuvaUlBQ4ODigYcOGuraAgAAkJSXxUSYhhNQ5k71Jxr59+9CnT58K7ePGjYONjQ3Gjh2Lli1b6j0nl8shlUr12qRSaZWHX1Qqle5ngUCg94ZBCCG1SaPRQKvVAtDPouoy2TP1Xr16QaVSVVjeeOMNnDt3DtHR0RVeI5VKUVJSotemUChga2tbpW3KZDKIxWKIxWLExcUZZT8IIaQq4uLidPkjk8kM7sdkQ53jOFhZWVVYfv31VyQlJcHZ2RkODg44fvw4pkyZgilTpqBp06bIz89Hbm6urp9r164hICCgStuUy+VQKpVQKpWIiYmprV2rVRqNBvPmzYNGo+G7FLNAx6t66HhVX1WPWUxMjC5/5HK5wdsz+zsfdevWDREREYiIiAAADBgwAJ6enli+fDmOHDmCkSNHIjk5Ge7u7k/tw5LufGRJ+1IX6HhVDx2v6jPkmNXkOJvsmLqh1q1bh0mTJsHd3R1ubm7YunXrMwOdEEIsidmfqRuDUqmERCKBXC43+7MPlUoFmUxmEftSF+h4VQ8dr+oz5Jg9ek1ZWRnEYnG1tkehjvIPU2vywQQhhNSGyq7oex4KdQBarRalpaWwsrICx3F8l0MIqecYY1Cr1bC2toZAUL3rWSjUCSHEgpjsJY2EEEKqj0KdEEIsCIU6IYRYEAp1QgixIBTqhBBiQSjULczp06fRrFkzvTa6G1TlEhMT0aZNG8hkMoSGhuLGjRt8l2Syli1bppuKA6Bj9zQ7duxAUFAQ7O3t0a5dO5w4cQJAHR8vRizGli1bmKOjI/Px8dFrHzRoEJs6dSorKytje/fuZY6OjiwvL4+XGk1FSUkJ8/DwYFu2bGFlZWVs/vz5rEuXLnyXZXJKS0vZ3LlzmUAgYOPGjWOM0bF7mps3bzJ7e3uWkJDANBoN27x5M3NycmKFhYV1erwo1C3Ed999x1q2bMk+//xzvVAvKipiQqGQZWVl6dr69+/Pvv32Wx6qNB179uxhQUFBusdqtZo5ODiwq1ev8liV6Rk1ahTr168fmzx5si7U6dhVLiEhgX3wwQd6bU5OTuyTTz6p0+NFwy8WYtCgQbh06RLat2+v1053g6pccnIyAgMDdY+FQiH8/f3r/XF50rJly7Br1y69SfHo2FWua9euWLJkie7xqVOnoFAooFar6/R4UaibkX379oHjuApLREQE3NzcKv068dPuBqVQKOqqbJNEx6VqPDw8KrTRsXu+1NRUDB06FHFxcRAKhXV6vCjUzcjT7ga1fv36p76mpneDslR0XAxHx+7ZTp8+jU6dOiEyMhIzZ86s8+NFoW5GnnY3qGdN+FPTu0FZqsDAQFy/fl33WKPRIDU1td4fl6qgY/d0+/fvR48ePfDpp59i3rx5AOr+eFGoWzh7e3v06dMHc+bMQWlpKfbv349jx45h8ODBfJfGq7CwMGRmZmLjxo1QKpVYuHAh/P390aJFC75LM3l07CqXkpKCYcOGYf369Zg4caKuva6PF4V6PbBu3Trcv38f7u7ueO+99+huUABsbGywe/durFy5Es7Ozjh48CC2b9/Od1lmgY5d5VavXg25XI5x48bB1tZWt5w5c6ZOjxdNvUsIIRaEztQJIcSCUKgTQogFoVAnhBALQqFOCCEWhEKdEEIsCIU6IYRYEAp1QgixIBTqhBBiQSjUCSHEglCoE0KIBaFQJ4QQC0KhTgghFoRCnRBCLAiFOiFVpFAo8MILL+DBgwe1uh2NRoOQkBCkpqbW6naIZaJQJ6SKYmNjMWjQoFqfi14oFGLu3LmIioqq1e0Qy0TzqRNSBVlZWfDz80NaWhpcXV1rfXuMMfj6+mLTpk145ZVXan17xHLQmTqpl+Lj48FxXIUlLCys0vW/++47tG/fXi/Qu3XrhoiIiEr7fSQiIgLdunXDmjVr4OvrC5lMhqFDh6KoqAh//vkngoKCYGtri969e+sN63Ach0GDBmHFihXG3XFi8az4LoAQPowcORK9e/fWPT5y5AjGjBmDWbNmVbr+rl27MGzYMIO2df78ebi7u2P37t148OABhg0bhmHDhoExho0bN0Kr1WLEiBGYNWsWNm7cqHtdnz59MGzYMKjValhZ0T9VUjX0m0LqJRsbG9jY2AAA0tLS8M477yA2NhZ9+vSpsK5Go8G5c+cQGxtr0LasrKwQHx8Pa2trBAUFYfjw4Vi3bh3u3bunG5+PjIzEypUr9V7XqlUryOVyJCUloXXr1gZtm9Q/NPxC6rWioiK8/vrr6Ny5M+bMmVPpOjk5OdBoNHBxcTFoG4GBgbC2ttY99vDwgIeHh94Hrh4eHsjMzNR7XcOGDQGgQjshz0KhTuotrVaL8PBwqNVqbNy4UW8s/HECgUC3/vNoNJoKbSKRSO8xx3GVtj15zcKj7T3aPiFVQcMvpN76+OOPceTIESQmJsLe3v6p6zk7O0MkEiE7O7vCc/fv39d7nJKSYrT6Hm2vti+hJJaFTgFIvbRp0yYsXrwY3377LZydnfHgwQPd8iSO49C2bVtcvHixwnOHDh3C+vXrkZaWht9++w2rV68GABw9erTCmXd1XbhwAfb29mjevHmN+iH1C4U6qZe+//57MMYwZswYuLm56ca5PTw8Kl2/f//+SEhIqNDet29fbN26FYGBgZg7dy5++OEHeHl5Ydy4cTUO9SNHjqBXr14VhmoIeRb68hEhVfDgwQP4+/vj2rVr8PLyAlB+nbqvry/i4+ONvj2NRoPGjRtjy5Yt6Natm9H7J5aLztQJqQJ3d3dERkbim2++qZPt/fbbb2jatCkFOqk2CnVCquiTTz7Bn3/+WeHDUWPTaDRYuHAh1qxZU6vbIZaJhl8IIcSC0Jk6IYRYEAp1QgixIBTqhBBiQSjUCSHEglCoE0KIBaFQJ4QQC0KhTgghFoRCnRBCLAiFOiGEWBAKdUIIsSAU6oQQYkEo1AkhxIJQqBNCiAWhUCeEEAtCoU4IIRbk/wEFv/J7Pl8hoAAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 375x375 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "trap[trap.power_tweezer] = 0.59* initial_power\n",
    "plot_solutions(trap,200,-1.5*zr,2*zr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "  0%|          | 0/150 [00:00<?, ?it/s]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      " 98%|█████████▊| 147/150 [10:15<00:02,  1.14it/s]<lambdifygenerated-1579>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -1.07417034054623e-38*z**2/(pi**5*(z**2/pi**2 + 1.00808875956951e-11)**3) + 2.68542585136557e-39/(pi**3*(z**2/pi**2 + 1.00808875956951e-11)**2)\n",
      "<lambdifygenerated-1580>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 6.44502204327736e-38*z**3/(pi**7*(z**2/pi**2 + 1.00808875956951e-11)**4) - 3.22251102163868e-38*z/(pi**5*(z**2/pi**2 + 1.00808875956951e-11)**3)\n",
      "<lambdifygenerated-1578>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 2.68542585136557e-39*z/(pi**3*(z**2/pi**2 + 1.00808875956951e-11)**2) - 2.76272760232557e-24\n",
      "<lambdifygenerated-1579>:2: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  return -1.07417034054623e-38*z**2/(pi**5*(z**2/pi**2 + 1.00808875956951e-11)**3) + 2.68542585136557e-39/(pi**3*(z**2/pi**2 + 1.00808875956951e-11)**2)\n",
      "<lambdifygenerated-1580>:2: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  return 6.44502204327736e-38*z**3/(pi**7*(z**2/pi**2 + 1.00808875956951e-11)**4) - 3.22251102163868e-38*z/(pi**5*(z**2/pi**2 + 1.00808875956951e-11)**3)\n",
      " 99%|█████████▊| 148/150 [10:16<00:01,  1.13it/s]<lambdifygenerated-1584>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 6.43808528192966e-38*z**3/(pi**7*(z**2/pi**2 + 1.00808875956951e-11)**4) - 3.21904264096483e-38*z/(pi**5*(z**2/pi**2 + 1.00808875956951e-11)**3)\n",
      "<lambdifygenerated-1582>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 2.68253553413736e-39*z/(pi**3*(z**2/pi**2 + 1.00808875956951e-11)**2) - 2.76272760232557e-24\n",
      "<lambdifygenerated-1583>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -1.07301421365494e-38*z**2/(pi**5*(z**2/pi**2 + 1.00808875956951e-11)**3) + 2.68253553413736e-39/(pi**3*(z**2/pi**2 + 1.00808875956951e-11)**2)\n",
      "<lambdifygenerated-1583>:2: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  return -1.07301421365494e-38*z**2/(pi**5*(z**2/pi**2 + 1.00808875956951e-11)**3) + 2.68253553413736e-39/(pi**3*(z**2/pi**2 + 1.00808875956951e-11)**2)\n",
      "<lambdifygenerated-1584>:2: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  return 6.43808528192966e-38*z**3/(pi**7*(z**2/pi**2 + 1.00808875956951e-11)**4) - 3.21904264096483e-38*z/(pi**5*(z**2/pi**2 + 1.00808875956951e-11)**3)\n",
      "100%|██████████| 150/150 [10:18<00:00,  4.12s/it]\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 375x375 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "trap[trap.power_tweezer] = initial_power\n",
    "plot_occupation(trap,200,-1.5*zr,2*zr,power_fac_down=0.56,power_fac_up=0.65,n_spill_steps=150)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### With lower magnetic gradient:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {},
   "outputs": [],
   "source": [
    "initial_power = 250 * si.uW \n",
    "\n",
    "trap: PancakeTrap = PancakeTrap(\n",
    "    power=0,  # Set pancake laser power to 0, no 2D trap\n",
    "    grad_z= 1 * si.G / si.cm,\n",
    "    grad_r=0,\n",
    "    power_tweezer=initial_power,\n",
    "    waist_tweezer=1.838 * si.um,\n",
    "    a=184.4*(4 * np.pi * const.epsilon_0 * const.value(\"Bohr radius\")**3)/(2 * const.epsilon_0 * const.c),\n",
    "\n",
    "    wvl = 1064 * si.nm,    \n",
    ")\n",
    "\n",
    "zr = float(trap.subs(trap.get_tweezer_rayleigh()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{\\omega_{t r}}{\\omega_{t ax}} \\approx 7.67$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "aspect_ratio = trap.get_omega_r_tweezer() / trap.get_omega_ax_tweezer()\n",
    "_aspect_ratio_latex = sp.latex(trap.omega_r_tweezer / trap.omega_ax_tweezer)\n",
    "display(Math(f\"{_aspect_ratio_latex} \\\\approx {trap.subs(aspect_ratio).evalf():.2f}\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-5.8525342246198116e-30\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 375x375 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "trap[trap.power_tweezer] = 0.58* initial_power\n",
    "plot_solutions(trap,999,-1.5*zr,2*zr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      " 84%|████████▍ | 126/150 [05:27<00:20,  1.16it/s]<lambdifygenerated-866>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 8.95310169976408e-40*z/(pi**3*(z**2/pi**2 + 1.00808875956951e-11)**2) - 9.2090920077519e-25\n",
      "<lambdifygenerated-867>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -3.58124067990563e-39*z**2/(pi**5*(z**2/pi**2 + 1.00808875956951e-11)**3) + 8.95310169976408e-40/(pi**3*(z**2/pi**2 + 1.00808875956951e-11)**2)\n",
      " 85%|████████▌ | 128/150 [05:29<00:18,  1.16it/s]<lambdifygenerated-874>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 8.93245657670543e-40*z/(pi**3*(z**2/pi**2 + 1.00808875956951e-11)**2) - 9.2090920077519e-25\n",
      "<lambdifygenerated-875>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -3.57298263068217e-39*z**2/(pi**5*(z**2/pi**2 + 1.00808875956951e-11)**3) + 8.93245657670543e-40/(pi**3*(z**2/pi**2 + 1.00808875956951e-11)**2)\n",
      " 86%|████████▌ | 129/150 [05:30<00:17,  1.18it/s]<lambdifygenerated-878>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 8.92213401517611e-40*z/(pi**3*(z**2/pi**2 + 1.00808875956951e-11)**2) - 9.2090920077519e-25\n",
      "<lambdifygenerated-879>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -3.56885360607044e-39*z**2/(pi**5*(z**2/pi**2 + 1.00808875956951e-11)**3) + 8.92213401517611e-40/(pi**3*(z**2/pi**2 + 1.00808875956951e-11)**2)\n",
      " 87%|████████▋ | 131/150 [05:32<00:16,  1.18it/s]<lambdifygenerated-887>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -3.56059555684699e-39*z**2/(pi**5*(z**2/pi**2 + 1.00808875956951e-11)**3) + 8.90148889211747e-40/(pi**3*(z**2/pi**2 + 1.00808875956951e-11)**2)\n",
      " 88%|████████▊ | 132/150 [05:32<00:15,  1.20it/s]<lambdifygenerated-891>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -3.55646653223526e-39*z**2/(pi**5*(z**2/pi**2 + 1.00808875956951e-11)**3) + 8.89116633058815e-40/(pi**3*(z**2/pi**2 + 1.00808875956951e-11)**2)\n",
      "<lambdifygenerated-892>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 2.13387991934116e-38*z**3/(pi**7*(z**2/pi**2 + 1.00808875956951e-11)**4) - 1.06693995967058e-38*z/(pi**5*(z**2/pi**2 + 1.00808875956951e-11)**3)\n",
      "<lambdifygenerated-890>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 8.89116633058815e-40*z/(pi**3*(z**2/pi**2 + 1.00808875956951e-11)**2) - 9.2090920077519e-25\n",
      "<lambdifygenerated-891>:2: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  return -3.55646653223526e-39*z**2/(pi**5*(z**2/pi**2 + 1.00808875956951e-11)**3) + 8.89116633058815e-40/(pi**3*(z**2/pi**2 + 1.00808875956951e-11)**2)\n",
      "<lambdifygenerated-892>:2: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  return 2.13387991934116e-38*z**3/(pi**7*(z**2/pi**2 + 1.00808875956951e-11)**4) - 1.06693995967058e-38*z/(pi**5*(z**2/pi**2 + 1.00808875956951e-11)**3)\n",
      " 89%|████████▉ | 134/150 [05:34<00:13,  1.18it/s]<lambdifygenerated-898>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 8.87052120752951e-40*z/(pi**3*(z**2/pi**2 + 1.00808875956951e-11)**2) - 9.2090920077519e-25\n",
      "<lambdifygenerated-899>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -3.5482084830118e-39*z**2/(pi**5*(z**2/pi**2 + 1.00808875956951e-11)**3) + 8.87052120752951e-40/(pi**3*(z**2/pi**2 + 1.00808875956951e-11)**2)\n",
      " 90%|█████████ | 135/150 [05:35<00:12,  1.17it/s]<lambdifygenerated-903>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -3.54407945840008e-39*z**2/(pi**5*(z**2/pi**2 + 1.00808875956951e-11)**3) + 8.86019864600019e-40/(pi**3*(z**2/pi**2 + 1.00808875956951e-11)**2)\n",
      "<lambdifygenerated-902>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 8.86019864600019e-40*z/(pi**3*(z**2/pi**2 + 1.00808875956951e-11)**2) - 9.2090920077519e-25\n",
      " 91%|█████████ | 136/150 [05:36<00:12,  1.16it/s]<lambdifygenerated-908>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 2.12397026027301e-38*z**3/(pi**7*(z**2/pi**2 + 1.00808875956951e-11)**4) - 1.0619851301365e-38*z/(pi**5*(z**2/pi**2 + 1.00808875956951e-11)**3)\n",
      "<lambdifygenerated-906>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 8.84987608447087e-40*z/(pi**3*(z**2/pi**2 + 1.00808875956951e-11)**2) - 9.2090920077519e-25\n",
      "<lambdifygenerated-907>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -3.53995043378835e-39*z**2/(pi**5*(z**2/pi**2 + 1.00808875956951e-11)**3) + 8.84987608447087e-40/(pi**3*(z**2/pi**2 + 1.00808875956951e-11)**2)\n",
      "<lambdifygenerated-907>:2: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  return -3.53995043378835e-39*z**2/(pi**5*(z**2/pi**2 + 1.00808875956951e-11)**3) + 8.84987608447087e-40/(pi**3*(z**2/pi**2 + 1.00808875956951e-11)**2)\n",
      "<lambdifygenerated-908>:2: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  return 2.12397026027301e-38*z**3/(pi**7*(z**2/pi**2 + 1.00808875956951e-11)**4) - 1.0619851301365e-38*z/(pi**5*(z**2/pi**2 + 1.00808875956951e-11)**3)\n",
      " 92%|█████████▏| 138/150 [05:38<00:10,  1.15it/s]<lambdifygenerated-915>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -3.53169238456489e-39*z**2/(pi**5*(z**2/pi**2 + 1.00808875956951e-11)**3) + 8.82923096141223e-40/(pi**3*(z**2/pi**2 + 1.00808875956951e-11)**2)\n",
      "<lambdifygenerated-916>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 2.11901543073893e-38*z**3/(pi**7*(z**2/pi**2 + 1.00808875956951e-11)**4) - 1.05950771536947e-38*z/(pi**5*(z**2/pi**2 + 1.00808875956951e-11)**3)\n",
      "<lambdifygenerated-914>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 8.82923096141223e-40*z/(pi**3*(z**2/pi**2 + 1.00808875956951e-11)**2) - 9.2090920077519e-25\n",
      "<lambdifygenerated-915>:2: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  return -3.53169238456489e-39*z**2/(pi**5*(z**2/pi**2 + 1.00808875956951e-11)**3) + 8.82923096141223e-40/(pi**3*(z**2/pi**2 + 1.00808875956951e-11)**2)\n",
      "<lambdifygenerated-916>:2: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  return 2.11901543073893e-38*z**3/(pi**7*(z**2/pi**2 + 1.00808875956951e-11)**4) - 1.05950771536947e-38*z/(pi**5*(z**2/pi**2 + 1.00808875956951e-11)**3)\n",
      " 93%|█████████▎| 139/150 [05:38<00:09,  1.17it/s]<lambdifygenerated-918>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 8.81890839988291e-40*z/(pi**3*(z**2/pi**2 + 1.00808875956951e-11)**2) - 9.2090920077519e-25\n",
      "<lambdifygenerated-919>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -3.52756335995316e-39*z**2/(pi**5*(z**2/pi**2 + 1.00808875956951e-11)**3) + 8.81890839988291e-40/(pi**3*(z**2/pi**2 + 1.00808875956951e-11)**2)\n",
      " 93%|█████████▎| 140/150 [05:39<00:08,  1.18it/s]<lambdifygenerated-923>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -3.52343433534143e-39*z**2/(pi**5*(z**2/pi**2 + 1.00808875956951e-11)**3) + 8.80858583835359e-40/(pi**3*(z**2/pi**2 + 1.00808875956951e-11)**2)\n",
      "<lambdifygenerated-924>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 2.11406060120486e-38*z**3/(pi**7*(z**2/pi**2 + 1.00808875956951e-11)**4) - 1.05703030060243e-38*z/(pi**5*(z**2/pi**2 + 1.00808875956951e-11)**3)\n",
      "<lambdifygenerated-922>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 8.80858583835359e-40*z/(pi**3*(z**2/pi**2 + 1.00808875956951e-11)**2) - 9.2090920077519e-25\n",
      "<lambdifygenerated-923>:2: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  return -3.52343433534143e-39*z**2/(pi**5*(z**2/pi**2 + 1.00808875956951e-11)**3) + 8.80858583835359e-40/(pi**3*(z**2/pi**2 + 1.00808875956951e-11)**2)\n",
      "<lambdifygenerated-924>:2: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  return 2.11406060120486e-38*z**3/(pi**7*(z**2/pi**2 + 1.00808875956951e-11)**4) - 1.05703030060243e-38*z/(pi**5*(z**2/pi**2 + 1.00808875956951e-11)**3)\n",
      " 94%|█████████▍| 141/150 [05:40<00:07,  1.19it/s]<lambdifygenerated-926>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 8.79826327682427e-40*z/(pi**3*(z**2/pi**2 + 1.00808875956951e-11)**2) - 9.2090920077519e-25\n",
      "<lambdifygenerated-927>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -3.51930531072971e-39*z**2/(pi**5*(z**2/pi**2 + 1.00808875956951e-11)**3) + 8.79826327682427e-40/(pi**3*(z**2/pi**2 + 1.00808875956951e-11)**2)\n",
      "<lambdifygenerated-928>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 2.11158318643782e-38*z**3/(pi**7*(z**2/pi**2 + 1.00808875956951e-11)**4) - 1.05579159321891e-38*z/(pi**5*(z**2/pi**2 + 1.00808875956951e-11)**3)\n",
      "<lambdifygenerated-927>:2: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  return -3.51930531072971e-39*z**2/(pi**5*(z**2/pi**2 + 1.00808875956951e-11)**3) + 8.79826327682427e-40/(pi**3*(z**2/pi**2 + 1.00808875956951e-11)**2)\n",
      "<lambdifygenerated-928>:2: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  return 2.11158318643782e-38*z**3/(pi**7*(z**2/pi**2 + 1.00808875956951e-11)**4) - 1.05579159321891e-38*z/(pi**5*(z**2/pi**2 + 1.00808875956951e-11)**3)\n",
      "<lambdifygenerated-925>:3: RuntimeWarning: overflow encountered in scalar multiply\n",
      "  return 4.36383363731854e-29*x0 - 4.36383363731854e-29*x0/(99197614347.6731*z**2/pi**2 + 1) - 9.2090920077519e-25*z\n",
      " 95%|█████████▍| 142/150 [05:41<00:06,  1.18it/s]<lambdifygenerated-930>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 8.78794071529494e-40*z/(pi**3*(z**2/pi**2 + 1.00808875956951e-11)**2) - 9.2090920077519e-25\n",
      "<lambdifygenerated-931>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -3.51517628611798e-39*z**2/(pi**5*(z**2/pi**2 + 1.00808875956951e-11)**3) + 8.78794071529494e-40/(pi**3*(z**2/pi**2 + 1.00808875956951e-11)**2)\n",
      " 95%|█████████▌| 143/150 [05:42<00:06,  1.10it/s]<lambdifygenerated-934>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 8.77761815376562e-40*z/(pi**3*(z**2/pi**2 + 1.00808875956951e-11)**2) - 9.2090920077519e-25\n",
      "<lambdifygenerated-935>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -3.51104726150625e-39*z**2/(pi**5*(z**2/pi**2 + 1.00808875956951e-11)**3) + 8.77761815376562e-40/(pi**3*(z**2/pi**2 + 1.00808875956951e-11)**2)\n",
      " 96%|█████████▌| 144/150 [05:43<00:05,  1.12it/s]<lambdifygenerated-940>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 2.10415094213671e-38*z**3/(pi**7*(z**2/pi**2 + 1.00808875956951e-11)**4) - 1.05207547106836e-38*z/(pi**5*(z**2/pi**2 + 1.00808875956951e-11)**3)\n",
      "<lambdifygenerated-938>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 8.7672955922363e-40*z/(pi**3*(z**2/pi**2 + 1.00808875956951e-11)**2) - 9.2090920077519e-25\n",
      "<lambdifygenerated-939>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -3.50691823689452e-39*z**2/(pi**5*(z**2/pi**2 + 1.00808875956951e-11)**3) + 8.7672955922363e-40/(pi**3*(z**2/pi**2 + 1.00808875956951e-11)**2)\n",
      "<lambdifygenerated-939>:2: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  return -3.50691823689452e-39*z**2/(pi**5*(z**2/pi**2 + 1.00808875956951e-11)**3) + 8.7672955922363e-40/(pi**3*(z**2/pi**2 + 1.00808875956951e-11)**2)\n",
      "<lambdifygenerated-940>:2: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  return 2.10415094213671e-38*z**3/(pi**7*(z**2/pi**2 + 1.00808875956951e-11)**4) - 1.05207547106836e-38*z/(pi**5*(z**2/pi**2 + 1.00808875956951e-11)**3)\n",
      " 97%|█████████▋| 145/150 [05:44<00:04,  1.15it/s]<lambdifygenerated-942>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 8.75697303070698e-40*z/(pi**3*(z**2/pi**2 + 1.00808875956951e-11)**2) - 9.2090920077519e-25\n",
      "<lambdifygenerated-943>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -3.50278921228279e-39*z**2/(pi**5*(z**2/pi**2 + 1.00808875956951e-11)**3) + 8.75697303070698e-40/(pi**3*(z**2/pi**2 + 1.00808875956951e-11)**2)\n",
      "<lambdifygenerated-944>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 2.10167352736968e-38*z**3/(pi**7*(z**2/pi**2 + 1.00808875956951e-11)**4) - 1.05083676368484e-38*z/(pi**5*(z**2/pi**2 + 1.00808875956951e-11)**3)\n",
      "<lambdifygenerated-943>:2: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  return -3.50278921228279e-39*z**2/(pi**5*(z**2/pi**2 + 1.00808875956951e-11)**3) + 8.75697303070698e-40/(pi**3*(z**2/pi**2 + 1.00808875956951e-11)**2)\n",
      "<lambdifygenerated-944>:2: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  return 2.10167352736968e-38*z**3/(pi**7*(z**2/pi**2 + 1.00808875956951e-11)**4) - 1.05083676368484e-38*z/(pi**5*(z**2/pi**2 + 1.00808875956951e-11)**3)\n",
      " 97%|█████████▋| 146/150 [05:45<00:03,  1.15it/s]<lambdifygenerated-948>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 2.09919611260264e-38*z**3/(pi**7*(z**2/pi**2 + 1.00808875956951e-11)**4) - 1.04959805630132e-38*z/(pi**5*(z**2/pi**2 + 1.00808875956951e-11)**3)\n",
      "<lambdifygenerated-946>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 8.74665046917766e-40*z/(pi**3*(z**2/pi**2 + 1.00808875956951e-11)**2) - 9.2090920077519e-25\n",
      "<lambdifygenerated-947>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -3.49866018767107e-39*z**2/(pi**5*(z**2/pi**2 + 1.00808875956951e-11)**3) + 8.74665046917766e-40/(pi**3*(z**2/pi**2 + 1.00808875956951e-11)**2)\n",
      "<lambdifygenerated-947>:2: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  return -3.49866018767107e-39*z**2/(pi**5*(z**2/pi**2 + 1.00808875956951e-11)**3) + 8.74665046917766e-40/(pi**3*(z**2/pi**2 + 1.00808875956951e-11)**2)\n",
      "<lambdifygenerated-948>:2: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  return 2.09919611260264e-38*z**3/(pi**7*(z**2/pi**2 + 1.00808875956951e-11)**4) - 1.04959805630132e-38*z/(pi**5*(z**2/pi**2 + 1.00808875956951e-11)**3)\n",
      " 98%|█████████▊| 147/150 [05:45<00:02,  1.15it/s]<lambdifygenerated-950>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 8.73632790764834e-40*z/(pi**3*(z**2/pi**2 + 1.00808875956951e-11)**2) - 9.2090920077519e-25\n",
      "<lambdifygenerated-951>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -3.49453116305934e-39*z**2/(pi**5*(z**2/pi**2 + 1.00808875956951e-11)**3) + 8.73632790764834e-40/(pi**3*(z**2/pi**2 + 1.00808875956951e-11)**2)\n",
      " 99%|█████████▊| 148/150 [05:46<00:01,  1.15it/s]<lambdifygenerated-954>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 8.72600534611902e-40*z/(pi**3*(z**2/pi**2 + 1.00808875956951e-11)**2) - 9.2090920077519e-25\n",
      "<lambdifygenerated-955>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -3.49040213844761e-39*z**2/(pi**5*(z**2/pi**2 + 1.00808875956951e-11)**3) + 8.72600534611902e-40/(pi**3*(z**2/pi**2 + 1.00808875956951e-11)**2)\n",
      "<lambdifygenerated-956>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 2.09424128306857e-38*z**3/(pi**7*(z**2/pi**2 + 1.00808875956951e-11)**4) - 1.04712064153428e-38*z/(pi**5*(z**2/pi**2 + 1.00808875956951e-11)**3)\n",
      "<lambdifygenerated-955>:2: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  return -3.49040213844761e-39*z**2/(pi**5*(z**2/pi**2 + 1.00808875956951e-11)**3) + 8.72600534611902e-40/(pi**3*(z**2/pi**2 + 1.00808875956951e-11)**2)\n",
      "<lambdifygenerated-956>:2: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  return 2.09424128306857e-38*z**3/(pi**7*(z**2/pi**2 + 1.00808875956951e-11)**4) - 1.04712064153428e-38*z/(pi**5*(z**2/pi**2 + 1.00808875956951e-11)**3)\n",
      " 99%|█████████▉| 149/150 [05:47<00:00,  1.12it/s]<lambdifygenerated-959>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -3.48627311383588e-39*z**2/(pi**5*(z**2/pi**2 + 1.00808875956951e-11)**3) + 8.7156827845897e-40/(pi**3*(z**2/pi**2 + 1.00808875956951e-11)**2)\n",
      "<lambdifygenerated-960>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 2.09176386830153e-38*z**3/(pi**7*(z**2/pi**2 + 1.00808875956951e-11)**4) - 1.04588193415076e-38*z/(pi**5*(z**2/pi**2 + 1.00808875956951e-11)**3)\n",
      "<lambdifygenerated-958>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 8.7156827845897e-40*z/(pi**3*(z**2/pi**2 + 1.00808875956951e-11)**2) - 9.2090920077519e-25\n",
      "<lambdifygenerated-959>:2: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  return -3.48627311383588e-39*z**2/(pi**5*(z**2/pi**2 + 1.00808875956951e-11)**3) + 8.7156827845897e-40/(pi**3*(z**2/pi**2 + 1.00808875956951e-11)**2)\n",
      "<lambdifygenerated-960>:2: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  return 2.09176386830153e-38*z**3/(pi**7*(z**2/pi**2 + 1.00808875956951e-11)**4) - 1.04588193415076e-38*z/(pi**5*(z**2/pi**2 + 1.00808875956951e-11)**3)\n",
      "100%|██████████| 150/150 [05:48<00:00,  2.32s/it]\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 375x375 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "trap[trap.power_tweezer] = initial_power\n",
    "plot_occupation(trap,200,-1.5*zr,2*zr,power_fac_down=0.51,power_fac_up=0.6,n_spill_steps=150)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Now using 532nm:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [],
   "source": [
    "initial_power = 1600 * si.uW \n",
    "\n",
    "trap: PancakeTrap = PancakeTrap(\n",
    "    power=0,  # Set pancake laser power to 0, no 2D trap\n",
    "    grad_z= 3 * si.G / si.cm,\n",
    "    grad_r=0,\n",
    "    power_tweezer=initial_power,\n",
    "    waist_tweezer=1.838 * si.um,\n",
    "    a=180*(4 * np.pi * const.epsilon_0 * const.value(\"Bohr radius\")**3)/(2 * const.epsilon_0 * const.c),\n",
    "\n",
    "    wvl = 532 * si.nm,    \n",
    ")\n",
    "\n",
    "zr = float(trap.subs(trap.get_tweezer_rayleigh()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-8.45108098415345e-29\n"
     ]
    },
    {
     "data": {
      "image/png": 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qwajy6mgYE87iYty7UpdDZeR4h+443qG71GUQMdRLQ5VXRsCrYX1cW7UOadt2SV0OEZUjDPVSoFCpUOPtiXDz8UbSG9OQe/mK1CURUTnhsqH+3//+F1FRUfD29kbTpk1x6NAhAMDhw4fRqFEj6HQ6tG3bFklJSbbXFLbN0dSVKqL61Amw3rqNc69OgrBYSu1cRER3uWSoJycnY8iQIViyZAkyMjIwYcIEPPPMM8jMzETv3r0xadIkpKeno2PHjoiOjgYA5OTkPHBbafFt1RwB/Xoi89ej+GvhklI9FxER4KKhfunSJYwcORLt2rWDUqnEoEGDAACLFi2Cn58fBg4cCLVajWnTpuHkyZNISEjAnj17HritNIWMHg5trTBc/nApbv10uFTPRUTkkqHerl07vPfee7bnv/zyC4xGIywWCyIjI23tKpUKYWFhOHXqFBISEh64rTQp1e6oGTsFSo0Hzr06Ceab6aV6PiIq31wy1O+VmJiIvn37Ii4uDiqVClqt1m67VquF0WiEwWB44LaiMJvNtofVan2kGjVVQ1Bt/CswX0tF4oQ3IYR4pNcTkbxZrVa7jCkJlw71X3/9Fa1atcLIkSMxceJEaLVaZGdn2+1jNBqh1+sL3VYUOp0OarUaarUacXFxj1xrxS5Pwq9jB2T8sBfXVn31yK8nIvmKi4uz5YtOpyvRsVw21Hfs2IGOHTtizpw5mD59OgAgMjISZ8+ete1jtVqRmJiIiIiIQrcVhcFggMlkgslkQkxMTLFqDp3wCtRBgbgY9y6yE88X6xhEJD8xMTG2fDEYDCU6lkuG+rlz59CvXz98/vnnGDFihK29Q4cOuHbtGlavXg2TyYTZs2cjLCwMderUKXRbUbi7u9seKpWqWHWrdFrUmDYReSYTzr02CXklfJtFRPKgUqnsMqYkXDLUly1bBoPBgKFDh0Kv19seR44cwZYtW7B48WL4+/tj165d2LhxIwDA09PzgdvKklf9KAQN7A/DH3/i7wUfl/n5iUjeFIKf2hXKbDZDrVbDZDIV+S+oMJlgufT3A7fnmc1IePkNGBPPI+rbL+H9eGNHlUsSuTvvS8M9myWuhFxdcTLnXi55pe7qlO7uqPH2JCjd3ZH42mRYMrOkLomIZIKhLhHP0KoIeelF5P71Ny7EzpG6HCKSCYa6hCr1ehrezZvi+oZvkbZ1p9TlEJEMMNQlpFAoUGPKeLj5+OD8pBiYrl6TuiQicnEMdYm5+/shdNJrsGTcQtKUWH7blIhKhKHuBCq0bQX/Tv9Cxg97cf0/30ldDhG5MIa6k6g6djTc/f1w4Z05yL1yVepyiMhFMdSdhJuXF0InjYU1MxNJk2I4DENExcJQdyK+LZvBv2tH3Np7AKnrv5G6HCJyQQx1J1P1lZFwr1QRF6fP5dqmRPTIGOpOxs1Lj+qTx8GaZUDSG9M4DENEj4Sh7oR8mjVBxe5dcOvAz0j9coPU5RCRC2GoO6mqL4+AOjAAF2b+GzmFTA5GRHQvhrqTUum0qD55HPKM2Tg/5R0OwxBRkTDUnZh300ao2K0Tbu3/CTe+/q/U5RCRC2CoO7mQl1+Em18FXJg+F+YbaVKXQ0ROjqHu5Ny8vFBt3EuwZNxCcswsqcshIifHUHcBFdq1hm+blkj7fhtu7vxR6nKIyIkx1F2AQqFAtQkvQ6XTIvmtmVwpiYgeiKHuItQV/REy5kWYUq7i0twFUpdDRE6Koe5CKnbvDH3Deri2ah1u/3pU6nKIyAkx1F2IQqlE9YmvQaF2R9LEt5GXkyt1SUTkZBjqLkZTNQSVowchJykZlz/+VOpyiMjJuHyoL1iwANHR0bbnEydOhEajgV6vh16vR8WKFW3bDh8+jEaNGkGn06Ft27ZISkqSoOKSCxzQB541quPyR58i+/wFqcshIifisqGem5uLmJgYTJo0ya49Pj4eX331FbKyspCVlYUbN24AAHJyctC7d29MmjQJ6enp6Nixo90fA1eidHNDtddfgTCZkTxtJqcQICIblw316OhoHDt2DCNHjrRrj4+PR4MGDfLtv2fPHvj5+WHgwIFQq9WYNm0aTp48iYSEhLIq2aG86kfZphBI+36r1OUQkZNw2VBfsGABNm/ejKCgIFtbSkoK0tLSMGHCBFSqVAktWrTAL7/8AgBISEhAZGSkbV+VSoWwsDCcOnWqzGt3lCqjh0Hl7YULsXNhuZ0pdTlE5ARcNtSDg4Pztd24cQPt27fH1KlTcfnyZYwYMQLdu3dHWloaDAYDtFqt3f5arRZGo7FI5zObzbaH1Wp1SB9Kyt3XByFjhsN8/Qb+mv+h1OUQUTFZrVa7jCkJlw31gtSrVw+7d+9Gy5YtoVarMWLECAQHB+PQoUPQarXIzs62299oNEKv1xfp2DqdDmq1Gmq1GnFxcaVRfrFU7NoR+nqP4erKdcj646TU5RBRMcTFxdnyRafTlehYsgr1Q4cOYenSpXZtJpMJGo0GkZGROHv2rK3darUiMTERERERRTq2wWCAyWSCyWRCTEyMQ+suCYVSiWoTXgEUwPmp0yGc5F0EERVdTEyMLV8MBkOJjiWrUPfw8MCkSZNw8OBBWCwWLFq0CDk5OXjiiSfQoUMHXLt2DatXr4bJZMLs2bMRFhaGOnXqFOnY7u7utodKpSrlnjwabVgNBPbvDUP8SVxbw+XviFyNSqWyy5iSkFWoN23aFEuWLEF0dDR8fHywYcMGbN68GRqNBp6entiyZQsWL14Mf39/7Nq1Cxs3bpS6ZIepPHQg1AGVcGneAphSr0tdDhFJRCF4k3OhzGYz1Go1TCZTkf+CCpMJFgnWFU0/8BOS3p6FSv17IfyDeWV+/vLseIfuAICGezZLXAm5uuJkzr1kdaVe3vm2aQnvxxvj+n++Q+aRY1KXQ0QSYKjLiEKhQNXXRkOhUiE5ZhY/NCUqhxjqMuMZWhUB/XvB8MefSN3wrdTlEFEZY6jLUOUhz8PdrwIuzV0AS8YtqcshojLEUJchlU6LKqOHw3IzHX+9v1jqcoioDDHUZcq/Uwfoourg6qqvYDh9RupyiKiMMNRlSqFUotq4MUBeHpLfnsXpeYnKCYa6jOkiaqHi052R+ctvSNu0XepyiKgMMNRlrsrIoVDp9bg489+wFnFGSiJyXQx1mXP39UGVF1+AKeUqrixdIXU5RFTKGOrlQKVnukETWhVXlqxA7pWrUpdDRKWIoV4OKNxUqPryCOTl5ODSvIVSl0NEpYihXk54N28K78cb48Y3/0VW/AmpyyGiUsJQLycUCgWqvjwCUCpxYfo83uJIJFMM9XLEs2Z1VOreBZm/HsXNLTukLoeISgFDvZypPHwwVDotLs5+D3k5uVKXQ0QOxlAvZ9wr+CJo8ADkXvobKV98KXU5RORgDPVyKLBfL6iDg3D5w6Uw30iTuhwiciCGejmkVLsjZMxwWDOz8Nd7nMWRSE4Y6uVUhXatoa8XhWtrN8J45pzU5RCRgzDUyymFQoGqr4wE8vJwYea7UpdDRA7CUC/HdHVqw69jB9zaewAZ+3+SuhwicgCGejlXZcQQKNzdcXH2fIi8PKnLIaIScvlQX7BgAaKjo23PDx8+jEaNGkGn06Ft27ZISkoq0rbyyiMoEAF9esB48jRu/HeL1OUQUQm5bKjn5uYiJiYGkyZNsrXl5OSgd+/emDRpEtLT09GxY0db4Be2rbwLHjwAKr0el+YtRF6uSepyiKgEXDbUo6OjcezYMYwcOdLWtmfPHvj5+WHgwIFQq9WYNm0aTp48iYSEhEK3lXdu3l4IfmEATH9fwdWVa6Uuh4hKwGVDfcGCBdi8eTOCgoJsbQkJCYiMjLQ9V6lUCAsLw6lTpwrdRkBA7x5QBwbg7w+XwpJxS+pyiKiYXDbUg4OD87UZDAZotVq7Nq1WC6PRWOi2ojCbzbaH1WotfuFOSumhRpUXX4D11m1c/vgzqcshKlesVqtdxpSEy4Z6QbRaLbKzs+3ajEYj9Hp9oduKQqfTQa1WQ61WIy4uzmE1OxO/jh3gGV4TKctXI/fyFanLISo34uLibPmi0+lKdCxZhXpkZCTOnj1re261WpGYmIiIiIhCtxWFwWCAyWSCyWRCTEyMw2t3BgqlEiFjhkOYTPjr3Q+lLoeo3IiJibHli8FgKNGxZBXqHTp0wLVr17B69WqYTCbMnj0bYWFhqFOnTqHbisLd3d32UKlUpdwT6fg83hjejzfG9W++h+FPfohMVBZUKpVdxpSErELd09MTW7ZsweLFi+Hv749du3Zh48aND91G9kJGDwMAXJz9nsSVENGjUgiua1Yos9kMtVoNk8lU5L+gwmSC5dLfpVxZ6Uqe/R7Sdv6IOl99Dt8nWkldjtM73qE7AKDhns0SV0KurjiZcy+HX6lbLBbk8evmLq/yiy9Aoeb0AUSupsShbjAY8PHHH6Nr166oWLEiPDw8oFarERgYiO7du+OTTz5BZmamI2qlMnRn+oBn7kwf8H+8+iRyFcUOdYvFgtmzZyMkJASfffYZGjZsiA8//BDbtm3Dpk2b8N577yEiIgLLly9HaGgoZs6cWeL7L6lsBQ9+FiovPS69+wHXMyVyEW7FfWGzZs3wxBNP4OjRo6hZs2aB+7zwwgsAgNOnT+Pjjz/G448/juPHjxf3lFTG3Ly8EDx4AP5eugJXV61D5f99gEpEzqvYH5ReuHAB1atXL/XXSK28flB6V16uCSdfGIW83Fw0+mkX3Hy8pS7JKfGDUnIUyT4ovTec//rrrwL3ycnJwerVqwt8DbkGpYcalYe/AEvGLU4fQOQCHHL3S/Xq1TF48GDk5OTYtd+6dQvDhvEtu6vz79genmE1/jd9QIrU5RBRIRwS6kII/Prrr2jZsiUuXLjgiEOSE1GoVAgZPQwiNxd/vb9Y6nKIqBAOCXWFQoEdO3YgLCwMTZs2xc6dOx1xWHIi3s2awKtJQ1z/z3cwnD4jdTlE9AAOu1LX6XT4+uuv8fLLL6N79+6YN2+erOdIKW8UCsWd6QPy8nBpzgKpyyGiByj2LY33UigUtn+fOXMm6tati2HDhuHnn392xOHJSegiasHvyXa4uXsfbv10GD6tmktdEhHdx2FX6vd69tlnceDAAfz++++OODw5kSojh0Lh5oaLs97L93snIuk5JNTz8vIQEBBg19a4cWMcOXIEn3/+uSNOQU7CIzgIlXo9DUP8CaRt2i51OUR0n2IPv/zxxx9F2q9Ro0bFPQU5qeAXnkPatl24NG8h/Lo8CaVaLXVJRPQ/xQ71hg0bQqFQ2L0Fvzu2fn+bHNf0LM/cfX0Q9Hx/XF6+CtfWbkTwsMFSl0RE/1PsUE9OTrZ7LoRA3bp1sXXrVoSGhpa4MHJuAf17IvW7zfh74RJU6tcLbl5FW+uViEpXsUO9oOBWKBQICQlhqJcDKo0GlYcNwsX5i3Dlk89RbdJYqUsiIshsOTsqWxW7dIQmtBpSln0B07VUqcshIjDUqQQUbnemD8jLzsZf738kdTlEBIY6lZBPq2bQ16+L1PXfIDvxvNTlEJV7xR5TX7RoUb42i8WClStXomLFinbtY8dyvFWuFAoFQsYMR8LLr+Pi3AWIXMErdiIpFXuRjBo1ahTtBAoFzp933Su48r5IRlElvTMb6fsOIeq7dfB+vLHU5ZQ5LpJBjlLSRTIcdksjlW9VRg5F+sGfcXHWfNT9bp3dfEBEVHYcMqZ+9OjRAttv3bqF0aNHO+IUj2TixInQaDTQ6/XQ6/W24aDDhw+jUaNG0Ol0aNu2LZKSksq8NrnSVA1Bpe5dkXXkGNJ37Ja6HKJyyyGh/tRTT+Hw4cN2bRs3bkRkZCQ2by77t6Px8fH46quvkJWVhaysLNy4cQM5OTno3bs3Jk2ahPT0dHTs2BHR0dFlXpucVY4eCKWnBhfnvA9hsUhdDlG55JBQf/3119GpUyccPHgQly5dwtNPP41Bgwahf//+OH36tCNO8Uji4+PRoEEDu7Y9e/bAz88PAwcOhFqtxrRp03Dy5EkkJCSUeX1y5e5XAYED+iAnKRmpX30tdTlE5ZJDQj0mJgazZ89G165dERUVhbS0NPz6669YtGgRvL3LdvX5lJQUpKWlYcKECahUqRJatGiBX375BQkJCYiMjLTtp1KpEBYWhlOnTpVpfXIXNKAP3Cr44q8FH8FqNEpdDlG547D71F999VUsWbIEZrMZsbGxks3OeOPGDbRv3x5Tp07F5cuXMWLECHTv3h23b9+GVqu121er1cJYxOAxm822BycoezCVVovKQwfCnHoDKctWSl0OkUuwWq12GVMSxQ71ChUqwM/Pz+4xbtw4WK1W9OzZ0669LNWrVw+7d+9Gy5YtoVarMWLECAQHB0OhUCA7O9tuX6PRCL2+aBNR6XQ6qNVqqNVqxMXFlUbpslGxRxd4hFTB5aXLYUq9LnU5RE4vLi7Oli86na5Exyr2LY0LFy50ytvWDh06hD/++AMvvfSSrc1kMqFhw4b45ptvbG1WqxWJiYmIiIgo0nENBoPtnlGlkl/ELYzSzQ0hY4Yh6e1ZuPTvDxD+/mypSyJyajExMZg2bRqAO6MCJQn2Yoe6s9454uHhgUmTJqFevXpo0aIFlixZgpycHHTs2BGjRo3C6tWr8dxzz2HevHkICwtDnTp1inRcd3f3Yn0RoLzybdMSXk0a4vqGbxE05DnoG9STuiQip6VSqaBSqRxyrGJfcrZp0wZ79+4t8v47d+5Eq1atinu6ImvatCmWLFmC6Oho+Pj4YMOGDdi8eTM8PT2xZcsWLF68GP7+/ti1axc2btxY6vWUVwqFAtVeHQUoFEh+Zw7XMyUqI8WeJuCPP/7AqFGjkJ2djX79+tnufPH09AQAZGVlIT4+Hnv37sWaNWug1+uxfPlyNGzY0JH1lzpOE1AyFz9Yguv/txm1Pn4PFXt1l7qcUsNpAshRSjpNQLFDHbiz2tH333+PRYsWYf/+/cjLy4NGo4EQArm5uXB3d8cTTzyBV155BT179izuaSTFUC8Zy63bODFoJFR6HRru3wrVfXcgyQVDnRxFsrlfgDtvsXv27ImePXsiKysLv//+O65duwalUong4GDUr1+/yHeXkDy5+XijyouDcemDpbj88XKukERUykoU6vfS6/V44oknHHU4kpFKPboh9b9bcWXpCgQ81weaqiFSl0QkW7w3j0qdwk2Faq+NhsjNxcWZ70pdDpGsMdSpTHg3aQjfJ1rh5tadSN+9T+pyiGSLoU5lptprY6D09ETy23Gw3vftXiJyDIY6lRl1QEVUefEF5F76G5c/WCp1OUSy5JAPSm/evInY2FgcO3YM2dnZ+b5o8vvvvzviNCQDAb174MaOH3Dlk89RsU8PaCNqSV0Skaw4JNSHDx+Ow4cPY8CAAahQoYIjDkkypXBTIfSN15Dw0us4/+Z0RH29BgrOpUPkMA4J9V27dmHXrl1lMg0AuT59nQhU6tkN17/bgusb/w8Bz/WVuiQi2XDIJZKfnx98fX0dcSgqJ6qMjIa7vx8uzJiH3JRrUpdDJBsOCfVJkyZh4sSJSE1NdcThqBxw0+sQ+sZrsN7OxPnJMZzwi8hBij38UqFCBbv51DMyMhAcHAy9Xp9vCsmbN28Wv0KSLd/WzeHf6V9I2/njnWGYAX2kLonI5RU71D/44AMHlkHlVdWxo3H76HFcmD4XPk+0hkdwoNQlEbm0Yof60KFDHVkHlVNuXl4InfgaEt+cgfOT3kbkmk+dckUtIlfBe8lIcr6tmsO/y1PI2HMAV1eulbocIpfGUCenUG3sGHhUCcbFme/C8GeC1OUQuSyGOjkFlU6LmjFTAKsVZ1+aAKvRKHVJRC6p2KH+1ltvYe/evTCbzY6sh8oxXZ3aqDIqGjlJyUiOmS11OUQuqdihrtPpEBsbi8DAQHTv3h2LFi3CmTNnHFkblUOBz/aGd7MmuL7+G6Ru+EbqcohcTonWKAXuLDD9448/YseOHdi5cydMJhM6deqETp064amnnnL5uWC4RmnZM2fcwulR42BOT0fUN1/Cq3EDqUt6KK5RSo5S0jVKSzymrtfr8cwzz+Djjz/GuXPnsHfvXjRp0gTr1q1DWFgYmjdvXtJTUDnj7uuD8FkxUCiUODPiNZiu8ZvKREXl8A9Ka9SogTFjxuD//u//cP36dbz//vuOPgWVA9raYQidPA7ma6k4M3IsrNk5UpdE5BJK9e4XlUqFNm3alOYpHtnhw4fRqFEj6HQ6tG3bFklJSVKXRA/g/1R7BA3sj6yjx5H42iQIq1XqkoicXrm6pTEnJwe9e/fGpEmTkJ6ejo4dOyI6OlrqsqgQVUYOhd+T7XBz2y4kvz2LE38RPUS5CvU9e/bAz88PAwcOhFqtxrRp03Dy5EkkJPDLLs5KoVSi+tTX4dW4Aa6t/gp/v79Y6pKInFq5CvWEhARERkbanqtUKoSFheHUqVMSVkUPo1S7I3xWDLQRtfD3wiX4671FvGIneoBih/qoUaOQlZVl13b06FG7LyOlpaWhdu3axa/OwQwGA7RarV2bVquFsQjfXjSbzbaHlWO7ZU6l06L2+7P+CfZ3P2Swk2xYrVa7jCmJYof6ihUr8oVhhw4d8Ndff9meWywWp/ogUqvVIjs7267NaDRCr9c/9LU6nQ5qtRpqtRpxcXGlVSIVws3LC7Xfnw1tZG1cXvQJzk+JhbBYpC6LqMTi4uJs+aLT6Up0rGKHekFXSc5+5RQZGYmzZ8/anlutViQmJiIiIuKhrzUYDDCZTDCZTIiJiSnNMqkQbl561H5/NrybNkLq2o04PfQlWO97x0jkamJiYmz5YjAYSnSscjWm3qFDB1y7dg2rV6+GyWTC7NmzERYWhjp16jz0te7u7rbH/Ss7Udly0+sQ/u8ZqNitE27tPYATPQbAeDZR6rKIik2lUtllTEmUq1D39PTEli1bsHjxYvj7+2PXrl3YuHGj1GVRMSjd3BA6eRyqjB6G7KRknOjWH6kbvnX6d4tEpa3YKx+5qiZNmuC3336TugxyAIVCgeCB/aGv+xjOz/w3kl5/C2lbdqDm3Fh4VKksdXlEkihRqC9fvtzuQ0aLxYKVK1eiYsWKAIDMzMySVUdUBF71oxC14iNcWrwMN3ftwfEO3RHy2mgEjRgClaen1OURlaliz9JYvXr1Iq8lmZycXJxTOAXO0uhabv16FJcWLkHulRS4BwagymujEPBsb6hKeEfBw3CWRnKUks7SWOKpd+WOoe568sxm3Ni0HVdWrYMl4xZU3l4IGNgfAc/2hjaiVqmck6FOjsJQL2UMdddlzc5B2s7dSP36e+RcuvP9Cc+IcPg/3Rk+rVtA36gBlB5qh5yLoU6OwlAvZQx11yfy8pB5/ATS9+xH+r5DsNy6DQBQeHhAXz8K2oha8IysBc+a1aEOCoQ6KBAqb68iDy8CDHVyHIZ6KWOoy0uexQJjwjlkHvsDt4/Fw3g2CdYCPtBXeHjAzUsPpU4LlU4HldYTCnd3KFQqQKWEQqWCQqkEVCooVErc2v8zoFDAv3vnO/u5u0Op/t8/NRq4+XjDrYIP3Hy8ofLxgbu/H9RBAVCqHfNOgeSDoV7KGOryJoSA+WY6ss9fQO7lFJjT0mC+cROmtJvIM2bDmp2NvOxsWLNz7kxJIASENQ/Iy4PIswLWPIi8PKA4/xspFHAPqASPykHwCKkCz/Aa8KwVDm1EODQ1qzPwyymGeiljqFNRnBwyGgBQZ+lC5JnNEBYLhNkCYTYjLycXlqxMWG5nwZqZBUtmJiw302FKvQFTaipMqTdgTrtpf0CVCtra4dA3bgCvJg2gb9wQnmE17rw7IFkraaiXuy8fEZWK/42/q3RaFGcSibzcXORc+hvZFy4h+8Il5Fy4CMOZRKSu3YjUtXe+9azy8YZP6xbwbdcaPu1aQ1M1xIEdILlgqBM5AaWHB7S1wqCtFWbXbkq9gaxTCTCcSkBm/Enc3LYLN7fuBABoaoSiwlPt4fd0Z3g1acireALAUCdyauqAivALaAO/9nfW+rXcuo3bv8fj9m+/4/ZvvyPls1VI+WwV3AMqwa9rR/h37wzvFo8z4MsxhjqRC3Hz8YZfh7bw69AWQggYz5xD+v5DSN/3E66tWodrq9ZBHVIZAf17oVL/3tCEVpW6ZCpj/KD0IfhBKRXFyaFjAAB1V30iyfmFEMg+fwE3d+9F2o4fYb6RBgDwat4UgYOehX/3Lg77ohWVLt79UsoY6lQUUof6vYTVittHjyNt2w9IP/gThMkM94r+CBg8AEEvDIA6KFDqEqkQvPuFiOwoVCr4NGsCn2ZNYLmdiRtbdyL1/zbj8gdLcOWjT+HXrROCRw6FV+MGUpdKpYChTiRjbt5eCHquLwL798KtX37DtW++R9r3W5H2/VZ4t26BKq+Ogk/blo80JQI5N4Y6UTmgUKng27oFfFu3QHbyRVxd9x+k7d6L24d+ga5BXVR5dRT8ujzFu2ZkgL9BonLGs0YoakybiHprV6BSr6dhPH0WZ0eORfyTzyBt604uCejiGOpE5ZRHcCBCJ7yC+hu+QNDA/si99BfOjhyLE0/3R8beAwx3F8VQJyrn3P0qIGT0MNT76nME9OsJ46kzOD1oJP7sOxi3Dx+Rujx6RAx1IgJwJ9yrvTYa9dYtR8XuXZB55Bj+7DMYCcNfQfb5C1KXR0XEUCciO+qASqg+aSzqrl6GCu3bIH3HbsR36I4LsXNhybgldXn0EAx1IiqQJqQKwma8hYjF8+EZVgMpy1fhWOtOSFmxGnlms9Tl0QPILtQ3b94Md3d36PV62+O3334DAFy/fh3dunWDl5cXatWqhe3bt0tcLZHz86ofhTqfLESNaROhcHfHhXfmIP7JZ5Cx/yepS6MCyC7U4+Pj8fLLLyMrK8v2ePzxxwEAo0aNQs2aNZGWlobFixdj4MCByMjIkLZgIhegUCrh3+lfqPvlp6g8bDBMf1/B6eeH4+xLE5Cbck3q8ugesgz1Bg3yf/05KysLmzZtQmxsLNRqNbp06YLWrVtj/fr1ElRJ5JpUGg0qRw9E1KpP4Nu6BdK+34bj7briyrIvOCTjJGQZ6hs2bEDlypURERGBL774AgBw7tw5+Pr6olKlSrZ9IyIicOrUKalKJXJZHsGBCJ/zDsLnxsLN2xsXZ/4bf3Tuw1sgnYBLhvr27duhUCjyPYYMGYKQkBAMGjQIycnJWLlyJd544w3s2bMHBoMBWq3W7jharRZGo1GiXhC5Pt9WzVF31VIEDx2InPMX8GefwUiaHAPLrdtSl1ZuueTcL507d4a5gLd6SqUSynvmrmjZsiUGDRqETZs2YfDgwcjOzrbb32g0Qq/XF+mc955PqVRCpSrOSpRE8qP08ECV4YPh36kDLr7/EVLX/gfpu/ai5txY+HV5SuryXILVakVeXh4AFJhtj8Ilr9QVCgXc3NzyPa5du4apU6fafb05NzcXGo0G4eHhyMjIwM2b/6zafubMGURERBTpnDqdDmq1Gmq1GnFxcQ7vE5Gr04RUQe0FcxA6eRzyjEacefFVnBk1DqbU61KX5vTi4uJs+aLT6Up0LFktkpGTk4PQ0FC8+eabGDt2LA4dOoQePXrg4MGDqFu3Lp555hlUqVIFCxcuxL59+zBgwAAkJCQgKCjogce8O2G9wWCwTVj/sCt1LpJR/jjTIhnOwJR2E5c+WIKM/T9B5eON6rFTUOnZPpzi9wHuv1LX6XTFXiTDJa/UH0Sj0WDTpk1Yv349vL29MXz4cCxfvhx169YFACxfvhwpKSkICgrC2LFjsX79+kID/V7u7u62B4deiAqn9vdDeNzbCIubBqVKhaTXp+H0wBeRe/mK1KU5JZVKZZcxJSGrK/XSwOXsqCh4pf5glsxM/L1kBW5s3QmVlx7VZ7yFSs/25lX7A5R0OTtZXakTkfNx8/JC9SnjEf7vGVCq1Uh6/S2cGf4Kx9pLCUOdiMqEb4vHEbVyKfyeao/0nT8i/l89kLaZU3U4GkOdiMqMm7cXasZMRs0ZbwF5AmdHj8fZV96AOT1D6tJkg6FORGXOr30bRK1cAt82LZD23RbE/6sHMvYfkrosWWCoE5Ek3P0qIGxWDKq/+QbyDAacfv5FXJgxD3m5JqlLc2kMdSKSjEKhQMUuT+KxFR9BF1UHKZ+uxIkez8J4Lknq0lwWQ52IJOcRHITIRe8iOHogjKfP4kSXvri6ej0Xvy4GhjoROQWFmwpVhg1GxKJ/w83XG8lvTseZF1+F+Wa61KW5FIY6ETkVr3pReGzFx3dufdyx+3+rLPFD1KJiqBOR03HT61AzZjJqTJsIa9adD1Evzn0fwmKRujSnx1AnIqfl3+lfiFqxGNrI2rjy0Wf4s98Q5F5Okbosp8ZQJyKn5lE5GJEfzUdA/17I/O13/NGpF9J37ZG6LKfFUCcip6d0d0e1V0chfM47EFYrEqJfwoWZ/+a6qAVgqBORy/Bt3QKPLV8M3WORSFn2Bf7sPQi5f1+WuiynwlAnIpfiERSIiMXvIvC5vsg69gfiO/bGzR27pS7LaTDUicjlKN3cUPWlFxE+bzoUCuDM8FdwIXYu8kycYoChTkQuy7dlMzy2/CPo60UhZfkq/Nl/KHJTrkldlqQY6kTk0tQBFVH7g7l3hmOOHMMfnXvj1sFfpC5LMgx1InJ5d4djwma+hbzsHJx6fjguf/xZuZw7hqFORLJRoV0bPLbsA2hCq+LSnPdx5sVXYbl1W+qyyhRDnYhkRVMtBHWWLrTNHfNH174wnDojdVllhqFORLKj8tSgxtuTUG38SzBdTsHJHgNw/T/fSV1WmWCoE5EsKRQKBPTugYhF70LlrUfi+Kk4P3W67FdWculQ//XXX1GrVi27tuvXr6Nbt27w8vJCrVq1sH379iJtIyJ50kdF4rHPFsOrSUNcW7MeJ3sPkvWkYC4b6uvWrUOXLl1gvm/uh1GjRqFmzZpIS0vD4sWLMXDgQGRkZDx0GxHJl7uvD2rPj0PQ4AEwxJ/AiW79cPuX36Quq1S4ZKgvW7YMs2fPxtSpU+3as7KysGnTJsTGxkKtVqNLly5o3bo11q9fX+g2IpI/hUqFkJFDERY3DVaDAacGDMPVlWtld9ujS4Z6r169cOLECTRr1syu/dy5c/D19UWlSpVsbRERETh16lSh24io/KjwRGvUWboQ6sAAJE+LQ9Ib05CXkyt1WQ7jtKG+fft2KBSKfI/o6GgEBgZCqcxfusFggFartWvTarUwGo2FbiOi8sWzRijqLFsI7+ZNcX3DtzjZZzByr1yVuiyHcJO6gAfp3LlzvvFyAAWG+V1arRbZ2dl2bUajEXq9vtBtRXFvLUqlEiqVqkivIyLn5OblhVpzY3H58y9x9csNONG1D2p/ugjezZuWeS1WqxV5eXkAUGDuPQqnvVJXKBRwc3PL9ygs1MPDw5GRkYGbN2/a2s6cOYOIiIhCtxWFTqeDWq2GWq1GXFxc8TtGRE7DNs4+8y1YDUacejYaV1euK/Nx9ri4OFu+6HS6Eh3LaUO9OLy9vdG1a1dMmzYNOTk52LFjBw4cOIDevXsXuq0oDAYDTCYTTCYTYmJiSrknRFSWKrRrgzpLFkAdWAnJ02aW+Th7TEyMLV8MBkOJjiWrUAeA5cuXIyUlBUFBQRg7dizWr1+PoKCgh257GHd3d9uDQy9E8uNZszrqLPsA3s2a3Bln7/tCmY2zq1Qqu4wpCYWQ2/08DmY2m6FWq2EymYr8wxYmEyyX/i7lysiZnBw6BgBQd9UnEldCJSWsVlxesQZX126EeyV/RHy2GF6PNy6z8xcnc+4luyt1IqKSUKhUCBkVjZoz3oI104A/nx2K1A3fSl1WkTHUiYgK4Ne+DSI/mg/3ChWQ9PpbuDBjHoTVKnVZD8VQJyJ6AG2tMNRZ9gH09R5DyqcrcXrIGFhuZ0pdVqEY6kREhXCv4IvaC+aiYrdOuLX3AE50fxbZ5y9IXdYDMdSJiB5CqXZH6ORxqPraKOQkX8SJp/sjY/8hqcsqEEOdiKgIFAoFAvv1Qq1/zwDy8nB68CikrFjtdBOCMdSJiB6BT7MmqPPJQnhUDsKFd+bg/OR3kGdynoU3GOpERI9IU/XOOqjezZogdd1/cOq5YTCn3Xz4C8sAQ52IqBjcvPSoNXc6Ap/tjczDR/FHt34w/JkgdVkMdSKi4lK4qVD1lZGoPmU8zFdTcbLX80jbtkvSmhjqREQlVLFbJ9T+YC6UHh44O+I1XF68TLIPUBnqREQO4FUvCnWWfQDPsBq4NG8hEsdOkWRFJYY6EZGDeAQGIPKj+fBp1Rw3vv0efz47FKbrN8q0Bqdd+ci1KaBwV0tdBJUlheLOP/h7L/fcfNSo9e+Z+PuTFbi6diNOPN0fdb/7Ch6VizbNd0lx6t2HKOk0mERUfqWu/wbpP+5H7aULoCjiOgwlzRyG+kMw1ImoJIQQUPzvnVxRcD51IiIn9iiB7ggMdSIiGWGoExHJCEOdiEhGGOpERDLCUCcikhGGOhGRjLh0qP/666+oVauWXdvmzZvh7u4OvV5ve/z2228AgOvXr6Nbt27w8vJCrVq1sH37dinKJiIqNS4b6uvWrUOXLl1gNpvt2uPj4/Hyyy8jKyvL9nj88ccBAKNGjULNmjWRlpaGxYsXY+DAgcjIyJCgeiKi0uGSob5s2TLMnj0bU6dOzbctPj4eDRo0yNeelZWFTZs2ITY2Fmq1Gl26dEHr1q2xfv36siiZiKhMuGSo9+rVCydOnECzZs3ybYuPj8eGDRtQuXJlRERE4IsvvgAAnDt3Dr6+vqhUqZJt34iICJw6darM6iYiKm1OG+rbt2+HQqHI94iOjkZgYCCUyvyl5+XlISQkBIMGDUJycjJWrlyJN954A3v27IHBYIBWq7XbX6vVwmg0llWXiIhKndNOvdu5c+d84+UACgzze7ft3r3b9rxly5YYNGgQNm3ahMGDByM7O9tuf6PRCL1eX6R67q1FqVRCVcQZ14iIHsZqtSIvLw8ACsy9R+G0V+oKhQJubm75HoWFekpKCqZOnWq3jFRubi40Gg3Cw8ORkZGBmzf/WfH7zJkziIiIKFI9Op0OarUaarUacXFxxe8YEdF94uLibPmi0+lKdCynDfXiqFChAr744gt8+OGHyMvLw4EDB7Bx40YMHDgQ3t7e6Nq1K6ZNm4acnBzs2LEDBw4cQO/evYt0bIPBAJPJBJPJhJiYmFLuCRGVJzExMbZ8MRgMJTqWrEJdo9Fg06ZNWL9+Pby9vTF8+HAsX74cdevWBQAsX74cKSkpCAoKwtixY7F+/XoEBRVtNRJ3d3fbg0MvRORIKpXKLmNKRFChTCaTACBMJpPUpRTKYrGI2NhYYbFYpC6l1LGv8lSe+irEg/tb0szhykcP4SorH7lKnY7AvspTeeor8OD+cuUjIiKycdpbGp3F3TcyJb3NqLTdrc/Z63QE9lWeylNfgQf39+7z4g6icPjlIYxGY4lvMSIielQFfWGyKBjqD5GXl4ecnBy4ubmV+QKyRFT+CCFgsVig0WgK/V7OgzDUiYhkhB+UEhHJCEOdiEhGGOpERDLCUCcikhGGOhGRjDDUXdyff/6JDh06wNfXFzVr1sRnn31m2ybHhbYPHz6MRo0aQafToW3btkhKSpK6JIf673//i6ioKHh7e6Np06Y4dOgQAHn3+9SpU9BoNLhw4QIAefY1KSkJTz75JPR6PSIiIrBt2zYApdTXYs9GQ06hdu3aYv78+cJisYjjx48Lf39/cfDgQSGEEL169RKvvPKKyM3NFdu2bRMVKlQQ6enp0hZcAtnZ2SI4OFisXbtW5ObmihkzZog2bdpIXZbDnD9/Xnh7e4u9e/cKq9UqvvzyS+Hn5ydu374t236bzWbRrFkzAUAkJyfL8ndstVpF3bp1xaxZs4TVahXbt28Xer1eZGZmlkpfGeou7MaNG6Jr167CarXa2vr06SPee+89kZmZKVQqlUhNTbVt6969u1i6dKkUpTrE1q1bRVRUlO25xWIRvr6+4vTp0xJW5Th79+4Vb7zxhl2bn5+fmDVrlmz7PXPmTPH666/bQl2Ov+ODBw+KsLAwkZeXZ2s7duxYqfWVwy8uzN/fH1u3brV96+zWrVs4ePAg6tWrJ8uFthMSEhAZGWl7rlKpEBYW5tJ9ule7du3w3nvv2Z7/8ssvMBqNsFgssuz33UXiZ82aZWuT4+/4+PHjeOyxx/DKK68gICAAjRs3RlZWVqn1laHuAgpbhPsuo9GI3r17o1mzZujYsaMsF9qWY58eJDExEX379kVcXBxUKpXs+m0ymTBs2DAsW7YMnp6etnY5/o7T09OxdetWNGjQAH///TcmT56Mnj17IjMzs1T6ylB3AXcX4b7/8fnnnwMAUlNT0b59e2g0GmzcuBEKhQJarbZEC207Izn2qSC//vorWrVqhZEjR2LixImy7PfMmTPRvn17tG7d2q5djn1Vq9UIDQ3F6NGjoVar8dxzz6FKlSoAUCp9Zai7gMIW4b548SJatGiBBg0a4Pvvv7dd9ZR0oW1nFBkZibNnz9qeW61WJCYmunSf7rdjxw507NgRc+bMwfTp0wHIs99ff/01VqxYAV9fX/j6+gIA6tevj6CgINn1tXbt2rh9+7Zdm9VqRcOGDUunryUakSdJmUwmERUVJcaOHVvg9h49eogxY8aI7OxssX37duHj4yNSUlLKuErHMRqNIjAwUKxatcp2t0Djxo2lLsthzp49K/R6vfj666/t2uXebyGE7YNSOfY1KytLBAYGijlz5gir1SrWrFlju6upNPrKUHdhmzZtEgCEVqsVOp3O9pg9e7YQQohr166Jnj17Ch8fH1G7dm2xbds2iSsuuSNHjoimTZsKvV4v2rRpIxITE6UuyWHeeOMNoVAo7H6XOp1O7N+/X9b9FuKfUBdCnr/jU6dOiXbt2glvb29Rt25dsX//fiFE6fSVU+8SEckIx9SJiGSEoU5EJCMMdSIiGWGoExHJCEOdiEhGGOpERDLCUCcikhGGOhGRjDDUiYhkhKFORCQjDHUiIhlhqBMRyQhDnYhIRhjqRMVkNBpRr149XL16tVTPY7Va0bhxYyQmJpbqeUgeGOpExRQbG4tevXohKCioVM+jUqnw9ttvY8yYMaV6HpIHzqdOVAypqamoUaMGkpOTERAQUOrnE0KgevXqWLNmDZ544olSPx+5Ll6pEwFYuXIlFApFvkeHDh0K3P+TTz5Bs2bN7AK9ffv2iI6OLvC4d0VHR6N9+/b49NNPUb16deh0OvTt2xeZmZn4/vvvERUVBb1ejy5dutgN6ygUCvTq1QsffvihYztOsuMmdQFEzmDAgAHo0qWL7fm+ffswePBgTJ48ucD9N2/ejH79+hXrXMeOHUNQUBC2bNmCq1evol+/fujXrx+EEFi9ejXy8vLw7LPPYvLkyVi9erXtdV27dkW/fv1gsVjg5sb/dalg/C+DCICnpyc8PT0BAMnJyXj11VcRGxuLrl275tvXarXi999/R2xsbLHO5ebmhpUrV0Kj0SAqKgr9+/fH8uXLceXKFdv4/MiRI7F48WK719WtWxcGgwGnTp1C/fr1i3Vukj8OvxDdIzMzEz169EDr1q0xbdq0AvdJS0uD1WpFxYoVi3WOyMhIaDQa2/Pg4GAEBwfbfeAaHByMa9eu2b2uUqVKAJCvneheDHWi/8nLy8PAgQNhsViwevVqu7HweymVStv+D2O1WvO1ubu72z1XKBQFtt1/D8Pd8909P1FBOPxC9D9vvvkm9u3bh8OHD8Pb2/uB+/n7+8Pd3R3Xr1/Pty0lJcXu+blz5xxW393zlfYtlOTa+CefCMCaNWswf/58LF26FP7+/rh69artcT+FQoEmTZogPj4+37bdu3fj888/R3JyMr799lssW7YMALB///58V96P6vjx4/D29kbt2rVLdBySN4Y6EYAVK1ZACIHBgwcjMDDQNs4dHBxc4P7du3fH3r1787V369YN69evR2RkJN5++2188cUXCAkJwdChQ0sc6vv27UPnzp3zDdUQ3YtfPiIqhqtXryIsLAxnzpxBSEgIgDv3qVevXh0rV650+PmsViuqVauGtWvXon379g4/PskHr9SJiiEoKAgjR47Exx9/XCbn+/bbbxEeHs5Ap4diqBMV06xZs/D999/n+3DU0axWK2bPno1PP/20VM9D8sDhFyIiGeGVOhGRjDDUiYhkhKFORCQjDHUiIhlhqBMRyQhDnYhIRhjqREQywlAnIpIRhjoRkYww1ImIZIShTkQkIwx1IiIZYagTEckIQ52ISEYY6kREMvL/A8PevCrmAuMAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 375x375 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "trap[trap.power_tweezer] = 0.5*initial_power\n",
    "plot_solutions(trap,600,-1.5*zr,2.9*zr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      " 95%|█████████▌| 143/150 [08:56<00:11,  1.66s/it]<lambdifygenerated-2482>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 2.14386839710037e-38*z/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2) - 2.76272760232557e-24\n",
      "<lambdifygenerated-2483>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -8.57547358840149e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 2.14386839710037e-38/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n",
      "<lambdifygenerated-2483>:2: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  return -8.57547358840149e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 2.14386839710037e-38/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n",
      "<lambdifygenerated-2484>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 5.1452841530409e-37*z**3/(pi**7*(z**2/pi**2 + 4.03235503827802e-11)**4) - 2.57264207652045e-37*z/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3)\n",
      "<lambdifygenerated-2484>:2: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  return 5.1452841530409e-37*z**3/(pi**7*(z**2/pi**2 + 4.03235503827802e-11)**4) - 2.57264207652045e-37*z/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3)\n",
      " 96%|█████████▌| 144/150 [08:58<00:09,  1.65s/it]<lambdifygenerated-2487>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -8.56974131996005e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 2.14243532999001e-38/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n",
      "<lambdifygenerated-2488>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 5.14184479197603e-37*z**3/(pi**7*(z**2/pi**2 + 4.03235503827802e-11)**4) - 2.57092239598802e-37*z/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3)\n",
      "<lambdifygenerated-2486>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 2.14243532999001e-38*z/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2) - 2.76272760232557e-24\n",
      "<lambdifygenerated-2487>:2: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  return -8.56974131996005e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 2.14243532999001e-38/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n",
      "<lambdifygenerated-2488>:2: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  return 5.14184479197603e-37*z**3/(pi**7*(z**2/pi**2 + 4.03235503827802e-11)**4) - 2.57092239598802e-37*z/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3)\n",
      " 97%|█████████▋| 145/150 [09:00<00:08,  1.64s/it]<lambdifygenerated-2490>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 2.14100226287965e-38*z/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2) - 2.76272760232557e-24\n",
      "<lambdifygenerated-2491>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -8.5640090515186e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 2.14100226287965e-38/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n",
      " 97%|█████████▋| 146/150 [09:01<00:06,  1.64s/it]<lambdifygenerated-2495>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -8.55827678307716e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 2.13956919576929e-38/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n",
      "<lambdifygenerated-2496>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 5.1349660698463e-37*z**3/(pi**7*(z**2/pi**2 + 4.03235503827802e-11)**4) - 2.56748303492315e-37*z/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3)\n",
      "<lambdifygenerated-2494>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 2.13956919576929e-38*z/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2) - 2.76272760232557e-24\n",
      "<lambdifygenerated-2495>:2: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  return -8.55827678307716e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 2.13956919576929e-38/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n",
      "<lambdifygenerated-2496>:2: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  return 5.1349660698463e-37*z**3/(pi**7*(z**2/pi**2 + 4.03235503827802e-11)**4) - 2.56748303492315e-37*z/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3)\n",
      " 98%|█████████▊| 147/150 [09:03<00:04,  1.63s/it]<lambdifygenerated-2498>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 2.13813612865893e-38*z/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2) - 2.76272760232557e-24\n",
      "<lambdifygenerated-2499>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -8.55254451463571e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 2.13813612865893e-38/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n",
      " 99%|█████████▊| 148/150 [09:04<00:03,  1.66s/it]<lambdifygenerated-2502>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 2.13670306154857e-38*z/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2) - 2.76272760232557e-24\n",
      "<lambdifygenerated-2503>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -8.54681224619427e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 2.13670306154857e-38/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n",
      " 99%|█████████▉| 149/150 [09:06<00:01,  1.66s/it]<lambdifygenerated-2506>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 2.13526999443821e-38*z/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2) - 2.76272760232557e-24\n",
      "<lambdifygenerated-2507>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -8.54107997775283e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 2.13526999443821e-38/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n",
      "100%|██████████| 150/150 [09:08<00:00,  3.65s/it]\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 375x375 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "trap[trap.power_tweezer] = initial_power\n",
    "plot_occupation(trap,600,-1.5*zr,2.9*zr,power_fac_down=0.5,power_fac_up=0.55,n_spill_steps=150)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### less magnetic gradient"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "initial_power = 500 * si.uW \n",
    "\n",
    "trap: PancakeTrap = PancakeTrap(\n",
    "    power=0,  # Set pancake laser power to 0, no 2D trap\n",
    "    grad_z= 1 * si.G / si.cm,\n",
    "    grad_r=0,\n",
    "    power_tweezer=initial_power,\n",
    "    waist_tweezer=1.838 * si.um,\n",
    "    a=180*(4 * np.pi * const.epsilon_0 * const.value(\"Bohr radius\")**3)/(2 * const.epsilon_0 * const.c),\n",
    "\n",
    "    wvl = 532 * si.nm,    \n",
    ")\n",
    "\n",
    "zr = float(trap.subs(trap.get_tweezer_rayleigh()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-2.691490705424976e-29\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 375x375 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "trap[trap.power_tweezer] = 0.56*initial_power\n",
    "plot_solutions(trap,400,-1.5*zr,2.9*zr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      " 87%|████████▋ | 131/150 [05:53<00:32,  1.71s/it]<lambdifygenerated-3531>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -2.86147675261375e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 7.15369188153438e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n",
      " 88%|████████▊ | 132/150 [05:54<00:30,  1.71s/it]<lambdifygenerated-3534>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 7.1492135468145e-39*z/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2) - 9.2090920077519e-25\n",
      "<lambdifygenerated-3535>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -2.8596854187258e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 7.1492135468145e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n",
      " 89%|████████▊ | 133/150 [05:56<00:28,  1.70s/it]<lambdifygenerated-3538>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 7.14473521209462e-39*z/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2) - 9.2090920077519e-25\n",
      "<lambdifygenerated-3539>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -2.85789408483785e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 7.14473521209462e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n",
      " 89%|████████▉ | 134/150 [05:58<00:27,  1.71s/it]<lambdifygenerated-3542>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 7.14025687737474e-39*z/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2) - 9.2090920077519e-25\n",
      "<lambdifygenerated-3543>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -2.8561027509499e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 7.14025687737474e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n",
      "<lambdifygenerated-3544>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 1.71366165056994e-37*z**3/(pi**7*(z**2/pi**2 + 4.03235503827802e-11)**4) - 8.56830825284969e-38*z/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3)\n",
      "<lambdifygenerated-3543>:2: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  return -2.8561027509499e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 7.14025687737474e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n",
      "<lambdifygenerated-3544>:2: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  return 1.71366165056994e-37*z**3/(pi**7*(z**2/pi**2 + 4.03235503827802e-11)**4) - 8.56830825284969e-38*z/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3)\n",
      " 91%|█████████ | 136/150 [06:01<00:24,  1.72s/it]<lambdifygenerated-3551>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -2.85252008317399e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 7.13130020793498e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n",
      "<lambdifygenerated-3552>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 1.7115120499044e-37*z**3/(pi**7*(z**2/pi**2 + 4.03235503827802e-11)**4) - 8.55756024952198e-38*z/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3)\n",
      "<lambdifygenerated-3550>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 7.13130020793498e-39*z/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2) - 9.2090920077519e-25\n",
      "<lambdifygenerated-3551>:2: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  return -2.85252008317399e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 7.13130020793498e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n",
      "<lambdifygenerated-3552>:2: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  return 1.7115120499044e-37*z**3/(pi**7*(z**2/pi**2 + 4.03235503827802e-11)**4) - 8.55756024952198e-38*z/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3)\n",
      " 91%|█████████▏| 137/150 [06:03<00:22,  1.73s/it]<lambdifygenerated-3555>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -2.85072874928604e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 7.12682187321511e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n",
      "<lambdifygenerated-3556>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 1.71043724957163e-37*z**3/(pi**7*(z**2/pi**2 + 4.03235503827802e-11)**4) - 8.55218624785813e-38*z/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3)\n",
      "<lambdifygenerated-3554>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 7.12682187321511e-39*z/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2) - 9.2090920077519e-25\n",
      "<lambdifygenerated-3555>:2: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  return -2.85072874928604e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 7.12682187321511e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n",
      "<lambdifygenerated-3556>:2: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  return 1.71043724957163e-37*z**3/(pi**7*(z**2/pi**2 + 4.03235503827802e-11)**4) - 8.55218624785813e-38*z/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3)\n",
      " 92%|█████████▏| 138/150 [06:05<00:20,  1.73s/it]<lambdifygenerated-3558>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 7.12234353849523e-39*z/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2) - 9.2090920077519e-25\n",
      "<lambdifygenerated-3559>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -2.84893741539809e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 7.12234353849523e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n",
      " 93%|█████████▎| 139/150 [06:06<00:18,  1.72s/it]<lambdifygenerated-3562>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 7.11786520377535e-39*z/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2) - 9.2090920077519e-25\n",
      "<lambdifygenerated-3563>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -2.84714608151014e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 7.11786520377535e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n",
      " 93%|█████████▎| 140/150 [06:08<00:17,  1.73s/it]<lambdifygenerated-3567>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -2.84535474762219e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 7.11338686905547e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n",
      "<lambdifygenerated-3568>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 1.70721284857331e-37*z**3/(pi**7*(z**2/pi**2 + 4.03235503827802e-11)**4) - 8.53606424286656e-38*z/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3)\n",
      "<lambdifygenerated-3566>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 7.11338686905547e-39*z/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2) - 9.2090920077519e-25\n",
      "<lambdifygenerated-3567>:2: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  return -2.84535474762219e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 7.11338686905547e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n",
      "<lambdifygenerated-3568>:2: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  return 1.70721284857331e-37*z**3/(pi**7*(z**2/pi**2 + 4.03235503827802e-11)**4) - 8.53606424286656e-38*z/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3)\n",
      " 95%|█████████▍| 142/150 [06:11<00:13,  1.72s/it]<lambdifygenerated-3575>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -2.84177207984628e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 7.10443019961571e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n",
      "<lambdifygenerated-3576>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 1.70506324790777e-37*z**3/(pi**7*(z**2/pi**2 + 4.03235503827802e-11)**4) - 8.52531623953885e-38*z/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3)\n",
      "<lambdifygenerated-3574>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 7.10443019961571e-39*z/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2) - 9.2090920077519e-25\n",
      "<lambdifygenerated-3575>:2: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  return -2.84177207984628e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 7.10443019961571e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n",
      "<lambdifygenerated-3576>:2: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  return 1.70506324790777e-37*z**3/(pi**7*(z**2/pi**2 + 4.03235503827802e-11)**4) - 8.52531623953885e-38*z/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3)\n",
      " 95%|█████████▌| 143/150 [06:13<00:12,  1.72s/it]<lambdifygenerated-3578>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 7.09995186489583e-39*z/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2) - 9.2090920077519e-25\n",
      "<lambdifygenerated-3579>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -2.83998074595833e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 7.09995186489583e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n",
      " 96%|█████████▌| 144/150 [06:15<00:10,  1.72s/it]<lambdifygenerated-3582>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 7.09547353017595e-39*z/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2) - 9.2090920077519e-25\n",
      "<lambdifygenerated-3583>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -2.83818941207038e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 7.09547353017595e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n",
      " 97%|█████████▋| 145/150 [06:17<00:08,  1.72s/it]<lambdifygenerated-3588>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 1.70183884690946e-37*z**3/(pi**7*(z**2/pi**2 + 4.03235503827802e-11)**4) - 8.50919423454729e-38*z/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3)\n",
      "<lambdifygenerated-3586>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 7.09099519545607e-39*z/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2) - 9.2090920077519e-25\n",
      "<lambdifygenerated-3587>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -2.83639807818243e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 7.09099519545607e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n",
      "<lambdifygenerated-3587>:2: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  return -2.83639807818243e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 7.09099519545607e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n",
      "<lambdifygenerated-3588>:2: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  return 1.70183884690946e-37*z**3/(pi**7*(z**2/pi**2 + 4.03235503827802e-11)**4) - 8.50919423454729e-38*z/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3)\n",
      " 97%|█████████▋| 146/150 [06:19<00:07,  1.82s/it]<lambdifygenerated-3592>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 1.70076404657669e-37*z**3/(pi**7*(z**2/pi**2 + 4.03235503827802e-11)**4) - 8.50382023288344e-38*z/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3)\n",
      "<lambdifygenerated-3590>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 7.0865168607362e-39*z/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2) - 9.2090920077519e-25\n",
      "<lambdifygenerated-3591>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -2.83460674429448e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 7.0865168607362e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n",
      "<lambdifygenerated-3591>:2: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  return -2.83460674429448e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 7.0865168607362e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n",
      "<lambdifygenerated-3592>:2: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  return 1.70076404657669e-37*z**3/(pi**7*(z**2/pi**2 + 4.03235503827802e-11)**4) - 8.50382023288344e-38*z/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3)\n",
      " 98%|█████████▊| 147/150 [06:20<00:05,  1.80s/it]<lambdifygenerated-3595>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -2.83281541040653e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 7.08203852601632e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n",
      "<lambdifygenerated-3596>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 1.69968924624392e-37*z**3/(pi**7*(z**2/pi**2 + 4.03235503827802e-11)**4) - 8.49844623121958e-38*z/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3)\n",
      "<lambdifygenerated-3594>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 7.08203852601632e-39*z/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2) - 9.2090920077519e-25\n",
      "<lambdifygenerated-3595>:2: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  return -2.83281541040653e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 7.08203852601632e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n",
      "<lambdifygenerated-3596>:2: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  return 1.69968924624392e-37*z**3/(pi**7*(z**2/pi**2 + 4.03235503827802e-11)**4) - 8.49844623121958e-38*z/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3)\n",
      " 99%|█████████▊| 148/150 [06:22<00:03,  1.78s/it]<lambdifygenerated-3600>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 1.69861444591114e-37*z**3/(pi**7*(z**2/pi**2 + 4.03235503827802e-11)**4) - 8.49307222955572e-38*z/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3)\n",
      "<lambdifygenerated-3598>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 7.07756019129644e-39*z/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2) - 9.2090920077519e-25\n",
      "<lambdifygenerated-3599>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -2.83102407651858e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 7.07756019129644e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n",
      "<lambdifygenerated-3599>:2: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  return -2.83102407651858e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 7.07756019129644e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n",
      "<lambdifygenerated-3600>:2: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  return 1.69861444591114e-37*z**3/(pi**7*(z**2/pi**2 + 4.03235503827802e-11)**4) - 8.49307222955572e-38*z/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3)\n",
      " 99%|█████████▉| 149/150 [06:24<00:01,  1.75s/it]<lambdifygenerated-3602>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 7.07308185657656e-39*z/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2) - 9.2090920077519e-25\n",
      "<lambdifygenerated-3603>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -2.82923274263062e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 7.07308185657656e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n",
      "<lambdifygenerated-3603>:2: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  return -2.82923274263062e-38*z**2/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3) + 7.07308185657656e-39/(pi**3*(z**2/pi**2 + 4.03235503827802e-11)**2)\n",
      "<lambdifygenerated-3604>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 1.69753964557837e-37*z**3/(pi**7*(z**2/pi**2 + 4.03235503827802e-11)**4) - 8.48769822789187e-38*z/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3)\n",
      "<lambdifygenerated-3604>:2: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  return 1.69753964557837e-37*z**3/(pi**7*(z**2/pi**2 + 4.03235503827802e-11)**4) - 8.48769822789187e-38*z/(pi**5*(z**2/pi**2 + 4.03235503827802e-11)**3)\n",
      "100%|██████████| 150/150 [06:25<00:00,  2.57s/it]\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 375x375 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "trap[trap.power_tweezer] = initial_power\n",
    "plot_occupation(trap,400,-1.5*zr,2.9*zr,power_fac_down=0.53,power_fac_up=0.58,n_spill_steps=150)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{\\omega_{t r}}{\\omega_{t ax}} \\approx 15.35$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "aspect_ratio = trap.get_omega_r_tweezer() / trap.get_omega_ax_tweezer()\n",
    "_aspect_ratio_latex = sp.latex(trap.omega_r_tweezer / trap.omega_ax_tweezer)\n",
    "display(Math(f\"{_aspect_ratio_latex} \\\\approx {trap.subs(aspect_ratio).evalf():.2f}\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1064nm and smaller waist"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "initial_power = 300 * si.uW \n",
    "\n",
    "trap: PancakeTrap = PancakeTrap(\n",
    "    power=0,  # Set pancake laser power to 0, no 2D trap\n",
    "    grad_z= 10 * si.G / si.cm,\n",
    "    grad_r=0,\n",
    "    power_tweezer=initial_power,\n",
    "    waist_tweezer= 1 * si.um,\n",
    "    a=180*(4 * np.pi * const.epsilon_0 * const.value(\"Bohr radius\")**3)/(2 * const.epsilon_0 * const.c),\n",
    "\n",
    "    wvl = 1064 * si.nm,    \n",
    ")\n",
    "\n",
    "zr = float(trap.subs(trap.get_tweezer_rayleigh()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{\\omega_{t r}}{\\omega_{t ax}} \\approx 4.18$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "aspect_ratio = trap.get_omega_r_tweezer() / trap.get_omega_ax_tweezer()\n",
    "_aspect_ratio_latex = sp.latex(trap.omega_r_tweezer / trap.omega_ax_tweezer)\n",
    "display(Math(f\"{_aspect_ratio_latex} \\\\approx {trap.subs(aspect_ratio).evalf():.2f}\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-4.377024173749289e-29\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 375x375 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "trap[trap.power_tweezer] = 0.47*initial_power\n",
    "plot_solutions(trap,999,-1.5*zr,3.3*zr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "  0%|          | 0/150 [00:00<?, ?it/s]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      " 99%|█████████▊| 148/150 [05:32<00:00,  3.63it/s]<lambdifygenerated-610>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 2.31536248469332e-40*z/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2) - 9.2090920077519e-24\n",
      "<lambdifygenerated-611>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -9.26144993877327e-40*z**2/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3) + 2.31536248469332e-40/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2)\n",
      "c:\\Users\\peter\\AppData\\Local\\anaconda3\\Lib\\site-packages\\scipy\\optimize\\_root_scalar.py:326: RuntimeWarning: Derivative was zero.\n",
      "  r, sol = methodc(f, x0, args=args, fprime=fprime, fprime2=fprime2, **kwargs)\n",
      " 99%|█████████▉| 149/150 [05:32<00:00,  3.40it/s]<lambdifygenerated-614>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 2.3109878733344e-40*z/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2) - 9.2090920077519e-24\n",
      "<lambdifygenerated-615>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -9.24395149333759e-40*z**2/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3) + 2.3109878733344e-40/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2)\n",
      "100%|██████████| 150/150 [05:32<00:00,  2.22s/it]\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 375x375 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "trap[trap.power_tweezer] = initial_power\n",
    "plot_occupation(trap,100,-1.5*zr,3.3*zr,power_fac_down=0.39,power_fac_up=0.5,n_spill_steps=150)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 197,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      " 99%|█████████▉| 247/250 [04:10<00:00,  3.69it/s]<lambdifygenerated-6171>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -9.26489340795539e-40*z**2/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3) + 2.31622335198885e-40/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2)\n",
      "<lambdifygenerated-6172>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 5.55893604477323e-39*z**3/(pi**7*(z**2/pi**2 + 8.83317315846006e-13)**4) - 2.77946802238662e-39*z/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3)\n",
      "<lambdifygenerated-6170>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 2.31622335198885e-40*z/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2) - 9.2090920077519e-24\n",
      "<lambdifygenerated-6171>:2: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  return -9.26489340795539e-40*z**2/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3) + 2.31622335198885e-40/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2)\n",
      "<lambdifygenerated-6172>:2: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  return 5.55893604477323e-39*z**3/(pi**7*(z**2/pi**2 + 8.83317315846006e-13)**4) - 2.77946802238662e-39*z/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3)\n",
      " 99%|█████████▉| 248/250 [04:10<00:00,  3.84it/s]<lambdifygenerated-6175>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -9.25442245064649e-40*z**2/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3) + 2.31360561266162e-40/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2)\n",
      "<lambdifygenerated-6176>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 5.5526534703879e-39*z**3/(pi**7*(z**2/pi**2 + 8.83317315846006e-13)**4) - 2.77632673519395e-39*z/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3)\n",
      "<lambdifygenerated-6174>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 2.31360561266162e-40*z/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2) - 9.2090920077519e-24\n",
      "<lambdifygenerated-6175>:2: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  return -9.25442245064649e-40*z**2/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3) + 2.31360561266162e-40/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2)\n",
      "<lambdifygenerated-6176>:2: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  return 5.5526534703879e-39*z**3/(pi**7*(z**2/pi**2 + 8.83317315846006e-13)**4) - 2.77632673519395e-39*z/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3)\n",
      "100%|█████████▉| 249/250 [04:11<00:00,  3.74it/s]<lambdifygenerated-6178>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 2.3109878733344e-40*z/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2) - 9.2090920077519e-24\n",
      "<lambdifygenerated-6179>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -9.24395149333759e-40*z**2/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3) + 2.3109878733344e-40/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2)\n",
      "100%|██████████| 250/250 [04:11<00:00,  1.01s/it]\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 375x375 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "trap[trap.power_tweezer] = initial_power\n",
    "plot_occupation(trap,100,-1.5*zr,3.3*zr,power_fac_down=0.39,power_fac_up=0.5,n_spill_steps=250,t_spill=0)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "base",
   "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": "3.12.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}