{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from helpers import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "initial_power = 49 * si.uW \n",
    "\n",
    "trap: PancakeTrap = PancakeTrap(\n",
    "    power=0,  # Set pancake laser power to 0, no 2D trap\n",
    "    grad_z= 0 * si.G / si.cm,\n",
    "    grad_r=0,\n",
    "    power_tweezer= initial_power,\n",
    "    waist_tweezer=1 * 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",
    "axial_width = trap.get_tweezer_rayleigh()\n",
    "zr = float(trap.subs(trap.get_tweezer_rayleigh()))\n",
    "\n",
    "x, y, z = trap.x, trap.y, trap.z"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3879.36034722613Hz\n",
      "1.29394674177543 uK\n"
     ]
    },
    {
     "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": [
    "print(f\"{float(trap.subs(trap.get_omega_ax_tweezer()))}Hz\")\n",
    "print(f\"{trap.subs(trap.a *2*trap.power_tweezer/(np.pi*trap.waist_tweezer**2)/ const.k) /si.uK} uK\")\n",
    "\n",
    "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": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle W_{t}\\left(\\frac{\\omega_{t r}}{\\omega_{t ax}} = 9\\right) = 2.16\\mathrm{\\mu m}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "eta_target = 9\n",
    "\n",
    "waist = trap.subs(\n",
    "    sp.solve(\n",
    "        trap.get_omega_r_tweezer() / trap.get_omega_ax_tweezer() - eta_target,\n",
    "        trap.waist_tweezer,\n",
    "    )[0]\n",
    ").evalf()\n",
    "\n",
    "display(\n",
    "    Math(\n",
    "        f\"{sp.latex(trap.waist_tweezer)}\\\\left({_aspect_ratio_latex} = {eta_target}\\\\right)\"\n",
    "        f\" = {waist/si.um:.2f}\\\\mathrm{{\\\\mu m}}\"\n",
    "    )\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{\\sqrt{2} \\pi W_{t}}{\\lambda}$"
      ],
      "text/plain": [
       "sqrt(2)*pi*W_t/lambda"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "aspect_ratio"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 507.875x507.875 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "wvls = np.array([532, 1064]) * si.nm\n",
    "waists = np.linspace(0.5,4) * si.um\n",
    "\n",
    "for i, wvl in enumerate(wvls):\n",
    "    eta = np.sqrt(2)*np.pi * waists/wvl\n",
    "    plt.plot(waists/si.um,eta,label=f\"{wvl/si.nm}nm\")\n",
    "\n",
    "plt.ylabel(\"eta\")\n",
    "plt.xlabel(\"waist [um]\")\n",
    "plt.grid()\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "----------------"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6070.8947739052155Hz\n",
      "3.16884916353168 uK\n"
     ]
    },
    {
     "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": [
    "initial_power = 120 * si.uW \n",
    "initial_grad = 5.3 * si.G/si.cm\n",
    "\n",
    "trap: PancakeTrap = PancakeTrap(\n",
    "    power=0,  # Set pancake laser power to 0, no 2D trap\n",
    "    grad_z= initial_grad,\n",
    "    grad_r=0,\n",
    "    power_tweezer= initial_power,\n",
    "    waist_tweezer=1 * 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",
    "axial_width = trap.get_tweezer_rayleigh()\n",
    "zr = float(trap.subs(trap.get_tweezer_rayleigh()))\n",
    "\n",
    "x, y, z = trap.x, trap.y, trap.z\n",
    "\n",
    "print(f\"{float(trap.subs(trap.get_omega_ax_tweezer()))}Hz\")\n",
    "print(f\"{trap.subs(trap.a *2*trap.power_tweezer/(np.pi*trap.waist_tweezer**2)/ const.k) /si.uK} uK\")\n",
    "\n",
    "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": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[5.20695434e+19 4.40731577e+14 2.01595102e+10 2.50518338e+06\n",
      " 7.34954500e+02 5.26538585e-01 1.34245312e-03] s\n",
      "-8.103227737230478e-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] = 1* initial_power\n",
    "plot_solutions(trap,50,-0.5*zr,1.9*zr,n_pot_steps=1000,display_plot=-1,state_mult=1e3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "  0%|          | 0/50 [00:00<?, ?it/s]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      " 86%|████████▌ | 43/50 [00:21<00:03,  1.94it/s]<lambdifygenerated-1982>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 1.89546959323095e-40*z/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2) - 7.55144813585406e-24\n",
      "<lambdifygenerated-1983>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -7.58187837292378e-40*z**2/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3) + 1.89546959323095e-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",
      "<lambdifygenerated-1984>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 4.54912702375427e-39*z**3/(pi**7*(z**2/pi**2 + 8.83317315846006e-13)**4) - 2.27456351187713e-39*z/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3)\n",
      "<lambdifygenerated-1983>:2: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  return -7.58187837292378e-40*z**2/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3) + 1.89546959323095e-40/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2)\n",
      "<lambdifygenerated-1984>:2: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  return 4.54912702375427e-39*z**3/(pi**7*(z**2/pi**2 + 8.83317315846006e-13)**4) - 2.27456351187713e-39*z/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3)\n",
      " 88%|████████▊ | 44/50 [00:21<00:02,  2.00it/s]<lambdifygenerated-1986>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 1.88308090307911e-40*z/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2) - 7.55144813585406e-24\n",
      "<lambdifygenerated-1987>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -7.53232361231643e-40*z**2/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3) + 1.88308090307911e-40/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2)\n",
      " 90%|█████████ | 45/50 [00:22<00:02,  1.99it/s]<lambdifygenerated-1990>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 1.87069221292727e-40*z/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2) - 7.55144813585406e-24\n",
      "<lambdifygenerated-1991>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -7.48276885170909e-40*z**2/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3) + 1.87069221292727e-40/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2)\n",
      " 92%|█████████▏| 46/50 [00:22<00:02,  1.98it/s]<lambdifygenerated-1994>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 1.85830352277544e-40*z/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2) - 7.55144813585406e-24\n",
      "<lambdifygenerated-1995>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -7.43321409110175e-40*z**2/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3) + 1.85830352277544e-40/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2)\n",
      " 94%|█████████▍| 47/50 [00:23<00:01,  2.03it/s]<lambdifygenerated-1998>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 1.8459148326236e-40*z/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2) - 7.55144813585406e-24\n",
      "<lambdifygenerated-1999>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -7.3836593304944e-40*z**2/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3) + 1.8459148326236e-40/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2)\n",
      " 96%|█████████▌| 48/50 [00:23<00:00,  2.09it/s]<lambdifygenerated-2002>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 1.83352614247176e-40*z/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2) - 7.55144813585406e-24\n",
      "<lambdifygenerated-2003>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -7.33410456988705e-40*z**2/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3) + 1.83352614247176e-40/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2)\n",
      " 98%|█████████▊| 49/50 [00:24<00:00,  2.13it/s]<lambdifygenerated-2006>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 1.82113745231993e-40*z/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2) - 7.55144813585406e-24\n",
      "<lambdifygenerated-2007>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -7.28454980927971e-40*z**2/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3) + 1.82113745231993e-40/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2)\n",
      "<lambdifygenerated-2008>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 4.37072988556783e-39*z**3/(pi**7*(z**2/pi**2 + 8.83317315846006e-13)**4) - 2.18536494278391e-39*z/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3)\n",
      "<lambdifygenerated-2007>:2: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  return -7.28454980927971e-40*z**2/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3) + 1.82113745231993e-40/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2)\n",
      "<lambdifygenerated-2008>:2: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  return 4.37072988556783e-39*z**3/(pi**7*(z**2/pi**2 + 8.83317315846006e-13)**4) - 2.18536494278391e-39*z/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3)\n",
      "100%|██████████| 50/50 [00:24<00:00,  2.02it/s]\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,50,-0.5*zr,1.9*zr,power_fac_down=0.75,power_fac_up=1,n_spill_steps=50,n_pot_steps=int(1e3),t_spill=0*si.ms)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "  0%|          | 0/50 [00:00<?, ?it/s]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 50/50 [01:40<00:00,  2.02s/it]\n"
     ]
    },
    {
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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",
    "trap[trap.grad_z] = initial_grad\n",
    "plot_occupation_grad(trap,100,-0.15*zr,1.9*zr,grad_fac_down=1.4,grad_fac_up=1,n_spill_steps=50,n_pot_steps=int(1e3),t_spill=25*si.ms)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "  0%|          | 0/50 [00:00<?, ?it/s]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      " 92%|█████████▏| 46/50 [01:19<00:00,  4.03it/s]<lambdifygenerated-387>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -1.21409163487995e-40*z**2/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3) + 3.03522908719988e-41/(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",
      "<lambdifygenerated-388>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 7.28454980927971e-40*z**3/(pi**7*(z**2/pi**2 + 8.83317315846006e-13)**4) - 3.64227490463986e-40*z/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3)\n",
      "<lambdifygenerated-386>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 3.03522908719988e-41*z/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2) - 1.21521695321431e-24\n",
      "<lambdifygenerated-387>:2: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  return -1.21409163487995e-40*z**2/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3) + 3.03522908719988e-41/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2)\n",
      "<lambdifygenerated-388>:2: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  return 7.28454980927971e-40*z**3/(pi**7*(z**2/pi**2 + 8.83317315846006e-13)**4) - 3.64227490463986e-40*z/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3)\n",
      " 94%|█████████▍| 47/50 [01:20<00:00,  4.40it/s]<lambdifygenerated-392>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 7.28454980927971e-40*z**3/(pi**7*(z**2/pi**2 + 8.83317315846006e-13)**4) - 3.64227490463986e-40*z/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3)\n",
      "<lambdifygenerated-390>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 3.03522908719988e-41*z/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2) - 1.2276210363268e-24\n",
      "<lambdifygenerated-391>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -1.21409163487995e-40*z**2/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3) + 3.03522908719988e-41/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2)\n",
      "<lambdifygenerated-391>:2: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  return -1.21409163487995e-40*z**2/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3) + 3.03522908719988e-41/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2)\n",
      "<lambdifygenerated-392>:2: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  return 7.28454980927971e-40*z**3/(pi**7*(z**2/pi**2 + 8.83317315846006e-13)**4) - 3.64227490463986e-40*z/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3)\n",
      " 96%|█████████▌| 48/50 [01:20<00:00,  4.68it/s]<lambdifygenerated-395>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -1.21409163487995e-40*z**2/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3) + 3.03522908719988e-41/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2)\n",
      "<lambdifygenerated-396>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 7.28454980927971e-40*z**3/(pi**7*(z**2/pi**2 + 8.83317315846006e-13)**4) - 3.64227490463986e-40*z/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3)\n",
      "<lambdifygenerated-394>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 3.03522908719988e-41*z/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2) - 1.24002511943928e-24\n",
      "<lambdifygenerated-395>:2: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  return -1.21409163487995e-40*z**2/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3) + 3.03522908719988e-41/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2)\n",
      "<lambdifygenerated-396>:2: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  return 7.28454980927971e-40*z**3/(pi**7*(z**2/pi**2 + 8.83317315846006e-13)**4) - 3.64227490463986e-40*z/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3)\n",
      " 98%|█████████▊| 49/50 [01:20<00:00,  4.76it/s]<lambdifygenerated-399>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -1.21409163487995e-40*z**2/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3) + 3.03522908719988e-41/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2)\n",
      "<lambdifygenerated-398>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 3.03522908719988e-41*z/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2) - 1.25242920255176e-24\n",
      "100%|██████████| 50/50 [01:20<00:00,  1.61s/it]\n"
     ]
    },
    {
     "ename": "TypeError",
     "evalue": "unsupported operand type(s) for /: 'tuple' and 'float'",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "Cell \u001b[1;32mIn[4], line 5\u001b[0m\n\u001b[0;32m      3\u001b[0m trap[trap\u001b[38;5;241m.\u001b[39mpower_tweezer] \u001b[38;5;241m=\u001b[39m initial_power\n\u001b[0;32m      4\u001b[0m trap[trap\u001b[38;5;241m.\u001b[39mgrad_z] \u001b[38;5;241m=\u001b[39m initial_grad\n\u001b[1;32m----> 5\u001b[0m plot_occupation_grad(trap,\u001b[38;5;241m100\u001b[39m,\u001b[38;5;241m-\u001b[39m\u001b[38;5;241m0.15\u001b[39m\u001b[38;5;241m*\u001b[39mzr,\u001b[38;5;241m1.9\u001b[39m\u001b[38;5;241m*\u001b[39mzr,grad_fac_down\u001b[38;5;241m=\u001b[39m\u001b[38;5;241m0.7\u001b[39m,grad_fac_up\u001b[38;5;241m=\u001b[39m\u001b[38;5;241m1\u001b[39m,n_spill_steps\u001b[38;5;241m=\u001b[39m\u001b[38;5;241m50\u001b[39m,n_pot_steps\u001b[38;5;241m=\u001b[39m\u001b[38;5;28mint\u001b[39m(\u001b[38;5;241m1e3\u001b[39m),t_spill\u001b[38;5;241m=\u001b[39m\u001b[38;5;241m25\u001b[39m\u001b[38;5;241m*\u001b[39msi\u001b[38;5;241m.\u001b[39mms)\n",
      "File \u001b[1;32mc:\\Users\\peter\\Uni-Bulk\\FerDy_Chomaz\\spilling_code\\diagonalisation\\helpers.py:612\u001b[0m, in \u001b[0;36mplot_occupation_grad\u001b[1;34m(trap, n_levels, left_cutoff, right_cutoff, t_spill, n_spill_steps, grad_fac_down, grad_fac_up, n_pot_steps)\u001b[0m\n\u001b[0;32m    610\u001b[0m ax\u001b[38;5;241m.\u001b[39mplot(spill_grad_factor, atom_number, marker\u001b[38;5;241m=\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mNone\u001b[39m\u001b[38;5;124m\"\u001b[39m)\n\u001b[0;32m    611\u001b[0m ax\u001b[38;5;241m.\u001b[39mfill_between(spill_grad_factor, atom_number, fc\u001b[38;5;241m=\u001b[39mcolors_alpha[\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mred\u001b[39m\u001b[38;5;124m\"\u001b[39m], alpha\u001b[38;5;241m=\u001b[39m\u001b[38;5;241m0.5\u001b[39m)\n\u001b[1;32m--> 612\u001b[0m ax\u001b[38;5;241m.\u001b[39mset_title(\u001b[38;5;124mf\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mpower:\u001b[39m\u001b[38;5;132;01m{\u001b[39;00minitial_power\u001b[38;5;241m/\u001b[39msi\u001b[38;5;241m.\u001b[39mmW\u001b[38;5;132;01m}\u001b[39;00m\u001b[38;5;124mmW, initial B\u001b[39m\u001b[38;5;124m'\u001b[39m\u001b[38;5;124m:\u001b[39m\u001b[38;5;132;01m{\u001b[39;00minitial_grad\u001b[38;5;241m/\u001b[39msi\u001b[38;5;241m.\u001b[39mG\u001b[38;5;241m*\u001b[39msi\u001b[38;5;241m.\u001b[39mcm\u001b[38;5;132;01m}\u001b[39;00m\u001b[38;5;124mG/cm, w_0:\u001b[39m\u001b[38;5;132;01m{\u001b[39;00mtrap[trap\u001b[38;5;241m.\u001b[39mwaist_tweezer]\u001b[38;5;241m/\u001b[39msi\u001b[38;5;241m.\u001b[39mum\u001b[38;5;132;01m}\u001b[39;00m\u001b[38;5;124mum, wvl:\u001b[39m\u001b[38;5;132;01m{\u001b[39;00mtrap[trap\u001b[38;5;241m.\u001b[39mwvl]\u001b[38;5;241m/\u001b[39msi\u001b[38;5;241m.\u001b[39mnm\u001b[38;5;132;01m}\u001b[39;00m\u001b[38;5;124mnm\u001b[39m\u001b[38;5;124m\"\u001b[39m)\n\u001b[0;32m    613\u001b[0m ax\u001b[38;5;241m.\u001b[39mset_xlabel(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mrel. gradient (a.u.)\u001b[39m\u001b[38;5;124m\"\u001b[39m)\n\u001b[0;32m    614\u001b[0m ax\u001b[38;5;241m.\u001b[39mset_ylabel(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124matom number\u001b[39m\u001b[38;5;124m\"\u001b[39m)\n",
      "\u001b[1;31mTypeError\u001b[0m: unsupported operand type(s) for /: 'tuple' and 'float'"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 375x375 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "initial_grad = -2.2 * si.G / si.cm\n",
    "\n",
    "trap[trap.power_tweezer] = initial_power\n",
    "trap[trap.grad_z] = initial_grad\n",
    "plot_occupation_grad(trap,100,-0.15*zr,1.9*zr,grad_fac_down=0.7,grad_fac_up=1,n_spill_steps=50,n_pot_steps=int(1e3),t_spill=25*si.ms)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "trap[trap.power_tweezer] = initial_power\n",
    "trap[trap.grad_z] = initial_grad\n",
    "\n",
    "params = np.array([float(trap.subs(trap.wvl)), float(trap.subs(trap.waist_tweezer)), float(trap.subs(trap.power_tweezer)), float(trap.subs(trap.grad_z)), float(trap.subs(aspect_ratio)), float(trap.subs(trap.get_omega_ax_tweezer())), float(trap.subs(trap.a *2*trap.power_tweezer/(np.pi*trap.waist_tweezer**2)/ const.k) /si.uK)])\n",
    "\n",
    "with open('stepsizes.txt', 'a') as file:\n",
    "    file.write(\"\\n\"+','.join(map(str, params)) + ',0.0271')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "----------------"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "  0%|          | 0/100 [00:00<?, ?it/s]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      " 86%|████████▌ | 86/100 [03:05<00:06,  2.14it/s]<lambdifygenerated-1547>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -7.60340215783404e-40*z**2/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3) + 1.90085053945851e-40/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2)\n",
      " 87%|████████▋ | 87/100 [03:06<00:06,  2.11it/s]<lambdifygenerated-1551>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -7.57887505409909e-40*z**2/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3) + 1.89471876352477e-40/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2)\n",
      "<lambdifygenerated-1552>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 4.54732503245946e-39*z**3/(pi**7*(z**2/pi**2 + 8.83317315846006e-13)**4) - 2.27366251622973e-39*z/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3)\n",
      "<lambdifygenerated-1550>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 1.89471876352477e-40*z/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2) - 7.55144813585406e-24\n",
      "<lambdifygenerated-1551>:2: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  return -7.57887505409909e-40*z**2/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3) + 1.89471876352477e-40/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2)\n",
      "<lambdifygenerated-1552>:2: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  return 4.54732503245946e-39*z**3/(pi**7*(z**2/pi**2 + 8.83317315846006e-13)**4) - 2.27366251622973e-39*z/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3)\n",
      " 89%|████████▉ | 89/100 [03:07<00:05,  2.17it/s]<lambdifygenerated-1558>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 1.8824552116573e-40*z/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2) - 7.55144813585406e-24\n",
      "<lambdifygenerated-1559>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -7.52982084662919e-40*z**2/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3) + 1.8824552116573e-40/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2)\n",
      " 90%|█████████ | 90/100 [03:07<00:04,  2.17it/s]<lambdifygenerated-1563>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -7.50529374289425e-40*z**2/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3) + 1.87632343572356e-40/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2)\n",
      "<lambdifygenerated-1564>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 4.50317624573655e-39*z**3/(pi**7*(z**2/pi**2 + 8.83317315846006e-13)**4) - 2.25158812286827e-39*z/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3)\n",
      "<lambdifygenerated-1562>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 1.87632343572356e-40*z/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2) - 7.55144813585406e-24\n",
      "<lambdifygenerated-1563>:2: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  return -7.50529374289425e-40*z**2/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3) + 1.87632343572356e-40/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2)\n",
      "<lambdifygenerated-1564>:2: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  return 4.50317624573655e-39*z**3/(pi**7*(z**2/pi**2 + 8.83317315846006e-13)**4) - 2.25158812286827e-39*z/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3)\n",
      " 91%|█████████ | 91/100 [03:08<00:04,  2.19it/s]<lambdifygenerated-1568>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 4.48845998349558e-39*z**3/(pi**7*(z**2/pi**2 + 8.83317315846006e-13)**4) - 2.24422999174779e-39*z/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3)\n",
      "<lambdifygenerated-1566>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 1.87019165978982e-40*z/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2) - 7.55144813585406e-24\n",
      "<lambdifygenerated-1567>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -7.4807666391593e-40*z**2/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3) + 1.87019165978982e-40/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2)\n",
      "<lambdifygenerated-1567>:2: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  return -7.4807666391593e-40*z**2/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3) + 1.87019165978982e-40/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2)\n",
      "<lambdifygenerated-1568>:2: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  return 4.48845998349558e-39*z**3/(pi**7*(z**2/pi**2 + 8.83317315846006e-13)**4) - 2.24422999174779e-39*z/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3)\n",
      " 92%|█████████▏| 92/100 [03:08<00:03,  2.18it/s]<lambdifygenerated-1571>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -7.45623953542435e-40*z**2/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3) + 1.86405988385609e-40/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2)\n",
      " 93%|█████████▎| 93/100 [03:08<00:03,  2.21it/s]<lambdifygenerated-1576>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 4.45902745901364e-39*z**3/(pi**7*(z**2/pi**2 + 8.83317315846006e-13)**4) - 2.22951372950682e-39*z/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3)\n",
      "<lambdifygenerated-1574>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 1.85792810792235e-40*z/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2) - 7.55144813585406e-24\n",
      "<lambdifygenerated-1575>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -7.4317124316894e-40*z**2/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3) + 1.85792810792235e-40/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2)\n",
      "<lambdifygenerated-1575>:2: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  return -7.4317124316894e-40*z**2/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3) + 1.85792810792235e-40/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2)\n",
      "<lambdifygenerated-1576>:2: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  return 4.45902745901364e-39*z**3/(pi**7*(z**2/pi**2 + 8.83317315846006e-13)**4) - 2.22951372950682e-39*z/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3)\n",
      " 94%|█████████▍| 94/100 [03:09<00:02,  2.17it/s]<lambdifygenerated-1578>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 1.85179633198861e-40*z/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2) - 7.55144813585406e-24\n",
      "<lambdifygenerated-1579>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -7.40718532795445e-40*z**2/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3) + 1.85179633198861e-40/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2)\n",
      "<lambdifygenerated-1580>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 4.44431119677267e-39*z**3/(pi**7*(z**2/pi**2 + 8.83317315846006e-13)**4) - 2.22215559838634e-39*z/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3)\n",
      "<lambdifygenerated-1579>:2: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  return -7.40718532795445e-40*z**2/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3) + 1.85179633198861e-40/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2)\n",
      "<lambdifygenerated-1580>:2: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  return 4.44431119677267e-39*z**3/(pi**7*(z**2/pi**2 + 8.83317315846006e-13)**4) - 2.22215559838634e-39*z/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3)\n",
      " 95%|█████████▌| 95/100 [03:09<00:02,  2.10it/s]<lambdifygenerated-1582>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 1.84566455605488e-40*z/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2) - 7.55144813585406e-24\n",
      "<lambdifygenerated-1583>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -7.3826582242195e-40*z**2/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3) + 1.84566455605488e-40/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2)\n",
      " 96%|█████████▌| 96/100 [03:10<00:01,  2.07it/s]<lambdifygenerated-1586>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 1.83953278012114e-40*z/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2) - 7.55144813585406e-24\n",
      "<lambdifygenerated-1587>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -7.35813112048456e-40*z**2/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3) + 1.83953278012114e-40/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2)\n",
      " 97%|█████████▋| 97/100 [03:10<00:01,  2.13it/s]<lambdifygenerated-1590>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 1.8334010041874e-40*z/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2) - 7.55144813585406e-24\n",
      "<lambdifygenerated-1591>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -7.33360401674961e-40*z**2/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3) + 1.8334010041874e-40/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2)\n",
      " 98%|█████████▊| 98/100 [03:11<00:00,  2.15it/s]<lambdifygenerated-1594>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 1.82726922825366e-40*z/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2) - 7.55144813585406e-24\n",
      "<lambdifygenerated-1595>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -7.30907691301466e-40*z**2/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3) + 1.82726922825366e-40/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2)\n",
      " 99%|█████████▉| 99/100 [03:11<00:00,  2.06it/s]<lambdifygenerated-1598>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 1.82113745231993e-40*z/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2) - 7.55144813585406e-24\n",
      "<lambdifygenerated-1599>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return -7.28454980927971e-40*z**2/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3) + 1.82113745231993e-40/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2)\n",
      "<lambdifygenerated-1600>:2: RuntimeWarning: overflow encountered in scalar power\n",
      "  return 4.37072988556783e-39*z**3/(pi**7*(z**2/pi**2 + 8.83317315846006e-13)**4) - 2.18536494278391e-39*z/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3)\n",
      "<lambdifygenerated-1599>:2: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  return -7.28454980927971e-40*z**2/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3) + 1.82113745231993e-40/(pi**3*(z**2/pi**2 + 8.83317315846006e-13)**2)\n",
      "<lambdifygenerated-1600>:2: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  return 4.37072988556783e-39*z**3/(pi**7*(z**2/pi**2 + 8.83317315846006e-13)**4) - 2.18536494278391e-39*z/(pi**5*(z**2/pi**2 + 8.83317315846006e-13)**3)\n",
      "100%|██████████| 100/100 [03:12<00:00,  1.92s/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",
    "spill_power_factor, atom_number = plot_occupation(trap,50,-0.5*zr,1.9*zr,power_fac_down=0.75,power_fac_up=1,n_spill_steps=100,n_pot_steps=int(1e3),t_spill=25*si.ms,results=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x2a4dcdf3800>]"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 507.875x507.875 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "bool_array = np.logical_and(np.abs(atom_number - np.round(atom_number,0)) < 0.05, atom_number > 0.05) #find points where atomnumber is close to integer\n",
    "bool_array = np.logical_and(bool_array, atom_number < 5.5)\n",
    "plt.plot(spill_power_factor,atom_number)\n",
    "plt.plot(spill_power_factor[bool_array],atom_number[bool_array],\"b.\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Lengths of blobs: 0.014141414141414144\n"
     ]
    }
   ],
   "source": [
    "diff = np.diff(bool_array.astype(int))  # Convert to int to use np.diff\n",
    "start_indices = np.where(diff == 1)[0] + 1  # Indices where blobs start\n",
    "end_indices = np.where(diff == -1)[0] + 1  # Indices where blobs end\n",
    "\n",
    "# Special case: handle if the array starts or ends with a True\n",
    "if bool_array[0]:\n",
    "    start_indices = np.insert(start_indices, 0, 0)  # Add the start of the array\n",
    "if bool_array[-1]:\n",
    "    end_indices = np.append(end_indices, len(bool_array))  # Add the end of the array\n",
    "\n",
    "#step length\n",
    "step_len = np.abs(np.mean(np.diff(spill_power_factor)))\n",
    "\n",
    "# Blob lengths\n",
    "blob_lengths = np.mean((end_indices - start_indices)*step_len)\n",
    "\n",
    "\n",
    "\n",
    "# Results\n",
    "print(\"Lengths of blobs:\", blob_lengths)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "-------------\n",
    "\n",
    "# Find the power to start at for a given gradient"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "285.07206864693904Hz\n",
      "0.654720901556131 uK\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{\\omega_{t r}}{\\omega_{t ax}} \\approx 18.37$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from helpers import *\n",
    "\n",
    "initial_power = 120 * si.uW \n",
    "initial_grad = -2 * si.G/si.cm\n",
    "\n",
    "trap: PancakeTrap = PancakeTrap(\n",
    "    power=0,  # Set pancake laser power to 0, no 2D trap\n",
    "    grad_z= initial_grad,\n",
    "    grad_r=0,\n",
    "    power_tweezer= initial_power,\n",
    "    waist_tweezer= 2.2 * 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",
    "axial_width = trap.get_tweezer_rayleigh()\n",
    "zr = float(trap.subs(trap.get_tweezer_rayleigh()))\n",
    "\n",
    "x, y, z = trap.x, trap.y, trap.z\n",
    "\n",
    "print(f\"{float(trap.subs(trap.get_omega_ax_tweezer()))}Hz\")\n",
    "print(f\"{trap.subs(trap.a *2*trap.power_tweezer/(np.pi*trap.waist_tweezer**2)/ const.k) /si.uK} uK\")\n",
    "\n",
    "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": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1.48618399e+29 2.22021498e+24 1.48238588e+20 2.15668597e+16\n",
      " 5.63216075e+12 2.44438384e+09 1.71858255e+06 1.98111053e+03\n",
      " 3.98652384e+00 1.68872845e-02] s\n",
      "-1.9011174490670204e-30\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 375x375 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "initial_power = 4/3/np.sqrt(3)*zr * np.pi* trap.subs(trap.m * trap.g + trap.mu_b * trap.grad_z) * trap.subs(trap.waist_tweezer**2/trap.a)\n",
    "trap[trap.power_tweezer] = initial_power *1.13\n",
    "plot_solutions(trap,50,-0.*zr,1.1*zr,n_pot_steps=200,display_plot=-2,state_mult=1e3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "  0%|          | 0/150 [00:00<?, ?it/s]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 150/150 [07:22<00:00,  2.95s/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",
    "spill_power_factor, atom_number = plot_occupation(trap,50,-0*zr,1.1*zr,power_fac_down=1,power_fac_up=1.13,n_spill_steps=150,n_pot_steps=int(0.2e3),t_spill=25*si.ms,results=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Lengths of blobs: 0.016964951528709922\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 507.875x507.875 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "bool_array = np.logical_and(np.abs(atom_number - np.round(atom_number,0)) < 0.1, atom_number > 0.05) #find points where atomnumber is close to integer\n",
    "bool_array = np.logical_and(bool_array, atom_number < 9.5)\n",
    "plt.plot(spill_power_factor,atom_number)\n",
    "plt.plot(spill_power_factor[bool_array],atom_number[bool_array],\"b.\")\n",
    "\n",
    "diff = np.diff(bool_array.astype(int))  # Convert to int to use np.diff\n",
    "start_indices = np.where(diff == 1)[0] + 1  # Indices where blobs start\n",
    "end_indices = np.where(diff == -1)[0] + 1  # Indices where blobs end\n",
    "\n",
    "# Special case: handle if the array starts or ends with a True\n",
    "if bool_array[0]:\n",
    "    start_indices = np.insert(start_indices, 0, 0)  # Add the start of the array\n",
    "if bool_array[-1]:\n",
    "    end_indices = np.append(end_indices, len(bool_array))  # Add the end of the array\n",
    "\n",
    "#step length\n",
    "step_len = np.abs(np.mean(np.diff(spill_power_factor)))\n",
    "\n",
    "# Blob lengths\n",
    "blob_lengths = np.mean((end_indices - start_indices)*step_len)\n",
    "\n",
    "# Results\n",
    "print(\"Lengths of blobs:\", blob_lengths)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Compare to 532nm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2380.714063424528Hz\n",
      "2.65195191238491 uK\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{\\omega_{t r}}{\\omega_{t ax}} \\approx 9.02$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from helpers import *\n",
    "\n",
    "initial_power = 120 * si.uW \n",
    "initial_grad = -2 * si.G/si.cm\n",
    "\n",
    "trap: PancakeTrap = PancakeTrap(\n",
    "    power=0,  # Set pancake laser power to 0, no 2D trap\n",
    "    grad_z= initial_grad,\n",
    "    grad_r=0,\n",
    "    power_tweezer= initial_power,\n",
    "    waist_tweezer= 1.08 * 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",
    "axial_width = trap.get_tweezer_rayleigh()\n",
    "zr = float(trap.subs(trap.get_tweezer_rayleigh()))\n",
    "\n",
    "x, y, z = trap.x, trap.y, trap.z\n",
    "\n",
    "print(f\"{float(trap.subs(trap.get_omega_ax_tweezer()))}Hz\")\n",
    "print(f\"{trap.subs(trap.a *2*trap.power_tweezer/(np.pi*trap.waist_tweezer**2)/ const.k) /si.uK} uK\")\n",
    "\n",
    "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": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle W_{t}\\left(\\frac{\\omega_{t r}}{\\omega_{t ax}} = 9\\right) = 1.08\\mathrm{\\mu m}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "eta_target = 9\n",
    "\n",
    "waist = trap.subs(\n",
    "    sp.solve(\n",
    "        trap.get_omega_r_tweezer() / trap.get_omega_ax_tweezer() - eta_target,\n",
    "        trap.waist_tweezer,\n",
    "    )[0]\n",
    ").evalf()\n",
    "\n",
    "display(\n",
    "    Math(\n",
    "        f\"{sp.latex(trap.waist_tweezer)}\\\\left({_aspect_ratio_latex} = {eta_target}\\\\right)\"\n",
    "        f\" = {waist/si.um:.2f}\\\\mathrm{{\\\\mu m}}\"\n",
    "    )\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4.89675243e+35 1.45804684e+30 2.13694506e+25 7.48376755e+20\n",
      " 5.14048185e+16 6.38561684e+12 1.39036504e+09 5.31676017e+05\n",
      " 3.70863309e+02 5.25090804e-01 2.21863734e-03] s\n",
      "-1.5550542503946148e-30\n"
     ]
    },
    {
     "data": {
      "image/png": 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hisPSsvGvZzQaRe3atYVWq7WG3q0E+fbt223GTU5OFgDEo48+KoQQ4uzZs3a/tQkhxHvvvVeuIJ8wYYIASndEuXTpkrU3qRDFHZUUCoXdHpuWg/+iRYuEEFUT5J999pkAIF577bVS8zx27JiQJEm0b9/eZvkGg6FU29Frr70mAFi/jP38888CgBg1apQwGo3W8bKyssS5c+fKPKDciCXIo6OjSy1/xYoVAoB48cUXhRD/nVF/9dVXpebz+++/C+C/XrY//vijzXbPy8sTWq1WPPXUU6XOcMPDw60dys6fP2/9Una9vLw8odPpRLNmzazDLEFuLyTLa8SIEQKAOHjwYKm/HThwQAAQjzzySJnTWz5vgwcPtvv3QYMGCQB2z5jmzJlj01M6Pj7e5qrWpUuXRNu2bYUkSaJPnz5i0qRJ1l7gXbt2FdnZ2Q4ftyRLp7WPPvrI7t8tn+3GjRuLzZs3i6ysLLFhwwZRt25dodfrbbZDRWo4ePCg0Gg0YsqUKdZhZYVzRca9XmFhoTU8b9Rz/mbbobzrVpF9Z9OmTdYvBMOHD7e5cvPGG2/YfP7sKU+Qb9682WZ4z549BQCxYsUKm+GWjnglrzBb2sl//PFHIcR/nfgWLlxoHad3795Co9GInJwcIYQQgwcPtvn/7XCpIFcqlTYHcQvLLRApKSnWM7eXX37Z7nzuu+8+AUDs2bPHOt+KBvn1l70OHjxoc6a/bNmyMsPMcpZzsyDfs2eP0Gq1Aii+FWTcuHHit99+K3WJ0t/f326HFSGKLy0B/12tqIogt1xJuP4Ll0VoaKjw9fW1WX7JS+gWH3zwgc3Ze05OjvWSd0BAgBgyZIhYunSpTTNJRVmC3N4B4Nq1awIovi1HCCH69+9f6ozKIi8vT0iSZF2PzMxMoVarxYMPPiiEEOKPP/6wbpPatWuLdu3aCSGE+PvvvwUAaycdy35zxx132L3VJygoSKhUKuuXlsjISOHt7X3L6y/Efx2WLJ+Hkiz76vW3hZV0+fLlGx74LcFw7dq1G9ZhubJm2WZCCGvAX9+j9/XXX7d+qXP0uCWFh4cLT0/PMoNeCCGefPJJIUmSzZno0KFDrVcfLF/Cy1uDyWQSbdq0EdHR0TYHfHufxYqMe73c3FxrcDVr1szaBHAr26G861aRfWfLli0CgFCr1SItLc1mvKKiIhERESG8vb1LfSG3KE+QX/+F2BLYhw8fthlub3tajiWW47rlSmHJpi3LGbjl7oXw8HCbk5rb4VJPdgsICIBKpSo13NvbGwCQk5ODzMxMAIDBYLA7jxo1aljHvVVardbm/5aHIQghAAAZGRk2dZVk6QhyM02aNEFycjIGDRqElJQUvPfee+jRowdCQkLw6quvWsfLzMx06LpWVHm2//X1XL89gdLbVKfTITk5GePHj4darcaXX36JBx98EKGhoXjooYdu2DHnZsLDw0sNs7x3lvfyRutl6WBoWS9vb2+0a9cOf/75JwBg7dq18PT0RIsWLdC+fXvs2LED+fn5WLVqFQCgR48eAID09HQAwJYtWzBjxoxSrytXrqCoqMhmXXU63S2vNwD4+fnZrGdJlmE36ojj4+MDhUJhd/qS8yhrf7CYMmUKQkJC8NtvvwEAzp07hz/++AP33HMPevfuXWrc2NhYLFmyBGaz2WHjlrRr1y6cP38eXbp0uWFH3bfffht79+7FW2+9hTlz5mDHjh1YunQprl69Co1GAz8/vwrV8P777yM5ORkLFiy46XtdkXFLSktLw913341ly5ahefPmWL16td1jV3m2Q0XWrSL7jmUfjI6Ohq+vr814SqUSDRs2RFZWls2DbCrKy8vL7nB7x6frRUVFITIy0trh7ffff0dMTIxNR8NOnToBKO74evr0aZw/fx533XXXLddbkksFeVlvuKXXup+fn3UHtNeTHYC113pAQACA/wLj+g/u7YTfjQ6OFQmcpk2b4ttvv0Vqair+/PNPTJ48GSqVCi+88AK++uorAMWhUd51Lcv16w7c+vqXZ/vfrJ6yBAcHY968ebhw4QJ2796NWbNmITY2FkuXLsWkSZNuaZ4AkJeXZ7dO4L9td6P1KioqQlZWls16devWDefPn8fRo0exbt06tG7dGhqNBklJSSgoKMC2bduwatUqREVFoV69egD+O5C88sorEMVXy+y+yjrI3oq4uDgAxXeDXM8yrG7dumVOr9FoEBkZaXd6yzxiY2OhVCpRUFCA1atX2+0Fr1AoEBERgbS0NJjNZpw9exYArNumJEmSEB8fj4KCAly+fNlh45a0YsUKAED//v3L3BYWjRo1woQJEzBx4kQ0b94cALBz507Ex8dDkqQK1fD9998DAO655x6bp6iVvIPEcgyryLgWKSkpaN++PbZs2YKOHTvizz//vOHJxs22Q0XWrSL7TnR0NJRKJQoLC+2Oa3li3O1+sb0dHTp0wK5du5CZmYkdO3ZYg9uiQYMGCAkJQXJyMrZs2QIA1TPICwoKsH//fpthOTk52LdvH6KiouDn54cmTZoAgM2tHhZCCGzcuBF6vd56C4NGowGAUreF2XucXnk1bdoUkiTZraHk7Qc3Mn/+fOutIVqtFh07dsSbb75pDfCNGzcCABISEnDp0iWcOHGi1Dw2bNgAoHgHKotGo7F7S5y99b/+IGBPQkICAPvb/+zZszh16tQN6ynLypUrMXbsWKSmpkKSJCQkJOCZZ57B9u3bodVqrdvjVth7Tyy3ZVluF7vRem3duhVGo9Fmvbp162ate8eOHejQoQOA/25VWb16NTZu3Gg9GwdgfUyjvXpMJhOmTJmCd999t8LrdyPt2rUDYP8WM8uta/ZuT7x+HqdOnSp1u9HJkydx5swZ6+MrCwoK0K1bN4waNarUPPLz83Hs2DFERUVBoVAgJCQEAMp8BOnx48eh1Wrh5+fnsHFLspxptW/f3u50AHDfffehVq1apb4Y79ixA2fPnkWXLl0AoEI1DBs2DNOmTSv1shznxo4di2nTpgFAhcYFik8qunXrhv3796NPnz5YsWLFTb8k3mw7VHT7lnff8fDwQPPmzXHy5MlSwV9YWIi///4btWrVuumVH0dKSkpCVlYWvvjiCxQVFZUKcqA4uP/++29s3boVOp0OrVq1qpyFV8oF+hIc3dlt0KBBNh0dLB0vZsyYUWrc63syW55YVLJN9IknnhAAxMcff2wdlp2dbb39wF4beXna0y29j3/99VfrsCtXroj4+PhytZEPHDhQALZPNhJCiA8//FAA/z1UwbK9e/ToUarXup+fn/Dx8bG2Kdl7bxo3biwUCoVNO9DRo0eFwWAo1UZuaecr2Z5qr9e6wWAQBoPBptd6Xl6etS+DpROYEOVvo7d0JHrppZdsxjt06JCQJEl07dr1htvTnpK91i2dVIQo7k3bpEkTodVqrW1cx44dE0qlUkRGRtp03EpNTbXeFnj907hq1qxp7ZBW8vauyMhI4ePjIwCI3377zWYayxPOSu43Qgjx5ptvWttbS86nIp+hsrRt21Z4eHjYvK+WJ7t16tTpptNbblcaMmSItf2+5NO5St650b17dwHY3n1gNpvFuHHjSn2OLbcFXr+NLPtCyU5SjhrXIjw8XAQGBt5wO1jaRUt2iExLSxMJCQlCq9Xa7De3UkNJFemJXta4o0ePtnZAs9f3yJ7ybIeKrFtF9p1PPvnE2m+lZL3Tp08XAMTUqVPLrKk8beTXH9ctNVx/C2dZ29NyPGnQoIGQJElcvny51LIWLlwoAIi6deuKe+65p8x6K8qlgtzLy0uEhISIli1biilTpljvr23evLnNm3DkyJEb3kdeslPDnj17hFKpFFqtVgwbNkxMmDBBREVFiVatWgm1Wn3LQX7s2DERFBQklEqlGDRokBg3bpyIiIgQMTEx5e7sptPphFarFUOGDBHPPvusGDhwoFCpVKJ27drWTjNms1n06dPHum7jx48XDzzwgNDpdEKtVlvvTxbC/ntjeZxicHCweOqpp8TIkSOFt7e3uPPOO0sFueUDk5SUZA1Ue/P89ttvrfeRP/DAA2L8+PEiLi5OAPbvIy9PkGdmZlq/BHXu3Fk888wzYtSoUcLX11dotVqxZcsW67Q//vijmDZtmt1bqkqyfPD8/f2FUqkUAwcOFOPGjbPeIjhnzhyb8efMmWPtbDd8+HAxZswYu/eRW4waNUoAEBqNxmafsRwIPD09RW5urs00Bw8eFAEBAUKSJNGrVy+b5yXUqlXLprPdjT5D5b2PXIjiZx7odDrh7e0tHnvsMTFmzBjh5eUlvL29Sz1rvaz5Wg56d9xxh83zsocPH24z3vHjx0VQUJCQJEn069dPTJw4UTRv3lwAxfcTl+zMuWvXLmEwGIRSqRT9+/cXU6ZMEZ07dxZA8bMjSt6p4ahxhSi+Fams/bSktLQ0ERERIdRqtXjooYfExIkTrY9ILXmicCs1XO92g/zUqVNCqVQKAOLxxx+327ny+iellXc7VHTdyrvvlDzWNWrUSEyePNn62WjcuPENe39XRZAL8d+dJE2aNLFbR8mTh5s9QbAiXCrIQ0JCxIEDB0THjh2Fh4eHCAkJEU899ZTdHpanT58Ww4cPF6GhoUKj0YiYmBjx7LPPWu/XLWnFihWiVatWwsPDQwQHB4uxY8eKjIwModVqbznIhSg+aA0ePFj4+/sLg8EghgwZYn0wQHkeArBr1y7Rr18/ERERITQajahZs6Z4/PHHRUpKis14RqNRzJkzRzRs2FBotVoRGBgo+vXrV+o2OXvvjdlsFnPnzhVxcXFCo9GI2NhY8dZbb1l7iZYM8itXrojOnTsLDw8PERAQILKzs8t8vzdt2iS6du0qfHx8hE6nE4mJiWL+/PmlbhMrb5ALUfyjFOPHjxexsbHWGvr162e9X9bC8kErOa09lg/VvffeK7788ksRExMjPD09RYsWLcq8h/aXX34R7du3F3q9Xnh7e4t27dqJr7/+2u64P/zwgwBg7aVuYdlm3bt3L7OuESNGiLCwMKHRaER0dLR47LHHSh0Ab/QZsuyr9h70Ys9ff/0lOnfuLLy8vIS/v7/o3r272Lt3b7nnW1BQIKZPn269vTMuLk7MmjXL5l5bi1OnTomhQ4eKwMBAoVarRVxcnJg5c6bdh8YcO3ZMDB06VAQHBwuVSiUiIiLE448/bveec0eNa7ktsH///jfahEKI4luq7rvvPhEaGmq9b7is+4QrUsP1bjfILbdL3eh1/b5Vke1QkXWryL5jNBrF7NmzRb169YRWqxXh4eHiySefvOkjTqsqyC1/s/fF3sJy9831x+fbIQnxb7dgIjfSr18/DB48GPfff3+Z45w6dQq1a9fGvffei6+//roKqyMiqjwu1dmNqDwuXryI9evXWzv5EBG5MwY5uZ2lS5fif//7H+rXry93KUREDlf66SpELu7pp5+WuwQioirDNnIiIiIXxkvrRERELoxBTkRE5MIY5ERERC6MQU5EROTCGOREREQujEFORETkwngfuZMwm83Iz8+HSqUq18+FEhHJRQiBoqIieHh4QKHg+aDcGOROIj8/H3q9Xu4yiIjKLScnBzqdTu4yqj0GuZNQqYrfipycHKjVapmrcS5GoxF6vZ7b5jZxO1YObsf/toHluEXy4rvgJCyX09VqdbU9ONwMt03l4HasHNyOYDOgk2DjBhERkQtjkJPTUygUmDZtGjvV3CZux8rB7UjOhj+a4iSMRiM0Gg0KCwur/eU6InJuPF45F36lJCIicmEMciIiIhfGICciInJhDHIiIiIXxiAnIiJyYQxyIiIiF8YgJyIicmEMciIiIhfGICciInJhDHIHWb9+PRo3bgyDwYAWLVpg27ZtcpdERERuiEHuACaTCQMGDMCcOXOQkZGB4cOH495775W7LCIickMMcgdIS0tDamoqjEYjhBBQKpXw9PSUuywiInJD/D1yBwgMDMTIkSPRo0cPa4j/8ccfcpdFRERuiGfkDmAymWAwGLBq1Srk5OTg5ZdfxqBBg5Cbm3vTaY1Go/VlMpmqoFoiopszmUw2xydyHgxyB/j+++9x+PBh3HPPPdBqtXjyySfh4eGB33///abT6vV6aDQaaDQazJw5swqqJSK6uZkzZ1qPTXq9Xu5yqAReWneAc+fOobCw0GaYWq0u1+/25uTkWMdTKG78PUsUFSFr5x5AoYChReIt10tEdDNTp07FCy+8AKD4yiHD3HnwjNwBOnXqhE2bNuHHH3+E2WzGp59+itTUVLRt2/am01oCX61WQ6lU3nBcs7EIB+8bjnNvf1BZpRMR2aVUKm2OT+Q8GOQO0KRJE3z++ed48cUX4efnh48//hjLly+HwWCo1OUoPT3gnZiArG07Yb7uCgBVjj0de2JPx55yl+F2uF2JKg8vrTvIgAEDMGDAAIcvx9C2FTK37kD27n0wtGru8OUREZFz4Rm5i/O5oxUAIGNTssyVEBGRHBjkLk7fuAEUnp7I2LxV7lKIiEgGDHIXp1Cr4Z3QENm79sJUjvvUiYjIvTDI3YB30yYQxiJkbd8pdylERFTFGORuwNAsAQCQsYmX14mIqhsGuRvwjI6CyteH7eRERNUQg9wNSAoFvBMaIefvgzCmpctdDhERVSEGuZvwTmwCCIHMrTvkLoWIiKoQg9xN/NdOzvvJiYiqEwa5m9CG14A6OBCZm7fJXQoREVUhBrmbkCQJhsQE5B07gcKUS3KXQ0REVYRB7ka8mzYBAGRs2S5zJUREVFUY5G7EkPhvkLOdnIio2mCQuxFNcCC0NcORsSkZQgi5yyEioirAIHczhsQEFJ6/iILTZ+UuhYiIqgCD3M14Wy6v8ylvRETVAoPczRiaNgbA564TEVUXDHI3o/IxwDM2Ghmbt7KdnIioGmCQuyFDswQUpV5D7uGjcpdCREQOxiB3Q5Z2cj7ljYjI/THI3ZB34waQlEreT05EVA0wyN2QUqeDrl4cMrfugCgqkrscIiJyIAa5mzIkJsCUlY3sfQfkLoWIiByIQe6m/msn521oRETujEHuprwa1INCq+X95EREbo5B7qYUGjW8GtVH5o5dMOcXyF0OERE5CIPcjXknNoEoKEDWzt1yl0JERA7CIHdjhsQEAEAG7ycnInJbDHI3pouLgdJLz/vJiYjcGIPcjUlKJbwTGiF7z98oysySuxwiInIABrmbMzRrCphMyNy6Q+5SiIjIARjkbs7QvCkAIGPDZpkrISIiR2CQuzltzXBogoOQvmGL3KUQEZEDMMjdnCRJ8G6WgPwTJ1Fw/qLc5RARUSVjkDvIiRMn0KlTJ3h5eaFu3bpYsWKFbLVYL69v4lk5EZG7YZA7gNlsRt++fXHXXXchMzMT8+bNw+DBg5GdnS1LPYZmCQDAy+tERG6IQe4AycnJyMvLw/PPPw+FQoEuXbpg48aNUKlUstSj9vOFZ2w0MjYmQ5jNstRARESOwSB3gD179qB+/foYO3YsgoODkZiYiOzsbHh4eMhWk6F5UxSlXkPuoaOy1UBERJWPQe4AaWlpWL58OZo0aYJz587h6aefRp8+fXDt2rWbTms0Gq0vk8lUaTVZ28k38jY0Iqo4k8lkc3wi58EgdwCNRoPIyEiMHj0aGo0G9913H8LDw7Fly83bqPV6PTQaDTQaDWbOnFlpNXk1qg9JrWY7ORHdkpkzZ1qPTXq9Xu5yqAR5Gm3dXFxcHDIzM22GmUwmmMvRPp2TkwO1Wg0AUCgq73uW0sMDXo3qI2vbTpjzC6Dw0FbavInI/U2dOhUvvPACgOIrhwxz58Ezcgfo3LkzlEolXnvtNZjNZnz++edISUlBx44dbzqtWq22vpRKZaXWZWjeFOb8fGT9xZ81JaKKUSqVNscnch4McgfQ6/VYu3YtVq1aBT8/P7z++uv46aef4O3tLWtd1tvQ2E5OROQ2eGndQerVq4d169bJXYYNXZ0YKA3eyNiYDDwndzVERFQZeEZejUhKJQyJTZCz7wCM19LkLoeIiCoBg7yaMTRrCgiBzM3b5C6FiIgqAYO8mjG0KL6fnO3kRETugUFezWjDQqENDytuJyciIpfHIK+GDM0SUHDmHPJPnZG7FCIiuk0M8mrI8rhWPuWNiMj1McirIe/EJoAkIWMjg5yIyNUxyKshlbc3dHXrIGPzVohK/GEWIiKqegzyasrQvClMGZnI3ndA7lKIiOg2MMirqf9+1pSX14mIXBmDvJryalAPCg8t0tfzfnIiIlfGIK+mFBo1vBMaI/uv3TBlZ8tdDhER3SIGeTVmaJEIUVSEjC3b5S6FiIhuEYO8GvNp1QwAkL52o8yVEBHRrWKQV2PaiHBowkKRvm4jhBByl0NERLeAQV6NSZIEnxaJxY9rPXla7nKIiOgWMMirOYPl8vo6Xl4nInJFDPJqztC0CSSlEunrNsldChER3QIGeTWn1Ougb1QfmVu2w1xQKHc5RERUQQxygk+LRJjz8pC1fafcpRARUQUxyAk+LZsDANLYTk5E5HIY5ATP2NpQ+fshg+3kREQuh0FOkBQK+DRvitzDR1Fw8ZLc5RARUQUwyAkAYGhZfBtaxgaelRMRuRIGOQEofu46JAnpaxnkRESuhEFOAAC1rw90cbFI37AZwmSSuxwiIionBjlZ+bRqBlNGJrL3/C13KUREVE4McrIytODjWomIXA2DnKy86sdD6aXn41qJiFwIg5ysJJUS3olNkL3nbxjT0uUuh4iIyoFBTjZ8WjYHzGZkrOdZORGRK2CQkw2f1v8+rvWP9TJXQkRE5cEgJxuaoEB4xkYjfe1G3oZGROQCql2QFxUVwWw2y12GU/Nt0wJFaenI3rVX7lKIiOgm3D7Ic3Jy8P7776Nbt24IDAyEVquFRqNBSEgIevbsiQULFiArK8thyz948CA8PDxw6tQphy2jsvm0aQWAl9eJiFyB2wZ5UVERXnnlFURERODjjz9GQkIC3nnnHaxYsQK//vorZs+ejbp162LhwoWIjIzESy+9BKPRWOk1DB8+HAUFBZU6X0fTx9eByteHQU5E5AJUchfgKC1btkT79u2xc+dOREdH2x3nwQcfBAAcOnQI77//Plq0aIE9e/ZUWg2vvfYa2rVrh+3bt1faPKuCpFTCp2UzpK7+EwUXUqCtESp3SUREVAa3PSP/4Ycf8Pbbb5cZ4iXVq1cP7733Hn766adKW/7evXvxzTff4OWXX660eVYlnzYtAADpf6yTtxAiIrohtw3yqKgo67/Pnj1rd5z8/HwsWbLE7jS3o7CwEMOHD8eHH34IT0/PCk1rNBqtL5OMvcYNLZoBSgUvrxMRAMBkMtkcn8h5uG2QlxQVFYWhQ4ciPz/fZnhGRgaGDx9e6ct76aWXkJSUhLZt21Z4Wr1eD41GA41Gg5kzZ1Z6beWl8vaCV6MGyNi0FeZ812rjJ6LKN3PmTOuxSa/Xy10OlVAtglwIge3bt6NNmzZV0nv8u+++wyeffAJfX1/4+voCABo3bowvv/zyptPm5OSgsLAQhYWFmDp1qoMrvTHf1i1gzstDRrJrtfETUeWbOnWq9diUk5MjdzlUQrUIckmSsGrVKsTExKB58+ZYvXq1Q5d3+PBhZGRkID09Henp6QCAffv2YciQITedVq1WW19KpdKhdd6MT5uWANhOTkSAUqm0OT6R86gWQS6EgF6vx3fffYfHH38cPXv2xKxZs2QPSmfnEVkTmrAQpP2+DkIIucshIiI73Pb2s5IkSbL++6WXXkLDhg0xfPhwJCcnV8nyXTUEJUmCT+sWuPLjMuQdOwFdXKzcJRER0XWqzRl5SYMHD8bGjRuxa9cumSpyHb7/Xl5n73UiIudULYLcbDYjODjYZlhiYiL++usvLFq0SKaqXIN3QmMoPDyQ9vs6uUshIiI73PbS+r59+8o1XtOmTR1ciWtTaDXwTmyCjG1/oSgjEyofg9wlERFRCW4b5AkJCZAkyeayuqWt/Pphcj54xRX4tmmBjC3bkL5+MwJ7d5O7HCIiKsFtg/zkyZM2/xdCoGHDhli+fDkiIyNlqso1+bQuflxr2u/rGORERE7GbYPcXlhLkoSIiAgGeQVpgoPgGRuN9D/WQRQVQVK57W5DRORyqkVnN7p9fne2QVF6BjK375S7FCIiKoFBTuXi27Y1ACBt1Z8yV0JERCUxyKlcPGOjoQkNxrVVv7vsA26IiNyR2zZ2zps3r9SwoqIiLF68GIGBgTbDn3jiiaoqy2VJkgTftq1x+ftfkHvoKPT168pdEhERwY2DfO7cuaWGhYaGYunSpTbDJElikJeTb7s2uPz9L7i26ncGORGRk3DbIL/+9jO6fd6NG0Lp7Y20VX+g5oSxcpdDRESoJm3kO3fa72mdkZGB0aNHV3E1rktSKeHbpgVy/j6IgvMX5C6HiIhQTYL87rvvxrZt22yGffvtt4iPj8eyZctkqso1+bYr7r1+bTV7rxMROYNqEeQTJ07EPffcg02bNuHMmTPo0aMHHnjgAQwaNAiHDh2SuzyXYmjRDJJGjbSVf8hdChERwY3byEuaOnUq/Pz80K1b8eNFGzRogO3bt/MHU26BUucJQ7MEZG7dgaL0DKh8feQuiYioWqsWZ+QAMG7cOHzwwQcwGo2YNm0aQ/w2+LZtA1FUhLQ/N8hdChFRtee2Z+R+fn7WXzsryWQyoU+fPvDy8rIOu3btWlWW5vJ872iJ05KEayt/R1D/XnKXQ0RUrbltkM+dO9dukNPtUwf4Q98gHulrN8CUlwelp6fcJRERVVtuG+TDhg2TuwS35tehHXL2H0L6uk0I6NZZ7nKIiKott20jb9euHdatW1fu8VevXo077rjDcQW5Gb8ObQEA135bJXMlRETVm9uekX/wwQd49NFHkZeXh4EDB6Jbt25o0KABPP+9DJydnY29e/di3bp1WLp0Kby8vLBw4UKZq3Yd2pBg6OvXRdqatTDnF0DhoZW7JCKiasltz8gbN26M5ORkvPTSS1i3bh3atGkDLy8v6PV66HQ6+Pj4oFOnTli/fj1ef/11/PXXX0hISJC7bJfi16EdTNk5SN+wWe5SiIiqLbc9IweKfxClT58+6NOnD7Kzs7Fr1y5cunQJCoUCYWFhaNy4sU3vdaoYvw5tcW7+J0hdtgr+99wldzlERNWSWwd5SV5eXmjfvr3cZbgVbVgodHXrIG3NnzAXFEKh1chdEhFRteO2l9apavh1aAtTZhYyNiXLXQoRUbXEIKfb4tehHQAglb3XiYhkwSCn2+IRUQOesdG4tvJ3mI1GucshIqp2GOR02/yS2sGUkYnMLdtuPjIREVWqatHZ7dq1a5g2bRp2796NvLw8CCFs/r5r1y6ZKnMP/h3a4cLCJUhdtgq+/15qJyKiqlEtgnzEiBHYtm0b7r33Xvj5+cldjtvxqBUBz9pRuLZiDWq/+j8o1Gq5SyIiqjaqRZCvWbMGa9as4SNYHcivU3tcWLgEGRu2wK9TB7nLISKqNqpFG7m/vz98fX3lLsOtBfwb3ld/+k3mSoiIqpdqEeRTpkzB5MmTcfnyZblLcVvaGmHQ14/HtZVrYMrLk7scIqJqw22D3M/PD/7+/vD398f06dOxcuVKhIWFwcfHxzrc8nKEn3/+GQ0aNIDBYEDz5s2xebP7P4/c/+4kmHPzkLZ6rdylEBFVG27bRv7222/LtuyTJ0/ioYcewi+//II777wTX331FXr37o1Tp07B29tbtroczb/jnTj73ke4+tMyBPbpLnc5RETVgtsG+cMPPyzbss+cOYNRo0ahQ4fiduMHHngATzzxBI4ePYpmzZrJVpejqf39YGiWgPS1G2BMS4faz1fukoiI3J7bXlqXU4cOHTB79mzr/7du3Yrc3FzUqVNHxqqqhv/dSRDGIlxbvlruUoiIqgUGuYMdP34cAwYMwMyZM2EwGG46vtFotL5MJlMVVFi5/O68A5JGjas/LpO7FCKqRCaTyeb4RM6DQe5A27dvxx133IFRo0Zh8uTJ5ZpGr9dDo9FAo9Fg5syZDq6w8in1Ovi2aYXMrTtQcCFF7nKIqJLMnDnTemzS6/Vyl0MluG2QP//881i3bp1s3xxXrVqFzp0749VXX8X06dPLPV1OTg4KCwtRWFiIqVOnOq5AB/K/OwkQAqm/LJe7FCKqJFOnTrUem3JycuQuh0pw2yDX6/WYNm0aQkJC0LNnT8ybNw9HjhypkmUfO3YMAwcOxKJFizBy5MgKTatWq60vpVLpoAody6dVcyi99Lj6Ey+vE7kLpVJpc3wi5+G2Qf7CCy9g/fr1OHPmDB599FEcOXIEPXv2RGRkJEaNGoX/+7//Q1pamkOW/eGHHyInJwcPP/wwvLy8rK+NGzc6ZHnORqHVwK99W+T8fRC5R47JXQ4RkVtz2yC38PLyQu/evfH+++/j2LFjWLduHZo1a4Yvv/wSMTExaNWqVaUvc/bs2TCbzcjOzrZ53XnnnZW+LGcV0PVuAMDlb36QuRIiIvfm9kF+vdq1a2PMmDH48ccfceXKFcyZM0fuktySV+MG0IbXwNXvf4GZPVyJiBym2gV5SUqlEu3a8fezHUGSJAR26wzj1VSkr60eTQpERHKo1kFOjhXQpROgUODy19/LXQoRkdtikJPDaIIDYWjeFOl/rIfxaqrc5RARuSUGOTlUYLfOEEVFuPL9L3KXQkTkltw2yB999FFkZ2fbDNu5c6fNA2JSU1MRFxdX1aVVK75tW0Pp7Y3L33wPIYTc5RARuR23DfJPPvkEubm5NsM6duyIs2fPWv9fVFSEEydOVHVp1YpCq4H/3R2Qd+Q4cvbul7scIiK347ZBbu/sj2eE8gjs1hkA7yknInIEtw1ych66uFh4xtTG1Z+WwZSXL3c5RERuhUFODidJEgK7d4YpMwvXlq2UuxwiIrfCIKcqEdClExRaLVKWfCV3KUREbkUldwGOtHDhQnh5eVn/X1RUhMWLFyMwMBAAkJWVJVdp1Y7K2xt+d7VH6oo1yNl/CPqG9eQuiYjILbhtkNeqVQsff/yxzbDQ0FAsXbq01HhUNYL79EDqijW4tPRrRL8+Q+5yiIjcgtsG+alTp+Quga6ji68DXVwsrvzwC2q9OAUqb6+bT0RERDfENnKqMpIkIahPd5hz83CVT3ojIqoUDHKqUv6dkqDU65Cy5Cve109EVAkY5FSllJ4eCOh+D/KOHEPm5m1yl0NE5PIY5FTlQvr3AiQJFz9eLHcpREQuj0FOVU5bIwy+bVsj7fd1yPvnlNzlEBG5NAY5ySJkUF8AQMqipTcekYiIbohBTrLwatIQnrHRuPzNDyjKyJS7HCIil8UgJ1lIkoSQQX1hzs3D5a/+T+5yiIhcFoOcZON/VweoA/xx4aPPYC4olLscIiKXxCAn2Sg0aoQM6gvjpcu48gMfEENEdCsY5CSroN7dofT2woUPFkKYTHKXQ0TkchjkJCulXofgvj2Q/88pXFuxRu5yiIhcDoOcZBc8oA8kjQbn3/+Yj20lIqogBjnJTu3ni6AeXZCz7wAyNmyWuxwiIpfCICenEHL/AEgqFc6+OY9n5UREFcAgJ6egDQlGYM8uyN69D+l/bpC7HCIil8EgJ6cRNvReSBo1zs7mWbm7MRcWouDiJeQd/we5h4/CnJ8Pc14+snbvQ+7ho8g/cw6FV67CnF8gd6lELkcldwFEFpqgQAT17o7L3/2MK7+tgl+XTnKXZP1CYTQaZa7EuQmzGfn/nEL+iZPIP3kaBafOoODUGRhTLsGYmgZTVpbd6fb3HFxqmMrXB+qQYGjCQqCtEQbP2Gh4xsVCFxcDTY0wSJLk6NUhcimS4KmPUzAajdBoNCgsLIRarS73dMJoRNHpsw6srGoZU69h3/2P4Gh2BoZdOQ25d87Pg6IAAEOvnJK1DmfjLSmQqNWhgdoD9TQeiFd7QK9Q2oyj0OuhDQkqDmZfX6h8faDQeUKhVuHyj8sASULI4H4wFxTAnF8Ac34+TJnZKLx2DcYrqTBeTYW5wPYMXemlhz6hEbybNYV3swR4JTaB2s+3CtecgFs/XpFj8IycnIo6wB/B/XpCfP09zn/1HXx6d5O1nsPdBgIAck4dkLUOuYmiIuTs3IOsTcnI2rQNeQcOAf+eAyg8POAZFwNd3TrwqB0JbXgYtBHh0Pr7QaGw33p3be1GAEDYkEFlL1MIFGVkIv/0GeSdOoP8U2eRe+IfZO/YjcxNW4tHkiToGzeAb9Kd8E1qB+/EJpBUPKxR9cIzcgfZtm0bxowZg6NHjyIxMRGLFy9GTExMmePzjPw/RVlZ+HvISCj0OrTbtREFMu6i1fmMXAWgmVaHjh7eaO/hBV9lcUBmmk2omXQnfFskwqtRA3jUioCkVN54ZtfZ//AYAEDDzxZUuC5zURHyTpxEzoHDyNr7NzJ37oEpKxsAoDR4w+/ujgjs3Q0+7dtCodVUeP50czwjdy4McgfIz89HdHQ0Zs+ejYEDB2LWrFlYs2YNNm7cWOY0DHJbl777CWff/Qg1Jo1D0JgRstVhOSOPX/GdbDVUJSEE8vYdQNoPvyJt2UqYMovbtj2io+BzZxsYWjaDZ2w01FrtbbVV306Ql6rZZELO4WPI2P4XMpJ3IPfIMQDFoe7fpROCBvaF4Y6WkMq4OkAVxyB3LgxyB1ixYgWmTJmC/fv3AwBMJhMCAwORnJyM+Ph4u9MwyG2ZjUYcePgxGNPT0e3EPqSZ5XkOe3U5IzdICnTX+aCnzgfRai0AwDOmNvzvag+/Dm3hUTOiUpdXmUF+vYKLKbi2diPS1m5E7tHjAABtZE2E3D8QQYP7QRMSXOnLrG4Y5M6FjUkOcPjwYZvAViqViImJwcGDB8sMcrKlUKsRMWYETkx9GdsmPIuo16bJUsf+zn0BAIVrjsqyfEfLO3IMlz79Aqk/LoMoKIDS2wu+d3VAcM8u0MfFyl3eLdGGhSJsyCCEDRmE/LPncPW31bi68necmTUXZ96cB/+ud6PGo8Pg3byp3KUSVQoGuQPk5ORAp9PZDNPpdMjNzb3ptCVvc1IoFFBWsO3Rnfje2QZeTRri6tffI+i+AdA3aSh3SW5BCIHM9ZuR8vFiZG3eBgDQ16+L4P694edm7coeNSMQMWYEaox8CBlbtuHKrytx7bdVuPbbKng1bYywR4cjoHtndpArB5PJBLPZDIC3Yzob7r0OoNPpkJeXZzMsNzcXXl5eN51Wr9db/z1t2jRMnz69sstzGZIkIXLCWBx4ZBx+7NYPI6+ehrmKa7BcWk/UuH64SQDaeXhhmJc/6mk8USQEAjt1QOigvvCq795XihQqFfzat4Vf+7bIO3UGl/7vJ6Su/gPHHpuAM7VqIvyJ0Qga2AcKXiYu08yZMzFjxgy5yyA72EbuAMuXL8dzzz2HvXv3Aij+JhsQEIDk5GTUq1fP7jSWNqecnBxrm1N5zsjdtY28pLMLFuHSV9+h5vRnETLsgSpdtuXSesM1P1XpciuTMJmQtnwNLr73EfKOHIOk0SCge2cEDe4HnUwPWHFkG3l5GdPScfmnZbj8/S8wZWVDWzMc4eNHI2hQXyjc4ItbZbv+jFyv17ON3EmwG6cDdOzYEZcuXcKSJUtQWFiIV155BTExMWWGeElqtdr6qs6X1Uuq8fAQaEKDcX72uyi8dFnuclyGEAJpK9bgwD398M/4KSg4cxYh9w1A468XIWrCWOjDa1Trp6Sp/XwRPnwoGn+zGDVGPoSijEz88/T/sKdDd1z9aRmEuaqv/zg3pVJpc3wi58EzcgfZuXMnxowZg8OHDyMhIYH3kd+m9M3bcPz5GdiQl4Vn0y5U2XJdtdd6osYTjxmC0EDjiRyzGd/lpOGN1cvhGRggd2kAnOOM/Hqm3Fxc/v5XpHz9HUzZOdA3boDIF6bAp11ruUtzOuy17lwY5E6CQX5zJ2bMQtqfGxA1+2UEDuxTJct0tUvrufsP4dwbbyNzwxZIKhUCenZB8AODofbzhUqlcpozcGcMcouijExc/PwbXP5xGYTRCN+72iNqxvPwjI6SuzSnwSB3LuzsRi4jcsJYZO/dj7MzZsG7TUtow8PkLslpFKZcwvk33kHqD78CkgT/zh0RPmIotDW4jSpK5WNAzbGjENy/N84v/AzXfl+HvZuSUWP0CIQ/MRrK6+5IIZIbz8idBM/Iyydj6w4ce2YadhTk4KnUcw7/URVnv7SugYT7vfzwkFcAPBUKeDVLQK3HR0IXGy13aTfkzGfk18vadwBn3v4AeSdOQhMehqjpz8G/W2enubohB56ROxeekZNL8WndAoG9uqLFrytx6p35CHvsEYcuz1kfCGPpyHbu1TkoPHcB2ohw1BgzAn5tW5X5QyV0a7wbN0D9j+bh8s+/4cKipTg66gn4dGiL6FenwSOqltzlEbHXOrmemmMfhUftSJx/cx4yk3fIXU6Vyz1wGEfvfwT/PD4JprR0RDw+Eg0Wf4CAO9swxB1EUikRMqA3Gi79CAFd70bG+s3Y26k3Ln78GYRJnscHE1nw0rqT4KX1isk/cw4HH30SV7OzMOzKaVw1FzlkOc50ad1PocQo70D01vlAoVAgsGdXhD/yoEv+HrcrXVq3J3P3Ppx+420UXEiBV/OmiJ3zCjydvDmjMvHSunNhkDsJBnnFXVu7Ef9Mfw36Zgmo++UnDnm0qDP0WjcXGnF5yZe48PYCmLOzoW/cELXGP+qyz0IHXD/IAcCUl4/znyzB5e9+hqRWo+bk8agxeni1eNwrg9y58DocuSz/jnci5N7+yNm5B6envOh2D/AQQiD9zw042LU/zr08GyovHaJnPI/4ea+7dIi7C6WnB2qNexR1330DmpAgnHl1Dv7ufT/y/jkld2lUzbj/V0dyaxGjh6PgYgpSf1mBd7/8Au9lXqnU+cv1rPXaKg2eMASjlYceCg8taox8CKGD+0Gh1VZpHXRz3o0aoMEn7+H8os9x6ZsfsK9LP9Se+SKC7u1frXu2U9XhpXUnwUvrt85cUIAjE19Azv6DiHhxMkJHPlxp867qS+vGa2m4MPd9XPnyO8Bkgt89dyHi0WHQBgVWyfKrijtcWrcnc9denHx1DoxXrsK/Z1fEvD4DKl8fucuqdLy07lx4Rk4uT6HVos6r/8PhcVNw7uXZUCqUqDF6eKXM23JG5eiDlbmwEJc++wpn33ofpsxM6BvWR61xj0JfL86hy6XKZUhsggaL3sfp2fNwbdlKZO/cg9h334BPm5Zyl0ZujEFObkHlY0Ddt1/DkYnP4/RLr8NcUICQSrjH3HLBylG/vyyEQPqqP3Du9bdRcPI0NCHBiJzwGPw6tudlWRelMngjesbzuLp8Nc7OW4CDgx5GxITHEfHU45D4Q0jkALy07iR4ab1yGNMzcHTSC8g7/g++zr6G9zOv4Hbu8nXk7WcttDqM8Q5EPY0ncs1mRI94EDWGDKwW7eDuemn9evlnz+HE9FnIO/4PfDq0RZ33ZkPt7yd3WbeNl9adC4PcSTDIK09RZhaOPTcDOfsPwtD+DkS/+wZUPrfWTumINvLsXXtx/s13kJW8A5JajYBeXRF8/0B4BgVWm7Pw6hLkQHEfjjPzPsTVZSuhCQtF3Idvw7tZgtxl3RYGuXPh7WfkdlQGb9Sd+xoCe9yDzA1bcLjvA8g/cFjuspD1124cGzEWh/sPRda2nQjo1hkNP/8IUU8+Bl1wULUJ8epGodUiasoTiHpuIoyp13Cg/1Bc/GQJeA5FlYVt5OSWFBo1Iqc8Cc+YaJz7YCH2974Pn6VfxqKsVBgr8FMrt3v7mQSgrVaPod4BaKzxhFkI+HVoi4hHHoInn9NdrQR2vRu6OjE4MfUVnPrfq8jasRsxb73CX1Oj28YgJ7clSRJCBvSGd0IjnJo1Fw8fNeHRJs0Q8fST8O3SqVxnwLf6oynGq6lI/eFXXPn6exT8cwqSWgW/uzsiaHBfeNWO4tl3NaWLqY16H72DU6/PReqvK5D3z0nEL3of2ohwuUsjF8Y2cifBNnLHMhcVIeWr75Dyxbcw5+VD36QhIp58DH6dOtzwkZp7OvYEACSsXXbzZRQUImPDZlz+9gekrV4LUVQElY8Bgd3vQfDAPtAEBlTa+ri66tRGbo8wm3Fx6de4sOhzqAL8UffjeTC0ai53WeXGNnLnwjNyqhYUKhVqPHgfgnp0wcUvvsWVn5fjyIixUAUFInBAb/jecxf0jRuUCvUb3X4mhEDBmXPI3r4TGes2IWPdRphzcgFJgqF5UwT26ALftq2h0PBAR7YkhQI1Hh4Cz9pROPnqbBwcPAy1X5mKkKH3yl0auSCekTsJnpFXrcIrV3F52SrsWvgpaqiK27+zzSbsLczDqaJCnCsqxBVTESb5hEBA4LX0S/BWKOCjUKKWSoNIlQZ11FoEKYvfK7MQOGDMxz1jxyCwUxK0YSFyrp7Tq+5n5CXlnjiJ4y/MROHFFIQ8PARRM56DwsnPcnlG7lwY5E6CQV71hBAwFhYiZ/8hZO3cg+zde5F75DhQjt+XltQqaGvVhL5BPPSNGsCrSUOo/f2gUqnY/l0ODHJbRRmZODHtVWTt3gef9ncg7sN3oDJ4y11WmRjkzoWX1qnakiQJGq0WmmYJ8Pv3vl5zUREKUy4h/9wFFF1Lw/mPP4MQAjUevh9Kb2+oDN7Q1giDNiyET+miSqPyMaDO7Jdx5u35uPrrCuzvOwT1ln4IbXgNuUsjF8AgJypBoVLBIyIcHv/2Ik755gcAQHC/XnKWRdWAQqVC5KRx0NYIxfkPP8XfPQYjfskCeDVuKHdp5OT4QBgiIichSRLChgxC9PTnUJSRgQP9H8S11X/KXRY5OQY5EZGT8e94J+rOnQWFRoMjj4zDxU8/l7skcmIMciIiJ+TVsB7i578FbXgYTr34Ms688Q4f60p2MciJiJyUR3gY4t+bDV18HM6/Mx//PDMNohx3VVD1wiAnInJial8f1J37GgwtEnH5i29xdPRTMOcXyF0WOREGORGRk1PqPBH72jT439UB11aswaGho1CUmSV3WeQkGORERC5AoVaj9tQpCO7fG5nJ23Fg4IMovHJV7rLICTDIiYhchKRQoOYTo1Fj5EPIPXAY+/vcj3w+2bHaY5ATEbkQSZJQ48H7EDlpPArOnsf+vkOQd/wfucsiGTHIiYhcUFDvboie+jSKUq9hf/+hyDl4RO6SSCYMciIiF+V/V3tEv/Q8TJlZODjoIWTv2y93SSQDBjkRkQvza9cGsa/+D6bcPBwcPAxZO3bJXRJVMQa5Axw4cAAdO3aEr68voqOj8fHHH8tdEhG5MZ+WzVDnjZcgiopwcMgjyNiyTe6SqAoxyB2gf//+6NGjB1JTU/Hjjz/iueeew+bNm+Uui4jcmKFpY8TNfhmSJOHQ0EeRvm6j3CVRFWGQV7LU1FTExMRg4sSJUCqVaNKkCTp06ICtW7fKXRoRuTmvhvURN/c1KLQaHB7+ONLWrJW7JKoCDPJKFhAQgOXLl0OhKN60GRkZ2LRpExo1aiRzZURUHejr1kHdt2dBqdPhyKNPIO33dXKXRA7GIL9FK1euhCRJpV7Dhg2zjpObm4t+/fqhZcuW6Ny5c7nmazQarS8TfxyBiG6BLqY26s59DUpPHY6MGo+0Pzfc9jxNJpPN8YmcB4P8FnXp0sVmp7a8Fi1aBAC4fPkykpKS4OHhgW+//RaSJJVrvnq9HhqNBhqNBjNnznTkKhCRG/OMjkLc3Feh9PTEkUfG3Xab+cyZM63HJr1eX0lVUmVgkN8iSZKgUqlKvRQKBU6fPo3WrVujSZMm+OWXX+Dp6Vnu+ebk5KCwsBCFhYWYOnWqA9eAiNydLqY24ua8AoWHFodHjEP6hlvvdDt16lTrsSknJ6cSq6TbxSCvZEajET169ECvXr3w8ccfQ6VSVWh6tVptfSmVSgdVSUTVha5OTHGYa9Q4POxxZGxMvqX5KJVKm+MTOQ8GeSVbtWoVDhw4gIULF8LLy8v6evXVV+UujYiqKX1cbHGYq9U4POwxZGzmXTTupGKni3RTPXv2hBBC7jKIiGzo69ZB3OyXcXTyCzj80BjU++JjGFq3kLssqgQ8Iyciqib09eJQ582ZgEKBQw+NRtauvXKXRJWAQU5EVI141Y9HnddnACYzDj0wCjn7D8ldEt0mXlp3dZIESa2Ruwr39e9tg9zGlYzbVVaGZk0R+/oMHJsyFQfvH4GGP30Jz5jacpdFt0gSbNB1CkajERqNBoWFhewRSkRVIm3NWqQs+QpxH74NpU5X7ul4vHIuDHInwQ8GEclBCFHuB1ZZ8HjlXNhGTkRUjVU0xMn5MMiJiIhcGIOciIjIhTHIiYiIXBiDnIiIyIUxyImIiFwYg5yIiMiFMciJiIhcGIOciIjIhTHIiYiIXBiDnIiIyIUxyImIiFwYg5yIiMiFMciJiIhcGIOciIjIhTHIiYiIXBiDnJyeyWTC9OnTYTKZ5C7FpXE7Vg5uR3I2khBCyF0EAUajERqNBoWFhVCr1XKX41S4bSoHt2Pl4HbkNnA2PCMnIiJyYSq5C6BilgsjRqNR5kqcj2WbcNvcHm7HysHt+N+684Kuc+CldSeRm5sLvV4vdxlEROWWk5MDnU4ndxnVHoPcSZjNZuTn50OlUkGSJLnLISIqkxACRUVF8PDwgELBFlq5MciJiIhcGL9KERERuTAGORERkQtjkBMREbkwBjkREZELY5ATERG5MAY5ObVt27ahadOm0Ov1uPPOO3HixAm5S3JJkydPhoeHB7y8vODl5YXAwEC5S3I5b731FoYNG2b9P/dNchYMcnJa+fn56NevH6ZMmYK0tDR07tzZ5kBK5bd371589dVXyM7ORnZ2Nq5evSp3SS6joKAAU6dOxZQpU6zDuG+SM+F95OS0VqxYgSlTpmD//v0Ain91KjAwEMnJyYiPj5e5OtcSHByMrVu3Ijo6Wu5SXM7999+PrKwsREREID8/H4sXL+a+SU6FZ+TktA4fPmxzUFQqlYiJicHBgwdlrMr1XLx4EampqZgwYQKCgoLQunVrbN26Ve6yXMZbb72FZcuWITQ01DqM+yY5EwY5OS17z3HW6XTIzc2VqSLXdPXqVSQlJeHZZ5/F+fPnMXLkSPTs2ROpqalyl+YSwsLCSg3jvknOhEFOTkun0yEvL89mWG5uLry8vGSqyDU1atQIf/zxB9q0aQONRoORI0ciLCwMmzdvlrs0l8V9k5wJg5ycVnx8PI4ePWr9v8lkwvHjx1G3bl0Zq3I9mzdvxvz5822GFRYWwsPDQ6aKXB/3TXImDHJyWh07dsSlS5ewZMkSFBYW4pVXXkFMTAzq1asnd2kuRavVYsqUKdi0aROKioowb9485Ofno3379nKX5rK4b5IzYZCT0/L09MRvv/2Gd999FwEBAVizZg2+/fZbuctyOc2bN8cHH3yAYcOGwcfHB9988w2WLVvGM/LbwH2TnAlvPyMiInJhPCMnIiJyYQxyIiIiF8YgJyIicmEMciIiIhfGICciInJhDHIiIiIXxiAnIiJyYQxyIiIiF8YgJyIicmEMciIiIhfGICciInJhDHIiIiIXxiAnIiJyYQxyIheWm5uLRo0aISUlxaHLMZlMSExMxPHjxx26HCKqOAY5kQubNm0a+vbti9DQUIcuR6lU4sUXX8SYMWMcuhwiqjj+HjmRi7p8+TJq166NkydPIjg42OHLE0IgKioKS5cuRfv27R2+PCIqH56REzmJxYsXQ5KkUq+OHTvaHX/BggVo2bKlTYgnJSVh2LBhdudrMWzYMCQlJeGjjz5CVFQU9Ho9BgwYgKysLPzyyy9o0KABvLy80LVrV5tL9pIkoW/fvnjnnXcqd8WJ6Lao5C6AiIrde++96Nq1q/X/69evx9ChQ/H000/bHX/ZsmUYOHDgLS1r9+7dCA0NxW+//YaUlBQMHDgQAwcOhBACS5YsgdlsxuDBg/H0009jyZIl1um6deuGgQMHoqioCCoVDx9EzoCfRCIn4enpCU9PTwDAyZMnMW7cOEybNg3dunUrNa7JZMKuXbswbdq0W1qWSqXC4sWL4eHhgQYNGmDQoEFYuHAhLly4YG1vHzVqFN59912b6Ro2bIicnBwcPHgQjRs3vqVlE1Hl4qV1IieTlZWFXr16oW3btnjhhRfsjpOamgqTyYTAwMBbWkZ8fDw8PDys/w8LC0NYWJhNp7mwsDBcunTJZrqgoCAAKDWciOTDICdyImazGUOGDEFRURGWLFli07ZdkkKhsI5/MyaTqdQwtVpt839JkuwOu74vrGV5luUTkfx4aZ3IiTz33HNYv349tm3bBoPBUOZ4AQEBUKvVuHLlSqm/Xbx40eb/x44dq7T6LMtz9O1uRFR+/FpN5CSWLl2KN998E/Pnz0dAQABSUlKsr+tJkoRmzZph7969pf72xx9/YNGiRTh58iR++OEHfPjhhwCADRs2lDrDrqg9e/bAYDAgLi7utuZDRJWHQU7kJD755BMIITB06FCEhIRY263DwsLsjt+zZ0+sW7eu1PDu3bvj66+/Rnx8PF588UV8+umniIiIwMMPP3zbQb5+/Xp06dKl1GV4IpIPHwhD5KJSUlIQExODI0eOICIiAkDxfeRRUVFYvHhxpS/PZDKhVq1a+OKLL5CUlFTp8yeiW8MzciIXFRoailGjRuH999+vkuX98MMPiI2NZYgTORkGOZELe/nll/HLL7+U6uBW2UwmE1555RV89NFHDl0OEVUcL60TERG5MJ6RExERuTAGORERkQtjkBMREbkwBjkREZELY5ATERG5MAY5ERGRC2OQExERuTAGORERkQtjkBMREbkwBjkREZELY5ATERG5MAY5ERGRC2OQExERuTAGORERkQtjkBMREbmw/weZEqDoP4sw9wAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 375x375 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "initial_power = 4/3/np.sqrt(3)*zr * np.pi* trap.subs(trap.m * trap.g + trap.mu_b * trap.grad_z) * trap.subs(trap.waist_tweezer**2/trap.a)\n",
    "trap[trap.power_tweezer] = initial_power *1.35\n",
    "plot_solutions(trap,50,-0.5*zr,1.9*zr,n_pot_steps=200,display_plot=-2,state_mult=1e3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 150/150 [07:59<00:00,  3.20s/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",
    "spill_power_factor, atom_number = plot_occupation(trap,50,-0.5*zr,1.9*zr,power_fac_down=1,power_fac_up=1.35,n_spill_steps=150,n_pot_steps=int(0.2e3),t_spill=25*si.ms,results=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Lengths of blobs: 0.016964951528709922\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 507.875x507.875 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "bool_array = np.logical_and(np.abs(atom_number - np.round(atom_number,0)) < 0.10, atom_number > 0.05) #find points where atomnumber is close to integer\n",
    "bool_array = np.logical_and(bool_array, atom_number < 9.5)\n",
    "plt.plot(spill_power_factor,atom_number)\n",
    "plt.plot(spill_power_factor[bool_array],atom_number[bool_array],\"b.\")\n",
    "\n",
    "diff = np.diff(bool_array.astype(int))  # Convert to int to use np.diff\n",
    "start_indices = np.where(diff == 1)[0] + 1  # Indices where blobs start\n",
    "end_indices = np.where(diff == -1)[0] + 1  # Indices where blobs end\n",
    "\n",
    "# Special case: handle if the array starts or ends with a True\n",
    "if bool_array[0]:\n",
    "    start_indices = np.insert(start_indices, 0, 0)  # Add the start of the array\n",
    "if bool_array[-1]:\n",
    "    end_indices = np.append(end_indices, len(bool_array))  # Add the end of the array\n",
    "\n",
    "#step length\n",
    "step_len = np.abs(np.mean(np.diff(spill_power_factor)))\n",
    "\n",
    "# Blob lengths\n",
    "blob_lengths = np.mean((end_indices - start_indices)*step_len)\n",
    "\n",
    "# Results\n",
    "print(\"Lengths of blobs:\", blob_lengths)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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
}