axial_potential.ipynb

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      "The watermark extension is already loaded. To reload it, use:\n",
      "  %reload_ext watermark\n",
      "Last updated: 2022-02-18T16:00:30.737694+01:00\n",
      "\n",
      "Python implementation: CPython\n",
      "Python version       : 3.7.6\n",
      "IPython version      : 7.12.0\n",
      "\n",
      "Compiler    : MSC v.1916 64 bit (AMD64)\n",
      "OS          : Windows\n",
      "Release     : 10\n",
      "Machine     : AMD64\n",
      "Processor   : AMD64 Family 23 Model 8 Stepping 2, AuthenticAMD\n",
      "CPU cores   : 12\n",
      "Architecture: 64bit\n",
      "\n"
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   "source": [
    "%load_ext watermark\n",
    "%watermark"
   ]
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  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Using matplotlib backend: TkAgg\n"
     ]
    }
   ],
   "source": [
    "# %pylab\n",
    "\n",
    "import numpy\n",
    "import matplotlib\n",
    "from matplotlib import pylab, mlab, pyplot\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "np = numpy\n",
    "plt = pyplot\n",
    "\n",
    "from pylab import *\n",
    "from numpy import *\n",
    "\n",
    "%matplotlib\n",
    "matplotlib.rcParams.update({'font.size': 25})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Warning: Cannot change to a different GUI toolkit: qt. Using tk instead.\n"
     ]
    }
   ],
   "source": [
    "matplotlib.rcParams['figure.figsize'] = [10.5,7]\n",
    "matplotlib.rcParams.update({'font.size': 25})\n",
    "%matplotlib qt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "$\\kappa_{simion}$ = 0.270471\n"
     ]
    }
   ],
   "source": [
    "# Constantes de la physique\n",
    "# ABSOLUMENT RECHARGER APRÈS AVOIR EXECUTÉ LES CASES D'IMPORT AU DESSUS\n",
    "\n",
    "C_e = 1.602e-19        # Coulomb\n",
    "kb = 1.38064852*1e-23  # Boltzman\n",
    "m_Ca = 40.078*1.66054e-27 # masse Ca 40.078\n",
    "m_GM = 1e6*1.66054e-27 # la masse de la GMol\n",
    "eps0 = 8.854187*1e-12  # permittivité électrique du vide\n",
    "\n",
    "\n",
    "r0 = 2.5e-3 # 2.5e-3   # rayon piège Ca+\n",
    "d0 = 4e-3/2            # longueur piège Ca+\n",
    "Omega = 2.045e6*2*pi # 2.047e6\n",
    "bk = 4 # nombre de barreaux par groupe (2 -> 4-pole , 4 -> 8-pole ...)\n",
    "\n",
    "mkappa = 0.23          # écrantage piège réel GiantMol\n",
    "wzLC = (2*pi*90806.9982303)**2\n",
    "kappa_simion = m_Ca*d0**2*wzLC/(2*C_e)\n",
    "print('%s = %f' % ('$\\kappa_{simion}$',kappa_simion) )\n",
    "\n",
    "zeta = kappa_simion*r0**2/d0**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [],
   "source": [
    "x=0\n",
    "y=0\n",
    "z = linspace(-50e-3,4e-3,50000)\n",
    "Udc = 2.63053512573242\n",
    "Q = 20\n",
    "kappa = 0.227\n",
    "\n",
    "omega_z = sqrt(2*kappa*C_e*Udc/(m_Ca*d0**2))\n",
    "U_z_quad = Udc*Q * 0.5*m_Ca*omega_z**2*(z**2-x**2-y**2) / C_e\n",
    "\n",
    "L = 0.0140608827209\n",
    "eta = 1/(4*(5+sqrt(10)))\n",
    "LL = eta*L**2\n",
    "U_z_gmol = Udc*Q *m_Ca*omega_z**2*LL*( 1-exp(-z**2/(2*LL)) ) / C_e"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [],
   "source": [
    "# plot with complicated scan plot only crystal part at the end\n",
    "\n",
    "fig = figure('pot_compare',clear='True')\n",
    "ax = fig.add_subplot(1, 1, 1)\n",
    "\n",
    "\n",
    "ax.plot(z*1000,U_z_quad,'-',color='C0',label=r'$\\Phi_z^{\\mathrm{quad}}$ Quadratic pot.',lw=2) # xkcd:prussian blue\n",
    "# ax.plot(z*1000,U_z_quad/2,'--',color='C0',label=r'$\\frac{1}{2}\\Phi_z^{\\mathrm{quad}}$',lw=2) # xkcd:prussian blue\n",
    "ax.plot(z*1000,U_z_gmol,'--',color='C1',label='$\\Phi_z^{\\mathrm{GM}}$ GiantMol axial pot.',lw=2)\n",
    "ax.vlines(-1.5,0,25,ls='dashdot',color='C1',label='pos. init.')\n",
    "\n",
    "ax.xaxis.set_major_locator(matplotlib.ticker.MultipleLocator(base=1))\n",
    "# text(-0.83, 8000, f'FWHM = ${2*sqrt(2*log(2)) * sig[to_plot] * 1000:.2f}$ MHz\\n        T = {temperature:.2f} K',\n",
    "# rotation=0,\n",
    "# horizontalalignment='left',\n",
    "# verticalalignment='bottom',\n",
    "# color='xkcd:vermillion',\n",
    "# fontsize=17,\n",
    "#      bbox=dict(facecolor='white'))\n",
    "\n",
    "ax.set_xlim(-2.2,4.3)\n",
    "ax.set_ylim(-0.01,25)\n",
    "ax.set_xlabel(r'$z$ [mm]')\n",
    "ax.set_ylabel('$U_{pot}$ [eV]')\n",
    "ax.legend(fontsize=16)\n",
    "\n",
    "ax.grid()\n",
    "tight_layout()\n",
    "\n",
    "# savefig('pot_compare_x1',dpi=300)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.3652335450575451, 1.8261677252877253, 3.6523354505754506, 7.304670901150901]\n",
      "[49.63476645494246, 48.173832274712275, 46.34766454942455, 42.6953290988491]\n",
      "[97.86213727 96.41115886 94.56613349 90.76363648]\n"
     ]
    }
   ],
   "source": [
    "E_f = 50 # eV\n",
    "M = 1e6*1.66053906660e-27\n",
    "Udc = 2.63053512573242\n",
    "z_i = -1.5e-3\n",
    "\n",
    "U_z_gmol_i = []\n",
    "E_i = []\n",
    "for Q in [1,5,10,20]:\n",
    "    rescale = m_Ca/M * Q/1\n",
    "    U_z_gmol_i.append( rescale*Udc*M*sqrt(wzLC)**2*LL*( 1-exp(-z_i**2/(2*LL)) ) / C_e )\n",
    "#     U_z_gmol_i.append( print(f'{U_z_gmol[argmin(abs(z+1.5e-3))]:.2f} eV') )\n",
    "    E_i.append( E_f - U_z_gmol_i[-1] )\n",
    "print(U_z_gmol_i)\n",
    "print(E_i)\n",
    "print(sqrt(2*divide(E_i,M)*C_e))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.007554705434561321"
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "LL / rescale"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.991189427312775\n",
      "1.042279411764706\n",
      "0.49778761061946897\n",
      "0.040564373897707305\n"
     ]
    }
   ],
   "source": [
    "print(4.52/2.27)\n",
    "print(56.7/54.4)\n",
    "\n",
    "print((4.52-2.27)/4.52)\n",
    "print((56.7-54.4)/56.7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "r = linspace(0,20e-3,50000)\n",
    "z = 0\n",
    "Udc = 1\n",
    "kappa = 0.227\n",
    "\n",
    "omega_z = sqrt(2*kappa*C_e*Udc/(m_Ca*d0**2))\n",
    "U_z_quad = 0.5*m_Ca*omega_z**2*(2*z**2-r**2) / C_e"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "# plot with complicated scan plot only crystal part at the end\n",
    "\n",
    "fig = figure('One res_noire',clear='True')\n",
    "ax = fig.add_subplot(1, 1, 1)\n",
    "\n",
    "ax.plot(r*1000,U_z_quad,'-',color='C0',label=r'$\\Phi_z^{\\mathrm{quad}}$ Quadratic pot.',lw=2)\n",
    "\n",
    "# ax.xaxis.set_major_locator(matplotlib.ticker.MultipleLocator(base=2))\n",
    "# text(-0.83, 8000, f'FWHM = ${2*sqrt(2*log(2)) * sig[to_plot] * 1000:.2f}$ MHz\\n        T = {temperature:.2f} K',\n",
    "# rotation=0,\n",
    "# horizontalalignment='left',\n",
    "# verticalalignment='bottom',\n",
    "# color='xkcd:vermillion',\n",
    "# fontsize=17,\n",
    "#      bbox=dict(facecolor='white'))\n",
    "\n",
    "# ax.set_xlim(-11.18,4.3)\n",
    "# ax.set_ylim(-0.01,1.10)\n",
    "ax.set_xlabel(r'$z$ [mm]')\n",
    "ax.set_ylabel('$U_{pot}$ [eV]')\n",
    "ax.legend(fontsize=18)\n",
    "\n",
    "ax.grid()\n",
    "tight_layout()\n",
    "\n",
    "# savefig('pot_compare_xynonnull',dpi=300)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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