{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Basics\n",
    "\n",
    "This notebook is designed to document some simple examples of ALP propagation problems to show how to use ALPRO. We'll also take a look at some of the classes used, and what needs to be initialised. In the other tutorials, there are more details on setting up your own models.   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt \n",
    "import numpy as np \n",
    "import alpro \n",
    "alpro.util.set_default_plot_params()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The top-level class that is used to interface with photon ALP conversion calculations is the \"Survival\" class. Any model is initialised through a call like this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "s = alpro.Survival()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The ALP parameters are set using the set_params method"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "s.set_params(g = 1e-13 * 1e-9, mass = 1e-13, invgev = False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can print out what is contained in the survival class at this stage. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "model                 None\n",
      "coherence_func        None\n",
      "available_models      ['1821', '1275a', '1275b', 'custom', 'file', 'uniform', 'libanov', None]\n",
      "get_P                 CPUDispatcher(<function get_P at 0x134b4d7a0>)\n",
      "pol_matrix_bool       False\n",
      "g_a                   1e-22\n",
      "mass                  1e-13\n"
     ]
    }
   ],
   "source": [
    "for k,v in vars(s).items(): \n",
    "    print (\"{:20s}  {}\".format(k,v))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "At this stage, we haven't really initialised anything in the model, and we minimally need a correctly set up domain class which stores the magentic field and density profile used as input to the ALP calculation. A simple way of getting this set up is to use one of the inbuild models, which you can see using the following command. We can pick one of those and see that the domain is now populated. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['1821', '1275a', '1275b', 'custom', 'file', 'uniform', 'libanov', None]\n"
     ]
    }
   ],
   "source": [
    "s.show_available_models()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "profile               None\n",
      "beta                  100\n",
      "coherence_r0          None\n",
      "Bz                    1.0\n",
      "r                     [0.]\n",
      "deltaL                [10.]\n",
      "rcen                  [5.]\n",
      "ne                    [0.]\n",
      "phi                   [0.]\n",
      "B                     [1.e-05]\n"
     ]
    }
   ],
   "source": [
    "s = alpro.Survival(\"uniform\")\n",
    "s.setup_regular_model(B = 1e-5, L = 10.0, ne = 0.0, N = 1, phi = 0.0)\n",
    "\n",
    "for k,v in vars(s.domain).items(): \n",
    "    print (\"{:20s}  {}\".format(k,v))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The variable $\\varphi$ is the angle made between the magnetic field vector and the $y$-axis. This model therefore is a single cell model with a $10\\mu$G magnetic field aligned with the $y$-axis, with a $10$\\,kpc domain size. We can now compute the conversion probability and compare with the analytic formula.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "tags": [
     "nbsphinx-thumbnail"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "s.set_params(g = 1e-12 * 1e-9, mass = 1e-11)   # set up ALP parameters in eV^-1 and eV \n",
    "energies = np.logspace(3,4,1000)               # energies in eV \n",
    "s.propagate(energies=energies, pol=\"y\")        # propagate the photon-ALP beam\n",
    "fig = s.default_plot(theory = s.analytic_pga)  # this will compare to the analytic formula\n",
    "plt.semilogy()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can re-initialise different ALP parameters and rerun -- let's try something with a larger $g$. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "s.set_params(g = 1e-10 * 1e-9, mass = 1e-11)   # set up ALP parameters in eV^-1 and eV \n",
    "s.propagate(energies=energies, pol=\"y\")        # propagate the photon-ALP beam\n",
    "fig = s.default_plot(theory = s.analytic_pga)  # this will compare to the analytic formula\n",
    "plt.semilogy()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also modify the magnetic field and rerun"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "s.set_params(g = 1e-10 * 1e-9, mass = 1e-11)   # set up ALP parameters in eV^-1 and eV \n",
    "s.domain.B *= 0.01                             # make the field 100x weaker\n",
    "s.propagate(energies=energies, pol=\"y\")        # propagate the photon-ALP beam\n",
    "fig = s.default_plot(theory = s.analytic_pga)  # this will compare to the analytic formula\n",
    "plt.semilogy()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You get the idea! "
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
