1D maxwellian distribution

created distribution.py
created test_distribution.py
change `part` argument to `particle` and minor docstrings
Added is_electron


Update formula docstring

plasmapy/examples/Distribution_exemple.ipynb

@@ -0,0 +1,252 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2017-10-04T10:38:17.117221Z",
+     "start_time": "2017-10-04T10:38:16.455734Z"
+    }
+   },
+   "outputs": [],
+   "source": [
+    "import importlib\n",
+    "import sys\n",
+    "sys.path.insert(0, '../../../PlasmaPy')\n",
+    "\n",
+    "import numpy as np\n",
+    "from astropy import units as u\n",
+    "import plasmapy\n",
+    "import matplotlib.pyplot as plt\n",
+    "\n",
+    "from plasmapy.constants import (m_p, m_e, c, mu0, k_B, e, eps0, pi, e)\n",
+    "from plasmapy.physics.distribution import Maxwellian_1D\n",
+    "\n",
+    "from imp import reload\n",
+    "reload(plasmapy.physics.distribution)\n",
+    "%matplotlib inline"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2017-10-04T10:38:24.834239Z",
+     "start_time": "2017-10-04T10:38:24.818209Z"
+    }
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/latex": [
+       "$5.9163297 \\times 10^{-7} \\; \\mathrm{\\frac{s}{m}}$"
+      ],
+      "text/plain": [
+       "<Quantity 5.916329687405701e-07 s / m>"
+      ]
+     },
+     "execution_count": 3,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "Maxwellian_1D(v=1*u.m/u.s, T= 30000*u.K, particle='e',V_drift=0*u.m/u.s)\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2017-10-04T10:38:34.361995Z",
+     "start_time": "2017-10-04T10:38:34.187756Z"
+    }
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "0.9999999999999999\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "[<matplotlib.lines.Line2D at 0x7f101b8146a0>]"
+      ]
+     },
+     "execution_count": 4,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAW4AAAEQCAYAAACQip4+AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAJAYghsAEkNwA0Bi/h99lO882H4frAAAAABJRU5ErkJggg==\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f101d8817b8>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# With a vertor (from Numpy)\n",
+    "start = -5000;\n",
+    "stop = - start;\n",
+    "dv = 10000 * u.m/u.s;\n",
+    "\n",
+    "v = np.arange(start,stop,dtype='float64')* dv;\n",
+    "\n",
+    "#Test the normationation to 1\n",
+    "integral = (Maxwellian_1D(v,T= 30000*u.K, particle='e')).sum()*dv\n",
+    "\n",
+    "print(integral)\n",
+    "\n",
+    "plt.plot(v,(Maxwellian_1D(v,T= 30000*u.K, particle='e')))\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2017-10-04T10:38:47.008876Z",
+     "start_time": "2017-10-04T10:38:46.994885Z"
+    }
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "1.0\n"
+     ]
+    }
+   ],
+   "source": [
+    "#test std \n",
+    "T =  30000*u.K\n",
+    "std = np.sqrt((Maxwellian_1D(v,T=T, particle='e')*v**2*dv).sum())\n",
+    "T_theo = (std**2/k_B*m_e).to(u.K)\n",
+    "\n",
+    "print(T_theo/T)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2017-10-04T10:39:00.264312Z",
+     "start_time": "2017-10-04T10:39:00.225670Z"
+    }
+   },
+   "outputs": [],
+   "source": [
+    "T_e = 30000*u.K;\n",
+    "V_drift = 10*u.m/u.s;\n",
+    "\n",
+    "start = -5000;\n",
+    "stop = - start;\n",
+    "dv = 10000 * u.m/u.s;\n",
+    "\n",
+    "v_vect = np.arange(start,stop,dtype='float64')* dv;"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2017-10-04T10:39:00.477616Z",
+     "start_time": "2017-10-04T10:39:00.467525Z"
+    }
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/latex": [
+       "$0 \\; \\mathrm{\\frac{m}{s}}$"
+      ],
+      "text/plain": [
+       "<Quantity 0.0 m / s>"
+      ]
+     },
+     "execution_count": 9,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "v_vect[Maxwellian_1D(v_vect,T=T_e, particle='e',V_drift = 0*u.m/u.s ).argmax()]"
+   ]
+  },
+  {
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+   "execution_count": null,
+   "metadata": {
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+     "end_time": "2017-10-04T08:41:33.617076Z",
+     "start_time": "2017-10-04T08:41:33.603795Z"
+    }
+   },
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
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+    "name": "ipython",
+    "version": 3
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+     "delete_cmd_prefix": "del ",
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+     "varRefreshCmd": "print(var_dic_list())"
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+    "r": {
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+    }
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+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}

plasmapy/physics/__init__.py

@@ -21,3 +21,5 @@
 from .relativity import Lorentz_factor
 
 from .transport import Coulomb_logarithm
+
+from .distribution import (Maxwellian_1D)

plasmapy/physics/distribution.py

@@ -0,0 +1,94 @@
+"""Functions to deal with distribution : generate, fit, calculate"""
+
+from astropy import units
+
+from astropy.units import (UnitConversionError, UnitsError, quantity_input,
+                           Quantity)
+
+from ..constants import (m_p, m_e, c, mu0, k_B, e, eps0, pi, e)
+from ..atomic import (ion_mass, charge_state)
+from ..atomic.atomic import _is_electron as is_electron
+import numpy as np
+
+from ..utils import _check_quantity, check_relativistic, check_quantity
+
+
+@units.quantity_input
+def Maxwellian_1D(v: units.m/units.s,
+                  T: units.K, particle="e",
+                  V_drift=0*units.m/units.s):
+    r"""Return the probability at the velocity `v` in m/s
+     to find a particle `particle` in a plasma of temperature `T`
+     following the Maxwellian distribution function
+
+    Parameters
+    ----------
+    v: Quantity
+        The velocity in units convertible to m/s
+
+    T: Quantity
+        The temperature in Kelvin
+
+    particle: string, optional
+        Representation of the particle species(e.g., 'p' for protons, 'D+'
+        for deuterium, or 'He-4 +1' for $He_4^{+1}$ : singly ionized helium-4),
+        which defaults to electrons.
+
+    Returns
+    -------
+    f : Quantity
+        probability in Velocity^-1, normized so that:
+        $\int_{- \infty}^{\infty} f(v) dv = 1}
+
+    Raises
+    ------
+    TypeError
+        The parameter arguments are not Quantities and
+        cannot be converted into Quantities.
+
+    UnitConversionError
+        If the parameters is not in appropriate units.
+
+    ValueError
+        If the temperature is negative, or the particle mass or charge state
+        cannot be found.
+
+    Notes
+    -----
+    In one dimension, the Maxwellian distribution function for a particle of
+    mass m, velocity v, a drift velocity V and with temperature T is:
+
+    .. math::
+    f = \sqrt{\frac{m}{2 \pi k_B T}} \exp(-\frac{m}{2 k_B T} (v-V)^2)
+
+
+    Example
+    -------
+    >>> from plasmapy.physics import Maxwellian_1D
+    >>> from astropy import units as u
+    >>> v=1*u.m/u.s
+    >>> Maxwellian_1D(v=v, T= 30000*u.K, particle='e',V_drift=0*u.m/u.s)
+    <Quantity 5.916329687405701e-07 s / m>
+    """
+
+    # pass to Kelvin
+
+    if T.unit.is_equivalent(units.K):
+        T = T.to(units.K, equivalencies=units.temperature_energy())
+
+    # Get mass
+
+    if is_electron(particle):
+        m_s = m_e
+
+    else:
+        try:
+            m_s = ion_mass(particle)
+        except Exception:
+            raise ValueError("Unable to find ion mass in Maxwellian_1D")
+
+    T = k_B*T
+
+    f = np.sqrt((m_s/(2*pi*T)))*np.exp(-m_s/(2*T)*(v-V_drift)**2)
+
+    return f.to(units.s/units.m)

plasmapy/physics/tests/test_distribution.py

@@ -0,0 +1,44 @@
+"""Tests for functions that uses Distribution functions."""
+
+import numpy as np
+import pytest
+from astropy import units as u
+
+
+from ...constants import (m_p, m_e, c, mu0, k_B, e, eps0, pi, e)
+from ...atomic import (ion_mass, charge_state)
+from ..distribution import (Maxwellian_1D)
+
+T_e = 30000*u.K
+V_drift = 1000000*u.m/u.s
+
+start = -5000
+stop = - start
+dv = 10000 * u.m/u.s
+
+v_vect = np.arange(start, stop, dtype='float64') * dv
+
+
+def test_Maxwellian_1D():
+    """test the 1D maxwellian distribution function"""
+
+    max_index = Maxwellian_1D(v_vect, T=T_e, particle='e', V_drift=0*u.m/u.s
+                              ).argmax()
+    assert np.isclose(v_vect[max_index].value, 0.0)
+
+    max_index = Maxwellian_1D(v_vect, T=T_e, particle='e', V_drift=V_drift
+                              ).argmax()
+    assert np.isclose(v_vect[max_index].value, V_drift.value)
+
+    # integral of the distribution over v_vect
+    integral = (Maxwellian_1D(v_vect, T=30000*u.K, particle='e')).sum()*dv
+    assert np.isclose(integral, 1.0)
+
+    std = (Maxwellian_1D(v_vect, T=T_e, particle='e')*v_vect**2*dv).sum()
+    std = np.sqrt(std)
+    T_distri = (std**2/k_B*m_e).to(u.K)
+
+    assert np.isclose(T_distri.value, T_e.value)
+
+    with pytest.raises(ValueError):
+        Maxwellian_1D(1*u.m/u.s, T=1*u.K, particle='XXX')