Electron distribution function in gas plasma per Maxwell
========================================================

In a gas discharge, electrons have a wide range of energies, which is described by the
electron energy distribution function. Electrons in a gas-discharge plasma acquire their
energy under the action of an electric field. Energy consumption occurs due to elastic
and, especially, inelastic collisions with atoms. In addition, energy exchange between
electrons is also possible in plasma. Depending on the relationship between all these
factors, different electron energy distributions are established. Under equilibrium
conditions, the Maxwell distribution is most common.

**Notation:**

#. :math:`e` (:code:`e`) is :attr:`~symplyphysics.quantities.elementary_charge`.

**Links:**

#. `Comsol, possible similar formula here <https://www.comsol.com/blogs/electron-energy-distribution-function>`__.

..
    TODO: find a more suitable link

.. py:currentmodule:: symplyphysics.laws.chemistry.electron_distribution_function_in_gas_plasma_by_maxwell

.. py:data:: distribution_function

    Electron distribution function.

Symbol:
    :code:`f`

Latex:
    :math:`f`

Dimension:
    :code:`dimensionless`


.. py:data:: voltage

    :attr:`~symplyphysics.symbols.electrodynamics.voltage` between electrodes.

Symbol:
    :code:`V`

Latex:
    :math:`V`

Dimension:
    :code:`voltage`


.. py:data:: electron_energy

    Electron :attr:`~symplyphysics.symbols.basic.energy`.

Symbol:
    :code:`E`

Latex:
    :math:`E`

Dimension:
    :code:`energy`


.. py:data:: energy_constant

    Constant equal to :math:`2.07 \, \text{eV}`.

Symbol:
    :code:`E_0`

Latex:
    :math:`E_0`

Dimension:
    :code:`energy`


.. py:data:: law

    :code:`f = E_0 * sqrt(e * V) / E^(3/2) * exp(-1.55 * e * V / E)`


    Latex:
        .. math::
            f = \frac{E_0 \sqrt{e V}}{E^{\frac{3}{2}}} \exp{\left(- \frac{1.55 e V}{E} \right)}