Interaction cross section in Coulomb's interaction model
========================================================

In a magnetron, the effective cross section of particle interaction can be calculated via the
ionization energy of gas atoms. See :ref:`Effective cross section <effective_cross_section>`.

**Notation:**

#. :math:`e` (:code:`e`) is :attr:`~symplyphysics.quantities.elementary_charge`.
#. :math:`\varepsilon_0` (:code:`epsilon_0`) is :attr:`~symplyphysics.quantities.vacuum_permittivity`.

..
    TODO: find link
    TODO: move to `magnetron` folder?

.. py:currentmodule:: symplyphysics.laws.chemistry.interaction_cross_section_in_coulomb_interaction_model

.. py:data:: interaction_cross_section

    :attr:`~symplyphysics.symbols.chemistry.cross_section` of the interaction of particles.

Symbol:
    :code:`sigma`

Latex:
    :math:`\sigma`

Dimension:
    :code:`area`


.. py:data:: ionization_energy

    Ionization :attr:`~symplyphysics.symbols.basic.energy` of atoms expressed in :attr:`~symplyphysics.symbols.electrodynamics.voltage`.

Symbol:
    :code:`E_i`

Latex:
    :math:`E_\text{i}`

Dimension:
    :code:`voltage`


.. py:data:: law

    :code:`sigma = e^2 / (2 * pi * epsilon_0^2 * E_i^2)`


    Latex:
        .. math::
            \sigma = \frac{e^{2}}{2 \pi \varepsilon_0^{2} E_\text{i}^{2}}