Geometric buckling from macroscopic cross sections and diffusion coefficient
============================================================================

Geometrical buckling is a quantity describing the reactor which depends only on its
geometry. It can also be calculated from the macroscopic cross sections and the
diffusion coefficient as well as the effective multiplicative factor and the neutron
production rate.

**Links:**

#. `Wikipedia, second part of second equation <https://en.wikipedia.org/wiki/Geometric_and_material_buckling#Material_Buckling>`__.

.. py:currentmodule:: symplyphysics.laws.nuclear.buckling.geometric_buckling_from_macroscopic_fission_cross_section_diffusion_coefficient

.. py:data:: neutrons_per_fission

    The average number of neutrons produced per fission. See :attr:`~symplyphysics.symbols.basic.particle_count`.

Symbol:
    :code:`nu`

Latex:
    :math:`\nu`

Dimension:
    :code:`dimensionless`


.. py:data:: effective_multiplication_factor

    :attr:`~symplyphysics.symbols.nuclear.effective_multiplication_factor`.

Symbol:
    :code:`k_eff`

Latex:
    :math:`k_\text{eff}`

Dimension:
    :code:`dimensionless`


.. py:data:: macroscopic_fission_cross_section

    :attr:`~symplyphysics.symbols.nuclear.macroscopic_cross_section` of fission.

Symbol:
    :code:`Sigma_f`

Latex:
    :math:`\Sigma_\text{f}`

Dimension:
    :code:`1/length`


.. py:data:: macroscopic_absorption_cross_section

    :attr:`~symplyphysics.symbols.nuclear.macroscopic_cross_section` of absorption.

Symbol:
    :code:`Sigma_a`

Latex:
    :math:`\Sigma_\text{a}`

Dimension:
    :code:`1/length`


.. py:data:: diffusion_coefficient

    :attr:`~symplyphysics.symbols.nuclear.neutron_diffusion_coefficient`.

Symbol:
    :code:`D`

Latex:
    :math:`D`

Dimension:
    :code:`length`


.. py:data:: geometric_buckling

    :attr:`~symplyphysics.symbols.nuclear.geometric_buckling`.

Symbol:
    :code:`B_g^2`

Latex:
    :math:`B_\text{g}^2`

Dimension:
    :code:`1/area`


.. py:data:: law

    :code:`B_g^2 = (nu / k_eff * Sigma_f - Sigma_a) / D`


    Latex:
        .. math::
            B_\text{g}^2 = \frac{\frac{\nu}{k_\text{eff}} \Sigma_\text{f} - \Sigma_\text{a}}{D}