Neutron flux for uniform sphere
===============================

Neutron flux for uniform sphere is a function of radial_distance :math:`r` to the center of the
sphere and depends on the radius :math:`r_0` of the sphere.

**Links:**

#. `NuclearPower, see end of page <https://www.nuclear-power.com/nuclear-power/reactor-physics/neutron-diffusion-theory/finite-spherical-reactor/>`__.

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

.. py:data:: dimension_factor

    Dimension factor that appears as a coefficient in the solution to the :ref:`differential
    equation <Diffusion equation from neutron flux>`. See :attr:`~symplyphysics.symbols.nuclear.neutron_flux`.

Symbol:
    :code:`Phi_0`

Latex:
    :math:`\Phi_{0}`

Dimension:
    :code:`1/(area*time)`


.. py:data:: radial_distance

    Radial distance, or :attr:`~symplyphysics.symbols.classical_mechanics.distance_to_origin` of coordinate system, i.e. the center
    of the sphere.

Symbol:
    :code:`r`

Latex:
    :math:`r`

Dimension:
    :code:`length`


.. py:data:: radius

    :attr:`~symplyphysics.symbols.classical_mechanics.radius` of the sphere.

Symbol:
    :code:`r_0`

Latex:
    :math:`r_{0}`

Dimension:
    :code:`length`


.. py:data:: neutron_flux

    :attr:`~symplyphysics.symbols.nuclear.neutron_flux` at a :attr:`radial_distance` from the center of the sphere.

Symbol:
    :code:`Phi`

Latex:
    :math:`\Phi`

Dimension:
    :code:`1/(area*time)`


.. py:data:: law

    :code:`Phi = Phi_0 * sin(pi / r_0 * r) / r`


    Latex:
        .. math::
            \Phi = \Phi_{0} \frac{\sin{\left(\frac{\pi}{r_{0}} r \right)}}{r}