Nuclear Physics (Symbols)
=========================

Symbols related to electrodynamics.

.. py:currentmodule:: symplyphysics.symbols.nuclear

.. py:data:: geometric_buckling

    **Geometric buckling** is a measure of neutron leakage in a nuclear reactor.

    **Links:**

    #. `Wikipedia <https://en.wikipedia.org/wiki/Geometric_and_material_buckling#>`__.

Symbol:
    :code:`B_g^2`

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

Dimension:
    :code:`1/area`


.. py:data:: multiplication_factor

    The **multiplication factor** denotes the rate of change of the neutron population in a
    system, and is the ratio of the neutron population in the following generation to the
    neutron population in the given generation.

    **Links:**

    #. `Wikipedia <https://en.wikipedia.org/wiki/Four_factor_formula#Multiplication>`__.

Symbol:
    :code:`k`

Latex:
    :math:`k`

Dimension:
    :code:`dimensionless`


.. py:data:: infinite_multiplication_factor

    The **infinite multiplication factor** is the :attr:`~multiplication_factor` when the
    medium is infinite so that neutrons cannot leak out of the system.

    **Links:**

    #. `Wikipedia <https://en.wikipedia.org/wiki/Four_factor_formula#Multiplication>`__.

Symbol:
    :code:`k_inf`

Latex:
    :math:`k_{\infty}`

Dimension:
    :code:`dimensionless`


.. py:data:: effective_multiplication_factor

    The **effective multiplication factor** is most often defined as the ratio of the rate
    of neutron production to the rate of neutron loss in a nuclear system.

    **Links:**

    #. `Wikipedia <https://en.wikipedia.org/wiki/Nuclear_chain_reaction#Effective_neutron_multiplication_factor>`__.

Symbol:
    :code:`k_eff`

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

Dimension:
    :code:`dimensionless`


.. py:data:: neutron_diffusion_area

    **Diffusion area** is a quantity that appears when calculating the average distance
    between the neutron's birth point as a thermal neutron and its absorption.

    **Links:**

    #. `NuclearPower <https://www.nuclear-power.com/nuclear-power/reactor-physics/neutron-diffusion-theory/diffusion-length/>`__.

Symbol:
    :code:`L^2`

Latex:
    :math:`L^{2}`

Dimension:
    :code:`area`


.. py:data:: neutron_flux

    **Neutron flux** is a scalar quantity defined as the total distance traveled by all free
    neutrons per unit time and volume.

    **Links:**

    #. `Wikipedia <https://en.wikipedia.org/wiki/Neutron_flux#>`__.

Symbol:
    :code:`Phi`

Latex:
    :math:`\Phi`

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


.. py:data:: material_buckling

    **Material buckling** is a measure of the difference between neutron production and
    neutron absorption in a nuclear reactor.

    **Links:**

    #. `Wikipedia <https://en.wikipedia.org/wiki/Geometric_and_material_buckling#>`__.

Symbol:
    :code:`B_m^2`

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

Dimension:
    :code:`1/area`


.. py:data:: fast_non_leakage_probability

    **Fast non-leakage probability** is defined as the ratio of the number of fast neutrons
    that do not leak from the reactor to the number of fast neutrons produced by all
    fissions.

Symbol:
    :code:`P_FNL`

Latex:
    :math:`P_\text{FNL}`

Dimension:
    :code:`dimensionless`


.. py:data:: thermal_non_leakage_probability

    **Thermal non-leakage probability** is defined as the ratio of the number of thermal
    neutrons that do not leak from the reactor to the number of thermal neutrons produced by
    all fissions.

Symbol:
    :code:`P_TNL`

Latex:
    :math:`P_\text{TNL}`

Dimension:
    :code:`dimensionless`


.. py:data:: fast_fission_factor

    **Fast fission factor** is the ratio of total number of fission neutrons to the number
    of fission neutrons from just thermal fissions.

    **Links:**

    #. `Wikipedia, see row 4 of the table <https://en.wikipedia.org/wiki/Six_factor_formula#>`__.

Symbol:
    :code:`epsilon`

Latex:
    :math:`\varepsilon`

Dimension:
    :code:`dimensionless`


.. py:data:: resonance_escape_probability

    **Resonance escape probability** is the probability that a neutron will slow down from
    fission energy to thermal energies without being captured by a nuclear resonance.

    **Links:**

    #. `Wikipedia <https://en.wikipedia.org/wiki/Resonance_escape_probability#>`__.

Symbol:
    :code:`p`

Latex:
    :math:`p`

Dimension:
    :code:`dimensionless`


.. py:data:: fast_absorption_fission_probability

    **Fast absorption fission probability** is the probability that a fast neutron
    absorption in fuel causes fission.

    **Links:**

    #. `Wikipedia, see list under the table <https://en.wikipedia.org/wiki/Six_factor_formula#>`__.

Symbol:
    :code:`P_FAF`

Latex:
    :math:`P_\text{FAF}`

Dimension:
    :code:`dimensionless`


.. py:data:: thermal_absorption_fission_probability

    **Thermal absorption fission probability** is the probability that a thermal neutron
    absorption in fuel causes fission.

    **Links:**

    #. `Wikipedia, see list under the table <https://en.wikipedia.org/wiki/Six_factor_formula#>`__.

Symbol:
    :code:`P_TAF`

Latex:
    :math:`P_\text{TAF}`

Dimension:
    :code:`dimensionless`


.. py:data:: thermal_utilization_factor

    **Thermal utilization factor** is defined as the ratio of the number of neutrons
    absorbed by the fuel isotope to the number of neutrons absorbed anywhere.

    **Links:**

    #. `Wikipedia, second row of the table <https://en.wikipedia.org/wiki/Six_factor_formula#>`__.

Symbol:
    :code:`f`

Latex:
    :math:`f`

Dimension:
    :code:`dimensionless`


.. py:data:: fast_utilization

    **Fast utilization** is the probability that a fast neutron is absorbed in fuel.

    **Links:**

    #. `Wikipedia, see list under the table <https://en.wikipedia.org/wiki/Six_factor_formula#>`__.

Symbol:
    :code:`u_f`

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

Dimension:
    :code:`dimensionless`


.. py:data:: neutron_fermi_age

    **Fermi age** is a measure of how far a neutron travels during moderation (e.g. in a
    graphite moderator), similar to the :attr:`~symplyphysics.symbols.nuclear.neutron_diffusion_area`.

Symbol:
    :code:`tau`

Latex:
    :math:`\tau`

Dimension:
    :code:`area`


.. py:data:: thermal_fission_factor

    **Thermal fission factor** is defined as the ratio of the number of neutrons produced
    from fission to the absorption in fuel isotope.

    **Links:**

    #. `Wikipedia, first line in table <https://en.wikipedia.org/wiki/Six_factor_formula#>`__.

Symbol:
    :code:`eta`

Latex:
    :math:`\eta`

Dimension:
    :code:`dimensionless`


.. py:data:: half_life

    **Half-life** is the time required for a quantity to reduce to half of its initial
    value.

    **Links:**

    #. `Wikipedia <https://en.wikipedia.org/wiki/Half-life#>`__.

Symbol:
    :code:`t_1/2`

Latex:
    :math:`t_{1/2}`

Dimension:
    :code:`time`


.. py:data:: macroscopic_cross_section

    The **macroscopic cross section** is an interaction rate per unit distance traveled by
    the neutron obtained by multiplying the microscopic cross section (expressed as an area)
    by atomic density (expressed as reciprocal volume).

    **Links:**

    #. `ScienceDirect <https://www.sciencedirect.com/topics/engineering/macroscopic-cross-section>`__.

Symbol:
    :code:`Sigma`

Latex:
    :math:`\Sigma`

Dimension:
    :code:`1/length`


.. py:data:: neutron_diffusion_coefficient

    **Diffusion coefficient** is the proportionality constant between the neutron current
    density and the neutron current, as per the first Fick's law of diffusion.

    **Links:**

    #. `NuclearPower <https://www.nuclear-power.com/nuclear-power/reactor-physics/neutron-diffusion-theory/diffusion-coefficient/>`__.

Symbol:
    :code:`D`

Latex:
    :math:`D`

Dimension:
    :code:`length`


.. py:data:: migration_area

    **Migration area**, or the square of the migration length, is the measure of the
    distance a neutron travels while slowing down as a fast neutron and diffusing as a
    thermal neutron.

Symbol:
    :code:`M^2`

Latex:
    :math:`M^{2}`

Dimension:
    :code:`area`


.. py:data:: reproduction_factor

    **Reproduction factor** is defined as the ratio of the number of neutrons produced from
    thermal fissions to the thermal absorption in fuel isotope.

    **Links:**

    #. `Wikipedia, first row in table <https://en.wikipedia.org/wiki/Four_factor_formula>`__.

Symbol:
    :code:`eta`

Latex:
    :math:`\eta`

Dimension:
    :code:`dimensionless`