The Radiation Transport Equation
Gnat solves the multi-group Radiation Transport Equation (RTE) where the scattering kernel and external sources have been expanded in spherical harmonics:
(1)In Eq. (1) is a position vector (), is the angular direction of travel (), is time (), is the radiation energy group, is the total number of energy groups, is the angular radiation flux for group (), is the radiation speed for a given energy group (), is the total macroscopic cross-section for group (), is the degree of the Legendre expansion on the scattering kernel, are the Legendre moments of the macroscopic scattering cross-section (), are the real spherical harmonics (), are the spherical harmonic moments of the angular flux (), is a group angular neutron source for group (). has the following definition in Gnat:
(2)where is the fission spectra for group , is the neutron production cross-section for group (), is the scalar neutron flux for group (), and is the degree of the spherical harmonics expansion of the group external source (). The fission source is only relevant to neutron transport problems, and is therefore excluded in gamma photon transport simulations.
The boundary conditions for Eq. (1) are the following:
(3)where
is the specular reflection direction ().
is the incoming angular neutron flux for energy group ().
is the specular reflection albedo (dimensionless).
is the specularly reflected angular neutron flux for energy group ().
is the boundary normal vector.
is the boundary surface.