Efficient yet accurate solution of the linear transport equation in the presence of internal sources: The exponential-linear-in-depth approximation

We present solutions to the linear transport equation valid for monoenergetic particles interacting with a multiple scattering and absorbing layered medium possessing a general anisotropic internal source term. A new exponential-linear approximation to the internal source as a function of scattering depth is introduced and compared to approximations that vary linearly and quadratically in scattering depth. The prime merit of this new approximation is to provide a very efficient yet accurate solution to the linear transport equation by substantially reducing the spatial mesh size. Numerical results pertaining to (1 ) an embedded thermal source and (2) a rapidly varying beam pseudosource demonstrate that the exponential-linear approximation is vastly superior both in speed and accuracy to a linear or quadratic approximation. Potential applications include neutral (photon, neutron) or charged (electron, ion) particle transport as well as linearized gas dynamics.