An Asymptotic Model for the Spreading of a Collimated Beam

We show, using asymptotics, that under conditions when the angular distribution is forward peaked, the transport equation can be reduced to an advection-diffusion equation for the scalar flux. This equation describes lateral diffusive spreading with depth of an initially collimated beam of arbitrary spatial cross section and is of particular significance when scattering is highly forward peaked. Numerical results for the scalar flux for a planar source (when lateral diffusion vanishes) and in the presence of strongly anisotropic scattering are contrasted with benchmark Monte Carlo results as well as with the scalar flux obtained from a novel modified multiple scattering method. We observe that the asymptotic model is only accurate over distances small compared with the transport mean free path. It is conjectured that carrying the asymptotic expansions to higher orders or using a different asymptotic scaling might extend the accuracy of the asymptotic model to higher orders in the transport mean free path.