A Generalized Fokker-Planck Model for Transport of Collimated Beams

A generalized Fokker-Planck (GFP) model is introduced for application to the problem of the angular spreading of a broad beam of charged particles. This approach extends the classic Fokker-Planck (FP) approximation of the scattering operator to instances when the differential scattering cross section is not sufficiently forward peaked for the strict FP representation to be valid. Our previously developed (1 - )ⁿ-moments method is used to construct a truncated hierarchy of moment equations from the GFP and transport equations. For slab thicknesses that are small compared to the transport mean-free-path, the scalar flux is explicitly represented as a Taylor expansion in the depth variable for different truncation orders and for different orders of the generalized Fokker-Planck expansion. Numerical results indicate that the GFP method is a viable method for dealing with larger scattering angles than are possible with the classic FP approximation.