A Regularized Boltzmann Scattering Operator for Highly Forward Peaked Scattering

Abstract

Extremely short collision mean free paths and near-singular elastic and inelastic differential cross sections (DCS) make analog Monte Carlo and deterministic computational approaches impractical for charged particle transport. The widely used alternative, the condensed history method, while efficient, also suffers from several limitations arising from the use of precomputed infinite medium distributions for sampling particle directions and energies. Accordingly, considerable attention has recently focused on the development of computationally efficient algorithms that implement the correct transport mechanics. Fokker-Planck [JEM81] and Boltzmann Fokker-Planck [CL83] approximations have historically proved very useful in handling highly peaked scattering in certain classes of problems but these approaches are limited in the accuracy they can ultimately deliver. A more general methodology that allows accuracy to be systematically increased with practically no enhancement of algorithmic complexity has become possible with the advent of recently proposed higher order Fokker-Planck expansions [GCP96] and their implementation in so-called Generalized Fokker-Planck models [LL01,PP01,PKH02]. The goal of these newer approaches is to approximate the analog transport problem by one which is characterized by longer or stretched mean free paths and nonsingular collision operators but which can be solved numerically with considerably less effort than the analog problem and whose accuracy and efficiency can be readily adapted to a broad class of problems. One such implementation that has proved particularly efficient uses purely discrete scattering angle and hybrid discrete-continuous scattering angle representations [FPKL1,FPKL2]. Moreover, generalizations of these methodologies to describe energy-loss straggling have been successfully demonstrated [PKH02].