Non-classical particle transport with angular-dependent path-length distributions. I: Theory

Abstract

This paper extends a recently introduced theory describing particle transport for random statistically homogeneous systems in which the distribution function p(s) for chord lengths between scattering centers is non-exponential. Here, we relax the previous assumption that p(s) does not depend on the direction of flight Ω; this leads to a new generalized linear Boltzmann equation that includes angular-dependent cross sections, and to a new generalized diffusion equation that accounts for anisotropic behavior resulting from the statistics of the system.