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

• We introduce a new generalized theory to address non-classical transport.
• The locations of the scattering centers are correlated and angular-dependent.
• We derive the integral formulation of the proposed theory.
• We derive asymptotic diffusion approximations of the new theory.

This paper extends a recently introduced theory describing particle transport for random statistically homogeneous systems in which the distribution function p(s)p(s) for chord lengths between scattering centers is non-exponential. Here, we relax the previous assumption that p(s)p(s) does not depend on the direction of flight ΩΩ; 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.