The Boltzmann/Spencer-Lewis smart scattering formulation of forward and adjoint coupled electron-positron-photon transport in three-dimensional multimedia regions.

Abstract

In this work a new method is developed that divides the physics of charged particle transport into two separate classes depending on the type of particle collisions that take place. The result is the Boltzmann/Spencer-Lewis SMART scattering formulation that combines a path length dependent description of the continuous slowing down approximation with the physics of catastrophic collisions. Both the forward and exact adjoint of the S(N)/diamond differenced numerical solution of this equation, using multigroup constants produced by a pre-existing cross section generating code, are developed for x-y-z multimedia geometry. Sample problems demonstrating the nearly perfect agreement between the forward and adjoint numerical algorithms are included. Evidence of the substantial difference between the adjoint of the continuous equation and the adjoint of the discretized equations is also presented.