Integrodifferential equations for the two-dimensional transition kernels of invariant imbedding

摘要

Invariant imbedding methods for two spatial dimensions are applied to derive a set of integrodifferential equations and related boundary conditions, in the kernels of transmission, left-turn, and right-turn transition operators for a two-dimensional particle transport theory problem. The operators describe the transition from incident to exiting physical states over rectangular regions. The set of equations is coupled only through the reflection kernel. This work is a continuation of and complements the earlier effort of the authors wherein an integrodifferential boundary-value problem for the reflection kernel is derived.