Planar Green's function in an infinite multiplying medium

摘要

Throughout the history of neutron transport theory, the study of simplified problems that have analytical or semi-analytical solutions has been a foundation for more complicated analyses. Analytical transport results are often used as benchmarks or in pedagogical settings. Benchmark problems in infinite homogeneous media have been studied continually, beginning with the monograph by Case, DeHoffmann, and Placzek. A fundamental problem considered in this work is the Green's function in an infinite medium. The Green's function problem considers an infinite planar source emitting neutral particles in the single directions'. Recently, this Green's function has been used to obtain solutions for finite media. These solutions, which hinge on accurate and fast evaluation of the infinite medium Green's function, use Fourier and Laplace transform inversion techniques for the evaluation. Until now, only absorbing media have been considered, and applications were therefore limited to non-multiplying media. In an effort to relax this limitation, the infinite medium Green's function is numerically evaluated for an infinite multiplying medium using the double-sided Laplace transform inversion. Of course, no steady-state mathematical solution exists for an infinite multiplying medium with a source present; however, the non-physical solution in an infinite medium can be used in finite media problems where the solution is physically realizable.