THE FERMI-EYGES BEAM ANALYSIS FOR A HETEROGENEOUS ABSORBING STOCHASTIC MEDIUM

The Fermi-Eyges beam analysis yields an approximate analytic solution for the energy dependent angular flux corresponding to the steady stat e, finite slab, searchlight problem with a monoenergetic, normally inc ident, beam. Their analysis, which treats a nearly collimated beam of particles, originally entering a source-free slab through one surface as a perfectly collimated pencil beam, was restricted to a purely scat tering, homogeneous medium. The purpose of this paper is to generalize the Fermi-Eyges analysis in two ways. First, in a straightforward gen eralization, the slab is allowed arbitrary heterogeneous properties, a nd further the absorption interaction is included. Second, and more si gnificantly, we analyze such beam transport through a slab comprised o f a stochastic mixture of two immiscible materials. If the material mi xing is taken as Markovian, an exact stochastic model for the ensemble -averaged solution is easily constructed. Explicit scalar flux solutio ns are obtained in two asymptotic limits, namely: (1) the small correl ation length limit; and (2) the limit of a small amount of relatively opaque material admired with a large amount of relatively transparent material. Copyright (C) 1996 Elsevier Science Ltd