Bj. Su et Gc. Pomraning, THE FERMI-EYGES BEAM ANALYSIS FOR A HETEROGENEOUS ABSORBING STOCHASTIC MEDIUM, Annals of nuclear energy, 23(14), 1996, pp. 1153-1177
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