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 state, finite slab, searchlight problem with a monoenergetic, normally incident, beam. Their analysis, which treats a nearly collimated beam of particles, originally entering a sourcefree slab through one surface as a perfectly collimated pencil beam, was restricted to a purely scattering, homogeneous medium. The purpose of this paper is to generalize the Fermi-Eyges analysis in two ways. First, in a straightforward generalization, the slab is allowed arbitrary heterogeneous properties, and further the absorption interaction is included. Second, and more significantly, we analyze such beam transport through a slab comprised of a stochastic mixture of two immiscible materials. If the material mixing is taken as Markovian, an exact stochastic model for the ensemble-averaged solution is easily constructed. Explicit scalar flux solutions are obtained in two asymptotic limits, namely: (1) the small correlation length limit; and (2) the limit of a small amount of relatively opaque material admixed with a large amount of relatively transparent material.