THE PLANAR SYMMETRY BEAM PROBLEM IN STOCHASTIC MEDIA

This paper considers planar symmetry, steady-state, energy dependent, linear transport of a normally incident radiation beam through a scatt ering/absorbing thin slab, composed of a stochastic mixture of two imm iscible materials. The scattering process is assumed sufficiently peak ed in both energy and angle so that the Fokker-Planck description is v alid. If the material mixing obeys Markovian statistics, and if partic le backscattering can be ignored, this situation is a joint Markov pro cess. As such, the stochastic Liouville master equation is valid, and we obtain a set of two coupled linear transport equations describing e xactly the ensemble-averaged solution for the particle intensity. We d evelop the small correlation length asymptotic limit of this set of tw o equations, which results in a single renormalized equation. The two- equation set is treated by an angular moments method, exploiting the a ssumed peakedness of the solution in angle. In a separate development, an explicit result is obtained for the spatial profile of the particl e density in the case of monoenergetic, purely scattering transport th rough a layered statistical mixture. Copyright (C) 1996 Elsevier Scien ce Ltd