SMALL CORRELATION LENGTH SOLUTIONS FOR PLANAR SYMMETRY BEAM TRANSPORTIN A STOCHASTIC MEDIUM

This paper considers planar symmetry, steady-state, monoenergetic line ar transport of a normally incident particle beam through a purely sca ttering thin slab, composed of a stochastic mixture of two immiscible materials. The scattering process is assumed sufficiently forward peak ed so that the Fokker-Planck description is valid. If the material mix ing obeys Markovian statistics, and ignoring particle backscattering, this situation is a joint Markov process. As such, the stochastic Liou ville master equation is valid, and we obtain a set of two coupled lin ear transport equations describing exactly the ensemble-averaged. solu tion for the particle intensity. An asymptotic expansion is used to re duce these two equations, in the small correlation length limit, to a single renormalized equation. This equation is treated by an angular m oments method, exploiting the assumed peakedness in angle of the solut ion. An analytic solution of these moment equations provides a simple and explicit solution for the spatial distribution of the particle den sity. The effect of stochasticity is to increase the solution over the corresponding nonstochastic result recently reported in the literatur e.