Gc. Pomraning, SMALL CORRELATION LENGTH SOLUTIONS FOR PLANAR SYMMETRY BEAM TRANSPORTIN A STOCHASTIC MEDIUM, Annals of nuclear energy, 23(10), 1996, pp. 843-861
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.