Transport Of Neutral Particles In A Finite Continuous Stochastic Medium With Gaussian Statistics

Abstract

The stationary solution of the one-speed transport equation in a finite stochastic medium with linear anisotropic scattering is considered. The solution is presented for an arbitrary absorption and scattering cross sections. The total cross section of medium is assumed to be a continuous random function of position, with fluctuations about the mean taken as Gaussian distributed. The Pomraning-Eddington technique is used at first to solve the problem in the deterministic case. Two correlated random variables appear in the solution; namely, the optical space variable and the optical thickness of the medium. The dual Gaussian-probability density function of these two random variables is derived from which the ensemble-averaged solution is calculated for an arbitrary correlation function. The first and the second statistical moments of some quantities of interest, such as radiant energy, net flux, reflectivity, and transmissivity, are calculated. The problem is treated with specular-refecting boundaries and an incident flux of particles on the medium from the left and with no flux from the right.