Neutron transport in spatially random media: An assessment of the accuracy of first order smoothing

A formalism has been developed for studying the transmission of neutrons through a spatially stochastic medium. The stochastic components are represented by absorbing plates of randomly varying strength and random position. This type of geometry enables the Feinberg-Galanin-Horning method to be employed and leads to the solution of a coupled set of linear equations for the flux at the plate positions. The matrix of the coefficients contains members that are random and these are solved by simulation. That is, the strength and plate positions are sampled from uniform distributions and the equations salved many times (in this case 10(5) simulations are carried out). Probability distributions for the plate transmission and reflection factors are constructed from which the mean and variance can be computed. These essentially exact solutions enable closure approximations to be assessed for accuracy. To this end, we have compared the mean and variance obtained from the first order smoothing approximation of Keller with the exact results and have found excellent agreement for the mean values but note deviations of up to 40% for the variance. Nevertheless, for the problems considered here, first order smoothing ap pears to be of practical value and is very efficient numerically in comparison with simulation.