Neutron Transport in Spatially Random Media: Eigenvalue Problems

The majority of earlier work on neutron transport in spatially random media has relied on special models of the random process, closure techniques or perturbation theory. The purpose of the present paper is to further develop a technique, which employs the source-sink method and simulation, and which in principle leads to exact probability distributions, to assess the accuracy of such approximate methods. To this end, we also use perturbation theory, and extend it to eigenvalue problems thereby enabling random fluctuations in reactivity to be studied and some measures of their statistical properties to be calculated. We have found, by comparing results for the variance in the reactivity fluctuations with essentially exact values, that the perturbation method is an accurate way to deal with stochastic equations and is far more efficient numerically than the more exact simulation method.