Neutron transport in one dimensional spherical geometry with stochastic fissile spheres

A binary statistical transport equation is derived in this paper for the binary stochastic media with randomly distributed fissile spheres. Monte Carlo method is used to calculate the mean chord length of the background sphere while the deterministic SN method is used to solve the statistical transport equation in 1-D spherical geometry. Test problems are constructed and discussed. The probability density function (PDF) of keff, the ensemble average value of keff and the flux distribution are calculated for cases with different scattering ratio, different chord-path ratio and different numbers of random fissile spheres. It is found that the ensemble average value of keff and flux distribution of the binary problem with randomly distributed fissile spheres can be predicted by the given model in most cases. (authors)