Solution of multiplying binary stochastic neutron transport equation in one dimensional spherical geometry

A statistical transport equation is presented in this paper to obtain the ensemble average k_eff for the binary stochastic media with random fissile pellets. Combined method of statistics and deterministics is proposed to directly solve the multiplying binary stochastic problem in 1-D spherical geometry. In the combined method, Monte Carlo sampling method is employed to determine the mean chord length of the stochastic system then deterministic S_N diamond difference, source iteration method is used to solve the statistical transport equation with eigenvalue. Test stochastic problems of different scattering ratio, different chord-path ratio and different number of random fissile spheres are constructed and compared with references and uniformly-distributed approximated cases. Results show that the mean value of k_eff for the given systems can be predicted accurately by the statistical equation in most given cases.