Solution of the multiplying binary stochastic media based on L-P equation in 1D spherical geometry

In order to obtain the ensemble average k_eff for the binary stochastic media system, a statistical transport equation with eigenvalue is derived based on the L-P equation. Combined method of statistical and deterministic is proposed to deal with this problem. In the first step, Monte Carlo approach is employed to calculate the mean chord length of the background scattering material, deterministic transport method using diamond difference and source iteration is applied to solve the eigenvalue L-P equation. Test problems of different scattering ratios, different chord-path ratios and different number of random fissile lumps and simple UO₂-H₂O problem are calculated and compared with references. Results show that the eigenvalue L-P equation can provide the mean value of k_eff for the given stochastic systems in most cases.