Monte Carlo solution of the reflected systems’ criticality problems with Anlı–Güngör, Inönü and tetra-anisotropic kernels for both fission and scattered neutrons

Abstract

Different deterministic solution methods are being used to solve the criticality problem of the reflected systems with different anisotropic behaviours for both fission neutrons and neutrons undergoing scattering. In the present study, the criticality problem is simulated using the developed Monte Carlo algorithm. Different angular distributions, such as Inönü, Anlı–Güngör and tetra-anisotropic kernels are taken into account. For each anisotropic kernel, the sampling method of the direction cosine of either newborn fission neutrons or scattered neutrons is presented by extracting the required probability distribution function (PDF). The simulation starts with an initial guess and following the presented procedure, the criticality thickness of the system is estimated with a certain convergence criterion. Different variance reduction methods, such as implicit capture, Russian-roulette and splitting, are also implemented to get more precise results with a reasonable computational time cost. The validity of the presented method is verified by comparing with the results of different deterministic methods. Finally, using an exact scattering function, the three considered kernels are compared with each other. It is seen that the tetra-anisotropic kernel is the best among the considered kernels.