On the conception of pseudo-cross sections for neutron escape in physical Monte Carlo simulations in finite domains

Abstract

The physical approach of the Monte Carlo method in neutron transport enables, mainly due to its versatility, the construction of pseudo-cross sections for neutron escape and thus allows for quantifying escape pseudo-interactions in finite domains, such as in nuclear reactors. An intrinsic characteristic of these pseudo-cross sections is that they tend towards infinity at the surfaces of the studied domain and can, theoretically, simulate a surface by initially considering an infinite domain, simplifying and facilitating the treatment of neutron transport problems. In this work, this geometric characteristic is validated for stochastic approaches. For this purpose, the pseudo-cross section for neutron escape for a specific configuration, similar to the configurations of the early criticality studies in spherical medium, was obtained from a Monte Carlo simulation. Subsequently, a similar simulation was performed, however, considering an infinite domain and using only the pseudo-cross section to handle the boundaries of the spherical medium. Comparing results, i.e. the neutron spectral flux and the effective multiplication factor, a good agreement was observed between the usual approach, in which a boundary is defined in the simulation, and the proposed approach, in which an infinite domain is considered and only the escape cross section is used to treat the boundaries of the medium. The good results pave the way for similar studies considering more complex geometries and their feedback to deterministic approaches.