Analysis of Zero-Variance Schemes for Radiation Shielding Problems Including Neutron Multiplication

In this work, we examine the behavior of zero-variance Monte Carlo games for radiation shielding problems in the presence of neutron multiplication, whose prominent application is the analysis of in-core and ex-core detector responses during reactor start-up. Prompted by previous investigations, which had shown that the conflict between the importance of the fissile regions and the importance of the detector might lead to numerical instabilities in Consistent Adjoint-Driven Importance Sampling (CADIS) strategies, we set out to explore these techniques within a simple benchmark configuration where exact zero-variance sampling can be implemented. The configurations examined here do not display any of the instabilities observed for CADIS-like schemes including neutron multiplication, which might be due to the use of branchless sampling for the collision events. Furthermore, our findings establish a clear framework that can be more broadly applied for the analysis of the robustness of ideal CADIS schemes.