Generational variance reduction in Monte Carlo criticality simulations as a way of mitigating unwanted correlations

Abstract

Monte Carlo criticality simulations are widely used in nuclear safety demonstrations, as they offer an arbitrarily precise estimation of global and local tallies while making very few assumptions. However, since the inception of such numerical approaches, it is well known that bias might affect both the estimation of errors on these tallies and the tallies themselves. In particular, stochastic modeling approaches developed in the past decade have shed light on the prominent role played by spatial correlations through a phenomenon called neutron clustering. This effect is particularly of great significance when simulating loosely coupled systems (i.e., with a high dominance ratio). In order to tackle this problem, this paper proposes to recast the power iteration technique of Monte Carlo criticality codes into a variance reduction technique called Adaptative Multilevel Splitting. The central idea is that iterating over neutron generations can be seen as pushing a sub-population of neutrons towards a generational detector (instead of a spatial detector as variance reduction techniques usually do). While both approaches allow for neutron population control, the former blindly removes or splits neutrons. In contrast, the latter optimizes spatial, generational, and spectral attributes of neutrons when they are removed or split through an adjoint flux estimation, hence tempering both generational and spatial correlations. This is illustrated in the present article with a simple case of a bare slab reactor in the one speed theory on which the Adaptive Multilevel Splitting was applied and compared to variations of the Monte Carlo power iteration method used in neutron transport. Besides looking at the resulting efficiency of the methods, this work also aims at highlighting the main mechanisms of the Adaptive Multilevel Splitting in criticality calculations.