The effect of branchless collisions and population control on correlations in Monte Carlo power iteration

TL;DR

This paper develops a framework to characterize spatial correlations in Monte Carlo power iteration and finds that branchless collisions significantly reduce these correlations, improving the accuracy of neutron transport simulations.

Contribution

It introduces new global and local tallies to quantify correlations and systematically assesses how sampling strategies and variance reduction techniques influence these correlations.

Findings

Branchless collisions reduce correlations in neutron histories.

Proposed tallies effectively characterize spatial correlations.

Sampling strategies impact correlation strength in Monte Carlo simulations.

Abstract

The investigation of correlations in Monte Carlo power iteration has been long dominated by the question of generational correlations and their effects on the estimation of statistical uncertainties. More recently, there has been a growing interest in spatial correlations, prompted by the discovery of neutron clustering. Despite several attempts, a comprehensive framework concerning how Monte Carlo sampling strategies, population control and variance reduction methods affect the strength of such correlations is still lacking. In this work, we propose a set of global and local (i.e., space-dependent) tallies that can be used to characterize the impact of correlations. These tallies encompass the Shannon entropy, the pair distance, the normalized variance and the Feynman moment. In order to have a clean, yet fully meaningful setting, we carry out our analysis in a few homogeneous and heterogeneous benchmark problems of varying dominance ratio. Several classes of collision sampling strategies, population control and variance reduction techniques are tested, and their relative advantages and drawbacks are assessed with respect to the proposed tallies. The major finding of our study is that branchless collisions, which suppress the emergence of branches in neutron histories, also considerably reduce the effects of correlations in most of the explored configurations.