Particle clustering in Monte Carlo criticality simulations

Strong space and cycle correlations affecting the neutron flux have been recently reported to occur in Monte Carlo criticality simulations of pressurized water reactors pin-cells with reflective boundary conditions: when the system size is large, neutrons are observed to gather together and form 'clusters' that wander around in space over many cycles. In most cases, the outcome of such clustering is that simulations display wild fluctuations, largely exceeding those expected around the equilibrium distribution. In this paper, we analyze the reasons behind the emergence of these phenomena: we show that the key mechanism is due to the asymmetry between neutron disappearance being uniformly distributed along the pin-cell, and neutron generation being localized at fission sites (i.e., only next to a parent particle). An explanation is provided by resorting to a simplified Brownian transport model coupled with a Galton-Watson birth and death process, which is sufficient to retain the essential features observed in realistic Monte Carlo simulations. An empirical space correlation function is proposed as a diagnostic tool for detecting clustering in criticality simulations.