Monte Carlo power iteration: Entropy and spatial correlations

Abstract

The behaviour of Monte Carlo criticality simulations is often assessed by examining the convergence of the so-called entropy function. In this work, we shall show that the entropy function may lead to a misleading interpretation, and that potential issues occur when spatial correlations induced by fission events are important. We will support our analysis by examining the higher-order moments of the entropy function and the center of mass of the neutron population. Within the framework of a simplified model based on branching processes, we will relate the behaviour of the spatial fluctuations of the fission chains to the key parameters of the simulated system, namely, the number of particles per generation, the reactor size and the migration area. Numerical simulations of a fuel rod and of a whole core suggest that the obtained results are quite general and hold true also for real-world applications.

A simple implicit coupling scheme for Monte Carlo neutronics and isotopic depletion

“…Recently the phenomenon of neutron clustering has been shown to strongly affect Monte Carlo burn-up simulations (Dumonteil et al, 2014;Zoia et al, 2014;de Mulatier et al, 2015;Nowak et al, 2016;Sutton and Mittal, 2017;Cosgrove et al, 2019). Minimising its effects entails simulating large numbers of neutrons per cycle for fewer cycles (Dumonteil et al, 2014;Sutton and Mittal, 2017).…”

Neutron clustering as a driver of Monte Carlo burn-up instability

“…Regardless, for either of the relations presented, when increasing the height of, say, a fuel pin problem, increasing the number of particles simulated per generation (or the number of generations) to ensure a constant particle density per unit length is insufficient: clustering will occur eventually unless particle numbers increase superlinearly with the characteristic dimension. This point has been made by some of the authors mentioned above (and is demonstrated by Nowak et al (2016)) but should be emphasised in the context of depletion: for some users, intuition might incorrectly suggest that a 4 m pin with 10 burnable regions might not even require as many particles as a 2D 17-by-17 PWR assembly, which will typically have many more burnable regions. The work by Sutton and Mittal (2017) provides another important insight for clustering in Monte Carlo simulations: using excessively many particle generations can worsen the results obtained.…”

“…For a PWR, the migration area is about 56 cm 2 , giving, for a 4 m pin, an N 0 on the order of 10,000. This particular scaling relation was investigated by Nowak et al (2016) for a series of geometries, including a 4 m reflected PWR pin. It was shown that on the order of 500,000 particles per generation were adequate for modelling the problem.…”

Multi-physics steady-state analysis of OECD/NEA modular high temperature gas-cooled reactor MHTGR-350

“…For convergence to happen, it is first necessary to check that the fission source distribution (FSD) used by the Monte Carlo code MCS at the beginning of each coupled step has reached stationarity. For that purpose, a given number of inactive coupled cycles are run, during which the FSD stationarity is checked by studying the evolution of the Shannon entropy [34], the centerof-mass of the FSD (center-of-mass of the weighted fission sources) [35] and the axial offset as a function of the number of inactive coupled cycles. The Shannon entropy of the fission distribution is calculated with a mesh of 10-cm-side cubes superimposed on the MHTGR-350 active core.…”