“K-effective of the World” and Other Concerns for Monte Carlo Eigenvalue Calculations

Abstract

Monte Carlo methods have been used to compute k eff and the fundamental mode eigenfunction of critical systems since the 1950s. Despite the sophistication of today’s Mont e Carlo codes for representing realistic geometry and physics interactions, correct results can be obtained in cri ticality problems only if users pay attention to source con- vergence in the Monte Carlo iterations and to running a suffi cient number of neutron histor ies to adequately sample all significant regions of the problem. Recommended best practices for criticality calculations are reviewed and ap- plied to several practical problems for nuc lear reactors and criticality safety, including the “K-effective of the World” problem. Numerical results illustrate the concerns about conv ergence and bias. The general conclusion of is that with today’s high-performance computers, improved understanding of the theory, new tools for diagnosing convergence (e.g., Shannon entropy of the fission distribution), and clear practical guidance for pe rforming calculations, practi- tioners will have a greater degree of confidence than ev er of obtaining correct results for Monte Carlo criticality calculations.