'K-effective of the World' and other concerns for Monte Carlo eigenvalue calculations

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 Monte Carlo codes for representing realistic geometry and physics interactions, correct results can be obtained in criticality problems only if users pay attention to source convergence in the Monte Carlo iterations and to running a sufficient number of neutron histories to adequately sample all significant regions of the problem. Recommended best practices for criticality calculations are reviewed and applied to several practical problems for nuclear reactors and criticality safety, including the 'K-effective of the World' problem. Numerical results illustrate the concerns about convergence 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 performing calculations, practitioners will have a greater degree of confidence than ever of obtaining correct results for Monte Carlo criticality calculations. (author)