Autocorrelation and Dominance Ratio in Monte Carlo Criticality Calculations

The cycle-to-cycle correlation (autocorrelation) in Monte Carlo criticality calculations is analyzed concerning the dominance ratio of fission kernels. The mathematical analysis focuses on how the eigenfunctions of a fission kernel decay if operated on by the cycle-to-cycle error propagation operator of the Monte Carlo stationary source distribution. The analytical results obtained can be summarized as follows: When the dominance ratio of a fission kernel is close to unity, autocorrelation of the k-effective tallies is weak and may be negligible, while the autocorrelation of the source distribution is strong and decays slowly. The practical implication is that when one analyzes a critical reactor with a large dominance ratio by Monte Carlo methods, the confidence interval estimation of the fission rate and other quantities at individual locations must account for the strong autocorrelation. Numerical results are presented for sample problems with a dominance ratio of 0.85-0.99, where Shannon and relative entropies are utilized to exclude the influence of initial nonstationarity.