On the Use of Shannon Entropy of the Fission Distribution for Assessing Convergence of Monte Carlo Criticality Calculations

Abstract

Monte Carlo calculations of k-eigenvalue problems are based on a power iteration procedure. To obtain correct results free of contamination from the initial guess for the fission distribution, it is imperative to determine when the iteration procedure has converged, so that a sufficient number of the initial batches are discarded prior to beginning the Monte Carlo tallies. In this paper, we examine the convergence behavior using both theory and numerical testing, demonstrating that keff may converge before the fission distribution for problems with a high dominance ratio. Thus, it is necessary to assess convergence of both keff and the fission distribution to obtain correct results. To this end, the Shannon entropy of the fission distribution has been found to be a highly effective means of characterizing convergence of the fission distribution. The latest version of MCNP5 includes new capabilities for computing and plotting the Shannon entropy of the fission distribution as an important new tool for assessing problem convergence. Examples of the application of this new tool are presented for a variety of practical criticality problems.