A power spectrum approach to tally convergence in Monte Carlo criticality calculation

In Monte Carlo criticality calculation, confidence interval estimation is based on the central limit theorem (CLT) for a series of tallies from generations in equilibrium. A fundamental assertion resulting from CLT is the convergence in distribution (CID) of the interpolated standardized time series (ISTS) of tallies. In this work, the spectral analysis of ISTS has been conducted in order to assess the convergence of tallies in terms of CID. Numerical results obtained indicate that the power spectrum of ISTS is equal to the theoretically predicted power spectrum of Brownian motion for tallies of effective neutron multiplication factor; on the other hand, the power spectrum of ISTS of a strongly correlated series of tallies from local powers fluctuates wildly while maintaining the spectral form of fractional Brownian motion. The latter result is the evidence of a case where a series of tallies are away from CID, while the spectral form supports normality assumption on the sample mean. It is also demonstrated that one can make the unbiased estimation of the standard deviation of sample mean well before CID occurs.