APPLICATION OF A DISCRETIZED PHASE SPACE APPROACH TO THE ANALYSIS OF MONTE CARLO UNCERTAINTIES

摘要

In the study of Monte Carlo statistical uncertainties for iterated-fission-source calculations, an important distinction is made between the 'real' and 'apparent' variances. The former is the actual variance of a Monte Carlo calculation result, while the latter is an estimate of the former obtained using the results of the fission generations in the formula for uncorrelated random variates. That the apparent variance is a biased estimate of the real variance has been known-and the reason for the bias understood-for years. More recently, several authors have noted various interesting phenomena regarding the apparent and real variances and the relationship between them. Some of these are: an increase in the apparent variance near surfaces with reflecting boundary conditions, a non-uniform spatial distribution of the ratio of the apparent-to-real variance, the dependence of this ratio on the size of the region over which the result is tallied, and a rate of convergence of the real variance that is less than the inverse of the number of neutron histories run. This paper discusses a theoretical description of the Monte Carlo process using a discretized phase space, and then uses it to explain the causes of these phenomena.