Underestimation of statistical uncertainty of local tallies in Monte Carlo eigenvalue calculation for simple and LWR lattice geometries

ABSTRACTA prediction method of the true variance of local tally in a Monte Carlo (MC) critical calculation is developed. In the MC calculation, the effective multiplication factor (keff) and the fission rate distribution are estimated by simulating fission chain reactions. The statistical uncertainty of calculation result is commonly estimated by the standard error based on the central limit theorem. However, the evaluated statistical uncertainty would be underestimated when the inter-cycle correlation is not appropriately taken into account. In this study, a theoretical formula of the underestimation ratio (UR) of the statistical uncertainty for a local tally is derived using the eigenfunction expansion and the Autoregressive model. Note that the UR is defined by the ratio of uncertainty estimated by a MC calculation to the true statistical uncertainty. The proposed method is applied to one-dimensional slab and multi-assembly geometries with reflective boundary conditions. In the one-dimensional slab geo...