Reconstruction of neutron multiplicity distributions from low-order statistical information

Abstract

A point-kinetic methodology for rapid and accurate computation of neutron multiplicity distributions in fixed time intervals is demonstrated. The approach uses an optimal combination of low-order count probabilities and low-order statistical moments, both of which are inexpensively computed from a backward Master equation, to reconstruct distributions valid for all count numbers. For high count numbers a generalized Laguerre polynomial representation is shown to accurately reconstruct the multiplicity distribution from five or fewer statistical moments when the zero-count probability is negligible. For intermediate count numbers and when the zero-count probability is significant, maximum information entropy reconstruction constrained by low-order moments and low-order count probabilities reproduces the overall count distribution very accurately. Numerical results for count number distributions and reconstruction accuracy as a function of number of constraints, relative to a system state-updating stochastic simulation MC algorithm (SSA), are presented to demonstrate the efficacy of this approach.