Methods For Efficient Computation Of Neutron Multiplicity Distributions

Neutron fingerprinting by neutron multiplicity measurement is a proven technique to establish unique signatures for identification, accountability and control of SNM in nuclear safeguards applications. Computational modeling of neutron multiplicity distributions is a vital complement to experiments but has traditionally relied on either grossly simplified models (singles, double, and triples) or computationally demanding Monte Carlo simulation. The ability to accurately and efficiently compute multiplicity distributions is recognized to be an essential component of the nuclear safeguards toolkit. We present a hierarchical point-kinetic methodology based on a backward Master equation formulation to numerically compute accurate time-gated neutron count number probability distributions of arbitrary order and statistical moments of these distributions. For low count numbers, we show that the multiplicity distribution can be efficiently computed by direct numerical solution of the sequential count probability equations generated from the backward Master equation. For high count numbers, on the other hand, a generalized Laguerre polynomial representation with a gamma distribution weight function is shown to accurately reconstruct the multiplicity distribution, requiring only low order statistical moments as input. For intermediate count numbers, a maximum entropy reconstruction is found to reproduce the count distribution very accurately when both moments and low-order discrete count probabilities are incorporated as constraints. Numerical results are presented for a number of different scenarios and benchmarked for accuracy against a stochastic simulation algorithm (SSA), a system state-updating Monte Carlo method that is more efficient than single-event Monte Carlo in point geometries.