Neutron Counting Statistics calculations Using Deterministic Transport

TL;DR

This paper develops a deterministic method to calculate neutron counting statistics, including moments and probabilities, by solving coupled transport equations, implemented in the PANDA code, with verification through numerical results and inter-code comparisons.

Contribution

It introduces a novel approach to compute neutron counting statistics using deterministic transport equations expanded to arbitrary order, including fission multiplicity moments.

Findings

Method successfully computes neutron counting moments.

Implementation in PANDA code verified with numerical comparisons.

Applicable to low-source reactor start-up and neutron coincidence counting.

Abstract

For a number of applications like low-source reactor start-up or neutron coincidence counting it is necessary to take into account the stochastic nature of neutron transport and go beyond the average neutron density, which is solution of a linear Boltzmann equation. In this work, we are particularly interested in calculating the moments and probabilities of the number of neutrons detected during a time window. It is known that in case of a single initial neutron these quantities are solution of a system of coupled adjoint transport equations and that a neutron source can be taken into account in a second time using summations with the source strength. The purpose of the present work is first to present the derivation of these equations in a form where they can be solved up an arbitrary order and where the fission terms are expanded according to the moments of the fission multiplicity. For simplicity, the derivation is first presented in a lumped also called point model approximation before considering the full phase-space case. Thereafter, we describe the implementation of the solution algorithm in the deterministic, discrete ordinates code PANDA and finally, we present some numerical results and inter-code comparisons for verification purposes and to illustrate the applicability of the method.