Neutron Counting Statistics Calculations Using Deterministic Transport

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.