The Varying Probability of Fission Model for Calculation of Neutron Moments and Applications

Neutron multiplicity analysis (NMA) is a non-destructive method for estimating fissile mass from the rate of detecting one, two or more emitted fission neutrons within a time gate, known as the neutron moments. NMA relies on the point model which expresses the neutron moments as analytic expressions of a constant and uniform probability for each neutron to induce fission. To use a constant probability of fission the point model approximates the geometry of assemblies of fissile materials as a single point in time and space, neglecting all geometry. This approximation significantly underestimates the fissile mass and enrichment for large assemblies. This work presents the Varying Probability of Fission (VPF) model, which extends the point kinetic model by allowing the probability of fission to vary with position and the number of fissions in each fission chain, termed the neutron collision number. While the VPF model requires a several values of the fission probability, additional constraints can be imposed to reduce the number of solved variables. These constraints can be modelled interpolation functions with parameters determined from Monte Carlo simulation. Additionally, the Associated Particle Imaging (API) technique provides additional information on interrogating neutron direction and transmission images. After applying a back projection step API systems provide imaged data of emitted neutron singles and doubles for induced fission at varying positions in addition to the transmission image. This work presents how the imaged data of neutron transmission, neutron singles and doubles can be incorporated into a VPF analysis and provide images of the spatially dependent induced neutron fission probability and the rate of induced neutron chains. The VPF model could enable a new, real-time quantitative assessment capability for nuclear material assemblies that are imaged by API systems.