An improved spatial-dependent model of neutron multiplicity counting for large-volume plutonium solution

Neutron multiplicity counting is a non-destructive, passive technique for monitoring plutonium inventory. However, when extending the application from plutonium metal/plutonium oxides to large-volume plutonium solution systems, the original “point model” reveals significant shortcomings. Currently, while two types of improvements for the original “point model” has been proposed: (a) improved “point model” suitable for small-volume solution systems and (b) volume-weighted “point model” correcting for spatial dependence of solid systems, neither is suitable for large-volume solution systems. Based on the improved “point model”, we firstly employ the volume-weighted approach to derive a volume-weighted model suitable for solution systems, which however neglects the disparity between the induced fission source distribution and the initial source distribution in our opinion. Furthermore, by additionally incorporating the distribution of induced fission reactions as a weighting factor for the spatial dependence correction, we propose the composite-weighted model. Comparative analysis of simulation results from the improved “point model”, volume-weighted model, and composite-weighted model demonstrates that the composite-weighted model has the best performance, offering superior universality and accuracy, thereby confirming the necessity and validity of the improvements. Theoretically, the methodology for addressing spatial dependence in large-volume solution systems introduced in this study can also be used for other large-volume plutonium-containing material systems.