General Analytical Solution for Two-group, Two-point Variance-to-mean Formulas and Their Application to Safeguards

Abstract

The theory of Feynman-alpha method was extended to two-point one-group, two-group onepoint, and two-point two-group versions by using the Kolmogorov forward master equation with complete description of various types of reactions for neutrons. The motivation for this work is related to the fact that the traditional one-group one-region Feynman-alpha formula was elaborated and used for thermal systems in which the thermal ux and the lifetime of thermal neutrons dominates. However, this approach does not fully describe the effects of the re ector in the fast neutron systems, as well as heavily re ected thermal systems. Therefore, in the present work the two-group one-point, the two-point one-group and twogroup two-point formulas were elaborated for different types of detections. Previously, the two-group one-point formula described only detections of fast neutrons and at the same time neglected the fast fissions, while the two-point one-group formula were limited to the case where source term and detections were considered only for a core region. The quantitative assessment of the formulas with regards to applications in safeguards and accelerator-driven system was made through MCNPX and MCNP-PoliMi simulations. The results indicate a possibility to use Feynman-alpha method to differentiate between various isotopic compositions of nuclear fuel.