Analysis of the neutron response to axially-propagating perturbations in a heterogeneous lattice of cylindrical fuel elements via the two-group slowing-down model

Abstract

The problem of the neutron response to an infinite frequency-dependent plane unit source in the moderator of an infinite regular heterogeneous lattice of cylindrical fuel elements is analyzed in the one-group diffusion approximation with a two-group slowing-down kernel, within the framework of the source-sink method of Feinberg and Galanin. It is shown that the neutron response divides naturally into a component with a long spatial relaxation length and one with a short relaxation length, which is equal to the thermal diffusion length in the moderator. The latter spatial decay mode is solely due to attenuation effects in the pure moderator and in contrast to the corresponding homogeneous diffusion theory analysis of the same problem, no other localized spatial decay mode exists. Finally, a simple void-propagation model is used for calculating the neutron spectra, due to axially-propagating perturbations of the moderator density in the heterogeneous and the corresponding homogenized system. Although the shapes of the spectra are similar, it is shown that both physically and mathematically, the analysis of this problem by homogeneous theories can lead to erroneous interpretations. © 1982.