A semi-analytical solution of the two-group Feinberg-Galanin kinetic adjoint equations for a heterogeneous lattice of cylindrical fuel elements

A solution of the two-group Feinberg-Galanin kinetic adjoint equations for a 2-D heterogeneous lattice of a finite number of cylindrical fuel rods is presented and the terms corresponding to the local component of the detector response-which are solely due to attenuation effects in the pure moderator-are identified in the solution. By considering two specific numerical examples, it is shown that the dominant contribution to the local component of the detector response arises from the term representing attenuation effects in the thermal kinetic adjoint, which has a spatial relaxation length equal to the thermal diffusion length in the pure moderator, and which is identical to the corresponding term derived if one pursues a one-group, with a two-group slowing-down kernel, analysis. (author)