On an extended variable separation method approach to the neutron space kinetics equations with two energy groups and six groups of delayed neutron precursors

In this work, an analytical solution for the three-dimensional neutron space kinetics equation system in Cartesian geometry is derived using an extension of the variable separation method. The considered diffusion problem is defined by the fast and thermal scalar neutron flux and six delayed neutron precursor concentrations. The relevant spectra of the separation constants were analyzed and the solution is represented by a convergent series, so that even after truncation the obtained solution is close to the exact solution. We present a numerical simulation for a sub-critical case, presenting the results for a spatial projection and a space-time projection for all fluxes and precursor concentrations. Future implications of the present work are also discussed.