Analytical approach to the neutron kinetics of the non-homogeneous reactor

This work is a revisitation of the rigorous analytical method to obtain the solution of the neutron space-time kinetic problem in diffusion theory for spatially non-homogeneous systems. The results obtained for simple plane geometry configurations may well serve for benchmarking numerical codes. The general problem for a multilayer reactor is considered and the analytical procedure for the solution by means of the Laplace transform and the identification of eigenvalues and spatial eigenfunctions are presented. The theory is applied to a symmetrically reflected slab reactor, with a detailed presentation of some mathematical features, such as the reality of the eigenvalues and the concept of orthogonality of the eigenfunctions. Afterwards, various transients are simulated and the study of the error associated to series truncation is carried out.