Analytic solutions of the multigroup space-time reactor kinetics equations in multiregion slab and spherical geometry

Abstract

Analytic solutions of the multigroup space-time reactor kinetics equations are developed for a bare slab and spherical reactor, and a reflected slab and spherical reactor for the zero flux, the zero current, and the extrapolated endpoint boundary conditions. The material properties of the reactors are assumed constant in space and time, but solutions involving spatially dependent source terms and initial conditions are investigated. The development of analytic and numerical solutions to the reactor kinetics equations is reviewed. The system of partial differential equations is reduced to a set of linear ordinary differential equations by the Laplace transform method, which are solved with matrix Green's functions, yielding a general matrix solution for the neutron flux and the precursor concentration in the Laplace transform space. The detailed pole structure of the matrix solution in the Laplace transform space is investigated. The temporally and spatially dependent solutions are determined from the inverse Laplace transform using the Cauchy residue theorem, a knowledge of the detailed pole structure, and matrix operators. Solutions are evaluated for one and two groups of prompt neutrons and six groups of delayed neutron precursors.