On the solution of the SN multigroup kinetics equations in multilayer slabs

Abstract Presented in this paper is an analytical representation for the solution of the slab-geometry neutron kinetics equations in energy-multigroup discrete ordinates (S N ) transport formulation with an arbitrary number of delayed neutron precursors. The basic idea involves: (i) the group neutron angular fluxes and the concentrations of delayed neutron precursors are expanded in truncated series of analytic functions; (ii) by substituting these expansion representations into the multigroup S N kinetics equations, a set of recursive systems of first-order ordinary differential equations results. It is assumed that the first equation of the system is source free and is the only one which satisfies the initial conditions. The remaining equations of the recursive system satisfy zero initial condition and the source term is written in terms of the solution of the previous step. At each step of the recursive system, the multigroup S N equations are solved by using the TLTS N method, which is based on applying the double Laplace transform technique: first in the time variable and then in the space variable. Numerical results are given to two model problems which consist of a subcritical slab stabilized by a time-independent neutron source distribution.