Legendre expansion of neutron flux over entire multilayer slab geometry

Abstract

The monoenergetic integral transport equation for a multilayer slab geometry has been solved by Legendre expansion method. The method utilizes an expansion of the neutron flux over entire multilayer slab geometry in Legendre polynomials of the position co-ordinate (Single Expansion Method—SEM). This formulation is an extension of Carlvik's (1968) method for a homogeneous slab. Earlier (Raghav, 1984) the expansion of the neutron flux was done in each layer in Legendre polynomials of the position co-ordinate (Multi Expansion Method—MEM). The aim in this paper is to compare both the approaches of SEM and MEM. A few multilayer slab systems with vacuum boundary conditions have been selected for this purpose and K eff, the effective multiplication factor of the system, has been compared. SEM requires the evaluation of the integrals where the limits are not −1 to +1 (as they are in MEM and where analytical expressions can be derived), in these cases we have derived recurrence relations (which are described in the Appendix) to evaluate such integrals.