A closed-form analytic solution for the - equations of neutron transport in slab geometry

Abstract

A closed-form analytic solution for the discrete-ordinates equations of neutron transport is obtained without recourse to integral transforms. The method is applied to the slab-geometry problem in the one-speed approximation using a one-sided set of boundary conditions. The solution is valid for any number of discrete ordinates and all possible orders of anisotropic scattering, and it does not require a priori knowledge of the particular solution. A set of algebraic expressions for the neutron balance at the boundaries of a slab is obtained and used as a basis for one iterative and one non-iterative numerical algorithm that are valid for all homogeneous and heterogeneous slabs. The numerical solutions are error free other than the roundoff of the computing system. The roundoff error is minimized by the Effective Albedo and Transmittance method.