Solution of the Energy-Dependent Neutron Transport Equation in Plane Geometry by Separation of Variables

Abstract

The authors give a new method for solving the energy-dependent transport equation in plane geometry by separating the space, lethargy, and angle variables. The method reduces the solution of the transport equation to the solution of a coupled pair of one-speed and slowing down equations. As these two equations have been studied in detail, their solution procedures are utilized to solve the more complicated energy-dependent equation. The method of this paper is thus basically promising, though it is not clear at the present how it can be implemented for general scattering anisotropy. The fundamental separation constant of the method is a continuous parameter, and the solution is in the form of an integral over this parameter. Suitable discretization of this separation constant reduces the solution to an infinite sum. The authors compare their solution to the exact, though formal, singular eigenfunction-Laplace transform technique and establish a correspondence between the two approaches.