A Modified Spherical Harmonics Approach to Solving the Neutron Transport Equation

Abstract

<p> Another approach is adopted for deriving the moments equations in spherical geometry using a spherical harmonics expansion of the neutron transport equation over a variable range of the direction cosine. Because of complications and uncertainties in establishing boundary conditions for the equations, only the zero'th order equations are solved, in an idealized situation, in order that a feel for equations and boundary conditions may be obtained.</p> <p> The equations are compared to equations given in a paper 'Directionally Discontinuous Harmonic Solutions of the Neutron Transport Equation in Spherical Geometry', by A. A. Harms and E. A. Attia. Analytical solutions for the zero'th order equations are given for equations developed there and to the equations developed in this paper. Numerical values are presented to give an idea of what accuracies might be expected. It is hoped that similar techniques can be used to solve the higher order equations analytically, and that appropriate boundary conditions can be found.</p>