Simplified spherical harmonic method for coupled electron-photon transport calculations

Abstract

In this paper we apply the simplified spherical harmonic ${(SP}_{N})$ approximation to coupled electron-photon transport problems in two-dimensional cylindrical geometry in the energy range from roughly 10 keV to 10 MeV. The ${\mathrm{SP}}_{N}$ equations represent an asymptotic approximation that does not necessarily converge to the exact transport solution as $\stackrel{\ensuremath{\rightarrow}}{N}\ensuremath{\infty},$ but can sometimes produce solutions that are much more accurate than diffusion theory at a fraction of the cost of a full transport treatment. To our knowledge, the ${\mathrm{SP}}_{N}$ approximation has previously been applied only to neutron transport problems. We investigate the applicability of the ${\mathrm{SP}}_{N}$ method to satellite electronics shielding calculations. In addition to applying the approximation, we generalize certain iterative convergence acceleration techniques originally developed for the one-dimensional ${S}_{N}$ (discrete ordinates) equations, and apply them to the two-dimensional ${\mathrm{SP}}_{N}$ equations. We present numerical comparisons with Monte Carlo calculations for the purpose of examining both the accuracy of the ${\mathrm{SP}}_{N}$ approximation and the computational efficiency of our solution techniques.