Simplified spherical harmonic method for coupled electron-photon transport calculations

In this paper we apply the simplified spherical harmonic (SPN) approximation to coupled electron-photon transport problems in two-dimensional cylindrical geometry in the energy range from roughly 10 keV to 10 MeV. The SPN equations represent an asymptotic approximation that does not necessarily converge to the exact transport solution as N→∞, 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 SPN approximation has previously been applied only to neutron transport problems. We investigate the applicability of the SPN 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 SN (discrete ordinates) equations, and apply them to the two-dimensional SPN equations. We present numerical comparisons with Monte Carlo calculations for the purpose of examining both the accuracy of the SPN approximation and the computational efficiency of our solution techniques. copyright 1998 The American Physical Society