Nonspherical Perturbations of Spherical Geometries in Transport Theory

It is often desirable to solve radiation transport problems in one-dimensional spherical geometries even if the actual object being modeled is not spherical. It may be possible to use perturbation theory to account for the difference between the real multidimensional system and the spherical approximation. This idea is tested using uncollided as well as multigroup inhomogeneous transport problems with upscattering. Asymmetric and nonuniform perturbations are made to the shielding (not the source) of spherical geometries, including transformations from a sphere to a cube (the surface transformation function is derived), and Schwinger, Roussopolos, and combined perturbation estimates are applied. For uncollided fluxes, perturbation theory, particularly the Schwinger estimate, worked very well when the response of interest was the flux measured at a symmetric spherical 4 detector external to the geometry, but perturbation theory did not work well when the response of interest was the flux measured at a single external point (unless extra care was taken to account for geometric effects). For neutron-induced gamma-ray line fluxes, the Roussopolos estimate worked well when the response of interest was the flux measured at an external 4 detector or an external point detector.