Ray-effect mitigation methods for two-dimensional neutron transport theory

Projection operators are used to rederive x-y geometry discrete ordinates-to-spherical harmonics (S/sub N/ → P/sub N-1/) fictitious sources defined in the literature as ray-effect mitigating devices. A new x-y geometry fictitious source is defined with certain properties that are superior to earlier sources. A detailed description of the S2 → P1 source, including a discussion of vacuum and reflective boundary conditions, is provided. Fictitious sources in r-z geometry are derived that give spherical harmonics and spherical-harmonics-like solutions. Finally, a simple algorithm is presented that allows a significant reduction in the iteration time needed to obtain ray-effect-free solutions. This algorithm effectively reduces the size of the fictitious source in energy groups where ray-effect distortions are not expected. The new sources and the algorithm for reduction of computation time make this approach viable for solving the ray-effect problem