Formulation of the streaming-ray method for electron-transport calculations in two dimensions

The method of streaming rays are expanded to two spatial dimensions (three-phase space dimensions, x, y, and s) and used as a basis for development of the electron-transport computer code SR2D. The streaming-ray algorithm is a Eulerian-Lagrangian hybrid. Electrons are followed as they traverse the medium along specified streaming rays. Fluxes, however, are computed at the centers of the fixed cells. The development of the SR2D code required the specification of a Lagrangian-streaming ray network overlaying a three-dimensional Eulerian grid. In contrast to its one-dimensional predecessor, the SR2D code accommodates non-uniform cell sizes and allows for arbitrary quadrature sets (S2, S4, S6, S8, S12, or S16). The critical aspect of the streaming ray method is the determination of the path lengths of each and every streaming ray through all of the Eulerian cells. These values must be precalculated and stored because of the iterative nature of the solution scheme. Although the number of pathlengths may be exceedingly large, computer memory requirements are minimized, however, in the two dimensional algorithm by the symmetry of the geometry in each pathlength increment. The SR2D code was used to calculate the energy-deposition profile for two kinds of sources, an isotropic point source and a monodirectional point at the periphery of a two-dimensional medium