Three-dimensional transport theory: An analytical solution for the internal beam searchlight problem, II

Multidimensional semi-analytical particle transport benchmarks to provide highly accurate standards of assessment are few and far between. Because of a well-established 1D theory for the analytical solution of the transport equation, it is sometimes possible however, to “bootstrap” 1D solutions to give more comprehensive solution representations. Here, we propose the internal searchlight problem in a half space, designated ISLP/HS, as a multidimensional benchmark to be constructed from 1D solutions. This is a variation of the usual SLP/HS where a source emits within the half space rather than striking its surface. Our primary interest is in the exiting intensity at the free surface established through a new Fn formulation. The benchmark features true 2/3D particle transport through integration of a point kernel to simulate 2/3D source emission. In this way, we accommodate a solid or hollow cylindrical source and a general line source in addition to the standard point, ring and disk sources featured in previous investigations.