Three-dimensional transport theory: An analytical solution of an internal beam searchlight problem, III

We describe a method for obtaining analytical solutions and numerical results for three-dimensional one-speed neutron transport problems in a half-space containing a variety of source shapes which emit neutrons mono-directionally in the direction away from the surface. Thus this paper is a supplement to Williams [Williams, M.M.R., 2009, Three-dimensional transport theory: an analytical solution for the internal beam searchlight problem I. Annals of Nuclear Energy 36, 767–783]. For example, we consider a point source, a ring source and a disk source, and calculate the surface scalar flux as a function of the radial co-ordinate when the source is at a fixed distance from the surface. The results are in full agreement with the work of Ganapol and Kornreich [Ganapol, B.D., Kornreich, D.E., this issue. Three-dimensional transport theory: an analytical solution for the internal beam searchlight problem II. Annals of Nuclear Energy]. Diffusion theory results are also included.