Radiation Transport in a Halfspace with a Source External to the Medium

In this paper the transport of radiation in a half space, due to a source external to the medium, is analyzed. This situation arises in certain radiation transport studies. In particular, we compare, in the diffusion description, the correct two-dimensional solution with a commonly used series of one-dimensional approximations. The results should be of help in determining, for a given problem, whether a full multidimensional transport calculation is required or if the one-dimensional approximation is adequate. In the case of radiative transfer, it is shown that a one-dimensional treatment is in general not adequate.