A multiray model for calculating electron pencil beam distribution

Based on the Fermi-Eyges theory, a set of recursion relations was derived for calculating electron distributions in the layered geometry. The electron distribution at a specific depth was obtained by convolving the upstream electron distribution with a kernel determined by the scattering parameters of the layer. Modifications were made to overcome some inherent limitations of the Fermi-Eyges theory. For each point in the medium, the most probable, or mean, path traversed by the electrons in reaching the point was derived. The skewness of the mean paths and the related energy degradation were included in a multiray model for pencil beam calculations. The resultant electron planar fluence distributions are no longer Gaussian as predicted by the original theory. The effects of edges or localized inhomogeneities are also included. Comparisons between our calculations and Monte Carlo simulations show good agreement.