A numerical method for electron transport calculations

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Abstract
A numerical algorithm for calculating the penetration of electrons in dense media is presented. The numerical algorithm is intended for future application to radiotherapy dose calculations. The method is generic in the sense that it may be used with different theoretical models describing the angular scattering of electrons with depth. It is also general enough that it may be applied to electron dose calculations in heterogeneous as well as homogeneous media. The assumptions used in the algorithm are examined and equations describing the evolution of the distribution of electrons with depth are presented. Calculations have been performed for 10 MeV broad beams and pencil beams incident on water. It is shown that the Fermi-Eyges analytical solutions are recovered if the angular scattering process is assumed to be a Gaussian Markov process and the cumulative angle of electron travel remains small. In the case where the small angle approximation is not imposed, the numerical method qualitatively reproduces, at large depths, the wide angle scattering 'tails' seen in Monte Carlo generated profiles.