Electron beam dose planning using Gaussian beams. Energy and spatial scaling with inhomogeneities

The penetration of an electron beam in matter is characterized by only two material dependent parameters within the range of validity of the small angle diffusion equation. These parameters characterize the relative importance of multiple scattering and energy loss for a given material and energy. By comparison with more accurate Monte Carlo calculations it is shown that the same two parameters can be used to scale the dose distribution from one material and energy to an equivalent energy in an arbitrary material with high precision also outside the limits of the small angle approximation. This scaling procedure has been generalized to the non-uniform case with plane parallel slab inhomogeneities by assuming the angular distribution on each side of the interfaces to be equal. The generalized recursive scaling procedure is finally tested by measurements on almost point monodirectional beams in water with inserted aluminum plates of varying thicknesses. The agreement with the scaling procedure is of the order of one per cent with regard to the radial dose profiles.