Electron energy and mean forward range in air resulting from the ETA factor treatment of scattering in the continuous slowing down approximation

This paper provides a method for making quick estimates of the electron-beam mean penetration depth and of the variation of mean electron energy and associated speed with propagation distance in the beam's forward direction. The continuous slowing down approximation is used with the eta-function modification developed by Longmire to account for scattering. The method is applied to electrons with initial kinetic energy ranging from 5 keV to 3 MeV slowing down in air at STP. Comparisons with Monte Carlo calculations indicate that the method is useful in determining the mean electron range in the forward direction. The method also provides rough estimates of the variation in mean electron energy and associated speed with propagation distance. However, these variations are better predicted by readily available electron transport codes. Results for 1-MeV electrons demonstrate that the electron energy is spread over a characteristic depth approximately equal to the extreme range of the electrons rather than to the mean forward range