Diffusion of fast electrons in the presence of an electric field

The diffusion of high-energy electrons (≥ 10 keV) in the presence of an electric field is discussed. Solutions are obtained by extending the Bethe age theory to include effects of the applied electric field. Since we restrict ourselves to the $P_1$ approximation, the results are only valid for diffuse beams, i.e., beams whose distribution function can be adequately described by a current and number density. The solution predicts a range enhancement in the presence of an accelerating electric field. A simple exponential decay is obtained when the electric field is large enough so that the electrons gain as much energy in the electric field as they lose by inelastic collisions. The validity and accuracy of the solutions and predictions are discussed.