Numerical Solution of the Electron Diffusion Equation

, A numerical solution to the integro-differential equation describing the energy'distribution of a beam of electrons which has passed through matter, losing energy by radiation only, has been obtained utilizing a finite difference mesh method. Solutions were obtained for thicknesses of up to 0.1 radiation lengths for a complete screening approximation to the energy loss equation. The accuracy of the method was checked by comparison of results with known solutions to the diffusion equation. The formulas of Mo-Tsai and Tsai for electron straggling distributions were compared to the numerical results. Good agreement was found near the high energy end of the distribution, the numerical results being within two percent of the theoretical predictions. At the low energy end of the distribution, the numerical results differ from those predicted by as much as eight percent at thicknesses of 0.1 radiation length. The disagreement was found to be proportional to thickness traversed by the beam.