RANGE SPECTRA IN ELECTRON PENETRATION PROBLEMS

The theory of electron penetration as predicted by the Fokker-Planck e quation is first reviewed within a restricted context that considers t he multiple scattering and transport of charged particles. We then bro aden the context and show that range straggling effects also fit succe ssfully into this framework, which completes an electron model initiat ed by Yang. We introduce those effects with a superposition of Fokker- Planck solutions, i.e., by using an incident beam that contains a spec trum of initial energies, or equivalently, a set of csda ranges. Strag gling effects appear to be a beam property in this approach but are re turned to the material when we use it. All the information needed to c onstruct the spectrum is obtained from a measurement of the electron r est charge distribution in polystyrene. To illustrate the correctness of this procedure, we consider the case of a 20 MeV electron beam inci dent on water. We predict the absorbed dose distribution as a function of depth and also measure it with an ionization chamber in a water ta nk. We find nearly perfect agreement between calculation and experimen t in this case when all the results derive and apply to a clinically o perational machine. (C) 1998 American Association of Physicists in Med icine.