Quantification of mean energy and photon contamination for accurate dosimetry of high-energy electron beams

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Abstract
The scientific background of the standard procedure for determination of the mean electron energy at the phantom surface from the half-value depth has been studied. The influence of energy, angular spread and range straggling on the shape of the depth dose distribution and the and ranges is described using the simple Gaussian range straggling model. The relation between the and ranges is derived in terms of the variance of the range straggling distribution. By describing the mean energy imparted by the electrons both as a surface integral over the incident energy fluence and as a volume integral over the associated absorbed dose distribution, the relation between and different range concepts, such as and the maximum dose and the surface dose related mean energy deposition ranges, and , is analysed. In particular the influence of multiple electron scatter and phantom generated bremsstrahlung on is derived. A simple analytical expression is derived for the ratio of the incident electron energy to the half-value depth. Also, an analytical expression is derived for the maximum energy deposition in monoenergetic plane-parallel electron beams in water for energies between 2 and 50 MeV. Simple linear relations describing the relative absorbed dose and mass ionization at the depth of the practical range deposited by the bremsstrahlung photons generated in the phantom are derived as a function of the incident electron energy. With these relations and a measurement of the extrapolated photon background at , the treatment head generated bremsstrahlung distribution can be determined. The identification of this photon contamination allows an accurate calculation of the absorbed dose in electron beams with a high bremsstrahlung contamination by accounting for the difference in stopping power ratios between a clean electron beam and the photon contamination. The absorbed dose determined using ionization chambers in heavily photon contaminated (10%) electron beams may be too low - by as much as 1.5% - without correction.