The spectral dependence of electron central-axis depth-dose curves

Electron linac fields are usually characterized by the central-axis practical range in water, Rp, and the depth of half maximum dose, R50, for dosimetry, quality assurance, and treatment planning. The quantitative relations between the range parameters and the intrinsic linac beam's energy structure are critically reviewed. The spectral quantity * is introduced which is defined as the mean energy of the incident spectral peak, termed the "peak mean energy." An analytical model is constructed to demonstrate the predicted relation between polyenergetic spectral shapes and the resulting depth-dose curves. The model shows that, in the absence of electrons at the patient plane with energies outside about * +/- 0.1 *, Rp and R50 are both determined by *. This analytical approximation is confirmed by a Monte Carlo calculation comparing two different idealized incident spectra. The effect of contaminant lower energy or wide-angle scattered electrons is also discussed. The effect of the width of the intrinsic energy spread on the shape of the depth-dose curve is investigated using Monte Carlo depth-dose simulations based on measured linac energy spectra having energy spreads (full width at half maximum) as large as 20%. These simulations show that the energy spread has only a small effect on the shape of the central-axis depth-dose curve.