An analytic calculation of the energy fluence spectrum of a linear accelerator

Calculation of photon dose by convolution methods requires a knowledge of the fluence spectrum of photons produced by the linear accelerator treatment head. But this spectrum is very difficult to measure accurately, and is often derived by Monte Carlo calculations modeling the elements of the treatment head. In this paper an analytic calculation technique and the corresponding computer tool for calculating the photon energy fluence spectral distribution at any point in a bremsstrahlung field are presented. Primary bremsstrahlung photon distributions are computed by modeling electron dispersion in layers in a thick target and using the thin target bremsstrahlung cross section formulas of Schiff. The first Compton scatter from all materials in a linear accelerator treatment head is computed analytically. Higher-order Compton scatter events and pair production annihilation photons are ignored, but the attenuation of both primary and first scattered photon fluence is computed. Predictions of the computer implementation of the model are compared to measurements of bremsstrahlung production in a thick target and to Monte Carlo calculations of the energy fluence emerging from a linear accelerator. Finally, the computer tool is used to investigate the source of collimator-dependent fluence fluctuations in air. In agreement with other measurements, the principal contribution to fluence outside the geometric field is found to be from scatter in the flattening filter.