A model for the energy and angular distribution of x rays emitted from an x-ray tube. Part I. Bremsstrahlung production

Purpose: To develop an analytical model for bremsstrahlung production in a thick x-ray target (i.e., the x-ray tube anode) that takes into account the intrinsic bremsstrahlung angular distribution.

Methods: X-ray spectrum models developed from theoretical principles have traditionally treated the angular distribution of the bremsstrahlung production as spherically uniform. This assumption stems from the rationale that electrons promptly attain a diffuse directional distribution in an x-ray target due to multiple scattering, thereby effectively masking the intrinsic bremsstrahlung angular distribution. In this work, a model that explicitly accounts for the angular distribution of the bremsstrahlung production is presented. The model combines Monte Carlo-calculated depth, energy, and angular distributions of electrons penetrating the x-ray target, and incorporates theoretical results for the differential bremsstrahlung cross section. The effects of using different simplified model assumptions for the electron penetration and the intrinsic bremsstrahlung angular distribution are analyzed for tungsten and molybdenum targets in the energy range 20-300 keV.

Results: Typical assumptions of previous models are shown to introduce errors in calculated spectra. Particularly, it is shown that predictions of fluence and air kerma free-in-air can be overestimated by 15-30% (2-3% in aluminum half-value layer thickness) for clinically relevant beam qualities. The present model is able to reproduce comprehensive Monte Carlo calculations of the bremsstrahlung production generally to within 1%.

Conclusions: The bremsstrahlung model developed in this work is an improvement over previous models in that the main features of the electron penetration and the resulting bremsstrahlung are considered in detail. The model can be used for more accurate predictions of the energy and angular distribution of x rays emitted from an x-ray tube.