Calculation of x‐ray spectra emerging from an x‐ray tube. Part I. Electron penetration characteristics in x‐ray targets

TLDR

Previous semi‑empirical electron‑transport models are reviewed and their limitations highlighted. The study investigates electron‑beam penetration characteristics in x‑ray targets for 50–150 keV incident energies. Monte Carlo simulations compute electron penetration depth distributions in tungsten (50–150 keV) and in Al, Mo, Re at 100 keV, and the results are combined with analytical models and experimental data to generalize the calculations. The work demonstrates the inadequacy of the Thomson‑Whiddington law for describing electron penetration and provides data useful for calculating bremsstrahlung self‑attenuation corrections in tungsten targets.

Abstract

The penetration characteristics of electron beams into x-ray targets are investigated for incident electron kinetic energies in the range 50-150 keV. The frequency densities of electrons penetrating to a depth x in a target, with a fraction of initial kinetic energy, u, are calculated using Monte Carlo methods for beam energies of 50, 80, 100, 120 and 150 keV in a tungsten target. The frequency densities for 100 keV electrons in Al, Mo and Re targets are also calculated. A mixture of simple modeling with equations and interpolation from data is used to generalize the calculations in tungsten. Where possible, parameters derived from the Monte Carlo data are compared to experimental measurements. Previous electron transport approximations in the semiempirical models of other authors are discussed and related to this work. In particular, the crudity of the use of the Thomson-Whiddington law to describe electron penetration and energy loss is highlighted. The results presented here may be used towards calculating the target self-attenuation correction for bremsstrahlung photons emitted within a tungsten target.