Quantitative simulation of electron beam's focal spot in thermionic emission

The focal spot size of an electron beam in x-ray photography lamps, which is formed on the anode, has an important effect on the contrast of x-ray images. Usually, the grid is used in x-ray production lamps only to stop or regulate the current of the electron beam, but its effect on the dimensions and size of the focal spot has not been investigated. In this article, we have calculated the electron beam current in a thermionic mode at three temperatures, 2300, 2500, and 2800 K, for a voltage difference of 50 and 100 kV. Our results show that in a thermionic regime without grid (T mode), a larger focal spot is obtained, but in a thermionic regime with grid (TG mode), the focal spot size is smaller. The result that the focal spot of the TG mode is smaller than the focal spot of the T mode was obtained independently of temperature and potential difference. The results of thermionic tracking emission models (T and TG) are compared for different temperatures in the form of three graphs, and we will show that these two regimes have differences in the dimensions of the focal spot formed in each case and that the TG mode gives better results.