Wavelength dispersive X-ray fluorescence spectrometer (WDXRF) is widely applied in disparate fields such as metallurgy, building materials, and geological surveys. Its detection principle involves employing a primary X-ray beam to excite a fluorescent beam on the sample, which is then dispersed by a dispersive crystal based on wavelength. The intensities at different wavelengths are measured and a spectrum is generated to qualitatively and quantitatively analyze the elemental composition of the sample. During the test, certain degree of intensity is lost due to the dispersion of X-ray fluorescence by the dispersive crystal. Thus, a higher intensity of the primary X-ray beam is required, which is typically achieved by an X-ray tube with high-power as the excitation source. X-ray tubes with high power can be categorized into two types of side-window and end-window X-ray tubes based on their structural forms. For end-window X-ray tubes, since the window does not absorb backscattered electrons, the beryllium window is relatively thinner, which increases the transmissivity of longer wavelength radiation and facilitates the excitation of light elements. The power of an X-ray tube is determined by the tube voltage and current. Higher tube voltage produces X-rays with higher energy, while larger tube current increases the X-ray brightness. The power of an X-ray tube is influenced by factors such as the distribution of the electric field between the two electrodes inside the tube, cathode material, temperature, surface area, and shape. Currently, Malvern Panalytical is a representative company overseas that produces end-window X-ray tubes with high power, with 75 kV/4 kW being the main specification. In China, end-window X-ray tubes are mainly focused on low-power applications, and no products are available on the market for end-window X-ray tubes with high power. They are still in the design and testing phase, and there is still a gap in power control and target focal spot control compared with the advanced international level. Therefore, further simulation studies are needed for the relevant structures of end-window X-ray tubes with high power.

We develop methods to address the problem that the beam current and power of domestically produced end-window X-ray tubes with high power are below the design values. First, the structure of the end-window X-ray tube with high power is analyzed, and the structure is simplified based on the requirements of finite element calculations. The simplification method of the end-window X-ray tube with high power is as follows. 1) The unclosed filament is simplified into a closed ring structure. 2) The influence of the water-cooled structure inside the anode on the simulation results is not considered. 3) As the target and anode are at the same potential, both of them are modeled as a whole. 4) The ceramic column, the support structure of the filament, and the end-window structure of the X-ray tube are ignored. Then, the limiting factors for beam current emission in the end-window X-ray tube with high power are determined based on the thermionic emission theory and the theory of space charge limited emission. Two optimization schemes are proposed based on the analysis of simulation results. Finally, the feasibility of the optimization schemes is verified through simulation analysis and experiments.

In the theoretical simulation calculations, the electron beam trajectory, beam current, and target focal spot are computed for the two theoretical models (Tables 2 and 3). The results based on the thermionic emission theory show that a large number of electrons return to the filament surface due to insufficient initial energy to overcome the potential near the cathode, resulting in a beam current reaching the target material of only 32.65 mA. Considering the space charge effect, the beam current value obtained from the theory of space charge limited emission is 18.01 mA. The analysis of simulation results indicates that the potential distribution near the cathode has a significant influence on the beam current reaching the target material. Based on this analysis, we propose two optimization schemes. One scheme is changing the filament potential and increasing the potential gradient near the filament to improve the influence of space charge effects. The other is changing the filament position to increase the accelerating voltage near the filament, thereby better extracting the beam current (Figs. 4 and 5).

According to the simulation results, both schemes can improve the beam current of existing X-ray tubes with high power. An experimental platform is set up to validate the simulation results. The experimental setup consists of a vacuum pump unit, voltage source, current source, variable resistor, vacuum chamber, X-ray tube filament, and copper electrodes. The experiments confirm the applicability of the emission models adopted in our study to end-window X-ray tubes with high power, and the maximum beam current limited by temperature is obtained when the filament current is 12 A, with a value of 63.4 mA. The feasibility of the two optimization schemes is also verified.