Analytical Calculation of Bremsstrahlung Spectrum for X-ray Tube at 10-50 keV

X-ray tube can easily produce X-ray, which is widely used in industry, archaeology and medicine. X-ray tubes use the interaction between high-speed electrons and anodic target atoms to generate X-rays, including discrete characteristic X-rays and continuous bremsstrahlung spectrum. Their spectral distribution is an important parameter index, which is the basis of subsequent applications. The spectral distribution can be obtained by actual measurement, Monte Carlo simulation and analytical calculation. Here, the analytical calculation of bremsstrahlung spectrum was mainly studied. Analytical calculation is to quickly calculate the bremsstrahlung spectrum produced by X-ray tube using known parameters. The key to its accuracy is the depth distribution of electrons in the anode target. By analyzing the depth distribution of electrons in the anode target, an analytical calculation model for the bremsstrahlung spectrum of electrons with incident energy from 10 to 50 keV in the copper target was established. Due to the elastic and inelastic interactions, the electron transport process in the target is very complex, and it is difficult to obtain the electron depth distribution by experimental or theoretical analysis. Monte Carlo simulation software Geant4 was used to simulate the interaction between the electron and copper target with incident energy of 10, 20, 30, 40 and 50 keV. The count, energy distribution and angle distribution of the electron at different penetration depths were obtained. The empirical formulas of electron depth distribution and path length correction coefficient of 10.50 keV electrons in copper target were obtained by fitting the simulated data. Since the penetration depth was scaled by using the continuous slowing down approximation range RCSDA, the parameters of the fitted empirical formula were approximately independent of the incident energy of electrons in this energy segment. The calculated results of the empirical formula for the electron depth distribution are in good agreement with the data of the electron depth distribution simulated by Geant4, which can accurately represent the electron depth distribution and the correction coefficient of path length. Combining the empirical formulas of electron depth distribution and path length correction coefficient with the corresponding bremsstrahlung cross-section data, an analytical calculation model of the bremsstrahlung spectrum of the thick target reflection type X-ray tube was established. Compared with Monte Carlo simulation results, the analytical calculation model has high accuracy and is in good agreement with the simulation results. When the electron incident energy is 15, 25, 35 and 45 keV, the spectral errors are 0.036 6, 0.041 7, 0.040 8 and 0.038 9, respectively. Compared with Monte Carlo simulation of X-ray tube bremsstrahlung spectrum, the analytical calculation speed is faster and can achieve high accuracy, which can be used in the need of fast calculation of X-ray tube bremsstrahlung spectrum.