Theoretical study of the enhancement of saturable absorption of Kr under x-ray free-electron laser

The generation of hollow atoms will reduce the probability of light absorption and provide a high-quality diffraction image in the experiment. In this paper, we calculated the ionization rate of the Kr atom under x-ray free-electron laser(XFEL) using Hartree–Fock–Slater model and simulated the ionization model of Kr atom using Monte–Carlo method to determine the response of the hollow atom of Kr atom to the XFEL photon energy. Calculating the correlation between the total photoionization cross-section of the ground state of Kr atom and the photon energy, we determined three particular photon energies of 1.75 ke V, 1.90 ke V, and 14.30 ke V. The dynamics simulation under the experimental condition's17.50 ke V photon energy was achieved by implementing the Monte–Carlo method and calibrating the photon flux modeling parameters. Consequently, our calculated data are more consistent with experimental phenomena than previous theoretical studies. The saturable absorption of Kr at 1.75 ke V, 1.90 ke V, 14.30 ke V, and 17.50 ke V energies was further investigated by using the optimized photon flux model theory. We compared the statistics on main ionization paths under those four specific photon energies and calculated the population changes of various Kr hollow atoms with different configurations.The results demonstrate that the population of hollow atoms produced at the critical ionization photon energy is high. Furthermore, the change of population with respect to position is smooth, which shows a significant difference between the generation mode of ions with low and high photon energies. The result is important for the study of medium-and high-Z element hollow atoms, which has substantial implications for the study of hollow atoms with medium and high charge states, as well as for the scaling of photon energy of free electron lasers.