In studies investigating the interaction of matter with ultraintense, ultrashort x-ray free electron laser (XFEL) pulses, the evolution kinetics are generally described by directly solving a time-dependent rate equation that considers single-photon and single-electron processes. In the present study, we show the effects of single-photon double photoionization and direct double Auger decay in the K-shell ionization kinetics of XFELs interaction with argon atoms. Because a huge number of coupled transition channels are present in the K-shell ionization, we develop a Monte Carlo method to simulate the complex ionization kinetic processes and give the level population evolution of ions and charge state distribution (CSD). The K-shell-dominated ionization dynamics of Ar irradiated by XFEL pulses with photon energies of 5000, 5500 and 6500 eV are investigated and compared with available experimental observations of the CSD. The results show that the population fractions of Ar5+, Ar6+ and Ar9+ are increased by 78%, 152% and 144%, respectively, by these higher-order processes at a photon energy of 5000 eV. Including the direct double-electron processes, the predicted CSDs are in better agreement with the experiments carried out at the photon energies of 5000, 5500 and 6500 eV. It is expected that the developed theoretical formalism can be used to more accurately calibrate the beam profile and intensity of XFELs.
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