We present a theoretical investigation of the level population evolution and charge-state kinetics of Kr atoms driven by ultrafast soft x rays in the 210–300-eV range, using a time-dependent rate-equation framework, which is based on a fine-structure-level approach combined with large-scale Monte Carlo simulations. Photoexcitation, photoionization, radiative decay, and single- and direct-double-Auger-decay (DDAD) channels are considered in the present calculation. The effects of DDAD on level population evolution and charge-state distribution are demonstrated quantitatively. This higher-order process, often neglected in previous studies, is shown to contribute approximately 10% to the yields of ${\mathrm{Kr}}^{2+}$ and ${\mathrm{Kr}}^{3+}$. Our results demonstrate that omitting DDAD can lead to systematic underestimation of low charge-state populations, thereby impacting the interpretation of x-ray free-electron-laser (XFEL) experiments. The present work establishes the necessity of including multielectron-decay pathways in precision modeling of inner-shell kinetics in heavy atoms interacting with XFEL.

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• Atomic orbital
• Autoionization & Auger processes
• Electron correlation calculations for atoms & ions
• Electronic transitions
• Fine & hyperfine structure