We investigate the influence of $3p\to 3d$ core-to-core resonance on the transient level populations of Kr driven by x-ray free-electron laser pulses, using rate-equation approaches. The process begins with the predominant photoionization of $3d$ electrons, creating transient $3d^{-1}$ core holes. These holes can then be resonantly filled by $3p$ electrons via $3p\to 3d$ excitations, a pathway that competes directly with the ultrafast Auger decay of the $3d^{-1}$ state. The signature of this resonant process is monitored through the resulting $3p^{-1}$ Auger electron spectra. Our calculated spectra show distinct resonant features which are in good agreement with recent experimental measurements of Fushitani et al. [Phys. Rev. A 107, L021101 (2023)]. At relatively low intensities ($\sim 7.0\times {10}^{13}{\mathrm{W}/\mathrm{cm}}^2$), the $3p\to 3d$ resonance suppresses the ${\mathrm{Kr}}^{2+}$ population by 2.5%, a suppression that increases to 8.6% at $5.0\times {10}^{14}{\mathrm{W}/\mathrm{cm}}^2$. For intensities beyond $5.0\times {10}^{14}{\mathrm{W}/\mathrm{cm}}^2$, the resonance saturates, yielding a maximum reduction in ${\mathrm{Kr}}^{2+}$ population of approximately 10%. Our work offers practical guidelines for the quantum control of innershell processes in future ultrafast x-ray experiments.

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• Atomic orbital
• Autoionization & Auger processes
• Electron correlation calculations for atoms & ions
• Electronic transitions
• Single- and few-photon ionization & excitation
• Spontaneous emission