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High-order harmonic generation with resonant core excitation by ultraintense x rays

High-order harmonic generation (HHG) is combined with resonant x-ray excitation of a core electron into the transient valence vacancy that is created in the course of the HHG process. To describe this setting, I develop a two-active-electron quantum theory for a single atom assuming no Coulomb interaction among the electrons; one electron performs a typical HHG three-step process whereas another electron is excited (or even Rabi flops) by intense x rays from the core shell into the valence hole after the first electron has left the atom. Depending on the amplitude to find a vacancy in the valence and the core, the returning continuum electron recombines with the valence and the core, respectively, emitting high-order harmonic (HH) radiation that is characteristic of the combined process. After presenting the theory of x-ray boosted HHG for continuous-wave light fields, I develop a description for x-ray pulses with a time-varying amplitude and phase. My prediction offers novel prospects for nonlinear x-ray physics, attosecond x rays, and HHG-based time-dependent chemical imaging involving core orbitals.