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Attosecond pulses at kiloelectronvolt photon energies from high-order harmonic generation with core electrons

High-order harmonic generation (HHG) in simultaneous intense near-infrared (NIR) laser light and brilliant x rays above an inner-shell absorption edge is examined. A tightly bound inner-shell electron is transferred into the continuum. Then, NIR light takes over and drives the liberated electron through the continuum until it eventually returns to the cation leading in some cases to recombination and emission of a high-order harmonic (HH) photon that is upshifted by the x-ray photon energy. We develop a theory of this scenario and apply it to $1s$ electrons of neon atoms. The boosted HH light is used to generate a single attosecond pulse in the kiloelectronvolt regime. Prospects for nonlinear x-ray physics and HHG-based spectroscopy involving core orbitals are discussed.