Attosecond x rays from x-ray-boosted high-order harmonic generation

We theoretically examine high-order harmonic generation~(HHG) by an intense near-infrared~(\textsc{nir}) laser in combination with intense x~rays from a free electron laser such as the Linac Coherent Light Source (LCLS) at SLAC. The x~rays are tuned above an absorption edge thus causing one-photon ionization of a tightly bound core electron. The liberated core electron is driven by the \textsc{nir}~light through the continuum; when the electric \textsc{nir}~field reverses its direction, the electron may eventually return to the cation leading to its recombination with the core hole and the emission of a high-harmonic photon that is upshifted in energy by the x-ray~photon energy. We develop a theory of this x-ray boosted HHG scenario and apply it to $1s$~electrons of neon atoms. HHG spectra are computed for LCLS pulses which are generated according to the self-amplification of spontaneous emission~(SASE) principle. A time-frequency analysis of HHG emission reveals the imprinting of the varying LCLS pulse shapes on the boosted HHG spectrum which may open up prospects for pulse diagnostic. The boosted HHG~light is used to generate a single attosecond pulse in the kiloelectronvolt regime by filtering out only the highest HHG photons close to the upshifted cutoff.