High gain inner-shell x-ray lasers pumped by x-ray free-electron laser system FLASH in DESY

The feasibility of generating high gain inner-shell x-ray lasers photo-ionization pumped by the DESY/XFEL facility is studied. The gain characteristics are analyzed for the two representative schemes of inner-shell x-ray transitions, the self-terminated x-ray lasing (1s)-1 → (2p)-1 (λ = 4.5nm) in carbon (Z = 6) and the quasi-stationary x-ray lasing (2p)-1 → (3s)-1 (λ = 4.1 nm) in calcium (Z = 20). When the third harmonic XFEL pumping pulses of 10 fs at 284 eV and 360 eV with the pumping intensities of 6 x 1014 W/cm2 and 1 x 1017 W/cm2 for C and Ca are available, respectively, a net gain of 120 cm-1 are predicted with quite short durations of 10 fs and 2fs. Our studies show that DESY/XFEL facility is sufficient to generate the high gain photo-ionization pumped Kα radiations in low Z atoms