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## Narrow-band hard-x-ray lasing

Lyu, Chunhai

The generation of narrow-band fully coherent x-ray lasers based on stimulated emission in highly charged ions is investigated. The lasing scheme we put forward leads to x-ray sources with high spatial and temporal coherence, enabling new applications in x-ray quantum optics. Highly charged ions can be generated in plasmas created by line-focused intense optical lasers. Population inversion between the 1s2l (l = s, p) and 1s^2 states in He-like ions is obtained by inner-shell photoionization of Li-like ions with intense x-ray free-electron laser pulses. We show that lasing can happen in elements such as Ne, Ar, Kr and Xe through E1, M1 or M2 transitions. The corresponding Maxwell– Bloch equations are developed with the inclusion of multipole interactions between the x-ray fields and the ions. Numerical simulations show that the x-ray lasers generated this way are characterized by high intensities and with femtosecond pulse durations. The relative bandwidths of $\delta\omega/\omega = 10^P{−5} – 10^{−7}$ achieved are by up to 3 orders of magnitude narrower than in pulses from state-of-art x-ray sources at wavelengths down to the sub-ångström regime. Analytical solutions of the Maxwell–Bloch equations in the exponential-gain approximation are found to give results consistent with numerical simulations for the pulse and spectral profiles.