Technique to produce coherent x-ray radiation via laser pumping of a relativistic ion beam

The level population of a beam of relativistic positive ions with Z≥2 having a single bound electron may be inverted by the application of a "π pulse" of laser radiation tuned to the Doppler-shifted 1s-2p transition. When the laser beam and ion beam move in opposite directions, the required laser frequency is reduced by a factor 2γ. Subsequently applied short wavelength resonant radiation moving in the same direction as the ion beam (with an inverted population) will be amplified via stimulated emission, the wavelength in the lab frame now being shorter than the original laser wavelength by a factor (2γ)².