Stimulated emission of coherent radiation from a relativistic ion beam

We consider a relativistic beam of Hydrogen-like ions with Z>1 having a single bound electron. In this two-level-system, the level population (1s and 2p) 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 the inverted population) will be amplified via stimulated emission: the wavelength in the laboratory frame now being shorter than the original laser wavelength by a factor (2γ)2. copyright 1999 American Institute of Physics