Line shape and ray trace calculations in saturated X-ray lasers: Application to Ni-like silver

Longitudinal coherence length in X-ray lasers depends strongly on the shape of the amplified line. We have modelled an experiment performed at the LULI facility of Ecole Polytechnique. The experiment was devoted to the study of the temporal (longitudinal) coherence of the transient Ni-like silver 4d-4p transition X-ray laser at 13.9 nm. Accurate line shape calculations using PPP, a spectral line shape code, confirm that the Voigt profile is a good approximation for this X-ray laser line. This allows us to extensively use the Voigt shape in conditions where the amplifier, i.e. the plasma produced by the interaction of a high intensity laser with a slab target, is neither stationary nor homogeneous. Our calculations involve a ray trace code which is a post-processor to the hydrodynamic simulation EHYBRID. As the effect of saturation is important for the level populations and gains we include the interaction between the amplified beam and the medium using the Maxwell-Bloch formalism. While the FWHM of the spontaneous emission profile is ∼10 mÅ, the amplified X-ray line exhibits gain narrowing leading to the smaller width ∼3 mÅ. Comparison with experiment is discussed.