Temporal coherence calculations in the Ni-like Pd x-ray laser

Longitudinal coherence length in x-ray lasers depends strongly on the shape of the amplified line. We have modeled an experiment performed at the Lawrence Livermor e National Laboratory. The experiment was devoted to the study of the temporal (longitudinal) coherence of the transient x-ray laser at 14.7 nm in Ni-like palladium (4d-4 p transition). Only electron (collisional) and Doppler broadening play a role in the line profile of the 0-1 4 d-4 p transition. This allows us to 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 use a ray trace code which is constructed as a post-processor of the hydro-atomic code EHYBRID. In the saturation regime, there is need to account properly for the in teraction between the x-ray laser field and the lasing ions. This is done in the framework of the Maxwell-Bloch formalism. The FWHM of the spontaneous emission profile is a 28 mA, while the width of the amplified x-ray line a 4 mA. Comparison with experiment is discussed. Keywords: x-ray laser, XUV sources