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

Abstract

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 Livermore 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 (4<i>d</i>-4<i>p</i> transition). Only electron (collisional) and Doppler broadening play a role in the line profile of the 0-1 4<i>d</i>-4<i>p</i> transition. This allows us to use the Voigt shape in conditions where the amplifier, <i>i.e.</i>, 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 interaction 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 ~28 m&angst;, while the width of the amplified x-ray line ~4 m&angst;. Comparison with experiment is discussed.