Speckle Statistics, Coherence and Polarization of a Collisional Soft X-Ray Laser

A simple model of dynamics of a collisional X-ray laser is given applying Maxwell-Bloch equations in a uniform approximation. The main considered parameters include polarization and coherence of the emitted radiation. Speckle pattern, typical for a radiation source of partial coherence, especially, if involving process of the amplified spontaneous emission (ASE), are used as an alternative source of information on the processes occurring in the active medium of an X-ray laser. A level of partial coherence is deduced by statistical analysis of the speckle pattern generated in the output beam of the laser. It is shown that plasma fluctuation and non-Gaussian character of the statistics are needed to reproduce the transverse coherence values reported in the experiment.