Speckle statistics and transverse coherence of an x-ray laser with fluctuations in its active medium

It is shown that the statistics of the intensity distribution in the output beam of a collisional X-ray laser, analysed in terms of the degree of freedom or equivalently the number of the coherence modes in the beam cross-section, has non-Gaussian character. The non-Gaussian character seems to be caused by the small-scale plasma/medium fluctuations. It was assumed that these overlap the modal structure imposed by the geometry of the medium and considered as equivalent to a large-scale inhomogeneity. Thus, the fluctuations decide about the character of the output beam transverse coherence. It is also shown that the relevant to this model compound statistics of the intensity fluctuations in the output beam is well described by the m-m-distribution, a specific form of the K-distribution. The deviation from the Gaussian statistics was confirmed by the field correlation function at the laser exit plane, retrieved from the experimental data.