Dynamics of amplified spontaneous emission in the laboratory x-ray laser with random optical inhomogeneities

The formation of the amplified spontaneous emission (ASE) in the laboratory x-ray laser with the Markov fluctuations of the dielectrical permittivity (epsilon) is studied by the method of paraxial equation for the transverse correlation function of the radiation field. The fluctuations (epsilon) are found to impose a limit on the ASE spatial coherence and to decrease the power of the coherent ASE. In the case of the weak regular refraction, the ASE scattering by (epsilon) is analogous to the linear absorption and decreases the gain observed. At the strong defocusing refraction the effect of (epsilon) on the ASE has a 'latent' character: an essential fall of the coherence length is accompanied by a relatively small decrease in the axial intensity and by a small broadening of the ASE beam as a whole.