Formation of the spatial coherence of amplified spontaneous emission. 1. Regularly inhomogeneous active medium

An equation for a transverse correlation function is used in a study of the spatial coherence of amplified spontaneous emission (ASE) at the exit from a plasma active medium of an x-ray laser. The case of large Fresnel numbers in the far-field zone is considered. If regular refraction occurs, in the far-field zone the correlation length of the ASE emerging through the end of the active medium rises exponentially with an increase in the length z of the medium, whereas the correlation length of the ASE emerging through the side surface of the active medium is relatively short and independent of z in the limiting cases of linear and saturated amplification. The region of the maximum correlation length in the ASE beam does not coincide with the region of maximum values of the flux density. Saturation of the amplification and nonresonant losses reduce the spatial coherence. A model calculation is reported of the spatial coherence of a Ne-like selenium x-ray laser in a direction perpendicular to the target. The agreement between the calculated coherence coefficient and the experimental value is obtained on the assumption that the ASE emitted through the side surface predominates at the measurement point.