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We analyze soft-x-ray beam propagation and amplification in gain-guided amplifiers of cylindrical geometry for arbitrary gain and density profiles. A general relation that must be fulfilled for refraction not to be an impediment to the exponential growth of the intensity is obtained. It is shown that for sufficiently long plasma columns the effective gain, reduced by refraction, is determined solely by the gain and the curvature of the density profile at the position of maximum density, evendoi:10.1364/josab.13.002841 fatcat:q3f6ampcrjgc5axyxzpnkbw6v4