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Summary form only given. Soft X-ray lasers utilize as gain medium high density plasmas of small lateral dimensions, in which refraction of the amplified X-ray radiation can result from electron density gradients. Recently, large soft X-ray amplification was demonstrated for the first time in a plasma column created by a discharge. A fast capillary discharge was utilized to generate amplification in the J=0-1 line of neon-like argon at 46.9 nm by collisional electron excitation, by creating a hot plasma column of small diameter and cylindrical symmetry. The analysis of the soft X-ray beam propagation and amplification in such plasma column requires one to take into account a two dimensional variation of the plasma parameters, which can be non parabolic.

Beam optics of gain-guided soft-x-ray lasers in cylindrical plasmas