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We propose a method for amplifying a train of sub-femtosecond pulses ofcircularly or elliptically polarized extreme ultraviolet (XUV) radiationconstituted by high-order harmonics of an infrared (IR) laser field, in aneon-like active medium of a plasma-based X-ray laser, additionally irradiatedwith a replica of a fundamental frequency IR field. It is shown that theellipticity of the pulses can be maintained or increased during theamplification process. The experimental implementation is suggested in anactive medium of an X-ray laser based on neon-like Ti^{12+} ions irradiated byan IR laser field with a wavelength of 3.9 microns.

Amplification of Elliptically Polarized Sub-Femtosecond Pulses in IR-Field-Dressed Neon-Like Active Medium of a Plasma-Based X-ray Laser