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In [I.R. Khairulin et al., submitted to Phys. Rev. Lett.] we propose a methodfor amplifying a train of sub-femtosecond pulses of circularly or ellipticallypolarized extreme ultraviolet (XUV) radiation, constituted by high-orderharmonics of an infrared (IR) laser field, in a neon-like active medium of aplasma-based X-ray laser, additionally irradiated with a replica of afundamental frequency laser field used to generate harmonics, and show thepossibility of maintaining or enhancing the ellipticity of high-harmonicradiation during its amplification. In the present paper we describe thisprocess in detail both for a single harmonic component and a sub-femtosecondpulse train formed by a set of harmonics. We derive the analytical theory anddescribe both analytically and numerically the evolution of the high-harmonicfield during its propagation through the medium. We discuss also thepossibility of an experimental implementation of the suggested technique 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 and ellipticity enhancement of sub-femtosecond XUV pulses in IR-field-dressed neon-like active medium of a plasma-based X-ray laser