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We suggest a technique to amplify a train of attosecond pulses, produced byhigh-harmonic generation (HHG) of an infrared (IR) laser field, in an activemedium of a plasma-based X-ray laser. This technique is based on modulation oftransition frequency of the X-ray laser by the same IR field, as used togenerate the harmonics, via linear Stark effect, which results inredistribution of the resonant gain and simultaneous amplification of a wideset of harmonics in the incident field. We propose an experimentalimplementation of the suggested technique in active medium of C5+ ions atwavelength 3.4 nm in the "water window" range and show the possibility toamplify by two orders of magnitude a train of attosecond pulses with pulseduration down to 100 as. We show also a possibility to isolate a singleattosecond pulse from the incident attosecond pulse train during itsamplification in optically deep modulated medium.

Attosecond Pulse Amplification in a Plasma-Based X-Ray Laser Dressed by an Infrared Laser Field