Mutual amplification of high-order harmonics in an optically dressed hydrogenlike plasma-based x-ray laser

Abstract

In a recent work [V. A. Antonov, K. C. Han, T. R. Akhmedzhanov, M. Scully, and O. Kocharovskaya, Phys. Rev. Lett. 123, 243903 (2019)] a method of amplifying a train of attosecond pulses, produced via high-order harmonic generation of an infrared (IR) laser field, in an active medium of a plasma-based x-ray laser dressed by a replica of the IR field of the fundamental frequency was proposed. The specific case of independent amplification of each incident harmonic was considered, corresponding to a dense plasma of multiply charged ions (such as ${\mathrm{C}}^{5+}$ ions) which is strongly dispersive for the IR field. In the present paper, we consider a general case when the laser field modulation leads not only to the direct amplification of high harmonics (HHs), but also to the scattering of the harmonics into each other. The mutual coherent scattering process plays an important role in a relatively low-density plasma with a lower ion charge, corresponding to a weakly dispersive plasma at the frequency of the IR field. Constructive interference between the amplified HHs and the coherently scattered field may result in a significant enhancement of the total output field. We call this effect the mutual amplification of high-order harmonics. Considering the plasma of hydrogenlike ${\mathrm{Li}}^{2+}$ ions with an inverted transition wavelength of 13.5 nm as an example, we analytically and numerically show that synchronization of a coherently scattered field with the radiation of amplified HHs makes it possible to increase the intensity of attosecond pulses by several times compared to the case of an independent amplification of HHs.