High-order harmonic generation with standing wave pump of relativistic intensity

High-order harmonic generation (HHG) in laser fields of relativistic intensity is studied. It is shown that due to relativistic longitudinal displacement of the electrons a significant HHG suppression occurs. Such suppression is greater for low-frequency part of HHG spectrum than for high-frequency part. We propose to use standing wave pump instead of traveling wave to overcome this effect and enhance HHG efficiency. The efficiency of utilizing atoms in standing wave decreases with the pump intensity growth. However, in traveling wave HHG efficiency decrease is still greater, therefore using standing wave allows to obtain HHG intensity essentially greater than in traveling wave (for example, a gain factor of 10(2) can be achieved when pumping Ar8+ ions with radiation of intensity 10(18) W/cm(2) and wavelength 0.3 mum).