  A theoretical model is developed describing high-order harmonic generation
(HHG) from a gas of multiply-charged ions driven by a laser field of
relativistic intensity. Macroscopic propagation of harmonics is investigated in
a relativistic HHG setup where the relativistic drift is suppressed by means of
x-ray field assistance of the driving laser field. The possibility of
phase-matched emission of the harmonics is shown. The laser field geometry is
optimized to maximize the HHG yield with the corresponding phase-matching
schemes. Crucial issues determining the macroscopic HHG yield are discussed in
detail.
