  High-order harmonic generation (HHG) by hydrogenlike atoms/ions in the
uniform periodic electric field, formed by the two linearly polarized
counterpropagating laser beams of relativistic intensities, is studied. The
relativistic quantum theory of HHG in such fields, at which the impeding factor
of relativistic magnetic drift of a strong wave can be eliminated, is presented
arising from the Dirac equation. Specifically, a scheme of HHG in underdense
plasma with the copropagating ultraintense laser and fast ion beams is
proposed.
