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High-order harmonic generation (HHG) by hydrogenlike atoms/ions in theuniform periodic electric field, formed by the two linearly polarizedcounterpropagating laser beams of relativistic intensities, is studied. Therelativistic quantum theory of HHG in such fields, at which the impeding factorof relativistic magnetic drift of a strong wave can be eliminated, is presentedarising from the Dirac equation. Specifically, a scheme of HHG in underdenseplasma with the copropagating ultraintense laser and fast ion beams isproposed.

Relativistic quantum theory of high harmonic generation on atoms/ions by strong laser fields