On the base of the quantum kinetic equation for density matrix in plasma at the stimulated bremsstrahlung of electrons on ions, the nonlinear absorption rate for high-intensity shortwave radiation in plasma has been obtained within relativistic quantum theory. Both classical Maxwellian and degenerate quantum plasma are considered for x-ray lasers of high intensities. Essentially different dependences of nonlinear absorption rate on polarization of strong laser radiation is stated.
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