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We consider a relativistic quantum heat engine that goes through athermodynamical cycle consisting of stages involving laser-assisted cooling ofelectrons and the generation of Xray radiation. Quantum treatment of theprocesses makes it possible to obtain the necessary condition and the amount ofwork extracted from the interaction ingredients, as well as the efficiency ofthe heat engine. We have also found that the efficiency of the relativisticengine is less than the one for the nonrelativistic case for the same momenta.The obtained results set the limits to the cooling, as well as the intensity ofX-ray radiation, in the quantum regime of the interaction of electrons withlaser fields.

X-Ray Radiation Generation in Heat Engines Using Electron Cooling