Formulas derived in fundamental studies by A.A. Sokolov and I.M. Ternov on synchrotron radiation are used for the probabilities of induced transition, wave functions, and the electron energy spectrum in a magnetic field. The expression for the electron energy is used in derivinga formula for the radiation frequency, which is considerably higher than the nonrelativistic cyclotron frequency in the ultrarelativistic case. Products of matrix elements in the Dirac matrices are derived, and a formula is derived for the probabilities of induced emission and absorption on the assumption that the incident electromagnetic wave is linearly polarized. The values are substituted into the formula for the power in the stimulated transitions to derive an expression for the power in the induced emission for a relativistic rotatin gelectron. The formula implies that relativistic electrons can be used to generate high-power electromagnetic radiation in the submillimeter and infrared wavelength ranges.
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