[en] A beam cooling method which uses a stimulated emission of radiation by relativistic electrons in a magnetic field, is proposed to apply to an electron beam in synchrotron radiation rings. The stimulation is produced by a traveling RF electric field in a transmission line against the beam. Averaging the emission power over electron energy distributions, the net emission from the beam is taken place in a certain frequency region. Some conditions for the energy emission are discussed. The emission power is shown to be enough large to decrease the horizontal emittance of the beam to a very small value in typical synchrotron radiation rings. (author)