Acceleration of Energetic Electrons by the Synchrotron Radiation with Rayleigh-Jeans Spectrum

It is shown that in an optically thick medium, the extremely relativistic electrons in the Maxwellian distribution will generate in a magnetic field low frequency synchrotron radiation with the Rayleigh-Jeans spectrum. Based on the Fokker-Plank equation, the fast electrons accelerated by this kind of wave field will have a power-law energy spectrum. Considering the physical conditions of the coronal active regions the observed electron spectra at about 10 Mev in solar flares are probably due to the acceleration of fast electrons by the synchrotron radiation.