Abstract
The evolution of a system of electrons with a given initial distribution in an external magnetic field is considered. An equation describing the evolution of the electron distribution function in a uniform magnetic field is derived for the case of arbitrarily relativistic electrons, and an exact solution to this equation is found. Asymptotics of this solution corresponding to the cases of synchrotron radiation and relativistic dipole radiation are calculated, and the evolution of the radiation spectra for these limiting cases is analyzed. The curvature of the magnetic field lines is taken into account phenomenologically, which demonstrates the presence of an exponential dependence in the case of synchrotron radiation.
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