Quasi-linear stage of synchrotron instability I. The limit of low initial radiation energy density

We consider the initial problem of quasi-linear relaxation of synchrotron instability in a spatially homogeneous system of relativistic electrons embedded in a cold plasma. We analyze evolution of the energy spectrum of electrons and the frequency spectrum of radiation at the limit of low initial radiation energy density. At this limit, the problem is reduced to the solution of a diffusion equation with a stationary diffusion coefficient for the electron distribution over momentum which does not depend on the initial radiation energy density. The radiation frequency spectrum is approximated by the Gaussian profile, and its parameters are expressed via the electron energy density at the given and initial instants of time. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 49, No. 11, pp. 964–976, November 2006.