Results and problems in the investigation of the synchrotron instability

A brief resumé of the results of the linear theory of the synchrotron instability is presented, obtained using the quantum method with the Einstein coefficients and the classical method with the kinetic equation. The full equivalence is shown for the results of quantum and classical treatment of synchrotron instability.The expression for the growth-rate of synchrotron radiation in a system of relativistic electrons with an anisotropic momentum distribution is also found and investigated. Such a distribution might be realised in certain sources of cosmic radio emission (for example in pulsars). Certain problems are noted which have not yet been properly solved in studies of the synchroton instability (the instability of a highly rarified plasma, the quasi linear theory of the synchrotron instability, and so on).