Solar and stellar radio spikes - Limits on the saturation of the electron-cyclotron maser

The solar millisecond radio 'spikes' have been explained in terms of X-mode radiation generated by a maser near the electron gyrofrequency, acting on fast coronal electrons with a loss cone. This maser is a phenomenon described by quasi-linear theory. It is sensitive to the small first-relativistic correction to the gyrofrequency. Thus, it might be disrupted rather easily by nonlinear effects. The maximum radiation density that can be reached before the radiation entrains (phase-locks) the electrons and saturates the maser is discussed. If the observed durations of solar radio spikes are a measure of the rate of scattering into the loss-cone, then the inferred energy density is at least two orders of magnitude less than the energy density at which entrainment sets in. Also, maser emission from auroral kilometric radiation does not reach wave energies critical for electron entrainment. Maser emissions from flare stars, however, show 3-4 orders of magnitude higher radio fluxes and brightness temperatures than for the solar case and are likely to be saturated by entrainment.