Electron-cyclotron maser theory for noninteger ratio emission frequencies in solar microwave spike bursts

An electron-cyclotron maser theory is developed to explain the recent observations of solar microwave millisecond spike bursts in which multiple bands were observed with frequency ratios not consistent with emission at integer harmonics of the cyclotron frequency, as predicted by standard theory. It is proposed here that several adjacent Bernstein modes are excited via the cyclotron maser mechanism and that the radiation escapes the corona via nonlinear wave-wave interactions. The growth rate is evaluated for a model electron distribution to demonstrate that several modes grow simultaneously at similar rates and that the observed frequency ratios are consistent with this model. The condition for saturation of the nonlinear process of Bernstein wave coalescence is shown to be satisfied for typical parameters and can account for the observed brightness temperatures and timescales of solar microwave spike bursts. These conclusions are only weakly dependent on the free parameters in the model.