The saturation of the electron-cyclotron maser instability and the interpretation of solar millisecond spikes

A self-consistent numeric two-dimensional code of the kinetic wave-particle equations developed to investigate the maser dynamics in the solar context is applied to solar millisecond-spike observations in order to improve the diagnostic capabilities of the theory of the electron-cyclotron maser instablitity. Attention is given to the inhomogeneity of the magnetic field selecting magneto-ionic modes with relatively short saturation lengths and suppressing mechanisms such as collisional deflection, free-free absorption, and gyroresonance absorption. The time scales of maser saturation in respect to time scales of global particle changes in a magnetic loop are covered, relevant observations of solar millisecond spikes are described, and the interpretation in terms of physical parameters deduced from the quasi-linear maser simulations are presented. It is demonstrated that the quasi-linear simulations make it possible to constrain the physical parameters from the observed time scale and frequency.