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Kinetic Simulation of the Electron-Cyclotron Maser Instability: Relaxation of Electron Horseshoe Distributions

The electron-cyclotron maser instability (ECMI) is responsible for generation of the planetary auroral radio emissions. Most likely, the same mechanism produces radio bursts from ultracool dwarfs. We investigate amplification of plasma waves by the horseshoe-like electron distribution (similar to those observed in the terrestrial magnetosphere) as well as relaxation of this distribution due to the ECMI. We aim to determine parameters of the generated plasma waves, timescales of the relaxation process, and the conversion efficiency of the particle energy into waves. We have developed a kinetic relativistic quasi-linear 2D code for simulating the coevolution of an electron distribution and the high-frequency plasma waves. The code includes the processes of wave growth and particle diffusion which are assumed to be much faster than other processes (particle injection, etc.). A number of simulations have been performed for different parameter sets which seem to be typical for the magnetospheres of ultracool dwarfs (in particular, the plasma frequency is much less than the cyclotron one). The calculations have shown that the fundamental extraordinary mode dominates strongly. The generated waves have the frequency slightly below the electron cyclotron frequency and propagate across the magnetic field. The final intensities of other modes are negligible. The conversion efficiency of the electron energy into the extraordinary waves is typically around 10%. Complete relaxation of the unstable electron distribution takes much less than a second. Energy efficiency of the ECMI is more than sufficient to provide the observed intensity of radio emission from ultracool dwarfs. On the other hand, the observed light curves of the emission are not related to the properties of this instability and reflect, most likely, dynamics of the electron acceleration process and/or geometry of the radiation source.