| Abstract
| - Context. The electron-cyclotron maser instability is responsible for the generation of the auroral kilometric radiation of the Earth and similar phenomena at other magnetized planets of the Solar System. The recently discovered radio emission from ultracool dwarfs has many similarities with the planetary auroral radio emission. The in situ measurements in the terrestrial magnetosphere indicate that the radiation is produced by nonthermal electrons with a horseshoe-like distribution. Kinetic simulations of the electron-cyclotron maser instability for these distribitions have not yet been performed. Aims. We investigate the amplification of plasma waves by the horseshoe-like electron distribution, as well as the relaxation of this distribution due to the electron-cyclotron maser instability. We determine the parameters of the generated plasma waves, the timescales of the relaxation process, and the conversion efficiency of the particle energy into waves. Methods. We developed a kinetic relativistic quasi-linear 2D code to simulate the coevolution of an electron distribution and 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 were performed for different parameter sets that seem to be typical of the magnetospheres of ultracool dwarfs (in particular, the plasma frequency is much less than the cyclotron one). Results. Our calculations indicate that the fundamental extraordinary mode dominates strongly. The generated waves have a frequency that is 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. Conclusions. Energy efficiency of the electron-cyclotron maser instability 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, the dynamics of the electron acceleration process and/or geometry of the radiation source.
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