Electron-cyclotron emission model of solar radio zebras with high gyro-harmonic numbers

Solar radio zebras detected as fine structures of Type IV radio bursts help to diagnose the coronal plasma at kinetic micro-scales. One of the models of the radio zebras is the electron-cyclotron maser instability based on a double plasma resonance at gyro-harmonics of the electron cyclotron frequency when ω_pe > ω_ce. Though the gyro-harmonic numbers estimated for zebra observations are very high, in some cases exceeding 100, it is still uncertain how the instability can grow and generate zebra stripes for them. To investigate the instability evolution, we studied its growth and saturation by utilizing analytical calculations and particle-in-cell simulations. We found that the growth rates and saturation energies as functions of the cyclotron-to-plasma frequency ratio form a profile that peaks approximately at the integer harmonics of the cyclotron frequency. Nonetheless, the peaks shift to lower frequencies with increasing the plasma loss-cone temperature, and they broaden and decrease with increasing the gyro-harmonic number. These results suggest that emissions for very high gyro-harmonic numbers should not be formed. Hence, to explain the detected high gyro-harmonic numbers of one hundred, we also investigated the growth rates as a function of the loss-cone angle and found that distributions with very  high loss-cone angles can interpret the observations. We proposed that such large loss-cone angles can be generated in magnetic loops with small magnetic field gradients or below an X-point of the magnetic reconnection.