Zebra stripes with high gyro-harmonic numbers

Abstract: Solar radio zebras are used in the determination of the plasma density and magnetic field in solar flare plasmas. Analyzing observed zebra stripes and assuming their generation by the double-plasma resonance (DPR) instability, high values of the gyro-harmonic number are found. In some cases, they exceed one hundred, in disagreement with the DPR growth rates computed up to now, which decrease with increasing gyro-harmonic number. We address the question of how the zebras with high values of the gyro-harmonic numbers $s$ are generated. For this purpose, we compute growth rates of the DPR instability in a very broad range of $s$, considering a loss-cone $\kappa$-distribution of superthermal electrons and varying the loss-cone angle, electron energies, and background plasma temperature. We numerically calculated dispersion relations and growth rates of the upper-hybrid waves and found that the growth rates increase with increasing gyro-harmonic numbers if the loss-cone angles are $\sim80^\circ$. The highest growth rates for these loss-cone angles are obtained for the velocity $v_\kappa = 0.15\,c$. The growth rates as function of the gyro-harmonic number still show well distinct peaks, which correspond to zebra-stripe frequencies. The contrast of the growth rate peaks to surrounding growth rate levels increases as the $\kappa$ index increases and the background temperature decreases. Zebras with high values of $s$ can be generated in regions where loss-cone distributions of superthermal electrons with large loss-cone angles ($\sim80^\circ$) are present. Furthermore, owing to the high values of $s$, the magnetic field is relatively weak and has a small spatial gradient in such regions.