Zebra stripes with high gyro-harmonic numbers

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.