Growth-rates of the electrostatic waves in the double plasma resonance model of solar radio zebras

Jan Benáček, Masaryk University

Radio zebras are detected in radio observations from Sun, Jupiter and also from Crab Nebula pulsar. In solar case, they are fine structures of Type IV bursts and can be used for diagnostics of flare plasma parameters (density, magnetic field). One of the models of the solar radio zebra is based on the double plasma resonance instability, which supposes the dense and cold background isotropic plasma and rare hot component with a loss-cone type of the distribution function. At resonances between the plasma and cyclotron frequency, $\omega_\mathrm{pe} = s \omega_\mathrm{ce}$ ($s$ is an integer), this instability generates the upper-hybrid waves which are transformed into electromagnetic radiation and emitted in a narrow cone towards the observer. We used analytical theory for growth-rates and 3D electromagnetic relativistic Particle-in-Cell simulation for an analysis of this instability. For DGH velocity distribution function of hot electrons we found that increasing its temperature the growth-rate maxima are shifted to lower values of the ratio $\omega_\mathrm{pe} / \omega_\mathrm{ce}$ and for temperatures $v_\mathrm{t} \geq 0.3\, c$ the maxima are not distinguishable. From zebra observations, we estimated the brightness temperature of the zebra source, its size, the energy density in the source and the conversion rate to electromagnetic waves. We also calculated the growth-rates for loss-cone power-law and loss-cone kappa distributions having different loss-cone angles.