Growth Rates of the Upper-hybrid Waves for Power-law and Kappa Distributions with a Loss-cone Anisotropy. (arXiv:1904.05110v1 [astro-ph.SR])
<a href="http://arxiv.org/find/astro-ph/1/au:+Yasnov_L/0/1/0/all/0/1">Leonid V. Yasnov</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Benacek_J/0/1/0/all/0/1">Jan Benáček</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Karlicky_M/0/1/0/all/0/1">Marian Karlický</a>
Fine structures of radio bursts play an important role in diagnostics of the
solar flare plasma. Among them the zebras, which are prevalently assumed to be
generated by the double plasma resonance instability, belong to the most
important. In this paper we compute the growth rate of this instability for two
types of the electron distribution: a) for the power-law distribution and b)
for the kappa distribution, in the both cases with the loss-cone type
anisotropy. We found that the growth rate of the upper-hybrid waves for the
power-law momentum distribution strongly depends on the pitch-angle boundary.
The maximum growth rate was found for the pitch-angle $theta_mathrm{c}
approx$ 50$^circ$. For small angles the growth rate profile is very flat and
for high pitch-angles the wave absorption occurs. Furthermore, analyzing the
growth rate of the upper hybrid waves for the kappa momentum distribution we
found that a decrease of the characteristic momentum $p_kappa$ shifts the
maximum of the growth rate to lower values of the ratio of the electron-plasma
and electron-cyclotron frequencies, and the frequency widths of the growth rate
peaks are very broad. But, if we consider the kappa distribution which is
isotropic up to some large momentum $p_m$ and anisotropic with loss-cone above
this momentum then distinct peaks of the growth rate appear and thus distinct
zebra stripes can be generated. It means that the restriction for small momenta
for the anisotropic part of distributions is of principal importance for the
zebra stripes generation. Finally, for the 1 August 2010 zebra stripes, the
growth rates in dependence on radio frequency were computed. It was shown that
in this case the growth rate peaks are more distinct than in usually presented
dependencies of growth rates on the ratio of the plasma and cyclotron
frequencies.
Fine structures of radio bursts play an important role in diagnostics of the
solar flare plasma. Among them the zebras, which are prevalently assumed to be
generated by the double plasma resonance instability, belong to the most
important. In this paper we compute the growth rate of this instability for two
types of the electron distribution: a) for the power-law distribution and b)
for the kappa distribution, in the both cases with the loss-cone type
anisotropy. We found that the growth rate of the upper-hybrid waves for the
power-law momentum distribution strongly depends on the pitch-angle boundary.
The maximum growth rate was found for the pitch-angle $theta_mathrm{c}
approx$ 50$^circ$. For small angles the growth rate profile is very flat and
for high pitch-angles the wave absorption occurs. Furthermore, analyzing the
growth rate of the upper hybrid waves for the kappa momentum distribution we
found that a decrease of the characteristic momentum $p_kappa$ shifts the
maximum of the growth rate to lower values of the ratio of the electron-plasma
and electron-cyclotron frequencies, and the frequency widths of the growth rate
peaks are very broad. But, if we consider the kappa distribution which is
isotropic up to some large momentum $p_m$ and anisotropic with loss-cone above
this momentum then distinct peaks of the growth rate appear and thus distinct
zebra stripes can be generated. It means that the restriction for small momenta
for the anisotropic part of distributions is of principal importance for the
zebra stripes generation. Finally, for the 1 August 2010 zebra stripes, the
growth rates in dependence on radio frequency were computed. It was shown that
in this case the growth rate peaks are more distinct than in usually presented
dependencies of growth rates on the ratio of the plasma and cyclotron
frequencies.
http://arxiv.org/icons/sfx.gif
