Magnetospheric chorus wave instability induced by relativistic Kappa-type distributions

We study the field-aligned propagating magnetospheric chorus wave instability using a fully relativistic wave growth formula, the previously developed relativistic Kappa-type (KT) distribution and the regular Kappa distribution of energetic electrons. We demonstrate that the peak growth rate using the nonrelativistic Kappa simulation is higher than that using either the relativistic KT or the Kappa simulation at/above 100 keV, because the significant relativistic effect yields a reduction in the relativistic anisotropy. The relativistic anisotropy A_rel basically decreases as the thermal parameter θ² increases, allowing the peak growth by relativistic KT or Kappa distribution to stay at the lower frequency region. The growth rates tend to increase with the loss-cone parameter l because the overall anisotropy increases. Moreover, at high energy ~1.0 MeV, both the growth rate and the upper cutoff frequency become smaller as l increases for the relativistic KT calculation because the significant relativistic effect reduces both the resonant anisotropy and the number of the hot electrons, which is in contrast to the relativistic and nonrelativistic Kappa distribution calculations because the less relativistic or non-relativistic effect enhances the resonant anisotropy as l increases. The above results can be applied to the whistler-mode wave instability in the outer radiation belts of the Earth, the Jovian inner magnetosphere and other astrophysical plasmas where relativistic electrons often exist.