Energetic electron distributions fitted with a relativistic kappa-type function at geosynchronous orbit

In this study, we utilize a recently introduced relativistic kappa-type (KT) distribution function to model the omnidirectional differential flux of energetic electrons observed by the SOPA instrument on board the 1989- 046 and LANL-01A satellites at geosynchronous orbit. We derive a useful correlation between the differential flux and the distribution of particles which can directly offer those best fitting parameters (e. g., the number density N, the thermal characteristic speed theta and the spectral index k) strongly associated with evaluation of the electromagnetic wave instability. We adopt the assumption of a nearly isotropic pitch angle distribution (PAD) and the typical LMFIT function in the program IDL to perform a non-linear least squared fitting, and find that the new KT distribution fits well with the observed data during different universal times both in the lower and higher energies. We also carry out the direct comparisons with the generalized Lorentzian (kappa) distribution and find that kappa distribution fits well with observational data at the relatively lower energies but display deviations at higher energies, typically above hundreds of keV. Furthermore, the fitting spectral index k basically takes 4, 5 or 6 while the fitting parameters N and q are quite different due to different differential fluxes of electrons at different universal times. These results, which are applied to the case of a nearly isotropic PAD, demonstrate that the particle flux satisfies the power law not only at the lower energies but also at the relativistic energies, and the new KT distribution may present valuable insights into the dynamical features in those space plasmas (e. g., the Earth's outer radiation belts and the inner Jovian magnetosphere) where highly energetic particles exist.