Energetic particles found in planetary magnetospheres and other plasmas often display a power law and an anisotropy (including loss cone and temperature anisotropy). In a recent study, a full relativistic kappa-loss cone (KLC) distribution fκL is initially introduced to model energetic particles, but fκL is only associated with loss cone anisotropy. We extend this previous study and develop a generalized relativistic kappa-type (KT) distribution fκT which incorporates either temperature anisotropy or both loss cone and temperature anisotropy. We carry out numerical calculations for a direct comparison between the new KT distribution, the previous KLC distribution and the kappa distribution fκ, respectively. We find that (a) analogous to fκL, fκT satisfies the power law not only at lower energies but also at relativistic energies; (b) analogous to fκ, fκT contains either temperature anisotropy or both loss cone and temperature anisotropy; (c) the regular kappa distribution is found to decrease faster than the KT distribution with kinetic energy Ek especially when θ2 increases (where θ2 is the thermal characteristic parameter), e.g. fκ/fκT ≲ 10−2 for Ek ≳ 2.0 MeV and θ2 ≳ 0.3; (d) no big difference occurs between both KT and kappa distributions through energies up to ∼500 keV for θ2 ≲ 0.03 and (e) the three distributions show different anisotropy behaviors even for the same overall anisotropy. The results suggest that the new generalized KT distribution may be applied in space plasmas and other plasmas including laboratory machines where highly energetic particles exist.
Solitary structures with ion and electron thermal anisotropy