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[1] In this study, we report dynamic evolutions of 30-500 keV energetic electrons (in flux and pitch-angle distribution) in the radiation belt region with 1.6 < L < 6.2. Those evolutions were observed by the IES instrument on board the Polar spacecraft during the Halloween storm period on October 31, 2003 when the radiation belt was strongly distorted. This injection of energetic electrons into the slot region may be associated with the plasmapause movement and Hiss/Chorus enhancement. This flux enhancement is possibly associated with convective transport from the plasma sheet, enhanced radial diffusion and local wave-particle interaction acceleration. By adopting a fitting parameter of loss time t L we solved the bounce-averaged pitch angle diffusion equation driven by field-aligned whistler-mode waves (including chorus and hiss). We show that pitch-angle scattering can account for the pitch-angle distribution evolution in 30-500 keV electrons in the innermost radiation belt near L = 1.7 (as observed by Polar satellite) and the slot region 2 < L < 3. In particular, simulated results indicate that the loss-cone region is almost empty, and outside the loss-cone region both flux and anisotropy of energetic electrons are reduced with the gyroresonant time. The obtained time scale for the pitch-angle distribution evolution is found to be approximately tens of hours, consistent with observation.

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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 f κL is initially introduced to model energetic particles, but f κL is only associated with loss cone anisotropy. We extend this previous study and develop a generalized relativistic kappa-type (KT) distribution f κT 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 f κ , respectively. We find that (a) analogous to f κL , f κT satisfies the power law not only at lower energies but also at relativistic energies; (b) analogous to f κ , f κT 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 E k especially when θ 2 increases (where θ 2 is the thermal characteristic parameter), e.g. f κ /f κT 10 −2 for E k 2.0 MeV and θ 2 0.3; (d) no big difference occurs between both KT and kappa distributions through energies up to ∼500 keV for θ 2 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.

[1] A parametric study is presented on the temporal evolution of the phase space density (PSD) of the outer radiation belt energetic electrons driven by the superluminous right-hand extraordinary (R-X) mode waves at the location L = 4.5. Bounce-averaged diffusion rates in pitch angle and momentum are calculated by varying the peak wave frequency, the wave normal angle distribution, and the wave latitudinal distribution. Those diffusion rates are used as inputs to solve a 2-D momentum-pitch angle diffusion equation. In particular, three cases are considered: momentum diffusion rates alone, momentum +pitch angle diffusion rates, and momentum +pitch angle +cross diffusion rates. Numerical results show that at 24 h, electron PSDs can enhance substantially for 1 MeV energy at higher pitch angles. Momentum diffusion dominates the dynamic evolution of energetic electrons, whereas the contribution of pitch angle or cross-diffusion rates is insignificant using the specified wave model. In addition, PSD evolutions are sensitively dependent on the assumed different wave normal angle distributions and tend to be located in lower pitch angles when wave normal angles move to smaller regions. Diffusion coefficients and PSD evolution are largely determined by the wave latitudinal distributions. High-latitude R-X mode waves primarily contribute to pitch angle scattering of energetic electrons, whereas equatorial (or lower latitude) R-X mode waves yield efficient acceleration of electrons. This result supports the previous findings that superluminous R-X mode waves potentially contribute to dramatic variation in the outer radiation belt electron dynamics under appropriate conditions.