Bounce-Averaged Acceleration of Energetic Electrons by Whistler Mode Chorus in the Magnetosphere

We construct the bounce-averaged diffusion coefficients and study the bounce-averaged acceleration for energetic electrons in gyroresonance with whistler mode chorus. Numerical calculations have been performed for a band of chorus frequency distributed over a standard Gaussian spectrum specifically in the region near L = 4.5, where peaks of the electron phase space density occur. It is found that whistler mode chorus can efficiently accelerate electrons and can increase the phase space density at energies of about 1 MeV by more than one order of magnitude about one day, in agreement with the satellite observations during the recovery phase of magnetic storms.     

Chorus-Driven Outer Radiation Belt Electron Dynamics at Different L-Shells

Energetic outer radiation belt electron phase space density （PSD） evolution due to interaction with whistler-mode chorus at different L-shells is investigated by solving the diffusion equation including cross diffusion terms. It is found that the difference of diffusion rates for different L-shells occurs primarily at pitch angles 0°-50° and around 90°. In particular, diffusion rates for L = 6.5 are found to be 5-10 times larger than that for L = 3.5 at these pitch angles. In the presence of cross terms, PSD for - MeV electrons after 24h decreases by about 25, 12, 10 and 8 times at L = 3.5, 4.5, 5.5 and 6.5 near the loss cone, and increases by about 55, 45, 30 and 20 times at larger pitch angles, respectively. After 24 h, the ratios between - MeV electron PSDs from simulations without and with cross diffusion at L = 3.5, 4.5, 5.5 and 6.5 are about 350, 600, 800 and 800 near the loss cone, and become 5, 5.5, 6.5 and 8 at pitch angle 90°, respectively. These results demonstrate that neglect of cross diffusion generally results in the overestimate of PSD, and the cross diffusion plays a more significant role in the resonant interaction between chorus waves and outer radiation belt electrons at larger L.     

Effects of Spatial Variation of Thermal Electrons on Whistler-Mode Waves in Magnetosphere

A ray-tracing method is developed to evaluate the wave growth/damping and specifically propagation trajectories of the magnetospherically reflected Whistler-mode waves. The methodology is valid for weak wave growth/damping when plasma is comprised of a cold electron population and a hot electron population, together with background neutralizing ions, e.g. protons. The effect of anisotropic thermal electrons on the propagation of Whistler-mode waves is studied in detail. Numerical results are obtained for a realistic spatial variation model of plasma population, including the cold electron density distribution, and the thermal electron density and temperature distribution. It is found that, analogous to the case of the typical cold plasma approximation, the overall ray path of Whistler-mode waves is insensitive to the thermal electron density and temperature anisotropy, and the ray path reflects where wave frequency is below or comparable to the local lower hybrid resonance frequency flhr. However, the wave growth is expected to be influenced by the thermal electron population. The results present a first detailed verification for the validity of the typical cold plasma approximation for the propagation of Whistler-mode waves and may account for the observation that the Whistler-mode waves tend to propagate on a particular magnetic shell L where the wave frequency is comparable to fthe.     

Energetic Electron Pitch Angle Diffusion due to Whistler Wave during Terrestrial Storms

A concise and elegant expression of cyclotron harmonic resonant quasi-pure pitch-angle diffusion is constructed for the parallel whistler mode waves, and the quasi-linear diffusion coefficient is prescribed in terms of the whistler mode wave spectral intensity. Numerical computations are performed for the specific case of energetic electrons interacting with a band of frequency of whistler mode turbulence at L ≈ 3. It is found that the quasi-pure pitch-angle diffusion driven by the whistler mode scatters energetic electrons from the larger pitch-angles into the loss cone, and causes pitch-angle distribution to evolve from the pancake-shaped before the terrestrial storms to the flat-top during the main phase. This probably accounts for the quasi-isotropic pitch-angle distribution observed by the combined release and radiation effects satellite spacecraft at L ≈ 3.     

Modelling Energetic Electrons by a Kappa-Loss-Cone Distribution at Geostationary Orbit

We adopt a recently developed relativistic kappa-loss-cone （KLC） distribution to model energetic electrons energy spectra observed at the geostatlonary orbit in the storm of 3-4 November 1993. The KLU distribution is found to fit well with the observed data from four satellites during different universal times. This suggests that the electron flux obeys the power-law not only at the lower energies but also at the relativistic energies, and the KLU distribution may provide a better understanding of environments in those space plasmas where relativistic electrons are present.     

Excitation of Whistler-Mode （Chorus） Emissions during Terrestrial Substorms

The enhanced growth rate of whistler mode waves has been evaluated during an injection event associated with an isolated terrestrial substorm that occurred at 23：00 UT, on January 21, 1991. The electron phase space density observed by an LEPA instrument on the board of the CRRES spacecraft is modelled by using a bi-loss-cone distribution function （composed of a high anisotropic component and a quasi-isotropic component）. During the injection event, the path integrated gain may increase by a factor of 5 over a frequency range near a few tenths of the electron gyrofrequency, which is consistent with the enhancement observed in the CRRES plasma wave experiment （PWE） emissions. Scattering of electrons by the enhanced whistler mode waves causes the pitch angle distribution of resonant electrons to a quasi isotropic （fiat-top） distribution during the terrestrial substorm injection event.     

Evolution of Ring Current Protons Induced by Electromagnetic Ion Cyclotron Waves

We investigate the evolution of the phase space density （PSD） of ring current protons induced by electromagnetic ion cyclotron （EMIC） waves at the location L=3.5, calculate the diffusion coefficients in pitch angle and momentum, and solve the standard two-dimensional Fokker-Planck diffusion equation. The pitch angle diffusion coefficient is found to be larger than the momentum diffusion coefficient by a factor of about 103 or above at lower pitch angles. We show that EMIC waves can produce efficient pitch angle scattering of energetic （- 100 keV） protons, yielding a rapid decrement in PSD, typically by a factor of - 10 within a few hours, consistent with observational data. This result further supports previous findings that wave-particle interaction is responsible for the rapid ring current decay.     

Bounce-averaged Pitch-angle Diffusion by Electromagnetic Ion Cyclotron Waves in Multi-ion Plasmas

We present a study on the gyroresonant interaction particles in multi-ion （H^＋, He^＋, and O^＋） plasmas between electromagnetic ion cyclotron waves and ring current We provide a first evaluation of the bounce-averaged pitch angle diffusion coefficient 〈Dαα〉 for three typical energies of 50, 100 and 150keV at L ≈ 3.5, the heart of the symmetrical ring current. We show that in the H^＋-band and He^＋-band, 〈Dαα〉 can approach - 10^-4 s^-1 for ion H^＋, and - 5 × 10^-5 s^-1 /or ion He^＋; meanwhile, in the O^＋-band, 〈Dαα〉 can reach - 10^-5 s^-1 for ions He^＋ and O^＋. The results above show that the EMIC wave can efficiently produce precipitation loss of energetic （- 100 keV） ions （H^＋, He^＋ and even O^＋）, and such a wave tends to be a serious candidate responsible for the ring current decay.     

Second-Order Resonant Interaction of Ring Current Protons with Whistler-Mode Waves

We present a study on the second-order resonant interaction between the ring current protons with Whistler-mode waves propagating near the quasi electrostatic limit following the previous second-order resonant theory. The diffusion coefficients are proportional to the electric field amplitude E, much greater than those for the regular first-order resonance, which are proportional to the electric field amplitudes square E^2. Numerical calculations for the pitch angle scattering are performed for typical energies of protons Ek = 50 keV and 100 keV at locations L = 2 and L = 3.5. The timescale for the loss process of protons by the Whistler waves is found to approach one hour, comparable to that by the EMIC waves, suggesting that Whistler waves may also contribute significantly to the ring current decay under appropriate conditions.