Van Allen radiation belts consist of relativistic electrons trapped by Earth's magnetic field. Trapped electrons often drift azimuthally around Earth and display a butterfly pitch angle distribution of a minimum at 90° further out than geostationary orbit. This is usually attributed to drift shell splitting resulting from day–night asymmetry in Earth's magnetic field. However, direct observation of a butterfly distribution well inside of geostationary orbit and the origin of this phenomenon have not been provided so far. Here we report high-resolution observation that a unusual butterfly pitch angle distribution of relativistic electrons occurred within 5 Earth radii during the 28 June 2013 geomagnetic storm. Simulation results show that combined acceleration by chorus and magnetosonic waves can successfully explain the electron flux evolution both in the energy and butterfly pitch angle distribution. The current provides a great support for the mechanism of wave-driven butterfly distribution of relativistic electrons.
The recent launching of Van Allen probes provides an unprecedent opportunity to investigate variations of the radiation belt relativistic electrons. During the 17–19 March 2013 storm, the Van Allen probes simultaneously detected strong chorus waves and substantial increases in fluxes of relativistic (2 − 4.5 MeV) electrons around L = 4.5. Chorus waves occurred within the lower band 0.1–0.5fce (the electron equatorial gyrofrequency), with a peak spectral density ∼10−4 nT2/Hz. Correspondingly, relativistic electron fluxes increased by a factor of 102–103 during the recovery phase compared to the main phase levels. By means of a Gaussian fit to the observed chorus spectra, the drift and bounce‐averaged diffusion coefficients are calculated and then used to solve a 2‐D Fokker‐Planck diffusion equation. Numerical simulations demonstrate that the lower‐band chorus waves indeed produce such huge enhancements in relativistic electron fluxes within 15 h, fitting well with the observation.
[1] A three dimensional ray tracing of fast magnetosonic (MS) waves is first performed by using a global core density model and a field-aligned density model. Simulating results show that MS waves are primarily confined within a few degrees of the geomagnetic equator due to magnetospheric reflection. MS waves originating from different L-shells on the dayside can propagate either into or out of the plasmasphere through the plasmapause. In particular, MS waves can propagate eastward (later MLT) or westward (earlier MLT) over a broad region of MLT. The current results further reveal a variety of propagation characteristics, particularly important for the MLT distribution of MS waves.
[1] We have constructed expressions of the relativistic diffusion coefficients in both pitch angle and momentum resulting from gyroresonant interactions between electrons and superluminous (R-X, L-O, L-X) wave modes that are generated as auroral kilometric radiation (AKR) in the Earth's magnetosphere. Detailed analysis is made of wave resonant frequencies for each given harmonic n, electron energy, wave normal angles for two typical regions of the magnetosphere: the higher-density region h = jW e j 2 /w 2 pe < 1 (e.g., near the geostationary orbit) and the lower-density region h > 1 (e.g., at the high latitude of the radiation belts), where jW e j and w pe are the electron gyrofrequency and the plasma frequency. The resonant frequency range in the higher-density region is found to be generally smaller than that in the lower-density region, and the efficient electron gyroresonance with the superluminous wave modes occurs mainly at the higher harmonics, e.g., jnj ! 3. In contrast to the subluminous waves, e.g., chorus which has easily up to three resonant frequencies, only one or two resonant frequencies were found for superluminous waves at each combination of wave and particle parameters of interest. Numerical calculations for diffusion coefficients of the momentum D pp , the pitch angle D aa , and the mixed D pa are performed specifically for the two typical regions above. It is found that the momentum diffusion generally dominates over the pitch angle diffusion, namely, D pp > jD pa j > D aa for the pitch angle a above a critical angle a c , whereas D aa generally dominates below the critical angle a c . Specifically, D pp /D aa can exceed 10 for a > a c % 7.5°and h = 0.2, while for a > a c % 30°and h = 20. This is a new result in contrast to the case of subluminous waves (e.g., whistler mode waves) in which basically D aa > jD pa j> D pp . We have also presented some estimates regarding what wave amplitudes are required to produce particular acceleration timescales and found that the required wave amplitudes in the lower-density region are much lower than those in the higher-density region. The results suggest that superluminous wave modes may contribute significantly to both the stochastic acceleration of trapped electrons (with larger pitch angle) and the loss process of untrapped electrons (with smaller pitch angles) during magnetic storms if those waves are found to be present in the radiation belts of the Earth, but this needs to be further investigated.Citation: Xiao, F., H. He, Q. Zhou, H. Zheng, and S. Wang (2006), Relativistic diffusion coefficients for superluminous (auroral kilometric radiation) wave modes in space plasmas,
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