Fuliang Xiao

Three‐dimensional simulations of outer radiation belt electron dynamics including cross‐diffusion terms

[1]xa0Using our recently introduced hybrid finite difference method, we develop a three-dimensional (3-D) code to solve a fully bounce-averaged pitch-angle and energy diffusion equation, including radial diffusion and particularly the cross-diffusion terms. We show that our 3-D code can successfully prevent the unstable numerical problems resulting from the large and rapidly varying cross diffusion coefficients. We present one of the first simulations to examine the effects of radial diffusion and chorus-electron interaction with/without cross diffusion terms on the radiation belt electron dynamics. Simulated results demonstrate that chorus waves may yield significant accelerations of energetic (∼MeV) electrons, leading to peaks in phase space density (PSD), which are subsequently smoothed by inward and outward radial diffusion. Moreover, neglecting cross-diffusion rates generally produces relatively large overestimates in the PSD evolution, implying that cross diffusion terms are very critical in the 3-D modeling of radiation belts dynamics. However, test case simulations show that such overestimates are sensitively dependent on the initial conditions together with wave models, deserving further thorough investigations.

Three‐dimensional ray tracing of fast magnetosonic waves

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.

Pitch-angle distribution evolution of energetic electrons in the inner radiation belt and slot region during the 2003 Halloween storm

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 tL 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 keVelectrons in the innermost radiation belt near L = 1.7 (as observed by Polar satellite) and the slot region 2 < L <3 . Inparticular,simulatedresultsindicatethattheloss-coneregionisalmostempty,andoutside 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.

Modeling solar energetic particle by a relativistic kappa-type distribution

A recently developed relativistic kappa-type (KT) is adopted to model the observed spectra of solar energetic protons. The KT distribution is found to fit well with the observed data in the energies of ~1–100 MeV and 100–1000 MeV, suggesting that the solar energetic proton flux follows the power law at both the lower energies and the relativistic energies, and the KT distribution may present a further physical insight into those space plasmas where energetic particles exist.

Nonstorm time scattering of ring current protons by electromagnetic ion cyclotron waves

We report correlated observation of enhanced electromagnetic ion cyclotron (EMIC) waves and dynamic evolution of ring current proton flux collected by Cluster satellite near the location L = 4.5 during March 26-27, 2003, a nonstorm period (D-st > -10). Energetic (5-30 keV) proton fluxes are found to drop rapidly (e.g., a half hour) at lower pitch angles, corresponding to intensified EMIC wave activities. By adopting a Gaussian fit to the observed spectra of EMIC waves, we present two-dimensional (2D) numerical simulations which demonstrate that EMIC wave can yield such decrements in proton flux within 30 minutes, consistent with the observational data. The current result provides a further understanding of ring current dynamics driven by wave-particle interaction under different geomagnetic activities.

Rapid acceleration of radiation belt energetic electrons by Z-mode waves

We present the first simulation of the effect of Z-mode waves on the outer radiation belt electron dynamics. We calculate bounce-averaged diffusion rates in pitch angle and momentum and then use them as inputs to solve a 2-D momentum-pitch angle diffusion equation. Numerical results show that the phase space density (PSD) of 1 MeV electrons can enhance substantially and very rapidly (e. g., 30 minutes). In particular, the momentum diffusion rate exceeds the pitch angle and cross diffusion rates at 0.5 MeV and above, a behavior completely different from that for EMIC and chorus waves. Consequently, momentum (instead of pitch angle or cross) diffusion plays a dominant role in the dynamic evolution of energetic electrons. Moreover, the PSD evolution is found to be very dependent upon the assumed initial particle distributions. These results provide further insights on the interplay between acceleration mechanisms of outer radiation belt electrons. Citation: Xiao, F., S. Zhang, Z. Su, Z. He, and L. Tang (2012), Rapid acceleration of radiation belt energetic electrons by Z-mode waves, Geophys. Res. Lett., 39, L03103, doi: 10.1029/2011GL050625.

Instability of whistler-mode waves by a relativistic kappa-loss-cone distribution in space plasmas

We investigate the growth rate of field-aligned whistler-mode waves in space plasmas by using a fully relativistic treatment, including a recently developed relativistic kappa-loss-cone (KLC) distribution and a fully relativistic growth rate formula. Numerical calculations are carried out for a direct comparison between the new KLC distribution and the current kappa distribution, respectively. It is found that, in the lower wave frequency (e.g. ω 0.1Ωe), the wave growth by the KLC distribution is generally higher than that by the kappa distribution, due to a larger fractional number of the resonant electrons ηrel (which controls the wave growth) for the KLC distribution; but is lower in the higher wave frequency. The growth rates, as expected, tend to increase with the thermal anisotropy A, and the peak wave growth increases more rapidly for the kappa distribution. The relativistic anisotropy Arel basically decreases as the thermal parameter θ2 increases; whereas the fractional number of the resonant electrons ηrel is found to be large in the case of θ2 ~ 150u2009keV, and results in a large wave growth. This indicates that hot electrons with typical energies of hundreds of keV may play a dominant role on the instability of whistler-mode waves. The results above have applications to plasma wave instability in the outer radiation belts of the Earth, the Jovian inner magnetosphere and other astrophysical plasmas where relativistic electrons are present.

A parametric study on outer radiation belt electron evolution by superluminous R‐X mode waves

[1]xa0A 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.

Excitation of electromagnetic ion cyclotron waves under different geomagnetic activities: THEMIS observation and modeling

Understanding excitation of electromagnetic ion cyclotron (EMIC) waves remains a considerable scientific challenge in the magnetospheric physics. Here we adopt correlated data from the Thermal Emission Imaging System (THEMIS) spacecraft under low (K-p = 1(+)) and medium (K-p = 4) geomagnetic activities to investigate the favorable conditions for the excitation of EMIC waves. We utilize a sum of bi-Maxwellian components and kappa components to fit the observed ion (6-25 keV) distributions collected by the electrostatic analyzer (ESA) onboard the THEMIS spacecraft. We show that the kappa distribution models better and more smoothly with the observations. Then we evaluate the local growth rate and path-integrated gain of EMIC waves by bi-Maxwellian and kappa distributions, respectively. We demonstrate that the path-integrated wave gain simulated from the kappa distribution is consistent with observations, with intensities 24 dB in H+ band and 33 dB in He+ band. However, bi-Maxwellian distribution tends to overestimate the wave growth rate and path-integrated gain, with intensities 49 dB in H+ band and 48 dB in He+ band. Moreover, compared to the He+ band, a higher proton anisotropy is needed to excite the H+ band waves. The current study presents a further observational support for the understanding of EMIC wave instability under different geomagnetic conditions and suggests that the kappa-type distributions representative of the power law spectra are probably ubiquitous in space plasmas. Citation: Zhou, Q., F. Xiao, J. Shi, C. Yang, Y. He, and L. Tang (2013), Excitation of electromagnetic ion cyclotron waves under different geomagnetic activities: THEMIS observation and modeling, J. Geophys. Res. Space Physics, 118, 340-349, doi:10.1029/2012JA018325.

Instability and propagation of EMIC waves in the magnetosphere by a kappa distribution

Electromagnetic ion cyclotron (EMIC) waves are excited near the magnetic equator by anisotropic ring current ions with energies near a few tens of keV. We investigate the instability and the path-integrated gain of EMIC waves during wave propagation. Calculations are performed by a global core density model, a field-aligned density model and particularly the hot ring current ions modeled by a kappa distribution. Simulating results show that the instability of EMIC waves is influenced primarily by the parameters of hot ring current ions, the wave normal angle and the composition of background plasma. A larger path-integrated gain occurs when the initial wave vector points toward lower L shells. During the storm main phase, the most common EMIC wave is the He+ band wave which occurs in the outer magnetosphere beyond the plasmapause with frequency just below the cyclotron frequency of He+. During the recovery phase, EMIC wave occurs in H+ band and He+ band with almost the same intensity in cases of interest. The O+ band EMIC waves are very weak and quite rare. This result presents a further insight into propagation and instability of EMIC waves under different geomagnetic activities.