Lun Xie

Resonant scattering of outer zone relativistic electrons by multiband EMIC waves and resultant electron loss time scales

To improve our understanding of the role of electromagnetic ion cyclotron (EMIC) waves in radiation belt electron dynamics, we perform a comprehensive analysis of EMIC wave-induced resonant scattering of outer zone relativistic (>0.5 MeV) electrons and resultant electron loss time scales with respect to EMIC wave band, L shell, and wave normal angle model. The results demonstrate that while H+-band EMIC waves dominate the scattering losses of ~1–4 MeV outer zone relativistic electrons, it is He+-band and O+-band waves that prevail over the pitch angle diffusion of ultrarelativistic electrons at higher energies. Given the wave amplitude, EMIC waves at higher L shells tend to resonantly interact with a larger population of outer zone relativistic electrons and drive their pitch angle scattering more efficiently. Obliquity of EMIC waves can reduce the efficiency of wave-induced relativistic electron pitch angle scattering. Compared to the frequently adopted parallel or quasi-parallel model, use of the latitudinally varying wave normal angle model produces the largest decrease in H+-band EMIC wave scattering rates at pitch angles  ~5 MeV. At a representative nominal amplitude of 1 nT, EMIC wave scattering produces the equilibrium state (i.e., the lowest normal mode under which electrons at the same energy but different pitch angles decay exponentially on the same time scale) of outer belt relativistic electrons within several to tens of minutes and the following exponential decay extending to higher pitch angles on time scales from <1 min to ~1 h. The electron loss cone can be either empty as a result of the weak diffusion or heavily/fully filled due to approaching the strong diffusion limit, while the trapped electron population at high pitch angles close to 90° remains intact because of no resonant scattering. In this manner, EMIC wave scattering has the potential to deepen the anisotropic distribution of outer zone relativistic electrons by reshaping their pitch angle profiles to “top-hat.” Overall, H+-band and He+-band EMIC waves are most efficient in producing the pitch angle scattering loss of relativistic electrons at ~1–2 MeV. In contrast, the presence of O+-band EMIC waves, while at a smaller occurrence rate, can dominate the scattering loss of 5–10 MeV electrons in the entire region of the outer zone, which should be considered in future modeling of the outer zone relativistic electron dynamics.

Global view of dayside magnetic reconnection with the dusk-dawn IMF orientation: A statistical study for Double Star and Cluster data

Double Star/TC-1 and Cluster data show that both component reconnection and anti-parallel reconnection occur at the magnetopause when the interplanetary magnetic field ( IMF) is predominantly dawnward. The occurrence of these different features under these very similar IMF conditions are further confirmed by a statistical study of 290 fast flows measured in both the low and high latitude magnetopause boundary layers. The directions of these fast flows suggest a possible S-shaped configuration of the reconnection X-line under such a dawnward dominated IMF orientation.

Formation of energetic electron butterfly distributions by magnetosonic waves via Landau resonance

Radiation belt electrons can exhibit different types of pitch angle distributions in response to various magnetospheric processes. Butterfly distributions, characterized by flux minima at pitch angles around 90°, are broadly observed in both the outer and inner belts and the slot region. Butterfly distributions close to the outer magnetospheric boundary have been attributed to drift shell splitting and losses to the magnetopause. However, their occurrence in the inner belt and the slot region has hitherto not been resolved. By analyzing the particle and wave data collected by the Van Allen Probes during a geomagnetic storm, we combine test particle calculations and Fokker-Planck simulations to reveal that scattering by equatorial magnetosonic waves is a significant cause for the formation of energetic electron butterfly distributions in the inner magnetosphere. Another event shows that a large-amplitude magnetosonic wave in the outer belt can create electron butterfly distributions in just a few minutes.

Interactions between magnetosonic waves and radiation belt electrons: Comparisons of quasi‐linear calculations with test particle simulations

Quasi-linear theory (QLT) has been commonly used to study the Landau resonant interaction between radiation belt electrons and magnetosonic (MS) waves. However, the long-parallel wavelengths of MS waves can exceed their narrow spatial confinement and cause a transit-time effect during interactions with electrons. We perform a careful investigation to validate the applicability of QLT to interactions between MS waves, which have a distribution in frequency and wave normal angle, and radiation belt electrons using test particle simulations. We show agreement between these two methods for scattering rate of intense MS waves at L = 4.5 inside the plasmapause, but find a significant inconsistency for MS waves outside the plasmapause, due to the broad transit-time region in (Ek,α) space. Consequently, we introduce a particle-independent criterion to justify the validity of QLT for MS waves: the wave spatial confinement should be longer than two parallel wavelengths.

Spatial structures of magnetic depression in the Earth's high-altitude cusp: Cluster multipoint observations

Magnetic depression structures (magnetic holes) of short time duration from seconds to minutes have been studied using Cluster data in the high-latitude cusp. Our multispacecraft analysis revealed that the magnetic depressions are spatial structures traveling across the spacecraft, and this result was further strengthened by the calculation of the boundary normal directions and velocities using various methods. In this article, we show that multiple properties of the magnetic depressions are consistent with those of mirror structures observed in the magnetosheath or solar wind. The plasma in the cusp is rarely unstable with respect to mirror instability. However, as has been shown by previous studies, once a large magnetic hole is created by mirror instability, it becomes relatively stable and can survive for extended periods of time even if surrounding plasma conditions drop well below the mirror threshold. Although local generation of these structures cannot be completely ruled out in some cases, we propose an interpretation of the magnetic depressions observed in the cusp as mirror structures generated upstream and convected to the cusp by plasma flow. Specifically, the magnetic holes could be generated in the magnetosheath and enter the cusp due to the open geometry of the cusp magnetic field.

Cluster observations of the entry layer equatorward of the cusp under northward interplanetary magnetic field

[1] Various boundary crossings in the vicinity of the high-altitude cusp region were experienced by the Cluster spacecraft when the interplanetary magnetic field (IMF) was northward. In contrast to the southward IMF cases, in which a turbulent and diffusive entry layer is present equatorward of the cusp, a transition layer (without significant turbulence and diffusive properties) that shows clear differences in plasma parameters (sometimes step-like profile) compared to the adjacent regions was observed. We suggest that this transition layer, which contains both magnetosheath and magnetospheric populations, is the entry layer during northward IMF conditions. This transition layer is possibly formed by dual-lobe reconnection when the IMF is northward. The plasma property and the closed field line geometry of this layer indicate that it is possibly linked to the low-latitude boundary layer. The width of this layer varies from 480 to 2200 km. The results support the notion that high-latitude dual-lobe reconnection is a potential mechanism of the transport of solar wind into the magnetosphere during northward IMF through the formation of a high-altitude entry layer. The observations of different sublayers with evident density and temperature differences are consistent with the view that the reconnection process at the magnetopause is not steady.

Energy filter effect for solar wind particle entry to the plasma sheet via flank regions during southward interplanetary magnetic field

Several mechanisms have been used to explain solar wind plasma entry into the plasma sheet in the magnetotail. In this paper, we focus on the gradient drift entry (GDE) process in the equatorial flanks of the magnetosphere, based on the magnetopause picture of a tangential discontinuity with a small tangential electric field as was suggested by Alfven (1968). We discuss the GDE efficiency in different conditions using the adiabatic theory. It can be clearly shown that the GDE efficiency is much lower during southward interplanetary magnetic field (IMF), with a strong energy filter effect for incoming solar wind particles. Given a typical condition, a critical energy for particle entry is calculated to be several kiloelectron volts. Only those particles with higher energy can penetrate the magnetopause, a condition which can be also proved by test particle simulations. The lower efficiency than that during northward IMF during periods of southward IMF is in agreement with the different properties of the plasma sheet observed, i.e., hot and tenuous when the IMF is southward, cold and dense for northward IMF.

Occurrence characteristics of outer zone relativistic electron butterfly distribution: A survey of Van Allen Probes REPT measurements

Using Van Allen Probes Relativistic Electron Proton Telescope (REPT) pitch angle resolved electron flux data from September 2012 to March 2015, we investigate in detail the global occurrence pattern of equatorial (|λ| ≤ 3°) butterfly distribution of outer zone relativistic electrons and its potential correlation with the solar wind dynamic pressure. The statistical results demonstrate that these butterfly distributions occur with the highest occurrence rate ~ 80% at ~ 20–04 magnetic local time (MLT) and L > ~ 5.5 and with the second peak (> ~ 50%) at ~ 11–15 MLT of lower L shells ~ 4.0. They can also extend to L = 3.5 and to other MLT intervals but with the occurrence rates predominantly < ~25%. It is further shown that outer zone relativistic electron butterfly distributions are likely to peak between 58° and 79° for L = 4.0 and 5.0 and between 37° and 58° for L = 6.0, regardless of the level of solar wind dynamic pressure. Relativistic electron butterfly distributions at L = 4.0 also exhibit a pronounced day-night asymmetry in response to the Pdyn variations. Compared to the significant L shell and MLT dependence of the global occurrence pattern, outer zone relativistic electron butterfly distributions show much less but still discernable sensitivity to Pdyn, geomagnetic activity level, and electron energy, the full understanding of which requires future attempts of detailed simulations that combine and differentiate underlying physical mechanisms of the geomagnetic field asymmetry and scattering by various magnetospheric waves.

Variational symplectic algorithm for guiding center dynamics in the inner magnetosphere

Charged particle dynamics in magnetosphere has temporal and spatial multiscale; therefore, numerical accuracy over a long integration time is required. A variational symplectic integrator (VSI) [H. Qin and X. Guan, Phys. Rev. Lett. 100, 035006 (2008) and H. Qin, X. Guan, and W. M. Tang, Phys. Plasmas 16, 042510 (2009)] for the guiding-center motion of charged particles in general magnetic field is applied to study the dynamics of charged particles in magnetosphere. Instead of discretizing the differential equations of the guiding-center motion, the action of the guiding-center motion is discretized and minimized to obtain the iteration rules for advancing the dynamics. The VSI conserves exactly a discrete Lagrangian symplectic structure and has better numerical properties over a long integration time, compared with standard integrators, such as the standard and adaptive fourth order Runge-Kutta (RK4) methods. Applying the VSI method to guiding-center dynamics in the inner magnetosphere, we can accurately ...

Comparison of formulas for resonant interactions between energetic electrons and oblique whistler-mode waves

perpendicular motion for the lth-order resonance. This article presents the detailed derivation process of the generalized resonance formulas, and suggests a check of the signs for self-consistency, which is independent of the choice of conventions, that is, the energy variation equation resulting from the momentum equations should not contain any wave magnetic components, simply because the magnetic field does not contribute to changes of particle energy. In addition, we show that the wave centripetal force, which was considered small and was neglect in previous studies of nonlinear interactions, has a profound time derivative and can significantly enhance electron phase trapping especially in high frequency waves. This force can also bounce the low pitch angle particles out of the loss cone. We justify both the sign problem and the missing wave centripetal force by demonstrating wave-particle interaction examples, and comparing the gyro-averaged particle motion to the full particle motion under the Lorentz force. V C 2015 AIP Publishing LLC.