Jinxing Li

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.

Nonlinear bounce resonances between magnetosonic waves and equatorially mirroring electrons

Equatorially mirroring energetic electrons pose an interesting scientific problem, since they generally cannot resonate with any known plasma waves and hence cannot be scattered down to lower pitch angles. Observationally it is well known that the flux of these equatorial particles does not simply continue to build up indefinitely, and so a mechanism must necessarily exist that transports these particles from an equatorial pitch angle of 90 degrees down to lower values. However, this mechanism has not been uniquely identified yet. Here we investigate the mechanism of bounce resonance with equatorial noise (or fast magnetosonic waves). A test particle simulation is used to examine the effects of monochromatic magnetosonic waves on the equatorially mirroring energetic electrons, with a special interest in characterizing the effectiveness of bounce resonances. Our analysis shows that bounce resonances can occur at the first three harmonics of the bounce frequency (n omega(b), n = 1, 2, and 3) and can effectively reduce the equatorial pitch angle to values where resonant scattering by whistler mode waves becomes possible. We demonstrate that the nature of bounce resonance is nonlinear, and we propose a nonlinear oscillation model for characterizing bounce resonances using two key parameters, effective wave amplitude (A) over tilde and normalized wave number (k) over tilde (z). The threshold for higher harmonic resonance is more strict, favoring higher (A) over tilde and (k) over tilde (z), and the change in equatorial pitch angle is strongly controlled by (k) over tilde (z). We also investigate the dependence of bounce resonance effects on various physical parameters, including wave amplitude, frequency, wave normal angle and initial phase, plasma density, and electron energy. It is found that the effect of bounce resonance is sensitive to the wave normal angle. We suggest that the bounce resonant interaction might lead to an observed pitch angle distribution with a minimum at 90 degrees.

Ultrarelativistic electron butterfly distributions created by parallel acceleration due to magnetosonic waves

The Van Allen Probe observations during the recovery phase of a large storm that occurred on 17 March 2015 showed that the ultrarelativistic electrons at the inner boundary of the outer radiation belt (L* = 2.6–3.7) exhibited butterfly pitch angle distributions, while the inner belt and the slot region also showed evidence of sub-MeV electron butterfly distributions. Strong magnetosonic waves were observed in the same regions and at the same time periods as these butterfly distributions. Moreover, when these magnetosonic waves extended to higher altitudes (L* = 4.1), the butterfly distributions also extended to the same region. Combining test particle calculations and Fokker-Planck diffusion simulations, we successfully reproduced the formation of the ultrarelativistic electron butterfly distributions, which primarily result from parallel acceleration caused by Landau resonance with magnetosonic waves. The coexistence of ultrarelativistic electron butterfly distributions with magnetosonic waves was also observed in the 24 June 2015 storm, providing further support that the magnetosonic waves play a key role in forming butterfly distributions.

Analytical approximation of transit time scattering due to magnetosonic waves

© 2015. American Geophysical Union. All Rights Reserved. Recent test particle simulations have shown that energetic electrons traveling through fast magnetosonic (MS) wave packets can experience an effect which is specifically associated with the tight equatorial confinement of these waves, known as transit time scattering. However, such test particle simulations can be computationally cumbersome and offer limited insight into the dominant physical processes controlling the wave-particle interactions, that is, in determining the effects of the various wave parameters and equatorial confinement on the particle scattering. In this paper, we show that such nonresonant effects can be effectively captured with a straightforward analytical treatment that is made possible with a set of reasonable, simplifying assumptions. It is shown that the effect of the wave confinement, which is not captured by the standard quasi-linear theory approach, acts in such a way as to broaden the range of particle energies and pitch angles that can effectively resonate with the wave. The resulting diffusion coefficients can be readily incorporated into global diffusion models in order to test the effects of transit time scattering on the dynamical evolution of radiation belt fluxes.

Radiation belt electron acceleration during the 17 March 2015 geomagnetic storm: Observations and simulations

Various physical processes are known to cause acceleration, loss, and transport of energetic electrons in the Earths radiation belts, but their quantitative roles in different time and space need further investigation. During the largest storm over the past decade (17 March 2015), relativistic electrons experienced fairly rapid acceleration up to ~7 MeV within 2 days after an initial substantial dropout, as observed by Van Allen Probes. In the present paper, we evaluate the relative roles of various physical processes during the recovery phase of this large storm using a 3-D diffusion simulation. By quantitatively comparing the observed and simulated electron evolution, we found that chorus plays a critical role in accelerating electrons up to several MeV near the developing peak location and produces characteristic flat-top pitch angle distributions. By only including radial diffusion, the simulation underestimates the observed electron acceleration, while radial diffusion plays an important role in redistributing electrons and potentially accelerates them to even higher energies. Moreover, plasmaspheric hiss is found to provide efficient pitch angle scattering losses for hundreds of keV electrons, while its scattering effect on > 1 MeV electrons is relatively slow. Although an additional loss process is required to fully explain the overestimated electron fluxes at multi-MeV, the combined physical processes of radial diffusion and pitch angle and energy diffusion by chorus and hiss reproduce the observed electron dynamics remarkably well, suggesting that quasi-linear diffusion theory is reasonable to evaluate radiation belt electron dynamics during this big storm.

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.

Physical mechanism causing rapid changes in ultrarelativistic electron pitch angle distributions right after a shock arrival: Evaluation of an electron dropout event

Three mechanisms have been proposed to explain relativistic electron flux depletions (dropouts) in the Earths outer radiation belt during storm times: adiabatic expansion of electron drift shells due to a decrease in magnetic field strength, magnetopause shadowing and subsequent outward radial diffusion, and precipitation into the atmosphere (driven by EMIC wave scattering). Which mechanism predominates in causing electron dropouts commonly observed in the outer radiation belt is still debatable. In the present study, we evaluate the physical mechanism that may be primarily responsible for causing the sudden change in relativistic electron pitch angle distributions during a dropout event observed by Van Allen Probes during the main phase of the 27 February 2014 storm. During this event, the phase space density of ultrarelativistic (>1 MeV) electrons was depleted by more than 1 order of magnitude over the entire radial extent of the outer radiation belt (3 < L* < 5) in less than 6 h after the passage of an interplanetary shock. We model the electron pitch angle distribution under a compressed magnetic field topology based on actual solar wind conditions. Although these ultrarelativistic electrons exhibit highly anisotropic (peaked in 90°), energy-dependent pitch angle distributions, which appear to be associated with the typical EMIC wave scattering, comparison of the modeled electron distribution to electron measurements indicates that drift shell splitting is responsible for this rapid change in electron pitch angle distributions. This further indicates that magnetopause loss is the predominant cause of the electron dropout right after the shock arrival.

“Zipper-Like” Periodic Magnetosonic Waves: Van Allen Probes, THEMIS, and Magnetospheric Multiscale Observations†

An interesting form of “zipper-like” magnetosonic waves consisting of two bands of interleaved periodic rising-tone spectra was newly observed by the Van Allen Probes, the THEMIS, and the Magnetospheric Multiscale (MMS) missions. The two discrete bands are distinct in frequency and intensity, however, they maintain the same periodicity which varies in space and time, suggesting that they possibly originate from one single source intrinsically. In one event, the “zipper-like” magnetosonic waves exhibit the same periodicity as a constant frequency magnetosonic wave and an electrostatic emission, but the modulation comes from neither density fluctuations nor ULF waves. A statistical survey based on 3.5 years of multi-satellite observations shows that “zipper-like” magnetosonic waves mainly occur on the dawn-to-noon side, in a frequency range between 10 fcp and fLHR. The “zipper-like” magnetosonic waves may provide a new clue to nonlinear excitation or modulation process while its cause still remains to be fully understood.