Bibliography

Origin of Electron Boomerang Stripes: Statistical Study

Abstract In the outer radiation belt, localized ULF waves can interact with energetic electrons by drift resonance, leading to quasiperiodic oscillations. The oscillations in the pitch angle spectrum can be characterized by either boomerang-shaped or straight stripes. Previous studies have shown that boomerang-shaped stripes evolve from straight ones when electrons drift away from the localized wave interaction region. Based on the time-of-flight technique on the pitch angle-dependent drift velocity, the origin can be remotely identified from the pitch angle dispersion. We report 27 straight stripe events and 86 boomerang-shaped events observed by Van Allen Probes from 2013/01/01 to 2017/12/31. Statistical study shows a good coincidence between the locations of straight ones and traceback regions from boomerang-shaped ones. These locations, mainly located in noon-to-dusk region, coincide well with the plasmaspheric plumes. Thus localized ULF waves trapped in the plume may result in the preference of localized ULF waves-electron interactions at noon-to-dusk region.

Zhao, X.; Hao, Y.; Zong, Q.; Zhou, X.; Yue, Chao; Chen, X.; Liu, Y.; Liu, Z.-Y.; Blake, J.; Claudepierre, S.; Reeves, G.;

Published by: Geophysical Research Letters      Published on: 05/2021

YEAR: 2021     DOI: https://doi.org/10.1029/2021GL093377

Localized ULF waves; Energetic Elctrons; drift resonance; Time-of-flight Technique; source region; boomerang-shaped stripes; Van Allen Probes

Origin of Electron Boomerang Stripes: Localized ULF Wave-Particle Interactions

Ultralow frequency (ULF) wave-particle interactions play a significant role in the radiation belt dynamic process, during which drift resonance can accelerate and transport energetic electrons in the outer radiation belt. Observations of wave-electron drift resonance are characterized by quasiperiodic straight or “boomerang-shaped” stripes in the pitch angle spectrogram. Here we present an ULF wave event on 1 December 2015, during which both kinds stripes were observed by Van Allen Probes A and B, respectively. Using the time-of-flight technique based on the pitch angle dependence of electron drift velocities, the “boomerang-shaped” stripes are inferred to originate from straight stripes at the time and location covered by Probe B. Given that straight stripes were indeed observed by Probe B, our observations strongly support the charged particle interacting with azimuthally localized ULF waves. A new method is provided to identify the location of ULF wave-particle interaction on the basis of remote observations of electron flux modulations.

Zhao, X.; Hao, Y.; Zong, Q.-G.; Zhou, X.-Z.; Yue, Chao; Chen, X.; Liu, Y.; Blake, J.; Claudepierre, S.; Reeves, G.;

Published by: Geophysical Research Letters      Published on: 07/2020

YEAR: 2020     DOI: https://doi.org/10.1029/2020GL087960

boomerang-shaped stripes; ULF waves; drift resonance; time of flight; Van Allen Probes

Simultaneous Observations of Localized and Global Drift Resonance

In this study, we present Van Allen Probe observations showing that seed (hundreds of keV) and core ( 1 MeV) electrons can resonate with ultra-low-frequency (ULF) wave modes with distinctive m values simultaneously. An unusual electron energy spectrogram with double-banded resonant structure was recorded by energetic particle, composition, and thermal plasma (ECT)-magnetic electron ion spectrometer (MagEIS) and, meanwhile, boomerang stripes in pitch angle spectrogram appeared at the lower energy band. A localized drift resonance with m = 10 wave component was responsible for the resonant band peaked at ∼200 keV while a global drift resonance with m = 3 component gave rise to the upper band resonance peaked at ∼1 MeV. Time-Of-Flight on boomerang stripes suggested that the localized drift resonance with ∼200 keV electrons was confined within the plasmaspheric plume. Electron flux modulations were reproduced by numerical simulations in good consistency with the observations, supporting the scenario that localized and global drift resonance could coexist in the outer belt electron dynamics simultaneously.

Hao, Y.; Zhao, X.; Zong, Q.-G.; Zhou, X.-Z.; Rankin, R.; Chen, X.; Liu, Y.; Fu, S; Blake, J.; Reeves, G.; Claudepierre, S.;

Published by: Geophysical Research Letters      Published on: 05/2020

YEAR: 2020     DOI: https://doi.org/10.1029/2020GL088019

drift resonance; ULF waves; Radiation Belt Dynamics; boomerang stripes; azimuthal wave number; multiple resonances; Van Allen Probes

Diagnosis of ULF Wave-Particle Interactions With Megaelectron Volt Electrons: The Importance of Ultrahigh-Resolution Energy Channels

Electron flux measurements are an important diagnostic for interactions between ultralow-frequency (ULF) waves and relativistic (\~1 MeV) electrons. Since measurements are collected by particle detectors with finite energy channel width, they are affected by a phase mixing process that can obscure these interactions. We demonstrate that ultrahigh-resolution electron measurements from the Magnetic Electron Ion Spectrometer on the Van Allen Probes mission\textemdashobtained using a data product that improves the energy resolution by roughly an order of magnitude\textemdashare crucial for understanding ULF wave-particle interactions. In particular, the ultrahigh-resolution measurements reveal a range of complex dynamics that cannot be resolved by standard measurements. Furthermore, the standard measurements provide estimates for the ULF flux modulation amplitude, period, and phase that may not be representative of true flux modulations, potentially leading to ambiguous conclusions concerning electron dynamics.

Hartinger, M.; Claudepierre, S.; Turner, D.; Reeves, G.; Breneman, A.; Mann, I.; Peek, T.; Chang, E.; Blake, J.; Fennell, J.; O\textquoterightBrien, T.; Looper, M.;

Published by: Geophysical Research Letters      Published on: 10/2018

YEAR: 2018     DOI: 10.1029/2018GL080291

drift resonance; particle detector; Pc5; Radiation belts; ULF wave; Van Allen Probes; Wave-particle interaction

Nonlinear drift resonance between charged particles and ultra-low frequency waves: Theory and Observations

In Earth\textquoterights inner magnetosphere, electromagnetic waves in the ultra-low frequency (ULF) range play an important role in accelerating and diffusing charged particles via drift resonance. In conventional drift-resonance theory, linearization is applied under the assumption of weak wave-particle energy exchange so particle trajectories are unperturbed. For ULF waves with larger amplitudes and/or durations, however, the conventional theory becomes inaccurate since particle trajectories are strongly perturbed. Here, we extend the drift-resonance theory into a nonlinear regime, to formulate nonlinear trapping of particles in a wave-carried potential well, and predict the corresponding observable signatures such as rolled-up structures in particle energy spectrum. After considering how this manifests in particle data with finite energy resolution, we compare the predicted signatures with Van Allen Probes observations. Their good agreement provides the first observational evidence for the occurrence of nonlinear drift resonance, highlighting the importance of nonlinear effects in magnetospheric particle dynamics under ULF waves.

Li, Li; Zhou, Xu-Zhi; Omura, Yoshiharu; Wang, Zi-Han; Zong, Qiu-Gang; Liu, Ying; Hao, Yi-Xin; Fu, Sui-Yan; Kivelson, Margaret; Rankin, Robert; Claudepierre, Seth; Wygant, John;

Published by: Geophysical Research Letters      Published on: 08/2018

YEAR: 2018     DOI: 10.1029/2018GL079038

drift resonance; nonlinear process; Particle acceleration; Radiation belts; ULF waves; Van Allen Probes; wave-particle interactions

Van Allen Probes Observation of a Fundamental Poloidal Standing Alfv\ en Wave Event Related to Giant Pulsations

The Van Allen Probes-A spacecraft observed an \~9 mHz ultra-low-frequency wave on 6 October 2012, at L\~ 5.7, in the dawn sector, and very near the magnetic equator. The wave had a strong electric field that was initially stronger in the azimuthal component and later in the radial component, exhibited properties of a fundamental standing Alfv\ en wave, and was associated with giant pulsations observed on the ground near the magnetic field footprint of the spacecraft. The wave was accompanied by oscillations of the flux of energetic protons (jH+). The amplitude of urn:x-wiley:jgra:media:jgra54254:jgra54254-math-0001 oscillations was large at equatorial pitch angles away from 90\textdegree, and the energy dependence of the phase and amplitude of the oscillations exhibited features consistent with drift resonance of \~140 keV protons with a westward-propagating wave having an azimuthal wave number of \~-40. The wave was detected when the spacecraft entered a region of an earthward gradient of the proton phase space density, in support of a theoretical prediction that such a gradient can drive fundamental poloidal waves.

Takahashi, Kazue; Claudepierre, S.; Rankin, Robert; Mann, Ian; Smith, C.;

Published by: Journal of Geophysical Research: Space Physics      Published on: 05/2018

YEAR: 2018     DOI: 10.1029/2017JA025139

drift resonance; Fundamental standing Alfven wave; Giant pulsation; Proton flux oscillation; Van Allen Probes

Relativistic electron dynamics produced by azimuthally localized poloidal mode ULF waves: Boomerang-shaped pitch angle evolutions

We present an analysis of \textquotedblleftboomerang-shaped\textquotedblright pitch angle evolutions of outer radiation belt relativistic electrons observed by the Van Allen Probes after the passage of an interplanetary shock on June 7th, 2014. The flux at different pitch angles is modulated by Pc5 waves, with equatorially mirroring electrons reaching the satellite first. For 90o pitch angle electrons, the phase change of the flux modulations across energy exceeds 180o, and increasingly tilts with time. Using estimates of the arrival time of particles of different pitch angles at the spacecraft location, a scenario is investigated in which shock-induced ULF waves interact with electrons through the drift resonance mechanism in a localized region westward of the spacecraft. Numerical calculations on particle energy gain with the modified ULF wave field reproduce the observed boomerang stripes and modulations in the electron energy spectrogram. The study of boomerang stripes and their relationship to drift-resonance taking place at a location different from the observation point adds new understanding of the processes controlling the dynamics of the outer radiation belt.

Hao, Y.; Zong, Q.-G.; Zhou, X.-Z.; Rankin, R.; Chen, X.; Liu, Y.; Fu, S; Spence, H.; Blake, J.; Reeves, G.;

Published by: Geophysical Research Letters      Published on: 07/2017

YEAR: 2017     DOI: 10.1002/2017GL074006

drift resonance; interplanetary shock; localized waves; Radiation belts; ULF waves; Van Allen Probes; Wave-particle interaction

Van Allen Probes observation of a 360\textdegree phase shift in the flux modulation of injected electrons by ULF waves

We present Van Allen Probe observation of drift-resonance interaction between energetic electrons and ultralow frequency (ULF) waves on 29 October 2013. Oscillations in electron flux were observed at the period of \~450 s, which is also the dominant period of the observed ULF magnetic pulsations. The phase shift of the electron fluxes (\~50 to 150 keV) across the estimated resonant energy (\~104 keV) is \~360\textdegree. This phase relationship is different from the characteristic 180\textdegree phase shift as expected from the drift-resonance theory. We speculate that the additional 180\textdegree phase difference arises from the inversion of electron phase space density (PSD) gradient, which in turn is caused by the drift motion of the substorm injected electrons. This PSD gradient adjusts the characteristic particle signatures in the drift-resonance theory, which indicates a coupling effect between the magnetotail and the radiation belt and helps to better understand the wave-particle interaction in the magnetosphere.

Chen, X.-R.; Zong, Q.-G.; Zhou, X.-Z.; Blake, Bernard; Wygant, J.; Kletzing, C.;

Published by: Geophysical Research Letters      Published on: 02/2017

YEAR: 2017     DOI: 10.1002/2016GL071252

drift resonance; injection; PSD gradient; ULF waves; Van Allen Probes

Charged particle behavior in the growth and damping stages of ultralow frequency waves: theory and Van Allen Probes observations

Ultralow frequency (ULF) electromagnetic waves in Earth\textquoterights magnetosphere can accelerate charged particles via a process called drift resonance. In the conventional drift-resonance theory, a default assumption is that the wave growth rate is time-independent, positive, and extremely small. However, this is not the case for ULF waves in the real magnetosphere. The ULF waves must have experienced an earlier growth stage when their energy was taken from external and/or internal sources, and as time proceeds the waves have to be damped with a negative growth rate. Therefore, a more generalized theory on particle behavior during different stages of ULF wave evolution is required. In this paper, we introduce a time-dependent imaginary wave frequency to accommodate the growth and damping of the waves in the drift-resonance theory, so that the wave-particle interactions during the entire wave lifespan can be studied. We then predict from the generalized theory particle signatures during different stages of the wave evolution, which are consistent with observations from Van Allen Probes. The more generalized theory, therefore, provides new insights into ULF wave evolution and wave-particle interactions in the magnetosphere.

Zhou, Xu-Zhi; Wang, Zi-Han; Zong, Qiu-Gang; Rankin, Robert; Kivelson, Margaret; Chen, Xing-Ran; Blake, Bernard; Wygant, John; Kletzing, Craig;

Published by: Journal of Geophysical Research: Space Physics      Published on: 03/2016

YEAR: 2016     DOI: 10.1002/2016JA022447

drift resonance; Radiation belt; ULF waves; Van Allen Probes; wave growth and damping; Wave-particle interaction

Imprints of impulse-excited hydromagnetic waves on electrons in the Van Allen radiation belts

Ultralow frequency electromagnetic oscillations, interpreted as standing hydromagnetic waves in the magnetosphere, are a major energy source that accelerates electrons to relativistic energies in the Van Allen radiation belt. Electrons can rapidly gain energy from the waves when they resonate via a process called drift resonance, which is observationally characterized by energy-dependent phase differences between electron flux and electromagnetic oscillations. Such dependence has been recently observed and interpreted as spacecraft identifications of drift resonance electron acceleration. Here we show that in the initial wave cycles, the observed phase relationship differs from that characteristic of well-developed drift resonance. We further examine the differences and find that they are imprints of impulse-excited, coupled fast-Alfv\ en waves before they transform into more typical standing waves. Our identification of such imprints provides a new understanding of how energy couples in the inner magnetosphere, and a new diagnostic for the generation and growth of magnetospheric hydromagnetic pulsations.

Zhou, Xu-Zhi; Wang, Zi-Han; Zong, Qiu-Gang; Claudepierre, Seth; Mann, Ian; Kivelson, Margaret; Angelopoulos, Vassilis; Hao, Yi-Xin; Wang, Yong-Fu; Pu, Zu-Yin;

Published by: Geophysical Research Letters      Published on: 08/2015

YEAR: 2015     DOI: 10.1002/grl.v42.1510.1002/2015GL064988

drift resonance; Radiation belt; ULF waves; Van Allen Probes; wave growth; Wave-particle interaction