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2018 
In Earth\textquoterights inner magnetosphere, electromagnetic waves in the ultralow frequency (ULF) range play an important role in accelerating and diffusing charged particles via drift resonance. In conventional driftresonance theory, linearization is applied under the assumption of weak waveparticle 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 driftresonance theory into a nonlinear regime, to formulate nonlinear trapping of particles in a wavecarried potential well, and predict the corresponding observable signatures such as rolledup 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, XuZhi; Omura, Yoshiharu; Wang, ZiHan; Zong, QiuGang; Liu, Ying; Hao, YiXin; Fu, SuiYan; 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; waveparticle interactions 
2016 
Ultralow frequency (ULF) electromagnetic waves in Earth\textquoterights magnetosphere can accelerate charged particles via a process called drift resonance. In the conventional driftresonance theory, a default assumption is that the wave growth rate is timeindependent, 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 timedependent imaginary wave frequency to accommodate the growth and damping of the waves in the driftresonance theory, so that the waveparticle 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 waveparticle interactions in the magnetosphere. Zhou, XuZhi; Wang, ZiHan; Zong, QiuGang; Rankin, Robert; Kivelson, Margaret; Chen, XingRan; 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; Waveparticle interaction 
2015 
Imprints of impulseexcited 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 energydependent 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 welldeveloped drift resonance. We further examine the differences and find that they are imprints of impulseexcited, coupled fastAlfv\ 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, XuZhi; Wang, ZiHan; Zong, QiuGang; Claudepierre, Seth; Mann, Ian; Kivelson, Margaret; Angelopoulos, Vassilis; Hao, YiXin; Wang, YongFu; Pu, ZuYin; 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; Waveparticle interaction 
2004 
Relativistic electrons in the outer radiation belt: Differentiating between acceleration mechanisms Many theoretical models have been developed to explain the rapid acceleration to relativistic energies of electrons that form the Earth\textquoterights radiation belts. However, after decades of research, none of these models has been unambiguously confirmed by comparison to observations. Proposed models can be separated into two types: internal and external source acceleration mechanisms. Internal source acceleration mechanisms accelerate electrons already present in the inner magnetosphere (L < 6.6), while external source acceleration mechanisms transport and accelerate a source population of electrons from the outer to the inner magnetosphere. In principle, the two types of acceleration mechanisms can be differentiated because they imply that different radial gradients of electron phase space density expressed as a function of the three adiabatic invariants will develop. Model predictions can be tested by transforming measured electron flux (given as a function of pitch angle, energy, and position) to phase space density as a function of the three invariants, μ, K, and Φ. The transformation requires adoption of a magnetic field model. Phase space density estimates have, in the past, produced contradictory results because of limited measurements and field model errors. In this study we greatly reduce the uncertainties of previous work and account for the contradictions. We use data principally from the Polar High Sensitivity Telescope energetic detector on the Polar spacecraft and the Tsyganenko and Stern [1996] field model to obtain phase space density. We show how imperfect magnetic field models produce phase space density errors and explore how those errors modify interpretations. On the basis of the analysis we conclude that the data are best explained by models that require acceleration of an internal source of electrons near L* \~ 5. We also suggest that outward radial diffusion from a phase space density peak near L* \~ 5 can explain the observed correspondence between flux enhancements at geostationary orbit and increases in ULF wave power. Published by: Journal of Geophysical Research Published on: 03/2004 YEAR: 2004 DOI: 10.1029/2003JA010153 
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