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

Li, Jinxing; Bortnik, J.; Xie, Luhua; Pu, Z. Y.; Chen, Lunjin; Ni, Binbin; Tao, X.; Thorne, R. M.; Fu, S. Y.; Yao, Zhonghua; Guo, Ruilong

doi:10.1063/1.4914852

Cited by 16 publications

(25 citation statements)

References 37 publications

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“…By accelerating or pitch angle scattering energetic electrons through quasi‐linear or nonlinear interactions (e.g., Bortnik & Thorne, ; Bortnik et al, ; Horne et al, ; J. Li et al, ; Omura et al, ; da Silva et al, ; Summers et al, ; Tao et al, ), chorus waves provide a significant contribution to acceleration of highly relativistic electrons in the outer radiation belt, especially during storm times (e.g., Bingham et al, ; W. Li et al, ; Li, Mourenas, et al, ; Li, Thorne, et al, ; Ma et al, ; Meredith et al, ; Shen et al, ; Thorne et al, ; Tu et al, ; Turner et al, ; Xiao et al, ). Moreover, chorus waves are one of the most important loss mechanisms of plasma sheet electrons via pitch angle scattering (e.g., Horne et al, ).…”

Section: Introductionmentioning

confidence: 99%

“…By accelerating or pitch angle scattering energetic electrons through quasi-linear or nonlinear interactions (e.g., Bortnik & Thorne, 2007;Bortnik et al, 2008;Horne et al, 2003;J. Li et al, 2015;Omura et al, 2015;da Silva et al, 2018;Summers et al, 2007;Tao et al, 2014), chorus waves provide a significant contribution to acceleration of highly relativistic electrons in the outer radiation belt, especially during storm times (e.g., Bingham et al, 2018;W.…”

Section: Introductionmentioning

confidence: 99%

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Statistical Analysis of Transverse Size of Lower Band Chorus Waves Using Simultaneous Multisatellite Observations

Shen

et al. 2019

Geophysical Research Letters

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Chorus waves are known to accelerate or scatter energetic electrons via quasi‐linear or nonlinear wave‐particle interactions in the Earth's magnetosphere. In this letter, by taking advantage of simultaneous observations of chorus waveforms from at least a pair of probes among Van Allen Probes and/or Time History of Events and Macroscale Interactions during Substorms (THEMIS) missions, we statistically calculate the transverse size of lower band chorus wave elements. The average size of lower band chorus wave element is found to be ~315±32 km over L shells of ~5–6. Furthermore, our results suggest that the scale size of lower band chorus tends to be (1) larger at higher L shells; (2) larger at higher magnetic latitudes, especially on the dayside; and (3) larger in the azimuthal direction than in the radial direction. Our findings are crucial to quantify wave‐particle interaction process, particularly the nonlinear interactions between chorus and energetic electrons.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Statistical Analysis of Transverse Size of Lower Band Chorus Waves Using Simultaneous Multisatellite Observations

Shen

et al. 2019

Geophysical Research Letters

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“…The test particles interact with EMIC waves in a certain latitudinal range (0–15°, see Figures a and c), whose dynamics could be solved in principle by the Newton‐Lorentz equations:

\frac{normald bold-italicp}{normald t} = - e ([], E_{w} + \frac{1}{γ m_{e}} bold-italicp \times false(B_{w} + B_{0} false)),

\frac{normald bold-italicr}{normald t} = \frac{1}{γ m_{e}} bold-italicp,

where e is the absolute value of elementary charge, m e is electron rest mass, γ is the Lorentz factor, r and p are electron's position and momentum, E w and B w are electric and magnetic components of the wavefield, and B 0 is the background geomagnetic field. In actual simulation, gyro‐averaged formalism of equations and is employed, and the gyro‐averaged equations can be found from, for example, Chang and Inan () and Li et al ().…”

Section: Simulation Methodsmentioning

confidence: 99%

Modeling Energetic Electron Nonlinear Wave‐Particle Interactions With Electromagnetic Ion Cyclotron Waves

2019

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Electromagnetic ion cyclotron (EMIC) waves in duskside plasmasphere and plasmaspheric plume scatter megaelectron volt electrons into the loss cone and are considered a major loss mechanism for the outer radiation belt. Wave‐particle interaction between energetic electrons and EMIC waves has been studied extensively by the quasi‐linear diffusion theory. However, EMIC waves are typically strong enough to trigger nonlinear wave‐particle interaction effects and transport electrons in very different ways from quasi‐linear diffusion. New mathematical method is therefore in demand to study the evolution of energetic electron distribution in response to nonlinear wave‐particle interaction. In this work, we present a Markov chain description of the wave‐particle interaction process, in which the electron distribution is represented by a state vector and is evolved by the Markov matrix. The Markov matrix is a matrix form of the electron response Green's function and could be determined from test particle simulations. Our modeling results suggest that electron loss rate is not significantly affected by phase bunching and phase trapping, but for strong EMIC waves, electron distribution is more saturated near loss cone than quasi‐linear theory prediction, and negative electron phase space density slope develops inside loss cone.

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“…In this study, m is the rest mass of a proton and q is the unit charge, p = γm v is the proton momentum, where

γ = \sqrt{1 + {(p / m c)}^{2}}

is the relativistic factor with c as the light speed in free space, the electromagnetic field is divided into two parts:

bold-italicB ((), λ) = \frac{B_{E}}{L^{3}} \frac{{((), 1 + 3 \sin^{2} λ)}^{1 / 2}}{\cos^{6} λ}

is the background dipole magnetic field (where B E is the equatorial magnetic field on the Earth's surface, L is the magnetic shell, and λ is the geomagnetic latitude) and the electromagnetic field of MS waves ( B w and E w ). To reduce the computational cost and focus on the resonance phase, we follow the detailed study of Li et al [], which corrected the sign problem in the work of Bortnik and Thorne [] and emphasized the importance of wave centripetal force in phase trapping compared to previous studies [e.g., Bell , ; Tao and Bortnik , ], to rewrite the particle motion equation in a relativistic gyroaveraged form for given resonance order N ; i.e.,

{\overset{true.}{p}}_{∥} = F_{∥}^{w} normalsin η - \frac{1}{2 B} \frac{p_{⊥}^{2}}{γ m} \frac{\partial B}{\partial z}

{\overset{true.}{p}}_{⊥} = F_{⊥}^{w} normalsin η + \frac{1}{2 B} \frac{p_{⊥} p_{∥}}{γ m} \frac{\partial B}{\partial z}

\overset{η}{true} = \frac{N F_{θ}^{w}}{p_{⊥}} normalcos η + ω - \frac{k_{∥} p_{∥}}{γ m} - \frac{N ω_{c p}}{γ}

…”

Section: Test Particle Simulation Methods and Model Adoptionmentioning

confidence: 99%

Interactions between magnetosonic waves and ring current protons: Gyroaveraged test particle simulations

et al. 2016

JGR Space Physics

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Gyroaveraged test particle simulations are implemented to quantitatively investigate interactions between linearly polarized magnetosonic waves (i.e., equatorial noises) and ring current protons inside and outside the plasmasphere at L = 4.5. For magnetosonic waves at the frequency of 33.3 Hz (fw/fcp = 6.4 at the magnetic equator, for L = 4.5), it is found that wave‐particle interactions at the resonance order corresponding to the lowest resonant proton energy (i.e., N = 6) are dominant. The interactions at other resonance orders make much less contribution. Near the equatorial loss cone at L = 4.5, magnetosonic waves produce strongest proton pitch angle diffusion at ~ 20 keV inside the plasmasphere and at ~ 100 keV outside the plasmasphere, respectively, reaching a rate above 10−6 s−1. The corresponding energy diffusion dominates over pitch angle diffusion at high pitch angles; therefore, magnetosonic waves are likely to accelerate protons at a few keV inside the plasmasphere and at ~ 10 keV outside the plasmasphere. Due to the emission equatorial confinement, the effect of transit time scattering also occurs for interactions of magnetosonic waves with ring current protons and tends to be increasingly important outside the plasmasphere, which is consistent with previous studies on interactions of magnetosonic waves with radiation belt electrons.

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

Cited by 16 publications

References 37 publications

Statistical Analysis of Transverse Size of Lower Band Chorus Waves Using Simultaneous Multisatellite Observations

Statistical Analysis of Transverse Size of Lower Band Chorus Waves Using Simultaneous Multisatellite Observations

Modeling Energetic Electron Nonlinear Wave‐Particle Interactions With Electromagnetic Ion Cyclotron Waves

Interactions between magnetosonic waves and ring current protons: Gyroaveraged test particle simulations

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