Theoretical bounce resonance diffusion coefficient for waves generated near the equatorial plane

Tao, X.; Li, X.

doi:10.1002/2016gl070139

Cited by 41 publications

(80 citation statements)

References 29 publications

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“…To investigate quantitatively the bounce resonant interactions between low‐frequency hiss and radiation belt electrons, we calculate the corresponding bounce resonance scattering rates following the method of Tao and Li (). The scattering rates are the summation over the bounce resonance order l from the lowest to the highest order and are proportional to the wave power spectral intensity.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…It has been proposed by Shprits () that magnetosonic and H + band electromagnetic ion cyclotron (EMIC) waves, which have frequencies comparable to the electron bounce frequency or its harmonics, have the potential to bounce resonate with near‐equatorially mirroring electrons by violating the second invariant associated with the electron bounce motion. Bounce resonant interactions with magnetosonic and H + band EMIC waves have been subsequently proved by recent studies (e.g., Chen et al, ; Cao et al, ; Li et al, ; Shprits, ; Tao & Li, ; Tao et al, ) to account for the pitch angle scattering of electrons with ~90° equatorial pitch angles. For typical plasmaspheric hiss with wave frequencies much higher than the electron bounce frequency, its bounce resonance with near‐equatorially mirroring electrons tends to be insignificant.…”

Section: Introductionmentioning

confidence: 95%

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Bounce Resonance Scattering of Radiation Belt Electrons by Low‐Frequency Hiss: Comparison With Cyclotron and Landau Resonances

Cao

Summers

et al. 2017

Geophysical Research Letters

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Bounce resonant interactions with magnetospheric waves have been proposed as an important contributing mechanism for scattering near‐equatorially mirroring electrons by violating the second adiabatic invariant associated with the electron bounce motion along a geomagnetic field line. This study demonstrates that low‐frequency plasmaspheric hiss with significant wave power below 100 Hz can bounce resonate efficiently with radiation belt electrons. By performing quantitative calculations of pitch angle scattering rates, we show that low‐frequency hiss‐induced bounce resonant scattering of electrons has a strong dependence on equatorial pitch angle αeq. For electrons with αeq close to 90°, the timescale associated with bounce resonance scattering can be comparable to or even less than 1 h. Cyclotron and Landau resonant interactions between low‐frequency hiss and electrons are also investigated for comparisons. It is found that while the bounce and Landau resonances are responsible for the diffusive transport of near‐equatorially mirroring electrons to lower αeq, pitch angle scattering by cyclotron resonance could take over to further diffuse electrons into the atmosphere. Bounce resonance provides a more efficient pitch angle scattering mechanism of relativistic (≥1 MeV) electrons than Landau resonance due to the stronger scattering rates and broader resonance coverage of αeq, thereby demonstrating that bounce resonance scattering by low‐frequency hiss can contribute importantly to the evolution of the electron pitch angle distribution and the loss of radiation belt electrons.

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Section: Numerical Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 95%

Bounce Resonance Scattering of Radiation Belt Electrons by Low‐Frequency Hiss: Comparison With Cyclotron and Landau Resonances

Cao

Summers

et al. 2017

Geophysical Research Letters

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“…Based on previous theories (Cao et al, ; Tao & Li, ), the electron scattering rates caused by bounce resonance are given as follows:

D_{αα} = D_{WW} {(\frac{{sin}^{2} α_{eq} tan α_{eq}}{2 M B_{eq}})}^{2}, D_{αE} = - D_{WW} \frac{{sin}^{2} α_{eq} tan α_{eq}}{2 M B_{eq}} \frac{1}{γ}, D_{EE} = D_{WW} {(\frac{1}{γ})}^{2},

where

D_{WW} = \frac{1}{2 normalπ} {(\frac{p cos α_{eq}}{m_{normale}})}^{2} \sum_{l = 1}^{\infty} \int scriptF ((),, l ω_{b}, k_{∥}) ([], {(∆ W_{1 l} + ∆ W_{2 l})}^{2} + ∆ {W_{3 l}}^{2}) d k_{∥},

∆ W_{1 l} = \frac{l}{z_{0}} J_{l} ((), z_{0}) ([], 2 θ_{m} + sin ((), 2 θ_{m})),

∆ W_{2 l} = \sum_{\begin{matrix} (||, l^{'} - l) \neq 1 \\ l^{'} - l = odd \end{matrix}} J_{l^{'}} ((), z_{0}) ([], sin ((), l_{+} θ_{}))

…”

Section: Effect Of Low‐harmonic Ms Waves On the Radiation Belt Electronsmentioning

confidence: 99%

“…Recently, wave‐particle interaction is put forward to explain the formation of butterfly distribution far away from the magnetopause. MS waves are believed to be a candidate mechanism responsible for the butterfly formation through Landau resonance (Horne et al, ; Li, Yu, et al, ; Xiao et al, ; Yang et al, ), transit time scattering (Bortnik & Thorne, ; Li et al, ; J. Li, Ni, et al, ; Ni et al, , ), and bounce resonance (Chen et al, ; Li & Tao, ; Maldonado et al, ; Shprits, ; Tao & Li, ). Landau resonance occurs when the parallel phase velocity ( ω / k ∥ ) of waves equals to the electron velocity parallel to background magnetic field ( v ∥ ; Artemyev et al, ) and the minimum resonant energy can be obtained according to the study of Horne et al ().…”

Section: Introductionmentioning

confidence: 99%

Effect of Low‐Harmonic Magnetosonic Waves on the Radiation Belt Electrons Inside the Plasmasphere

Cui

et al. 2019

JGR Space Physics

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In this paper, we presented two observational cases and simulations to indicate the relationship between the formation of butterfly‐like electron pitch angle distributions and the emission of low‐harmonic (LH) fast magnetosonic (MS) waves inside the high‐density plasmasphere. In the wave emission region, the pitch angle of relativistic (>1 MeV) electrons becomes obvious butterfly‐like distributions for both events (near‐equatorially mirroring electrons are transported to lower pitch angles). Unlike relativistic (>1 MeV) electrons, energetic electrons (<1 MeV) change slightly, except that relatively low‐energy electrons (<~150 keV) show butterfly‐like distributions in the 21 August 2013 event. In theory, the LH MS waves can affect different‐energy electrons through the bounce resonance, Landau resonance, and transit time scattering. By performing the Fokker‐Planck diffusion simulations, we demonstrate that the bounce resonance with the LH MS waves mainly leads to the butterfly pitch angle distribution of MeV electrons, whereas the Landau resonance and transit time scattering mainly affect energetic electrons in the high‐density region.

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“…Recently, MS waves have caught much attention because, by resonating with particles, they play a crucial role in radiation belt dynamics. On the one hand, numerous studies have found that these emissions are able to produce electron butterfly distributions via Landau resonance and bounce resonance energization (Horne et al, ; Shprits, ; Bortnik and Thorne, ; Li JX et al, ; Li LY et al, ; Ni BB et al, , ; Tao X and Li X, ; Xiao FL et al, ). On the other hand, MS waves are also found capable of interacting with protons through cyclotron resonance (Xiao FL et al, ; Fu S et al, ).…”

Section: Introductionmentioning

confidence: 99%

Ring current proton scattering by low-frequency magnetosonic waves

Wang

Cui

2019

Earth and Planetary Physics

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Magnetosonic (MS) waves are believed to have the ability to affect the dynamics of ring current protons both inside and outside the plasmasphere. However, previous studies have focused primarily on the effect of high‐frequency MS waves (f > 20 Hz) on ring current protons. In this study, we investigate interactions between ring current protons and low‐frequency MS waves (< 20 Hz) inside the plasmasphere. We find that low‐frequency MS waves can effectively accelerate < 20 keV ring current protons on time scales from several hours to a day, and their scattering efficiency is comparable to that due to high‐frequency MS waves (>20 Hz), from which we infer that omitting the effect of low‐frequency MS waves will considerably underestimate proton depletion at middle pitch angles and proton enhancement at large pitch angles. Therefore, ring current proton modeling should take into account the effects of both low‐ and high‐frequency MS waves.

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Theoretical bounce resonance diffusion coefficient for waves generated near the equatorial plane

Cited by 41 publications

References 29 publications

Bounce Resonance Scattering of Radiation Belt Electrons by Low‐Frequency Hiss: Comparison With Cyclotron and Landau Resonances

Bounce Resonance Scattering of Radiation Belt Electrons by Low‐Frequency Hiss: Comparison With Cyclotron and Landau Resonances

Effect of Low‐Harmonic Magnetosonic Waves on the Radiation Belt Electrons Inside the Plasmasphere

Ring current proton scattering by low-frequency magnetosonic waves

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