scholarly journals Approximate analytical solutions for the trapped electron distribution due to quasi‐linear diffusion by whistler mode waves

2014 ◽  
Vol 119 (12) ◽  
pp. 9962-9977 ◽  
Author(s):  
D. Mourenas ◽  
A. V. Artemyev ◽  
O. V. Agapitov ◽  
V. Krasnoselskikh ◽  
W. Li
Keyword(s):  
Analytical Solutions ◽  
Electron Distribution ◽  
Linear Diffusion ◽  
Whistler Mode ◽  
Approximate Analytical Solutions ◽  
Whistler Mode Waves ◽  
Trapped Electron

scholarly journals Long-term evolution of electron distribution function due to nonlinear resonant interaction with whistler mode waves

2018 ◽  
Vol 84 (2) ◽  
Author(s):  
Anton V. Artemyev ◽  
Anatoly I. Neishtadt ◽  
Alexei A. Vasiliev ◽  
Didier Mourenas
Keyword(s):  
Kinetic Equation ◽  
Electron Distribution ◽  
Resonant Interaction ◽  
Long Term Evolution ◽  
Radiation Belts ◽  
Linear Diffusion ◽  
Whistler Mode ◽  
Term Evolution ◽  
Whistler Mode Waves

Accurately modelling and forecasting of the dynamics of the Earth’s radiation belts with the available computer resources represents an important challenge that still requires significant advances in the theoretical plasma physics field of wave–particle resonant interaction. Energetic electron acceleration or scattering into the Earth’s atmosphere are essentially controlled by their resonances with electromagnetic whistler mode waves. The quasi-linear diffusion equation describes well this resonant interaction for low intensity waves. During the last decade, however, spacecraft observations in the radiation belts have revealed a large number of whistler mode waves with sufficiently high intensity to interact with electrons in the nonlinear regime. A kinetic equation including such nonlinear wave–particle interactions and describing the long-term evolution of the electron distribution is the focus of the present paper. Using the Hamiltonian theory of resonant phenomena, we describe individual electron resonance with an intense coherent whistler mode wave. The derived characteristics of such a resonance are incorporated into a generalized kinetic equation which includes non-local transport in energy space. This transport is produced by resonant electron trapping and nonlinear acceleration. We describe the methods allowing the construction of nonlinear resonant terms in the kinetic equation and discuss possible applications of this equation.

Statistical Study of Pitch Angle Diffusion during Substorm Injections

2020 ◽  
Author(s):  
Reihaneh Ghaffari ◽  
Christopher Cully
Keyword(s):  
Pitch Angle ◽  
Energetic Electron ◽  
Loss Cone ◽  
Linear Diffusion ◽  
Whistler Mode ◽  
Wave Measurements ◽  
Whistler Mode Waves ◽  
Substorm Injection ◽  
Injection Region

<p>Energetic Electron Precipitation (EEP) associated with substorm injections typically occurs when magnetospheric waves, particularly whistler-mode waves, resonantly interact with electrons to affect their equatorial pitch angle. This can be considered as a diffusion process that scatters particles into the loss cone. In this study, we investigate whistler-mode wave generation in conjunction with electron injections using in-situ wave measurements by the Themis mission. We calculate the pitch angle diffusion coefficient exerted by the observed wave activity using the quasi-linear diffusion approximation and estimate scattering efficiency in the substorm injection region to constrain where and how much scattering happens typically during these events.</p>

Gap formation around 0.5Ωe of whistler-mode waves excited by electron temperature anisotropy

2021 ◽  
Author(s):  
Huayue Chen ◽  
Xinliang Gao ◽  
Quanming Lu ◽  
Konrad Sauer
Keyword(s):  
Electron Temperature ◽  
Electron Distribution ◽  
Wave Spectrum ◽  
Linear Stage ◽  
Gap Formation ◽  
Temperature Anisotropy ◽  
Whistler Mode ◽  
Pic Simulation ◽  
Distribution Form ◽  
Whistler Mode Waves

<p>With a 1-D PIC simulation model, we have investigated the gap formation around 0.5Ω<sub>e</sub> of the quasi-parallel whistler-mode waves excited by an electron temperature anisotropy. When the frequencies of excited waves in the linear stage cross 0.5Ω<sub>e</sub>, or when they are slightly larger than 0.5Ω<sub>e </sub>but then drift to lower values, the Landau resonance can make the electron distribution form a beam-like/plateau population. Such an electron distribution only slightly changes the dispersion relation of whistler-mode waves, but can cause severe damping around 0.5Ω<sub>e</sub> via cyclotron resonance. At last, the wave spectrum is separated into two bands with a power gap around 0.5Ω<sub>e</sub>. The condition under different electron temperature anisotropy and plasma beta is also surveyed for such kind of power gap. Besides, when only the waves with frequencies lower than 0.5Ω<sub>e</sub> are excited in the linear stage, a power gap can also be formed due to the wave-wave interactions, i.e., lower band cascade. Our study provides a clue to reveal the well-known 0.5Ω<sub>e</sub> power gap of whistler-mode waves ubiquitously observed in the inner magnetosphere.</p>

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