Abstract
The nonlinear resonant interaction of intense whistler-mode waves and energetic electrons in the Earth's radiation belts is traditionally described by theoretical models based on the consideration of slow–fast resonant systems. Such models reduce the electron dynamics around the resonance to the single pendulum equation that provides solutions for the electron nonlinear scattering (phase bunching) and phase trapping. Applicability of this approach is limited to not-too-small electron pitch-angles (i.e., sufficiently large electron magnetic moments), whereas model predictions contradict to the test particle results for small pitch-angle electrons. This study is focused on such field-aligned (small pitch-angle) electron resonances. We show that the nonlinear resonant interaction can be described by the slow–fast Hamiltonian system with the separatrix crossing. For the first cyclotron resonance, this interaction results in the electron pitch-angle increase for all resonant electrons, contrast to the pitch-angle decrease predicted by the pendulum equation for scattered electrons. We derive the threshold value of the magnetic moment of the transition to a new regime of the nonlinear resonant interaction. For field-aligned electrons, the proposed model provides the magnitude of magnetic moment changes in the nonlinear resonance. This model supplements existing models for not-too-small pitch-angles and contributes to the theory of the nonlinear resonant electron interaction with intense whistler-mode waves.
Highlights
The wave-particle resonant interaction is the key process for energy exchange between different particle populations in collisionless plasma[1]
In an inhomogeneous ambient magnetic field the requirement for a low coherence is significantly relaxed[11,12], and electron scattering by the monochromatic low amplitude waves can be described by the quasi-linear diffusion[13,14]
For the nonlinear waveparticle interaction this parameter is about the ratio of a wave amplitude Bw and ambient magnetic field magnitude B0, i.e. a wave force ∼ kBw can compete with a mirror force ∼ B0/R and temporally trap electrons into the resonance[17,47,48]
Summary
The wave-particle resonant interaction is the key process for energy exchange between different particle populations in collisionless plasma[1]. The theory of nonlinear electron resonances with whistler-mode waves is based on individual orbit analysis, that reduces the electron motion equation to the pendulum equation with torque[15,44–47] Such analysis describes well both phase trapping and nonlinear scattering effects and provides typical amplitudes of energy and pitch-angle changes, ∆γ and ∆α. For the nonlinear waveparticle interaction this parameter is about the ratio of a wave amplitude Bw and ambient magnetic field magnitude B0, i.e. a wave force ∼ kBw can compete with a mirror force ∼ B0/R and temporally trap electrons into the resonance[17,47,48] This theoretical concept is invalid for systems with the second small parameter, e.g. for very small pitch-angle (almost field-aligned) electrons.
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