超低频波与带电粒子的非线性相互作用

Nonlinear interaction between particles and ultralow frequency waves

超低频波在日地能量传输和磁层—电离层耦合过程中都扮演着十分重要的角色,其在调节整个太阳—地球系统的能量流方面的研究一直是空间物理领域最重要的研究方向之一.超低频波是带电粒子在内磁层辐射带中加速和扩散的主要原因之一,磁层中的带电粒子具有典型的垂直于磁场的漂移运动和平行于磁场的弹跳运动,超低频波的频率范围能够覆盖带电粒子的漂移或弹跳频率,因此其与粒子之间会发生共振,超低频波正是通过与电子或离子发生漂移共振或漂移弹跳共振来完成能量的传递,从而实现对带电粒子的加速.自漂移共振理论提出以来,线性分析方法一直沿用至今,即假定粒子运动遵循未扰轨道,轨道因能量改变而造成的扰动一直被忽略不计.这一假设只有在粒子能量变化远小于粒子能量本身时才有效,而实际观测中经常存在振幅较大或持续时间较长的超低频波使得粒子能量变化很大,线性理论不再适用.本文结合理论分析、卫星观测总结了极向模和环向模超低频波与内磁层带电粒子的非线性漂移共振作用,给出了线性方法与非线性方法的使用范围,并从观测上给出了识别非线性漂移共振发生的方法.

One of the most important questions in space physics is how the energy of the solar wind is transmitted to energetic particles in the Earth's magnetosphere,part of which is in the form of ultra-low-frequency(ULF)electromagnetic waves in the mHz frequency range.More specifically,ULF waves can provide diagnostics of the magnetosphere.For example,ionospheric conductance and mass density structure can be derived;substorm onset can be timed;and geomagnetic field lines can be mapped.ULF waves can also modify the magnetosphere such as through nonlinear effects allowing Kelvin-Helmholtz surface wave energy at the magnetopause to penetrate into magnetosphere,and radial diffusion,which plays an essential role in flux enhancement and particle acceleration of the radiation belts.Hannes Alfvén first proposed the existence of transverse"electrohydrodynamic"waves in the magnetized plasma.The magnetohydrodynamic(MHD)theory was first applied to explain the observed geomagnetic pulsations in Earth's magnetosphere,which has been confirmed by spacecraft observations and ground-based magnetometers.ULF waves are usually categorized into poloidal and toroidal modes by different directions of the perturbed electromagnetic field.Magnetic line oscillations in the radial direction yields azimuthal electric fields(Eφ)and are referred to as poloidal waves,while the motion of field lines in the azimuthal direction yields electric field oscillations in the radial direction(Er)which are referred to as toroidal waves.Efficient interac-tion between ULF waves and charged particles requires comparable periods of waves and particle's drift motion.An acceleration mechanism capable of a continuous energy exchange between ULF waves and charged particles is wave-particle drift resonance.When such resonance occurs,the azimuthal drift speed of a resonant particle matches the wave propagation speed,and the particle experiences a constant phase of the wave electric field.This process enables a sustained energy exchange between ULF waves and charged particles,which provides a major source of particle acceleration and diffusion in the Van Allen radiation belts.The conventional drift resonance theory as-sumes that the particle trajectories are unperturbed despite their energy gain or loss from ULF waves.This assump-tion is usually invalid in Earth's magnetosphere because ULF waves can have larger amplitudes and/or durations.The large wave-particle energy exchange can modify the particle trajectory and cause significant nonlinear effects.This paper mainly reviews the nonlinear drift resonance between poloidal/toroidal ULF waves and charged particles in the inner magnetosphere.The particle behavior can be described by a pendulum equation in poloidal ULF waves,with the nonlinear trapping frequency determined by the ULF wave amplitude.We further predict,based on the newly-developed theory,the observable signatures of nonlinear drift resonance such as rolled-up structures in the energy spectrum of particle fluxes.After considering how this manifests in particle data with finite energy resolu-tion,we compare the predicted signatures with Van Allen Probes observations.Their good agreement provides the first observational identification of the nonlinear drift resonance,which highlights the importance of nonlinear ef-fects in magnetospheric particle dynamics under ULF waves.Drift resonance between particles and toroidal ULF waves can occur even without the noon-midnight asymmetry of background magnetic field.This effect originates from the wave-carried compressional magnetic field oscillations,which turn out to play a key role in the energy ex-change between toroidal ULF waves and charged particles.The resulting particle motion can be described by a modified pendulum equation with solutions depending on the wave number.These findings demonstrate that to-roidal ULF waves,like their poloidal counterparts,play an important role in magnetospheric particle dynamics.This is significant because the new derivation allows a large body of existing work and understanding on the pendu-lum equation to be brought to bear on the problem of ULF wave-particle interactions in the inner magnetosphere.As particle detector technology improves,more nonlinear features will become observable,allowing further tests of the theory presented here.