Simultaneous observation of characteristic 3-dimensional (3D) signatures in the electron velocity distribution function (VDF) and intense quasi-monochromatic waves by the Magnetospheric Multiscale (MMS) spacecraft in the terrestrial magnetosheath are investigated. The intense wave packets are characterised and modeled analytically as quasi-parallel circularly-polarized whistler waves and applied to a test-particle simulation in view of gaining insight into the signature of the wave-particle resonances in velocity space. Both the Landau and the cyclotron resonances were evidenced in the test-particle simulations. The location and general shape of the test-particle signatures do account for the observations, but the finer details, such as the symmetry of the observed signatures are not matched, indicating either the limits of the test-particle approach, or a more fundamental physical mechanism not yet grasped. Finally, it is shown that the energisation of the electrons in this precise resonance case cannot be diagnosed using the moments of the distribution function, as done with the classical ${\bf E}.{\bf J}$ "dissipation" estimate.
The Magnetospheric Multiscale (MMS) mission has observed electron whistler waves at the center and at the edges of magnetic holes in the dayside magnetosheath. The magnetic holes are nonlinear mirror structures since their magnitude is anti-correlated with particle density. In this article, we examine the growth mechanisms of these whistler waves and their interaction with the host magnetic hole. In the observations, as magnetic holes develop and get deeper, an electron population gets trapped and develops a temperature anisotropy favorable for whistler waves to be generated. In addition, the …
We study the wave-particle interactions between lower band chorus whistlers and an anisotropic tenuous population of relativistic electrons. We present the first direct comparison of first-principle Particle-in-Cell (PIC) simulations with a quasi-linear diffusion code, in this context. In the PIC approach, the waves are self-consistently generated by a temperature anisotropy instability that quickly saturates and relaxes the system towards marginal stability. We show that the quasi-linear diffusion and PIC results have significant quantitative mismatch in regions of energy/pitch angle where th…
Magnetic reconnection (MR) and the associated concurrently occurring waves have been extensively studied at large-scale plasma boundaries, in quasi-symmetric and asymmetric configurations in the terrestrial magnetotail and at the magnetopause. Recent high-resolution observations by MMS (Magnetospheric Multiscale) spacecraft indicate that MR can occur also in the magnetosheath where the conditions are highly turbulent when the upstream shock geometry is quasi-parallel. The strong turbulent motions make the boundary conditions for evolving MR complicated. In this paper it is demonstrated that th…
Chorus-like whistler-mode waves that are known to play a fundamental role in driving radiation-belt dynamics are excited on the Large Plasma Device by the injection of a helical electron beam into a cold plasma. The mode structure of the excited whistler wave is identified using a phase-correlation technique showing that the waves are excited through a combination of Landau resonance, cyclotron resonance and anomalous cyclotron resonance. The dominant wave mode excited through cyclotron resonance is quasi-parallel propagating, whereas wave modes excited through Landau resonance and anomalous c…
Thermalization and heating of plasma flows at shocks result in unstable charged-particle distributions which generate a wide range of electromagnetic waves. These waves, in turn, can further accelerate and scatter energetic particles. Thus, the properties of the waves and their implication for wave-particle interactions are critically important for modeling energetic particle dynamics in shock environments. Whistler-mode waves, excited by the electron heat flux or a temperature anisotropy, arise naturally near shocks and foreshock transients. As a result, they can often interact with supra-the…
We present a self-consistent Particle-in-Cell simulation of the resonant interactions between anisotropic energetic electrons and a population of whistler waves, with parameters relevant to the Earths radiation belt. By tracking PIC particles, and comparing with test-particle simulations we emphasize the importance of including nonlinear effects and time evolution in the modeling of wave-particle interactions, which are excluded in the resonant limit of quasi- linear theory routinely used in radiation belt studies. In particular we show that pitch angle diffusion is enhanced during the linear …
Whistler waves are thought to play an essential role in the dynamics of collisionless shocks. We use the magnetospheric multiscale (MMS) spacecraft to study whistler waves around the lower hybrid frequency, upstream of 11 quasi-perpendicular super-critical shocks. We apply the 4-spacecraft timing method to unambiguously determine the wave vector $\mathbf{k}$ of whistler waves. We find that the waves are oblique to the background magnetic field with a wave-normal angle between $20^{\circ}$ and $42^{\circ}$, a wavelength around 100 km which is close to the ion inertial length. We also find that …
Magnetic holes are plasma structures that trap a large number of particles in a magnetic field that is weaker than the field in its surroundings. The unprecedented high time-resolution observations by NASA's Magnetospheric Multi-Scale (MMS) mission enable us to study the particle dynamics in magnetic holes in the Earth's magnetosheath in great detail. We reveal the local generation mechanism of whistler waves by a combination of Landau-resonant and cyclotron-resonant wave-particle interactions of electrons in response to the large-scale evolution of a magnetic hole. As the magnetic hole conver…
A range of nonlinear wave structures, including Langmuir waves, unipolar electric fields and bipolar electric fields, are often observed in association with whistler-mode chorus waves in the near-Earth space. We demonstrate that the three seemingly different nonlinear wave structures originate from the same nonlinear electron trapping process by whistler-mode chorus waves. The ratio of the Landau resonant velocity to the electron thermal velocity controls the type of nonlinear wave structures that will be generated.
Electron Heat Flux and Whistler Instability in the Earth's Magnetosheath
Swedish Institute of Space Physics（瑞典空间物理研究所）；Uppsala University（乌普萨拉大学）；Chalmers University of Technology（查尔姆斯理工大学）；Laboratory of Physics and Chemistry of the Environment and Space (LPC2E), OSUC, Univ Orleans, CNRS, CNES（环境与空间物理化学实验室（LPC2E）、OSUC、奥尔良大学、CNRS、CNES）；Laboratory for Atmospheric and Space Physics, University of Colorado（科罗拉多大学大气与空间物理实验室）；Imperial College London（帝国理工学院）
Resonances with electromagnetic whistler-mode waves are the primary driver for the formation and dynamics of energetic electron fluxes in various space plasma systems, including shock waves and planetary radiation belts. The basic and most elaborated theoretical framework for the description of the integral effect of multiple resonant interactions is the quasi-linear theory, that operates through electron diffusion in velocity space. The quasi-linear diffusion rate scales linearly with the wave intensity, D(QL) is proportional to Bw2, which should be small enough to satisfy the applicability c…
We present surprising observations by the NASA Van Allen Probes spacecraft of whistler waves with substantial electric field power at harmonics of the whistler wave fundamental frequency. The wave power at harmonics is due to nonlinearly steepened whistler electrostatic field that becomes possible in the two-temperature electron plasma due to whistler wave coupling to the electron-acoustic mode. The simulation and analytical estimates show that the steepening takes a few tens of milliseconds. The hydrodynamic energy cascade to higher frequencies facilitates efficient energy transfer from cyclo…
When a wave packet composed of short wavelength lower hybrid modes traveling in an homogeneous plasma region encounters an inhomogeneity, it can resonantly excite long wavelength whistler waves via a linear mechanism known as mode conversion. An enhancement of lower hybrid/whistler activity has been often observed by sounding rockets and satellites in the presence of density depletions (striations) in the upper ionosphere. We address here the process of linear mode conversion of lower hybrid to whistler waves, mediated by a density striation, using a scalar-field formalism (in the limit of col…
The role of solar wind expansion in generating whistler waves is investigated using the EB-iPic3D code, which models solar wind expansion self-consistently within a fully kinetic semi-implicit approach. The simulation is initialized with an electron velocity distribution function modeled after Parker Solar Probe observations during its first perihelion at 0.166 au, consisting of a dense core and an anti-sunward strahl. This distribution function is initially stable with respect to kinetic instabilities. Expansion drives the solar wind into successive regimes where whistler heat flux instabilit…
Effects of increasing whistler amplitude and propagation angle are studied through a variational test particle simulation and calculations of the resonance width. While high amplitude and oblique whistlers in typical 1 AU solar wind parameters are capable of forming an isotropic population without any additional processes, anomalous interactions with quasi-parallel whistlers may be essential to the process of halo formation near the Sun. High amplitude and quasi-parallel whistlers can scatter strahl electrons to low velocities (less than the wave phase velocity) to form a halo population, as l…
The electrons are an essential particle species in the solar wind. They often exhibit non-equilibrium features in their velocity distribution function. These include temperature anisotropies, tails (kurtosis), and reflectional asymmetries (skewness), which contribute a significant heat flux to the solar wind. If these non-equilibrium features are sufficiently strong, they drive kinetic micro-instabilities. We develop a semi-graphical framework based on the equations of quasi-linear theory to describe electron-driven instabilities in the solar wind. We apply our framework to resonant instabilit…
In this paper, we develop a model to describe the generalized wave-particle instability in a quasi-neutral plasma. We analyze the quasi-linear diffusion equation for particles by expressing an arbitrary unstable and resonant wave mode as a Gaussian wave packet, allowing for an arbitrary direction of propagation with respect to the background magnetic field. We show that the localized energy density of the Gaussian wave packet determines the velocity-space range in which the dominant wave-particle instability and counter-acting damping contributions are effective. Moreover, we derive a relation…
In this study we consider the Hamiltonian approach for the construction of a map for a system with nonlinear resonant interaction, including phase trapping and phase bunching effects. We derive basic equations for a single resonant trajectory analysis and then generalize them into the map in the energy/pitch-angle space. The main advances of this approach are the possibility to consider effects of many resonances and to simulate the evolution of the resonant particle ensemble on long time ranges. For illustrative purposes we consider the system with resonant relativistic electrons and field-al…
Electron resonant scattering by whistler-mode waves is one of the most important mechanisms responsible for electron precipitation to the Earth's atmosphere. We investigate temporal and spatial scales of such precipitation with measurements from the two low-altitude ELFIN CubeSats. We compare the variations in energetic electron precipitation at the same L-shells but on successive data collection orbit tracks by the two ELFIN satellites. Variations seen at the smallest inter-satellite separations are likely associated with whistler-mode chorus elements or with the scale of chorus wave packets …
Large amplitude whistler waves at frequencies of 0.2 to 0.4 times electron cyclotron frequency are frequently observed in the solar wind. The waves are obliquely propagating close to the resonance cone, with significant electric fields parallel to the background magnetic field, enabling strong interactions with electrons. Propagation angles are distinctly different from whistlers usually observed in the solar wind, and amplitudes are significantly larger. Waves occur most often in association with stream interaction regions (SIRs), and are often close-packed. 68 percent of the 54 SIRs had narr…
Long-term simulations of energetic electron fluxes in many space plasma systems require accounting for two groups of processes with well separated time-scales: microphysics of electron resonant scattering by electromagnetic waves and electron adiabatic heating/transport by mesoscale plasma flows. Examples of such systems are Earth's radiation belts and Earth's bow shock, where ion-scale plasma injections and cross-shock electric fields determine the general electron energization, whereas electron scattering by waves relax anisotropy of electron distributions and produces small populations of h…
The SWEAP instrument suite on Parker Solar Probe (PSP) has detected numerous proton beams associated with coherent, circularly polarized, ion-scale waves observed by PSP's FIELDS instrument suite. Measurements during PSP Encounters 4-8 revealed pronounced complex shapes in the proton velocity distribution functions (VDFs), in which the tip of the beam undergoes strong perpendicular diffusion, resulting in VDF level contours that resemble a `hammerhead.' We refer to these proton beams, with their attendant `hammerhead' features, as the ion strahl. We present an example of these observations occ…
The nature of solar wind turbulence in the dissipation range at scales much smaller than the large MHD scales remains under debate. Here a two-dimensional model based on the hybrid code abbreviated as A.I.K.E.F. is presented, which treats massive ions as particles obeying the kinetic Vlasov equation and massless electrons as a neutralizing fluid. Up to a certain wavenumber in the MHD regime, the numerical system is initialized by assuming a superposition of isotropic Alfvén waves with amplitudes that follow the empirically confirmed spectral law of Kolmogorov. Then turbulence develops and ener…
Using linear Vlasov theory of plasma waves and quasi-linear theory of resonant wave-particle interaction, the dispersion relations and the electromagnetic field fluctuations of fast and Alfven waves are studied for a low-beta multi-ion plasma in the inner corona. Their probable roles in heating and accelerating the solar wind via Landau and cyclotron resonances are quantified. We assume that (1) low-frequency Alfven and fast waves have the same spectral shape and the same amplitude of power spectral density; (2) these waves eventually reach ion cyclotron frequencies due to a turbulence cascade…
An innovative field-particle correlation technique is proposed that uses single-point measurements of the electromagnetic fields and particle velocity distribution functions to investigate the net transfer of energy from fields to particles associated with the collisionless damping of turbulent fluctuations in weakly collisional plasmas, such as the solar wind. In addition to providing a direct estimate of the local rate of energy transfer between fields and particles, it provides vital new information about the distribution of that energy transfer in velocity space. This velocity-space signat…
