Landau Resonance Research Articles

Electromagnetic Landau Resonance: Nonlinear Dynamics and Harmonic Generation

AbstractIn situ particle observations provide useful information for determining the significance of nonlinearity in wave‐particle interactions. Here, we examine an electromagnetic Landau resonance event observed by the Magnetospheric Multiscale mission near the dayside magnetopause along this line of thought. During this event, protons with energy 748 eV and pitch angle are observed to resonate with electromagnetic‐ion‐cyclotron waves. Detailed data analysis reveals the existence of a second harmonic signal in proton modulation. Using an observation‐based test particle simulation, this signal is explained as a low‐resolution manifestation of phase space rolled‐up structures, which themselves are not observable due to limited instrument resolution. The presence of these rolled‐up structures suggests that the waves induce significant displacement of the protons in phase space, consequently confirming the nonlinear nature of the observed interaction. Based on the observations, we further discuss the possibility of the nonlinear electromagnetic Landau resonance generating second harmonic waves.

A Statistical Examination of Interactions Between 1‐Hz Whistler Waves and Ions in the Earth's Foreshock

AbstractThe 1 Hz whistler wave precursors attached to shock‐like structures are often observed in the foreshock. Using observations from the Magnetospheric Multiscale mission, we investigate the interactions between 1 Hz waves and ions. Incoming solar wind ions do not cyclotron‐resonate with the wave, since typically the wave is right‐handed in their frame. We demonstrate that solar wind ions commonly exhibit 180° gyro‐phase bunching from the wave magnetic field, understanding it with a reconciled linear theory and non‐linear trapping theory for non‐cyclotron‐resonant modulations. Along the longitudinal direction, solar wind ions experience Landau resonance, exhibiting either modulations at small wave potentials or trapping in phase‐space holes at large potentials. The results also improve our understanding of foreshock structure evolution and 1 Hz wave excitation. Shock‐like structures start with having incoming solar wind and remotely reflected ions from further downstream. The ion‐scale 1 Hz waves can already appear during this stage. The excitation may be due to shock‐like dispersive radiation or kinetic instabilities resonant with these remotely reflected ions. Ions reflected by local shock‐like structures occur later, so they are not always necessary for generating 1 Hz waves. The wave leads to ion reflection further upstream, which may cause reformation of shock‐like structures. In one event, locally reflected ions exhibit non‐cyclotron‐resonant modulation in the early stage, and later approach the anomalous cyclotron resonant condition with gyro‐phases ∼270°. The latter is possibly due to nonlinear trapping in regions with an upstream‐pointing magnetic field gradient, linked to reformation. Some additional special features, such as frequency dispersions, are observed, encouraging further investigations.

Particle Simulation Study of Obliquely Propagating Whistler Waves in Low‐Beta Plasmas

AbstractWhistler mode waves, which are electromagnetic emissions commonly observed in various space plasma environments, play critical roles in electron dynamics. While most whistler waves are driven by temperature anisotropy and propagate parallel to the background magnetic field, these waves can also be excited in the oblique direction when electron plasma beta is very low (<0.025). Although linear theory accounts for the excitation processes of obliquely propagating whistler waves, the subsequent evolution and saturation processes remain inadequately understood. This study utilizes two‐dimensional self‐consistent simulations to investigate the complete wave‐particle interaction process. By scanning a broad parameter range, we derive scaling laws for the wave intensity, linking the wave properties to initial and final plasma conditions. The saturated temperature anisotropy from simulations can explain the upper bound anisotropy constraint observed by spacecraft well. Additional phase space analysis shows that both Landau and cyclotron resonance play critical roles in the evolution of electron velocity distribution, albeit in different energy ranges. Oblique whistler waves can effectively heat electrons through Landau resonance, creating a plateau distribution in the parallel direction. This research advances our understanding of the mechanisms behind obliquely propagating whistler waves in low‐beta plasmas and their impact on electron dynamics.

Identification of Coupled Landau and Anomalous Resonances in Space Plasmas.

Wave-particle resonance, a ubiquitous process in the plasma universe, occurs when resonant particles observe a constant wave phase to enable sustained energy transfer. Here, we present spacecraft observations of simultaneous Landau and anomalous resonances between oblique whistler waves and the same group of protons, which are evidenced, respectively, by phase-space rings in parallel-velocity spectra and phase-bunched distributions in gyrophase spectra. Our results indicate the coupling between Landau and anomalous resonances via the overlapping of the resonance islands.

Electron Dynamics Associated With Advection and Diffusion in Self‐Consistent Wave‐Particle Interactions With Oblique Chorus Waves

AbstractChorus waves are intense electromagnetic emissions critical in modulating electron dynamics. In this study, we perform two‐dimensional particle‐in‐cell simulations to investigate self‐consistent wave‐particle interactions with oblique chorus waves. We first analyze the electron dynamics sampled from cyclotron and Landau resonances with waves, and then quantify the advection and diffusion coefficients through statistical studies. It is found that phase‐trapped cyclotron resonant electrons satisfy the second‐order resonance condition and gain energy from waves. While phase‐bunched cyclotron resonant electrons cannot remain in resonance for long periods. They transfer energy to waves and are scattered to smaller pitch angles. Landau resonant electrons are primarily energized by waves. For both types of resonances, advection coefficients are greater than diffusion coefficients when the wave amplitude is large. Our study highlights the important role of advection in electron dynamics modulation resulting from nonlinear wave‐particle interactions.

Beam‐Driven Electron Cyclotron Harmonic and Electron Acoustic Waves as Seen in Particle‐In‐Cell Simulations

AbstractRecent study has demonstrated that electron cyclotron harmonic (ECH) waves can be excited by a low energy electron beam. Such waves propagate at moderately oblique wave normal angles (∼70°). The potential effects of beam‐driven ECH waves on electron dynamics in Earth's plasma sheet is not known. Using two‐dimensional Darwin particle‐in‐cell simulations with initial electron distributions that represent typical plasma conditions in the plasma sheet, we explore the excitation and saturation of such beam‐driven ECH waves. Both ECH and electron acoustic waves are excited in the simulation and propagate at oblique wave normal angles. Compared with the electron acoustic waves, ECH waves grow much faster and have more intense saturation amplitudes. Cold, stationary electrons are first accelerated by ECH waves through cyclotron resonance and then accelerated in the parallel direction by both the ECH and electron acoustic waves through Landau resonance. Beam electrons, on the other hand, are decelerated in the parallel direction and scattered to larger pitch angles. The relaxation of the electron beam and the continuous heating of the cold electrons contribute to ECH wave saturation and suppress the excitation of electron acoustic waves. When the ratio of plasma to electron cyclotron frequency ωpe/ωce increases, the ECH wave amplitude increases while the electron acoustic wave amplitude decreases. Our work reveals the importance of ECH and electron acoustic waves in reshaping sub‐thermal electron distributions and improves our understanding on the potential effects of wave‐particle interactions in trapping ionospheric electron outflows and forming anisotropic (field‐aligned) electron distributions in the plasma sheet.

The excitation of whistler waves and wave-particle interaction in magnetic reconnection

A 2.5D PIC kinetic code is executed to simulate the excitation of electron whistlers and ion cyclotron whistler (L wave) during magnetic reconnection. Our simulation results suggest that quasi-parallel and anti-parallel whistler waves can be excited in the separatrix region near X-Line and in the outflow region, respectively. Electron whistlers play a crucial role in energy release and transfer, as the small mass of electrons allows them to move rapidly under the perturbation of a magnetic field during magnetic reconnection. The L wave excited near the separatrix region far from X-Line, it propagate obliquely to the local magnetic field. Velocity distribution functions (VDFs) indicate that these waves are associated with temperature anisotropy instabilities of electron-beams (ion-beam). The electron whistler in the separatrix region is excited by cyclotron resonance due to the electron beam. The electron whistler observed in the outflow region is generated by Landau resonance owing to beam-mode, where the v∥ is close to the phase speed vph of the wave. Regarding L wave, their excitation mechanism is attributed to significant perpendicular temperature anisotropy instability (Ti⊥>Ti∥) of ion-beam, and satisfies cyclotron resonance condition. Meanwhile, our simulation results illustrate that the existence of energy conversion between particles and waves during the wave excitation by using the Wave-Particle Interaction Analyzer (WPIA).

Resonant Electron Signatures in the Formation of Chorus Wave Subpackets

AbstractA 2‐D GCPIC simulation in a dipole field system has been conducted to explore the excitation of oblique whistler mode chorus waves driven by energetic electrons with temperature anisotropy. The rising tone chorus waves are initially generated near the magnetic equator, consisting of a series of subpackets, and become oblique during their propagation. It is found that electron holes in the wave phase space, which are formed due to the nonlinear cyclotron resonance, oscillate in size with time during subpacket formation. The associated inhomogeneity factor varies accordingly, giving rise to various frequency chirping in different phases of subpackets. Distinct nongyrotropic electron distributions are detected in both wave gyrophase and stationary gyrophase. Landau resonance is found to coexist with cyclotron resonance. This study provides multidimensional electron distributions involved in subpacket formation, enabling us to comprehensively understand the nonlinear physics in chorus wave evolution.

Electromagnetic Landau Resonance: MMS Observations

AbstractTheoretical analysis has revealed a specific resonance that shares the same condition as Landau resonance, but instead involves wave electromagnetic fields rather than traditionally electrostatic fields. While this resonance, referred to as electromagnetic Landau resonance due to its properties, is considered significant for magnetospheric dynamics, rare reports or evaluations based on observations have been made thus far. Here, we present an event detected by the Magnetospheric Multiscale mission near the dayside magnetopause. During this event, ∼748‐eV protons are observed to be in resonance with a wave. Detailed data analysis demonstrates the resonant velocity closely matches the wave's parallel phase speed, which, combined with the significant work done by wave perpendicular electric field, confirms this interaction as electromagnetic Landau resonance. Further investigation indicates these protons are being secularly accelerated within this resonance. Consequently, our observations provide the first empirical evidence supporting the previously suggested theoretical importance of the electromagnetic Landau resonance.

Evaluation of Particle Scattering by Oxygen Ion Cyclotron Harmonic Waves in the Inner Magnetosphere

AbstractThe scattering of charged particles by oxygen ion cyclotron harmonic (OCH) waves in the inner magnetosphere is investigated by evaluating the relevant quasi‐linear diffusion coefficients. Recent studies demonstrated that OCH waves are oxygen ion Bernstein modes and their complex kinetic dispersion relation has made it challenging to assess their role in scattering charged particles. The present study calculates the quasi‐linear diffusion coefficients for the scattering of electrons and ions by OCH waves using their kinetic dispersion relation. The results show that OCH waves can effectively scatter electrons between ∼100 eV and 100s keV via Landau resonance. They are also capable of heating cold helium and oxygen ions through cyclotron resonances. Specially, it is found that the 4th harmonic of OCH waves can lead to effective heating of helium ions, while oxygen ions would interact more efficiently with lower harmonics of OCH waves.

Modeling the Global Distribution of Chorus Wave Induced Relativistic Microburst Spatial Characteristics

AbstractThe full spatiotemporal distribution of chorus wave‐induced relativistic electron microburst is modeled for chorus waves originated from different L shells and MLTs, based on the newly developed numerical precipitation model (Kang et al., 2022, https://doi.org/10.1029/2022gl100841). The wave‐particle interaction process that induces each microburst is analyzed in detail, and its relation to the chorus wave propagation effects is explained. The global distribution of maximum precipitation fluxes and scale sizes of relativistic microbursts is then obtained by modeling chorus waves at different L‐shells and local times. The characteristics of dawn and midnight sector microbursts have little difference, but the noon sector has much larger maximum flux and much smaller full width at half maximum, which may be due to dayside's low electron flux in the Landau resonance range. This suggests the controlling effect of keV electrons on the MeV electron precipitation intensity and properties and the overall relativistic electron loss in the outer radiation belt.

Nonlinear Landau resonant interaction between whistler waves and electrons: Excitation of electron-acoustic waves

Electron-acoustic waves (EAWs) as well as electron-acoustic solitary structures play a crucial role in thermalization and acceleration of electron populations in Earth's magnetosphere. These waves are often observed in association with whistler-mode waves, but the detailed mechanism of EAW and whistler wave coupling is not yet revealed. We investigate the excitation mechanism of EAWs and their potential relation to whistler waves using particle-in-cell simulations. Whistler waves are first excited by electrons with a temperature anisotropy perpendicular to the background magnetic field. Electrons trapped by these whistler waves through nonlinear Landau resonance form localized field-aligned beams, which subsequently excite EAWs. By comparing the growth rate of EAWs and the phase mixing rate of trapped electron beams, we obtain the critical condition for EAW excitation, which is consistent with our simulation results across a wide region in parameter space. These results are expected to be useful in the interpretation of concurrent observations of whistler-mode waves and nonlinear solitary structures and may also have important implications for investigation of cross-scale energy transfer in the near-Earth space environment.

Excitation characterization of whistler waves and electrostatic oscillation in asymmetric magnetic reconnection

Utilizing the 2.5D Particle-in-Cell (PIC) method, we observe that large-amplitude whistler waves are present near the separatrix on the magnetospheric side and in the outflow region during asymmetric magnetic reconnection. Minimum variance analyses confirm their quasi-parallel and anti-parallel propagation to the background magnetic field, respectively, and their accuracy is validated through parallel Poynting fluxes (S∥). The excited whistler waves have intermittent property due to the evolution and movement of the reconnection layer. Wave-Particle Interaction Analysis (WPIA) reveals a pronounced energy conversion between the waves and electrons. Our simulation results demonstrate that whistler waves near the separatrix are excited by the cyclotron resonance duo to the instability of electron beam by analyzing the electron velocity distribution functions (VDFs). Meanwhile, the electrostatic oscillation is generated by the positive parallel drift of electron beam. However, the whistler waves in the outflow region are excited by the Landau resonance duo to anisotropic instability distributions of electron beam-mode.

Velocity-space Signatures of Resonant Energy Transfer between Whistler Waves and Electrons in the Earth’s Magnetosheath

Wave–particle interactions play a crucial role in transferring energy between electromagnetic fields and charged particles in space and astrophysical plasmas. Despite the prevalence of different electromagnetic waves in space, there is still a lack of understanding of fundamental aspects of wave–particle interactions, particularly in terms of energy flow and velocity-space characteristics. In this study, we combine a novel quasilinear model with observations from the Magnetospheric Multiscale mission to reveal the signatures of resonant interactions between electrons and whistler waves in magnetic holes, which are coherent structures often found in the Earth’s magnetosheath. We investigate the energy transfer rates and velocity-space characteristics associated with Landau and cyclotron resonances between electrons and slightly oblique propagating whistler waves. In the case of our observed magnetic hole, the loss of electron kinetic energy primarily contributes to the growth of whistler waves through the n = −1 cyclotron resonance, where n is the order of the resonance expansion in linear Vlasov–Maxwell theory. The excitation of whistler waves leads to a reduction of the temperature anisotropy and parallel heating of the electrons. Our study offers a new and self-consistent understanding of resonant energy transfer in turbulent plasmas.

Energy Transfer Between Various Electron Populations Via Resonant Interaction With Whistler Mode Wave

AbstractElectron energization in the Earth's radiation belts caused by resonant interaction with whistler mode waves is currently under intense investigation. When the waves are excited due to cyclotron instability in collisionless plasma, that is, when the energy source for the waves is the free energy of unstable electron distribution, particle energization by excited waves is nothing but energy transfer from one group of electrons to another mediated by the waves. An example of such a process is considered in which a quasi‐monochromatic whistler mode wave packet with the frequency and the wave normal angle corresponding to the maximum growth rate is excited at the equator. Since the maximum growth rate corresponds to parallel propagating wave, only the first cyclotron resonance particles play a part in this excitation. While propagating from the equator toward the Earth, the wave normal vector becomes more and more oblique, and all cyclotron resonances, in particular, Landau resonance come into play. Wave‐particle interaction at Landau resonance leads to the wave damping and the corresponding particle energization on the average. Moreover, we show that the mean square variation of resonant particle energy greatly exceeds the average value, thus, the energy increase of some particles is much larger than the Landau resonance particles get from the wave on the average. This means that the exchange of energy between different groups of particles through a wave is a more efficient process than the amplification or damping of a wave due to its resonant interaction with particles.

Electrostatic Waves Around a Magnetopause Reconnection Secondary Electron Diffusion Region Modulated by Whistler and Lower‐Hybrid Waves

AbstractWe investigate electrostatic waves in a magnetopause reconnection event around a secondary electron diffusion region. Near the current sheet mid‐plane, parallel electron beam‐mode waves are modulated by whistler waves. We conclude that the anisotropy of energized electrons in the reconnection exhaust excites whistler waves, which produce spatially modulated electron beams through nonlinear Landau resonance, and these beams excite beam‐mode electrostatic waves. In the separatrix region, parallel propagating electrostatic waves associated with field‐aligned electron beams and perpendicular propagating electron cyclotron harmonic waves with loss cone distributions exhibit modulation frequencies in the lower‐hybrid wave (LHW) frequency range. We infer that LHWs scatter electrons to produce beams and alter loss cones to modulate electrostatic waves. The results advance our understanding about the regimes and mechanisms of electrostatic waves in reconnection, with an emphasis on their coupling with lower‐frequency electromagnetic waves.

Quasilinear theory of Brillouin resonances in rotating magnetized plasmas

Both spin and orbital angular momentum can be exchanged between a rotating wave and a rotating magnetized plasma. Through resonances the spin and orbital angular momentum of the wave can be coupled to both the cyclotron rotation and the drift rotation of the particles. It is, however, shown that the Landau and cyclotron resonance conditions which classically describe resonant energy–momentum exchange between waves and particles are no longer valid in a rotating magnetized plasma column. In this case a new resonance condition which involves a resonant matching between the wave frequency, the cyclotron frequency modified by inertial effects and the harmonics of the guiding centre rotation is identified. A new quasilinear equation describing orbital and spin angular momentum exchanges through these new Brillouin resonances is then derived, and used to expose the wave-driven radial current responsible for angular momentum absorption.

MAS: a versatile Landau-fluid eigenvalue code for plasma stability analysis in general geometry

We have developed a new global eigenvalue code, multiscale analysis for plasma stabilities (MAS), for studying plasma problems with wave toroidal mode number (n) and frequency (ω) in a broad range of interest in general tokamak geometry, based on a five-field Landau-fluid description of thermal plasmas. Beyond keeping the necessary plasma fluid response, we further retain the important kinetic effects including diamagnetic drift, ion finite Larmor radius, finite parallel electric field (), ion and electron Landau resonances in a self-consistent and non-perturbative manner without sacrificing the attractive efficiency in computation. The physical capabilities of the code are evaluated and examined in terms of both theory and simulation. In theory, the comprehensive Landau-fluid model implemented in MAS can be reduced to the well-known ideal magnetohydrodynamic (MHD) model, electrostatic ion-fluid model, and drift-kinetic model in various limits, which clearly delineates the physics validity regime. In simulation, MAS has been well benchmarked with theory and other gyrokinetic and kinetic-MHD hybrid codes in a manner of adopting the unified physical and numerical framework, which covers the kinetic Alfvén wave, ion sound wave, low-n kink, high-n ion temperature gradient mode and kinetic ballooning mode. Moreover, MAS is successfully applied to model the Alfvén eigenmode (AE) activities in DIII-D discharge #159243, which faithfully captures the frequency sweeping of reversed shear AE, the tunneling damping of toroidal AE, as well as the polarization characteristics of kinetic beta-induced AE and beta-induced Alfvén-acoustic eigenmode being consistent with former gyrokinetic theory and simulation. With respect to the key progress contributed to the community, MAS has the advantage of combining rich physics ingredients, realistic global geometry and high computation efficiency together for plasma stability analysis in the linear regime.

Kappa-Distributed Electrons in Solar Outflows: Beam-Plasma Instabilities and Radio Emissions

Electrostatic (ES) wave instabilities are assumed to be at the origin of radio emissions from interplanetary shocks, and solar coronal sources are most likely induced by electron beams, more energetic but less dense than electron strahls in the solar wind. In this paper, we present the results of a new dispersion and stability analysis for electron populations with Kappa velocity distributions, as often indicated by in situ observations. We investigate, both theoretically and numerically, three electron plasma beam configurations with different implications in the generation of radio emissions. The same three cases, but for Maxwellian distributed electrons, were considered in numerical simulations by Thurgood and Tsiklauri (Astronomy and Astrophysics 584:A83, 2015). Our kinetic plasma approach clarifies the nature of the unstable mode as being an electron beam ES instability (and not a Langmuir instability) in all cases, and for both Kappa and Maxwellian approaches. Electron beam waves are Landau resonant and with frequencies of the fastest growing modes close to but below the plasma frequency (i.e., $\omega \lesssim \omega _{pe}$ ). Suprathermal Kappa tails tend to inhibit the instability by reducing the growth rates, but these effects become minor if the drift speed of the beam is sufficiently high compared to the thermal speed of the electrons. The frequency downshift, also revealed by the observations, clearly tends to increase in the presence of a Kappa-distributed beam. Particle-in-cell (PIC) simulations confirm the inhibiting effects of (initially) Kappa-distributed electrons, but these minor effects in the linear and quasi-linear phases unexpectedly lead to significant decreases in the wave energy levels of the (primary) ES fluctuations near the plasma frequency and higher harmonics. As a result, EM radio (secondary) emissions generated nonlinearly after saturation are even more drastically reduced and can even be completely suppressed. However, the EM emissions around the second harmonic ( $\omega \lesssim 2 \, \omega _{pe}$ ) are markedly powered by two symmetric countermoving beams, even in the presence of Kappa electrons. These results offer real promise for a realistic interpretation and modeling of radio emissions observed in heliosphere, arguing in favor of a rigorous spectral analysis of the wave instabilities at their origin.

Unraveling the Role of Electron Plateau Distributions in the Power Gap Formation of Chorus Waves: Van Allen Probes Observations

AbstractThe power gap of chorus waves at ∼0.5fce has been discovered for decades, but its generation mechanism is still under debate. Previous studies have revealed that electron plateau distributions are vitally important for the gap formation. By analyzing over one‐year Van Allen Probes data, we have studied chorus waves with (banded events) and without a power gap (no‐gap events), and their correlations with the electron plateau distribution. Although there is no significant difference in the morphology of velocity distributions in banded and no‐gap events, banded chorus events are typically accompanied by a plateau component with about one order higher number density than no‐gap events. The plateau components can cause severe damping at ∼0.5fce through cyclotron resonance rather than Landau resonance, and the gap frequency is roughly determined by the bulk velocity of plateau components. Our study provides new observational constraints on the generation mechanisms of power gap.