Wave-particle Interaction Processes Research Articles

The Wave Growth, Saturation, and Electron Heating of Lower Hybrid Waves in the Magnetic Reconnection Exhaust

Lower hybrid waves are commonly observed in magnetic reconnection. Based on in situ measurements and the application of an extended quasi-linear model, we investigate the occurrence, saturation, and electron heating of lower hybrid waves in the region of magnetopause reconnection outflows. Lower hybrid waves are statistically favored when the density gradient length scale (L n ) normalized by the ion gyroradius (ρ i ) is small. The occurrence of lower hybrid waves is significantly higher in the regime of L n /ρ i < 1 and plasma beta β < 1. These features of wave occurrence are consistent with the linear theory of the wave growth rate. Evidence indicates that the saturation level and the parallel electron heating of waves both increase as the normalized gradient scale L n /ρ i decreases. The parallel electron temperature increases ∼30%–70% as L n /ρ i < 1. We show that the observation of saturation and electron heating is consistent with an extended quasi-linear model. In this scenario, lower hybrid waves are driven by density gradients and then quickly saturate in tens of ion gyroperiods. The parallel electron heating from lower hybrid waves is achieved through Landau damping before the nonlinear saturation. Our results provide comprehensive evidence for an end-to-end process of electron heating through lower hybrid waves in reconnection exhausts. L n /ρ i is the key parameter that determines the extent of the wave growth, saturation energy, and electron heating in this wave–particle interaction process.

Simulation of Plasma Emission in Magnetized Plasmas

Abstract The recent Parker Solar Probe observations of type III radio bursts show that the effects of the finite background magnetic field can be an important factor in the interpretation of data. In the present paper, the effects of the background magnetic field on the plasma-emission process, which is believed to be the main emission mechanism for solar coronal and interplanetary type III radio bursts, are investigated by means of the particle-in-cell simulation method. The effects of the ambient magnetic field are systematically surveyed by varying the ratio of plasma frequency to electron gyrofrequency. The present study shows that for a sufficiently strong ambient magnetic field, the wave–particle interaction processes lead to a highly field-aligned longitudinal mode excitation and anisotropic electron velocity distribution function, accompanied by a significantly enhanced plasma emission at the second-harmonic plasma frequency. For such a case, the polarization of the harmonic emission is almost entirely in the sense of extraordinary mode. On the other hand, for moderate strengths of the ambient magnetic field, the interpretation of the simulation result is less clear. The underlying nonlinear-mode coupling processes indicate that to properly understand and interpret the simulation results requires sophisticated analyses involving interactions among magnetized plasma normal modes, including the two transverse modes of the magneto-active plasma, namely, the extraordinary and ordinary modes, as well as electron-cyclotron-whistler, plasma oscillation, and upper-hybrid modes. At present, a nonlinear theory suitable for quantitatively analyzing such complex-mode coupling processes in magnetized plasmas is incomplete, which calls for further theoretical research, but the present simulation results could provide a guide for future theoretical efforts.

Proton cyclotron and mirror instabilities in marginally stable solar wind plasma

ABSTRACT This paper formulates a velocity moment-based quasi-linear theory that combines the impacts of weakly unstable proton–cyclotron- (or, equivalently, electromagnetic ion cyclotron) and proton-mirror instabilities on the solar wind plasma initially characterized by an excessive perpendicular proton temperature anisotropy. The present formalism is an alternative to the existing model in that the weakly unstable modes are characterized by analytical formalism that involves the assumption of weak growth rate and/or fluid-theoretical dispersion relation, in place of numerical root-finding method based on the transcendental plasma dispersion function. This results in an efficient numerical platform for analyzing the quasi-linear development of the said instabilities. Such a formalism may be useful in the larger context of global solar wind modelling effort where an efficient calculation of self-consistent wave–particle interaction process is called for. A direct comparison with spacecraft observations of solar wind proton data distribution shows that the present weak growth rate formalism of quasi-linear calculation produces results that are consistent with the observation.

On the Role of Solar Wind Expansion as a Source of Whistler Waves: Scattering of Suprathermal Electrons and Heat Flux Regulation in the Inner Heliosphere

Abstract 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 observations of the Parker Solar Probe during its first perihelion at 0.166 au, consisting of a dense core and an antisunward strahl. This distribution function is initially stable with respect to kinetic instabilities. Expansion drives the solar wind into successive regimes where whistler heat flux instabilities are triggered. These instabilities produce sunward whistler waves initially characterized by predominantly oblique propagation with respect to the interplanetary magnetic field. The excited waves interact with the electrons via resonant scattering processes. As a consequence, the strahl pitch angle distribution broadens and its drift velocity reduces. The strahl electrons are scattered in the direction perpendicular to the magnetic field, and an electron halo is formed. At a later stage, resonant electron firehose instability is triggered and further affects the electron temperature anisotropy as the solar wind expands. Wave–particle interaction processes are accompanied by a substantial reduction of the solar wind heat flux. The simulated whistler waves are in qualitative agreement with observations in terms of wave frequencies, amplitudes, and propagation angles. Our work proposes an explanation for the observations of oblique and parallel whistler waves in the solar wind. We conclude that solar wind expansion has to be factored in when trying to explain kinetic processes at different heliocentric distances.

Phase condensation and evaporation: Another look at wave-particle interactions and Landau damping.

Phase synchronization is a universal concept in macro- and microstate coupling of complex systems. In this Rapid Communication, we demonstrate the existence of phase synchronization dynamics in a wave-particle interaction process under the framework of a Vlasov-Poisson (VP) system. Starting from a random phase setup, it is shown that the phases of the electrons spontaneously develop coherent patterns in its velocity space. The most interesting finding is that, mediated by the long-wavelength electrostatic mode, the phases of the electrons tend to attract each other, condense into a mean phase, and form a chimera pattern. Due to the finite-time singularity of the mean phase, the phase pattern gets evaporated and recondenses into a different chimera pattern. For the scenario of a finite wavelength, the random phases rapidly condense to slashing lines, which become steeper and steeper through a sequence of evaporation-condensation processes. The slashing pattern drives the mixing of the distribution function in the velocity space, which then induces the damping of the electrostatic mode. This phase self-organization dynamics uncovers another aspect of wave-particle interaction physics, and sheds light onto the longstanding enigma of Landau damping.

Estimation of Growth Rate of Electromagnetic Plasma Wave through Vlasov-Maxwell Mathematical Frame in Ionospheric Plasma

Unique forms of nonlinear wave energy exchange phenomena are observed in the Earth’sionosphere region. Energy upconversion of nonresonant plasma waves in the top ionospheric and auroral zone are noticed.Origin of these phenomena are tried to explained by linear andnonlinear theoretical approach.Wave-wave and wave-particle-wave interaction processes may be possible role takes place here.In this theoretical investigation we wish to derive probable growthrate expression of high frequency electromagnetic O-mode wave in the presence of low frequency electrostatic ion sound wave through wave-particle interaction process known as plasma maserinstability and estimate its value by using observational data.

Simulation of high-efficiency gyrotron with the system of multistage energy recovery

The results of simulations of helical electron beam formation and collecting, as well as high frequency wave-particle interaction processes, in the moderate-power experimental gyrotron with the frequency of 74.2 GHz are presented. Various methods of beam quality and electron efficiency improvement via optimization of electric and magnetic field distributions in the cathode region were realized. In the optimal operating regime with high pitch ratio and low velocity spread, the electron efficiency of about 46 % was calculated for the gyrotron with the magnetron injection gun including a control electrode and a cathode with sectioned emission. In the gyrotron collector region, a system of 4-stage electron energy recovery was used for enhancement of total efficiency of the device. By improving the quality of the electron beam and efficient energy recovery in the collector region, the total efficiency of the gyrotron equal to 71.8% was achieved.

Reply to 'The dynamics of Van Allen belts revisited'

It is well-known that there are many wave-particle interaction processes which have the potential to affect the dynamics of the radiation belts [see e.g., the review by Mauk et al., 2013]. The issue that has continued to obstruct significant advances in our understanding of the radiation belts to the point of predictability is our ability to represent the nature of the magnetospheric processes controlling belt dynamics with sufficient accuracy to establish which dominate. In relation to the case examined here it is to determine which process or processes can act to create a third Van Allen radiation belt morphology in September 2012 as reported by Baker et al., (2013). As described in the main text of our Reply, and further expanded upon in the Supplementary Material presented here, we show that the original conclusion from Mann et al. (2016) remains valid. That is, a remnant belt and the third radiation belt morphology which arises following a subsequent flux recovery at higher L-shells, can be explained by the action of very fast outwards ULF wave radial diffusion associated with magnetopause shadowing. Contrary to the claims of the Comment by Shprits et al. (2017; hereafter S17), and the conclusions of modelling by Shprits et al. (2013; hereafter S13), the action of EMIC waves is not required.

Kinetic instabilities in a mirror-confined plasma sustained by high-power microwave radiation

This paper summarizes the studies of plasma kinetic instabilities in the electron cyclotron frequency range carried out over the last decade at the Institute of Applied Physics in Nizhny Novgorod. We investigate the nonequilibrium plasma created and sustained by high-power microwave radiation of a gyrotron under the electron cyclotron resonance condition. Resonant plasma heating results in the formation of at least two electron components, one of which, more dense and cold, determines the dispersion properties of the high-frequency waves, and the other, a small group of energetic electrons with a highly anisotropic velocity distribution, is responsible for the excitation of unstable waves. Dynamic spectra and the intensity of stimulated electromagnetic emission are studied with high temporal resolution. Interpretation of observed data is based on the cyclotron maser paradigm; in this context, a laboratory modeling of non-stationary wave-particle interaction processes has much in common with similar processes occurring in the magnetosphere of Earth, planets, and solar coronal loops.

Transverse eV ion heating by random electric field fluctuations in the plasmasphere

Charged particle acceleration in the Earth inner magnetosphere is believed to be mainly due to the local resonant wave-particle interaction or particle transport processes. However, the Van Allen Probes have recently provided interesting evidence of a relatively slow transverse heating of eV ions at distances about 2–3 Earth radii during quiet times. Waves that are able to resonantly interact with such very cold ions are generally rare in this region of space, called the plasmasphere. Thus, non-resonant wave-particle interactions are expected to play an important role in the observed ion heating. We demonstrate that stochastic heating by random transverse electric field fluctuations of whistler (and possibly electromagnetic ion cyclotron) waves could explain this weak and slow transverse heating of H+ and O+ ions in the inner magnetosphere. The essential element of the proposed model of ion heating is the presence of trains of random whistler (hiss) wave packets, with significant amplitude modulations produced by strong wave damping, rapid wave growth, or a superposition of wave packets of different frequencies, phases, and amplitudes. Such characteristics correspond to measured characteristics of hiss waves in this region. Using test particle simulations with typical wave and plasma parameters, we demonstrate that the corresponding stochastic transverse ion heating reaches 0.07–0.2 eV/h for protons and 0.007–0.015 eV/h for O+ ions. This global temperature increase of the Maxwellian ion population from an initial Ti∼0.3 eV could potentially explain the observations.

Inferring electromagnetic ion cyclotron wave intensity from low altitude POES proton flux measurements: A detailed case study with conjugate Van Allen Probes observations

Electromagnetic ion cyclotron (EMIC) waves play an important role in the magnetospheric particle dynamics and can lead to resonant pitch-angle scattering and ultimate precipitation of ring current protons. Commonly, the statistics of in situ EMIC wave measurements is adopted for quantitative investigation of wave-particle interaction processes, which however becomes questionable for detailed case studies especially during geomagnetic storms and substorms. Here we establish a novel technique to infer EMIC wave amplitudes from low-altitude proton measurements onboard the Polar Operational Environmental Satellites (POES). The detailed procedure is elaborated regarding how to infer the EMIC wave intensity for one specific time point. We then test the technique with a case study comparing the inferred root-mean-square (RMS) EMIC wave amplitude with the conjugate Van Allen Probes EMFISIS wave measurements. Our results suggest that the developed technique can reasonably estimate EMIC wave intensities from low-altitude POES proton flux data, thereby providing a useful tool to construct a data-based, near-real-time, dynamic model of the global distribution of EMIC waves once the proton flux measurements from multiple POES satellites are available for any specific time period.

Resonant scattering of energetic electrons in the outer radiation belt by HAARP-induced ELF/VLF waves

Several extremely low-frequency (ELF)/very low-frequency (VLF) wave generation experiments have been performed successfully at High-Frequency Active Auroral Research Program (HAARP) heating facility and the artificial ELF/VLF signals can leak into the outer radiation belt and contribute to resonant interactions with energetic electrons. Based on the artificial wave properties revealed by many of in situ observations, we implement test particle simulations to evaluate the effects of energetic electron resonant scattering driven by the HAARP-induced ELF/VLF waves. The results indicate that for both single-frequency/monotonic wave and multi-frequency/broadband waves, the behavior of each electron is stochastic while the averaged diffusion effect exhibits temporal linearity in the wave–particle interaction process. The computed local diffusion coefficients show that, the local pitch-angle scattering due to HARRP-induced single-frequency ELF/VLF whistlers with an amplitude of ∼10pT can be intense near the loss cone with a rate of ∼10−2 rad2 s−1, suggesting the feasibility of HAARP-induced ELF/VLF waves for removal of outer radiation belt energetic electrons. In contrast, the energy diffusion of energetic electrons is relatively weak, which confirms that pitch-angle scattering by artificial ELF/VLF waves can dominantly lead to the precipitation of energetic electrons. Moreover, diffusion rates of the discrete, broadband waves, with the same amplitude of each discrete frequency as the monotonic waves, can be much larger, which suggests that it is feasible to trigger a reasonable broadband wave instead of the monotonic wave to achieve better performance of controlled precipitation of energetic electrons. Moreover, our test particle scattering simulation show good agreement with the predictions of the quasi-linear theory, confirming that both methods are applied to evaluate the effects of resonant interactions between radiation belt electrons and artificially generated discrete ELF/VLF waves.

Two dimensional kinetic analysis of electrostatic harmonic plasma waves

Electrostatic harmonic Langmuir waves are virtual modes excited in weakly turbulent plasmas, first observed in early laboratory beam-plasma experiments as well as in rocket-borne active experiments in space. However, their unequivocal presence was confirmed through computer simulated experiments and subsequently theoretically explained. The peculiarity of harmonic Langmuir waves is that while their existence requires nonlinear response, their excitation mechanism and subsequent early time evolution are governed by essentially linear process. One of the unresolved theoretical issues regards the role of nonlinear wave-particle interaction process over longer evolution time period. Another outstanding issue is that existing theories for these modes are limited to one-dimensional space. The present paper carries out two dimensional theoretical analysis of fundamental and (first) harmonic Langmuir waves for the first time. The result shows that harmonic Langmuir wave is essentially governed by (quasi)linear process and that nonlinear wave-particle interaction plays no significant role in the time evolution of the wave spectrum. The numerical solutions of the two-dimensional wave spectra for fundamental and harmonic Langmuir waves are also found to be consistent with those obtained by direct particle-in-cell simulation method reported in the literature.

Two-dimensional time evolution of beam-plasma instability in the presence of binary collisions

Energetic electrons produced during solar flares are known to be responsible for generating solar type III radio bursts. The radio emission is a byproduct of Langmuir wave generation via beam-plasma interaction and nonlinear wave-wave and wave-particle interaction processes. In addition to type III radio bursts, electrons traveling downwards toward the chromosphere lead to the hard X-ray emission via electron-ion collisions. Recently, the role of Langmuir waves on the X-ray-producing electrons has been identified as important, because Langmuir waves may alter the electron distribution, thereby affecting the X-ray profile. Both Coulomb collisions and wave-particle interactions lead electrons to scattering and energy exchange that necessitates considering the two-dimensional (2D) problem in velocity space. The present paper investigates the influence of binary collisions on the beam-plasma instability development in 2D in order to elucidate the nonlinear dynamics of Langmuir waves and binary collisions. The significance of the present findings in the context of solar physics is discussed.

Laboratory study of kinetic instabilities in a nonequilibrium mirror-confined plasma

Kinetic instabilities of nonequilibrium plasma heated by powerful radiation of gyrotron in electron cyclotron resonance conditions and confined in a mirror magnetic trap are reported. Instabilities are manifested as the generation of short pulses of electromagnetic radiation accompanied by precipitation of hot electrons from magnetic trap. Measuring electromagnetic field with high temporal resolution allowed to observe various dynamic spectra of electromagnetic radiation related to at least five types of kinetic instabilities. This paper may be of interest in the context of a laboratory modeling of nonstationary wave-particle interaction processes in nonequilibrium space plasma since the observed phenomena have much in common with similar processes occurring in the magnetosphere of the Earth, planets, and in solar coronal loops.

EVIDENCE OF LANDAU AND CYCLOTRON RESONANCE BETWEEN PROTONS AND KINETIC WAVES IN SOLAR WIND TURBULENCE

The wave–particle interaction processes occurring in the solar wind provide crucial information to understand the wave dissipation and simultaneous particle heating in plasma turbulence. One requires observations of both wave fluctuations and particle kinetics near the dissipation range, which have, however, not yet been analyzed simultaneously. Here we show new evidence of wave–particle interactions by combining the diagnosis of wave modes with the analysis of particle kinetics on the basis of measurements from the WIND spacecraft with a high cadence of about 3 s. Solar wind protons appear to be highly dynamic in their velocity distribution consisting of varying anisotropic core and beam components. The basic scenario of solar wind proton heating through wave–particle interaction is suggested to be the following. Left-handed cyclotron resonance occurs continuously, and is evident from the observed proton core velocity distribution and the concurrent quasi-parallel left-handed Alfven cyclotron waves. Landau and right-handed cyclotron resonances are persistent and indicated by the observed drifting anisotropic beam and the simultaneous quasi-perpendicular right-handed kinetic Alfven waves in a general sense. The persistence of non-gyrotropic proton distributions may cast new light on the nature of the interaction between particles and waves near and beyond the proton gyro-frequency.

Hamiltonian models for resonant wave-particle interaction processes in magnetized and inhomogeneous plasmas

The kinetic theory of plasmas, based on the Vlasov-Poisson system of equations, can efficiently solve only some aspects of the extremely large panel of problems involving wave-particle and wave-wave interaction processes in plasmas. Therefore the dynamics of charged particles and waves has been modeled by other approaches as, for example, Hamiltonian models describing the self-consistent wave-particle and wave-wave interactions in homogeneous or inhomogeneous magnetized plasmas. Various physical problems could be efficiently studied by such methods, concerning nonlinear and turbulent stages of different instabilities of electron or ion distributions, wave packets’ saturation and particles fluxes’ relaxation processes, particle trapping and detrapping mechanisms by waves, wave-particle interactions at multiple resonances, quasilinear diffusion processes of particles in waves, wave turbulence in randomly inhomogeneous plasmas, acceleration of particles, wave focusing, scattering, reflection and decay, etc. In particular, the aim of the paper, after a brief description of such Hamiltonian models, is to present the most recent simulation results obtained when studying Langmuir turbulence in the presence of electron beams propagating in inhomogeneous plasmas as the solar wind, where random density fluctuations with average levels up to several percents of the background plasma density have been measured.

Vlasov simulations of kinetic Alfvén waves at proton kinetic scales

Kinetic Alfvén waves represent an important subject in space plasma physics, since they are thought to play a crucial role in the development of the turbulent energy cascade in the solar wind plasma at short wavelengths (of the order of the proton gyro radius ρp and/or inertial length dp and beyond). A full understanding of the physical mechanisms which govern the kinetic plasma dynamics at these scales can provide important clues on the problem of the turbulent dissipation and heating in collisionless systems. In this paper, hybrid Vlasov-Maxwell simulations are employed to analyze in detail the features of the kinetic Alfvén waves at proton kinetic scales, in typical conditions of the solar wind environment (proton plasma beta βp = 1). In particular, linear and nonlinear regimes of propagation of these fluctuations have been investigated in a single-wave situation, focusing on the physical processes of collisionless Landau damping and wave-particle resonant interaction. Interestingly, since for wavelengths close to dp and βp ≃ 1 (for which ρp ≃ dp) the kinetic Alfvén waves have small phase speed compared to the proton thermal velocity, wave-particle interaction processes produce significant deformations in the core of the particle velocity distribution, appearing as phase space vortices and resulting in flat-top velocity profiles. Moreover, as the Eulerian hybrid Vlasov-Maxwell algorithm allows for a clean almost noise-free description of the velocity space, three-dimensional plots of the proton velocity distribution help to emphasize how the plasma departs from the Maxwellian configuration of thermodynamic equilibrium due to nonlinear kinetic effects.

Latitudinal dependence of nonlinear interaction between electromagnetic ion cyclotron wave and terrestrial ring current ions

Electromagnetic ion cyclotron (EMIC) waves can lead to the rapid decay (on a timescale of hours) of the terrestrial ring current. Such decay process is usually investigated in the framework of quasi-linear theory. Here, both theoretical analysis and test-particle simulation are performed to understand the nonlinear interaction between ring current ions and EMIC waves. In particular, the dependence of the nonlinear wave-particle interaction processes on the ion initial latitude is investigated in detail. These nonlinear processes are classified into the phase trapping and phase bunching, and the phase bunching is further divided into the channel and cluster effects. Compared to the prediction of the quasi-linear theory, the ring current decay rate can be reduced by the phase trapping, increased by the channel effect phase bunching, but non-deterministically influenced by the cluster effect phase bunching. The ion initial latitude changes the occurrence of the phase trapping, modulates the transport direction and strength of the cluster effect phase bunching, and only slightly affects the channel effect phase bunching. The current results suggest that the latitudinal dependence of these nonlinear processes should be considered in the evaluation of the ring current decay induced by EMIC waves.

Electrostatic instability in magnetically confined inhomogeneous plasma driven by nonlinear force

Abstract A theoretical investigation on amplification of electrostatic ion acoustic wave in magnetically confined plasma has been presented in this paper. This investigation considers nonlinear wave–particle interaction process, called plasma maser effect, in presence of drift wave turbulence supported by magnetically confined inhomogeneous plasma. The role of associated nonlinear dissipative force in this effect in a confined plasma has been analyzed. The nonlinear force, which arises as a result of resonant interaction between electrons and modulated fields, is shown to drive the instability. Using the ion fluid equation and the ion equation of continuity, the nonlinear dispersion relation of a test ion acoustic wave has been derived, and the growth rate of ion acoustic wave in presence of low frequency drift wave turbulence has been estimated using Helimak data.