Electromagnetic Electron Cyclotron Research Articles

Electromagnetic ion cyclotron emission from ion-scale magnetic holes

Ion-scale magnetic holes are nonlinear plasma structures commonly observed in the solar wind and Earth's magnetosphere. These holes are characterized by the magnetic field depletion filled by hot, transversely anisotropic ions and electrons and are likely formed during the nonlinear stage of ion mirror instability. Due to the plasma thermal anisotropy within magnetic holes, they serve as a host of electromagnetic ion cyclotron waves, whistler-mode waves, and electron cyclotron harmonic waves. This makes magnetic holes an important element of the Earth's inner magnetosphere, where electromagnetic waves generated within may strongly contribute to energetic ion and electron scattering. Such scattering, however, will modify the hot-ion distribution that is trapped within magnetic holes and responsible for the magnetic field stress balance. Therefore, hot ion scattering within magnetic holes likely determines the hole lifetime. In this study, we investigate how ion scattering by electromagnetic waves affects the stress balance and lifetime of magnetic holes. For illustration, we used typical characteristics of magnetic holes, ion populations, and ion cyclotron waves observed in the Earth's magnetosphere. We have demonstrated that ion distribution isotropization via scattering by waves does not change significantly magnetic hole magnitude, but ion losses due to scattering into the atmosphere may limit the hole life-times to 10–30 min in the Earth's inner magnetosphere.

Exact numerical analysis of EMEC mode instability in more realistic Cairns distributed non-thermal plasmas

Non-thermal plasma systems beyond the state of thermal equilibrium must have non-thermality dependent effective temperatures. These particle populations cannot have Maxwellian temperatures T∥,⊥e(M) which are typically considered at thermal equilibrium in the context of Maxwellian plasmas. Previously, in such dilute environments, numerous non-thermal distributions incorporating the concept of Maxwellian temperature T∥,⊥e(M) have been utilized, one of them is Cairns distribution (here termed as type-A). To ameliorate this inconsistency, we propose a more realistic form of Cairns distribution (type-B) with the vigorous definition of effective temperature and effective thermal velocity. Both Cairns distributions (A and B) are utilized to calculate the transverse dielectric response function (TDERF) of electromagnetic electron cyclotron (EMEC) mode. The exact numerical solution of TDERFs of EMEC instability reveals interesting and more promising repercussions in the case of Cairns-B i.e. an augmentation in the behavior of oscillatory and imaginary frequencies of the instability.

Wave Emission of Nonthermal Electron Beams Generated by Magnetic Reconnection

Magnetic reconnection in solar flares can efficiently generate nonthermal electron beams. The energetic electrons can, in turn, cause radio waves through microscopic plasma instabilities as they propagate through the ambient plasma along the magnetic field lines. We aim at investigating the wave emission caused by fast-moving electron beams with characteristic nonthermal electron velocity distribution functions (EVDFs) generated by kinetic magnetic reconnection: two-stream EVDFs along the separatrices and in the diffusion region, and perpendicular crescent-shaped EVDFs closer to the diffusion region. For this purpose, we utilized 2.5D fully kinetic Particle-In-Cell code simulations in this study. We found the following: (1) the two-stream EVDFs plus the background ions are unstable to electron/ion (streaming) instabilities, which cause ion-acoustic waves and Langmuir waves due to the net current. This can lead to multiple-harmonic plasma emission in the diffusion region and the separatrices of reconnection. (2) The perpendicular crescent-shaped EVDFs can cause multiple-harmonic electromagnetic electron cyclotron waves through the electron cyclotron maser instabilities in the diffusion region of reconnection. Our results are applicable to diagnose the plasma parameters, which are associated to magnetic reconnection in solar flares by means of radio wave observations.

Electromagnetic Electron-Cyclotron Wave for Ring Distribution with Alternating Current (AC) Electric Field in Saturn Magnetosphere

During their respective missions, the spacecraft Voyager and Cassini measured several Saturn magnetosphere parameters at different radial distances. As a result of information gathered throughout the journey, Voyager 1 discovered hot and cold electron distribution components, number density, and energy in the 6–18 Rs range. Observations made by Voyager of intensity fluctuations in the 20–30 keV range show electrons are situated in the resonance spectrum’s high energy tail. Plasma waves in the magnetosphere can be used to locate Saturn’s inner magnetosphere’s plasma clusters, which are controlled by Saturn’s spin. Electromagnetic electron cyclotron (EMEC) wave ring distribution function has been investigated. Kinetic and linear approaches have been used to study electromagnetic cyclotron (EMEC) wave propagation. EMEC waves’ stability can be assessed by analyzing the dispersion relation’s effect on the ring distribution function. The primary goal of this study is to determine the impact of the magnetosphere parameters which is observed by Cassini. The magnetosphere of Saturn has also been observed. When the plasma parameters are increased as the distribution index, the growth/damping rate increases until the magnetic field model affects the magnetic field at equator, as can be seen in the graphs. We discuss the outputs of our model in the context of measurements made in situ by the Cassini spacecraft.

Electron mirror and cyclotron instabilities for solar wind plasma

ABSTRACT The solar wind plasma is characterized by unequal effective kinetic temperatures defined in perpendicular and parallel directions with respect to the ambient magnetic field. For electrons, the excessive perpendicular temperature anisotropy leads to quasi-parallel electromagnetic electron cyclotron (or whistler) instability and aperiodic electron-mirror instability with oblique wave vectors. The present paper carries out a direct side-by-side comparison of quasi-linear (QL) theory and particle-in-cell (PIC) simulation of combined mirror and cyclotron instabilities acting upon the initially anisotropic electron temperatures, and find that the QL theory satisfactorily encapsulates the non-linear aspect of the combined instability effects. However, a discrepancy between the present study and a previous PIC simulation result is also found, which points to the need for further investigation to resolve such an issue.

Relativistic study of electromagnetic electron cyclotron instability based on trapped electrons in kappa‐Maxwellian auroral plasmas

AbstractThe presence of relativistic electrons in the Earth's magnetosphere may excite EMEC waves via resonant interaction. The understanding of EMEC waves induced by such electrons requires relativistic treatment. Therefore, we present here the investigation of EMEC waves based on relativistic trapped electrons represented by kappa‐Maxwellian distribution in auroral plasmas. The analytical expressions of real frequency and relativistic growth rate are derived. Our numerical outcomes report that relativistic approximation increases the wave growth and causes reduction in the threshold value of drift velocity of trapped electrons for instability. The wave frequency that corresponds to the maximum growth decreases as we go from nonrelativistic limit to relativistic. The maximum growth increases with the increment in plasma frequency, perpendicular thermal velocity, drift velocity of trapped electrons, and Lorentz factor γ. Moreover, the relativistic effects on maximum growth are more pronounced for smaller values of drift velocity and perpendicular thermal velocity.

Interplay of parallel electric field and trapped electrons in kappa-Maxwellian auroral plasma for EMEC instability

In this paper, propagation characteristics of electromagnetic electron cyclotron (EMEC) waves based on kappa-Maxwellian distribution have been investigated to invoke the interplay of the electric field parallel to the Earth’s magnetic field and auroral trapped electrons. The dispersion relation for EMEC waves in kappa-Maxwellian distributed plasma has been derived using the contribution of the parallel electric field and trapped electron speed. Numerical results show that the presence of the electric field has a stimulating effect on growth rate, which is more pronounced at low values of wave number. It is also observed that as the threshold value of trapped electron speed is surpassed, it dominates the effect of the parallel electric field and EMEC instability is enhanced significantly. The electric field acts as another source of free energy, and growth can be obtained even in the absence of trapped electron drift speed and for very small values of temperature anisotropy. Thus the present study reveals the interplay of the parallel electric field and trapped electron speed on the excitation of EMEC waves in the auroral region.

Toward a general quasi-linear approach for the instabilities of bi-Kappa plasmas. Whistler instability

Kappa distributions are ubiquitous in space and astrophysical poorly collisional plasmas, such as the solar wind, suggesting that microscopic and macroscopic properties of these non-equilibrium plasmas are highly conditioned by the wave–particle interactions. The present work addresses the evolution of anisotropic bi-Kappa (or bi-κ-)distributions of electrons triggering instabilities of electromagnetic electron-cyclotron (or whistler) modes. The new quasi-linear approach proposed here includes time variations of the κ parameter during the relaxation of temperature anisotropy. Numerical results show that κ may increase for short interval of times at the beginning, but then decreases toward a value lower than the initial one, while the plasma beta and temperature anisotropy indicate a systematic relaxation. Our results suggest that the electromagnetic turbulence plays an important role on the suprathermalization of the plasma, ultimately lowering the parameter κ. Even though the variation of κ is in general negative () this variation seems to depend of the initial conditions of anisotropic electrons, which can vary very much in the inner heliosphere.

Electron Temperature Anisotropy and Electron Beam Constraints from Electron Kinetic Instabilities in the Solar Wind

Abstract Electron temperature anisotropies and electron beams are nonthermal features of the observed nonequilibrium electron velocity distributions in the solar wind. In collision-poor plasmas these nonequilibrium distributions are expected to be regulated by kinetic instabilities through wave–particle interactions. This study considers electron instabilities driven by the interplay of core electron temperature anisotropies and the electron beam, and first gives a comprehensive analysis of instabilities in arbitrary directions to the background magnetic field. It clarifies the dominant parameter regime (e.g., parallel core electron plasma beta , core electron temperature anisotropy , and electron beam velocity V eb) for each kind of electron instability (e.g., the electron beam-driven electron acoustic/magnetoacoustic instability, the electron beam-driven whistler instability, the electromagnetic electron cyclotron instability, the electron mirror instability, the electron firehose instability, and the ordinary-mode instability). It finds that the electron beam can destabilize electron acoustic/magnetoacoustic waves in the low- regime, and whistler waves in the medium- and large- regime. It also finds that a new oblique fast-magnetosonic/whistler instability is driven by the electron beam with in a regime where and A ec < 1. Moreover, this study presents electromagnetic responses of each kind of electron instability. These results provide a comprehensive overview for electron instability constraints on core electron temperature anisotropies and electron beams in the solar wind.

Linear dispersion theory of parallel electromagnetic modes for regularized Kappa-distributions

The velocity particle distributions measured in situ in space plasmas deviate from Maxwellian (thermal) equilibrium, showing enhanced suprathermal tails that are well described by the standard Kappa-distribution (SKD). Despite its successful application, the SKD is frequently disputed due to a series of unphysical implications such as diverging velocity moments, preventing a macroscopic description of the plasma. The regularized Kappa-distribution (RKD) has been introduced to overcome these limitations, but the dispersion properties of RKD-plasmas have not yet been explored. In the present paper, we compute the wavenumber dispersion of the frequency and damping or growth rates for the electromagnetic modes in plasmas characterized by the RKD. This task is accomplished by using the grid-based kinetic dispersion solver LEOPARD (“Linear Electromagnetic Oscillations in Plasmas with Arbitrary Rotationally symmetric Distributions”) developed for arbitrary gyrotropic distributions [P. Astfalk and F. Jenko, J. Geophys. Res. 122, 89 (2017)]. By reproducing previous results obtained for the SKD and Maxwellian, we validate the functionality of the code. Furthermore, we apply the isotropic and anisotropic RKDs to investigate stable electromagnetic electron-cyclotron (EMEC) and ion-cyclotron (EMIC) modes, as well as temperature-anisotropy-driven instabilities, for both T⊥/T∥>1 (EMEC and EMIC instabilities) and T⊥/T∥<1 cases (proton and electron firehose instabilities), where ∥ and ⊥ denote directions parallel and perpendicular to the local time-averaged magnetic field. Provided that the cutoff parameter α is small enough, the results show that the RKDs reproduce the dispersion curves of the SKD plasmas at both qualitative and quantitative levels. For higher values, however, a physically significant deviation occurs.

EMEC instability based on kappa-Maxwellian distributed trapped electrons in auroral plasma

In space plasmas, particle distributions are often observed having high energy tails and are well fitted by kappa distribution function. However, in auroral region electrons are expected to be accelerated mainly along the magnetic field lines and one may expect Maxwellian behaviour in perpendicular direction. Therefore, in the present study propagation characteristics of electromagnetic electron cyclotron (EMEC) waves is studied by employing kappa-Maxwellian distribution function for energetic trapped electrons in auroral region. Real frequency and the growth rate expressions have been solved numerically for kappa-Maxwellian plasma and then analyzed by considering the effect of different plasma parameters for wide range of auroral altitudes. The numerical results obtained show that growth rate increases with the increase in ratio \({\omega_{pe}} / {\varOmega_{e}}\), plasma beta, temperature anisotropy \({T_{\bot}} / {T_{\parallel}}\) and trapped electron drift speed but decreases when superthermal electron population increases.

Study of Electromagnetic Electron Cyclotron Waves for Kappa Distribution with AC Field in the Magnetosphere of Saturn

Parallel propagating electromagnetic electron cyclotron (EMEC) waves in the extended plasma sheet (~12RS) and in the outer magnetosphere (~18RS) of Saturn have been studied. A dispersion relation for parallel propagating relativistic EMEC waves has been applied to the magnetosphere of Saturn, and comparisons have been made with the data of Voyager 1 at these radial distances. The detailed investigations for EMEC waves have been done in the presence of the perpendicular AC electric field, using the kappa distribution function. The relativistic temporal growth rate is calculated by the method of characteristic solution with the data provided by Voyager 1. The effect of the suprathermal electron density, temperature anisotropy, frequency of AC electric field, thermal energy of ions, and relativistic factor on the temporal growth rate of EMEC wave emission has been studied. The simulation results show that the growth of parallel propagating EMEC waves is significantly affected by variations in the temperature anisotropy, electron density, ion thermal energy, and relativistic factor in both the extended plasma sheet and the outer magnetosphere of Saturn. The temperature anisotropy (T⊥/T║), ion thermal energy (KBT║i), and electron density (n0) have been found to be a major source of free energy for parallel propagating EMEC waves in both regions.

Simulation and Quasi‐Linear Theory of Whistler Anisotropy Instability

AbstractThe whistler anisotropy (or electromagnetic electron cyclotron) instability may be operative in many geomagnetic and heliospherical environments, including the radiation belt, solar wind, and the solar corona. The present investigation carries out a comparative analysis between the two‐dimensional particle‐in‐cell simulation of weakly growing whistler anisotropy instability and the velocity moment‐based two‐dimensional quasi‐linear theory under the assumption of bi‐Maxwellian electron distribution function. It is shown that the simplified quasi‐linear theory provides a qualitative agreement with the more rigorous particle‐in‐cell simulation, but some discrepancies are also found. Possible causes for the differences in either method are discussed, and future improvements on the theory are suggested. Potential applicability of the present finding in the context of the space and astrophysics is discussed.

Electromagnetic Electron Cyclotron Instability in the Solar Wind

AbstractThe abundant reports on the existence of electromagnetic high‐frequency fluctuations in space plasmas have increased the expectations that theoretical modeling may help understand their origins and implications (e.g., kinetic instabilities and dissipation). This paper presents an extended quasi‐linear approach of the electromagnetic electron cyclotron instability in conditions typical for the solar wind, where the anisotropic electrons (T⊥>T∥) exhibit a dual distribution combining a bi‐Maxwellian core and bi‐Kappa halo. Involving both the core and halo populations, the instability is triggered by the cumulative effects of these components, mainly depending of their anisotropies. The instability is not very sensitive to the shape of halo distribution function conditioned in this case by the power index κ. This result seems to be a direct consequence of the low density of electron halo, which is assumed more dilute than the core component in conformity with the observations in the ecliptic. Quasi‐linear time evolutions predicted by the theory are confirmed by the particle‐in‐cell simulations, which also suggest possible explanations for the inherent differences determined by theoretical constraints. These results provide premises for an advanced methodology to characterize, realistically, the electromagnetic electron cyclotron instability and its implication in the solar wind.

Study of Electron Beam on Electron Cyclotron Waves with AC Field in the Magnetosphere of Uranus

In this paper, we investigate the electromagnetic electron cyclotron (EMEC) waves in the magnetosphere of Uranus. By using the method of characteristic solution, the expression for dispersion relation is drawn. Following kinetic approach, the growth rate and real frequency of EMEC waves is studied theoretically, considering the injection of cold plasma beam in the Uranian system. The observations made by a space probe launched by NASA, Voyager 2, showed unusual orientation of planet’s spin axis and presence of more particles in high energy tail in Uranian magnetospheric plasma. Therefore, in this paper Kappa distribution is employed instead of usual Maxwellian distribution. The study is extended to the parallel as well as the oblique propagation of EMEC waves with variation in temperature anisotropy, number density of electrons and angle of propagation with respect to magnetic field direction. It is found that these parameters support the growth rate of EMEC waves. But response of real frequency of these waves is not same as that of growth rate for all the cases. Numerical analysis also revealed that as the ratio of number density of cold to hot plasma increases growth rate of EMEC waves also increases. Thus, denser the beam is injected, more the growth can be observed. These results are appropriate for applications to space plasma environments and magnetospheric regimes for detailed comparative planetary study.

Electron temperature anisotropy regulation by whistler instability

AbstractThe solar wind electron temperature anisotropy is regulated by a number of physical processes, which include adiabatic expansion, electron Coulomb collisions, and microinstabilities. In the collisionless limit, the measured electron temperature anisotropy is constrained by the marginal threshold conditions for whistler (electromagnetic electron cyclotron or EMEC) and firehose instabilities, which are excited by excessive perpendicular and parallel temperature anisotropies, respectively. In the literature, these thresholds are expressed as inverse relationships between the electron temperature ratio and parallel beta, which are constructed on the basis of linear stability analysis and empirical fitting. In the present paper, macroscopic quasi‐linear kinetic theory of whistler (or EMEC) instability is employed in order to investigate the time development of the instability. One‐dimensional particle‐in‐cell (PIC) simulation is also carried out, and it is found that PIC simulation confirms the validity of the macroscopic quasi‐linear approach. It is also found that the saturation stage of the instability naturally corresponds to the threshold condition, thus confirming the inverse relationship. The present finding shows that the macroscopic quasi‐linear kinetic theory may be a valid theoretical tool for dynamical description of the solar wind.

Towards realistic characterization of the solar wind suprathermal populations and their effects

This Brief Communication presents a straightforward analytical method for estimating the effects of suprathermal particle populations present in space plasmas, based on a refined Kappa modelling of the velocity distributions which enables comparison with the thermal (core) component. If the observed distribution with suprathermal tails can be reproduced by a Kappa power-law, the core is extracted as a particular Maxwellian limit which needs to be cooler and contain a less number of particles. This approach enables study of the kinetic instabilities driven by anisotropic bi-Kappa distributions, among other applications. Thus, the electromagnetic electron cyclotron instability is found to be stimulated by the suprathermal electrons, confirming the existence of an additional free energy in these populations. Limiting to a standard Maxwellian modelling, as was and still is customary for the analysis of distributions observed in the solar wind, may therefore lead to misleading interpretations of these instabilities and other kinetic effects involving suprathermal populations.

Characteristics of heat flux and electromagnetic electron-cyclotron instabilities driven by solar wind electrons

Characteristics of heat flux and electromagnetic electron-cyclotron instabilities driven by solar wind electrons

Macroscopic quasi‐linear theory of electromagnetic electron cyclotron instability associated with core and halo solar wind electrons

AbstractSpacecraft observations made near 1 AU show that both core and halo solar wind electrons exhibit temperature anisotropies that appear to be regulated by marginal electromagnetic electron cyclotron instability condition. In the literature, the threshold conditions of this instability, operative for T⊥>T∥, have been expressed as an inverse correlation between the temperature anisotropy, T⊥/T∥, and parallel beta, β∥, but such a relation was deduced on the basis of linear stability analysis combined with empirical fitting. The present paper, on the other hand, employs macroscopic quasi‐linear analysis for core‐halo two‐component model of the solar wind electrons, in order to follow the self‐consistent time history of the core and halo temperature development as well as the dynamics of magnetic field perturbation wave energy. In the present analysis, the inverse correlation for core and halo temperature anisotropy and parallel beta naturally emerges from the solutions of self‐consistent theory. The present findings indicate that the macroscopic quasi‐linear method may be useful for modeling the dynamics of solar wind electrons.

Destabilizing effects of the suprathermal populations in the solar wind

Context. Suprathermal populations are ubiquitous in the solar wind, indicating plasma states out of thermal equilibrium, and an excess of free energy expected to enhance the kinetic instabilities. However, recent endeavors to disclose the effects of these populations on the electromagnetic instabilities driven by the temperature anisotropy do not confirm this expectation, but mainly show that these instabilities are inhibited by the suprathermals.Aims. In an attempt to clarify the effect of the suprathermals, we propose to revisit the existing models for the anisotropic velocity distributions of plasma particles and to provide an alternative comparative analysis that unveils the destabilizing effects of the suprathermal populations.Methods. Suprathermal tails of the observed distributions are best fitted by the Kappa power laws (with the bi-Kappa variant to model temperature anisotropies), which are nearly Maxwellian at low speeds (thermal core) and decrease as a power law at high speeds (suprathermal halo). To unveil the destabilizing effects of the suprathermal populations, the existing methods (A) compare Kappa and Maxwellian distributions of the same effective temperature, while the alternative comparative method (B) proposed in this paper allows for an increase of the effective temperature with increasing the suprathermal populations. Both of these two methods are invoked here to quantify and compare the effects of suprathermal electrons on the electromagnetic electron-cyclotron (EMEC) instability, driven by the temperature anisotropy T e,⊥ >T e,∥ of the electrons (where ∥,⊥ are directions with respect to the magnetic field).Results. Only the Maxwellian limit of lower effective temperature shapes the Kappa model at low energies (method B), enabling a realistic comparison between the Maxwellian core and the global best-fitting Kappa, which incorporates both the core and suprathermal tails. In this case, the EMEC instability is found to be markedly and systematically enhanced by the suprathermal populations for any level of the temperature anisotropy. The results of the present study may provide valuable premises for a realistic description of the suprathermal populations and their destabilizing effects for the whole spectrum of kinetic instabilities in the solar wind.