Electromagnetic Electron Cyclotron Instability Research Articles

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.

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.

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.

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.

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.

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.

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.

Nonlinear evolution of the electromagnetic electron-cyclotron instability in bi-Kappa distributed plasma

This paper presents a numerical study of the linear and nonlinear evolution of the electromagnetic electron-cyclotron (EMEC) instability in a bi-Kappa distributed plasma. Distributions with high energy tails described by the Kappa power-laws are often observed in collision-less plasmas (e.g., solar wind and accelerators), where wave-particle interactions control the plasma thermodynamics and keep the particle distributions out of Maxwellian equilibrium. Under certain conditions, the anisotropic bi-Kappa distribution gives rise to plasma instabilities creating low-frequency EMEC waves in the whistler branch. The instability saturates nonlinearly by reducing the temperature anisotropy until marginal stability is reached. Numerical simulations of the Vlasov-Maxwell system of equations show excellent agreement with the growth-rate and real frequency of the unstable modes predicted by linear theory. The wave-amplitude of the EMEC waves at nonlinear saturation is consistent with magnetic trapping of the electrons.

Towards realistic parametrization of the kinetic anisotropy and the resulting instabilities in space plasmas. Electromagnetic electron–cyclotron instability in the solar wind

Measuredin situ, the particle velocity distributions in the solar wind plasma reveal two distinct components: a Maxwellian (thermal) core, and a less dense but hotter suprathermal halo with a power-law distribution described by Lorentzian/Kappa distribution function. Despite this evidence, the existing attempts to parametrize anisotropic distributions and the resulting wave instabilities are limited to idealized models, which either ignore the suprathermal populations, or minimize the core, assuming it is cold. Here, a more realistic approach is identified, combining an isotropic Maxwellian core and an anisotropic bi-Kappa halo. This model is relevant at large heliocentric distances and for the slow winds, when the field-aligned strahl is less pronounced and kinetic energy densities in the core and halo are comparable. A comparative study with the cold-core-based model is performed on the electron whistler–

The interplay of Kappa and core populations in the solar wind: Electromagnetic electron cyclotron instability

AbstractRecently, a realistic parameterization was proposed for the kinetic anisotropy and the resulting instabilities in the solar wind plasma. This parameterization is based on observations of the particle velocity distribution, which always comprises a Maxwellian population at low energies, viz. the core, and a suprathermal halo in the tail of the distribution which is best described by the Kappa (power law) models. The cyclotron instability, driven by an anisotropic electron halo, was found to be inhibited by the finite thermal spread in the core, and this effect is highly dependent on the halo‐core relative density. In this paper, the interplay between the Kappa and Maxwellian populations is further investigated for more complex (less idealized) situations when both the core and halo temperatures are anisotropic. Growth of this instability is markedly stimulated by the core anisotropy. The wave numbers that are stable for an isotropic core become unstable even for small anisotropies of this population. Just a modest increase of the core anisotropy from Ac=T⊥/T∥=1.2 to 2 causes the growth rates to enhance by 1 order of magnitude, and the range of unstable wave numbers to extend considerably. When the anisotropies in the core and halo are comparable, the growth rate exhibits two distinct peaks, the first driven by the halo at lower wave numbers and the second driven by the core. However, the first peak is inhibited by the suprathermal populations, while the second peak is sustained, suggesting a more intricate connection between the core and Kappa populations.

Whistler‐mode wave generation around interplanetary shocks in and out of the ecliptic plane

We present a study of whistler‐mode wave generation and wave particle interaction in the vicinity of interplanetary shocks in and out of the ecliptic plane, as observed by the Ulysses spacecraft. We focus here on one shock in the ecliptic plane as a reference and three shocks obtained at −30, −54 and −55.4 degrees of heliographic latitude respectively. Generally the whistler‐mode waves (measured in the frequency range 0.22–448 Hz) are observed downstream of the shocks where they persist for some hours. From the electron distribution functions in the energy range 1.6 to 862 eV, we compute the temperature anisotropy and the wave growth rate of the electromagnetic electron cyclotron instability for the case of parallel propagation of the waves with respect to the interplanetary magnetic field (IMF) B. In general, in agreement with the wave measurements, the instability grows only downstream of the shock fronts. Following the wave activity, velocity space diffusion of the electrons results in a marginally stable state with some sporadic fluctuations. Broadening of the wave reduced frequency range of the instability and an increase of the temperature anisotropy with latitude are observed.

Electromagnetic electron cyclotron instability in a hot plasma having an electron current

The presence of an electron current on the electromagnetic electron cyclotron instability due to temperature anisotropy of the background hot electrons is analysed. The growth rate depends on the strength of the electron current. The application of the present study to the gap at μ = ½ in the equational magnetosphere suggest that the FAC must be of at least 1 μA/m2.

A theory of electron cyclotron waves generated along auroral field lines observed by ground facilities

A generation mechanism for radio waves in the frequency range 150–700 kHz observed by ground facilities is suggested in terms of an electromagnetic electron cyclotron instability driven by auroral electrons. The excited waves can propagate downward along the ambient magnetic field lines and are thus observable with ground facilities. The trapped auroral electrons are supposed to play an important role in the generation process, because they give rise to a thermal anisotropy which consequently leads to the instability. The present work is a natural extension of the theory proposed earlier by Wu et al. [1983] which was discussed in a different context but may be used to explain the observed waves originated at low altitudes (< 0.5 RE). This paper presents a possible wave generation mechanism valid in the entire auroral field line region of interest.

Comparative study of the axial and azimuthal bunching mechanisms in electromagnetic cyclotron instabilities

A comparative study is presented of the axial and azimuthal bunching mechanisms of the electromagnetic electron cyclotron instability. Axial bunching can be described with a nonrelativistic treatment, but azimuthal bunching is relativistic in origin. As is well known, the axial bunching mechanism drives the Weibel-type instability while the azimuthal bunching mechanism drives the electron cyclotron maser instability. For an electron ensemble of cold helical trajectories, a unified physical interpretation of both instabilities is presented. It is shown that the two bunching mechanisms are actually simultaneously present in either instability and compete with one another. As a result, the dominant mechanism determines the type of instability. A criterion for distinguishing the two types of instabilities is derived. It is shown that the energy of the electrons plays an insignificant role in the criterion and, hence, should not be a factor in the justification of a nonrelativistic treatment. Regimes of validity of nonrelativistic models are defined, however. Applications to gyrotron experiments are discussed.