Perpendicular Temperature Anisotropy Research Articles

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).

MMS Observations of Lower Hybrid and Whistler Waves Inside a Foreshock Transient

AbstractWe report Magnetospheric Multiscale observations of lower hybrid and whistler waves at the compression region of a foreshock transient. Lower hybrid waves (LHWs) are observed at the boundaries of the compression region and excited by the instability associated with the density gradient. Electron fluxes parallel to the magnetic field exhibit oscillations at the frequency band close to the LHWs. Associated with LHWs, electron plateau‐like distributions in the parallel direction are observed during burst intervals. Evidence suggests that the LHWs likely contribute to parallel electron heating through Landau damping. Within the compression region, whistler waves are found driven by the electron perpendicular temperature anisotropy associated with the magnetic field pileup. These two types of plasma waves are intrinsically linked to the expansion of the transient. These results provide insights on the kinetic‐scale wave‐particle interactions associated with foreshock transients.

Observations of Whistler-mode Waves and Large-amplitude Electrostatic Waves Associated with a Dipolarization Front in the Bursty Bulk Flow

Plasma jets and jet fronts are common phenomena in planetary magnetospheres. They are usually associated with many plasma waves and can play a key role in the energy conversion, the excitation of wave emissions, particle acceleration, and the evolution of many astrophysical phenomena, which are major issues in the study of helio-terrestrial space physics. In this paper, we carefully investigated the properties of the whistler-mode wave and large-amplitude electrostatic wave in a plasma jet (bursty bulk flow (BBF)) using the Magnetospheric Multiscale mission data on the Earth's magnetosphere. At the leading part of the BBF, intense whistler-mode waves were observed inside the ion mirror-mode structures, which should be excited by the perpendicular temperature anisotropy of trapping electrons. A small-scale dipolarization front (DF) was then observed at the center of this BBF as a boundary between the leading and trailing parts of the BBF. Behind the DF, both an ion mirror-mode structure and whistler-mode waves disappear, while a large-amplitude electrostatic wave was detected and was associated with the cold ions at the trailing part of the BBF. The electrostatic wave is supposed to be generated by ion beam instability. These results will significantly improve the understanding of the kinetic process associated with the important boundary layer DF within plasma jets. The corresponding wave–particle interaction in space and the plasma environment can be further understood.

Whistler waves generated by nongyrotropic and gyrotropic electron beams during asymmetric guide field reconnection

Using a two-dimensional particle-in-cell simulation of asymmetric reconnection with a guide field whose strength is 0.3 times the reconnecting magnetic field, we study electron distribution functions and wave intensities in the diffusion region, focusing on the electron diffusion region (EDR). Wave activities with frequencies below the electron cyclotron frequency are observed, and these are whistler waves propagating almost anti-parallel to the magnetic field. The waves are concentrated near the magnetospheric separatrix away from the X line, but the wave activity also spreads through the EDR near the X line. The reconnection outflows are asymmetric in the outflow direction in the magnetospheric side, and the wave intensity is stronger in the side of the faster electron outflow. We study the whistler waves using the fast Fourier transform, analyses of electron velocity distribution functions, and the dispersion solver calculation. Along the magnetospheric separatrix in the stronger outflow side, highly anisotropic electron beams exist with super-Alfvénic drift speeds. The dispersion analysis shows that there are two modes: a temperature anisotropy mode and a beam mode. Outside the EDR, the whistler wave intensity is highest near the separatrix, but the wave intensity decreases if we move away from the separatrix toward the magnetic neutral line because of the increase in the electron population near zero parallel velocity. In the EDR, in the velocity plane perpendicular to the magnetic field, ring/crescent electron distribution functions are observed. Near the X-line, the wave power is enhanced where nongyrotropic electrons contribute to increase the perpendicular temperature anisotropy.

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.

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.

Statistical Characteristics in the Spectrum of Whistler Waves Near the Diffusion Region of Dayside Magnetopause Reconnection

AbstractUsing Magnetospheric Multiscale (MMS) data, we present a statistical analysis revealing characteristics in the frequency spectrum of whistler waves in the vicinity of the diffusion region of magnetopause reconnection. On the magnetosphere side of reconnection, whistler waves are highly centered around the 1/2 electron cyclotron frequency (Ωe). On the magnetosheath side of reconnection, whistler waves are mainly below 1/2 Ωe and peaked around 0.2 Ωe. The electron temperature anisotropy associated with the waves is evaluated. The occurrence rate of the whistler waves is large in the presence of perpendicular electron temperature anisotropy (Te⊥/Te‖ > 1). However, a large part of the whistler waves events occurs in association with parallel electron temperature anisotropy (Te⊥/Te‖ < 1) on the magnetosheath side of reconnection, reflecting a large number of the total observations with this electron condition. These results shed new lights on the whistler‐related electron kinetic processes near the reconnection diffusion region.

Combined electron firehose and electromagnetic ion cyclotron instabilities: quasilinear approach

ABSTRACT Various plasma waves and instabilities are abundantly present in the solar wind plasma, as evidenced by spacecraft observations. Among these, propagating modes and instabilities driven by temperature anisotropies are known to play a significant role in the solar wind dynamics. In situ measurements reveal that the threshold conditions for these instabilities adequately explain the solar wind conditions at large heliocentric distances. This paper pays attention to the combined effects of electron firehose instability driven by excessive parallel electron temperature anisotropy (T⊥e < T∥e) at high beta conditions, and electromagnetic ion cyclotron instability driven by excessive perpendicular proton temperature anisotropy (T⊥i > T∥i). By employing quasilinear kinetic theory based upon the assumption of bi-Maxwellian velocity distribution functions for protons and electrons, the dynamical evolution of the combined instabilities and their mutual interactions mediated by the particles is explored in depth. It is found that while in some cases, the two unstable modes are excited and saturated at distinct spatial and temporal scales, in other cases, the two unstable modes are intermingled such that a straightforward interpretation is not so easy. This shows that when the dynamics of protons and electrons are mutually coupled and when multiple unstable modes are excited in the system, the dynamical consequences can be quite complex.

Investigation of Electron Distribution Functions Associated With Whistler Waves at Dipolarization Fronts in the Earth's Magnetotail: MMS Observations

AbstractUsing burst mode Magnetospheric Multiscale (MMS) observations in the plasma sheet (PS), we study the dynamics of electron anisotropy and its relation to quasi‐parallel narrowband whistler bursts in 37 dipolarization fronts (DFs) propagating in the Earth's magnetotail along with fast flows at −25 RE ≤ X ≤ −17 RE. The bursts were observed at the DFs and behind them in the dipolarizing flux bundle (DFB) region with frequencies fpeak ~ (0.1–0.6) fce ( fce is electron gyrofrequency) and durations approximately a few seconds. The majority of the whistler waves were associated with perpendicular electron temperature anisotropy TPER/TPAR > 1, and the value of this anisotropy decreased by the end of the bursts suggesting electron scattering by the waves. We found that the major contribution to the growth rate of whistler waves is made by resonant electrons with energies Wres ~ 1–5 keV and pitch angles αres ~ 40–75° and ~100–135°. In the majority of cases, the largest Wres was observed at the DF and immediately behind it, while in the DFB the Wres decreased. The sources of the majority of whistler bursts were not confined near the neutral plane but could be extended into the PS where the perpendicular anisotropy of the local electron distribution provided the positive growth rate of the whistler waves. We show that the observed whistler waves play a significant role in the dynamics of electron velocity distribution in DFs, leading to energy exchange between various parts of electron population and constraining temperature anisotropy of electron distribution.

On quasi-parallel whistler waves in the solar wind

Recent simulations showed that the whistler heat flux instability, which presumably produces the most of quasi-parallel coherent whistler waves in the solar wind, is not efficient in regulating the electron heat conduction. In addition, recent spacecraft measurements indicated that some fraction of coherent whistler waves in the solar wind may propagate anti-parallel to the electron heat flux, being produced due to a perpendicular temperature anisotropy of suprathermal electrons. We present the analysis of properties of parallel and anti-parallel whistler waves unstable at electron heat fluxes and temperature anisotropies of suprathermal electrons typical of the pristine solar wind. Assuming the electron population consisting of counterstreaming dense thermal core and tenuous suprathermal halo populations, we perform a linear stability analysis to demonstrate that anti-parallel whistler waves are expected to have smaller frequencies, wave numbers, and growth rates compared to parallel whistler waves. The stability analysis is performed over a wide range of parameters of core and halo electron populations. Using the quasi-linear scaling relation, we show that anti-parallel whistler waves saturate at amplitudes of one order of magnitude smaller than parallel whistler waves, which is about 10−3 B0 in the pristine solar wind. The analysis shows that the presence of anti-parallel whistler waves in the pristine solar wind is more likely to be obscured by turbulent magnetic field fluctuations because of lower frequencies and smaller amplitudes compared to parallel whistler waves. The presented results will also be valuable for numerical simulations of the electron heat flux regulation in the solar wind.

Electron mirror instability: particle-in-cell simulations

Properties of the electron mirror instability and its competition with the usually dominant whistler (electron cyclotron) instability driven by the electron perpendicular temperature anisotropy are investigated at the linear level using a Vlasov linear solver and at the nonlinear level using a two-dimensional full particle code. The simulation results show that the linearly subdominant electron mirror instability may compete at the nonlinear level with the whistler instability and may even eventually become the dominant mode that generates robust non-propagating sub-ion-scale coherent structures in the form of magnetic peaks.

Wave Phenomena and Beam-Plasma Interactions at the Magnetopause Reconnection Region.

This paper reports on Magnetospheric Multiscale observations of whistler mode chorus and higher‐frequency electrostatic waves near and within a reconnection diffusion region on 23 November 2016. The diffusion region is bounded by crescent‐shaped electron distributions and associated dissipation just upstream of the X‐line and by magnetic field‐aligned currents and electric fields leading to dissipation near the electron stagnation point. Measurements were made southward of the X‐line as determined by southward directed ion and electron jets. We show that electrostatic wave generation is due to magnetosheath electron beams formed by the electron jets as they interact with a cold background plasma and more energetic population of magnetospheric electrons. On the magnetosphere side of the X‐line the electron beams are accompanied by a strong perpendicular electron temperature anisotropy, which is shown to be the source of an observed rising‐tone whistler mode chorus event. We show that the apex of the chorus event and the onset of electrostatic waves coincide with the opening of magnetic field lines at the electron stagnation point.

MMS observations of whistler waves in electron diffusion region

AbstractWhistler waves that can produce anomalous resistivity by affecting electrons' motion have been suggested as one of the mechanisms responsible for magnetic reconnection in the electron diffusion region (EDR). Such type of waves, however, has rarely been observed inside the EDR so far. In this study, we report such an observation by Magnetospheric Multiscale (MMS) mission. We find large‐amplitude whistler waves propagating away from the X line with a very small wave‐normal angle. These waves are probably generated by the perpendicular temperature anisotropy of the ~300 eV electrons inside the EDR, according to our analysis of dispersion relation and cyclotron resonance condition; they significantly affect the electron‐scale dynamics of magnetic reconnection and thus support previous simulations.

Mirror Instability in the Turbulent Solar Wind

Abstract The relationship between a decaying strong turbulence and the mirror instability in a slowly expanding plasma is investigated using two-dimensional hybrid expanding box simulations. We impose an initial ambient magnetic field perpendicular to the simulation box, and we start with a spectrum of large-scale, linearly polarized, random-phase Alfvénic fluctuations that have energy equipartition between kinetic and magnetic fluctuations and a vanishing correlation between the two fields. A turbulent cascade rapidly develops, magnetic field fluctuations exhibit a Kolmogorov-like power-law spectrum at large scales and a steeper spectrum at sub-ion scales. The imposed expansion (taking a strictly transverse ambient magnetic field) leads to the generation of an important perpendicular proton temperature anisotropy that eventually drives the mirror instability. This instability generates large-amplitude, nonpropagating, compressible, pressure-balanced magnetic structures in a form of magnetic enhancements/humps that reduce the perpendicular temperature anisotropy.

Waves in the innermost open boundary layer formed by dayside magnetopause reconnection

AbstractWe present two Time History of Events and Macroscale Interactions during Substorms observations of whistler mode and electrostatic wave events in the innermost open boundary layer (IOBL), formed by dayside magnetopause reconnection. The IOBL is identified by high‐speed electrons from the magnetosheath on the magnetospheric side of the ion outflow from the reconnection site. Quasi‐parallel whistler mode waves propagating toward the reconnection region are observed, along with a partial shortage of magnetospheric electrons moving away from the reconnection region. Calculation of wave linear growth rates shows that the waves can be excited by the perpendicular electron temperature anisotropy that develops due to the partial shortage of field‐aligned magnetospheric electrons. Electrostatic waves close to the lower hybrid resonance frequency are observed in the IOBL in the second event, which occurred during the main phase of a magnetospheric storm. Magnetospheric electrons are almost completely lost in the event, except at pitch angles close to 90°, yet whistler mode waves are not observed. An electron beam from the magnetosheath and counterstreaming cold electrons originating from the plasmaspheric plume are observed in association with the electrostatic waves. Growth rate calculations show that the waves are likely to be ion acoustic waves excited via couplings between the flowing cold electrons and background cold ions. We suggest that differences in solar wind conditions and magnetic reconnection characteristics may control the shapes of the electron velocity distribution functions and the resulting plasma wave properties in the IOBL.

Multispacecraft analysis of dipolarization fronts and associated whistler wave emissions using MMS data

AbstractDipolarization fronts (DFs), embedded in bursty bulk flows, play a crucial role in Earth's plasma sheet dynamics because the energy input from the solar wind is partly dissipated in their vicinity. This dissipation is in the form of strong low‐frequency waves that can heat and accelerate energetic electrons up to the high‐latitude plasma sheet. However, the dynamics of DF propagation and associated low‐frequency waves in the magnetotail are still under debate due to instrumental limitations and spacecraft separation distances. In May 2015 the Magnetospheric Multiscale (MMS) mission was in a string‐of‐pearls configuration with an average intersatellite distance of 160 km, which allows us to study in detail the microphysics of DFs. Thus, in this letter we employ MMS data to investigate the properties of dipolarization fronts propagating earthward and associated whistler mode wave emissions. We show that the spatial dynamics of DFs are below the ion gyroradius scale in this region (∼500 km), which can modify the dynamics of ions in the vicinity of the DF (e.g., making their motion nonadiabatic). We also show that whistler wave dynamics have a temporal scale of the order of the ion gyroperiod (a few seconds), indicating that the perpendicular temperature anisotropy can vary on such time scales.

Whistler mode waves and Hall fields detected by MMS during a dayside magnetopause crossing

AbstractWe present Magnetospheric Multiscale (MMS) mission measurements during a full magnetopause crossing associated with an enhanced southward ion flow. A quasi‐steady magnetospheric whistler mode wave emission propagating toward the reconnection region with quasi‐parallel and oblique wave angles is detected just before the opening of the magnetic field lines and the detection of escaping energetic electrons. Its source is likely the perpendicular temperature anisotropy of magnetospheric energetic electrons. In this region, perpendicular and parallel currents as well as the Hall electric field are calculated and found to be consistent with the decoupling of ions from the magnetic field and the crossing of a magnetospheric separatrix region. On the magnetosheath side, Hall electric fields are found smaller as the density is larger but still consistent with the decoupling of ions. Intense quasi‐parallel whistler wave emissions are detected propagating both toward and away from the reconnection region in association with a perpendicular anisotropy of the high‐energy part of the magnetosheath electron population and a strong perpendicular current, which suggests that in addition to the electron diffusion region, magnetosheath separatrices could be a source region for whistler waves.

Electron vortex magnetic holes: A nonlinear coherent plasma structure

We report the properties of a novel type of sub-proton scale magnetic hole found in two dimensional particle-in-cell simulations of decaying turbulence with a guide field. The simulations were performed with a realistic value for ion to electron mass ratio. These structures, electron vortex magnetic holes (EVMHs), have circular cross-section. The magnetic field depression is associated with a diamagnetic azimuthal current provided by a population of trapped electrons in petal-like orbits. The trapped electron population provides a mean azimuthal velocity and since trapping preferentially selects high pitch angles, a perpendicular temperature anisotropy. The structures arise out of initial perturbations in the course of the turbulent evolution of the plasma, and are stable over at least 100 electron gyroperiods. We have verified the model for the EVMH by carrying out test particle and PIC simulations of isolated structures in a uniform plasma. It is found that (quasi-)stable structures can be formed provided that there is some initial perpendicular temperature anisotropy at the structure location. The properties of these structures (scale size, trapped population, etc.) are able to explain the observed properties of magnetic holes in the terrestrial plasma sheet. EVMHs may also contribute to turbulence properties, such as intermittency, at short scale lengths in other astrophysical plasmas.

Simulation and quasilinear theory of proton firehose instability

The electromagnetic proton firehose instability is driven by excessive parallel temperature anisotropy, T∥ > T⊥ (or more precisely, parallel pressure anisotropy, P∥ > P⊥) in high-beta plasmas. Together with kinetic instabilities driven by excessive perpendicular temperature anisotropy, namely, electromagnetic proton cyclotron and mirror instabilities, its role in providing the upper limit for the temperature anisotropy in the solar wind is well-known. A recent Letter [Seough et al., Phys. Rev. Lett. 110, 071103 (2013)] employed quasilinear kinetic theory for these instabilities to explain the observed temperature anisotropy upper bound in the solar wind. However, the validity of quasilinear approach has not been rigorously tested until recently. In a recent paper [Seough et al., Phys. Plasmas 21, 062118 (2014)], a comparative study is carried out for the first time in which quasilinear theory of proton cyclotron instability is tested against results obtained from the particle-in-cell simulation method, and it was demonstrated that the agreement was rather excellent. The present paper addresses the same issue involving the proton firehose instability. Unlike the proton cyclotron instability, however, it is found that the quasilinear approximation enjoys only a limited range of validity, especially for the wave dynamics and for the relatively high-beta regime. Possible causes and mechanisms responsible for the discrepancies are speculated and discussed.

Proton temperature-anisotropy-driven instabilities in weakly collisional plasmas: Hybrid simulations

Kinetic instabilities in weakly collisional, high beta plasmas are investigated using two-dimensional hybrid expanding box simulations with Coulomb collisions modeled through the Langevin equation (corresponding to the Fokker-Planck one). The expansion drives a parallel or perpendicular temperature anisotropy (depending on the orientation of the ambient magnetic field). For the chosen parameters the Coulomb collisions are important with respect to the driver but are not strong enough to keep the system stable with respect to instabilities driven by the proton temperature anisotropy. In the case of the parallel temperature anisotropy the dominant oblique fire hose instability efficiently reduces the anisotropy in a quasilinear manner. In the case of the perpendicular temperature anisotropy the dominant mirror instability generates coherent compressive structures which scatter protons and reduce the temperature anisotropy. For both the cases the instabilities generate temporarily enough wave energy so that the corresponding (anomalous) transport coefficients dominate over the collisional ones and their properties are similar to those in collisionless plasmas.