Electron Temperature Anisotropy Research Articles

Whistler and Electron Firehose Instability Control of Electron Distributions in and Around Dipolarizing Flux Bundles

AbstractElectromagnetic fluctuations associated with various plasma instabilities have been previously identified near dipolarization fronts in Earth's magnetotail. However, the potential effect of these fluctuations on particle distributions and energy conversion is poorly understood. The most important instabilities responsible for electron acceleration and scattering are the whistler instability and the electron firehose instability. Utilizing 10 years of Time History of Events and Macroscale Interactions during Substorms satellite observations, we explore the occurrence probability and intensity of these instabilities near dipolarization fronts, as function of electron anisotropy and plasma beta. Electron temperature anisotropies are well constrained by the marginal stability conditions of the whistler and oblique electron firehose instabilities. In fact, the observed enhancement of magnetic field fluctuations near the instability thresholds provides good evidence for the operation of these instabilities on electrons near fronts. Since the build‐up of electron anisotropy is limited by wave‐particle interactions, we conclude that such interactions are important enough to affect electron dynamics and energetics.

Obliquely propagating magnetosonic waves in a plasma modeled by bi-anisotropic Cairns distribution

Waves and instabilities have very often been an object of fascination since the introduction of non-Maxwellian features in space plasmas. To date, the dispersion relation, including real frequency, damping, and growth rates of magnetosonic waves has been studied in many different types of non-Maxwellian distributions. However, these characteristics have been overlooked in the temperature bi-anisotropic Cairns distribution, characterized by the free parameter Λ. By employing the linearized Vlasov–Maxwell system in homogeneous plasma, the dispersion relation is analytically solved. It is found that the non-Maxwellian features, Λ ≠ 0 along with electron temperature anisotropy, notably modify the real frequency, damping, and growth rates—both in the hydrodynamic as well as in the kinetic regimes. Interestingly, the growth rate in the kinetic regime is entirely due to the correlation of Λ with the electron temperature anisotropy which is otherwise absent in the Maxwellian distribution. Due to their relevance, the results are applicable to solar wind plasma.

Generation of Electron Whistler Waves at the Mirror Mode Magnetic Holes: MMS Observations and PIC Simulation

AbstractThe Magnetospheric Multiscale mission has observed electron whistler waves at the center and at the edges of magnetic holes in the dayside magnetosheath. The magnetic holes are nonlinear mirror structures since their magnitude is anticorrelated with particle density. In this article, we examine the growth mechanisms of these whistler waves and their interaction with the host magnetic hole. In the observations, as magnetic holes develop and get deeper, an electron population gets trapped and develops a temperature anisotropy favorable for whistler waves to be generated. In addition, the decrease in magnetic field magnitude and the increase in density reduce the electron resonance energy, which promotes the electron cyclotron resonance. To investigate this process, we used expanding box particle‐in‐cell simulations to produce the mirror instability, which then evolve into magnetic holes. The simulation shows that whistler waves can be generated at the center and edges of magnetic holes, which reproduces the primary features of the MMS observations. The simulation shows that the electron temperature anisotropy develops in the center of the magnetic hole once the mirror instability reaches its nonlinear stage of evolution. The plasma is then unstable to whistler waves at the minimum of the magnetic field structures. In the saturation regime of mirror instability, when magnetic holes are developed, the electron temperature anisotropy appears at the edges of the holes and electron distributions become more isotropic at the magnetic field minimum. At the edges, the expansion of magnetic holes decelerates the electrons, which leads to temperature anisotropies.

Beaming electromagnetic (or heat-flux) instabilities from the interplay with the electron temperature anisotropies

In space plasmas, kinetic instabilities are driven by the beaming (drifting) components and/or the temperature anisotropy of charged particles. The heat-flux instabilities are known in the literature as electromagnetic modes destabilized by the electron beams (or strahls) aligned to the interplanetary magnetic field. A new kinetic approach is proposed here in order to provide a realistic characterization of heat-flux instabilities under the influence of electrons with temperature anisotropy. Numerical analysis is based on the kinetic Vlasov-Maxwell theory for two electron counter-streaming (core and beam) populations with temperature anisotropies and stationary, isotropic protons. The main properties of electromagnetic heat-flux instabilities are found to be markedly changed by the temperature anisotropy of the electron beam Ab=T⊥/T∥≠1, leading to stimulation of either the whistler branch if Ab>1 or the firehose branch for Ab<1. For a high temperature anisotropy, whistlers switch from heat-flux to a standard regime, when their instability is inhibited by the beam.

Observations of Whistler Waves Correlated with Electron-scale Coherent Structures in the Magnetosheath Turbulent Plasma

Abstract A new type of electron-scale coherent structure, referred to as electron vortex magnetic holes, was identified recently in the Earth’s magnetosheath turbulent plasma. These electron-scale magnetic holes are characterized by magnetic field strength depression, electron density enhancement, temperature and temperature anisotropy increase (a significant increase in perpendicular temperature and a decrease in parallel temperature), and an electron vortex formed by the trapped electrons. The strong increase of electron temperature indicates that these magnetic holes have a strong connection with the energization of electrons. Here, using high time resolution in situ measurements from the MMS mission, it is further shown that electron-scale whistler waves coexist with electron-scale magnetic holes. These whistler waves were found not propagating from remote regions, but generated locally due to electron temperature anisotropy (T e⊥/T e∥) inside the magnetic holes. This study provides new insights into the electron-scale plasma dynamics in turbulent plasmas.

Electron Heating in Low Mach Number Perpendicular Shocks. II. Dependence on the Pre-shock Conditions

Abstract Recent X-ray observations of merger shocks in galaxy clusters have shown that the post-shock plasma is two-temperature, with the protons being hotter than the electrons. In this work, the second of a series, we investigate the efficiency of irreversible electron heating in perpendicular low Mach number shocks, by means of two-dimensional particle-in-cell simulations. We consider values of plasma beta (the ratio of thermal and magnetic pressures) in the range 4 ≲ β p0 ≲ 32, and sonic Mach number (the ratio of shock speed to pre-shock sound speed) in the range 2 ≲ M s ≲ 5, as appropriate for galaxy cluster shocks. As shown in Paper I, magnetic field amplification—induced by shock compression of the pre-shock field, or by strong proton cyclotron and mirror modes accompanying the relaxation of proton temperature anisotropy—can drive the electron temperature anisotropy beyond the threshold of the electron whistler instability. The growth of whistler waves breaks the electron adiabatic invariance, and allows for efficient entropy production. We find that the post-shock electron temperature T e2 exceeds the adiabatic expectation by an amount (here, T e0 is the pre-shock temperature), which depends only weakly on the plasma beta over the range 4 ≲ β p0 ≲ 32 that we have explored, as well as on the proton-to-electron mass ratio (the coefficient of ≃0.044 is measured for our fiducial , and we estimate that it will decrease to ≃0.03 for the realistic mass ratio). Our results have important implications for current and future observations of galaxy cluster shocks in the radio band (synchrotron emission and Sunyaev–Zel’dovich effect) and at X-ray frequencies.

Influence of field ionization effect on the divergence of laser-driven fast electrons

The effect of field ionization on the divergence of fast electrons (Ek ≥ 50 keV), driven by ultrashort-ultraintense laser pulse interaction with plasma, is studied by using 2D3V particle-in-cell simulations. It is found that, due to temperature anisotropy of the fast electrons in the ionizing target, strong fluctuant magnetic fields in the preplasma region is generated through Weibel instability. In turn, the field induces an enhancement of the hot electron divergence for the target with ionization process. Meanwhile, compared with the target without an ionization process, larger divergence of hot electrons can also be seen in the ionizing target with laser intensity varying from 5 × 1019 W/cm2 to 5 × 1020 W/cm2 and the divergence is weakly dependent on target materials for a fixed profile of preplasma. The results here are useful for the application of laser-driven fast electron beams.

Whistler waves with electron temperature anisotropy and non-Maxwellian distribution functions

The previous works on whistler waves with electron temperature anisotropy narrated the dependence on plasma parameters, however, they did not explore the reasons behind the observed differences. A comparative analysis of the whistler waves with different electron distributions has not been made to date. This paper attempts to address both these issues in detail by making a detailed comparison of the dispersion relations and growth rates of whistler waves with electron temperature anisotropy for Maxwellian, Cairns, kappa and generalized (r, q) distributions by varying the key plasma parameters for the problem under consideration. It has been found that the growth rate of whistler instability is maximum for flat-topped distribution whereas it is minimum for the Maxwellian distribution. This work not only summarizes and complements the previous work done on the whistler waves with electron temperature anisotropy but also provides a general framework to understand the linear propagation of whistler waves with electron temperature anisotropy that is applicable in all regions of space plasmas where the satellite missions have indicated their presence.

Dependence of Generation of Whistler Mode Chorus Emissions on the Temperature Anisotropy and Density of Energetic Electrons in the Earth's Inner Magnetosphere

AbstractWe carry out a series of self‐consistent electron hybrid code simulations for the dependence of chorus generation process on the temperature anisotropy and density of energetic electrons in the Earth's inner magnetosphere. We use the same magnetic field gradient in the simulation system and different temperature anisotropy AT for the initial distribution of energetic electrons at the magnetic equator. We conduct 6 sets of simulations for different AT from 4 to 9, changing the initial number density Nh of energetic electrons at the equator in each set of simulations. By analyzing the spectra obtained in the simulation results, we identify chorus elements with rising tones in the results for higher Nh but no distinct chorus in smaller Nh. We compare the simulation results with estimations of the threshold and optimum amplitude proposed by the nonlinear wave growth theory. We find that the chorus generation processes reproduced in the simulation results are consistently explained by the theoretical estimates. We also compare the simulation results with linear growth rates for all simulation runs. We find clear disagreement between the spectral characteristics of reproduced chorus and the predictions by the linear theory. The present study clarifies that the spectra of chorus are essentially different from those predicted by the linear theory and are determined fully by nonlinear processes of wave‐particle interactions in the chorus generation region.

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.

Electron Heating in Low-Mach-number Perpendicular Shocks. I. Heating Mechanism

Abstract Recent X-ray observations of merger shocks in galaxy clusters have shown that the postshock plasma has two temperatures, with the protons hotter than the electrons. By means of two-dimensional particle-in-cell simulations, we study the physics of electron irreversible heating in low-Mach-number perpendicular shocks, for a representative case with sonic Mach number of 3 and plasma beta of 16. We find that two basic ingredients are needed for electron entropy production: (1) an electron temperature anisotropy, induced by field amplification coupled to adiabatic invariance; and (2) a mechanism to break the electron adiabatic invariance itself. In shocks, field amplification occurs at two major sites: at the shock ramp, where density compression leads to an increase of the frozen-in field; and farther downstream, where the shock-driven proton temperature anisotropy generates strong proton cyclotron and mirror modes. The electron temperature anisotropy induced by field amplification exceeds the threshold of the electron whistler instability. The growth of whistler waves breaks the electron adiabatic invariance and allows for efficient entropy production. For our reference run, the postshock electron temperature exceeds the adiabatic expectation by , resulting in an electron-to-proton temperature ratio of . We find that the electron heating efficiency displays only a weak dependence on mass ratio (less than drop, as we increase the mass ratio from up to ). We develop an analytical model of electron irreversible heating and show that it is in excellent agreement with our simulation results.

Excitation of chorus-like waves by temperature anisotropy in dipole research experiment (DREX): A numerical study**Project supported by the National Natural Science Foundation of China (Grant Nos. 41674165, 41631071, 41474142, and 41674174) and the China Postdoctoral Science Foundation (Grant No. 2015M570283).

Due to their significant roles in the radiation belts dynamics, chorus waves are widely investigated in observations, experiments, and simulations. In this paper, numerical studies for the generation of chorus-like waves in a launching device, dipole research experiment (DREX), are carried out by a hybrid code. The DREX plasma is generated by electron cyclotron resonance (ECR), which leads to an intrinsic temperature anisotropy of energetic electrons. Thus the whistler instability can be excited in the device. We then investigate the effects of three parameters, i.e., the cold plasma density nc, the hot plasma density nh, and the parallel thermal velocity of energetic electrons, on the generation of chorus-like waves under the DREX design parameters. It is obtained that a larger temperature anisotropy is needed to excite chorus-like waves with a high nc with other parameters fixed. Then we fix the plasma density and parallel thermal velocity, while varying the hot plasma density. It is found that with the increase of nh, the spectrum of the generated waves changes from no chorus elements, to that with several chorus elements, and then further to broad-band hiss-like waves. Besides, different structures of chorus-like waves, such as rising-tone and/or falling-tone structures, can be generated at different parallel thermal velocities in the DREX parameter range.

MMS Observation of Magnetic Reconnection in the Turbulent Magnetosheath

AbstractIn this paper we use the full armament of the MMS (Magnetospheric Multiscale) spacecraft to study magnetic reconnection in the turbulent magnetosheath downstream of a quasi‐parallel bow shock. Contrarily to the magnetopause and magnetotail cases, only a few observations of reconnection in the magnetosheath have been reported. The case study in this paper presents, for the first time, both fluid‐scale and kinetic‐scale signatures of an ongoing reconnection in the turbulent magnetosheath. The spacecraft are crossing the reconnection inflow and outflow regions and the ion diffusion region (IDR). Inside the reconnection outflows D shape ion distributions are observed. Inside the IDR mixing of ion populations, crescent‐like velocity distributions and ion accelerations are observed. One of the spacecraft skims the outer region of the electron diffusion region, where parallel electric fields, energy dissipation/conversion, electron pressure tensor agyrotropy, electron temperature anisotropy, and electron accelerations are observed. Some of the difficulties of the observations of magnetic reconnection in turbulent plasma are also outlined.

Electron Cooling and Isotropization during Magnetotail Current Sheet Thinning: Implications for Parallel Electric Fields

AbstractMagnetotail current sheet thinning is a distinctive feature of substorm growth phase, during which magnetic energy is stored in the magnetospheric lobes. Investigation of charged particle dynamics in such thinning current sheets is believed to be important for understanding the substorm energy storage and the current sheet destabilization responsible for substorm expansion phase onset. We use Time History of Events and Macroscale Interactions during Substorms (THEMIS) B and C observations in 2008 and 2009 at ~18 − 25 RE to show that during magnetotail current sheet thinning, the electron temperature decreases (cooling), and the parallel temperature decreases faster than the perpendicular temperature, leading to a decrease of the initially strong electron temperature anisotropy (isotropization). This isotropization cannot be explained by pure adiabatic cooling or by pitch angle scattering. We use test particle simulations to explore the mechanism responsible for the cooling and isotropization. We find that during the thinning, a fast decrease of a parallel electric field (directed toward the Earth) can speed up the electron parallel cooling, causing it to exceed the rate of perpendicular cooling, and thus lead to isotropization, consistent with observation. If the parallel electric field is too small or does not change fast enough, the electron parallel cooling is slower than the perpendicular cooling, so the parallel electron anisotropy grows, contrary to observation. The same isotropization can also be accomplished by an increasing parallel electric field directed toward the equatorial plane. Our study reveals the existence of a large‐scale parallel electric field, which plays an important role in magnetotail particle dynamics during the current sheet thinning process.

Generation of Highly Oblique Lower Band Chorus Via Nonlinear Three‐Wave Resonance

AbstractChorus in the inner magnetosphere has been observed frequently at geomagnetically active times, typically exhibiting a two‐band structure with a quasi‐parallel lower band and an upper band with a broad range of wave normal angles. But recent observations by Van Allen Probes confirm another type of lower band chorus, which has a large wave normal angle close to the resonance cone angle. It has been proposed that these waves could be generated by a low‐energy beam‐like electron component or by temperature anisotropy of keV electrons in the presence of a low‐energy plateau‐like electron component. This paper, however, presents an alternative mechanism for generation of this highly oblique lower band chorus. Through a nonlinear three‐wave resonance, a quasi‐parallel lower band chorus wave can interact with a mildly oblique upper band chorus wave, producing a highly oblique quasi‐electrostatic lower band chorus wave. This theoretical analysis is confirmed by 2‐D electromagnetic particle‐in‐cell simulations. Furthermore, as the newly generated waves propagate away from the equator, their wave normal angle can further increase and they are able to scatter low‐energy electrons to form a plateau‐like structure in the parallel velocity distribution. The three‐wave resonance mechanism may also explain the generation of quasi‐parallel upper band chorus which has also been observed in the magnetosphere.

Unique features of parallel whistler instability in a plasma with anisotropic Cairns distribution

In this paper, whistler waves propagating parallel to the ambient magnetic field with electron temperature anisotropy are investigated by employing the kinetic theory of plasmas. The electron distribution function is considered to follow the Cairns distribution. The dispersion relation for the whistler waves with Cairns distribution is derived, and the condition for the onset of instability is also obtained. It is found that the Cairns distribution significantly modifies the instability condition for the growth of whistler instability. The comparison of the dispersion characteristics and the growth rate with Maxwellian distribution is also made, and it is observed that Cairns distributed electrons yield a higher growth rate in comparison to their Maxwellian counterparts. It is also shown that unlike the kappa distribution where parallel electron beta was found to play the key role, whistler instability with Cairns distributed electrons shows a greater sensitivity towards electron temperature anisotropy. It is shown that the real frequency of the whistler waves shows a greater dependence on the choice of parallel electron beta. Interestingly, it is found that a particular combination of parallel electron beta and electron temperature anisotropy is deleterious for the whistler instability.

MMS Observations of Reconnection at Dayside Magnetopause Crossings During Transitions of the Solar Wind to Sub‐Alfvénic Flow

AbstractWe present MMS observations during two dayside magnetopause crossings under hitherto unexamined conditions: (i) when the bow shock is weakening and the solar wind transitioning to sub‐Alfvénic flow and (ii) when it is reforming. Interplanetary conditions consist of a magnetic cloud with (i) a strong B (∼20 nT) pointing south and (ii) a density profile with episodic decreases to values of ∼0.3 cm−3 followed by moderate recovery. During the crossings the magnetosheath magnetic field is stronger than the magnetosphere field by a factor of ∼2.2. As a result, during the outbound crossing through the ion diffusion region, MMS observed an inversion of the relative positions of the X and stagnation (S) lines from that typically the case: the S line was closer to the magnetosheath side. The S line appears in the form of a slow expansion fan near which most of the energy dissipation is taking place. While in the magnetosphere between the crossings, MMS observed strong field and flow perturbations, which we argue to be due to kinetic Alfvén waves. During the reconnection interval, whistler mode waves generated by an electron temperature anisotropy (Te⊥>Te∥) were observed. Another aim of the paper is to distinguish bow shock‐induced field and flow perturbations from reconnection‐related signatures. The high‐resolution MMS data together with 2‐D hybrid simulations of bow shock dynamics helped us to distinguish between the two sources. We show examples of bow shock‐related effects (such as heating) and reconnection effects such as accelerated flows satisfying the Walén relation.

Effects of a Guide Field on the Larmor Electric Field and Upstream Electron Temperature Anisotropy in Collisionless Asymmetric Magnetic Reconnection

Abstract We perform the first study of the properties of the Larmor electric field (LEF) in collisionless asymmetric magnetic reconnection in the presence of an out-of-plane (guide) magnetic field for different sets of representative upstream parameters at Earth’s dayside magnetopause with an ion temperature greater than the electron temperature (the ion-to-electron temperature ratio fixed at 2) using two-dimensional particle-in-cell simulations. We show that the LEF does persist in the presence of a guide field. We study how the LEF thickness and strength change as a function of guide field and the magnetospheric temperature and reconnecting magnetic field strength. We find that the thickness of the LEF structure decreases, while its magnitude increases when a guide field is added to the reconnecting magnetic field. The added guide field makes the Larmor radius smaller, so the scaling with the magnetospheric ion Larmor radius is similar to that reported for the case without a guide field. Note, however, that the physics causing the LEF is not well understood, so future work in other parameter regimes is needed to fully predict the LEF for arbitrary conditions. We also find that a previously reported upstream electron temperature anisotropy arises in the vicinity of the LEF region both with and without a guide field. We argue that the generation of the anisotropy is linked to the existence of the LEF. The LEF can be used in combination with the electron temperature anisotropy as a signature to effectively identify dayside reconnection sites in observations.

Bursty emission of whistler waves in association with plasmoid collision

Abstract. A new mechanism to generate whistler waves in the course of collisionless magnetic reconnection is proposed. It is found that intense whistler emissions occur in association with plasmoid collisions. The key processes are strong perpendicular heating of the electrons through a secondary magnetic reconnection during plasmoid collision and the subsequent compression of the ambient magnetic field, leading to whistler instability due to the electron temperature anisotropy. The emissions have a bursty nature, completing in a short time within the ion timescales, as has often been observed in the Earth's magnetosphere. The whistler waves can accelerate the electrons in the parallel direction, contributing to the generation of high-energy electrons. The present study suggests that the bursty emission of whistler waves could be an indicator of plasmoid collisions and the associated particle energization during collisionless magnetic reconnection.

Electron temperature anisotropy associated to field‐aligned currents in the Earth's magnetosphere inferred from Rosetta MIP‐RPC observations during 2009 flyby

AbstractA new approach is proposed for data interpretation of the Mutual Impedance Probe (MIP) instrument from the Rosetta Plasma Consortium (RPC) during the 2009 Earth's flyby gravity assist through the magnetosphere, from dusk to dawn regions. The spacecraft trajectory of ±8 RE (Earth's radius) was crossing several structures of field‐aligned currents (FACs) and radiations belts on both legs of the closest approach (CA, 2.450 km altitude). As routinely revealed by several pioneering space missions, natural and forced electrostatic wave emissions called Fqs were observed over ±3 RE at around CA using a dedicated mode of the MIP instrument. These emissions are lying between consecutive harmonics of the electron‐cyclotron frequency, and their wavelength is perpendicular to the magnetic field lines. Provided that the Fq's wavelengths projected along the MIP antenna might be estimated, it is shown that the local value of the Larmor radius can be deduced; hence, the electron temperature component perpendicular to the magnetic field is subsequently derived. On the other hand, during the time of Fq's observations, the presence of VLF hiss emissions usually observed in these regions gives us the possibility to determine the electron temperature anisotropy associated to the electrostatic electron anisotropy instability according to the theoretical model proposed by Gary and Cairns (JGR, vol. 104, 1999). Significant dynamic constraints revealed by crossing successive series of FACs tubes are shown being controlled by this anisotropy, and the fact that the magnetic pressure is significantly larger than the thermal pressure suggests that the FACs lobes are nonforce free.