Electron Temperature Anisotropy Research Articles

Kinetic theory of double layers driven by temperature anisotropy in a non-homogeneous magnetic field

A double layer (DL) is created in a plasma when the plasma is perturbed in the presence of a temperature anisotropy. We derive a new simple theory for the existence of an unstable, non-oscillatory electrostatic DL-like structure in the presence of a magnetic field gradient in a collisionless plasma with a temperature anisotropy in the direction perpendicular to the magnetic field. The DL is treated as a wave perturbation in the plasma using kinetic theory with a gyro-kinetic approximation to obtain a dispersion relation. The presence of an electron temperature anisotropy is the necessary condition to obtain an exponentially growing instability, and the corresponding growth rate is found to be the ratio of the electron kinetic energy and the electric field energy across the DL region. The theoretical predictions are then validated against a one-dimensional electrostatic particle simulation carried out in a traveling magnetic field thruster environment. An anisotropy ratio parameter was introduced, and the theoretical growth rates were found to be in good agreement with the simulation for different anisotropy ratios. An ion beam, associated with the DL dynamics, is observed within the simulation domain. A parametric study revealed that the DL-like structure loses its ambipolar shape for temperature ratios less than 10. It has been found that a stronger anisotropy is required to obtain the DL-like structure.

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

Abstract The role of solar wind expansion in generating whistler waves is investigated using the EB-iPic3D code, which models solar wind expansion self-consistently within a fully kinetic semi-implicit approach. The simulation is initialized with an electron velocity distribution function modeled after observations of the Parker Solar Probe during its first perihelion at 0.166 au, consisting of a dense core and an antisunward strahl. This distribution function is initially stable with respect to kinetic instabilities. Expansion drives the solar wind into successive regimes where whistler heat flux instabilities are triggered. These instabilities produce sunward whistler waves initially characterized by predominantly oblique propagation with respect to the interplanetary magnetic field. The excited waves interact with the electrons via resonant scattering processes. As a consequence, the strahl pitch angle distribution broadens and its drift velocity reduces. The strahl electrons are scattered in the direction perpendicular to the magnetic field, and an electron halo is formed. At a later stage, resonant electron firehose instability is triggered and further affects the electron temperature anisotropy as the solar wind expands. Wave–particle interaction processes are accompanied by a substantial reduction of the solar wind heat flux. The simulated whistler waves are in qualitative agreement with observations in terms of wave frequencies, amplitudes, and propagation angles. Our work proposes an explanation for the observations of oblique and parallel whistler waves in the solar wind. We conclude that solar wind expansion has to be factored in when trying to explain kinetic processes at different heliocentric distances.

Characteristics of Resonant Electrons Interacting With Whistler Waves in the Nearest Dipolarizing Magnetotail

AbstractThe Magnetospheric Multiscale spacecraft observations in the burst mode allow the determination of the characteristics of resonant electrons interacting with quasi‐parallel whistler waves during prolonged dipolarizations in the near Earth magnetotail at −22 RE < X ≤ −8 RE. We have detected 163 whistler bursts observed during 48 dipolarization events. The bursts were registered within ∼13 min following the dipolarization onset when the burst mode observations were available. In the majority of events, electrons with energies Wres ≥ 10 keV and pitch angles αres ∼ 100°–130° and αres ∼ 50°–80°made the maximum positive contribution to the growth rate of whistler waves propagating quasi‐parallel and antiparallel to the ambient magnetic field, respectively. Our analysis shows that electrons with Wres ∼ 10–20 keV could potentially be scattered into the loss cone by the low frequency whistler waves with fw ∼ (0.05–0.2)fce (fw is the wave frequency and fce is the electron gyrofrequency). The electrons that are scattered into the loss cone can contribute to electron precipitation within ∼13 min following the dipolarization onset. We suggest that whistler waves that are excited due to cyclotron instability driven by the temperature anisotropy of suprathermal electrons (≥2 keV) may, in turn, affect electron distribution in this energy range. Specifically, lower energy resonant electrons transfer a part of their kinetic energy to waves, while more energetic electrons absorb wave energy increasing their kinetic energy. This may lead to the transformation of higher‐energy part of electron distribution from Maxwellian to the power law shape.

Effects of Multiscale Plasma Waves on Electron Preacceleration at Weak Quasi-perpendicular Intracluster Shocks

Abstract Radio relics associated with merging galaxy clusters indicate the acceleration of relativistic electrons in merger-driven shocks with low sonic Mach numbers (M s ≲ 3) in the intracluster medium (ICM). Recent studies have suggested that electron injection to diffusive shock acceleration (DSA) could take place through the so-called Fermi-like acceleration in the shock foot of β = P gas/P B ≈ 20–100 shocks and the stochastic shock drift acceleration (SSDA) in the shock transition of β ≈ 1–5 shocks. Here, we explore how the SSDA can facilitate electron preacceleration in weak quasi-perpendicular (Q ⊥) shocks in β ≈ 20–100 plasmas by performing particle-in-cell simulations in a two-dimensional domain large enough to properly encompass ion-scale waves. We find that in supercritical shocks with M s ≳ M AIC * ∼ 2.3 , multiscale waves are excited by the ion and electron temperature anisotropies in the downstream of the shock ramp, and that through stochastic pitch-angle scattering off the induced waves, electrons are confined in the shock transition for an extended period. Gaining energy through the gradient-drift along the motional electric field, electrons could be preaccelerated all the way to injection to DSA at such ICM shocks. Our findings imply that the electron DSA process at weak ICM shocks could explain the origin of radio relics. However, a further investigation of electron acceleration at subcritical shocks with M s < 2.3 is called for, since the Mach numbers of some observed radio relic shocks derived from radio or X-ray observations are as low as M s ∼ 1.5.

2D particle-in-cell simulations of the electron temperature anisotropy driven whistler instability in plasmas having kappa velocity distributions

This study presents the results of 2D particle-in-cell (PIC) simulations of the electron temperature anisotropy driven whistler instability for plasmas in which the electron species is modeled by a bi-kappa velocity distribution. These simulations utilize our previously developed method to generate the initial multi-dimensional kappa velocity distributions. The use of multi-dimensional kappa loadings in PIC simulations provides insights into the non-linear regime of wave evolution in plasmas having non-equilibrium velocity distributions. Three cases are considered, corresponding to κe=2,3, and ∞ (Maxwellian case). Owing to the use of a large value of electron anisotropy required for reasonable simulation run times, the Maxwellian electron run has the fastest growth rate, reaching saturation earliest. The κe=2 case exhibits the slowest growth rate. Spectral analysis of the fluctuating fields reveals considerable wave intensity at frequencies and wavenumbers that satisfy the linear whistler wave dispersion relation. In the runs with kappa distributions, the regions of most intense fluctuations comprise frequencies and wavenumbers that agree only qualitatively with linear whistler wave theory. The results suggest that after saturation, there is some degree of Landau damping of the oblique whistler modes, which returns energy to the electron species. The rate of damping of the oblique modes is highest in the Maxwellian case and lowest for κe=2. Evidence of significant superthermal acceleration of electrons in the direction parallel to the ambient magnetic field is also observed. Thus, the power-law index of the electron distribution is reduced by the anisotropic whistler turbulence produced.

Microinstabilities in the Transition Region of Weak Quasi-perpendicular Intracluster Shocks

Abstract Microinstabilities play important roles in both entropy generation and particle acceleration in collisionless shocks. Recent studies have suggested that in the transition region of quasi-perpendicular (Q ⊥) shocks in the high-beta (β = P gas/P B) intracluster medium (ICM), the ion temperature anisotropy due to the reflected-gyrating ions could trigger the Alfvén ion cyclotron (AIC) instability and the ion-mirror instability, while the electron temperature anisotropy induced by magnetic field compression could excite the whistler instability and the electron-mirror instability. Adopting the numerical estimates for ion and electron temperature anisotropies found in the particle-in-cell (PIC) simulations of Q ⊥ shocks with sonic Mach numbers, M s = 2–3, we carry out a linear stability analysis for these microinstabilities. The kinetic properties of the microinstabilities and the ensuing plasma waves on both ion and electron scales are described for wide ranges of parameters, including β and the ion-to-electron mass ratio. In addition, the nonlinear evolution of the induced plasma waves are examined by performing 2D PIC simulations with periodic boundary conditions. We find that for β ≈ 20–100, the AIC instability could induce ion-scale waves and generate shock surface ripples in supercritical shocks above the AIC critical Mach number, M AIC * ≈ 2.3 . Also, electron-scale waves are generated primarily by the whistler instability in these high-β shocks. The resulting multiscale waves from electron to ion scales are thought to be essential in the electron injection to diffusive shock acceleration in Q ⊥ shocks in the ICM.

Gap Formation Around 0.5Ωe of Whistler‐Mode Waves Excited by Electron Temperature Anisotropy

AbstractWith a one‐dimensional particle‐in‐cell simulation model, we have investigated the gap formation around 0.5 of the quasi‐parallel whistler‐mode waves excited by an electron temperature anisotropy. When the frequencies of excited waves in the linear stage cross 0.5, or when they are slightly larger than 0.5 but then drift to lower values, the Landau resonance can make the electron distribution form a beam‐like/plateau population. Such an electron distribution only slightly changes the dispersion relation of whistler‐mode waves, but can cause severe damping around 0.5 via cyclotron resonance. At last, the wave spectrum is separated into two bands with a power gap around 0.5. The condition under different electron temperature anisotropy and plasma beta is also surveyed for such kind of power gap. Besides, when only the waves with frequencies lower than 0.5 are excited in the linear stage, a power gap can also be formed due to the wave‐wave interactions, i.e., lower band cascade. Our study provides a clue to reveal the well‐known 0.5 power gap of whistler‐mode waves ubiquitously observed in the inner magnetosphere.

Impact of electron temperature anisotropy on the collisionless tearing mode instability in the presence of a strong guide field

We derive and analyze a dispersion relation for the growth rate of collisionless tearing modes, driven by electron inertia and accounting for equilibrium electron temperature anisotropy in a strong guide field regime. For this purpose, a new gyrofluid model is derived and subsequently simplified to make the derivation of the dispersion relation treatable analytically. The main simplifying assumptions consist in assuming cold ions, neglecting electron finite Larmor radius effects, decoupling ion gyrocenter fluctuations, and considering β⊥e≪1, with β⊥e indicating the ratio between the perpendicular electron thermal pressure and the magnetic pressure exerted by the guide field. This simplified version of the gyrofluid model is shown to possess a noncanonical Hamiltonian structure. The dispersion relation is obtained by applying the theory of asymptotic matching and does not predict an enhancement of the growth rate as the ratio Θe between perpendicular and parallel equilibrium electron temperatures increases. This indicates a significant difference with respect to the case of absent or moderate guide field. For an equilibrium magnetic shear length of the order of the perpendicular sonic Larmor radius and at a fixed β⊥e, we obtain that the tearing mode in the strong guide field regime gets actually weakly damped, as Θe increases. In the isotropic limit Θe=1, the dispersion relation reduces to a previously known formula. The analytical predictions are tested against numerical simulations, showing a very good quantitative agreement. We also provide a detailed discussion of the range of validity of the derived dispersion relation and of the compatibility among the different adopted assumptions.

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.

Lower Hybrid Drift Waves During Guide Field Reconnection

AbstractGeneration and propagation of lower hybrid drift wave (LHDW) near the electron diffusion region (EDR) during guide field reconnection at the magnetopause is studied with data from the Magnetospheric Multiscale mission and a theoretical model. Inside the current sheet, the electron beta (βe) determines which type of LHDW is excited. Inside the EDR, where the electron beta is high (βe ∼ 5), the long‐wavelength electromagnetic LHDW is observed propagating obliquely to the local magnetic field. In contrast, the short‐wavelength electrostatic LHDW, propagating nearly perpendicular to the magnetic field, is observed slightly away from the EDR, where βe is small (∼0.6). These observed LHDW features are explained by a local theoretical model, including effects from the electron temperature anisotropy, finite electron heat flux, electrostatics, and parallel current. The short‐wavelength LHDW is capable of generating significant drag force between electrons and ions.

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.

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.

Linear stability of magnetic vortex chains in a plasma in the presence of equilibrium electron temperature anisotropy

The linear stability of chains of magnetic vortices in a plasma is investigated analytically in two dimensions by means of a reduced fluid model assuming a strong guide field and accounting for equilibrium electron temperature anisotropy. The chain of magnetic vortices is modeled by means of the classical ‘cat’s eyes’ solutions and the linear stability is studied by analysing the second variation of a conserved functional, according to the energy-Casimir method. The stability analysis is carried out on the domain bounded by the separatrices of the vortices. Two cases are considered, corresponding to a ratio between perpendicular equilibrium ion and electron temperature much greater or much less than unity, respectively. In the former case, equilibrium flows depend on an arbitrary function. Stability is attained if the equilibrium electron temperature anisotropy is bounded from above and from below, with the lower bound corresponding to the condition preventing the firehose instability. A further condition sets an upper limit to the amplitude of the vortices, for a given choice of the equilibrium flow. For cold ions, two sub-cases have to be considered. In the first one, equilibria correspond to those for which the velocity field is proportional to the local Alfvén velocity. Stability conditions imply: an upper limit on the amplitude of the flow, which automatically implies firehose stability, an upper bound on the electron temperature anisotropy and again an upper bound on the size of the vortices. The second sub-case refers to equilibrium electrostatic potentials which are not constant on magnetic flux surfaces and the resulting stability conditions correspond to those of the first sub-case in the absence of flow.

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.

Effects of Electron Temperature Anisotropy on Proton-beam Instability in the Solar Wind

Abstract Solar wind observations often show that the drift velocity of a proton beam relative to a background proton decreases with the heliocentric distance. Proton-beam instability has been suggested to play an important role in the deceleration of the proton-beam velocity; the effects of electron temperature anisotropy on the proton-beam instability have not been examined. Based on a general kinetic dispersion relation solver for magnetized plasma (PDRK), we investigate the effects of electron temperature anisotropy on the oblique Alfvén/ion-cyclotron (A/IC) and parallel magnetosonic/whistler (M/W) instabilities driven by proton beams in the solar wind. The results show that the growth rates, real frequencies, and threshold conditions for both instabilities are sensitive to the electron temperature anisotropy T e⊥/T e∣∣ and the parallel electron beta β e∣∣. In the low-beta regime with , where is a critical plasma beta for which the threshold velocities of both instabilities are equal, the growth rate of the oblique A/IC instability is weakly dependent on the electron temperature anisotropy. In the high-beta regime with , the growth rate of the parallel M/W instability increases with decreasing T e⊥/T e∣∣. Moreover, the threshold velocities of both instabilities are shifted to lower values as T e⊥/T e∣∣ decreases, especially for the parallel M/W instability in the regime with β e∣∣ ≥ 1. The theoretical results for the threshold velocity together with the observed parallel electron beta and/or electron temperature anisotropy are used to explain the observed proton-beam drift velocity in the solar wind.

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.

Excitation of Whistler Waves Through the Bidirectional Field‐Aligned Electron Beams With Electron Temperature Anisotropy: MMS Observations

AbstractUsing four‐point measurements from the Magnetospheric Multiscale (MMS) mission, we identify whistler waves at the boundary of an ion scale magnetic hole, which should be locally excited rather than propagated from other regions. Based on the measured local plasma parameters, which include those for bidirectional electron beams with electron temperature anisotropy, the frequency range with the growth rate derived from kinetic theory is consistent with the observations, while the growth rate in the absence of such beams is negative; hence, the observed whistler waves are locally excited by the bidirectional electron beams with electron temperature anisotropy. The dispersion relation, derived from one‐dimensional particle‐in‐cell simulations that are conducted using the inputs of the bidirectional electron beams with electron temperature anisotropy, agrees well with the one from kinetic theory, which further supports this excitation mechanism. Our results shed light on a new excitation mechanism for whistler waves.

Hot Plasma Effects on the Pitch-angle Scattering Rates of Radiation Belt Electrons Due to Plasmaspheric Hiss

Abstract Plasmaspheric hiss is known to be a major contributor to the dynamic losses of Earth’s radiation belt electrons. While previous computation attempts of hiss-driven electron losses are limited to the cold plasma approximation, in this study we find that hot plasma effects will modify the hiss dispersion relation and result in changes in the electron bounce-averaged electron pitch angle diffusion coefficients. Cold plasma approximation tends to overestimate the diffusion coefficients of ≲100 keV electrons by orders of magnitude, while the scattering efficiency of higher energy electrons is not greatly affected. As the L-shell decreases or the parameter decreases (where is the electron gyrofrequency and is the plasma frequency), the decrease of diffusion coefficients of low energy electrons caused by hot plasma effects become more pronounced. It is also shown that both the increase of hot electron abundance and temperature anisotropy can weaken the scattering efficiency of ≲100 keV electrons at almost all pitch angles, while the diffusion coefficients of higher energy electrons decrease at large pitch angles. Our study confirms the importance of including hot plasma effects in evaluations of hiss-driven scattering loss of radiation belt electrons.

Electron Firehose Instabilities in High-β Intracluster Shocks

Abstract The preacceleration of electrons through reflection and shock drift acceleration (SDA) is essential for the diffusive shock acceleration of nonthermal electrons in collisionless shocks. Previous studies suggested that, in weak quasi-perpendicular (Q ⊥) shocks in the high-β ( ) intracluster medium (ICM), the temperature anisotropy due to SDA-reflected electrons can drive the electron firehose instability, which excites oblique nonpropagating waves in the shock foot. In this paper, we investigate, through a linear analysis and particle-in-cell simulations, the firehose instabilities driven by an electron temperature anisotropy (ETAFI) and also by a drifting electron beam (EBFI) in β ∼ 100 ICM plasmas. The EBFI should be more relevant to describing the self-excitation of upstream waves in Q ⊥-shocks, since backstreaming electrons in the shock foot behave more like an electron beam rather than an anisotropic bi-Maxwellian population. We find that the basic properties of the two instabilities, such as the growth rate, γ, and the wavenumber of fast-growing oblique modes, are similar in the ICM environment, with one exception; while the waves excited by the ETAFI are nonpropagating (ω r = 0), those excited by the EBFI have a nonzero frequency ( ). However, the frequency is small with ω r < γ. Thus, we conclude that the interpretation of previous studies for the nature of upstream waves based on the ETAFI remains valid in Q ⊥-shocks in the ICM.

Particle-in-cell Simulations of the Parallel Proton Firehose Instability Influenced by the Electron Temperature Anisotropy in Solar Wind Conditions

Abstract In situ observations of the solar wind show a limited level of particle temperature anisotropy with respect to the interplanetary magnetic field direction. Kinetic electromagnetic instabilities are efficient to prevent the excessive growth of the anisotropy of particle velocity distribution functions. Among them, the firehose instabilities are often considered to prevent the increase of the parallel temperature and hence to shape the velocity distribution functions of electrons and protons in the solar wind. We present a nonlinear modeling of the parallel firehose instability, retaining a kinetic description for both the electrons and protons. One-dimensional (1D) fully kinetic particle-in-cell simulations using the energy conserving semi-implicit method (ECsim) are performed to clarify the role of the electron temperature anisotropy in the development of the parallel proton firehose instability. We found that in the presence of an electron temperature anisotropy, such that the temperature parallel to the background magnetic field is higher than the temperature in the perpendicular direction, the onset of the parallel proton firehose instability occurs earlier and its growth rate is faster. The enhanced wave fluctuations contribute to the particle scattering reducing the temperature anisotropy to a stable, nearly isotropic state. The simulation results compare well with linear theory. A test case of 1D simulations at oblique angles with respect to the magnetic field is also considered, as a first step to study the cumulative effect of protons and electrons on the full spectrum of instabilities.