Parallel Firehose Instability Research Articles

Proton temperature relaxation in the solar wind by combined collective and collisional processes

AbstractIt is well established that various plasma instabilities regulate the proton temperature anisotropy in the solar wind. However, the question of why majority of data in phase space are broadly distributed near isotropic conditions has not been successfully addressed. Among possible causes are local perpendicular heating, binary collisions, and geometrical effects. The present paper examines the influence of binary collisions, based upon recently formulated collisional transport theory for magnetized plasmas combined with macroscopic quasilinear theory for proton cyclotron and parallel firehose instabilities. The spatial development of perpendicular and parallel temperatures for protons as well as spatial distribution of excited wave magnetic field energy density are studied by making use of model solar wind. The present finding suggests that binary collisions may contribute toward the isotropization process but does not completely explain the isotropization.

A STRINGENT LIMIT ON THE AMPLITUDE OF ALFVÉNIC PERTURBATIONS IN HIGH-BETA LOW-COLLISIONALITY PLASMAS

ABSTRACT It is shown that low-collisionality plasmas cannot support linearly polarized shear-Alfvén fluctuations above a critical amplitude , where β is the ratio of thermal to magnetic pressure. Above this cutoff, a developing fluctuation will generate a pressure anisotropy that is sufficient to destabilize itself through the parallel firehose instability. This causes the wave frequency to approach zero, interrupting the fluctuation before any oscillation. The magnetic field lines rapidly relax into a sequence of angular zig-zag structures. Such a restrictive bound on shear-Alfvén-wave amplitudes has far-reaching implications for the physics of magnetized turbulence in the high-β conditions prevalent in many astrophysical plasmas, as well as for the solar wind at ∼1 au where β ≳ 1.

Effects of alpha-proton drift velocity on alpha particle firehose instability

In situ measurements have shown that the less-abundant alpha particles are characterized by temperature anisotropy which could drive the anisotropy-driven kinetic instabilities in the solar wind. In the collisionless plasma, the differential alpha-proton flow velocity Vd=Vα−Vp usually has a non-zero value of the order of the local Alfvén velocity. The presence of such differential flow may affect the properties of dispersion relations for anisotropy-driven instabilities. Based upon linear Vlasov dispersion theory in a homogeneous plasma, the present study investigates the effects of the alpha-proton drift velocity on the parallel and oblique firehose instabilities driven by an excessive parallel temperature anisotropy of alpha particles, where the parallel and oblique represent directions of fluctuation propagation relative to the background magnetic field. It is found that for oblique firehose mode as well as parallel mode, the dispersion properties are affected by the presence of the alpha-proton drift velocity, which in turn results in the increase of the maximum growth rates as Vd increases and consequently leads to the modification of the marginal stability conditions in the parameter space (β∥α,T⊥α/T∥α). We discuss the relevance of our results to the measured temperature anisotropy of alpha particles in the solar wind context.

Limits on the ion temperature anisotropy in the turbulent intracluster medium

Turbulence in the weakly collisional intracluster medium of galaxies (ICM) is able to generate strong thermal velocity anisotropies in the ions (with respect to the local magnetic field direction), if the magnetic moment of the particles is conserved in the absence of Coulomb collisions. In this scenario, the anisotropic pressure magnetohydrodynamic (AMHD) turbulence shows a very different statistical behaviour from the standard MHD one and is unable to amplify seed magnetic fields, in disagreement with previous cosmological MHD simulations which are successful to explain the observed magnetic fields in the ICM. On the other hand, temperature anisotropies can also drive plasma instabilities which can relax the anisotropy. This work aims to compare the relaxation rate with the growth rate of the anisotropies driven by the turbulence. We employ quasilinear theory to estimate the ions scattering rate due to the parallel firehose, mirror, and ion-cyclotron instabilities, for a set of plasma parameters resulting from AMHD simulations of the turbulent ICM. We show that the ICM turbulence can sustain only anisotropy levels very close to the instabilities thresholds. We argue that the AMHD model which bounds the anisotropies at the marginal stability levels can describe the Alfvenic turbulence cascade in the ICM.

Parallel and oblique firehose instability thresholds for bi‐kappa distributed protons

AbstractThe parallel and the oblique firehose instability are generally accepted as the leading mechanisms shaping the boundaries of the protons' pressure anisotropies observed in the solar wind for p∥>p⊥. However, it is still an open question which instability dominates this process. Only recently, first attempts were made to study the linear growth of the parallel firehose assuming more realistic bi‐kappa velocity distributions instead of traditionally used bi‐Maxwellians. We apply a newly developed, fully kinetic dispersion solver to numerically derive the instability thresholds for both firehose instabilities. In contrast to former findings, we observe that the presence of suprathermal populations yields a growth amplification which lowers the instability threshold of the parallel firehose. This is due to enhanced cyclotron resonance. For the first time, we also look at the oblique firehose threshold and find a contrary picture. Here the presence of suprathermal particles leads to an increase of the instability threshold. The enhancement of the parallel firehose and the suppression of the oblique firehose are expected to be of relevance in the solar wind and may alter the competition between both instabilities. Based on our findings, we propose a method how solar wind data could be used to identify the instability mechanism dominating this competition and shaping the observed anisotropy boundary.

FIRE HOSE INSTABILITY DRIVEN BY ALPHA PARTICLE TEMPERATURE ANISOTROPY

We investigate properties of a solar wind-like plasma including a secondary alpha particle population exhibiting a parallel temperature anisotropy with respect to the background magnetic field, using linear and quasi-linear predictions and by means of one-dimensional hybrid simulations. We show that anisotropic alpha particles can drive a parallel fire hose instability analogous to that generated by protons, but that, remarkably, the instability can be triggered also when the parallel plasma beta of alpha particles is below unity. The wave activity generated by the alpha anisotropy affects the evolution of the more abundant protons, leading to their anisotropic heating. When both ion species have sufficient parallel anisotropies both of them can drive the instability, and we observe generation of two distinct peaks in the spectra of the fluctuations, with longer wavelengths associated to alphas and shorter ones to protons. If a non-zero relative drift is present, the unstable modes propagate preferentially in the direction of the drift associated with the unstable species. The generated waves scatter particles and reduce their temperature anisotropy to marginally stable state, and, moreover, they significantly reduce the relative drift between the two ion populations. The coexistence of modes excited by both species leads to saturation of the plasma in distinct regions of the beta/anisotropy parameter space for protons and alpha particles, in good agreement with in situ solar wind observations. Our results confirm that fire hose instabilities are likely at work in the solar wind and limit the anisotropy of different ion species in the plasma.

Proton‐cyclotron and firehose instabilities in inhomogeneous plasmas

AbstractBy combining the kinetic‐fluid model for macroscopic quantities and quasilinear kinetic theory for microscopic plasma instabilities, the present paper investigates quasi‐stationary spatial distribution and characteristics of the electromagnetic proton‐cyclotron and parallel firehose instabilities in inhomogeneous plasma, as well as their influence on macroscopic variables. The present paper considers diverging magnetic field along a flux tube, as well as the associated density model, with various source region boundary conditions, in order to investigate the spatial locations at which the excitation, saturation, and damping of the proton‐cyclotron and firehose instabilities occur in a medium with field‐aligned inhomogeneity. Potential application may be on the solar wind model in which the temperature anisotropy threshold rigorously follows as a result of quasilinear relaxation process.

EFFECTS OF ELECTRONS ON THE SOLAR WIND PROTON TEMPERATURE ANISOTROPY

Among the kinetic microinstabilities, the firehose instability is one of the most efficient mechanisms to restrict the unlimited increase of temperature anisotropy in the direction of an ambient magnetic field as predicted by adiabatic expansion of collision-poor solar wind. Indeed, the solar wind proton temperature anisotropy detected near 1 AU shows that it is constrained by the marginal firehose condition. Of the two types of firehose instabilities, namely, parallel and oblique, the literature suggests that the solar wind data conform more closely to the marginal oblique firehose condition. In the present work, however, it is shown that the parallel firehose instability threshold is markedly influenced by the presence of anisotropic electrons, such that under some circumstances, the cumulative effects of both electron and proton anisotropies could describe the observation without considering the oblique firehose mode.

The Electron Firehose and Ordinary-Mode Instabilities in Space Plasmas

The selfgenerated wave fluctuations are particularly interesting in the solar wind and magnetospheric plasmas, where Coulomb collisions are rare and cannot explain the observed states of quasi-equilibrium. Linear theory predicts that the firehose and the ordinary-mode instabilities can develop under the same conditions, confusing the role of these instabilities in conditioning the space-plasma properties. The hierarchy of these two instabilities is reconsidered here for nonstreaming plasmas with an electron temperature anisotropy $T_\parallel > T_\perp$, where $\parallel$ and $\perp$ denote directions with respect to the local mean magnetic field. In addition to the previous comparative analysis, here the entire 3D wave-vector spectrum of the competing instabilities is investigated, paying particular attention to the oblique firehose instability and the relatively poorly known ordinary-mode instability. Results show a dominance of the oblique firehose instability with a threshold lower than the parallel firehose instability and lower than the ordinary-mode instability. For larger anisotropies, the ordinary mode can grow faster, with maximum growth rates exceeding the ones of the oblique firehose instability. In contrast to previous studies that claimed a possible activity of the ordinary-mode in the small $\beta [< 1]$ regimes, here it is rigorously shown that only the large $\beta [> 1]$ regimes are susceptible to these instabilities.

Quasilinear theory of anisotropy‐beta relations for proton cyclotron and parallel firehose instabilities

The solar wind and the Earth's magnetosheath frequently possess proton temperature anisotropies that violate the predictions of adiabatic fluid theory. In the literature, various threshold conditions expressed as inverse correlations between the proton anisotropy, T⊥/T∥, and parallel beta, β∥, have been constructed on the basis of linear stability analysis for anisotropy‐driven instabilities, hybrid simulations, or by simply fitting the observations. ForT⊥/T∥ &gt; 1, proton cyclotron and mirror instabilities are operative, while for T∥ &gt; T⊥, parallel and oblique firehose instabilities can be taken into account in the construction of the inverse correlation. In the present paper, quasilinear kinetic theory of parallel proton cyclotron and firehose instabilities are employed to self‐consistently construct theT⊥/T∥ vs β∥threshold conditions. In principle, such an approach eliminates the necessity for empirical models of inverse correlations, since inverse correlations should naturally emerge as the time‐asymptotic states of quasilinear processes. It is found that the self‐consistent threshold conditions constructed on the basis of quasilinear formalism compare reasonably well with available models, thus confirming that quasilinear method is a reasonable approach.

INSTABILITY-DRIVEN LIMITS ON HELIUM TEMPERATURE ANISOTROPY IN THE SOLAR WIND: OBSERVATIONS AND LINEAR VLASOV ANALYSIS

Kinetic microinstabilities in the solar wind arise when the plasma deviates too far from thermal equilibrium. Previously published work has provided strong evidence that the cyclotron, mirror, and parallel and oblique firehose instabilities limit proton (i.e., ionized hydrogen) temperature anisotropy. However, few studies have thoroughly explored whether a less-abundant ion species can also trigger these instabilities. This study considered the possibility of similar instability-driven limits on ?-particle (i.e., fully ionized helium) temperature anisotropy. Linear Vlasov analysis was used to derive the expected threshold conditions for instabilities driven by ?-particle temperature anisotropy. Measurements in situ of ?-particle temperature anisotropy from the Wind spacecraft's Faraday cups were found to be consistent with the limits imposed by these instability thresholds. This strongly suggests that ?-particles, which only constitute ~5% of ions in the solar wind, can drive an instability if their temperature anisotropy becomes sufficiently extreme.

EFFECT OF DIFFERENTIAL FLOW OF ALPHA PARTICLES ON PROTON PRESSURE ANISOTROPY INSTABILITIES IN THE SOLAR WIND

In the solar wind, when the effects of proton-proton Coulomb collisions are negligible, alpha particles usually flow faster than the protons in such a way that the differential alpha-proton flow velocity V{sub d} = V{sub {alpha}} - V{sub p} is on the order of the Alfven speed, is directed away from the Sun, and is nearly aligned with the local mean magnetic field. When this differential flow is taken into account, solutions of the hot plasma dispersion relation show that for the parallel propagating electromagnetic ion cyclotron (EMIC) instability driven by the proton temperature anisotropy T{sub perpendicularp} > T{sub ||p}, the maximum growth rate occurs in the + V{sub d} direction and for the parallel firehose instability driven by the opposite proton temperature anisotropy T{sub ||p} > T{sub perpendicularp}, the maximum growth rate occurs in the - V{sub d} direction. Thus, the EMIC instability preferentially generates left circularly polarized Alfven-ion-cyclotron waves propagating away from the Sun and the parallel firehose instability preferentially generates right circularly polarized magnetosonic-whistler waves propagating toward the Sun with the maximum growth rates occurring for frequencies on the order of the proton cyclotron frequency and wavenumbers on the order of the proton inertial length. Because ofmore » the Doppler shift caused by the motion of the solar wind, both types of waves are left circularly polarized in the spacecraft frame for observations taken when the local mean magnetic field is collinear with the solar wind flow velocity. Theoretical investigation of these instabilities also shows that regions of parameter space exist where the unstable waves are generated propagating unidirectionally such as, for the EMIC instability for example, when the temperature anisotropy is small |(T{sub perpendicular{sub p}}/T{sub ||{sub p}}) - 1| < 1. Taken together, the above properties can explain the origin of parallel propagating electromagnetic waves recently observed near the proton inertial length in high-speed solar wind. The observed waves are most likely produced in situ by these instabilities. A remarkable property of the proposed mechanism that may be of practical importance is that the magnetic helicity of the unstable waves has the same sign no matter whether the proton temperature anisotropy (T{sub p{sub perpendicular}}/T{sub p{sub ||}}) - 1 is positive or negative.« less

Proton core-beam system in the expanding solar wind: Hybrid simulations

[1] Results of a two-dimensional hybrid expanding box simulation of a proton beam-core system in the solar wind are presented. The expansion with a strictly radial magnetic field leads to a decrease of the ratio between the proton perpendicular and parallel temperatures as well as to an increase of the ratio between the beam-core differential velocity and the local Alfvén velocity creating a free energy for many different instabilities. The system is indeed most of the time marginally stable with respect to the parallel magnetosonic, oblique Alfvén, proton cyclotron and parallel fire hose instabilities which determine the system evolution counteracting some effects of the expansion and interacting with each other. Nonlinear evolution of these instabilities leads to large modifications of the proton velocity distribution function. The beam and core protons are slowed with respect to each other and heated, and at later stages of the evolution the two populations are not clearly distinguishable. On the macroscopic level the instabilities cause large departures from the double adiabatic prediction leading to an efficient isotropization of effective proton temperatures in agreement with Helios observations.

A non-linear theory of the parallel firehose and gyrothermal instabilities in a weakly collisional plasma

Weakly collisional magnetized cosmic plasmas have a dynamical tendency to develop pressure anisotropies with respect to the local direction of the magnetic field. These anisotropies trigger plasma instabilities at scales just above the ion Larmor radius ρi and much below the mean free path λmfp. They have growth rates of a fraction of the ion cyclotron frequency, which is much faster than either the global dynamics or even local turbulence. Despite their microscopic nature, these instabilities dramatically modify the transport properties and, therefore, the macroscopic dynamics of the plasma. The non-linear evolution of these instabilities is expected to drive pressure anisotropies towards marginal stability values, controlled by the plasma beta βi. Here this non-linear evolution is worked out in an ab initio kinetic calculation for the simplest analytically tractable example – the parallel (k⊥= 0) firehose instability in a high-beta plasma. An asymptotic theory is constructed, based on a particular physical ordering and leading to a closed non-linear equation for the firehose turbulence. In the non-linear regime, both the analytical theory and the numerical solution predict secular (∝t) growth of magnetic fluctuations. The fluctuations develop a k−3∥ spectrum, extending from scales somewhat larger than ρi to the maximum scale that grows secularly with time (∝t1/2); the relative pressure anisotropy (p⊥−p∥)/p∥ tends to the marginal value −2/βi. The marginal state is achieved via changes in the magnetic field, not particle scattering. When a parallel ion heat flux is present, the parallel firehose mutates into the new gyrothermal instability (GTI), which continues to exist up to firehose-stable values of pressure anisotropy, which can be positive and are limited by the magnitude of the ion heat flux. The non-linear evolution of the GTI also features secular growth of magnetic fluctuations, but the fluctuation spectrum is eventually dominated by modes around a maximal scale ∼ρilT/λmfp, where lT is the scale of the parallel temperature variation. Implications for momentum and heat transport are speculated about. This study is motivated by our interest in the dynamics of galaxy cluster plasmas (which are used as the main astrophysical example), but its relevance to solar wind and accretion flow plasmas is also briefly discussed.

Parallel proton fire hose instability in gyrotropic Hall MHD model

The linear theory and nonlinear evolution of parallel or classical fire hose instability previously studied based on hybrid particle simulations are examined within the framework of a gyrotropic Hall magnetohydrodynamic (MHD) model that incorporates the ion inertial effects arising from the Hall current but neglects the electron inertia in the generalized Ohm's law. Both the ion cyclotron and whistler waves become fire hose unstable for β∥ − &gt; 2 + λi2k2/2 with right‐handed circular polarization, where λi and k are the ion inertial length and wave number, respectively, implying that the ion inertia plays a stabilizing role in parallel fire hose instability. Substantial noncoplanar components of the magnetic field and flow velocity may develop as a result of Hall current. The evolution characteristics of magnetic field fluctuations may depend on the Hall parameter h = λi/λr, where λr is the resistive length. For moderately and highly dispersive cases the instability may be purely growing in the early stage with the development of soliton‐like structures with depressed magnetic field on the order of a few ion inertial lengths and become propagating with right‐handed circular polarization in the late phase when the waves have inversely cascaded to large‐amplitude Alfvén waves of longer wavelengths. Oscillatory and damping behavior resembling those found in the kinetic model may be reproduced for single‐mode perturbations of long wavelengths with h ≤ 1. The saturated magnetic field is found to comply with the quasi‐linear theory.

Magnetofluid dynamics of magnetized cosmic plasma: firehose and gyrothermal instabilities

Both global dynamics and turbulence in magnetized weakly collisional cosmic plasmas are described by general magnetofluid equations that contain pressure anisotropies and heat fluxes that must be calculated from microscopic plasma kinetic theory. It is shown that even without a detailed calculation of the pressure anisotropy or the heat fluxes, one finds the macroscale dynamics to be generically unstable to microscale Alfvenically polarized fluctuations. Two instabilities are considered in detail: the parallel firehose instability (including the finite-Larmor-radius effects that determine the fastest growing mode) and the gyrothermal instability (GTI). The latter is a new result - it is shown that a parallel ion heat flux destabilizes Alfvenically polarized fluctuations even in the absence of the negative pressure anisotropy required for the firehose. The main conclusion is that both pressure anisotropies and heat fluxes trigger plasma microinstabilities and, therefore, their values will likely be set by the nonlinear evolution of these instabilities. Ideas for understanding this nonlinear evolution are discussed. It is argued that cosmic plasmas will generically be "three-scale systems," comprising global dynamics, mesoscale turbulence and microscale plasma fluctuations. The astrophysical example of cool cores of galaxy clusters is considered and it is noted that observations point to turbulence in clusters being in a marginal state with respect to plasma microinstabilities and so it is the plasma microphysics that is likely to set the heating and conduction properties of the intracluster medium. In particular, a lower bound on the scale of temperature fluctuations implied by the GTI is derived.