Firehose Instability Research Articles

Development of Firehose Instability of a Magnetosonic Type in the Presence of High-Speed Proton Beams

One of the varieties of firehose instability, whose cause is not the temperature anisotropy of plasma particles but the dynamic pressure of the beam, is considered. It is shown that such a generation mechanism can lead to an effective increase in low-frequency perturbations not only of the Alfven type but also of the magnetosonic type and also lead to instability not only in the finite and high-pressure plasma but also in a low-pressure plasma. The characteristics of magnetosonic waves that are generated during the development of instability are investigated. The growth rate, the maximum inclination angle of the wave vector, the propagation velocity of the perturbations, and the criterion for the development of instability are found. The influence of the beam temperature on the characteristics of the generated perturbations is studied. As an example of the development of such instability, the formation process of the turbulent region in front of the shock wave of the Earth, as well as before the shock wave from the supernova, is analyzed.

Development of firehose instability of magnetosonic type in the presence of high-speed proton beams

Development of firehose instability of magnetosonic type in the presence of high-speed proton beams

Parallel firehose instability in electron-positron plasmas.

In a magnetized uniform plasma, firehose instability may arise as a result of pressure anisotropy of P_{||}>P_{⊥}, where P_{||} and P_{⊥} are the thermal pressure parallel and perpendicular to the magnetic field, respectively. In this paper, we examine the parallel firehose instability in electron-positron plasmas based on the particle simulations along with the linear fluid theory, which may give rise to the dispersion relation, instability criteria, and growth rate, etc., for comparisons with those calculated from the kinetic simulations. As for the firehose instability in electron-proton plasmas, the magnetic field grows rapidly and then decreases with oscillations. The nonlinear saturated state complies with the linear stability criterion, α=μ_{0}(P_{||}-P_{⊥})/B^{2}=1, derived from the fluid theory only for relatively smaller values of initial α or ω_{p}/ω_{c}, where ω_{p} and ω_{c} are the plasma and cyclotron frequencies, respectively. For relatively larger values of initial α and ω_{p}/ω_{c}, the saturated α values are smaller than 1 as a result of kinetic resonant effects. The dominant wave numbers are kc/ω_{p}<0.5 and the growth rates are in the range of 0.1-0.3ω_{c}, which are approximately consistent with the linear fluid theory for the same wavelengths. Both electrostatic and electromagnetic modes predicted by the linear fluid theory are identified in the kinetic simulations.

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.

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 &lt; 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.

Linear dispersion theory of parallel electromagnetic modes for regularized Kappa-distributions

The velocity particle distributions measured in situ in space plasmas deviate from Maxwellian (thermal) equilibrium, showing enhanced suprathermal tails that are well described by the standard Kappa-distribution (SKD). Despite its successful application, the SKD is frequently disputed due to a series of unphysical implications such as diverging velocity moments, preventing a macroscopic description of the plasma. The regularized Kappa-distribution (RKD) has been introduced to overcome these limitations, but the dispersion properties of RKD-plasmas have not yet been explored. In the present paper, we compute the wavenumber dispersion of the frequency and damping or growth rates for the electromagnetic modes in plasmas characterized by the RKD. This task is accomplished by using the grid-based kinetic dispersion solver LEOPARD (“Linear Electromagnetic Oscillations in Plasmas with Arbitrary Rotationally symmetric Distributions”) developed for arbitrary gyrotropic distributions [P. Astfalk and F. Jenko, J. Geophys. Res. 122, 89 (2017)]. By reproducing previous results obtained for the SKD and Maxwellian, we validate the functionality of the code. Furthermore, we apply the isotropic and anisotropic RKDs to investigate stable electromagnetic electron-cyclotron (EMEC) and ion-cyclotron (EMIC) modes, as well as temperature-anisotropy-driven instabilities, for both T⊥/T∥&amp;gt;1 (EMEC and EMIC instabilities) and T⊥/T∥&amp;lt;1 cases (proton and electron firehose instabilities), where ∥ and ⊥ denote directions parallel and perpendicular to the local time-averaged magnetic field. Provided that the cutoff parameter α is small enough, the results show that the RKDs reproduce the dispersion curves of the SKD plasmas at both qualitative and quantitative levels. For higher values, however, a physically significant deviation occurs.

Magnetohydrodynamic wave modes in relativistic anisotropic quantum plasma

This paper presents an overview of waves and instabilities in relativistic degenerate plasma using magnetohydrodynamic double polytropic laws. The model equations are closed by the double polytropic laws. The general dispersion relation has been derived using the normal mode analysis, which consists of two interesting modes, i.e., shear Alfvén mode and modified magnetosonic modes (both slow and fast). The shear Alfvén mode is significantly modified by anisotropic pressure and relativistic effects and remains unaffected from quantum effects. The shear Alfvén mode develops the firehose instability, which is free from the relativistic factor. The obtained slow and fast magnetosonic modes are further discussed in parallel, perpendicular, and oblique modes of propagation. The Alfvén and sound waves propagate in parallel mode, while only the magnetosonic mode propagates in perpendicular mode. The sound wave and magnetosonic wave modes are found to be modified by relativistic and quantum effects. The oblique wave propagation provides fast and slow modes, which propagate with the combined force of anisotropic pressure, Bohm force, magnetic field, and exchange potential. The applicability of the results obtained from the dispersion relation in the relativistic degenerate anisotropic magnetohydrodynamic model can be to the pulsar magnetosphere environment.

Proton Temperature Anisotropy Variations in Inner Heliosphere Estimated with the First Parker Solar Probe Observations

We report proton temperature anisotropy variations in the inner heliosphere with Parker Solar Probe (PSP) observations. Using a linear fitting method, we derive proton temperature anisotropy with temperatures measured by the Solar Probe Cup (SPC) from the SWEAP instrument suite and magnetic field observations from the FIELDS instrument suite. The observed radial dependence of temperature variations in the fast solar wind implies stronger perpendicular heating and parallel cooling than previous results from Helios measurements made at larger radial distances. The anti-correlation between proton temperature anisotropy and parallel plasma beta is retained in fast solar wind. However, the temperature anisotropies of the slow solar wind seem to be well constrained by the mirror and parallel firehose instabilities. The perpendicular heating of the slow solar wind inside 0.24 AU may contribute to its same trend up against mirror instability thresholds as fast solar wind. These results suggest that we may see stronger anisotropy heating than expected in inner heliosphere.

On the shock induced instabilities in collisionless plasma

Firehose, mirror and ion-acoustic instabilities behind MHD shock waves are discussed for collisionless anisotropic plasma with heat fluxes. For the parallel shock wave it has been demonstrated that initially stable plasma can be destabilized by the shock which leads to turbulence generation in the downstream flow. Upstream parameter domains are determined where such destabilization occurs.

Proton firehose instability: An interplay of thermal core and non-thermal halo protons

Higher levels of solar wind temperatures are reported to be constrained. Microinstabilities play a key role under dilute space plasma conditions. The present study highlights the role of proton firehose instability in defining parallel temperatures of protons. Considering reality, we chose a bi-Maxwellian model for core protons, while halo protons are best modeled with kappa distribution. Taking different sets of input parameters like temperature anisotropy, plasma beta, and kappa index into account, the growth rate levels and associated domains for an unstable firehose mode are investigated.

An introductory guide to fluid models with anisotropic temperatures. Part 1. CGL description and collisionless fluid hierarchy

We present a detailed guide to advanced collisionless fluid models that incorporate kinetic effects into the fluid framework, and that are much closer to the collisionless kinetic description than traditional magnetohydrodynamics. Such fluid models are directly applicable to modelling the turbulent evolution of a vast array of astrophysical plasmas, such as the solar corona and the solar wind, the interstellar medium, as well as accretion disks and galaxy clusters. The text can be viewed as a detailed guide to Landau fluid models and it is divided into two parts. Part 1 is dedicated to fluid models that are obtained by closing the fluid hierarchy with simple (non-Landau fluid) closures. Part 2 is dedicated to Landau fluid closures. Here in Part 1, we discuss the fluid model of Chew–Goldberger–Low (CGL) in great detail, together with fluid models that contain dispersive effects introduced by the Hall term and by the finite Larmor radius corrections to the pressure tensor. We consider dispersive effects introduced by the non-gyrotropic heat flux vectors. We investigate the parallel and oblique firehose instability, and show that the non-gyrotropic heat flux strongly influences the maximum growth rate of these instabilities. Furthermore, we discuss fluid models that contain evolution equations for the gyrotropic heat flux fluctuations and that are closed at the fourth-moment level by prescribing a specific form for the distribution function. For the bi-Maxwellian distribution, such a closure is known as the ‘normal’ closure. We also discuss a fluid closure for the bi-kappa distribution. Finally, by considering one-dimensional Maxwellian fluid closures at higher-order moments, we show that such fluid models are always unstable. The last possible non Landau fluid closure is therefore the ‘normal’ closure, and beyond the fourth-order moment, Landau fluid closures are required.

Braginskii viscosity on an unstructured, moving mesh accelerated with super-time-stepping

ABSTRACT We present a method for efficiently modelling Braginskii viscosity on an unstructured, moving mesh. Braginskii viscosity, i.e. anisotropic transport of momentum with respect to the direction of the magnetic field, is thought to be of prime importance for studies of the weakly collisional plasma that comprises the intracluster medium (ICM) of galaxy clusters. Here, anisotropic transport of heat and momentum has been shown to have profound consequences for the stability properties of the ICM. Our new method for modelling Braginskii viscosity has been implemented in the moving mesh code arepo. We present a number of examples that serve to test the implementation and illustrate the modified dynamics found when including Braginskii viscosity in simulations. These include (but are not limited to) damping of fast magnetosonic waves, interruption of linearly polarized Alfvén waves by the firehose instability, and the inhibition of the Kelvin–Helmholtz instability by Braginskii viscosity. An explicit update of Braginskii viscosity is associated with a severe time-step constraint that scales with (Δx)2, where Δx is the grid size. In our implementation, this restrictive time-step constraint is alleviated by employing second-order accurate Runge–Kutta–Legendre super-time-stepping. We envision including Braginskii viscosity in future large-scale simulations of Kelvin–Helmholtz unstable cold fronts in cluster mergers and AGN-generated bubbles in central cluster regions.

Turbulence versus Fire-hose Instabilities: 3D Hybrid Expanding Box Simulations

Abstract The relationship between a decaying plasma turbulence and proton fire hose instabilities in a slowly expanding plasma is investigated using three-dimensional hybrid expanding box simulations. We impose an initial ambient magnetic field along the radial direction, and we start with an isotropic spectrum of large-scale, linearly polarized, random-phase Alfvénic fluctuations with zero cross-helicity. A turbulent cascade rapidly develops and leads to a weak proton heating that is not sufficient to overcome the expansion-driven perpendicular cooling. The plasma system eventually drives the parallel and oblique fire hose instabilities that generate quasi-monochromatic wave packets that reduce the proton temperature anisotropy. The fire hose wave activity has a low amplitude with wave vectors quasi-parallel/oblique with respect to the ambient magnetic field outside of the region dominated by the turbulent cascade and is discernible in one-dimensional power spectra taken only in the direction quasi-parallel/oblique with respect to the ambient magnetic field; at quasi-perpendicular angles the wave activity is hidden by the turbulent background. These waves are partly reabsorbed by protons and partly couple to and participate in the turbulent cascade. Their presence reduces kurtosis, a measure of intermittency, and the Shannon entropy, but increases the Jensen–Shannon complexity of magnetic fluctuations; these changes are weak and anisotropic with respect to the ambient magnetic field and it is not clear if they can be used to indirectly discern the presence of instability-driven waves.

Onset and Evolution of the Oblique, Resonant Electron Firehose Instability in the Expanding Solar Wind Plasma

A double adiabatically expanding solar wind would quickly develop large parallel to perpendicular temperature anisotropies in electrons and ions that are not observed. One reason is that firehose instabilities would be triggered, leading to an ongoing driving/saturation evolution mechanism. We verify this assumption here for the first time for the electron distribution function and the electron firehose instability (EFI), using fully kinetic simulations with the Expanding Box Model. This allows the self-consistent study of onset and evolution of the oblique, resonant EFI in an expanding solar wind. We characterize how the competition between EFI and adiabatic expansion plays out in high- and low-beta cases, in high- and low-speed solar wind streams. We observe that, even when competing against expansion, the EFI results in perpendicular heating and parallel cooling. These two concurrent processes effectively limit the expansion-induced increase in temperature anisotropy and parallel electron beta. We show that the EFI goes through cycles of stabilization and destabilization: when higher wave number EFI modes saturate, lower wave number modes are destabilized by the effects of the expansion. We show how resonant wave/ particle interaction modifies the electron velocity distribution function after the onset of the EFI. The simulations are performed with the fully kinetic, semi-implicit expanding box code EB-iPic3D.

Effect of anisotropic Cairns distribution on drift magnetosonic wave

Non-monotonic shoulder like velocity distributions and high-energy tails are often observed in space plasmas, e.g., in solar wind. In this work, these effects are studied for obliquely propagating drift mode in an anisotropic and spatially inhomogeneous environment of solar wind at about 1 AU, using the Cairns distribution. Different cases are studied to see the interrelationship between Cairns parameter $\Lambda$, density inhomogeneity factor $\eta$, and the temperature anisotropy $ T_{\Vert \alpha}/T_{\perp \alpha} > 1$. It is observed that while the temperature anisotropy alone gives only damping on kinetic scale for drift magnetosonic mode, but in conjunction with $\Lambda$ (showing the extent of non-thermality), it can generate instability. The three interesting effects together automatically satisfy the firehose instability condition. Further, when we consider reactive-type instability, the electron temperature anisotropy $ T_{\Vert e}/T_{\perp e} > 1$ can independently generate resonant firehose instability for $R(\omega ) = 0$, which develops at oblique propagation of the wave at comparatively high $ \beta_{\Vert e}$. These results are quite important for all non-thermal environments where the plasma is inhomogeneous and temperature anisotropic, such as in space and astrophysical plasmas. The results might be helpful in understanding the phenomena of heating and acceleration of particles in solar corona and solar wind via Landau damping and in explaining the physical nature of coronal Extreme-ultraviolet Imaging Telescope (EIT) waves.

MHD Waves and Instabilities in Two-Component Anisotropic Plasma

Based on the 16-moment MHD transport equations, the propagation of linear waves in an anisotropic homogeneous cosmic plasma is considered. A general dispersion relation is derived with allowance for two plasma components (electrons and protons) and heat flux along the magnetic field. This dispersion relation is a generalization of the previously studied cases of one-component (ion) plasma. The case in which the effects associated with the heat flux are ignored is analyzed in more detail. In the limit of longitudinal propagation, the wave modes fully consistent with the modes known in the low-frequency kinetic theory of collisionless plasma are classified. Firehose and mirror instabilities are analyzed. It is shown that taking into account the electron component modifies the growth rates and thresholds of instabilities.

Electron Preacceleration in Weak Quasi-perpendicular Shocks in High-beta Intracluster Medium

Abstract Giant radio relics in the outskirts of galaxy clusters are known to be lit up by the relativistic electrons produced via diffusive shock acceleration (DSA) in shocks with low sonic Mach numbers, M s ≲ 3. The particle acceleration at these collisionless shocks critically depends on the kinetic plasma processes that govern the injection to DSA. Here, we study the preacceleration of suprathermal electrons in weak, quasi-perpendicular (Q ⊥) shocks in the hot, high-β (β = P gas/P B) intracluster medium (ICM) through two-dimensional particle-in-cell simulations. Guo et al. showed that, in high-β Q ⊥-shocks, some of the incoming electrons could be reflected upstream and gain energy via shock drift acceleration (SDA). The temperature anisotropy due to the SDA-energized electrons then induces the electron firehose instability (EFI), and oblique waves are generated, leading to a Fermi-like process and multiple cycles of SDA in the preshock region. We find that such electron preacceleration is effective only in shocks above a critical Mach number . This means that, in ICM plasmas, Q ⊥-shocks with M s ≲ 2.3 may not efficiently accelerate electrons. We also find that, even in Q ⊥-shocks with M s ≳ 2.3, electrons may not reach high enough energies to be injected to the full Fermi-I process of DSA, because long-wavelength waves are not developed via the EFI alone. Our results indicate that additional electron preaccelerations are required for DSA in ICM shocks, and the presence of fossil relativistic electrons in the shock upstream region may be necessary to explain observed radio relics.

On the Influence of the Shape of Kappa Distributions of Ions and Electrons on the Ion Firehose Instability

We consider a plasma with electrons and ions described by different combinations of different forms of Kappa distributions, and also by bi-Maxwellian distributions, for investigation of the ion firehose instability. The investigation considers Kappa distributions with small value of the kappa index, which enhance the differences between Kappa distributions and bi-Maxwellian distributions. The results obtained show that different forms of anisotropic Kappa distributions for the ions can have significantly different effect on the growth rates of the instability. The results obtained also show significant effect of the shape of the electron distribution, as well as effect of the anisotropy of electron temperatures, on the growth rates and on the unstable spectral range of the ion firehose instability.

Contributions of protons in electron firehose instability driven by solar wind core–halo electrons

Contributions of protons in electron firehose instability driven by solar wind core–halo electrons

Buckling instability in tidally induced galactic bars

Strong galactic bars produced in simulations tend to undergo a period of buckling instability that weakens and thickens them and forms a boxy/peanut structure in their central parts. This theoretical prediction has been confirmed by identifying such morphologies in real galaxies. The nature and origin of this instability, however, remain poorly understood with some studies claiming that it is due to fire-hose instability while others relating it to vertical instability of stellar orbits supporting the bar. One of the channels for the formation of galactic bars is via the interaction of disky galaxies with perturbers of significant mass. Tidally induced bars offer a unique possibility of studying buckling instability because their formation can be controlled by changing the strength of the interaction while keeping the initial structure of the galaxy the same. We used a set of four simulations of flyby interactions where a galaxy on a prograde orbit forms a bar, which is stronger for stronger tidal forces. We studied their buckling by calculating different kinematic signatures, including profiles of the mean velocity in the vertical direction, as well as distortions of the bars out of the disk plane. Although our two strongest bars buckle most strongly, there is no direct relation between the ratio of vertical to horizontal velocity dispersion and the bar’s susceptibility to buckling, as required by the fire-hose instability interpretation. While our weakest bar buckles, a stronger one does not, its dispersion ratio remains low, and it grows to become the strongest of all at the end of evolution. Instead, we find that during buckling the resonance between the vertical and radial orbital frequencies becomes wide and therefore able to modify stellar orbits over a significant range of radii. We conclude that vertical orbital instability is the more plausible explanation for the origin of buckling.