Proton mirror modes are large amplitude nonpropagating structures frequently observed in the magnetosheath. It has been suggested that electron temperature anisotropy can enhance the proton mirror instability growth rate while leaving the proton cyclotron instability largely unaffected, therefore causing the proton mirror instability to dominate the proton cyclotron instability in Earth's magnetosheath. Here, we use particle-in-cell simulations to investigate the electron temperature anisotropy effects on proton mirror instability evolution. Contrary to the hypothesis, electron temperature anisotropy leads to excitement of the electron whistler instability. Our results show that the electron whistler instability grows much faster than the proton mirror instability and quickly consumes the electron free energy, so that there is no electron temperature anisotropy left to significantly impact the evolution of the proton mirror instability.
Slow dynamical changes in magnetic-field strength and invariance of the particles' magnetic moments generate ubiquitous pressure anisotropies in weakly collisional, magnetized astrophysical plasmas. This renders them unstable to fast, small-scale mirror and firehose instabilities, which are capable of exerting feedback on the macroscale dynamics of the system. By way of a new asymptotic theory of the early nonlinear evolution of the mirror instability in a plasma subject to slow shearing or compression, we show that the instability does not saturate quasilinearly at a steady, low-amplitude lev…
Properties of the electron mirror instability and its competition with the usually dominant whistler (electron cyclotron) instability driven by the electron perpendicular temperature anisotropy are investigated on the linear level using a Vlasov linear solver and on the nonlinear level using a two-dimensional full particle code. The simulation results show that the linearly subdominant electron mirror instability may compete on the nonlinear level with the whistler instability and may even become eventually the dominant mode that generates robust non-propagating sub-ion-scale coherent structur…
The relationship between a decaying strong turbulence and the mirror instability in a slowly expanding plasma is investigated using two-dimensional hybrid expanding box simulations. We impose an initial ambient magnetic field perpendicular to the simulation box, and we start with a spectrum of large-scale, linearly-polarized, random-phase Alfvenic fluctuations which have energy equipartition between kinetic and magnetic fluctuations and vanishing correlation between the two fields. A turbulent cascade rapidly develops, magnetic field fluctuations exhibit a Kolmogorov-like power-law spectrum at…
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 non-linear modeling of the parallel firehose instability, retaining a kin…
In this work linear stability analysis of a magnetized dusty plasma with an anisotropic dust component having transversal motions much stronger than motions parallel to the external magnetic field, and isotropic light plasma components is described. Such a situation presumably establishes in a shock compressed space dusty plasma downstream the shock front. Oblique low-frequency magneto-hydrodynamic waves ($ω\ll ω_{cd}$, $ω_{cd}$ being the dust cyclotron frequency) are shown to be undergone to the mirror instability. Consequences for nonthermal dust destruction behind shock fronts in the inters…
In collision-poor plasmas from space, e.g., the solar wind and planetary magnetospheres, the kinetic anisotropy of the plasma particles is expected to be regulated by the kinetic instabilities. Driven by an excess of ion (proton) temperature perpendicular to the magnetic field $(~T_\perp >T_\parallel)$, the electromagnetic ion-cyclotron (EMIC) instability is fast enough to constrain the proton anisotropy, but the observations do not conform to the instability thresholds predicted by the standard theory for bi-Maxwellian models of the plasma particles. This paper presents an extended investigat…
The shape of the anisotropic velocity distribution function, beyond the realm of strict Maxwellians can play a significant role in determining the evolution of the Weibel instability dictating the dynamics of self-generated magnetic fields. For non-Maxwellian distribution functions, we show that the direction of the maximum growth rate wavevector changes with shape. We investigate different laser-plasma interaction model distributions which show that their Weibel generated magnetic fields may require closer scrutiny beyond the second moment (temperature) anisotropy ratio characterization.
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…
Kinetic instabilities in a dense plasma of a continuous ECR discharge in a mirror magnetic trap at the GISMO setup are studied. We experimentally define unstable regimes and corresponding plasma parameters, where the excitation of electromagnetic emission is observed, accompanied by the precipitation of energetic electrons from the magnetic trap. Comprehensive experimental study of the precipitating electron energy distribution and plasma electromagnetic emission spectra, together with theoretical estimates of the cyclotron instability increment proves that under the experimental conditions th…
The nonlinear evolution of the Kelvin Helmholtz instability in a magnetized plasma with a perpendicular flow close to, or in, the supermagnetosonic regime can produce a significant parallel-to-perpendicular pressure anisotropy. This anisotropy, localized inside the flow shear region, can make the configuration unstable either to the mirror or to the firehose instability and, in general, can affect the development of the KHI. The interface between the solar wind and the Earth's magnetospheric plasma at the magnetospheric equatorial flanks provides a relevant setting for the development of this …
Context. Solar outflows are a considerable source of free energy which accumulates in multiple forms like beaming (or drifting) components and/or temperature anisotropies. However, kinetic anisotropies of plasma particles do not grow indefinitely and particle-particle collisions are not efficient enough to explain the observed limits of these anisotropies. Instead, the self-generated wave instabilities can efficiently act to constrain kinetic anisotropies, but the existing approaches are simplified and do not provide satisfactory explanations. Thus, small deviations from isotropy shown by the …
Kinetic instabilities in weakly collisional, high beta plasmas are investigated using two-dimensional hybrid expanding box simulations with Coulomb collisions modeled through the Langevin equation (corresponding to the Fokker-Planck one). The expansion drives a parallel or perpendicular temperature anisotropy (depending on the orientation of the ambient magnetic field). For the chosen parameters the Coulomb collisions are important with respect to the driver but are not strong enough to keep the system stable with respect to instabilities driven by the proton temperature anisotropy. In the cas…
This letter presents the results of an advanced parametrization of the solar wind electron temperature anisotropy and the instabilities resulting from the interplay of the (bi-)Maxwellian core and (bi-)Kappa halo populations in the slow solar wind. A large set of observational data (from the Ulysses, Helios and Cluster missions) is used to parametrize these components and establish their correlations. The instabilities are significantly stimulated in the presence of suprathermals, and the instability thresholds shape the limits of the temperature anisotropy for both the core and halo populatio…
The firehose and mirror instabilities are thought to arise in a variety of space and astrophysical plasmas, constraining the pressure anisotropies and drifts between particle species. The plasma stability depends on all species simultaneously, meaning that a combined analysis is required. Here, we present the first such analysis in the solar wind, using the long-wavelength stability parameters to combine the anisotropies and drifts of all major species (core and beam protons, alphas, and electrons). At the threshold, the firehose parameter was found to be dominated by protons (67%), but also t…
We study the time-dependent formation and evolution of a current sheet (CS) in a magnetized, collisionless, high-beta plasma using hybrid-kinetic particle-in-cell simulations. An initially tearing-stable Harris sheet is frozen into a persistently driven incompressible flow so that its characteristic thickness gradually decreases in time. As the CS thins, the strength of the reconnecting field increases, and adiabatic invariance in the inflowing fluid elements produces a field-biased pressure anisotropy with excess perpendicular pressure. At large plasma beta, this anisotropy excites the mirror…
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…
The proton temperature anisotropy in the solar wind is known to be constrained by the theoretical thresholds for pressure anisotropy-driven instabilities. Here we use approximately 1 million independent measurements of gyroscale magnetic fluctuations in the solar wind to show for the first time that these fluctuations are enhanced along the temperature anisotropy thresholds of the mirror, proton oblique firehose, and ion cyclotron instabilities. In addition, the measured magnetic compressibility is enhanced at high plasma beta ($β_\parallel \gtrsim 1$) along the mirror instability threshold bu…
Since the first observations by Kaufmann et al.\ (1970), special attention has been paid to static pressure-balanced structures in the form of magnetic holes or humps observed in regions of the solar wind and of planetary magnetosheaths where the $β$ parameter is relatively large and the ion perpendicular temperature exceeds the parallel one. Although alternative interpretations have been proposed, these structures are usually viewed as associated with the mirror instability discovered in 1957 by Vedenov and Sagdeev. After reviewing observational results provided by satellite missions, high-re…
An instability driven by the thermal anisotropy of a single electron species is investigated in a 2D particle-in-cell (PIC) simulation. This instability is the one considered by Weibel and it differs from the beam driven filamentation instability. A comparison of the simulation results with analytic theory provides similar exponential growth rates of the magnetic field during the linear growth phase of the instability. We observe in accordance with previous works the growth of electric fields during the saturation phase of the instability. Some components of this electric field are not account…
In the first part we present a review of our results concerning the weakly nonlinear regime of the mirror instability in the framework of an asymptotic model. This model belongs to the class of gradient type systems for which the free energy can only decrease in time. It reveals a behavior typical for subcritical bifurcations: below the mirror instability threshold, all localized stationary structures are unstable, while above threshold, the system displays a blow-up behavior. It is shown that taking the electrons into account (non-zero temperature) does not change the structure of the asympto…
We present the first three-dimensional hybrid simulations of the evolution of ion-scale current sheets, with an investigation of the role of temperature anisotropy and associated kinetic instabilities on the growth of the tearing instability and particle heating. We confirm the ability of the ion cyclotron and firehose instabilities to enhance or suppress reconnection, respectively. The simulations demonstrate the emergence of persistent three-dimensional structures, including patchy reconnection sites and the fast growth of a narrow-band drift-kink instability, which suppresses reconnection f…
The mirror mode evolving in collisionless magnetised high-temperature thermally anisotropic plasmas is shown to develop an interesting macro-state. Starting as a classical zero frequency ion fluid instability it saturates quasi-linearly at very low magnetic level, while forming elongated magnetic bubbles which trap the electron component to perform an adiabatic bounce motion along the magnetic field. {Further evolution of the mirror mode towards a stationary state is determined by the bouncing trapped electrons which interact with the thermal level of ion sound waves, generate attractive wake …
We investigate the role of kinetic instabilities driven by a proton anisotropy on the onset of magnetic reconnection by means of 2-D hybrid simulations. The collisionless tearing of a current sheet is studied in the presence of a proton temperature anisotropy in the surrounding plasma. Our results confirm that anisotropic protons within the current sheet region can significantly enhance/stabilize the tearing instability of the current. Moreover, fluctuations associated to linear instabilities excited by large proton temperature anisotropies can significantly influence the stability of the plas…
In collisionless and weakly collisional plasmas, such as hot accretion flows onto compact objects, the magnetorotational instability (MRI) can differ significantly from the standard (collisional) MRI. In particular, pressure anisotropy with respect to the local magnetic-field direction can both change the linear MRI dispersion relation and cause nonlinear modifications to the mode structure and growth rate, even when the field and flow perturbations are small. This work studies these pressure-anisotropy-induced nonlinearities in the weakly nonlinear, high-ion-beta regime, before the MRI satura…
In the absence of efficient collisions, deviations from thermal equilibrium of plasma particle distributions are controlled by the self-generated instabilities. The whistler instability is a notorious example, usually responsible for the regulation of electron temperature anisotropy $A = T_{\perp}/T_\parallel>$ (with $\perp, \parallel$ respective to the magnetic field direction) observed in space plasmas, e.g., solar wind and planetary magnetospheres. Suprathermal electrons present in these environments change the plasma dispersion and stability properties, with expected consequences on the ki…
Using high-resolution data from Solar Orbiter, we investigate the plasma conditions necessary for the proton temperature anisotropy driven mirror-mode and oblique firehose instabilities to occur in the solar wind. We find that the unstable plasma exhibits dependencies on the angle between the direction of the magnetic field and the bulk solar wind velocity which cannot be explained by the double-adiabatic expansion of the solar wind alone. The angle dependencies suggest that perpendicular heating in Alfvénic wind may be responsible. We quantify the occurrence rate of the two instabilities as a…
A Particle-in-Cell (PIC) numerical simulation of the electron Weibel instability is applied in a frame of Darwin (radiationless) approximation of the self-consistent fields of sparse plasma. As a result, we were able to supplement the classical picture of the instability and, in particular, to obtain the dependency of the basic characteristics (the time of development and the maximum field energy) of the thermal anisotropy parameter, to trace the dynamic restructuring of current filaments accompanying the nonlinear stage of the instability and to trace in detail the evolution of the initial an…
The electron beam Weibel instability in the electrostatic collisionless shock is studied via particle in cell simulation. When the non-relativistic incoming plasmas collide with cold dilute plasmas, an electrostatic shock forms near the interface. Following that, a filamentary out-of-plane magnetic field is formed as a result of the Weibel instability. It is demonstrated that the anisotropy of incoming hot electrons is insufficient to trigger the Weibel instability. And the Weibel instability is excited by cold electrons in dilute plasmas. After being accelerated to relativistic velocities by …
The indefinite increase of temperature predicted by the solar wind expansion in the direction parallel to the interplanetary magnetic field is already notorious for not being confirmed by the observations. In hot and dilute plasmas from space particle-particle collisions are not efficient in constraining large deviations from isotropy, but the resulting firehose instability provides in this case plausible limitations for the temperature anisotropy of the thermal (core) populations of both the electron and proton species. The present paper takes into discussion the suprathermal (halo) electrons…
The nonlinear state of a high-beta collisionless plasma is investigated when an imposed linear shear amplifies or diminishes a uniform magnetic field, driving pressure anisotropies and hence firehose/mirror instabilities. The evolution of the resulting microscale turbulence is considered when the shear is switched off or reversed after one shear time (mimicking local behaviour of a macroscopic flow), so a new macroscale configuration is superimposed on the microscale state left behind by the previous one. There is a threshold value of plasma beta: when $β\llΩ/S$ (ion cyclotron frequency/shear …
Cosmic ray propagation in the Milky Way and other galaxies is largely diffusive, with mean free path determined primarily by pitch angle scattering from hydromagnetic waves with wavelength of order the cosmic ray gyroradius. In the theory of cosmic ray self confinement, the waves are generated by instabilities driven by the cosmic rays themselves. The dominant instability is due to bulk motion, or streaming, of the cosmic rays, parallel to the background magnetic field B, and transfers cosmic ray momentum and energy to the thermal gas as well as confining the cosmic rays. Classical arguments a…
Particle velocity distributions measured in the weakly collisional solar wind are frequently found to be non-Maxwellian, but how these non-Maxwellian distributions impact the physics of plasma turbulence in the solar wind remains unanswered. Using numerical solutions of the linear dispersion relation for a collisionless plasma with a bi-Maxwellian proton velocity distribution, we present a unified framework for the four proton temperature anisotropy instabilities, identifying the associated stable eigenmodes, highlighting the unstable region of wavevector space, and presenting the properties o…
We use particle-in-cell (PIC) simulations to study the nonlinear evolution of ion velocity space instabilities in an idealized problem in which a background velocity shear continuously amplifies the magnetic field. We simulate the astrophysically relevant regime where the shear timescale is long compared to the ion cyclotron period, and the plasma beta is ~ 1-100. The background field amplification in our calculation is meant to mimic processes such as turbulent fluctuations or MHD-scale instabilities. The field amplification continuously drives a pressure anisotropy with the perpendicular pre…
A variety of nonthermal characteristics like kinetic, e.g., temperature, anisotropies and suprathermal populations (enhancing the high energy tails of the velocity distributions) are revealed by the in-situ observations in the solar wind indicating quasistationary states of plasma particles out of thermal equilibrium. Large deviations from isotropy generate kinetic instabilities and growing fluctuating fields which should be more efficient than collisions in limiting the anisotropy (below the instability threshold) and explain the anisotropy limits reported by the observations. The present pap…
We demonstrate using linear theory and particle-in-cell (PIC) simulations that a synchrotron-cooling collisionless plasma acquires pressure anisotropy and, if the plasma beta is sufficiently high, becomes unstable to the firehose instability, in a process that we dub the synchrotron firehose instability (SFHI). The SFHI channels free energy from the pressure anisotropy of the radiating, relativistic electrons (and/or positrons) into small-amplitude, kinetic-scale magnetic-field fluctuations, which pitch-angle scatter the particles and bring the plasma to a near-thermal state of marginal instab…
Based on now historical magnetic and plasma data and available wave spectra from the AMPTE-IRM spacecraft, and on as well historical Equator-S high-cadence magnetic field observations of mirror modes in the magnetosheath near the dayside magnetopause, we present some observational evidence for a recent theoretical evaluation by Noreen et al. (2017) of the contribution of a global electron temperature anisotropy to the evolution of mirror modes in the high-temperature anisotropic collisionless plasma of the magnetosheath causing a separate electron mirror branch. These old data most probably in…
Tearing Instability in Gyrotropic MHD: Effects of Equilibrium Pressure Anisotropy
Escola de Artes, Ciências e Humanidades, University of São Paulo（圣保罗大学艺术、科学与人文学院）；Astrophysics Division, National Institute for Space Research（国家空间研究所天体物理部）
Zebra-like patterns have been observed in the electron cyclotron emission spectra from strongly nonequilibrium plasma confined in a table-top mirror magnetic trap. The analysis of the experimental data suggests that the formation of zebra-like patterns could eventually be related to modulation of the whistler waves by the ion-acoustic waves excited during the abrupt ejection of electrons into a loss cone caused by the development of the whistler instability under the electron cyclotron resonance condition.
Anisotropy in electronic structures may ignite intriguing anisotropic optical responses, as has been well demonstrated in various systems including superconductors, semiconductors, and even topological Weyl semimetals. Meanwhile, it is well established in metal optics that the metal reflectance declines from one to zero when the photon frequency is above the plasma frequency ωp , behaving as a plasma mirror. However, the exploration of anisotropic plasma mirrors and corresponding applications remains elusive, especially at room temperature. Here, we discover a pronounced anisotropic plasma ref…
Using hybrid-kinetic particle-in-cell simulation, we study the evolution of an expanding, collisionless, magnetized plasma in which strong Alfvénic turbulence is persistently driven. Temperature anisotropy generated adiabatically by the plasma expansion (and consequent decrease in the mean magnetic-field strength) gradually reduces the effective elasticity of the field lines, causing reductions in the linear frequency and residual energy of the Alfvénic fluctuations. In response, these fluctuations modify their interactions and spatial anisotropy to maintain a scale-by-scale "critical balance"…
Using two-dimensional hybrid expanding box simulations we study the competition between the continuously driven parallel proton temperature anisotropy and fire hose instabilities in collisionless homogeneous plasmas. For quasi radial ambient magnetic field the expansion drives $T_{\mathrm{p}\|}>T_{\mathrm{p}\perp}$ and the system becomes eventually unstable with respect to the dominant parallel fire hose instability. This instability is generally unable to counteract the induced anisotropization and the system typically becomes unstable with respect to the oblique fire hose instability later o…
The kinetic instabilities of the Weibel-type are presently invoked in a large variety of astrophysical scenarios because anisotropic plasma structures are ubiquitous in space. The Weibel instability is driven by a temperature anisotropy which is commonly modeled by a bi-axis distribution function, such as a bi-Maxwellian or a generalized bi-Kappa. Previous studies have been limited to a bi-Kappa distribution and found a suppression of this instability in the presence of suprathermal tails. In the present paper it is shown that the Weibel growth rate is rather more sensitive to the shape of the…
Effects of finite ion temperature on plasma flow in the converging-diverging magnetic field, the magnetic mirror, or equivalently, magnetic nozzle configuration, are studied using a quasineutral paraxial two-fluid MHD model with isothermal electrons and warm magnetized ions. The ion acceleration was studied with an emphasis on the role of the singularity at the sonic point transition. It is shown that the regularity of the sonic point defines a global solution describing plasma acceleration from subsonic to supersonic velocity. Stationary accelerating solutions were obtained and compared with …
The dynamo mechanism is a process of magnetic field self-excitation in a moving electrically conducting fluid. One of the most interesting applications of this mechanism related to the astrophysical systems is the case of a random motion of plasma. For the very first stage of the process, the governing dynamo equation can be reduced to a system of first order ordinary differential equations. For this case we suggest a regular method to calculate the growth rate of magnetic energy. Based on this method we calculate the growth rate for random flow with finite memory time and anisotropic statisti…
3D particle-in-cell simulations demonstrate that the enhanced transparency of a relativistically hot plasma is sensitive to how the energy is partitioned between different degrees of freedom. For an anisotropic electron distribution, propagation characteristics, like the critical density, will depend on the polarization of the electromagnetic wave. Despite the onset of the Weibel instability in such plasmas, the anisotropy can persist long enough to affect laser propagation. This plasma can then function as a polarizer or a waveplate to dramatically alter the pulse polarization.
We analyze the magneto-rotational instability (MRI) effects on gravitational collapse and its influence on the instability critical scale. In particular, we study an axisymmetric nonstratified differentially rotating cloud, embedded in a small magnetic field, and we perform a local linear stability analysis, including the self gravity of the system. We demonstrate that the linear evolution of the perturbations is characterized by the emergence of an anisotropy degree of the perturbed mass densities. Starting with spherical growing overdensities, we see that they naturally acquire an anisotropy…
The extent to which angular momentum transport in accretion discs is primarily local or non-local and what determines this is an important avenue of study for understanding accretion engines. Taking a step along this path, we analyze simulations of the magnetorotational instability (MRI) by calculating energy and stress power spectra in stratified isothermal shearing box simulations in several new ways. We divide our boxes in two regions, disc and corona where the disc is the MRI unstable region and corona is the magnetically dominated region. We calculate the fractional power in different qua…
