Instability Of Current Sheets Research Articles

HIGH-TEMPERATURE IONIZATION IN PROTOPLANETARY DISKS

We calculate the abundances of electrons and ions in the hot (> 500 K), dusty parts of protoplanetary disks, treating for the first time the effects of thermionic and ion emission from the dust grains. High-temperature ionization modeling has involved simply assuming that alkali elements such as potassium occur as gas-phase atoms and are collisionally ionized following the Saha equation. We show that the Saha equation often does not hold, because free charges are produced by thermionic and ion emission and destroyed when they stick to grain surfaces. This means the ionization state depends not on the first ionization potential of the alkali atoms, but rather on the grains' work functions. The charged species' abundances typically rise abruptly above about 800 K, with little qualitative dependence on the work function, gas density, or dust-to-gas mass ratio. Applying our results, we find that protoplanetary disks' dead zone, where high diffusivities stifle magnetorotational turbulence, has its inner edge located where the temperature exceeds a threshold value ~1000 K. The threshold is set by ambipolar diffusion except at the highest densities, where it is set by Ohmic resistivity. We find that the disk gas can be diffusively loaded onto the stellar magnetosphere at temperatures below a similar threshold. We investigate whether the "short-circuit" instability of current sheets can operate in disks and find that it cannot, or works only in a narrow range of conditions; it appears not to be the chondrule formation mechanism. We also suggest that thermionic emission is important for determining the rate of Ohmic heating in hot Jupiters.

Instability of current sheets with a localized accumulation of magnetic flux

The longstanding problem of whether a current sheet with curved magnetic field lines associated with a small “normal” Bz component is stable is investigated using two-dimensional electromagnetic particle-in-cell simulations, employing closed boundary conditions analogous to those normally assumed in energy principle calculations. Energy principle arguments [Sitnov and Schindler, Geophys. Res. Lett. 37, L08102 (2010)] have suggested that an accumulation of magnetic flux at the tailward end of a thin current sheet could produce a tearing instability. Two classes of such current sheet configurations are probed: one with a monotonically increasing Bz profile and the other with a localized Bz “hump.” The former is found to be stable (in 2D) over any reasonable time scale, while the latter is prone to an ideal-like instability that shifts the hump peak in the direction of the curvature normal and erodes the field on the opposite side. The growth rate of this instability is smaller by an order of magnitude than previous suggestions of an instability in an open system. An example is given that suggests that such an unstable hump configuration is unlikely to be produced by external driving of a current sheet with no Bz accumulation even in the presence of open boundary conditions.

Plasmoid instability in double current sheets

The linear behavior of plasmoid instability in double current sheet configurations, namely, double plasmoid mode (DPM), is analytically and numerically investigated within the framework of a reduced magnetohydrodynamic model. Analytical analysis shows that if the separation of double current sheets is sufficiently small [κxs≪κ2/9SL1/3], the growth rate of DPMs scales as κ2/3SL0 in the non-constant-ψ regime, where κ=kLCS/2 is the wave vector measured by the half length of the system LCS/2, 2xs is the separation between two resonant surfaces, and SL=LCSVA/2η is Lundquist number with VA and η being Alfven velocity and resistivity, respectively. If the separation is very large [κxs≫κ2/9SL1/3], the growth rate scales as κ−2/5SL2/5 in the constant-ψ regime. Furthermore, it is also analytically found that the maximum wave number scales as xs−9/7SL3/7 at the transition position between these two regimes, and the corresponding maximum growth rate scales as xs−6/7SL2/7 there. The analytically predicted scalings are verified in some limits through direct numerical calculations.

Instabilities of collisionless current sheets revisited: The role of anisotropic heating

In this work, we investigate the influence of the anisotropic heating on the spontaneous instability and evolution of thin Harris-type collisionless current sheets, embedded in antiparallel magnetic fields. In particular, we explore the influence of the macroparticle shape-function using a 2D version of the PIC code ACRONYM. We also investigate the role of the numerical collisionality due to the finite number of macroparticles in PIC codes. It is shown that it is appropriate to choose higher order shape functions of the macroparticles compared to a larger number of macroparticles per cell. This allows to estimate better the anisotropic electron heating due to the collisions of macroparticles in a PIC code. Temperature anisotropies can stabilize the tearing mode instability and trigger additional current sheet instabilities. We found a good agreement between the analytically derived threshold for the stabilization of the anisotropic tearing mode and other instabilities, either spontaneously developing or initially triggered ones. Numerical effects causing anisotropic heating at electron time scales become especially important for higher mass ratios (above mi/me=180). If numerical effects are carefully taken into account, one can recover the theoretical estimated linear growth rates of the tearing instability of thin isotropic collisionless current sheets, also for higher mass ratios.

Nonlinear evolution of three-dimensional instabilities of thin and thick electron scale current sheets: Plasmoid formation and current filamentation

Nonlinear evolution of three dimensional electron shear flow instabilities of an electron current sheet (ECS) is studied using electron-magnetohydrodynamic simulations. The dependence of the evolution on current sheet thickness is examined. For thin current sheets (half thickness =de=c/ωpe), tearing mode instability dominates. In its nonlinear evolution, it leads to the formation of oblique current channels. Magnetic field lines form 3-D magnetic spirals. Even in the absence of initial guide field, the out-of-reconnection-plane magnetic field generated by the tearing instability itself may play the role of guide field in the growth of secondary finite-guide-field instabilities. For thicker current sheets (half thickness ∼5 de), both tearing and non-tearing modes grow. Due to the non-tearing mode, current sheet becomes corrugated in the beginning of the evolution. In this case, tearing mode lets the magnetic field reconnect in the corrugated ECS. Later thick ECS develops filamentary structures and turbulence in which reconnection occurs. This evolution of thick ECS provides an example of reconnection in self-generated turbulence. The power spectra for both the thin and thick current sheets are anisotropic with respect to the electron flow direction. The cascade towards shorter scales occurs preferentially in the direction perpendicular to the electron flow.

Two-fluid description of wave-particle interactions in strong Buneman turbulence

To understand the nature of anomalous resistivity in magnetic reconnection, we investigate turbulence-induced momentum transport and energy dissipation while a plasma is unstable to the Buneman instability in force-free current sheets. Using 3D particle-in-cell simulations, we find that the macroscopic effects generated by wave-particle interactions in Buneman instability can be approximately described by a set of electron fluid equations. We show that both energy dissipation and momentum transport along electric current in the current layer are locally quasi-static, but globally dynamic and irreversible. Turbulent drag dissipates both the streaming energy of the current sheet and the associated magnetic energy. The net loss of streaming energy is converted into the electron component heat conduction parallel to the magnetic field and increases the electron Boltzmann entropy. The growth of self-sustained Buneman waves satisfies a Bernoulli-like equation that relates the turbulence-induced convective momentum transport and thermal momentum transport. Electron trapping and de-trapping drive local momentum transports, while phase mixing converts convective momentum into thermal momentum. The drag acts like a micro-macro link in the anomalous heating processes. The decrease of magnetic field maintains an inductive electric field that re-accelerates electrons, but most of the magnetic energy is dissipated and converted into the component heat of electrons perpendicular to the magnetic field. This heating process is decoupled from the heating of Buneman instability in the current sheets. Ion heating is weak but ions play an important role in assisting energy exchanges between waves and electrons. Cold ion fluid equations together with our electron fluid equations form a complete set of equations that describes the occurrence, growth, saturation and decay of the Buneman instability.

Three dimensional instabilities of an electron scale current sheet in collisionless magnetic reconnection

In collisionless magnetic reconnection, electron current sheets (ECS) with thickness of the order of an electron inertial length form embedded inside ion current sheets with thickness of the order of an ion inertial length. These ECS's are susceptible to a variety of instabilities which have the potential to affect the reconnection rate and/or the structure of reconnection. We carry out a three dimensional linear eigen mode stability analysis of electron shear flow driven instabilities of an electron scale current sheet using an electron-magnetohydrodynamic plasma model. The linear growth rate of the fastest unstable mode was found to drop with the thickness of the ECS. We show how the nature of the instability depends on the thickness of the ECS. As long as the half-thickness of the ECS is close to the electron inertial length, the fastest instability is that of a translational symmetric two-dimensional (no variations along flow direction) tearing mode. For an ECS half thickness sufficiently larger or smaller than the electron inertial length, the fastest mode is not a tearing mode any more and may have finite variations along the flow direction. Therefore, the generation of plasmoids in a nonlinear evolution of ECS is likely only when the half-thickness is close to an electron inertial length.

Numerical simulation of current sheet instabilities in a small plasma focus

A comparison between numerical simulations of discharges in the Plasma Focus device PF-50J using the code Cshock is presented. The code was able to reproduce kinetics and circuit parameter experimental measurements as well as the particular current sheath instability observed in this specific device.

Gyrokinetic theory of electrostatic lower-hybrid drift instabilities in a current sheet with guide field

A kinetic electrostatic eigenvalue equation for the lower-hybrid drift instability (LHDI) in a thin Harris current sheet with a guide field is derived based on the gyrokinetic electron and fully kinetic ion(GeFi) description. Three-dimensional nonlocal analyses are carried out to investigate the influence of a guide field on the stabilization of the LHDI by finite parallel wavenumber, k∥. Detailed stability properties are first analyzed locally, and then as a nonlocal eigenvalue problem. Our results indicate that at large equilibrium drift velocities, the LHDI is further destabilized by finite k∥ in the short-wavelength domain. This is demonstrated in a local stability analysis and confirmed by the peak in the eigenfunction amplitude. We find the most unstable modes localized at the current sheet edges, and our results agree well with simulations employing the GeFi code developed by Lin et al. [Plasma Phys. Controlled Fusion 47, 657 (2005); Plasma Phys. Controlled Fusion 53, 054013 (2011)].

On ballooning instability in current sheets

The problem of instability of the magnetotail current sheet to azimuthally small-scale Alfvén and slow magnetosonic (SMS) waves is solved. The solutions describe unstable oscillations in the presence of a current sheet and correspond to the region of stretched closed field lines of the magnetotail. The spectra of eigen-frequencies of several basic harmonics of standing Alfvén and SMS waves are found in the local and Wentzel–Kramers–Brillouin (WKB) approximation, which are compared. It is shown that the oscillation properties obtained in these approximations differ radically. In the local approximation, the Alfvén waves are stable in the entire range of magnetic shells. SMS waves go into the aperiodic instability regime (the regime of the ‘ballooning’ instability), on magnetic shells crossing the current sheet. In the WKB approximation, both the Alfvén and SMS oscillations go into an unstable regime with a non-zero real part of their eigen-frequency, on magnetic shells crossing the current sheet. The structure of azimuthally small-scale Alfvén waves across magnetic shells is determined.

The hemispheric conjugate observation of postnoon “bright spots”/auroral spirals

Using the Polar ultraviolet imager (UVI) above the Arctic and the all‐sky camera (ASC) at Chinese Zhongshan Station (ZHS) in Antarctica, an outstanding hemispheric conjugate observation of postnoon “bright spots” in the Arctic and auroral spirals in Antarctica is presented. Multiple bright auroral spirals, which are counterclockwise rotation viewed along the direction of the magnetic field, in postnoon auroral arcs are seen on the field of view (FOV) of ASC at ZHS in the Southern Hemisphere, while multiple bright spots are seen at the conjugate FOV of ASC on postnoon auroral oval in the Northern Hemisphere by Polar UVI. We consider that the auroral spirals in postnoon arcs are the visible characteristic of postnoon UV bright spots on ground‐based observation and suggest that the current sheet instability above the parallel electric field region, which could produce the arcs, is the origin for bright spots occurring at the ionosphere, and the hemispheric symmetry/asymmetry of postnoon upward field‐aligned currents, which is affected by the IMF BY and season, can control the conjugacy/nonconjugacy of postnoon bright spots/auroral spirals between the two hemispheres.

Effect of guide field on lower-hybrid drift instabilities in current sheet containing energetic particles

The effect of a guide field on the linear lower-hybrid drift instability (LHDI) in a thin current sheet containing energetic particles is investigated using kinetic theory. It is found that the symmetry properties of the LHD modes are destroyed by the guide field. The LHDI growth rate decreases with the strength of the latter, and the perturbed magnetic field is much higher than that of the guide-field free case.

Phase diagram for magnetic reconnection in heliophysical, astrophysical, and laboratory plasmas

Recent progress in understanding the physics of magnetic reconnection is conveniently summarized in terms of a phase diagram which organizes the essential dynamics for a wide variety of applications in heliophysics, laboratory, and astrophysics. The two key dimensionless parameters are the Lundquist number and the macrosopic system size in units of the ion sound gyroradius. In addition to the conventional single X-line collisional and collisionless phases, multiple X-line reconnection phases arise due to the presence of the plasmoid instability either in collisional and collisionless current sheets. In particular, there exists a unique phase termed “multiple X-line hybrid phase” where a hierarchy of collisional islands or plasmoids is terminated by a collisionless current sheet, resulting in a rapid coupling between the macroscopic and kinetic scales and a mixture of collisional and collisionless dynamics. The new phases involving multiple X-lines and collisionless physics may be important for the emerging applications of magnetic reconnection to accelerate charged particles beyond their thermal speeds. A large number of heliophysical and astrophysical plasmas are surveyed and grouped in the phase diagram: Earth’s magnetosphere, solar plasmas (chromosphere, corona, wind, and tachocline), galactic plasmas (molecular clouds, interstellar media, accretion disks and their coronae, Crab nebula, Sgr A*, gamma ray bursts, and magnetars), and extragalactic plasmas (active galactic nuclei disks and their coronae, galaxy clusters, radio lobes, and extragalactic jets). Significance of laboratory experiments, including a next generation reconnection experiment, is also discussed.

An improved gyrokinetic electron and fully kinetic ion particle simulation scheme: benchmark with a linear tearing mode

An improved gyrokinetic electron and fully kinetic ion (GeFi) particle simulation scheme is presented for the investigation of linear collisionless tearing mode instability in a two-dimensional Harris current sheet under a finite guide field BG and a realistic ion-to-electron mass ratio mi/me. Due to the removal of the rapid electron cyclotron motion while retaining the finite electron Larmor radii, wave–particle interaction, and off-diagonal components of the electron pressure tensor, the GeFi model can be used to investigate the physics of magnetic reconnection with a realistic mi/me in a large-scale current sheet, which in general possesses wave modes ranging from Alfvén waves to lower hybrid/whistler waves, with wave frequency ω < Ωe, where Ωe is the electron gyrofrequency. As a necessary step of utilizing the code for magnetic reconnection, the linearized GeFi scheme is benchmarked by comparing the simulation results using a δf method against direct numerical solutions of the tearing-instability eigenmode equations, as well as those obtained analytically via asymptotic matching.

A NEW MECHANISM FOR DISSIPATION OF ALTERNATING FIELDS IN POYNTING-DOMINATED OUTFLOWS

Reconnection of alternating magnetic fields is an important energy transformation mechanism in Poynting dominated outflows. We show that the reconnection is facilitated by the Kruskal-Schwarzschild instability of current sheets separating the oppositely directed fields. This instability, which is a magnetic counterpart of the Rayleigh-Taylor instability, develops if the flow is accelerated. Then the plasma drips out of the current sheet providing conditions for rapid reconnection. Since the magnetic dissipation leads to the flow acceleration, the process is self-sustaining. In pulsar winds, this process could barely compete with the earlier proposed dissipation mechanisms. However, the novel mechanism turns out to be very efficient at AGN and GRB conditions.

Spontaneous non-steady magnetic reconnection within the solar environment

This work presents a 2.5-dimensional simulation study of the instability of current-sheets located in a medium with a strong density variation along the current layer. The initial force-free configuration is observed to undergo a two-stage evolution consisting of an abrupt regime transition from a slow to a fast reconnection process leading the system to a final chaotic configuration. Yet, the onset of the fast phase is not determined by the presence of any anomalous enhancement in plasma's local resistivity, but rather is the result of a new mechanism discovered in Lapenta (2008)* and captured only when sufficient resolution is present. Hence, the effects of the global resistivity, the global viscosity and the plasma beta on the overall dynamics are considered. This mechanism allowing the transition from slow to fast reconnection provides a simple but effective model of several processes taking place within the solar atmosphere from the high chromosphere up to the low corona. In fact, the understanding of a spontaneous transition to a self-feeding fast reconnection regime as well as its macroscopic evolution is the first and fundamental step to produce realistic models of all those phenomena requiring fast (and high power) triggering events (* Lapenta G. 2008, Phys. Rev. Lett., 100, 235001).

Linear plasmoid instability of thin current sheets with shear flow

This paper presents linear analytical and numerical studies of plasmoid instabilities in the presence of shear flow in high-Lundquist-number plasmas. Analysis demonstrates that the stability problem becomes essentially two dimensional as the stabilizing effects of shear flow become more prominent. Scaling results are presented for the two-dimensional instabilities. An approximate criterion is given for the critical aspect ratio of thin current sheets at which the plasmoid instability is triggered.

Roles of ion and electron dynamics in the onset of magnetic reconnection due to current sheet instabilities

Roles of ion and electron kinetic effects in the trigger mechanism of magnetic reconnection due to current sheet instabilities are investigated by means of (2+1∕2)D explicit particle simulation. The simulation is performed for the Harris equilibrium without guide fields in the plane perpendicular to the antiparallel magnetic fields. The instabilities excited in the vicinity of the neutral sheet are classified into two modes, i.e., one is a longer wavelength kink mode and the other is a shorter wavelength kink mode. The growth of the longer kink mode depends only on the ion mass, while the growth of the shorter one depends only on the electron mass. Before the growth of these kink modes, the lower hybrid drift instability leads to two types of plasma diffusion: diffusion at the periphery controlled by ions and diffusion in the vicinity of the neutral sheet controlled by electrons. The diffusion at the periphery affects the ion distribution function at the neutral sheet through the ion meandering motion, and the ion-ion kink mode is destabilized as the electron-independent longer kink mode. The generation of the reconnection electric field at the neutral sheet due to the longer wavelength kink mode is characterized only by the ion dynamics and can take place commonly in ion-scale current sheets observed in the magnetosphere and laboratories.

Tackling Substorm Problems: New Observational and Modeling Capabilities: Ninth International Conference on Substorms; Graz, Austria, 5–9 May 2008

Geomagnetic substorms, responsible for creating brightly lit aurorae that can disrupt satellite communications and electric power grids, comprise a wealth of dynamic plasma processes. These processes and their interplay were discussed by about 130 scientists at a conference at Austria's Seggau Castle, organized by the Space Research Institute of the Austrian Academy of Sciences.Recent advances in observational and computational capabilities have allowed closer comparison between observation and theory on current sheet instabilities associated with reconnection, ballooning modes, and different wave properties. For example, presentations at the meeting showed how theory combined with observations from ESA's Cluster satellite helped scientists conclude that the formation of an embedded current sheet occurred before the growth of the instability rather than from thinning the entire plasma sheet. Additionally, the evolution of instabilities leading to magnetic reconnection was reported by several theoretical studies at the meeting, which were complemented by presentations of in situ observations seen from Cluster and NASA's Time History of Events and Macroscale Interactions During Substorms (THEMIS) mission that detailed the characteristics of the reconnecting current sheet. Observations at the inner magnetosphere where the magnetic field configuration changes from tail‐like to dipolar fields showed that instabilities such as ballooning modes are needed to explain the initial auroral arc formation near the equatorward edge of plasma sheet electron precipitation.

Drift kink instability in the current sheet with a kappa-distribution

Superthermal particle distributions well-described by the family of κ-distributions have been observed in various astrophysical plasmas. In this paper, the drift kink instability in the current sheet with a κ-distribution is investigated in the framework of linear kinetic theory. The orbit integrals are treated numerically using the exact unperturbed particle orbits, and the resulting eigenvalue problem of the integro-differential equations is solved using the spectral method. The growth rate, eigenmode structure, and parametric dependencies of the kink mode are examined and compared with the case of the standard Harris current sheet. The results show that the drift kink instability in the κ-distribution current sheet resembles its counterpart in the standard Harris sheet, but has a smaller growth rate and real frequency for small value of κ. It is also demonstrated that a background population can enhance the growth rate of the kink mode, making the growth rate significant at the physical value of the ion-electron mass ratio.