Instability Of Current Sheets Research Articles

Collisionless instability of thin current sheets in the presence of sheared parallel flows

The first results of an ongoing investigation of the influence of sheared parallel flows on the onset of collisionless magnetic reconnection in thin current sheets are reported. In particular, an exact kinetic equilibrium that incorporates flow with a symmetric profile into the well-known Harris model is proposed and its linear stability is described. The complete linearized Vlasov–Maxwell system is solved using a numerical approach that introduces no approximations regarding the shape of the particle orbits or relative magnitude of the different components of the electromagnetic potentials. Thus accurate results are obtained in a difficult, but practically important limit where the characteristic length scales for the variation of the equilibrium magnetic field and flow are comparable to the ion kinetic length scales. In particular, the dispersion relation for an instability that produces magnetic reconnection is traced as a function of the flow speed V0 at the center of the sheet, starting with the collisionless tearing mode at V0=0. The effects of the sheared flow are shown to qualitatively depend on the thickness of the current sheet. In relatively thick sheets the characteristic features of the dispersion relation depend mostly on the value of the flow shear. In this regime there exist regions of the parameter space where the flow is destabilizing. However, the growth rate of the instability never significantly exceeds that of the collisionless tearing mode and the mode is always stabilized at high enough values of V0. When the sheet is thinner than the ion gyroradius in the asymptotic magnetic field, the flow shear introduces strong non-Maxwellian features into the equilibrium distribution function. In this regime, the flow is purely stabilizing for the equilibrium considered. The instability produces magnetic reconnection in all the parameter regimes considered. Finally, the results of the linear analysis are verified using large-scale particle-in-cell simulations.

A particle simulation of current sheet instabilities under finite guide field

The instability of a Harris current sheet under a broad range of finite guide field (BG) is investigated using a linearized (δf) gyrokinetic electron and fully kinetic ion particle simulation code. The simulation is carried out in the two-dimensional plane containing the guide field along y and the current sheet normal along z. In this particle model, the rapid electron cyclotron motion is removed, while the realistic mass ratio mi∕me, finite electron Larmor radii, and wave-particle interactions are kept. It is found that for a finite BG∕Bx0⩽1, where Bx0 is the asymptotic antiparallel component of magnetic field, three unstable modes, i.e., modes A, B, and C, can be excited in the current sheet. Modes A and C, appearing to be quasielectrostatic modified two-stream instability/whistler mode, are located mainly on the edge of the current sheet. Mode B, on the other hand, is confined in the current sheet center and carries a compressional magnetic field (δBy) perturbation along the direction of electron drift velocity. Our new finding suggests that mode B may contribute directly to the electron anomalous resistivity in magnetic reconnection. In the cases with extremely large BG∕Bx0⪢1, the wave modes evolve to a globally propagating instability. The simulation shows that the presence of finite BG modifies the physics of the current sheet significantly.

Instability of current sheets and formation of plasmoid chains

Current sheets formed in magnetic reconnection events are found to be unstable to high-wavenumber perturbations. The instability is very fast: its maximum growth rate scales as S1∕4vA∕LCS, where LCS is the length of the sheet, vA the Alfvén speed, and S the Lundquist number. As a result, a chain of plasmoids (secondary islands) is formed, whose number scales as S3∕8.

Substorms and Their Solar Wind Causes

Consequences of the solar wind input observed as large scale magnetotail dynamics during substorms are reviewed, highlighting results from statistical studies as well as global magnetosphere/ionosphere observations. Among the different solar wind input parameters, the most essential one to initiate reconnection relatively close to the Earth is a southward IMF or a solar wind dawn-to-dusk electric field. Larger substorms are associated with such reconnection events closer to the Earth and the magnetotail can accumulate larger amounts of energy before its onset. Yet, how and to what extent the magnetotail configuration before substorm onset differs for different solar wind driver is still to be understood. A strong solar wind dawn-to-dusk electric field is, however, only a necessary condition for a strong substorm, but not a sufficient one. That is, there are intervals when the solar wind input is processed in the magnetotail without the usual substorm cycle, suggesting different modes of flux transport. Furthermore, recent global observations suggest that the magnetotail response during the substorm expansion phase can be also controlled by plasma sheet density, which is coupled to the solar wind on larger time-scales than the substorm cycle. To explain the substorm dynamics it is therefore important to understand the different modes of energy, momentum, and mass transport within the magnetosphere as a consequence of different types of solar wind-magnetosphere interaction with different time-scales that control the overall magnetotail configuration, in addition to the internal current sheet instabilities leading to large scale tail current sheet dissipation.

New role of the lower-hybrid drift instability in the magnetic reconnection

Kinetic simulation results reveal that the growth of the lower-hybrid drift instability (LHDI) in current sheets has an important effect on the onset and nonlinear development of magnetic reconnection. The LHDI does this by heating electrons anisotropically, by increasing the peak current density, by producing current bifurcation, and by causing ion velocity shear. The role of these in magnetic reconnection is explained. Confidence in the results is strongly enhanced by agreement between implicit and massively-parallel-explicit particle-in-cell simulations.

An Explanation for the “Switch‐On” Nature of Magnetic Energy Release and Its Application to Coronal Heating

A large class of coronal heating theories postulate that the random mixing of magnetic footpoints by photospheric motions leads to the formation of current sheets in the corona and, consequently, to energy release there via magnetic reconnection. Parker pointed out that in order for this process to supply the observed energy flux into the corona, the stress in the coronal magnetic field must have a fairly specific value at the time that the energy is released. In particular, he argued that the misalignment between reconnecting flux tubes must be roughly 30° in order to match the observed heating. No physical origin for this number was given, however. In this paper we propose that secondary instability is the mechanism that switches on the energy release when the misalignment angle in the corona reaches the correct value. We calculate both the three-dimensional linear and fully nonlinear development of the instability in current sheets corresponding to various misalignment angles. We find that no secondary instability occurs for angles less than about 45°, but for larger angles the instability grows at a rapid rate, and there is an explosive release of energy. We compare our results with the observed properties of the corona and discuss the implications for future observations.

Filamentation Instability of Thin Current Sheets in Low-β Plasmas

An analytic theory is presented for the collisionless filamentation instability of thin current sheets in the frequency domain of lower-hybrid waves in low-β plasmas. In a configuration with a strong guide field, the plasma dynamics is studied in a fluid description, accounting for the effects of electron polarization and finite Larmor radii, as well as of the motion of unmagnetized ions in the presence of perpendicular electric fields. In the linear phase, two types of unstable perturbations of a thin current sheet with steep edges are identified that correspond to its filamentation or tearing and bending. Using a surface-wave formalism for the modes whose wavelength is larger than the current sheet thickness, the corresponding growth rates are calculated as the contributions of singularities in the dispersion function of surface waves. These are governed by the electron inertia and by linear coupling with local plasma modes propagating in the perpendicular direction that are subjected to the Buneman instability. This new linear instability provides a suitable channel for the dissipation of current sheets that evolve during the collisionless magnetic reconnection in shear- and kinetic-Alfvén regimes, and for the creation of anomaluos resistivity.

Small-scale reconnection due to lower-hybrid drift instability in current sheets with sheared fields

The consequences of small-scale lower-hybrid drift (LHD) instability for reconnection through thin current sheets are investigated in dependence on guide magnetic field By0 by three-dimensional Vlasov-code simulations. The LHD waves are amplified by inverse resonant Landau damping on ion flow. In current sheets separating antiparallel magnetic fields the LHD waves can trigger global current-aligned eigenmodes, which directly couple to the tearing-mode instability. Depending on the initial conditions either small-scale, three-dimensional, or small-scale two-dimensional reconnection prevails. In the presence of a moderate guide magnetic field up to By0=B0, where B0 is the asymptotic Bx field, the unstable LHD waves propagate obliquely to the current direction, at different angles from the opposite sides of the current sheet. The resulting patchy three-dimensional small-scale reconnection grows significantly slower, compared to reconnection in antiparallel fields.

Nonlinear instability of thin current sheets in antiparallel and guided magnetic fields

The influence of a current-aligned guide magnetic field on the nonlinear resonant instability of thin current sheets is investigated by means of three-dimensional Vlasov-code simulations. Similarly to the zero-guide field case, the pressure gradient excites lower-hybrid-drift (LHD) waves at the current sheet edges. However, since the LHD waves are excited perpendicular to the local magnetic field they propagate obliquely to the current direction. As a result, the number of resonant particles, i.e., the drift-resonance efficiency, decreases with increasing guide field strength. Hence, the driving of global current sheet kink/sausage instabilities becomes less efficient.

Kinetic instabilities of thin current sheets: Results of two-and-one-half-dimensional Vlasov code simulations

Nonlinear triggering of the instability of thin current sheets is investigated by two-and-one-half- dimensional Vlasov code simulations. A global drift-resonant instability (DRI) is found, which results from the lower-hybrid-drift waves penetrating from the current sheet edges to the center where they resonantly interact with unmagnetized ions. This resonant nonlinear instability grows faster than a Kelvin–Helmholtz instability obtained in previous studies. The DRI is either asymmetric or symmetric mode or a combination of the two, depending on the relative phase of the lower-hybrid-drift waves at the edges of the current sheet. With increasing particle mass ratio the wavenumber of the fastest-growing mode increases as kLz∼(mi/me)1/2/2 and the growth rate of the DRI saturates at a finite level.

The unexpected role of the lower hybrid drift instability in magnetic reconnection in three dimensions

The growth of the lower hybrid drift instability (LHDI) in unstable current sheets induces a fluid velocity shear that drives a Kelvin–Helmholtz instability (KHI). The KHI results in kinking of the current sheet, so that any subsequent magnetic reconnection across the current sheet must occur in three dimensions. While this increases the complexity of modeling reconnection, it is of interest for its possible resolution of the stability to tearing of current sheets with a perpendicular magnetic field. Identification of the role of the LHDI in current sheet kinking required advances in simulation technique that allowed simulations at more realistic mass ratio and long time and length scales. Confidence in the results is strongly enhanced by confirmation with a standard plasma simulation using massively parallel computation. The results of this study have obvious relevance not only to magnetic reconnection and substorms in the Earth’s magnetotail, where the LHDI has been observed, but also where thin current sheets occur, such as the solar corona.

Current-sheet kink instability at ion-electron hybrid scale

Current sheet instabilities having wavenumber vectors parallel to the current direction are studied as a linear eigenvalue problem in a two-fluid system where electrons are treated as a finite-mass charge neutralizing component. Focusing on ion-scale current sheets, we show that a hybrid scale current sheet kink instability (CSKI) is one of the major instabilities to appear. The hybrid scale CSKI in a magnetotail-like situation has a wavelength much shorter than the well-studied drift-kink instability (DKI). While most of the previous studies have focused on the long-wavelength range, a full-particle simulation with much larger ion-to-electron mass ratio ( R M = 400) shows the growth of the hybrid scale CSKI as predicted by linear analyses. We also show that the CSKI has large growth rates in a magnetopause-like situation.

Instabilities of collisionless current sheets: Theory and simulations

The problem of Harris current sheet stability is investigated. A linear dispersion relation in the long-wavelength limit is derived for instabilities, propagating in the neutral plane at an arbitrary angle to the magnetic field but symmetric across the sheet. The role of electrostatic perturbations is especially investigated. It appears, that for the tearing-mode instability electrostatic effects are negligible. However, for obliquely propagating modes the modulation of the electrostatic potential φ is essential. In order to verify the theoretical results, the limiting cases of tearing and sausage instabilities are compared to the two-dimensional (2D) Vlasov code simulations. For tearing the agreement between theory and simulations is good for all mass ratios. For sausage-modes, the theory predicts fast stabilization for mass ratios mi/me⩾10. This is not observed in simulations due to the diminishing of the wavelength for higher mass ratios, which leads beyond the limit of applicability of the theory developed here.

Auroral substorm response to solar wind pressure shock

Two cases of auroral substorms have been studied with the Polar UVI data, which were associated with solar wind pressure shock arriving at the Earth. The global aurora activities started about 1–2 min after pressure shocks arrived at dayside magnetopause, then nightside auroras intensified rapidly 3–4 min later, with auroral substorm onset. The observations in synchronous orbit indicated that the compressing effects on magnetosphere were observed in their corresponding sites about 2 min after the pressure shocks impulse magnetopause. We propose that the auroral intensification and substorm onset possibly result from hydromagnetic wave produced by the pressure shock. The fast-mode wave propagates across the magnetotail lobes with higher local Alfven velocity, magnetotail was compressed rapidly and strong lobe field and cross-tail current were built in about 1–2 min, and furthermore the substorm was triggered due to an instability in current sheet.

Geomagnetic substorms as perturbed self-organized critical dynamics of the magnetosphere

The effect of self-organized criticality (SOC), known from the theory of complex nonlinear systems, is considered as an internal mechanism of geomagnetic fluctuations accompanying the development of magnetospheric substorms. It is suggested that spatially localized current sheet instabilities, followed by magnetic reconnection in the magnetotail, can be considered as SOC avalanches, the superposition of which leads naturally to the 1/ f β power spectra ( f — frequency, β — numerical parameter) of geomagnetic activity. A running 2D avalanche model with controlled dissipation rate is proposed for numerical investigation of the multi-scale plasma sheet behavior in stationary and nonstationary states of the magnetosphere. Two basic types of perturbations have been studied, the first induced by an increase in the solar wind energy input rate and the second induced by a decrease in critical current density in the magnetotail. The intensity of large-scale perturbations in the model depends on accumulated energy level and internal dissipation in a manner similar to the dependence characteristic of real magnetospheric substorms. A spectral structure of model dynamics exposed to variations of solar wind parameters reveals distinctive features similar to natural geomagnetic fluctuations, including a spectral break at 5 h separating frequency bands with different spectral slopes.

Spheromaks, solar prominences, and Alfvén instability of current sheets

Three related efforts underway at Caltech are discussed: experimental studies of spheromak formation, experimental simulation of solar prominences, and Alfven wave instability of current sheets. Spheromak formation has been studied by using a coaxial magnetized plasma gun to inject helicity-bearing plasma into a very large vacuum chamber. The spheromak is formed without a flux conserver and internal λ profiles have been measured. Spheromak-based technology has been used to make laboratory plasmas having the topology and dynamics of solar prominences. The physics of these structures is closely related to spheromaks (low β, force-free, relaxed state equilibrium) but the boundary conditions and symmetry are different. Like spheromaks, the equilibrium involves a balance between hoop forces, pinch forces, and magnetic tension. It is shown theoretically that if a current sheet becomes sufficiently thin (of the order of the ion skin depth or smaller), it becomes kinetically unstable with respect to the emission of Alfven waves and it is proposed that this wave emission is an important aspect of the dynamics of collisionless reconnection.

Alfven wave instability of current sheets in force-free plasmas: comparison to ion acoustic instability

Current sheets necessarily form at the interface between adjacent twisted flux tubes and so are ubiquitous to magnetic configurations having non-trivial field topology. In an earlier publication (P. M. Bellan, Phys. Rev. Letters, 83,4768, 1999) the author showed that current sheets in a low β plasma will be kinetically unstable with respect to Alfvén wave emission if the current sheet becomes sufficiently thin for the field-aligned electron flow to become super-Alfvenic. At first sight it might appear that before the current sheet becomes thin enough to develop a super-Alfvenic flow, ion acoustic instabilities will develop when the sheet becomes thin enough for the electron flow to exceed the ion acoustic velocity. However, it is shown here that because of strong ion Landau damping on ion acoustic waves for plasmas with comparable electron and ion temperatures, ion acoustic waves have a much higher instability threshold than the Alfvén instability. Thus, Alfvén instability should dominate ion acoustic instability in thin current sheets.

Sausage mode instability of thin current sheets as a cause of magnetospheric substorms

Abstract. Observations have shown that, prior to substorm explosions, thin current sheets are formed in the plasma sheet of the Earth's magnetotail. This provokes the question, to what extent current-sheet thinning and substorm onsets are physically, maybe even causally, related. To answer this question, one has to understand the plasma stability of thin current sheets. Kinetic effects must be taken into account since particle scales are reached in the course of tail current-sheet thinning. We present the results of theoretical investigations of the stability of thin current sheets and about the most unstable mode of their decay. Our conclusions are based upon a non-local linear dispersion analysis of a cross-magnetic field instability of Harris-type current sheets. We found that a sausage-mode bulk current instability starts after a sheet has thinned down to the ion inertial length. We also present the results of three-dimensional electromagnetic PIC-code simulations carried out for mass ratios up to Mi / me=64. They verify the linearly predicted properties of the sausage mode decay of thin current sheets in the parameter range of interest.Key words. Magnetospheric physics (plasma waves and instabilities; storms and substorms) · Space plasma physics (magnetic reconnection)

Sausage mode instability of thin current sheets as a cause of magnetospheric substorms

Observations have shown that, prior to substorm explosions, thin current sheets are formed in the plasma sheet of the Earth's magnetotail. This provokes the question, to what extent current-sheet thinning and substorm onsets are physically, maybe even causally, related. To answer this question, one has to understand the plasma stability of thin current sheets. Kinetic effects must be taken into account since particle scales are reached in the course of tail current-sheet thinning. We present the results of theoretical investigations of the stability of thin current sheets and about the most unstable mode of their decay. Our conclusions are based upon a non-local linear dispersion analysis of a cross-magnetic field instability of Harris-type current sheets. We found that a sausage-mode bulk current instability starts after a sheet has thinned down to the ion inertial length. We also present the results of three-dimensional electromagnetic PIC-code simulations carried out for mass ratios up to Mi / me=64. They verify the linearly predicted properties of the sausage mode decay of thin current sheets in the parameter range of interest.Key words. Magnetospheric physics (plasma waves and instabilities; storms and substorms) · Space plasma physics (magnetic reconnection)

Properties of the resistive instability in double current sheet systems with strong shear flows

The resistive instability in double current sheet (DCS) systems with shear flows are explored by using a magnetohydrodynamic simulation method. The results showed that the linear growth rate of the antisymmetric and symmetric magnetic reconnection modes depend on the relative vicinity of the two current sheets. When the shear flows are strong and have velocities near or larger than the local Alfvén speed, the growth of the antisymmetric mode resistive instability in DCS systems is further increased. It is also found that the growth rate of the resistive instability decreases as the plasma beta increases.