Instability Of Current Sheets Research Articles

Plasmoid-mediated reconnection during nonlinear peeling–ballooning edge-localized modes

Plasmoid-mediated reconnection is investigated for nonlinear peeling–ballooning edge-localized modes (P-B ELMs). The formation of current sheets and the transition to 3D current sheet instability is demonstrated through fully nonlinear resistive MHD simulations of P-B ELMs in DIII-D discharges. Large-scale axisymmetric current sheets, as well as small-scale poloidally extended current sheets, are formed as the coherent P-B ELM filaments nonlinearly evolve. It is observed that, at high Lundquist numbers, these current sheets break during a reconnection burst, i.e. a secondary exponential growth of intermediate modes followed by relaxation due to the suppression of P-B drive.

Configuration of Magnetotail Current Sheet Prior to Magnetic Reconnection Onset

AbstractThe magnetotail current sheet configuration determines magnetic reconnection properties that control the substorm onset, one of the most energetic phenomena in the Earth’s magnetosphere. The quiet‐time current sheet is often approximated as a two‐dimensional (2D) magnetic field configuration balanced by isotropic plasma pressure gradients. However, reconnection onset is preceded by the current sheet thinning and the formation of a nearly one‐dimensional (1D) magnetic field configuration. In this study, using particle‐in‐cell simulations, we investigate the force balance of such thin current sheets when they are driven by plasma inflow. We demonstrate that the magnetic field configuration transitions from 2D to 1D thanks to the formation of plasma pressure nongyrotropy and reveal its origin in the nongyrotropic terms of the ion distributions. We show that substorm onset may be controlled by the instability and dynamics of such nongyrotropic current sheets, having properties much different from the most commonly investigated 2D isotropic configuration.

Probing Current Sheet Instabilities from Flare Ribbon Dynamics

Abstract The presence of current sheet instabilities, such as the tearing mode instability, are needed to account for the observed rate of energy release in solar flares. Insights into these current sheet dynamics can be revealed by the behavior of flare ribbon substructure, as magnetic reconnection accelerates particles down newly reconnected field lines into the chromosphere to mark the flare footpoints. Behavior in the ribbons can therefore be used to probe processes occurring in the current sheet. In this study, we use high-cadence (1.7 s) IRIS Slit Jaw Imager observations to probe for the growth and evolution of key spatial scales along the flare ribbons—resulting from dynamics across the current sheet of a small solar flare on 2016 December 6. Combining analyses of spatial scale growth with Si iv nonthermal velocities, we piece together a timeline of flare onset for this confined event, and provide evidence of the tearing mode instability triggering a cascade and inverse cascade toward a power spectrum consistent with plasma turbulence.

Dynamic mitigation of the tearing mode instability in a collisionless current sheet

Dynamic mitigation for the tearing mode instability in the current sheet in collisionless plasmas is demonstrated by applying a wobbling electron current beam. The initial small amplitude modulations imposed on the current sheet induce the electric current filamentation and the reconnection of the magnetic field lines. When the wobbling or oscillatory motion is added from the electron beam having a form of a thin layer moving along the current sheet, the perturbation phase is mixed and consequently the instability growth is saturated remarkably, like in the case of the feed-forward control.

Fluid simulations of three-dimensional reconnection that capture the lower-hybrid drift instability

Fluid models that approximate kinetic effects have received attention recently in the modelling of large-scale plasmas such as planetary magnetospheres. In three-dimensional reconnection, both reconnection itself and current sheet instabilities need to be represented appropriately. We show that a heat flux closure based on pressure gradients enables a 10-moment fluid model to capture key properties of the lower-hybrid drift instability (LHDI) within a reconnection simulation. Characteristics of the instability are examined with kinetic and fluid continuum models, and its role in the three-dimensional reconnection simulation is analysed. The saturation level of the electromagnetic LHDI is higher than expected, which leads to strong kinking of the current sheet. Therefore, the magnitude of the initial perturbation has significant impact on the resulting turbulence.

An Alfvenic reconnecting plasmoid thruster

A new concept for the generation of thrust for space propulsion is introduced. Energetic thrust is generated in the form of plasmoids (confined plasma in closed magnetic loops) when magnetic helicity (linked magnetic field lines) is injected into an annular channel. Using a novel configuration of static electric and magnetic fields, the concept utilizes a current-sheet instability to spontaneously and continuously create plasmoids via magnetic reconnection. The generated low-temperature plasma is simulated in a global annular geometry using the extended magnetohydrodynamic model. Because the system-size plasmoid is an Alfvenic outflow from the reconnection site, its thrust is proportional to the square of the magnetic field strength and does not ideally depend on the mass of the ion species of the plasma. Exhaust velocities in the range of 20 to $500\ \textrm {km}\ \textrm {s}^{-1}$ , controllable by the coil currents, are observed in the simulations.

Electromagnetic Drift Waves at Substorm Onset: Theory and Observations

AbstractThe onset of a modest substorm observed by THEMIS is studied and interpreted using a new model of current sheet instability. The wave‐like structuring of the first observed auroral arc is characterized using auroral imagers. Similarly, the magnetic fluctuations measured by the THEMIS satellites, located in the near‐Earth current sheet (10 RE) and magnetically connected to the arc, are determined. Both sets of measurements show that oscillatory components with periods from 7 to 20 s are detected at the very early phase of the onset. This is compared with the predictions of a recent theoretical model (Tsareva et al., 2019, https://doi.org/10.1017/S002237781900028X) that describes the kinetic instability of electromagnetic drift waves in 2‐D Harris sheet configurations. They are in a reasonable agreement with the observations since the measured magnetic fluctuations are characterized by frequencies, growth rates, and polarization that are consistent with the model. It is also remarkable that the oscillations are observed when the ion perpendicular velocity (drift velocity) exceeds 90–100 km/s. The theory indeed shows that the drift is the main trigger of the instability, with a possible threshold at 80–100 km/s. This suggests that above a threshold of magnetic stress, and thus ion drift, the current sheet equilibrium is affected by the generation of electromagnetic drift waves.

Fast Magnetic Reconnection: Secondary Tearing Instability and Role of the Hall Term

Magnetic reconnection provides the primary source for explosive energy release, plasma heating and particle acceleration in many astrophysical environments. The last years witnessed a revival of interest in the MHD tearing instability as a driver for efficient reconnection. It has been established that, provided the current sheet aspect ratio becomes small enough ($a/L \sim S^{-1/3}$ for a given Lundquist number $S\gg 1$), reconnection occurs on ideal Alfv\'en timescales and becomes independent on $S$. Here we investigate, by means of two-dimensional simulations, the \emph{ideal} tearing instability in the Hall-MHD regime, which is appropriate when the width of the resistive layer $\delta$ becomes comparable to the ion inertial length $d_i$. Moreover, we study in detail the spontaneous development and reconnection of secondary current sheets, which for high $S$ naturally adjust to the ideal aspect ratio and hence their evolution proceeds very rapidly. For moderate low $S$, the aspect ratio tends to the Sweet-Parker scaling ($a/L \sim S^{-1/2}$), in order to fulfill the condition $\delta \ll a$ necessary for the onset of a tearing instability. When the Hall term is included, the reconnection rate of this secondary nonlinear phase is enhanced and, depending on the ratio $d_i/\delta$, can be twice with respect to the pure MHD case, and up to ten times larger than the linear phase. Therefore, the evolution of the tearing instability in thin current sheets in the Hall-MHD regime naturally leads to an explosive disruption of the reconnecting site and to energy release on super-Alfv\'enic timescales, as required to explain astrophysical observations.

Fast Recursive Reconnection and the Hall Effect: Hall-MHD Simulations

Abstract Magnetohydrodynamic (MHD) theory and simulations have shown that reconnection is triggered via a fast “ideal” tearing instability in current sheets whose inverse aspect ratio decreases to , with S as the Lundquist number defined by the half-length L of the current sheet (of a thickness of 2a). Ideal tearing, in 2D sheets, triggers a hierarchical collapse via stretching of X-points and recursive instability. At each step, the local Lundquist number decreases, until the subsequent sheet thickness either approaches kinetic scales or the Lundquist number becomes sufficiently small. Here we carry out a series of Hall-MHD simulations to show how the Hall effect modifies recursive reconnection once the ion inertial scale is approached. We show that as the ion inertial length becomes of the order of the inner, singular layer thickness at some step of the recursive collapse, reconnection transits from the plasmoid-dominant regime to an intermediate plasmoid+Hall regime and then to the Hall-dominant regime. The structure around the X-point, the reconnection rate, the dissipation property, and the power spectra are also modified significantly by the Hall effect.

Three-dimensional plasmoid-mediated reconnection and the effect of toroidal guide field in simulations of coaxial helicity injection

Physics of three-dimensional plasmoid-mediated magnetic reconnection during transient Coaxial Helicity Injection (CHI) plasma start-up is investigated using nonlinear MHD simulations in a spherical tokamak. We numerically examine (i) the role of three-dimensional magnetic fluctuations arising from current-sheet instabilities on the formation of plasmoid-mediated closed flux surfaces, and (ii) the effect of toroidal guide field on the MHD stability during transient CHI. We find that even in the presence of nonaxisymmetric edge magnetic fluctuations, current-carrying axisymmetric (n = 0) plasmoids are rapidly formed while twisted open field lines are being injected and are merged to form a large current-carrying magnetic bubble for plasma startup in a tokamak. It is also found that the 3-D physics response is drastically different for simulations at a higher toroidal field, and complete stabilization of nonaxisymmetric fluctuations was achieved at a higher toroidal flux.

Stochastic Reconnection for Large Magnetic Prandtl Numbers

Abstract We consider stochastic magnetic reconnection in high-β plasmas with large magnetic Prandtl numbers, Pr m > 1. For large Pr m , field line stochasticity is suppressed at very small scales, impeding diffusion. In addition, viscosity suppresses very small-scale differential motions and therefore also the local reconnection. Here we consider the effect of high magnetic Prandtl numbers on the global reconnection rate in a turbulent medium and provide a diffusion equation for the magnetic field lines considering both resistive and viscous dissipation. We find that the width of the outflow region is unaffected unless Pr m is exponentially larger than the Reynolds number Re. The ejection velocity of matter from the reconnection region is also unaffected by viscosity unless Re ∼ 1. By these criteria the reconnection rate in typical astrophysical systems is almost independent of viscosity. This remains true for reconnection in quiet environments where current sheet instabilities drive reconnection. However, if Pr m > 1, viscosity can suppress small-scale reconnection events near and below the Kolmogorov or viscous damping scale. This will produce a threshold for the suppression of large-scale reconnection by viscosity when . In any case, for Pr m > 1 this leads to a flattening of the magnetic fluctuation power spectrum, so that its spectral index is ∼−4/3 for length scales between the viscous dissipation scale and eddies larger by roughly . Current numerical simulations are insensitive to this effect. We suggest that the dependence of reconnection on viscosity in these simulations may be due to insufficient resolution for the turbulent inertial range rather than a guide to the large Re limit.

Plasmoid Instability in Forming Current Sheets

Abstract The plasmoid instability has revolutionized our understanding of magnetic reconnection in astrophysical environments. By preventing the formation of highly elongated reconnection layers, it is crucial in enabling the rapid energy conversion rates that are characteristic of many astrophysical phenomena. Most previous studies have focused on Sweet–Parker current sheets, which are unattainable in typical astrophysical systems. Here we derive a general set of scaling laws for the plasmoid instability in resistive and visco-resistive current sheets that evolve over time. Our method relies on a principle of least time that enables us to determine the properties of the reconnecting current sheet (aspect ratio and elapsed time) and the plasmoid instability (growth rate, wavenumber, inner layer width) at the end of the linear phase. After this phase the reconnecting current sheet is disrupted and fast reconnection can occur. The scaling laws of the plasmoid instability are not simple power laws, and they depend on the Lundquist number (S), the magnetic Prandtl number (P m ), the noise of the system ( ), the characteristic rate of current sheet evolution ( ), and the thinning process. We also demonstrate that previous scalings are inapplicable to the vast majority of astrophysical systems. We explore the implications of the new scaling relations in astrophysical systems such as the solar corona and the interstellar medium. In both of these systems, we show that our scaling laws yield values for the growth rate, wavenumber, and aspect ratio that are much smaller than the Sweet–Parker–based scalings.

Electron flat-top distributions and cross-scale wave modulations observed in the current sheet of geomagnetic tail

We present new observations of electron distributions and the accompanying waves during the current sheet activities at ∼60 RE in the geomagnetic tail detected by the ARTEMIS (Acceleration, Reconnection, Turbulence, and Electrodynamics of the Moon's Interaction with the Sun) spacecraft. We find that electron flat-top distribution is a common feature near the neutral sheet of the tailward flowing plasmas, consistent with the electron distributions that are shaped in the reconnection region. Whistler mode waves are generated by the anisotropic electron temperature associated with the electron flat-top distributions. These whistler mode waves are modulated by low frequency ion scale waves that are possibly excited by the high-energy ions injected during the current sheet instability. The magnetic and electric fields of the ion scale waves are in phase with electron density variations, indicating that they are compressional ion cyclotron waves. Our observations present examples of the dynamical processes occurring during the current sheet activities far downstream of the geomagnetic tail.

Nonlinear reconnecting edge localized modes in current-carrying plasmas

Nonlinear edge localized modes in a tokamak are examined using global three-dimensional resistive magnetohydrodynamics simulations. Coherent current-carrying filament (ribbon-like) structures wrapped around the torus are nonlinearly formed due to nonaxisymmetric reconnecting current sheet instabilities, the so-called peeling-like edge localized modes. These fast growing modes saturate by breaking axisymmetric current layers isolated near the plasma edge and go through repetitive relaxation cycles by expelling current radially outward and relaxing it back. The local bi-directional fluctuation-induced electromotive force (emf) from the edge localized modes, the dynamo action, relaxes the axisymmetric current density and forms current holes near the edge. The three-dimensional coherent current-carrying filament structures (sometimes referred to as 3-D plasmoids) observed here should also have strong implications for solar and astrophysical reconnection.

Dynamo-driven plasmoid formation from a current-sheet instability

Axisymmetric current-carrying plasmoids are formed in the presence of nonaxisymmetric fluctuations during nonlinear three-dimensional resistive MHD simulations in a global toroidal geometry. We utilize the helicity injection technique to form an initial poloidal flux in the presence of a toroidal guide field. As helicity is injected, two types of current sheets are formed from (1) the oppositely directed field lines in the injector region (primary reconnecting current sheet), and (2) the poloidal flux compression near the plasma edge (edge current sheet). We first find that nonaxisymmetric fluctuations arising from the current-sheet instability isolated near the plasma edge have tearing parity but can nevertheless grow fast (on the poloidal Alfven time scale). These modes saturate by breaking up the current sheet. Second, for the first time, a dynamo poloidal flux amplification is observed at the reconnection site (in the region of the oppositely directed magnetic field). This fluctuation-induced flux amplification increases the local Lundquist number, which then triggers a plasmoid instability and breaks the primary current sheet at the reconnection site. The plasmoids formation driven by large-scale flux amplification, i.e., a large-scale dynamo, observed here has strong implications for astrophysical reconnection as well as fast reconnection events in laboratory plasmas.

Multi-D magnetohydrodynamic modelling of pulsar wind nebulae: recent progress and open questions

In the last decade, the relativistic magnetohydrodynamic (MHD) modelling of pulsar wind nebulae, and of the Crab nebula in particular, has been highly successful, with many of the observed dynamical and emission properties reproduced down to the finest detail. Here, we critically discuss the results of some of the most recent studies: namely the investigation of the origin of the radio emitting particles and the quest for the acceleration sites of particles of different energies along the termination shock, by using wisp motions as a diagnostic tool; the study of the magnetic dissipation process in high magnetization nebulae by means of new long-term three-dimensional simulations of the pulsar wind nebula evolution; the investigation of the relativistic tearing instability in thinning current sheets, leading to fast reconnection events that might be at the origin of the Crab nebula gamma-ray flares.

Study of instability of the nonelectroneutral current sheets in quasilinear approximation

The techniques of investigation of low-frequency instabilities of the current sheet in quasi-linear approximation with due regard to the effect of plasma polarization is described. This makes it possible to study the mechanism of the reverse impact of the developing instability modes of nonelectroneutral current sheet on the background distribution function.Evolution equations of the equilibrium distribution function of the plasma current sheet and the perturbation of the electromagnetic field are derived. Algorithms for solution of evolution equations are developed. A dispersion curve for the plasma wave with damping decrement propagating along the magnetic field is derived.

Long-period irregular pulsations under the conditions of a quiet magnetosphere

Simultaneous observations of high-latitude long-period irregular pulsations at frequencies of 2.0–6.0 mHz (ipcl) and magnetic field disturbances in the solar wind plasma at low geomagnetic activity (Kp ~ 0) have been studied. The 1-s data on the magnetic field registration at Godhavn (GDH) high-latitude observatory and the 1-min data on the solar wind plasma and IMF parameters for 2011–2013 were used in an analysis. Ipcl (irregular pulsations continuous, long), which were observed against a background of the IMF Bz reorientation from northward to southward, have been analyzed. In this case other solar wind plasma and IMF parameters, such as velocity V, density n, solar wind dynamic pressure P = ρV2 (ρ is plasma density), and strength magnitude B, were relatively stable. The effect of the IMF Bz variation rate on the ipcl spectral composition and intensity has been studied. It was established that the ipcl spectral density reaches its maximum (~10–20 min) after IMF Bz sign reversal in a predominant number of cases. It was detected that the ipcl average frequency (f) is linearly related to the IMF Bz variation rate (ΔBz/Δt). It was shown that the dependence of f on ΔBz/Δt is controlled by the α = arctan(By/Bx) angle value responsible for the MHD discontinuity type at the front boundary of magnetosphere. The results made it possible to assume that the formation of the observed ipcl spectrum, which is related to the IMF Bz reorientation, is caused by solar wind plasma turbulence, which promotes the development of current sheet instability and surface wave amplification at the magnetopause.

“Ideal” tearing and the transition to fast reconnection in the weakly collisional MHD and EMHD regimes

AbstractThis paper discusses the transition to fast growth of the tearing instability in thin current sheets in the collisionless limit where electron inertia drives the reconnection process. It has been previously suggested that in resistive MHD there is a natural maximum aspect ratio (ratio of sheet length and breadth to thickness) which may be reached for current sheets with a macroscopic length L, the limit being provided by the fact that the tearing mode growth time becomes of the same order as the Alfvén time calculated on the macroscopic scale. For current sheets with a smaller aspect ratio than critical the normalized growth rate tends to zero with increasing Lundquist number S, while for current sheets with an aspect ratio greater than critical the growth rate diverges with S. Here we carry out a similar analysis but with electron inertia as the term violating magnetic flux conservation: previously found scalings of critical current sheet aspect ratios with the Lundquist number are generalized to include the dependence on the ratio , where de is the electron skin depth, and it is shown that there are limiting scalings which, as in the resistive case, result in reconnecting modes growing on ideal time scales. Finite Larmor radius effects are then included, and the rescaling argument at the basis of “ideal” reconnection is proposed to explain secondary fast reconnection regimes naturally appearing in numerical simulations of current sheet evolution.

Visco-resistive plasmoid instability

The plasmoid instability in visco-resistive current sheets is analyzed in both the linear and nonlinear regimes. The linear growth rate and the wavenumber are found to scale as S1/4(1+Pm)−5/8 and S3/8(1+Pm)−3/16 with respect to the Lundquist number S and the magnetic Prandtl number Pm. Furthermore, the linear layer width is shown to scale as S−1/8(1+Pm)1/16. The growth of the plasmoids slows down from an exponential growth to an algebraic growth when they enter into the nonlinear regime. In particular, the time-scale of the nonlinear growth of the plasmoids is found to be τNL∼S−3/16(1+Pm)19/32τA,L. The nonlinear growth of the plasmoids is radically different from the linear one, and it is shown to be essential to understand the global current sheet disruption. It is also discussed how the plasmoid instability enables fast magnetic reconnection in visco-resistive plasmas. In particular, it is shown that the recursive plasmoid formation can trigger a collisionless reconnection regime if S≳Lcs(ϵclk)−1(1+Pm)1/2, where Lcs is the half-length of the global current sheet and lk is the relevant kinetic length scale. On the other hand, if the current sheet remains in the collisional regime, the global (time-averaged) reconnection rate is shown to be 〈dψ/dt|X〉≈ϵcvA,uBu(1+Pm)−1/2, where ϵc is the critical inverse aspect ratio of the current sheet, while vA,u and Bu are the Alfvén speed and the magnetic field upstream of the global reconnection layer.