Unstable Current Sheets Research Articles

Spectral signatures of recursive magnetic field reconnection

ABSTRACT We use 2.5D magnetohydrodynamic simulations to investigate the spectral signatures of the non-linear disruption of a tearing unstable current sheet via the generation of multiple secondary current sheets and magnetic islands. During the non-linear phase of tearing mode evolution, there develops a regime in which the magnetic energy density shows a spectrum with a power law close to B(k)2 ∼ k−0.8. Such an energy spectrum is found in correspondence of the neutral line, within the diffusion region of the primary current sheet, where energy is conveyed towards smaller scales via a ‘recursive’ process of fast tearing-type instabilities. Far from the neutral line, we find that magnetic energy spectra evolve towards slopes compatible with the ‘standard’ Kolmogorov spectrum. Starting from a self-similar description of the non-linear stage at the neutral line, we provide a model that predicts a reconnecting magnetic field energy spectrum scaling as k−4/5, in good agreement with numerical results. An extension of the predicted power law to generic current sheet profiles is also given and possible implications for turbulence phenomenology are discussed. These results provide a step forward to understand the ‘recursive’ generation of magnetic islands (plasmoids), which has been proposed as a possible explanation for the energy release during flares, but which, more in general, can have an impact on the subsequent turbulent evolution of unstable sheets that naturally form in the high Lundquist number and collisionless plasmas found in most of the astrophysical environments.

Diffusive shock acceleration and turbulent reconnection

Diffusive Shock Acceleration (DSA) cannot efficiently accelerate particles without the presence of self-consistently generated or pre-existing strong turbulence ($ \delta B/B \sim 1 $) in the vicinity of the shock. The problem we address in this article is: if large amplitude magnetic disturbances are present upstream and downstream of a shock then Turbulent Reconnection (TR) will set in and will participate not only in the elastic scattering of particles but also in their heating and acceleration. We demonstrate that large amplitude magnetic disturbances and Unstable Current Sheets (UCS), spontaneously formed in the strong turbulence in the vicinity of a shock, can accelerate particles as efficiently as DSA in {\bf large scale systems and on long time scales}. We start our analysis with "elastic" scatterers upstream and downstream and estimate the energy distribution of particles escaping from the shock, recovering the well known results from the DSA theory. Next we analyze the additional interaction of the particles with active scatterers (magnetic disturbances and UCS) upstream and downstream of the shock. We show that the asymptotic energy distribution of the particles accelerated by DSA/TR has very similar characteristics with the one due to DSA alone, but the synergy of DSA with TR is much more efficient: The acceleration time is an order of magnitude shorter and the maximum energy reached two orders of magnitude higher. We claim that DSA is the dominant acceleration mechanism in a short period before TR is established, and then strong turbulence will dominate the heating and acceleration of the particles. In other words, the shock serves as the mechanism to set up a strongly turbulent environment, in which the acceleration mechanism will ultimately be the synergy of DSA and TR.

Synergy of Stochastic and Systematic Energization of Plasmas during Turbulent Reconnection

Abstract The important characteristic of turbulent reconnection is that it combines large-scale magnetic disturbances with randomly distributed unstable current sheets (UCSs). Many well-known nonlinear MHD structures (strong turbulence, current sheet(s), shock(s)) lead asymptotically to the state of turbulent reconnection. We analyze in this article, for the first time, the energization of electrons and ions in a large-scale environment that combines large-amplitude disturbances propagating with sub-Alfvénic speed with UCSs. The magnetic disturbances interact stochastically (second-order Fermi) with the charged particles and play a crucial role in the heating of the particles, while the UCSs interact systematically (first-order Fermi) and play a crucial role in the formation of the high-energy tail. The synergy of stochastic and systematic acceleration provided by the mixture of magnetic disturbances and UCSs influences the energetics of the thermal and nonthermal particles, the power-law index, and the length of time the particles remain inside the energy release volume. We show that this synergy can explain the observed very fast and impulsive particle acceleration and the slightly delayed formation of a superhot particle population.

Particle Acceleration and Fractional Transport in Turbulent Reconnection

Abstract We consider a large-scale environment of turbulent reconnection that is fragmented into a number of randomly distributed unstable current sheets (UCSs), and we statistically analyze the acceleration of particles within this environment. We address two important cases of acceleration mechanisms when particles interact with the UCS: (a) electric field acceleration and (b) acceleration by reflection at contracting islands. Electrons and ions are accelerated very efficiently, attaining an energy distribution of power-law shape with an index 1–2, depending on the acceleration mechanism. The transport coefficients in energy space are estimated from test-particle simulation data, and we show that the classical Fokker–Planck (FP) equation fails to reproduce the simulation results when the transport coefficients are inserted into it and it is solved numerically. The cause for this failure is that the particles perform Levy flights in energy space, while the distributions of the energy increments exhibit power-law tails. We then use the fractional transport equation (FTE) derived by Isliker et al., whose parameters and the order of the fractional derivatives are inferred from the simulation data, and solving the FTE numerically, we show that the FTE successfully reproduces the kinetic energy distribution of the test particles. We discuss in detail the analysis of the simulation data and the criteria that allow one to judge the appropriateness of either an FTE or a classical FP equation as a transport model.

Reconnection and particle acceleration in interacting flux ropes I. Magnetohydrodynamics and test particles in 2.5D

Magnetic reconnection and non-thermal particle distributions associated with current-driven instabilities are investigated by means of resistive magnetohydrodynamics (MHD) simulations combined with relativistic test particle methods. We propose a system with two parallel, repelling current channels in an initially force-free equilibrium, as a simplified representation of flux ropes in a stellar magnetosphere. The current channels undergo a rotation and separation on Alfv\'enic timescales, forming secondary islands and (up to tearing unstable) current sheets in which non-thermal energy distributions are expected to develop. Using the recently developed particle module of our open-source grid-adaptive MPI-AMRVAC software, we simulate MHD evolution combined with test particle treatments in MHD snapshots. We explore under which plasma-$\beta$ conditions the fastest reconnection occurs in two-and-a-half dimensional (2.5D) scenarios and in these settings test particles are evolved. We quantify energy distributions, acceleration mechanisms, relativistic corrections to the particle equations of motion and effects of resistivity in magnetically dominated proton-electron plasmas. Due to large resistive electric fields and indefinite acceleration of particles in the infinitely long current channels, hard energy spectra are found in 2.5D configurations. Solutions to these numerical artifacts are proposed for both 2.5D setups and future 3D work. We discuss the magnetohydrodynamics of an additional kink instability in 3D setups and the expected effects on energy distributions. The obtained results hold as a proof-of-principle for test particle approaches in MHD simulations, relevant to explore less idealised scenarios like solar flares and more exotic astrophysical phenomena, like black hole flares, magnetar magnetospheres and pulsar wind nebulae.

‘Ideally’ unstable current sheets and the triggering of fast magnetic reconnection

Magnetic reconnection is thought to be the dynamical mechanism underlying many explosive phenomena observed both in space and in the laboratory, although the question of how fast magnetic reconnection is triggered in such high Lundquist ($S$) number plasmas has remained elusive. It has been well established that reconnection can develop over time scales faster than those predicted traditionally once kinetic scales are reached. It has also been shown that, within the framework of resistive magnetohydrodynamics (MHD), fast reconnection is achieved for thin enough sheets via the onset of the so-called plasmoid instability. The latter was discovered in studies specifically devoted to the Sweet–Parker current sheet, either as an initial condition or an apparent transient state developing in nonlinear studies. On the other hand, a fast tearing instability can grow on an ideal, i.e. $S$-independent, time scale (dubbed ‘ideal’ tearing) within current sheets whose aspect ratio scales with the macroscopic Lundquist number as $L/a\sim S^{1/3}$ – much smaller than the Sweet–Parker one – suggesting a new way to approach to the initiation of fast reconnection in collapsing current configurations. Here we present an overview of what we have called ‘ideal’ tearing in resistive MHD, and discuss how the same reasoning can be extended to other plasma models commonly used that include electron inertia and kinetic effects. We then discuss a scenario for the onset of ‘ideal’ fast reconnection via collapsing current sheets and describe a quantitative model for the interpretation of the nonlinear evolution of ‘ideally’ unstable sheets in two dimensions.

Complexity methods applied to turbulence in plasma astrophysics

In this review many of the well known tools for the analysis of Complex systems are used in order to study the global coupling of the turbulent convection zone with the solar atmosphere where the magnetic energy is dissipated explosively. Several well documented observations are not easy to interpret with the use of Magnetohydrodynamic (MHD) and/or Kinetic numerical codes. Such observations are: (1) The size distribution of the Active Regions (AR) on the solar surface, (2) The fractal and multi fractal characteristics of the observed magnetograms, (3) The Self-Organised characteristics of the explosive magnetic energy release and (4) the very efficient acceleration of particles during the flaring periods in the solar corona. We review briefly the work published the last twenty five years on the above issues and propose solutions by using methods borrowed from the analysis of complex systems. The scenario which emerged is as follows: (a) The fully developed turbulence in the convection zone generates and transports magnetic flux tubes to the solar surface. Using probabilistic percolation models we were able to reproduce the size distribution and the fractal properties of the emerged and randomly moving magnetic flux tubes. (b) Using a Non Linear Force Free (NLFF) magnetic extrapolation numerical code we can explore how the emerged magnetic flux tubes interact nonlinearly and form thin and Unstable Current Sheets (UCS) inside the coronal part of the AR. (c) The fragmentation of the UCS and the redistribution of the magnetic field locally, when the local current exceeds a Critical threshold, is a key process which drives avalanches and forms coherent structures. This local reorganization of the magnetic field enhances the energy dissipation and influences the global evolution of the complex magnetic topology. Using a Cellular Automaton and following the simple rules of Self Organized Criticality (SOC), we were able to reproduce the statistical characteristics of the observed time series of the explosive events, (d) finally, when the AR reaches the turbulently reconnecting state (in the language of the SOC theory this is called SOC state) it is densely populated by UCS which can act as local scatterers (replacing the magnetic clouds in the Fermi scenario) and enhance dramatically the heating and acceleration of charged particles.

THEMIS observations of the current sheet dynamics in response to the intrusion of the high‐velocity plasma flow into the near‐Earth magnetotail

AbstractA small separation between Time History of Events and Macroscale Interactions during Substorms (THEMIS) probes allows us to analyze a sudden activation in the near‐Earth current sheet (CS) at microscales. The start of the activation coincides with the appearance of an earthward plasma flow and dipolarization front (DF) at THEMIS location. The time sequence of observations of the fast plasma flow and the associated DF by three THEMIS probes denotes their dawnward displacement and the localization of the flow channel in the dawn‐dusk direction. The onset of kink perturbations of the CS was generated on the dawn side of the flow. These fluctuations also propagated dawnward and were followed by the CS thinning (L ~ ρi) and by the development of tearing instability with transient appearance of a magnetic null point. The region of the unstable CS with a magnetic null point was localized in the X and, possibly, in the Y directions. The CS perturbations were most likely triggered by the intrusion of the fast flow into the ambient plasma in the course of the global dawnward displacement of the flow structure. Although no substorm onset was observed during the CS activation, a ground signature of a pseudobreakup was detected just after the excitement of the tearing mode in the near‐Earth tail. Probably the pseudobreakup was caused by a localized diversion of the current, which could result from the disruption of the cross‐tail current in a localized region of the near‐Earth CS.

Explosive reconnection of double tearing modes in relativistic plasmas: application to the Crab flares

Abstract Magnetic reconnection associated to the double tearing mode is investigated by means of resistive relativistic magnetohydrodynamic simulations. A linearly unstable double current sheet system in two-dimensional Cartesian geometry is considered. For initial perturbations of large enough longitudinal wavelengths, a fast reconnection event is triggered by a secondary instability that is structurally driven by the non-linear evolution of the magnetic islands. The latter reconnection phase and time-scale appear to weakly depend on the plasma resistivity and magnetization parameter. We discuss the possible role of such explosive reconnection dynamics to explain the MeV flares observed in the Crab Pulsar nebula. Indeed, the time-scale and the critical minimum wavelength give constraints on the Lorentz factor of the striped wind and on the location of the emission region, respectively.

On the onset of the plasmoid instability

A numerical study of magnetic reconnection in two-dimensional resistive magnetohydrodynamics for marginally unstable Sweet-Parker current sheets that are subject to plasmoid formation is carried out. Despite the procedure used to form the primary Sweet-Parker-like current layer, that is different with respect to previous studies, the reconnection layer is unstable to the plasmoid instability for a Lundquist number greater than the expected critical value Sc≈104. For Lundquist numbers S≳Sc, the instability exhibits a quasi-periodic behaviour consisting of formation, rapid growth, and evacuation of a moving magnetic island. The so called “plasmoid” breaks up the primary current layer and significantly enhances the maximum current density over the value expected from Sweet-Parker theory. This local enhancement spatially coincides with the downstream X-point of the magnetic island and is associated with the formation of a pair of slow-mode Petschek-like shocks bounding the outflowing plasma. These results suggest that the inter-plasmoid current layers forming in high-Lundquist-number plasmas (S≫Sc) could not be simply described as marginally stable Sweet-Parker current sheets.

Fast reconnection in high-Lundquist-number plasmas due to the plasmoid Instability

Thin current sheets in systems of large size that exceed a critical value of the Lundquist number are unstable to a super-Alfvenic tearing instability. The scaling of the growth rate of the fastest growing instability with respect to the Lundquist number is shown to follow from the classical dispersion relation for tearing modes. As a result of this instability, the system realizes a nonlinear reconnection rate that appears to be weakly dependent on the Lundquist number, and larger than the Sweet-Parker rate by an order of magnitude (for the range of Lundquist numbers considered). This regime of fast reconnection appears to be realizable in a dynamic and highly unstable thin current sheet, without requiring the current sheet to be turbulent.

A new fast reconnection model in a collisionless regime

Based on the first principles [i.e., (i) by balancing the magnetic field advection with the term containing electron pressure tensor nongyrotropic components in the generalized Ohm’s law; (ii) using the conservation of mass; and (iii) assuming that the weak magnetic field region width, where electron meandering motion supports electron pressure tensor off-diagonal (nongyrotropic) components, is of the order of electron Larmor radius] a simple model of magnetic reconnection in a collisionless regime is formulated. The model is general, resembling its collisional Sweet–Parker analog in that it is not specific to any initial configuration, e.g., Harris-type tearing unstable current sheet, X-point collapse or otherwise. In addition to its importance from the fundamental point of view, the collisionless reconnection model offers a much faster reconnection rate [Mc′less=(c∕ωpe)2∕(rL,eL)] than Sweet–Parker’s classical one (Msp=S−1∕2). The width of the diffusion region (current sheet) in the collisionless regime is found to be δc′less=(c∕ωpe)2∕rL,e, which is independent of the global reconnection scale L and is only prescribed by microphysics (electron inertial length, c∕ωpe, and electron Larmor radius, rL,e). Amongst other issues, the fastness of the reconnection rate alleviates, e.g., the problem of interpretation of solar flares by means of reconnection, as for the typical solar coronal parameters the obtained collisionless reconnection time can be a few minutes, as opposed to Sweet–Parker’s equivalent value of less than a day. The new theoretical reconnection rate is compared to the Magnetic Reconnection Experiment device experimental data by Yamada et al. [Phys. Plasmas 13, 052119 (2006)] and Ji et al. [Geophys. Res. Lett. 35, 13106 (2008)], and a good agreement is obtained.

Particle Acceleration in an Evolving Network of Unstable Current Sheets

We study the acceleration of electrons and protons interacting with localized, multiple, small-scale dissipation regions inside an evolving, turbulent active region. The dissipation regions are Unstable Current Sheets (UCS), and in their ensemble they form a complex, fractal, evolving network of acceleration centers. Acceleration and energy dissipation are thus assumed to be fragmented. A large-scale magnetic topology provides the connectivity between the UCS and determines in this way the degree of possible multiple acceleration. The particles travel along the magnetic field freely without loosing or gaining energy, till they reach a UCS. In a UCS, a variety of acceleration mechanisms are active, with the end-result that the particles depart with a new momentum. The stochastic acceleration process is represented in the form of Continuous Time Random Walk (CTRW), which allows to estimate the evolution of the energy distribution of the particles. It is found that under certain conditions electrons are heated and accelerated to energies above 1 MeV in much less than a second. Hard X-ray (HXR) and microwave spectra are calculated from the electrons' energy distributions, and they are found to be compatible with the observations. Ions (protons) are also heated and accelerated, reaching energies up to 10 MeV almost simultaneously with the electrons. The diffusion of the particles inside the active region is extremely fast (anomalous super-diffusion). Although our approach does not provide insight into the details of the specific acceleration mechanisms involved, its benefits are that it relates acceleration to the energy release, and it well describes the stochastic nature of the acceleration process.

Reconnection and scale‐free avalanching in a driven current‐sheet model

Uritsky et al. [2002], through a study of Polar UVI auroral image sequences, have produced a set of scale‐free probability distributions for several characteristic properties of the evolving bright emission regions in the nightside auroral oval. These distributions almost certainly reflect the dynamics of the plasma sheet. A scale‐free avalanching process involving reconnection and/or current diversion over an exceptionally broad range of spatiotemporal scales is implied. The most straightforward, and at present sole, explanation for this behavior is that the plasma sheet dynamics is in the neighborhood of self‐organized criticality (SOC). However, the auroral images provide only an indirect measure of the plasma sheet dynamics. Confirmation of this state in the plasma sheet would require multispatiotemporal‐scale in situ plasma sheet studies that, with the advent of multispacecraft missions, are now possible. To suggest specific tests for such studies, a numerical current‐sheet model has been constructed and analyzed to develop the properties and requirements of SOC in a plasma physical setting. The model incorporates the anomalous resistivity of a current‐driven kinetic instability into a two‐dimensional resistive MHD system. The disparate scales of these two systems enable multiscale behavior in the intervening range. Several novel features in the model's behavior are enabled through the assumption of hysteresis in the kinetic instability threshold. Under steady loading of plasma containing a reversed magnetic field topology, an irregular loading‐unloading cycle is established in which unloading is due primarily to annihilation at the field reversal. Following a loading interval during which the current‐sheet supporting the field reversal thins and intensifies, an unloading event originates at a localized reconnection site that then becomes the source of waves of unstable current sheets. These current sheets propagate away from the reconnection site, each leaving a trail of anomalous resistivity behind. An expanding cascade of field line merging results. Some statistical properties of this cascade are examined. It is shown that the diffusive contribution to the Poynting flux in these cascades occurs in bursts, whose duration, integrated size, and total energy content exhibit scale‐free power law probability distributions over large ranges of scales. Although not conclusive, these distributions do provide strong evidence that the model has evolved into SOC.

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.

Laboratory experiments on magnetic reconnection and current systems

After a brief review of laboratory experiments involving magnetic reconnection a series of basic physics experiments on reconnection phenomena is described. These include magnetic annihilation, transport of magnetic energy by waves, stable and unstable current sheets, energy conversion mechanisms and the role of global current systems vs. local reconnection processes. The present laboratory experiment deals with current systems driven by electric fields resulting in particle flows. Currents are dominantly carried by electrons. The self-consistent current sheet thickness is usually smaller than an ion Larmor radius. Consequently, MHD concepts such as frozen-in magnetic fields, wave transport at the Alfvén speed, and absence of electrostatic electric fields break down. Instead, the dynamics of reconnection is controlled by the fast speed of electrons, i.e. magnetic fields propagate at whistler wave speeds, current sheets tear by electron tearing modes, ions are accelerated by space charge electric fields, and anisotropic particle distributions are common occurrences. The role of a magnetic field component B y along the separator has been investigated. Although three-dimensional reconnection with kinetic effects is a difficult topic for theory and simulations it is likely to be important in various space and laboratory plasmas.

A predicted energetic ion signature of a neutral line in the geomagnetic tail

Under certain assumptions one can predict the formation of a magnetic neutral line on theoretical grounds, generally as a result of an unstable current sheet. Neutral points also seem to form spontaneously in a wide variety of plasma simulations, from MHD to fully kinetic. Hence such magnetic null regions are central to some models of magnetotail energization and magnetic substorms. Yet the observational evidence for such regions remains controversial. In this paper we present a new signature of a neutral line: the field‐aligned ion beam characteristic of current sheet acceleration becomes dispersed into a “ridge” in the velocity space distribution function as a neutral line is approached. The results were obtained using single‐particle simulations in a fixed magnetic field model. The origin of the ridge is shown to be due to initially earthward going ions which pass through the neutral line region. These ions come from a smaller part of the initially antiearthward flowing distribution, generating the depletion of the distribution function below the ridge.