Electric Current Sheet Research Articles

A fundamental mechanism of solar eruption initiation

Solar eruptions are spectacular magnetic explosions in the Sun’s corona, and how they are initiated remains unclear. Prevailing theories often rely on special magnetic topologies that may not generally exist in the pre-eruption source region of corona. Here, using fully three-dimensional magnetohydrodynamic simulations with high accuracy, we show that solar eruptions can be initiated in a single bipolar configuration with no additional special topology. Through photospheric shearing motion alone, an electric current sheet forms in the highly sheared core field of the magnetic arcade during its quasi-static evolution. Once magnetic reconnection sets in, the whole arcade is expelled impulsively, forming a fast-expanding twisted flux rope with a highly turbulent reconnecting region underneath. The simplicity and efficacy of this scenario argue strongly for its fundamental importance in the initiation of solar eruptions.

The Onset of 3D Magnetic Reconnection and Heating in the Solar Corona

Abstract Magnetic reconnection, a fundamentally important process in astrophysics, is believed to be initiated by the tearing instability of an electric current sheet, a region where magnetic field abruptly changes direction. Recent studies have suggested that the amount of magnetic shear in these structures is a critical parameter for the switch-on nature of magnetic reconnection in the solar atmosphere, at large spatial scales. We present results of visco-resistive magnetohydrodynamic simulations of magnetic reconnection in 3D current sheets with conditions appropriate to the solar corona. We follow the evolution of the linear and nonlinear 3D tearing instability. We find that, depending on the parameter space, magnetic shear can play a vital role in the onset of significant energy release and plasma heating. Two regimes in our study exist, dependent on whether the current sheet is longer or shorter than the wavelength of the fastest growing mode, thus determining whether subharmonics are present in the actual system. In one parameter regime, where the fastest growing parallel mode has subharmonics, the subsequent coalescence of 3D plasmoids dominates the nonlinear evolution, with magnetic shear playing only a weak role in the amount of energy released. In the second parameter regime, where the fastest growing parallel mode has no subharmonics, only strongly sheared current sheets, where 3D effects are strong enough, show any significant energy release. We expect both regimes to exist on the Sun, and so our results have important consequences for the question of reconnection onset in various solar physics applications.

Current closure in the pulsar magnetosphere

ABSTRACT Current closure in the pulsar magnetosphere holds the key to its structure. We must determine not only the global electric circuit, but also the source of its electric charge carriers. We address this issue with the minimum number of assumptions: (1) The magnetosphere is everywhere ideal and force free, except above the polar cap and in some finite part of the current sheet; and (2) pairs are produced above the polar cap with multiplicity κ. We show that a thin region of width δ ≈ rpc/2κ ≪ rpc along the rim of the polar cap provides all the charges that are needed in the equatorial and separatrix electric current sheet. These charges are transferred to the current sheet in a narrow dissipation zone just outside the magnetospheric Y-point. The maximum accelerating potential in this region is equal to the potential drop in the thin polar cap rim, which is approximately equal to 1/κ times the potential drop from the centre to the edge of the polar cap. The dissipated electromagnetic energy is approximately equal to 1.5/κ times the total pulsar spin-down energy loss. Our framework allows to calculate the high-energy emission in terms of the pair multiplicity.

A Multiscale Unconditionally Stable Time-Domain (MUST) Solver Unifying Electrodynamics and Micromagnetics

A rigorous yet computationally efficient 3-D numerical method has been proposed based on modified alternatingdirection-implicit finite-difference time-domain (ADI FDTD) methods. It has the capability of modeling the anisotropic and dispersive properties of magnetic material. The proposed algorithm solves Maxwell's equations and Landau-Lifshitz-Gilbert equation jointly and simultaneously, requiring only tridiagonal matrix inversion as in ADI FDTD. The accuracy of the modeling has been validated by: 1) the nonreciprocity of an X-band ferrite resonance isolator; 2) the attenuation constant of a magnetically tunable waveguide filter; and 3) the dispersive permeability of a 2-μm-thick magnetic thin film. Time steps that are up to 5000 times larger than the Courant-Friedrichs-Lewy limit have been used in these simulations without encountering stability issues. The simulation results agree with the predictions made from the theory, the commercial software or the experiments. Moreover, the algorithm has been applied to predict the effect of high permeability thin films in platform effect reduction. An electric current sheet close to a perfect electrically conducting plane coated with a 2-μm-thick magnetic thin film is simulated, which exhibits an enhanced surface resistance by three orders of magnitude higher than that without the magnetic thin film.

Bianisotropic metasurfaces: physics and applications

AbstractMetasurfaces as optically thin composite layers can be modeled as electric and magnetic surface current sheets flowing in the layer volume in the metasurface plane. In the most general linear metasurface, the electric surface current can be induced by both incident electric and magnetic fields. Likewise, magnetic polarization and magnetic current can be induced also by external electric field. Metasurfaces which exhibit magnetoelectric coupling are called bianisotropic metasurfaces. In this review, we explain the role of bianisotropic properties in realizing various metasurface devices and overview the state-of-the-art of research in this field. Interestingly, engineered bianisotropic response is seen to be required for realization of many key field transformations, such as anomalous refraction, asymmetric reflection, polarization transformation, isolation, and more. Moreover, we summarize previously reported findings on uniform and gradient bianisotropic metasurfaces and envision novel and prospective research directions in this field.

Reconstruction of a Large-scale Pre-flare Coronal Current Sheet Associated with a Homologous X-shaped Flare

Abstract As a fundamental magnetic structure in the solar corona, electric current sheets (CSs) can form either prior to or during a solar flare, and they are essential for magnetic energy dissipation in the solar corona because they enable magnetic reconnection. However, the static reconstruction of a CS is rare, possibly due to limitations that are inherent in the available coronal field extrapolation codes. Here we present the reconstruction of a large-scale pre-flare CS in solar active region 11967 using an MHD-relaxation model constrained by the SDO/HMI vector magnetogram. The CS is associated with a set of peculiar homologous flares that exhibit unique X-shaped ribbons and loops occurring in a quadrupolar magnetic configuration.This is evidenced by an ’X’ shape, formed from the field lines traced from the CS to the photosphere. This nearly reproduces the shape of the observed flare ribbons, suggesting that the flare is a product of the dissipation of the CS via reconnection. The CS forms in a hyperbolic flux tube, which is an intersection of two quasi-separatrix layers. The recurrence of the X-shaped flares might be attributed to the repetitive formation and dissipation of the CS, as driven by the photospheric footpoint motions. These results demonstrate the power of a data-constrained MHD model in reproducing a CS in the corona as well as providing insight into the magnetic mechanism of solar flares.

Field topologies in ideal and near-ideal magnetohydrodynamics and vortex dynamics

Magnetic field topology frozen in ideal magnetohydrodynamics (MHD) and its breakage in near-ideal MHD are reviewed in two parts, clarifying and expanding basic concepts. The first part gives a physically complete description of the frozen field topology derived from magnetic flux conservation as the fundamental property, treating four conceptually related topics: Eulerian and Lagrangian descriptions of three dimensional (3D) MHD, Chandrasekhar-Kendall and Euler-potential field representations, magnetic helicity, and inviscid vortex dynamics as a fluid system in physical contrast to ideal MHD. A corollary of these developments clarifies the challenge of achieving a high degree of the frozen-in condition in numerical MHD. The second part treats field-topology breakage centered around the Parker Magnetostatic Theorem on a general incompatibility of a continuous magnetic field with the dual demand of force-free equilibrium and an arbitrarily prescribed, 3D field topology. Preserving field topology as a global constraint readily results in formation of tangential magnetic discontinuities, or, equivalently, electric current-sheets of zero thickness. A similar incompatibility is present in the steady force-thermal balance of a heated radiating fluid subject to an anisotropic thermal flux conducted strictly along its frozen-in magnetic field in the low-β limit. In a weakly resistive fluid the thinning of current sheets by these general incompatibilities inevitably results in sheet dissipation, resistive heating and topological changes in the field notwithstanding the small resistivity. Strong Faraday induction drives but also macroscopically limits this mode of energy dissipation, trapping or storing free energy in self-organized ideal-MHD structures. This property of MHD turbulence captured by the Taylor hypothesis is reviewed in relation to the Sun’s corona, calling for a basic quantitative description of the breakdown of flux conservation in the low-resistivity limit. A cylindrical initial-boundary value problem provides specificity in the general MHD ideas presented.

BLACK HOLE MAGNETOSPHERES

We investigate the structure of the steady-state force-free magnetosphere around a Kerr black hole in various astrophysical settings. The solution Psi(r,theta) depends on the distributions of the magnetic field line angular velocity omega(Psi) and the poloidal electric current I(Psi). These are obtained self-consistently as eigenfunctions that allow the solution to smoothly cross the two singular surfaces of the problem, the Inner Light Surface (ILS) inside the ergosphere, and the Outer Light Surface (OLS), which is the generalization of the pulsar light cylinder. Magnetic field configurations that cross both singular surfaces (e.g. monopole, paraboloidal) are uniquely determined. Configurations that cross only one light surface e.g. the artificial case of a rotating black hole embedded in a vertical magnetic field) are degenerate. We show that, similarly to pulsars, black hole magnetospheres naturally develop an electric current sheet that potentially plays a very important role in the dissipation of black hole rotational energy and in the emission of high-energy radiation.

NEWTONIAN AND NON-NEWTONIAN MAGNETIC-FIELD RELAXATIONS IN SOLAR-CORONAL MHD

This paper treats the relaxation of a magnetic field into a minimum-energy force-free state in a cold (pressure-less) viscous fluid, under the frozen-in condition of perfect electrical conductivity and letting the viscosity-dissipated energy be completely lost. A non-Newtonian fluid in popular use is studied in relation to the Newtonian viscous fluid, as two alternative numerical means to (1) construct force-free fields representing solar coronal structures in realistic geometry and (2) investigate the Parker theory of spontaneous formation of electric current sheets as a basic MHD process. Faraday's induction equation imposes an independent condition on the fluid velocity at rigid, perfectly conducting boundaries. This boundary condition is quite compatible with Newtonian mechanics but not with the non-Newtonian fluid model where velocity is equated to the Lorentz force with a free, positive multiplicative-factor. This defining property gives rise to unphysical or artificial singularities not previously known that are completely distinct from the physically admissible singularities representing the current sheets of the Parker theory. In particular, the non-Newtonian fluid takes a magnetic field with neutral points from any one of a continuum of initial states into an unphysical state instead of the proper force-free end-state accessible by Newtonian relaxation. The validity of previously published MHD results based on this non-Newtonian fluid, including some counterclaims against the Parker theory, is dubious. Investigating the Parker theory requires numerical relaxation models capable of anticipating and accurately describing inevitable current-sheet singularities. By including a weak resistivity to dissipate the inevitable current sheets as they form, the field can change topology intermittently to seek a terminal force-free state free of singularities. The minimum-energy state of this more complete model corresponds to the long-lived relaxed structures in the corona.

Analytic theory of Titan’s Schumann resonance: Constraints on ionospheric conductivity and buried water ocean

This study presents an approximate model for the atypical Schumann resonance in Titan’s atmosphere that accounts for the observations of electromagnetic waves and the measurements of atmospheric conductivity performed with the Huygens Atmospheric Structure and Permittivity, Wave and Altimetry (HASI–PWA) instrumentation during the descent of the Huygens Probe through Titan’s atmosphere in January 2005. After many years of thorough analyses of the collected data, several arguments enable us to claim that the Extremely Low Frequency (ELF) wave observed at around 36Hz displays all the characteristics of the second harmonic of a Schumann resonance. On Earth, this phenomenon is well known to be triggered by lightning activity. Given the lack of evidence of any thunderstorm activity on Titan, we proposed in early works a model based on an alternative powering mechanism involving the electric current sheets induced in Titan’s ionosphere by the Saturn’s magnetospheric plasma flow. The present study is a further step in improving the initial model and corroborating our preliminary assessments. We first develop an analytic theory of the guided modes that appear to be the most suitable for sustaining Schumann resonances in Titan’s atmosphere. We then introduce the characteristics of the Huygens electric field measurements in the equations, in order to constrain the physical parameters of the resonating cavity. The latter is assumed to be made of different structures distributed between an upper boundary, presumably made of a succession of thin ionized layers of stratospheric aerosols spread up to 150km and a lower quasi-perfect conductive surface hidden beneath the non-conductive ground. The inner reflecting boundary is proposed to be a buried water–ammonia ocean lying at a likely depth of 55–80km below a dielectric icy crust. Such estimate is found to comply with models suggesting that the internal heat could be transferred upwards by thermal conduction of the crust, while convective processes cannot be ruled out.

Kink-like mode of a double gradient instability in a compressible plasma current sheet

A linear MHD instability of the electric current sheet, characterized by a small normal magnetic field component, varying along the sheet, is investigated. The tangential magnetic field component is modeled by a hyperbolic function, describing Harris-like variations of the field across the sheet. For this problem, which is formulated in a 3D domain, the conventional compressible ideal MHD equations are applied. By assuming Fourier harmonics along the electric current, the linearized 3D equations are reduced to 2D ones. A finite difference numerical scheme is applied to examine the time evolution of small initial perturbations of the plasma parameters. This work is an extended numerical study of the so called “double gradient instability”, – a possible candidate for the explanation of flapping oscillations in the magnetotail current sheet, which has been analyzed previously in the framework of a simplified analytical approach for an incompressible plasma. The dispersion curve is obtained for the kink-like mode of the instability. It is shown that this curve demonstrates a quantitative agreement with the previous analytical result. The development of the instability is investigated also for various enhanced values of the normal magnetic field component. It is found that the characteristic values of the growth rate of the instability shows a linear dependence on the square root of the parameter, which scales uniformly the normal component of the magnetic field in the current sheet.

On spontaneous formation of current sheets: Untwisted magnetic fields

This is a study of the spontaneous formation of electric current sheets in an incompressible viscous fluid with perfect electrical conductivity, governed by the magnetohydrodynamic Navier–Stokes equations. Numerical solutions to two initial value problems are presented for a three-dimensional, periodic, untwisted magnetic field evolving, with no change in magnetic topology under the frozen-in condition and at characteristic fluid Reynolds numbers of the order of 500, from a nonequilibrium initial state with the fluid at rest. The evolution converts magnetic free energy into kinetic energy to be all dissipated away by viscosity so that the field settles into a minimum-energy, static equilibrium. The solutions demonstrate that, as a consequence of the frozen-in condition, current sheets must form during the evolution despite the geometric simplicity of the prescribed initial fields. In addition to the current sheets associated with magnetic neutral points and field reversal layers, other sheets not associated with such magnetic features are also in evidence. These current sheets form on magnetic flux surfaces. This property is used to achieve a high degree of the frozen-in condition in the simulations, by describing the magnetic field entirely in terms of the advection of its flux surfaces and integrating the resulting governing equations with a customized version of a general-purpose high-resolution (viz., nonoscillatory) hydrodynamical simulation code EULAG [J. M. Prusa et al., Comput. Fluids 37, 1193 (2008)]. Incompressibility imposes the additional global constraint that the flux surfaces must evolve with no change in the spatial volumes they enclose. In this approach, current sheet formation is demonstrated graphically by the progressive pressing together of suitably selected flux surfaces until their separation has diminished below the minimal resolved distance on a fixed grid. The frozen-in condition then fails in the simulation as the field reconnects through an effecting numerical resistivity. The principal results are related to the Parker theory of current-sheet formation and dissipation in the solar corona.

The pulsar synchrotron in 3D: curvature radiation

We investigate the strong electric current sheet that develops at the tip of the pulsar closed line region through time dependent three-dimensional numerical simulations of a rotating magnetic dipole. We show that curvature radiation from relativistic electrons and positrons in the current sheet may naturally account for several features of the high-energy pulsar emission. We obtain light curves and polarization profiles for the complete range of magnetic field inclination angles and observer orientations, and compare our results to recent observations from the Fermi gamma-ray telescope.

CURRENT BUILDUP IN EMERGING SERPENTINE FLUX TUBES

The increase of magnetic flux in the solar atmosphere during active-region formation involves the transport of the magnetic field from the solar convection zone through the lowest layers of the solar atmosphere, through which the plasma {beta} changes from >1 to <1 with altitude. The crossing of this magnetic transition zone requires the magnetic field to adopt a serpentine shape also known as the sea-serpent topology. In the frame of the resistive flux-emergence model, the rising of the magnetic flux is believed to be dynamically driven by a succession of magnetic reconnections which are commonly observed in emerging flux regions as Ellerman bombs. Using a data-driven, three-dimensional (3D) magnetohydrodynamic numerical simulation of flux emergence occurring in active region 10191 on 2002 November 16-17, we study the development of 3D electric current sheets. We show that these currents buildup along the 3D serpentine magnetic-field structure as a result of photospheric diverging horizontal line-tied motions that emulate the observed photospheric evolution. We observe that reconnection can not only develop following a pinching evolution of the serpentine field line, as usually assumed in two-dimensional geometry, but can also result from 3D shearing deformation of the magnetic structure. In addition, we report for themore » first time on the observation in the UV domain with the Transition Region and Coronal Explorer (TRACE) of extremely transient loop-like features, appearing within the emerging flux domain, which link several Ellermam bombs with one another. We argue that these loop transients can be explained as a consequence of the currents that build up along the serpentine magnetic field.« less

Hinode observations reveal boundary layers of magnetic elements in the solar photosphere

We study the structure of the magnetic elements in network-cell interiors. A quiet Sun area close to the disc centre was observed with the spectro-polarimeter of the Solar Optical Telescope on board the Hinode space mission, which yielded the best spatial resolution ever achieved in polarimetric data of the Fe I 630 nm line pair. For comparison and interpretation, we synthesize a similar data set from a three-dimensional magneto-hydrodynamic simulation. We find several examples of magnetic elements, either roundish (tube) or elongated (sheet), which show a central area of negative Stokes-V area asymmetry framed or surrounded by a peripheral area with larger positive asymmetry. This pattern was predicted some eight years ago on the basis of numerical simulations. Here, we observationally confirm its existence for the first time. We gather convincing evidence that this pattern of Stokes-V area asymmetry is caused by the funnel-shaped boundary of magnetic elements that separates the flux concentration from the weak-field environment. We also conclude that this kind of magnetic element of the internetwork is accompanied by electric current sheets.

Catastrophic Eruption of Magnetic Flux Rope in the Corona and Solar Wind With and Without Magnetic Reconnection

It is generally believed that the magnetic free energy accumulated in the corona serves as a main energy source for solar explosions such as coronal mass ejections (CMEs). In the framework of the flux rope catastrophe model for CMEs, the energy may be abruptly released either by an ideal magnetohydrodynamic (MHD) catastrophe, which belongs to a global magnetic topological instability of the system, or by a fast magnetic reconnection across preexisting or rapidly developing electric current sheets. Both means of magnetic energy release are thought to be important to CME dynamics. To disentangle their contributions, we construct a flux rope catastrophe model in the corona and solar wind and compare different cases in which we either prohibit or allow magnetic reconnection to take place across rapidly growing current sheets during the eruption. It has been demonstrated that CMEs, even fast ones, can be produced taking the ideal MHD catastrophe as the only process of magnetic energy release. Nevertheless, the eruptive speed can be significantly enhanced after magnetic reconnection sets in. In addition, a smooth transition from slow to fast eruptions is observed when increasing the strength of the background magnetic field, simply because in a stronger field there is more free magnetic energy at the catastrophic point available to be released during an eruption. This suggests that fast and slow CMEs may have an identical driving mechanism.

Finite Element Analysis of Permanent Magnet Assembly With High Field Strength Using Preisach Theory

This paper presents a method to simulate the characteristics of permanent magnet materials with a magnetic field varying arbitrarily. Combining Preisach model and finite element analysis, a dynamic magnetic field computation is implemented for a permanent magnet assembly in a process of assembling. The hysteresis characteristic including local loop and rotational magnetization are considered in the formulation of the method proposed. The numerical results are compared with the ones of a conventional method, the electric current sheet equivalent, and the measured values to verify the validity of the presented method

A jet-like structure revealed by a numerical simulation of rotating spherical-shell magnetoconvection

Numerical results on thermally driven nonlinear magnetoconvection in a rapidly rotating fluid spherical shell are reported. A uniform magnetic field that is parallel to the rotation axis is imposed externally. The Ekman number is 2 × 10−6, representing a state of negligible viscosity, as in the Earth's core. The convection pattern is characterized by a few large-scale vortex columns superimposed on a fast westward (retrograde) zonal flow. In the equatorial region, an anticyclonic vortex is intensified, in which an induced axial magnetic field is stored. Interaction between the magnetized vortex and the zonal flow leads to a thin jet at the western side of the vortex. The jet is also characterized by a thin electric current sheet caused by a steep gradient of the axial magnetic field. Because of this structure, the jet region can be designated as a magnetic front by analogy with fronts in mid-latitude atmospheric cyclones. It can be estimated from an order-of-magnitude analysis that the jet width decreases in inverse proportion to the zonal flow speed, and that the jet speed and the sheet-like electric current are proportional to the square of the zonal flow speed.

Two energy release processes for CMEs: MHD catastrophe and magnetic reconnection

It remains an open question how magnetic energy is rapidly released in the solar corona so as to create solar explosions such as solar flares and coronal mass ejections (CMEs). Recent studies have confirmed that a system consisting of a flux rope embedded in a background field exhibits a catastrophic behavior, and the energy threshold at the catastrophic point may exceed the associated open field energy. The accumulated free energy in the corona is abruptly released when the catastrophe takes place, and it probably serves as the main means of energy release for CMEs at least in the initial phase. Such a release proceeds via an ideal MHD process in contrast with nonideal ones such as magnetic reconnection. The catastrophe results in a sudden formation of electric current sheets, which naturally provide proper sites for fast magnetic reconnection. The reconnection may be identified with a solar flare associated with the CME on one hand, and produces a further acceleration of the CME on the other. On this basis, several preliminary suggestions are made for future observational investigations, especially with the proposed Kuafa satellites, on the roles of the MHD catastrophe and magnetic reconnection in the magnetic energy release associated with CMEs and flares.

Simulation study of the Solar flare onset mechanism and the self-organization in the Solar coronal plasma

Three-dimensional magnetobydrodynamics of the Solar coronal plasma is investigated by numerical simulation, aiming to understand the mechanisms of the Solar flare onset. It is demonstrated by the simulations that the resistive tearing mode instability growing on the magnetic shear inversion layer can drive the large-scale eruption through the mutual excitation of double reconnections. It is also revealed that the instability is able to cause the magnetohydrodynamic energy relaxation, in which the typical sigmoidal structure is self-organized prior to the onset of eruption. The simulation insults predict that both the formation of sigmoids and the onset of flares should occur around the electric current sheet where the magnetic shear is steeply reversed. It is consistent with the reversed-shear flare model and tlie vector inagnetograph observations.