Formation Of Current Sheets Research Articles

THE SIGNATURE OF INITIAL CONDITIONS ON MAGNETOHYDRODYNAMIC TURBULENCE

We demonstrate that the initial correlation between velocity and current density fluctuations can lead to the formation of enormous current sheets in freely evolving magnetohydrodynamic (MHD) turbulence. These coherent structures are observed at the peak of the energy dissipation rate and are the carriers of long-range correlations despite all of the nonlinear interactions during the formation of turbulence. The size of these structures spans our computational domain, dominating the scaling of the energy spectrum, which follows a E∝k−2 power law. As the Reynolds number increases, the curling of the current sheets due to Kelvin–Helmholtz-type instabilities and reconnection modifies the scaling of the energy spectrum from k−2 toward k−5/3. This transition occurs due to the decorrelation of the velocity and the current density which is proportional to . Finite Reynolds number behavior is observed without reaching a finite asymptote for the energy dissipation rate even for a simulation of Reλ ≃ 440 with 20483 grid points. This behavior demonstrates that even state-of-the-art numerical simulations of the highest Reynolds numbers can be influenced by the choice of initial conditions and consequently they are inadequate to deduce unequivocally the fate of universality in MHD turbulence. Implications for astrophysical observations are discussed.

GENERATION OF MAGNETIC STRUCTURES ON THE SOLAR PHOTOSPHERE

The lower solar atmosphere is a partially ionized plasma consisting of electrons, ions, and neutral atoms. In this, which is essentially a three-fluid system, the Hall effect arises from the treatment of the electrons and ions as two separate fluids and the ambipolar diffusion arises from the inclusion of neutrals as the third fluid. The Hall effect and ambipolar diffusion have been shown to be operational in a region beginning from near the photosphere up to the chromosphere. In a partially ionized plasma, the magnetic induction is subjected to ambipolar diffusion and the Hall drift in addition to the usual resistive dissipation. These nonlinear effects create sharp magnetic structures which then submit themselves to various relaxation mechanisms. A first-principles derivation of these effects in a three-fluid system and an analytic solution to the magnetic induction equation in a stationary state are presented, which in the general case includes the Hall effect, ambipolar diffusion, and ohmic dissipation. The temporal evolution of the magnetic field is then investigated under the combined as well as the individual effects of the Hall drift and ambipolar diffusion to demonstrate the formation of steep magnetic structures and the resultant current sheet formation. These structures have just the right features for the release of magnetic energy into the solar atmosphere.

The Monge–Ampère trajectory correction for semi-Lagrangian schemes

Requiring that numerical estimates of the flow trajectories comply with the fundamental Euler expansion formula that governs the evolution of a volume of fluid leads to a second-order nonlinear Monge–Ampère partial differential equation (MAE). In Cossette and Smolarkiewicz (2011) [15], a numerical algorithm based on solving the MAE with an inexact Newton–Krylov solver has been developed and used to correct standard estimates of the departure points of flow trajectories provided by a classical semi-Lagrangian scheme in the context of an incompressible fluid. Here we extend the theoretical analysis of the elemental rotational and deformational motions presented in Cossette and Smolarkiewicz (2011) [15]. In particular, closed-form analytic solutions are derived for both cases that serve to illustrate the mechanics of the enhanced trajectory scheme and to address the issues of existence and uniqueness. Scalar advection shows that the MA correction improves mass conservation substantially by suppressing anomalous fluid contraction. The impact of the MA correction on complex flows is studied in the framework of an ideal magneto-fluid in which the formation of current sheets leads to topological changes and reconnection of field lines. The use of the MA correction improves the numerical stability of the solutions and prevents trajectory intersections as well as the spurious growth of the magnetic energy. 2D and 3D examples are presented and the computational performance of the solver is documented.

On the abrupt growth dynamics of nonlinear resistive tearing mode and the viscosity effects

The nonlinear evolution of the resistive tearing mode exhibits an abrupt growth after an X-point collapse once the magnetic island exceeds a certain critical width Δ′wc for large instability parameter Δ′, leading to a current sheet formation [N. F. Loureiro et al., Phys. Rev. Lett. 95, 235003 (2005)]. In this work, we investigate the underlying mechanism of the X-point collapse as well as the current sheet formation including the viscosity effects, based on a secondary instability analysis. The secondary instability is excited due to the quasilinear current modification by the zonal current. In particular, it is identified that the current peaking effect is plausibly responsible for the onset of the X-point collapse and the current sheet formation, leading to the explosive growth of reconnected flux. In the presence of finite viscosity, the Δ′wc scaling with the resistivity gets modified. A transition behavior is revealed at Pr≈1 for the viscosity dependence of Δ′wc and the linear tearing instability. However, the explosive growth seems to be independent of the viscosity in the magnetic Prandtl number Pr<1 regime, while large viscosity plays a strong dissipation role.

Formation of magnetic discontinuities through viscous relaxation

According to Parker's magnetostatic theorem, tangential discontinuities in magnetic field, or current sheets (CSs), are generally unavoidable in an equilibrium magnetofluid with infinite electrical conductivity and complex magnetic topology. These CSs are due to a failure of a magnetic field in achieving force-balance everywhere and preserving its topology while remaining in a spatially continuous state. A recent work [Kumar, Bhattacharyya, and Smolarkiewicz, Phys. Plasmas 20, 112903 (2013)] demonstrated this CS formation utilizing numerical simulations in terms of the vector magnetic field. The magnetohydrodynamic simulations presented here complement the above work by demonstrating CS formation by employing a novel approach of describing the magnetofluid evolution in terms of magnetic flux surfaces instead of the vector magnetic field. The magnetic flux surfaces being the possible sites on which CSs develop, this approach provides a direct visualization of the CS formation, helpful in understanding the governing dynamics. The simulations confirm development of tangential discontinuities through a favorable contortion of magnetic flux surfaces, as the magnetofluid undergoes a topology-preserving viscous relaxation from an initial non-equilibrium state with twisted magnetic field. A crucial finding of this work is in its demonstration of CS formation at spatial locations away from the magnetic nulls.

Forced reconnection in the near magnetotail: Onset and energy conversion in PIC and MHD simulations

Using two‐dimensional particle‐in‐cell (PIC) together with magnetohydrodynamic (MHD) simulations of magnetotail dynamics, we investigate the evolution toward onset of reconnection and the subsequent energy transfer and conversion. In either case, reconnection onset is preceded by a driven phase, during which magnetic flux is added to the tail at the high‐latitude boundaries, followed by a relaxation phase, during which the configuration continues to respond to the driving. The boundary deformation leads to the formation of thin embedded current sheets, which are bifurcated in the near tail, converging to a single sheet farther out in the MHD simulations. The thin current sheets in the PIC simulation are carried by electrons and are associated with a strong perpendicular electrostatic field, which may provide a connection to parallel potentials and auroral arcs and an ionospheric signal even prior to the onset of reconnection. The PIC simulation very well satisfies integral entropy conservation (intrinsic to ideal MHD) during this phase, supporting ideal ballooning stability. Eventually, the current intensification leads to the onset of reconnection, the formation and ejection of a plasmoid, and a collapse of the inner tail. The earthward flow shows the characteristics of a dipolarization front: enhancement of Bz, associated with a thin vertical electron current sheet in the PIC simulation. Both MHD and PIC simulations show a dominance of energy conversion from incoming Poynting flux to outgoing enthalpy flux, resulting in heating of the inner tail. Localized Joule dissipation plays only a minor role.

Viscosity Effects on Explosive Growth Dynamics of the Nonlinear Resistive Tearing Mode

A collapse of the X-point occurs above a critical island width, Δ'wc , in the resistive tearing mode for large instability parameter, Δ', leading to current sheet formation [N.F. Loureiro et al. Phys. Rev. Lett. 95, 235003 (2005)]. In this study, we analyze this problem by including viscosity effects on the onset of the X-point collapse and the explosive nonlinear growth dynamics of the reconnected flux. While explosive growth seems to be independent of viscosity in the magnetic Prandtl number regime Pr < 1, a transition behavior is revealed at Pr ≈ 1 for the viscosity dependence of Δ'wc , for the X-point collapse as well as the linear tearing instability. A secondary instability analysis, which included quasi-linear modifications of the equilibrium current profile due to the zonal current, shows that current peaking is plausibly responsible for the onset of the X-point collapse and the explosive growth of reconnected flux, which leads to the current sheet formation.

Coronal heating and nanoflares: current sheet formation and heating

Aims. Solar photospheric footpoint motions can produce strong, localised currents in the corona. A detailed understanding of the formation process and the resulting heating is important in modelling nanoflares, as a mechanism for heating the solar corona.Methods. A 3D MHD simulation is described in which an initially straight magnetic field is sheared in two directions. Grid resolutions up to 5123 were used and two boundary drivers were considered; one where the boundaries are continuously driven and one where the driving is switched off once a current layer is formed.Results. For both drivers a twisted current layer is formed. After a long time we see that, when the boundary driving has been switched off, the system relaxes towards a lower energy equilibrium. For the driver which continuously shears the magnetic field we see a repeating cycle of strong current structures forming, fragmenting and decreasing in magnitude and then building up again. Realistic coronal temperatures are obtained.

Microwave radiation of solar active regions before X flares according to the RATAN-600 observations in 2011

The evolution of the microwave radiation from four active regions, where strong X-ray flares (X-class, GOES) occurred in 2011, has been studied. Daily multiwavelength RATAN-600 radio observations of the Sun in the 1.6–8.0 cm range have been used. It has been indicated that the radiosource above the photospheric magnetic field neutral line (above the region with the maximal convergence of the fields opposite in sign) becomes predominant in the structure of the active region microwave radiation one to two days before a powerful flare as in the eruptive events previously studied with RATAN-600. The appearance of such a radiosource possibly reflects the current sheet formation in the corona above the active region. The energy necessary for a flare is stored in the magnetic field of active region, which can be considered as a factor for predicting a powerful flare.

SDO/AIA OBSERVATIONS OF A PARTIALLY ERUPTING PROMINENCE

We report an observation of a partially erupting prominence and associated dynamical plasma processes based on observations recorded by the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamics Observatory (SDO). The prominence first goes through a slow rise (SR) phase followed by a fast rise (FR). The slow rise phase started after a couple of small brightenings seen toward the footpoints. At the turning point from SR to FR, the prominence had already become kinked. The prominence shows strong brightening at the central kink location during the start of FR. We interpret this as internal magnetic reconnection occurring at a vertical current sheet forming between the two legs of the erupting prominence (flux-rope). The brightening at the central kink location is seen in all the EUV channels of AIA. The contributions of differential emission at higher temperatures are larger compared to that for typical coronal temperatures supporting a reconnection scenario at the central kink location. The plasma above the brightening location gets ejected as a hot plasmoid-like structure embedded in a CME, and those below drain down in the form of blobs moving towards the Sun's surface. The unique time resolution of the AIA has allowed all of these eruptive aspects, including SR-to-FR, kinking, central current sheet formation, plasmoid-like eruption, and filament "splitting", to be observed in a single event, providing strong and comprehensive evidence in favour of the model of partially erupting flux ropes.

Formation of magnetic discontinuities through superposition of force-free magnetic fields: Periodic boundaries

In ideal magnetohydrodynamics characterized by an infinite electrical conductivity, the magnetic flux across an arbitrary fluid surface is conserved in time. The magnetofluid then can be partitioned into contiguous subvolumes of fluid, each of which entraps its own subsystem of magnetic flux. During dynamical evolution of the magnetofluid, these subvolumes press into each other; and in the process, two such subvolumes may come into direct contact while ejecting a third interstitial subvolume. Depending on the orientations of magnetic fields of the two interacting subvolumes, the magnetic field at the common surface of interaction may become discontinuous and a current sheet is formed there. This process of current sheet formation and their subsequent decay is believed to be a plausible mechanism for coronal heating and may also be responsible for various eruptive phenomena at the solar corona. In this work, we explore this theoretical concept through numerical simulations of a viscous, incompressible magnetofluid characterized by infinite electrical conductivity. In particular, we show that if the initial magnetic field is prescribed by superposition of two linear force-free fields with different torsion coefficients, then formation of current sheets are numerically realizable in the neighborhood of magnetic nulls.

CURRENT SHEETS FORMATION IN TANGLED CORONAL MAGNETIC FIELDS

We investigate the dynamical evolution of magnetic fields in closed regions of solar and stellar coronae. To understand under which conditions current sheets form, we examine dissipative and ideal reduced magnetohydrodynamic models in cartesian geometry, where two magnetic field components are present: the strong guide field $B_0$, extended along the axial direction, and the dynamical orthogonal field $\mathbf{b}$. Magnetic field lines thread the system along the axial direction, that spans the length $L$, and are line-tied at the top and bottom plates. The magnetic field $b$ initially has only large scales, with its gradient (current) length-scale of order $\ell_b$. We identify the magnetic intensity threshold $b/B_0 \sim \ell_b/L$. For values of $b$ below this threshold, field-line tension inhibits the formation of current sheets, while above the threshold they form quickly on fast ideal timescales. In the ideal case, above the magnetic threshold, we show that current sheets thickness decreases in time until it becomes smaller than the grid resolution, with the analyticity strip width $\delta$ decreasing at least exponentially, after which the simulations become under-resolved.

CURRENT SHEETS AND COLLISIONLESS DAMPING IN KINETIC PLASMA TURBULENCE

We present the first study of the formation and dissipation of current sheets at electron scales in a wave-driven, weakly collisional, 3D kinetic turbulence simulation. We investigate the relative importance of dissipation associated with collisionless damping via resonant wave-particle interactions versus dissipation in small-scale current sheets in weakly collisional plasma turbulence. Current sheets form self-consistently from the wave-driven turbulence, and their filling fraction is well correlated to the electron heating rate. However, the weakly collisional nature of the simulation necessarily implies that the current sheets are not significantly dissipated via Ohmic dissipation. Rather, collisionless damping via the Landau resonance with the electrons is sufficient to account for the measured heating as a function of scale in the simulation, without the need for significant Ohmic dissipation. This finding suggests the possibility that the dissipation of the current sheets is governed by resonant wave-particle interactions and that the locations of current sheets correspond spatially to regions of enhanced heating.

Ultra-intense attosecond pulses emitted from laser wakefields in non-uniform plasmas

AbstractA scheme of generating ultra-intense attosecond pulses in ultra-relativistic laser interaction with under-dense plasmas is proposed. The attosecond pulse emission is caused by an oscillating transverse current sheet formed by an electron density spike composed of trapped electrons in the laser wakefield and the residual transverse momentum of electrons left behind the laser pulse when its front is strongly modulated. As soon as the attosecond pulse emerges, it tends to feed back to further enhance the transverse electron momentum and the transverse current. Consequently, the attosecond pulse is enhanced and developed into a few cycles later until the density spike is depleted out due to the pump laser depletion. To control the formation of the transverse current sheet, a non-uniform plasma slab with an up-ramp density profile in front of a uniform region is adopted, which enables one to obtain attosecond pulses with higher amplitudes than that in a uniform plasma slab.

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.

SYMPATHETIC MAGNETIC BREAKOUT CORONAL MASS EJECTIONS FROM PSEUDOSTREAMERS

We present high resolution 2.5-dimensional MHD simulation results of magnetic breakout-initiated coronal mass ejections (CMEs) originating from a coronal pseudostreamer configuration. The coronal null point in the magnetic topology of pseudostreamers means the initiation of consecutive sympathetic eruptions is a natural consequence of the system's evolution. A generic source region energization process -- ideal footpoint shearing parallel to the pseudostreamer arcade polarity inversion lines -- is all that is necessary to store sufficient magnetic energy to power consecutive CME eruptions given that the pseudostreamer topology enables the breakout initiation mechanism. The second CME occurs because the eruptive flare reconnection of the first CME simultaneously acts as the overlying pre-eruption breakout reconnection for the sympathetic eruption. We examine the details of the magnetic and kinetic energy evolution and the signatures of the overlying null point distortion, current sheet formation, and magnetic breakout reconnection giving rise to the runaway expansion that drives the flare reconnection below the erupting sheared field core. The numerical simulation's spatial resolution and output cadence are sufficient to resolve the formation of magnetic islands during the reconnection process in both the breakout and eruptive flare current sheets. We quantify the flux transfer between the pseudostreamer arcades and show the eruptive flare reconnection processes flux ~10 times faster than the pre-eruption breakout reconnection. We show that the breakout reconnection jets cause bursty, intermittent upflows along the pseudostreamer stalk as well as downflows in the adjacent pseudostreamer arcade, both of which may be observable as pre-eruption signatures. Finally, we examine the flux rope CME trajectories and show that the breakout current sheet provides a path of least resistance as an...

Intermittent Dissipation at Kinetic Scales in Collisionless Plasma Turbulence

High resolution kinetic simulations of collisionless plasma driven by shear show the development of turbulence characterized by dynamic coherent sheetlike current density structures spanning a range of scales down to electron scales. We present evidence that these structures are sites for heating and dissipation, and that stronger current structures signify higher dissipation rates. Evidently, kinetic scale plasma, like magnetohydrodynamics, becomes intermittent due to current sheet formation, leading to the expectation that heating and dissipation in astrophysical and space plasmas may be highly nonuniform and patchy.

Spine-fan reconnection

Context. From observations, the atmosphere of the Sun has been shown to be highly dynamic with perturbations of the magnetic field often lacking temporal or spatial symmetry. Despite this, studies of the spine-fan reconnection mode at 3D nulls have so far focused on the very idealised case with symmetric driving of a fixed spatial extent. Aims. We investigate the spine-fan reconnection process for less idealised cases, focusing on asymmetric driving and drivers with different length scales. We look at the initial current sheet formation and whether the scalings developed in the idealised models are robust in more realistic situations. Methods. The investigation was carried out by numerically solving the resistive compressible 3D magnetohydrodynamic equations in a Cartesian box containing a linear null point. The spine-fan collapse was driven at the null through tangential boundary driving of the spine foot points. Results. We find significant differences in the initial current sheet formation with asymmetric driving. Notable is the displacement of the null point position as a function of driving velocity and resistivity (η). However, the scaling relations developed in the idealised case are found to be robust (albeit at reduced amplitudes) despite this extra complexity. Lastly, the spatial variation is also shown to play an important role in the initial current sheet formation through controlling the displacement of the spine foot points. Conclusions. We conclude that during the early stages of spine-fan reconnection both the temporal and spatial nature of the driving play important roles, with the idealised symmetrically driven case giving a “best case” for the rate of current development and connectivity change. As the most interesting eruptive events occur in relatively short time frames this work clearly shows the need for high temporal and spatial knowledge of the flows for accurate interpretation of the reconnection scenario. Lastly, since the scalings developed in the idealised case remain robust with more complex driving we can be more confident of their use in interpreting reconnection in complex magnetic field structures.

Turbulent coronal heating mechanisms: coupling of dynamics and thermodynamics

Context. Photospheric motions shuffle the footpoints of the strong axial magnetic field that threads coronal loops giving rise to turbulent nonlinear dynamics characterized by the continuous formation and dissipation of field-aligned current sheets where energy is deposited at small-scales and the heating occurs. Previous studies show that current sheets thickness is orders of magnitude smaller than current state of the art observational resolution (~700 km). Aim. In order to understand coronal heating and interpret correctly observations it is crucial to study the thermodynamics of such a system where energy is deposited at unresolved small-scales. Methods. Fully compressible three-dimensional magnetohydrodynamic simulations are carried out to understand the thermodynamics of coronal heating in the magnetically confined solar corona. Results. We show that temperature is highly structured at scales below observational resolution and nonhomogeneously distributed so that only a fraction of the coronal mass and volume gets heated at each time. Conclusions. This is a multi-thermal system where hotter and cooler plasma strands are found one next to the other also at sub-resolution scales and exhibit a temporal dynamics.

Theory of magnetic reconnection in solar and astrophysical plasmas

Magnetic reconnection is a fundamental process in a plasma that facilitates the release of energy stored in the magnetic field by permitting a change in the magnetic topology. In this paper, we present a review of the current state of understanding of magnetic reconnection. We discuss theoretical results regarding the formation of current sheets in complex three-dimensional magnetic fields and describe the fundamental differences between reconnection in two and three dimensions. We go on to outline recent developments in modelling of reconnection with kinetic theory, as well as in the magnetohydrodynamic framework where a number of new three-dimensional reconnection regimes have been identified. We discuss evidence from observations and simulations of Solar System plasmas that support this theory and summarize some prominent locations in which this new reconnection theory is relevant in astrophysical plasmas.