Coronal Heating Topology: The Interplay of Current Sheets and Magnetic Field Lines

Abstract. Thin current sheets represent important and puzzling sites of magnetic energy storage and subsequent fast release. Such structures are observed in planetary magnetospheres, solar atmosphere and are expected to be widespread in nature. The thin current sheet structure resembles a collapsing MHD solution with a plane singularity. Being potential sites of effective energy accumulation, these structures have received a good deal of attention during the last decade, especially after the launch of the multiprobe CLUSTER mission which is capable of resolving their 3D features. Many theoretical models of thin current sheet dynamics, including the well-known current sheet bifurcation, have been developed recently. A self-consistent 1D analytical model of thin current sheets in which the tension of the magnetic field lines is balanced by the ion inertia rather than by the plasma pressure gradients was developed earlier. The influence of the anisotropic electron population and of the corresponding electrostatic field that acts to restore quasi-neutrality of the plasma is taken into account. It is assumed that the electron motion is fluid-like in the direction perpendicular to the magnetic field and fast enough to support quasi-equilibrium Boltzmann distribution along the field lines. Electrostatic effects lead to an interesting feature of the current density profile inside the current sheet, i.e. a narrow sharp peak of electron current in the very center of the sheet due to fast curvature drift of the particles in this region. The corresponding magnetic field profile becomes much steeper near the neutral plane although the total cross-tail current is in all cases dominated by the ion contribution. The dependence of electrostatic effects on the ion to electron temperature ratio, the curvature of the magnetic field lines, and the average electron magnetic moment is also analyzed. The implications of these effects on the fine structure of thin current sheets and their potential impact on substorm dynamics are presented.

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Coronal Heating through Braiding of Magnetic Field Lines

The Astrophysical Journal ◽

10.1086/427168 ◽

2004 ◽

Vol 617 (1) ◽

pp. L85-L88 ◽

Cited By ~ 90

Author(s):

Hardi Peter ◽

Boris V. Gudiksen ◽

Åke Nordlund

Keyword(s):

Magnetic Field ◽

Coronal Heating ◽

Field Lines

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Solar and Stellar Magnetic Fields and Atmospheric Structures: Theory

International Astronomical Union Colloquium ◽

10.1017/s0252921100031936 ◽

1989 ◽

Vol 104 (1) ◽

pp. 271-288

Author(s):

E. N. Parker

Keyword(s):

Magnetic Field ◽

Magnetic Fields ◽

Dynamical Behavior ◽

Convective Zone ◽

Coronal Heating ◽

The Sun ◽

Current Sheets ◽

Spontaneous Formation ◽

Stellar Magnetic Fields ◽

The Magnetic Field

AbstractThis presentation reviews selected ideas on the origin of the magnetic field of the Sun, the dynamical behavior of the azimuthal field in the convective zone, the fibril state of the field at the photosphere, the formation of sunspots, prominences, the spontaneous formation of current sheets in the bipolar field above the surface of the Sun, coronal heating, and flares.

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The Parker problem: existence of smooth force-free fields and coronal heating

Living Reviews in Solar Physics ◽

10.1007/s41116-020-00026-5 ◽

2020 ◽

Vol 17 (1) ◽

Author(s):

David I. Pontin ◽

Gunnar Hornig

Keyword(s):

Magnetic Field ◽

Coronal Heating ◽

Plasma Parameters ◽

Astrophysical Plasmas ◽

Plasma Dynamics ◽

Open Questions ◽

Free Fields ◽

Field Lines ◽

The Many ◽

Ideal Plasma

AbstractParker (Astrophys J 174:499, 1972) put forward a hypothesis regarding the fundamental nature of equilibrium magnetic fields in astrophysical plasmas. He proposed that if an equilibrium magnetic field is subjected to an arbitrary, small perturbation, then—under ideal plasma dynamics—the resulting magnetic field will in general not relax towards a smooth equilibrium, but rather, towards a state containing tangential magnetic field discontinuities. Even at astrophysical plasma parameters, as the singular state is approached dissipation must eventually become important, leading to the onset of rapid magnetic reconnection and energy dissipation. This topological dissipation mechanism remains a matter of debate, and is a key ingredient in the nanoflare model for coronal heating. We review the various theoretical and computational approaches that have sought to prove or disprove Parker’s hypothesis. We describe the hypothesis in the context of coronal heating, and discuss different approaches that have been taken to investigating whether braiding of magnetic field lines is responsible for maintaining the observed coronal temperatures. We discuss the many advances that have been made, and highlight outstanding open questions.

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The Evolution of a Sheared Potential Magnetic Field in the Solar Corona

Symposium - International Astronomical Union ◽

10.1017/s007418090008815x ◽

1990 ◽

Vol 142 ◽

pp. 309-312

Author(s):

J. T. Karpen ◽

S. K. Antiochos ◽

C. R. DeVore

Keyword(s):

Magnetic Field ◽

Solar Corona ◽

Boundary Surface ◽

Null Point ◽

Current Sheets ◽

Field Lines ◽

Line Tying ◽

Analytic Models ◽

Coronal Field ◽

A Current

Several theoretical studies have proposed that, in response to photospheric foot-point motions, current sheets can be generated in the solar corona without the presence of a null point in the initial potential magnetic field. In these analytic models, current sheets form wherever the coronal field dips down and is parallel to the photosphere. A fundamental assumption in these analyses — commonly referred to as the line-tying assumption — is that all coronal field lines are anchored to a boundary surface representing the top of the dense, gas-pressure-dominated photosphere. In theoretical arguments presented elsewhere (Karpen, Antiochos, and DeVore 1989), however, we show that line-tying is not valid for “dipped” coronal fields, and hence that the conclusions of the line-tied models are incorrect. We contend that current sheets will not form if the photosphere-corona interface is represented by a physically valid model. Here we summarize a numerical investigation of the response of a “dipped” potential magnetic field in a hydrostatic-equilibrium atmosphere to shearing motions of the foot points. Our results show that, in the absence of artificial line-tying conditions, a current sheet indeed does not form at the location of the dip. Rather, the dipped magnetic field rises, causing upflows of photospheric and chromospheric plasma.

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Stochastic properties of the magnetic field lines in the presence of current sheets

Physica Scripta ◽

10.1088/0031-8949/1996/t63/053 ◽

1996 ◽

Vol T63 ◽

pp. 284-287

Author(s):

S Bulanov ◽

D Farina

Keyword(s):

Magnetic Field ◽

Current Sheets ◽

Field Lines ◽

Stochastic Properties ◽

The Magnetic Field

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Coronal heating and flaring in QSLs

Proceedings of the International Astronomical Union ◽

10.1017/s1743921311015304 ◽

2010 ◽

Vol 6 (S273) ◽

pp. 233-241 ◽

Cited By ~ 2

Author(s):

Guillaume Aulanier

Keyword(s):

Magnetic Field ◽

Magnetic Energy ◽

Free Field ◽

Active Regions ◽

Coronal Heating ◽

Small Scale ◽

Flux Tubes ◽

Solar Instruments ◽

Field Lines ◽

New Generation

AbstractQuasi-Separatrix Layers (QSLs) are 3D geometrical objects that define narrow volumes across which magnetic field lines have strong, but finite, gradients of connectivity from one footpoint to another. QSLs extend the concept of separatrices, that are topological objects across which the connectivity is discontinuous. Based on analytical arguments, and on magnetic field extrapolations of the Sun's coronal force-free field above observed active regions, it has long since been conjectured that QSLs are favorable locations for current sheet (CS) formation, as well as for magnetic reconnection, and therefore are good predictors for the locations of magnetic energy release in flares and coronal heating. It is only up to recently that numerical MHD simulations and solar observations, as well as a laboratory experiment, have started to address the validity of these conjectures. When put all together, they suggest that QSL reconnection is involved in the displacement of EUV and SXR brightenings along chromospheric flare ribbons, that it is related with the heating of EUV coronal loops, and that the dissipation of QSL related CS may be the cause of coronal heating in initially homogeneous, braided and turbulent flux tubes, as well as in coronal arcades rooted in the slowly moving and numerous small-scale photospheric flux concentrations, both in active region faculae and in the quiet Sun. The apparent ubiquity of QSL-related CS in the Sun's corona, which will need to be quantified with new generation solar instruments, also suggests that QSLs play an important role in stellar's atmospheres, when their surface radial magnetic fields display complex patterns.

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