Exact solutions for steady reconnective annihilation revisited

Titov, V. S.; Tassi, Emanuele; Hornig, G.

doi:10.1063/1.1789159

Cited by 11 publications

(9 citation statements)

References 17 publications

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“…This lead them to so-called "reconnective annihilation" solutions, where only one of the two separatrix-lines is crossed, and the other is only tangent to the converging streamlines. The current sheet has a one-dimensional structure (straight line), while curvilinear current sheets were subsequently studied by Tassi et al (2002) and Titov et al (2004). The results found by Craig and Henton (1995) and Craig and Rickard (1994) confirm the results found earlier by Priest and Cowley (1975), who found more "shear-like" flows instead of typical stagnation point flows.…”

Section: Introductionsupporting

confidence: 80%

“…If the non-idealness has a one-dimensional, sheet-like structure, the plasma flow can only cross one part of the separatrix, similar to well known magnetic reconnective annihilation solutions. Therefore, our mathematical model proves and explains well the properties of analytical reconnective annihilation solutions of Craig and Henton (1995), Tassi et al (2002), Titov et al (2004), and Watson and Craig (1998). Our model delivers a necessary condition for all existing 2-D models of magnetic reconnection.…”

Section: Discussionmentioning

confidence: 88%

“…The case s = ±1 therefore reflects the 1-D character of the nonidealness, which can also be found, e.g. in the papers of Craig and Henton (1995), Tassi et al (2002), Titov et al (2004), and Watson and Craig (1998). This implies that for complete crossing of all separatrices, a 2-D shape of the non-ideal term is necessary.…”

Section: If the Flow Close To The Null Point Is In Good Approximationmentioning

confidence: 99%

“…E z = const (see, e.g. Titov et al, 2004). To satisfy one necessary condition for magnetic reconnection, we have to assume E z = 0.…”

Section: The Basic Incompressible Resistive Mhd Equations and Assumptmentioning

confidence: 99%

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Topological skeleton of the 2-D slightly non-ideal MHD system close to X-type magnetic null points – an analysis of the general solution for the generic case

2012

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Abstract. The appearance of eruptive space plasma processes, e.g. in eruptive flares as observed in the solar atmosphere, is usually assumed to be caused by magnetic reconnection, often connected with singular points of the magnetic field.We are interested in the general relation between the eigenvalues of the Jacobians of the plasma velocity and the magnetic field and their relation to the shape of a spatially varying, localized non-idealness or resistivity, i.e. we are searching for the general solution. We perform a local analysis of almost all regular, generic, structurally stable non-ideal or resistive MHD solutions. Therefore we use Taylor expansions of the magnetic field, the velocity field and all other physical quantities, including the non-idealness, and with the method of comparison of coefficients, the non-linear resistive MHD system is solved analytically, locally in a close vicinity of the null point.We get a parameterised general solution that provides us with the topological and geometrical skeleton of the resistive MHD fields. These local solutions provide us with the "roots" of field and streamlines around the null points of basically all possible 2-D reconnection solutions. We prove mathematically that necessarily, the flow close to the magnetic X-point must also be of X-point type to guarantee positive dissipation of energy and annihilation of magnetic flux. We also prove that, if the non-idealness has only a onedimensional, sheet-like structure, only one separatrix line can be crossed by the plasma flow, similar to known reconnective annihilation solutions.

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Section: Introductionsupporting

confidence: 80%

Section: Discussionmentioning

confidence: 88%

Section: If the Flow Close To The Null Point Is In Good Approximationmentioning

confidence: 99%

“…E z = const (see, e.g. Titov et al, 2004). To satisfy one necessary condition for magnetic reconnection, we have to assume E z = 0.…”

Section: The Basic Incompressible Resistive Mhd Equations and Assumptmentioning

confidence: 99%

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Topological skeleton of the 2-D slightly non-ideal MHD system close to X-type magnetic null points – an analysis of the general solution for the generic case

2012

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“…It has been suggested that solutions for spine reconnection in incompressible plasmas [47] may not be dynamically accessible, and while incompressible fan solutions [6] are dynamically accessible [8,[71][72][73], this breaks down when the incompressibility assumption is relaxed [71]. It turns out that the generic null point reconnection mode that is observed in numerical experiments in response to shearing motions is one in which there is a strong fan current with flow across both spine and fan, and which is in some sense a combination of the spine and fan reconnection of Priest and Titov [7].…”

Section: Kinematic Resistive Modelsmentioning

confidence: 99%

Three-dimensional null point reconnection regimes

2009

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Recent advances in theory and computational experiments have shown the need to refine the previous categorisation of magnetic reconnection at three-dimensional null points -points at which the magnetic field vanishes. We propose here a division into three different types, depending on the nature of the flow near the spine and fan of the null. The spine is an isolated field line which approaches the null (or recedes from it), while the fan is a surface of field lines which recede from it (or approach it).So-called torsional spine reconnection occurs when field lines in the vicinity of the fan rotate, with current becoming concentrated along the spine, so that nearby field lines undergo rotational slippage. In torsional fan reconnection field lines near the spine rotate and create a current that is concentrated in the fan with a rotational flux mismatch and rotational slippage. In both of these regimes, the spine and fan are perpendicular and there is no flux transfer across spine or fan. The third regime, called spine-fan reconnection, is the most common in practice and combines elements of the previous spine and fan models. In this case, in response to a generic shearing motion, the null point collapses to form a current sheet that is focused at the null itself, in a sheet that locally spans both the spine and fan. In this regime the spine and fan are no longer perpendicular and there is flux transfer across both of them.

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Viscous Energy Dissipation by Flux Pile-Up Merging in the Solar Corona

Litvinenko

2005

Sol Phys

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Magnetic field annihilation in resistive viscous incompressible plasmas is analyzed. Anisotropic viscous transport is modeled by the dominant terms in the Braginskii viscous stress tensor. An analytical solution for steady-state magnetic merging, driven by vortical plasma flows in two dimensions, is derived. Resistive and viscous energy dissipation rates are calculated. It is shown that, except in the limiting case of zero vorticity, viscous heating can significantly exceed Joule heating at the merging site. The results strongly suggest that viscous dissipation can provide a significant fraction of the total energy release in solar flares, which may have far-reaching implications for flare models.

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Exact solutions for steady reconnective annihilation revisited

Cited by 11 publications

References 17 publications

Topological skeleton of the 2-D slightly non-ideal MHD system close to X-type magnetic null points – an analysis of the general solution for the generic case

Topological skeleton of the 2-D slightly non-ideal MHD system close to X-type magnetic null points – an analysis of the general solution for the generic case

Three-dimensional null point reconnection regimes

Viscous Energy Dissipation by Flux Pile-Up Merging in the Solar Corona

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