An Exact Solution for Steady State Magnetic Reconnection in Three Dimensions

Craig, I. J. D.; Fabling, R.B.; Henton, S.M.; Rickard, Graham

doi:10.1086/309822

Cited by 50 publications

(31 citation statements)

References 7 publications

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“…This expression immediately brings out the problem with steady-state, flux pile-up solutions, in which Q 2 increases indefinitely as →0. 11,[13][14][15] Since p 0 must scale as Q 2 /2 to maintain positive pressures in the reconnection region, we see that unbounded pressures are required in the limit of small . More physically, we can identify p 0 with the magnitude of external hydromagnetic pressures which sustain the background flows that stretch and amplify the disturbance field.…”

Section: E the Plasma Pressurementioning

confidence: 81%

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Dynamic magnetic reconnection in three space dimensions: Fan current solutions

Craig

Fabling

1998

Physics of Plasmas

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The problem of incompressible, nonlinear magnetic reconnection in three-dimensional ''open'' geometries is considered. An analytic treatment shows that dynamic ''fan current'' reconnection may be driven by superposing long wavelength, finite amplitude, plane wave disturbances onto three-dimensional magnetic X-points. The nonlinear reconnection of the field is preceded by an advection phase in which magnetic shear waves drive large currents as they localize in the vicinity of the magnetic null. Analytic arguments, reinforced by detailed simulations, show that the ohmic dissipation rate can be independent of the plasma resistivity if the merging is suitably driven.

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Section: E the Plasma Pressurementioning

confidence: 81%

“…Exact steady-state solutions of the fan current mechanism are already available. 11 What we develop here is a fully dynamic description.…”

Section: A Introductionmentioning

confidence: 99%

Dynamic magnetic reconnection in three space dimensions: Fan current solutions

Craig

Fabling

1998

Physics of Plasmas

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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%

“…A key point is that in three dimensions reconnection occurs where a component of the electric field parallel to the magnetic field is present -and this can be in many different field configurations. For example, reconnection may occur either at null points [e.g., [6][7][8][9][10][11][12][13] or in the absence of null points at quasi-separatrix layers or hyperbolic flux tubes [14][15][16][17][18][19][20][21][22][23] or it may occur along separators that join one null point to another [7,[24][25][26][27][28][29][30][31].…”

Section: Introductionmentioning

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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“…Under the simplistic assumptions made by Priest & Titov (1996) this was expected to lead to current accumulation in the entire fan plane. Although it appears that such a situation would indeed occur in an incompressible plasma (Craig et al 1995;Craig & Fabling 1998;Pontin et al 2007b), when plasma compressibility is included, a local collapse of the null occurs, destroying the planar nature of the fan surface. A localised current sheet forms which is focused around the null itself, with the result that the geometry of the magnetic field around the null is significantly different from the initial linear profile.…”

Section: Introductionmentioning

confidence: 99%

Steady state reconnection at a single 3D magnetic null point

Galsgaard¹,

Pontin

2011

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Aims. We systematically stress a rotationally symmetric 3D magnetic null point by advecting the opposite footpoints of the spine axis in opposite directions. This stress eventually concentrates in the vicinity of the null point, thereby forming a local current sheet through which magnetic reconnection takes place. The aim is to look for a steady state evolution of the current sheet dynamics, which may provide scaling relations for various characteristic parameters of the system. Methods. The evolution is followed by solving numerically the non-ideal MHD equations in a Cartesian domain. The null point is embedded in an initially constant density and temperature plasma. Results. It is shown that a quasi-steady reconnection process can be set up at a 3D null by continuous shear driving. It appears that a true steady state is unlikely to be realised because the current layer tends to grow until it is restricted by the geometry of the computational domain and the imposed driving profile. However, ratios between characteristic quantities clearly settle after some time to stable values, so that the evolution is quasi-steady. The experiments show a number of scaling relations, but they do not provide a clear consensus for extending to lower magnetic resistivity or faster driving velocities. More investigations are needed to fully clarify the properties of current sheets at magnetic null points.

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An Exact Solution for Steady State Magnetic Reconnection in Three Dimensions

Cited by 50 publications

References 7 publications

Dynamic magnetic reconnection in three space dimensions: Fan current solutions

Dynamic magnetic reconnection in three space dimensions: Fan current solutions

Three-dimensional null point reconnection regimes

Steady state reconnection at a single 3D magnetic null point

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