Dynamic magnetic reconnection in three space dimensions: Fan current solutions

Craig, I. J. D.; Fabling, R.B.

doi:10.1063/1.872754

Cited by 25 publications

(21 citation statements)

References 14 publications

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“…Here a power law appears to fit best for both. Comparing to the flux pileup regimes the power law scaling for peak current (η −0.65 ) is comparable with those of the dynamic incompressible fan solutions of Craig & Fabling (1998): η −3/4 and those found empirically for the continuously driven case: η −0.6 ∼ η −0.8 . The reconnection rate however scales slightly faster compared to the η 0.25 scaling found in the other two cases.…”

Section: Null Displacementsupporting

confidence: 60%

Spine-fan reconnection

Wyper

Jain

Pontin

2012

A&A

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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.

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Section: Null Displacementsupporting

confidence: 60%

Spine-fan reconnection

Wyper

Jain

Pontin

2012

A&A

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“…For most simulations it can safely be set to zero, but if it is required it is set at an extremely small value (e.g., 2 ¼ 10 À10 ) so that it only acts over a few grid points near the origin and its influence on the rest of the solution is negligible. Similar time-dependent analyses of the Craig & Henton (1995) problem have been carried out by Craig & Fabling (1998). In addition, a related problem involving one-dimensional electric current and velocity profiles was studied by Bulanov et al (1990).…”

Section: Time-dependent Solutionsmentioning

confidence: 81%

“…This simple two-dimensional solution has since been modified to include the effects of threedimensionality, time dependence, and different spatial geometries (Craig & Fabling 1996, 1998Watson & Craig 2002). In this paper we extend the Craig & Henton solution to the two-fluid framework more appropriate for collisionless or semicollisional plasmas.…”

Section: Introductionmentioning

confidence: 99%

Exact Steady State Reconnection Solutions in Weakly Collisional Plasmas

Watson

Porcelli

2004

ApJ

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We consider the problem of reconnection in weakly collisional plasmas in the strong guide field limit. In this regime the standard resistive Ohm's law is modified to include electron compressibility and electron inertia effects. Despite the increased complexity of the governing equations, we show that analytic steady state solutions, like those discovered by Craig and Henton for the purely resistive case, can be developed for this new system. The resulting solutions are somewhat richer than those of Craig and Henton, and there are various different regimes in parameter space to consider that exhibit multiple length scales, boundary layer effects, and other features. We also examine the dynamical behavior of these new solutions by solving the time-dependent problem numerically. Subject headingg s: MHD -plasmas

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“…7 that the width of the current sheet depends on the imposed η value, and the graph indicates that as η approaches zero the sheet reaches a minimum thickness, controlled by numerical diffusion. Results for large η indicate a power law dependence for the thickness as a function of η, though with a smaller exponent than found in the incompressible models (Craig & Fabling 1998;Heerikhuisen & Craig 2004). One can use this to estimate the value of the numerical diffusivity, which takes effect only when structures collapse to the resolution limit, while its value decreases rapidly as the structures increase in size.…”

Section: Discussionmentioning

confidence: 97%

“…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

A&A

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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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Dynamic magnetic reconnection in three space dimensions: Fan current solutions

Cited by 25 publications

References 14 publications

Spine-fan reconnection

Spine-fan reconnection

Exact Steady State Reconnection Solutions in Weakly Collisional Plasmas

Steady state reconnection at a single 3D magnetic null point

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