D. I. Pontin

Three-dimensional null point reconnection regimes

Recent advances in theory and computational experiments have shown the need to refine the previous categorization 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.

Three-dimensional magnetic reconnection regimes: A review

Abstract The magnetic field in many astrophysical plasmas – such as the solar corona and Earth’s magnetosphere – has been shown to have a highly complex, three-dimensional structure. Recent advances in theory and computational simulations have shown that reconnection in these fields also has a three-dimensional nature, in contrast to the widely used two-dimensional (or 2.5-dimensional) models. Here we discuss the underlying theory of three-dimensional magnetic reconnection. We also review a selection of new models that illustrate the current state of the art, as well as highlighting the complexity of energy release processes mediated by reconnection in complicated three-dimensional magnetic fields.

Current sheet formation and nonideal behavior at three-dimensional magnetic null points

The nature of the evolution of the magnetic field, and of current sheet formation, at three-dimensional (3D) magnetic null points is investigated. A kinematic example is presented that demonstrates that for certain evolutions of a 3D null (specifically those for which the ratios of the null point eigenvalues are time-dependent), there is no possible choice of boundary conditions that renders the evolution of the field at the null ideal. Resistive magnetohydrodynamics simulations are described that demonstrate that such evolutions are generic. A 3D null is subjected to boundary driving by shearing motions, and it is shown that a current sheet localized at the null is formed. The qualitative and quantitative properties of the current sheet are discussed. Accompanying the sheet development is the growth of a localized parallel electric field, one of the signatures of magnetic reconnection. Finally, the relevance of the results to a recent theory of turbulent reconnection is discussed.

Kinematic reconnection at a magnetic null point: spine-aligned current

Magnetic reconnection at a three-dimensional null point is the natural extension of the familiar two-dimensional X-point reconnection. A model is set up here for reconnection at a spiral null point, by solving the kinematic, steady, resistive magnetohydrodynamic equations in its vicinity. A steady magnetic field is assumed, as well as the existence of a localised diffusion region surrounding the null point. Outside the diffusion region the plasma and magnetic field move ideally. Particular attention is focussed on the way that the magnetic flux changes its connections as a result of the reconnection. The resultant plasma flows are found to be rotational in nature, as is the change in connections of the magnetic field lines.

ON THE NATURE OF RECONNECTION AT A SOLAR CORONAL NULL POINT ABOVE A SEPARATRIX DOME

Three-dimensional magnetic null points are ubiquitous in the solar corona and in any generic mixed-polarity magnetic field. We consider magnetic reconnection at an isolated coronal null point whose fan field lines form a dome structure. Using analytical and computational models, we demonstrate several features of spine-fan reconnection at such a null, including the fact that substantial magnetic flux transfer from one region of field line connectivity to another can occur. The flux transfer occurs across the current sheet that forms around the null point during spine-fan reconnection, and there is no separator present. Also, flipping of magnetic field lines takes place in a manner similar to that observed in the quasi-separatrix layer or slip-running reconnection.

Dynamics of braided coronal loops - I. Onset of magnetic reconnection

Aims. The response of the solar coronal magnetic field to small-scale photospheric boundary motions including the possible formation of current sheets via the Parker scenario is one of open questions of solar physics. Here we address the problem via a numerical simulation. Methods. The three-dimensional evolution of a braided magnetic field which is initially close to a force-free state is followed using a resistive MHD code. Results. A long-wavelength instability takes place and leads to the formation of two thin current layers. Magnetic reconnection occurs across the current sheets with three-dimensional features shown, including an elliptic magnetic field structure about the reconnection site, and results in an untwisting of the global field structure.

Magnetic Braiding and Parallel Electric Fields

The braiding of the solar coronal magnetic field via photospheric motions—with subsequent relaxation and magnetic reconnection—is one of the most widely debated ideas of solar physics. We readdress the theory in light of developments in three-dimensional magnetic reconnection theory. It is known that the integrated parallel electric field along field lines is the key quantity determining the rate of reconnection, in contrast with the two-dimensional case where the electric field itself is the important quantity. We demonstrate that this difference becomes crucial for sufficiently complex magnetic field structures. A numerical method is used to relax a braided magnetic field toward an ideal force-free equilibrium; the field is found to remain smooth throughout the relaxation, with only large-scale current structures. However, a highly filamentary integrated parallel current structure with extremely short length-scales is found in the field, with the associated gradients intensifying during the relaxation process. An analytical model is developed to show that, in a coronal situation, the length scales associated with the integrated parallel current structures will rapidly decrease with increasing complexity, or degree of braiding, of the magnetic field. Analysis shows the decrease in these length scales will, for any finite resistivity, eventually become inconsistent with the stability of the coronal field. Thus the inevitable consequence of the magnetic braiding process is a loss of equilibrium of the magnetic field, probably via magnetic reconnection events.

MAGNETIC BRAIDING AND QUASI-SEPARATRIX LAYERS

The squashing factor Q, a property of the magnetic field line mapping, has been suggested as an indicator for the formation of current sheets, and subsequently magnetic reconnection, in astrophysical plasmas. Here, we test this hypothesis for a particular class of braided magnetic fields which serve as a model for solar coronal loops. We explore the relationship between quasi-separatrix layers (QSLs), that is, layer-like structures with high Q value, electric currents, and integrated parallel currents; the latter being a quantity closely related to the reconnection rate. It is found that as the degree of braiding of the magnetic field is increased, the maximum values of Q increase exponentially. At the same time, the distribution of Q becomes increasingly filamentary, with the width of the high-Q layers exponentially decreasing. This is accompanied by an increase in the number of layers so that as the field is increasingly braided the volume becomes occupied by a myriad of thin QSLs. QSLs are not found to be good predictors of current features in this class of braided fields. Indeed, despite the presence of multiple QSLs, the current associated with the field remains smooth and large scale under ideal relaxation; the field dynamically adjusts to a smooth equilibrium. Regions of high Q are found to be better related to regions of high integrated parallel current than to actual current sheets.

Dynamics and waves near multiple magnetic null points in reconnection diffusion region

Identifying the magnetic structure in the region where the magnetic field lines break and how reconnection happens is crucial to improving our understanding of three-dimensional reconnection. Here we show the in situ observation of magnetic null structures in the diffusion region, the dynamics, and the associated waves. Possible spiral null pair has been identified near the diffusion region. There is a close relation among the null points, the bipolar signature of the Z component of the magnetic field, and enhancement of the flux of energetic electrons up to 100 keV. Near the null structures, whistler-mode waves were identified by both the polarity and the power law of the spectrum of electric and magnetic fields. It is found that the angle between the fans of the nulls is quite close to the theoretically estimated maximum value of the group-velocity cone angle for the whistler wave regime of reconnection.

Non-linear tearing of 3D null point current sheets

The manner in which the rate of magnetic reconnection scales with the Lundquist number in realistic three-dimensional (3D) geometries is still an unsolved problem. It has been demonstrated that in 2D rapid non-linear tearing allows the reconnection rate to become almost independent of the Lundquist number (the “plasmoid instability”). Here, we present the first study of an analogous instability in a fully 3D geometry, defined by a magnetic null point. The 3D null current layer is found to be susceptible to an analogous instability but is marginally more stable than an equivalent 2D Sweet-Parker-like layer. Tearing of the sheet creates a thin boundary layer around the separatrix surface, contained within a flux envelope with a hyperbolic structure that mimics a spine-fan topology. Efficient mixing of flux between the two topological domains occurs as the flux rope structures created during the tearing process evolve within this envelope. This leads to a substantial increase in the rate of reconnection between the two domains.