The structure of current layers and degree of field line braiding in coronal loops

One proposed resolution to the long-standing problem of solar coronal heating involves the buildup of magnetic energy in the corona due to turbulent motions at the photosphere that braid the coronal field, and the subsequent release of this energy via magnetic reconnection. In this paper the ideal relaxation of braided magnetic fields modelling solar coronal loops is followed. A sequence of loops with increasing braid complexity is considered, with the aim of understanding how this complexity influences the development of small scales in the magnetic field, and thus the energy available for heating. It is demonstrated that the ideally accessible force-free equilibrium for these braided fields contains current layers of finite thickness. It is further shown that for any such braided field, if a force-free equilibrium exists then it should contain current layers whose thickness is determined by length scales in the field line mapping. The thickness and intensity of the current layers follow scaling laws, and this allows us to extrapolate beyond the numerically accessible parameter regime and to place an upper bound on the braid complexity possible at coronal plasma parameters. At this threshold level the braided loop contains $10^{26}$--$10^{28}{\rm ergs}$ of available free magnetic energy, more than sufficient for a large nanoflare.Comment: To appear in ApJ. 20 pages, 10 figure

Generalised models for torsional spine and fan magnetic reconnection

Three-dimensional null points are present in abundance in the solar corona, and the same is likely to be true in other astrophysical environments. Recent studies suggest that reconnection at such 3D nulls may play an important role in the coronal dynamics. In this paper the properties of the torsional spine and torsional fan modes of magnetic reconnection at 3D nulls are investigated. New analytical models are developed, which for the first time include a current layer that is spatially localised around the null, extending along either the spine or the fan of the null. These are complemented with numerical simulations. The principal aim is to investigate the effect of varying the degree of asymmetry of the null point magnetic field on the resulting reconnection process - where previous studies always considered a non-generic radially symmetric null. The geometry of the current layers within which torsional spine and torsional fan reconnection occur is found to be strongly dependent on the symmetry of the magnetic field. Torsional spine reconnection still occurs in a narrow tube around the spine, but with elliptical cross-section when the fan eigenvalues are different, and with the short axis of the ellipse being along the strong field direction. The spatiotemporal peak current, and the peak reconnection rate attained, are found not to depend strongly on the degree of asymmetry. For torsional fan reconnection, the reconnection occurs in a planar disk in the fan surface, which is again elliptical when the symmetry of the magnetic field is broken. The short axis of the ellipse is along the weak field direction, with the current being peaked in these weak field regions. The peak current and peak reconnection rate in this case are clearly dependent on the asymmetry, with the peak current increasing but the reconnection rate decreasing as the degree of asymmetry is increased

On the formation of current sheets in response to the compression or expansion of a potential magnetic field

The compression or expansion of a magnetic field that is initially potential is considered. It was recently suggested by Janse & Low [2009, ApJ, 690, 1089] that, following the volumetric deformation, the relevant lowest energy state for the magnetic field is another potential magnetic field that in general contains tangential discontinuities (current sheets). Here we examine this scenario directly using a numerical relaxation method that exactly preserves the topology of the magnetic field. It is found that of the magnetic fields discussed by Janse & Low, only those containing magnetic null points develop current singularities during an ideal relaxation, while the magnetic fields without null points relax toward smooth force-free equilibria with finite non-zero current.Comment: Accepted for publication in Ap

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 which 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 which renders the evolution of the field at the null ideal. Resistive MHD simulations are described which 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 localised 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 localised 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.Comment: to appear in Phys. Plasmas. A version with higher quality figures can be found at http://www.maths.dundee.ac.uk/~dpontin/ In this replacement version, typos have been corrected, and in addition references and some further discussion adde

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. We demonstrate using analytical and computational models 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 quasi-separatrix layer or slip-running reconnection.Comment: Accepted for publication in the Astrophysical Journa

Kelvin-Helmholtz instability in a current-vortex sheet at a 3D magnetic null

We report here, for the first time, an observed instability of a Kelvin-Helmholtz nature occurring in a fully three-dimensional (3D) current-vortex sheet at the fan plane of a 3D magnetic null point. The current-vortex layer forms self-consistently in response to foot point driving around the spine lines of the null. The layer first becomes unstable at an intermediate distance from the null point, with the instability being characterized by a rippling of the fan surface and a filamentation of the current density and vorticity in the shear layer. Owing to the 3D geometry of the shear layer, a branching of the current filaments and vortices is observed. The instability results in a mixing of plasma between the two topologically distinct regions of magnetic flux on either side of the fan separatrix surface, as flux is reconnected across this surface. We make a preliminary investigation of the scaling of the system with the dissipation parameters. Our results indicate that the fan plane separatrix surface is an ideal candidate for the formation of current-vortex sheets in complex magnetic fields and, therefore, the enhanced heating and connectivity change associated with the instabilities of such layers

Spine-fan reconnection. The influence of temporal and spatial variation in the driver

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

Magnetic field line braiding in the solar atmosphere

AbstractUsing a magnetic carpet as model for the near surface solar magnetic field we study its effects on the propagation of energy injectected by photospheric footpoint motions. Such a magnetic carpet structure is topologically highly non-trivial and with its magnetic nulls exhibits qualitatively different behavior than simpler magnetic fields. We show that the presence of magnetic fields connecting back to the photosphere inhibits the propagation of energy into higher layers of the solar atmosphere, like the solar corona. By applying certain types of footpoint motions the magnetic field topology is is greatly reduced through magnetic field reconnection which facilitates the propagation of energy and disturbances from the photosphere.</jats:p

Magnetic reconnection at 3D null points: effect of magnetic field asymmetry

The aim of this paper is to investigate the properties of magnetic reconnection at a 3D null point, with respect to their dependence on the symmetry of the magnetic field around the null. In particular we examine the rate of flux transport across the null point with symmetric/asymmetric diffusion regions, as well as how the current sheet forms in time, and its properties. Mathematical modelling and finite difference resistive MHD simulations are used. It is found that the basic structure of the mode of magnetic reconnection considered is unaffected by varying the magnetic field symmetry, that is, the plasma flow is found cross both the spine and fan of the null. However, the peak intensity and dimensions of the current sheet are dependent on the symmetry/ asymmetry of the field lines. As a result, the reconnection rate is also found to be strongly dependent on the field asymmetry.Comment: 23 pages, 9 figure

Current sheets at three-dimensional magnetic nulls:effect of compressibility

The nature of current sheet formation in the vicinity of three-dimensional (3D) magnetic null points is investigated. The particular focus is upon the effect of the compressibility of the plasma on the qualitative and quantitative properties of the current sheet. An initially potential 3D null is subjected to shearing perturbations, as in a previous paper [Pontin et al., Phys. Plasmas, in press (2007)]. It is found that as the incompressible limit is approached, the collapse of the null point is suppressed, and an approximately planar current sheet aligned to the fan plane is present instead. This is the case regardless of whether the spine or fan of the null is sheared. Both the peak current and peak reconnection rate are reduced. The results have a bearing on previous analytical solutions for steady-state reconnection in incompressible plasmas, implying that fan current sheet solutions are dynamically accessible, while spine current sheet solutions are not.Comment: to appear in Physics of Plasmas. This version contains updated figures and references, additional discussion, and typos are fixed. This is the second in a series of papers - the first of which (by the same authors) is located at astro-ph/0701462. A version with higher quality figures can be found at http://www.maths.dundee.ac.uk/~dpontin