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

Abstract

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.In astrophysical plasmas, such as the solar corona, the three-dimensional (3D) magnetic field topology is often highly complex. In such complex 3D magnetic fields, where traditional two-dimensional (2D) X-point magnetic reconnection models may no longer be applicable, determining the sites at which dynamic phenomena and energy release may occur is a crucial and non-trivial problem. Due to the typically very high Lundquist number, such events occur only at locations where intense currents (singular under an ideal MHD evolution) may form.One such site is a 3D magnetic null point (e.g. Refs. [1,2,3,4,5]). The nature of current sheet formation at such 3D nulls is investigated here.3D null points are predicted to be present in abundance in the solar corona (e.g. Refs. [6,7]). Furthermore, there is observational evidence that reconnection at a 3D null may be important in some solar flares 8 , as well as in eruptive phenomena in active regions 9 . In addition, the first in situ observation 10 of reconnection occurring at a 3D null point in the Earth's magnetotail has recently been made by the Cluster spacecraft. Moreover, current growth at 3D nulls has been observed in the laboratory 11 .The magnetic field topology and geometry in the vicinity of such a null can be described by the two sets of field lines which asymptotically approach, or recede from, the null. A pair of field lines approach (recede from) the null from opposite directions, defining the 'spine' (or γ-line) of the null. In addition, an infinite family of field lines recede from (approach) the null in a surface known as the fan (or Σ-) plane (see Refs. [2,12]).To this point, many studies of the MHD behaviour of 3D nulls have been kinematic, see e.g. Refs. [2,13,14,15]. However, a few solutions to the full set of MHD equations do exist for reconnection at current sheets located at 3D nulls, in incompressible plasmas. These incompressible solutions are based upon the technique first proposed by Craig & Henton 16 for the 2D reconnection problem. The solutions describe steady-state current sheets aligned...

Three-dimensional null point reconnection regimes

“…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].…”

The Nature of Flare Ribbons in Coronal Null-Point Topology

“…Pontin et al (2007a) had shown that intense currents in the fan were induced by the perturbation of the spine, and were even more likely to develop when taking into account the effect of compressibility (Pontin et al 2007b). The development of intense current at the null itself is also in agreement with the type of forcing that we imposed.…”

Spine-fan reconnection

“…With higher values of either parameter the plasma sound speed increases. This reduces the spine-fan collapse spreading the current sheet out across the fan plane (Pontin et al 2007b). As the null displacement depends upon the spine-fan collapse, this should mean that it is also a function of global plasma-β and γ.…”