Abstract
While theoretical models and simulations of magnetic reconnection often assume symmetry such that the magnetic null point when present is co-located with a flow stagnation point, the introduction of asymmetry typically leads to non-ideal flows across the null point. To understand this behavior, we present exact expressions for the motion of three-dimensional linear null points. The most general expression shows that linear null points move in the direction along which the magnetic field and its time derivative are antiparallel. Null point motion in resistive magnetohydrodynamics results from advection by the bulk plasma flow and resistive diffusion of the magnetic field, which allows non-ideal flows across topological boundaries. Null point motion is described intrinsically by parameters evaluated locally; however, global dynamics help set the local conditions at the null point. During a bifurcation of a degenerate null point into a null-null pair or the reverse, the instantaneous velocity of separation or convergence of the null-null pair will typically be infinite along the null space of the Jacobian matrix of the magnetic field, but with finite components in the directions orthogonal to the null space. Not all bifurcating null-null pairs are connected by a separator. Furthermore, except under special circumstances, there will not exist a straight line separator connecting a bifurcating null-null pair. The motion of separators cannot be described using solely local parameters because the identification of a particular field line as a separator may change as a result of non-ideal behavior elsewhere along the field line.
Highlights
While theoretical models and simulations of magnetic reconnection often assume symmetry such that the magnetic null point when present is co-located with a flow stagnation point, the introduction of asymmetry typically leads to non-ideal flows across the null point
Null point motion in resistive magnetohydrodynamics results from advection by the bulk plasma flow and resistive diffusion of the magnetic field, which allows non-ideal flows across topological boundaries
The first term on the right hand side corresponds to the magnetic field being carried with the electron flow velocity, Ve, rather than the bulk plasma flow; the second term corresponds to the resistive diffusion of the magnetic field at the null; and the third term corresponds to the Biermann battery.[71,72]
Summary
Magnetic reconnection[1,2,3,4] frequently occurs at and around magnetic null points: locations where the magnetic field strength equals zero.[5,6,7,8,9] Magnetospheric null points have been identified using multipoint in situ measurements as the nulls pass through the spacecraft constellation.[10,11,12,13,14,15,16] Null points in the solar atmosphere have been identified through extrapolation of the photospheric magnetic field and morphology in coronal emission.[17,18,19,20,21,22,23,24,25,26,27] Numerical simulations of magnetic reconnection and plasma turbulence at low guide fields frequently show the formation and evolution of null points,[28,29] as do numerical experiments of typical solar events such as flux emergence.[30,31]. Separatrix surfaces, spines, and separators are the topological boundaries that divide the magnetic field into distinct domains and are preferred locations for magnetic reconnection.[31,35,36,37] Three-dimensional magnetic reconnection can occur without nulls,[33,38,39,40,41,42] especially in regions such as quasi-separatrix layers where the magnetic connectivity changes quickly. There is in general a separation between these two points,[54,58–64] and in some cases a stagnation point might not even exist near a null point.[65] In all of these situations, there will generally be plasma flow across the magnetic null and the null will change position. We present exact expressions for the motion of linear null points in three dimensions and discuss the typical properties of the bifurcations of degenerate magnetic null points.
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