Three-dimensional Magnetic Null Points Research Articles

Method for creating a three-dimensional magnetic null point topology with an accurate spine axis.

Three-dimensional magnetic null points (3D nulls) are sites of dynamic activity in a wide range of naturally-occurring and laboratory plasma environments. The topology of a 3D null is defined by a two-dimensional fan plane of radial field lines and a one-dimensional, collimated spine axis. Here, we build on previous work that was able to form an extended 3D null topology using an assembly of circular conducting coils, with each coil carrying a constant current. While that magnetic field design decayed from the mathematically pure form away from the central null, this paper introduces an algorithm for modulating the current through each coil to form a more mathematically pure spine axis along the entirety of the coil assembly. By the method of solving an inverse problem, we demonstrate that unique currents exist for any arbitrary distribution of axially-aligned circular coils for creating an accurate spine axis in a 3D null topology. Tests of this algorithm are performed on spherical, cylindrical, and cone-shaped coil assemblies. Vector magnetic field mapping of these small-scale demonstrators verifies that an accurate spine axis is maintained along the entire central axis of the coil assemblies. The magnetic field accuracy is roughly maintained along the fan plane but decays strongly toward the outer extents of the coils. The inverse method presented here is not limited to 3D null topologies but can be adapted to match any theoretical form of the magnetic field along a single axis.

Conducting-Coil Assembly for Producing Three-Dimensional Magnetic Null Points

Three-dimensional magnetic null points (3D nulls) are sites of dynamic activity and particle acceleration in astrophysical environments. Future laboratory infrastructures to validate theoretical models of observed plasma dynamics about 3D nulls will benefit from an experimental infrastructure that closely reproduces these analytical potential magnetic fields. As such, a conducting-coil assembly is presented that closely matches the theoretical form of a 3D null within an interior volume. Exact magnetic field solutions are attained for a spherical aggregation of circular current-carrying coils with finite cross sections that create a central magnetic null point of vanishing magnetic energy density. This configuration is shown to replicate the fan-plane--spine-axis topology of 3D nulls to a high order within the central volume close to the null. Finally, numerical analyses demonstrate that the investigated architecture is scalable over wide size and energy ranges. Applications of the presented conducting-coil assembly include sophisticated next-generation plasma experiments and particle accelerators.

The appearance, motion, and disappearance of three-dimensional magnetic null points

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.

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.

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.

Jets of Energetic Particles Generated by Magnetic Reconnection at a Three-dimensional Magnetic Null

We investigate particle acceleration during magnetic reconnection at a three-dimensional magnetic null point, in the spine reconnection regime, using a test particle numerical code. We observe efficient particle acceleration and find that two energetic populations are produced: a trapped population of particles that remain in the vicinity of the null and an escaping population, which leave the configuration in two symmetric jets along field lines near the spine. While the parameters used in our simulation aim to represent solar coronal plasma conditions of relevance for acceleration in flares, the fact that the reconnection configuration we studied naturally results in energetic particle jets may be of importance in other astrophysical contexts.

Current singularities at finitely compressible three-dimensional magnetic null points

The formation of current singularities at line-tied two- and three-dimensional (2D and 3D, respectively) magnetic null points in a nonresistive magnetohydrodynamic environment is explored. It is shown that, despite the different separatrix structures of 2D and 3D null points, current singularities may be initiated in a formally equivalent manner. This is true no matter whether the collapse is triggered by flux imbalance within closed, line-tied null points or driven by externally imposed velocity fields in open, incompressible geometries. A Lagrangian numerical code is used to investigate the finite amplitude perturbations that lead to singular current sheets in collapsing 2D and 3D null points. The form of the singular current distribution is analyzed as a function of the spatial anisotropy of the null point, and the effects of finite gas pressure are quantified. It is pointed out that the pressure force, while never stopping the formation of the singularity, significantly alters the morphology of the current distribution as well as dramatically weakening its strength. The impact of these findings on 2D and 3D magnetic reconnection models is discussed.

Magnetic helicity reversal of a whistler vortex transmitted through a three-dimensional magnetic null point

The transmission of a magnetic vortex through a magnetic null point on a separatrix surface is studied experimentally in a large laboratory plasma. The plasma is in the electron magnetohydrodynamic parameter regime and the vortex is an antenna-produced magnetic field perturbation propagating in the whistler mode. Topologically, the background field is separated into two regions; a closed field line region and an open field line region. The two regions are separated by a surface of magnetic field lines with two cusp null points referred to as the separatrix. The vortex propagates into one of the null points. Its energy is partially transmitted through the separatrix and partially spreads away from the null along curving field lines. The self and mutual-helicity of the transmitted vortex reverses, thus the total magnetic helicity is not conserved. Helicity conservation breaks down because the field lines are not frozen to electron flows in the unmagnetized plasma region around the magnetic null point.

Instability of isolated three-dimensional magnetic null points

Although most magnetic neutral points occurring in nature seem to form part of a continuum, recent studies of reconnection have centred on static equilibria in the neighbourhood of an isolated three-dimensional null point. The linear stability of this configuration is studied here. It is found that one may choose a flux surface so that transverse oscillations localized around the surface and polarized within it must grow exponentially in time. This means that any static equilibrium containing an isolated three-dimensional null point is linearly unstable.

The 3D topology and interaction of complex magnetic flux systems

In order to understand the topology of complex flux systems we analyse in detail the rich structural properties of the magnetic field created in turn by two or three balanced or unbalanced flux sources. Passing through each three-dimensional magnetic null point (where the field vanishes) is an isolated spine field line and a flux surface known as a fan. The fans form separatrix surfaces which separate the volume into topologically distinct regions and generally intersect each other in separator field lines linking pairs of null points. Furthermore, the fan of one null can terminate at the spine of another null, whilst the spine terminates either at a source or at infinity. The skeleton of complex three-dimensional magnetic fields therefore comprises the magnetic null points and a network of spine curves and separatrix fan surfaces. The skeletons due to three sources are classified and found to be surprisingly complex. For example, a new discovery is that a configuration with a separator may be produced by only three sources.