3D Nulls Research Articles

Exploring the generation and annihilation of three-dimensional nulls through MHD simulations in initially chaotic magnetic field devoid of nulls

Three-dimensional (3D) magnetic nulls are abundant in the solar atmosphere, as has been firmly established through contemporary observations. They are established to be important magnetic structures in, for example, jets and circular ribbon flares. Although simulations and extrapolations support this, the mechanisms behind 3D null generation remain an open question. Recent magnetohydrodynamic simulations demonstrated magnetic reconnections to be responsible for both generating and annihilating 3D nulls. However, these simulations began with initial magnetic fields already supporting preexisting nulls, raising the question of whether magnetic reconnection can create nulls in fields initially devoid of them. Previously, this question was briefly explored in a simulation with an initial chaotic magnetic field. However, the study failed to precisely identify locations, topological degrees, and natures (spiral or radial) of nulls, and it approximated magnetic reconnection without tracking the magnetic field lines in time. In this paper, these findings are revisited in light of recent advancements and tools used to locate and trace nulls, along with the tracing of field lines, through which the concept of generation/annihilation of 3D nulls from chaotic fields is established in a precise manner.

Generation and annihilation of three dimensional magnetic nulls in extrapolated solar coronal magnetic field: data-based Implicit Large Eddy simulation

Three-dimensional (3D) magnetic nulls are the points where magnetic field vanishes and are preferential sites for magnetic reconnection: a fundamental process which converts magnetic energy into kinetic energy, heat, and energy of non-thermal particles along with a rearrangement of magnetic field lines. Reconnection is ubiquitous in nature and plays a major role in various magnetically confined laboratory and space/astrophysical plasmas. In the solar corona, the reconnection manifests as coronal transients including solar flares, coronal mass ejections and coronal jets—often associated with 3D nulls. The nulls are generally found to be collocated with complex active regions on the solar photosphere and merits further attention, particularly in terms of their generation. A recent idealized magnetohydrodynamics simulation initiated with an analytically constructed preexisting proper radial null has identified magnetic reconnection to be responsible for spontaneous generation of these 3D nulls. It is then imperative to further explore the plausibility of spontaneous generation of nulls in naturally occurring plasmas, identify the mechanism and verify the outcome vis-à-vis observations. An apt test bed for such an initiative is the solar atmosphere, as abundant space and ground-based observations are available. In the above backdrop, the paper attempts to investigate 3D null generation by carrying out a data-based simulation of a C6.6 class flare associated with the photospheric active region NOAA 11 977. The simulation confirms spontaneous pairwise generation of 3D nulls with magnetic reconnections as the underlying cause. Importantly, magnetic field lines associated with the spontaneously generated nulls are found to trace observed chromospheric bright points—highlighting their observational relevance. Overall, such spontaneous generation and annihilation of nulls through magnetic reconnections opens up a new avenue for solar coronal and chromospheric heating.

Direct imaging of magnetohydrodynamic wave mode conversion near a 3D null point on the sun

Mutual conversion of various kinds of magnetohydrodynamic (MHD) waves can have profound impacts on wave propagation, energy transfer, and heating of the solar chromosphere and corona. Mode conversion occurs when an MHD wave travels through a region where the Alfvén and sound speeds are equal (e.g., a 3D magnetic null point). Here we report the direct extreme ultraviolet (EUV) imaging of mode conversion from a fast-mode to a slow-mode MHD wave near a 3D null point using Solar Dynamics Observatory/Atmospheric Imaging Assembly (SDO/AIA) observations. An incident fast EUV wavefront associated with an adjacent eruptive flare propagates laterally through a neighboring pseudostreamer. Shortly after the passage of the fast EUV wave through the null point, a slow-mode wave appears near the null that propagates upward along the open structures and simultaneously downward along the separatrix encompassing the fan loops of the pseudostreamer base. These observations suggest the existence of mode conversion near 3D nulls in the solar corona, as predicted by theory and MHD simulations. Moreover, we observe decaying transverse oscillations in both the open and closed structures of the pseudostreamer, along with quasiperiodic type III radio bursts indicative of repetitive episodes of electron acceleration.

Hall effect on the magnetic reconnections during the evolution of a three-dimensional magnetic flux rope

We present a novel Hall magnetohydrodynamics (HMHD) numerical simulation of a three-dimensional (3D) magnetic flux rope (MFR)—generated by magnetic reconnections from an initial 3D bipolar sheared field. Magnetic reconnections during the HMHD evolution are compared with the MHD. In both simulations, the MFRs generate as a consequence of the magnetic reconnection at null points which has not been realized in contemporary simulations. Interestingly, the evolution is faster and more intricate in the HMHD simulation. Repetitive development of the twisted magnetic field lines (MFLs) in the vicinity of 3D nulls (reconnection site) is unique to the HMHD evolution of the MFR. The dynamical evolution of magnetic field lines around the reconnection site being affected by the Hall forcing correspondingly affects the large-scale structures.

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.

Magnetic Reconnections in the Presence of Three-Dimensional Magnetic Nulls and Quasi-Separatrix Layers

Three-dimensional (3D) magnetohydrodynamic simulations are carried out to explore magnetic reconnections in the presence of 3D magnetic nulls and quasi-separatrix layers (QSLs). The initial magnetic fields are created by superposing uniform vertical magnetic fields of two different magnitudes on a linear force-free field. The interior of the numerical box contains two 3D nulls with separatrix domes separated by a quasi-separator (or hyperbolic flux tube) with QSLs. In the first simulation, the uniform vertical field is so large that the nulls are located at low heights and the domes are separate. Initially unbalanced Lorentz forces drive rotational flows that form strong electric currents and strong torsional fan reconnection at the 3D nulls and weak QSL reconnection at the hyperbolic flux tube. Flipping or slipping of field lines is observed in both cases. In the second simulation, with a weaker vertical field and larger domes, the separatrix surfaces meet at the central quasi-separator and their rotation drives stronger QSL reconnection than before.

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.

Implosive Collapse about Magnetic Null Points: A Quantitative Comparison between 2D and 3D Nulls

Abstract Null collapse is an implosive process whereby MHD waves focus their energy in the vicinity of a null point, forming a current sheet and initiating magnetic reconnection. We consider, for the first time, the case of collapsing 3D magnetic null points in nonlinear, resistive MHD using numerical simulation, exploring key physical aspects of the system as well as performing a detailed parameter study. We find that within a particular plane containing the 3D null, the plasma and current density enhancements resulting from the collapse are quantitatively and qualitatively as per the 2D case in both the linear and nonlinear collapse regimes. However, the scaling with resistivity of the 3D reconnection rate—which is a global quantity—is found to be less favorable when the magnetic null point is more rotationally symmetric, due to the action of increased magnetic back-pressure. Furthermore, we find that, with increasing ambient plasma pressure, the collapse can be throttled, as is the case for 2D nulls. We discuss this pressure-limiting in the context of fast reconnection in the solar atmosphere and suggest mechanisms by which it may be overcome. We also discuss the implications of the results in the context of null collapse as a trigger mechanism of Oscillatory Reconnection, a time-dependent reconnection mechanism, and also within the wider subject of wave–null point interactions. We conclude that, in general, increasingly rotationally asymmetric nulls will be more favorable in terms of magnetic energy release via null collapse than their more symmetric counterparts.

Three-dimensional Oscillatory Magnetic Reconnection

Abstract Here we detail the dynamic evolution of localized reconnection regions about 3D magnetic null points using numerical simulation. We demonstrate for the first time that reconnection triggered by the localized collapse of a 3D null point that is due to an external magnetohydrodynamic (MHD) wave involves a self-generated oscillation, whereby the current sheet and outflow jets undergo a reconnection reversal process during which back-pressure formation at the jet heads acts to prise open the collapsed field before overshooting the equilibrium into an opposite-polarity configuration. The discovery that reconnection at fully 3D nulls can proceed naturally in a time-dependent and periodic fashion suggests that oscillatory reconnection mechanisms may play a role in explaining periodicity in astrophysical phenomena associated with magnetic reconnection, such as the observed quasi-periodicity of solar and stellar flare emission. Furthermore, we find that a consequence of oscillatory reconnection is the generation of a plethora of freely propagating MHD waves that escape the vicinity of the reconnection region.

Simulated evolution of three-dimensional magnetic nulls leading to generation of cylindrically-shaped current sheets

The performed magnetohydrodynamic simulation examines the importance of magnetofluid evolution, which naturally leads to current sheets in the presence of three-dimensional (3D) magnetic nulls. The initial magnetic field is constructed by superposing a 3D force-free field on a constant axial magnetic field. The initial field supports 3D magnetic nulls having the classical spine axis and the dome-shaped fan surface and exerts non-zero Lorentz force on the magnetofluid. Importantly, the simulation identifies the development of current sheets near the 3D magnetic nulls. The morphology of the current sheets is similar to a cylindrical surface where the surface encloses the spine axis. The development is because of favorable deformation of magnetic field lines constituting the dome-shaped fan surface. The deformation of field lines is found to be caused by the flow generated by magnetic reconnections at current sheets which are located away from the cylindrically shaped current sheets.

The nature of separator current layers in MHS equilibria

Separators, which are in many ways the three-dimensional equivalent to two-dimensional nulls, are important sites for magnetic reconnection. Magnetic reconnection occurs in strong current layers which have very short length scales. The aim of this work is to explore the nature of current layers around separators. A separator is a special field line which lies along the intersection of two separatrix surfaces and forms the boundary between four topologically distinct flux domains. In particular, here the current layer about a separator that joins two 3D nulls and lies along the intersection of their separatrix surfaces is investigated. A magnetic configuration containing a single separator embedded in a uniform plasma with a uniform electric current parallel to the separator is considered. This initial magnetic setup, which is not in equilibrium, relaxes in a non-resistive manner to form an equilibrium. The relaxation is achieved using the 3D MHD code, Lare3d, with resistivity set to zero. A series of experiments with varying initial current are run to investigate the characteristics of the resulting current layers present in the final (quasi-) equilibrium states. In each experiment, the separator collapses and a current layer forms along it. The dimensions and strength of the current layer increase with initial current. It is found that separator current layers formed from current parallel to the separator are twisted. Also the collapse of the separator is a process that evolves like an infinite-time singularity where the length, width and peak current in the layer grow slowly whilst the depth of the current layer decreases.

Reconnection at three dimensional magnetic null points: Effect of current sheet asymmetry

Asymmetric current sheets are likely to be prevalent in both astrophysical and laboratory plasmas with complex three dimensional (3D) magnetic topologies. This work presents kinematic analytical models for spine and fan reconnection at a radially symmetric 3D null (i.e., a null where the eigenvalues associated with the fan plane are equal) with asymmetric current sheets. Asymmetric fan reconnection is characterized by an asymmetric reconnection of flux past each spine line and a bulk flow of plasma across the null point. In contrast, asymmetric spine reconnection is characterized by the reconnection of an equal quantity of flux across the fan plane in both directions. The higher modes of spine reconnection also include localized wedges of vortical flux transport in each half of the fan. In this situation, two definitions for reconnection rate become appropriate: a local reconnection rate quantifying how much flux is genuinely reconnected across the fan plane and a global rate associated with the net flux driven across each semi-plane. Through a scaling analysis, it is shown that when the ohmic dissipation in the layer is assumed to be constant, the increase in the local rate bleeds from the global rate as the sheet deformation is increased. Both models suggest that asymmetry in the current sheet dimensions will have a profound effect on the reconnection rate and manner of flux transport in reconnection involving 3D nulls.

Spine-fan reconnection

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.

Magnetohydrodynamics dynamical relaxation of coronal magnetic fields

Context: The majority of studies on stressed 3D magnetic null points consider magnetic reconnection driven by an external perturbation, but the formation of a genuine current sheet equilibrium remains poorly understood. This problem has been considered more extensively in two-dimensions, but lacks a generalization into 3D fields. Aims: 3D magnetic nulls are more complex than 2D nulls and the field can take a greater range of magnetic geometries local to the null. Here, we focus on one type and consider the dynamical non-resistive relaxation of 3D spiral nulls with initial spine-aligned current. We aim to provide a valid magnetohydrostatic equilibrium, and describe the electric current accumulations in various cases, involving a finite plasma pressure. Methods: A full MHD code is used, with the resistivity set to zero so that reconnection is not allowed, to run a series of experiments in which a perturbed spiral 3D null point is allowed to relax towards an equilibrium, via real, viscous damping forces. Changes to the initial plasma pressure and other magnetic parameters are investigated systematically. Results: For the axi-symmetric case, the evolution of the field and the plasma is such that it concentrates the current density in two cone-shaped regions along the spine, thus concentrating the twist of the magnetic field around the spine, leaving a radial configuration in the fan plane. The plasma pressure redistributes in order to maintain the current density accumulations. However, it is found that changes in the initial plasma pressure do not modify the final state significantly. In the cases where the initial magnetic field is not axi-symmetric, a infinite-time singularity of current perpendicular to the fan is found at the location of the null.

Generalised models for torsional spine and fan magnetic reconnection

Context. Three-dimensional (3D) null points are present in abundance in the solar corona, and the same is likely to be true in other astrophysical environments. Recent results from solar observations and from simulations suggest that reconnection at such 3D nulls may play an important role in the coronal dynamics.

Development of electric currents in a magnetic field configuration containing a magnetic null point

Context. In the past the role of magnetic null points in the generation of electric currents was investigated mainly in the close vicinity of the null, with perturbations being applied at nearby boundaries, or for a magnetic null configuration with a dome-shaped fan. In the solar atmosphere, however, electric currents are generated by perturbations originating at the photosphere, far away from coronal 3D nulls, and the occurence of magnetic nulls with a dome-shaped fan is apparently not common.Aims. We investigate the consequences of photospheric motion for the development of electric currents in a coronal magnetic field configuration containing a null, located far away from the boundaries, and the influence of topological structures on the spatial distribution of the currents.Methods. We use a 3D resistive MHD code to investigate the consequences of photospheric plasma motion for the generation of currents in a coronal magnetic field containing a null. The plasma is considered fully compressible and is initially in hydrostatic equilibrium. The initial magnetic field is potential (current free).Results. The photospheric plasma motion causes magnetic field perturbations that propagate to the corona along the field lines at the local Alfven speed. The Alfvenic wave perturbations correspond to a propagating current directed mainly parallel to the magnetic field. Perpendicular currents connect to return currents to close the current system. The magnetic perturbations eventually reach the vicinity of the null. However, the currents forming in and around the null, near the fan surface or near the spine field lines, are not always the strongest currents developing in the simulation box. In our simulation, the strongest currents develop close to the bottom boundary, where the plasma is moved, and below the null point, in a region where field line connectivity considerably changes. Conclusions. Our simulation shows that the presence of a magnetic null point does not necessarily mean that the strongest currents will form in or around the null, at the fan surface or at the spine. Our results indicate that regions of considerable change in field line connectivity are fundamental for the development of strong and thin current sheets. Regions of connectivity change are important because they combine perturbations that are generated at different locations on the Sun. Our results also suggest that it is more important how the perturbations are mapped and combined in regions of considerable connectivity change than what is the driver of the perturbations itself. The driver does not necessarily need to create strong currents where it is applied. However, when the perturbations produced by the driver combine in the regions of considerable connectivity change, they can increase the current in regions for which the length scale is much smaller than the characteristic length scale of the system. The location of regions of connectivity change, combined with the mapping of the perturbations to those regions, can be a useful tool to predict where and when solar flares will occur.

Determination of the Topology Skeleton of Magnetic Fields in a Solar Active Region

Magnetic topology has been a key to the understanding of magnetic energy release mechanism. Based on observed vector magnetograms, we have determined the three-dimensional (3D) topology skeleton of the magnetic fields in the active region NOAA 10720. The skeleton consists of six 3D magnetic nulls and a network of corresponding spines, fans, and null-null lines. For the first time, we have identified a spiral magnetic null in Sun's corona. The magnetic lines of force twisted around the spine of the null, forming a `magnetic wreath' with excess of free magnetic energy and resembling observed brightening structures at extra-ultraviolet (EUV) wavebands. We found clear evidence of topology eruptions which are referred to as catastrophic changes of topology skeleton associated with a coronal mass ejection (CME) and an explosive X-ray flare. These results shed new lights on the structural complexity and its role in explosive magnetic activity. The concept of flux rope has been widely used in modelling explosive magnetic activity, although their observational identity is rather obscure or, at least, lacking of necessary details up to date. We suggest that the magnetic wreath associated with the 3D spiral null is likely an important class of the physical entity of flux ropes.