X-type Neutral Point Research Articles

Evolution of Three-dimensional Coherent Structures in Hall Magnetohydrodynamics

Abstract This work extends the computational model EULAG-MHD to include Hall magnetohydrodynamics (HMHD)—important to explore physical systems undergoing fast magnetic reconnection at the order of the ion inertial length scale. Examples include solar transients along with reconnections in magnetosphere, magnetotail, and laboratory plasmas. The paper documents the results of two distinct sets of implicit large-eddy simulations in the presence and absence of the Hall forcing term, initiated with an unidirectional sinusoidal magnetic field. The HMHD simulation while benchmarking the code also emphasizes the complexity of three-dimensional (3D) evolution over its two-dimensional counterpart. The magnetic reconnections onset significantly earlier in HMHD. Importantly, the magnetic field generated by the Hall term breaks any inherent symmetry, ultimately making the evolution 3D. The resulting 3D reconnections develop magnetic flux ropes (MFRs) and magnetic flux tubes. Projected on the reconnection plane, the ropes and tubes appear as magnetic islands, which later break into secondary islands, and finally coalesce to generate an X-type neutral point. These findings are in agreement with the theory and contemporary simulations of HMHD, and thus verify our extension of the EULAG-MHD model. The second set explores the influence of the Hall forcing on generation and ascend of an MFR from sheared magnetic arcades—a novel scenario instructive in understanding the coronal transients. The rope evolves through intermediate complex structures, ultimately breaking locally because of reconnections. Interestingly, the breakage occurs earlier in the presence of the Hall term, signifying faster dynamics leading to magnetic topology favorable for reconnections.

Plasmoid-mediated reconnection in solar UV bursts

Context. Ultraviolet bursts are transients in the solar atmosphere with an increased impulsive emission in the extreme UV lasting for one to several tens of minutes. They often show spectral profiles indicative of a bi-directional outflow in response to magnetic reconnection. Aims. To understand UV bursts, we study how motions of magnetic elements at the surface can drive the self-consistent formation of a current sheet resulting in plasmoid-mediated reconnection. In particular, we want to study the role of the height of the reconnection in the atmosphere. Methods. We conducted numerical experiments solving the 2D magnetohydrodynamic equations from the solar surface to the upper atmosphere. Motivated by observations, we drove a small magnetic patch embedded in a larger system of magnetic field of opposite polarity. This type of configuration creates an X-type neutral point in the initial potential field. The models are characterized by the (average) plasma-β at the height of this X point. Results. The driving at the surface stretches the X-point into a thin current sheet, where plasmoids appear, accelerating the reconnection, and a bi-directional jet forms. This is consistent with what is expected for UV bursts or explosive events, and we provide a self-consistent model of the formation of the reconnection region in such events. The gravitational stratification gives a natural explanation for why explosive events are restricted to a temperature range around a few 0.1 MK, and the presence of plasmoids in the reconnection process provides an understanding of the observed variability during the transient events on a timescale of minutes. Conclusions. Our numerical experiments provide a comprehensive understanding of UV bursts and explosive events, in particular of how the atmospheric response changes if the reconnection happens at different plasma-β, that is, at different heights in the atmosphere. This analysis also gives new insight into how UV bursts might be related to the photospheric Ellerman bombs.

INTERCHANGE RECONNECTION IN A TURBULENT CORONA

Magnetic reconnection at the interface between coronal holes and loops, so-called interchange reconnection, can release the hotter, denser plasma from magnetically confined regions into the heliosphere, contributing to the formation of the highly variable slow solar wind. The interchange process is often thought to develop at the apex of streamers or pseudo-streamers, near Y and X-type neutral points, but slow streams with loop composition have been recently observed along fanlike open field lines adjacent to closed regions, far from the apex. However, coronal heating models, with magnetic field lines shuffled by convective motions, show that reconnection can occur continuously in unipolar magnetic field regions with no neutral points: photospheric motions induce a magnetohydrodynamic turbulent cascade in the coronal field that creates the necessary small scales, where a sheared magnetic field component orthogonal to the strong axial field is created locally and can reconnect. We propose that a similar mechanism operates near and around boundaries between open and closed regions inducing a continual stochastic rearrangement of connectivity. We examine a reduced magnetohydrodynamic model of a simplified interface region between open and closed corona threaded by a strong unipolar magnetic field. This boundary is not stationary, becomes fractal, and field lines change connectivity continuously, becoming alternatively open and closed. This model suggests that slow wind may originate everywhere along loop-coronal hole boundary regions, and can account naturally and simply for outflows at and adjacent to such boundaries and for the observed diffusion of slow wind around the heliospheric current sheet.

Particle Acceleration in the Presence of Weak Turbulence at an X-Type Neutral Point

We simulate the likely noisy situation near a reconnection region by superposing many 2D linear reconnection eigenmodes. The superposition of modes on the steady state X-type magnetic field creates multiple X- and O-type neutral points close to the original neutral point and so increases the size of the non-adiabatic region. We study test particle trajectories of initially thermal protons in these fields. Protons become trapped in this region and are accelerated by the turbulent electric field to energies up to 1 MeV in time scales relevant to solar flares. Higher energies are achieved due to the interaction of particles with increasingly turbulent electric and magnetic fields.

Relativistic magnetic reconnection at X-type neutral points

Context. The relativistic effects in the oscillatory damping of magnetic disturbances near two-dimensional X-points are investigated.

An Experimental Platform for the Study on Magnetic Reconnection in Laboratory Plasmas

In order to investigate electron dynamics near the electron diffusion region in magnetic reconnection process, an upgrade in the linear magnetized plasma (LMP) device is accomplished at the University of Science and Technology of China. Radio frequency (RF) helicon discharge is used to generate a quasi-stationary plasma, and a time-dependent magnetic field is applied to the plasma, which exhibits an X-type neutral point in vacuum. A two-dimensional sophisticated mobile platform is built up, providing a high spatial resolution, below 0.5 mm, for the diagnostics.

Particle acceleration by fluctuating electric fields at a magnetic field null point

Particle acceleration consequences from fluctuating electric fields superposed on an X-type magnetic field in collisionless solar plasma are studied. Such a system is chosen to mimic generic features of dynamic reconnection, or the reconnective dissipation of a linear disturbance. We explore numerically the consequences for charged particle distributions of fluctuating electric fields superposed on an X-type magnetic field. Particle distributions are obtained by numerically integrating individual charged particle orbits when a time varying electric field is superimposed on a static X-type neutral point. This configuration represents the effects of the passage of a generic MHD disturbance through such a system. Different frequencies of the electric field are used, representing different possible types of wave. The electric field reduces with increasing distance from the X-type neutral point as in linear dynamic magnetic reconnection. The resulting particle distributions have properties that depend on the amplitude and frequency of the electric field. In many cases a bimodal form is found. Depending on the timescale for variation of the electric field, electrons and ions may be accelerated to different degrees and often have energy distributions of different forms. Protons are accelerated to $\gamma$-ray producing energies and electrons to and above hard X-ray producing energies in timescales of 1 second. The acceleration mechanism is possibly important for solar flares and solar noise storms but is also applicable to all collisionless plasmas.

Hall effects on dynamic magnetic reconnection at an X-type neutral point

Aims. The goal of this paper is the examine the impact of the Hall current effects on magnetic reconnection solutions. Methods. The problem of perturbing a line-tied current free X-point equilibrium is considered. Computational results are presented which highlight how Hall currents influence the initial reconnection rate and the later asymptotic decay. Results. Resistive scaling laws are derived which quantify the decay rates of perturbations in terms the dimensionless resistivity η of the plasma, and the ion skin depth d i . Numerical computations confirm that the solution geometry changes character in the regime d i > √η.

Forced Magnetic Reconnection at a Neutral X-Point

The response of a two-dimensional X-type neutral point magnetic field to a quasi-static perturbation is considered. The latter is specified by a redistribution of the magnetic flux at a circular boundary centered on the neutral point. A special role of the dipole (m = 1) azimuthal perturbation component is revealed as the only one that results in the formation of a current sheet and subsequent magnetic reconnection. The excess magnetic energy released by such reconnective relaxation is also derived.

Hybrid Simulation of Ion Orbits in Magnetic Reconnection

AbstractApplying a 2.5‐D hybrid simulation, we have studied the particle acceleration caused by magnetic reconnection. The results show that the reconnection process will not only heat all the particles, but also accelerate a few particles to comparatively high velocities (about 2.0vA). Such selective accelerating makes the velocity distribution of all particles changed from the Maxwellian distribution, to a shell or quasi‐shell distribution. In addition, this shape varies with the change of particle positions. In order to study the accelerating process occurring near the X‐type neutral point, we have observed the time‐variation of velocities and positions of selected particles. Among the particles flowed out inside the reconnection region, some are trapped in the magnetic mirror, with a convolution radius that outsteps the width of the reconnection region. These particles can thus construct the lowspeed part of the fluid near the boundary of outflow regions. On the other hand, there are three kinds of drifting trajectory for particles entering the reconnection region beside the X‐type neutral point: flee along the field lines, be trapped in the magnetic mirror, and traverse the local field lines. The ratios of particles undergoing the three kinds of trajectory are about 70%, 20%, 10%, respectively.

Separator current sheets: Generic features in minimum-energy magnetic fields subject to flux constraints

Equations are found for force-free magnetic equilibria in the “coronal half-space” z>0, subject to boundary conditions on the normal magnetic field at z=0. The distribution of normal field is assumed to be composed of NS isolated unipolar source regions of arbitrary shape, arranged arbitrarily on the plane. The equilibria are found by minimizing the magnetic energy subject to constraints on the total flux interconnecting pairs of source regions. For NS source regions interconnected in ND ways, there are Nc=ND−NS+1 distinct constraints on the field. Minimization subject to these constraints leads to an Nc-dimensional space of equilibria, for given boundary data. All field-lines connecting source regions are current-free, but the equilibrium contains Nc current-sheets lying at certain interfaces. In a two-dimensional magnetic field current sheets occur at points topologically equivalent to X-type neutral points in the potential field. In a three-dimensional field current sheets occur at points topologically equivalent to separators in the potential field. The free magnetic energy is a function of the Nc fluxes used to constrain the variation.

Nonlinear evolution of plasmoid structure

The plasmoid observed in the Earth’s magnetotail shows a wide variety of the complicated plasma structures that are not simply described by the standard Petschek reconnection model. The interaction of the plasmoid propagating tailward with the surrounding plasmas of the plasma sheet at rest may be important to understand the plasma sheet structure and the plasma heating observed in the magnetotail. The nonlinear time evolution of the plasmoid is studied by using a large-scale, high-resolution, two dimensional MHD simulation code. Several discontinuities/shocks are formed in association with magnetic reconnection: 1) a pair of the standard Petscheck-type slow shock waves emanating from the X-type neutral point, 2) the tangential discontinuity inside the plasmoid that separates the accelerated plasmas from the original plasma sheet plasmas, 3) the slow shock with a “crab-hand” structure surrounding the front-side of the plasmoid, 4) the intermediate shocks in the edge of the plasma sheet inside the plasmoid, and 5) the contact discontinuity inside the plasma sheet that separates the shock-heated plasmas from the Joule heated plasmas by the magnetic diffusion at the X-type neutral point. We also discuss how those plasma discontinuities/shocks structures are affected by the lobe/mantle plasma condition.

Magnetic field structure at the diamagnetic cavity boundary (Numerical simulations)

A three‐dimensional adaptive grid MHD simulation of the solar wind interaction with comet Halley shows that the boundary of the diamagnetic cavity is a closed, well defined surface. On this surface magnetic field neutral points should exist, and indeed, two O‐type neutral points were found at the cavity boundary. In addition, the transition from closed magnetic field lines around the diamagnetic cavity to open field lines in the comet tail requires the formation of at least one X‐type neutral point. Such a neutral point was also found in the simulated cometary ionosphere downstream from the cavity. The results of numerical simulations show that the plasma density near the neutral points increases significantly. This increase seems to be indicative of plasma escape from the diamagnetic cavity in the neighborhood of the neutral points, resulting in plasma jets.

Visco-resistive magnetic reconnection due to steady inertialess flows. Part 1. Exact analytical solutions

Magnetic reconnection at an X-type neutral point of a two-dimensional magnetic field is studied in an incompressible viscous resistive fluid whose flow is assumed to be slow enough that its inertia is negligible. In both the ideal and resistive magnetohydrodynamic approximations current singularities appear at the X-point and along the separatrices. It is shown here analytically that the combined effect of viscosity and resistivity can resolve these singularities with the flow crossing the separatrices. A wide class of exact solutions describing the structure of the flow and current density distribution is found. The results suggest that reconnection may occur with localized distributions of strong current density restricted to finite regions.

Particle Acceleration in Dynamical Collisionless Reconnection

We describe the characteristics of particle orbits in the presence of an MHD disturbance in a medium with a magnetic field containing an X-type neutral point. The scalar resistivity of the medium is assumed to be a parameter of the problem.

EVIDENCE OF MAGNETIC RECONNECTION FROM Hα, SOFT X-RAY AND PHOTOSPHERIC MAGNETIC FIELD OBSERVATIONS

A conventional view of magnetic reconnection is mainly based on the 2-D picture of an X-type neutral point, or on the extension of it to 3-D, and it is thought to be accompanied by flux transport across separatrices (places where the field-line mapping is discontinuous). This view is too restrictive when we realize the variety of configurations that are seen flaring. We designed an algorithm, called Source Method (SM), to determine the magnetic topology of active regions (ARs). The observed photospheric field was extrapolated to the corona using subphotospheric sources and the topology was defined by the link between these sources. Hα flare brightenings were found to be located at the intersection with the chromosphere of the separatrices so defined. These results and the knowledge we gained on the properties of magnetic field-line linkage, led us to generalize the concept of separatrices to ‘quasi-separatrix layers’ (QSLs) and to design a new method (‘quasi-separatrix layers method’, QSLM) to determine the magnetic topology of ARs. QSLs are regions where the magnetic field-line linkage changes drastically (discontinuously when they behave like separatrices) and the QSLM can be applied to ARs where the photospheric field has been extrapolated using any kind of technique. In this paper we apply the QSLM to observed flaring regions presenting very different configurations and also to a decaying AR where a minor phenomenon, like an X-ray bright point (XBP), is observed. We find that the locations of flare and XBP brightenings are related to the properties of the field-line linkage of the underlying magnetic region, as expected from recent developments of 3-D magnetic reconnection. The extrapolated coronal field lines representing the structures involved in the analyzed events have their photospheric footpoints located at both sides of QSLs. Our results strongly support the hypothesis that magnetic reconnection is at work in various coronal phenomena, ranging from the less energetic ones to large-scale eruptions.

Analysis of Petschek-type reconnection in a Y-type magnetic field distribution

An analytical investigation is performed of Petschek-type reconnection in an incompressible plasma medium with a non-uniform magnetic field distribution, given by B = √ ( 2 z ¯ ) in complex variable notation. The initial two-dimensional (2D) configuration contains a current sheet, modelled as a tangential discontinuity, which runs along the positive x-axis in the complex plane, and which terminates in a Y-type neutral point at one end ( x = 0). In the model, reconnection is initiated through the introduction of a tangential electric field component in a localized part of the current sheet referred to as the diffusion region. Outside the diffusion region, which we approximate as an X-type neutral point, the behaviour of the magnetic field and plasma flow is governed by the equations of ideal magnetohydrodynamics (MHD), which for the purpose of this analysis are transformed into a Lagrangian coordinate system. With the restriction of a small reconnection rate, a perturbation method is applied to solve the MHD equations for the outflow region, containing the reconnected plasma, and the surrounding inflow region. The outflow region is treated as a thin boundary layer, and the usual matching procedure for problems of this type is used. In agreement with the results of previous studies of Petschektype reconnection in non-uniform, asymmetric magnetic field and velocity distributions, the boundary and interior structure of the outflow region is found to consist of a combination of Petschek-type shocks and tangential discontinuities. This is in contrast to the case of an initially uniform magnetic field distribution, analysed originally by Petschek, where the outflow region is entirely bounded by Petschek-type shocks and contains no interior discontinuities. The new features arise because the shocks propagate at the local Alfvén velocity in the medium, whereas plasma entering the outflow region is accelerated to the Alfvén velocity as measured at the reconnection site. As a result of the discrepancy between the plasma outflow speed and the shock propagation speed in the model configuration analysed here, the behaviour of the field and flow is qualitatively and quantitatively different on opposite sides of the X-line. In particular, the outflow region propagating into the direction of increasing field strength (i.e. x increasing) is bounded entirely by Petschek-type shocks, but contains a tangential discontinuity which extends the original current sheet through the leading point (or nose) into the interior of the outflow region. On the other hand, the outflow region propagating into the direction of decreasing field strength ( x decreasing, but remaining positive) is bounded on the front by tangential discontinuities, which emerge out of Petschek-type shocks, and merge into the original current sheet at the nose. When the reconnection rate drops to zero, there is an additional reverse type of behaviour which occurs in the trailing part; tangential discontinuities develop to form the tail end boundary of the outflow region in the former case, and in the latter case a tangential discontinuity develops which penetrates through the tail into the outflow region. We also investigate the consequences of a reconnection site which moves along the current sheet, analyse what happens when there are two successive pulses of reconnection, and briefly discuss the situation when the outflow region propagates beyond the edge of the current sheet.

A model for X-ray bright points due to unequal cancelling flux sources

A recent discovery from the Big Bear Solar Observatory has linked the cancellation of opposite polarity magnetic fragments in the photosphere (i.e., so-called cancelling magnetic features) to X-ray bright points and has stimulated the setting up of a converging flux model for the process. Cancelling magnetic features can occur between magnetic fragments of differing strengths in many different situations. Here, therefore, we model two opposite polarity fragments of different strengths in the photosphere by two unequal sources in an overlying uniform field. Initially in thepre-interaction phase these sources are assumed to be unconnected, but as they move closer together theinteraction phase starts with an X-type neutral point forming, initially on the photosphere, then rising up into the chromosphere and corona before lowering back down to the photosphere. Thecapture phase then follows with the sources fully connected as they move together. Finally, after they come in to contact, during thecancellation phase the weaker source is cancelled by part of the stronger source. The height of the X-type neutral point varies with the separation of the sources and the ratio of the source strengths, as do the positions of the neutral points before connection and after complete reconnection of the two sources. The neutral point is the location of magnetic reconnection and therefore energy release which is believed to power the X-ray bright point in the corona. By using a current sheet approximation, where it is assumed no reconnection takes place as the two sources move together, the total amount of energy released during reconnection may be estimated. The typical total free magnetic energy is found to be of the order of 1020–1021 J, which is as required for an X-ray bright point. It is also found that, as the ratio of the source strengths increases, the height of the X-type neutral point decreases, as do the total energy released, and the lifetime of the bright point.

Magnetic Field Structures for Inverse Polarity Prominences

AbstractObservations (Leroy, 1985) have shown that most large, high prominences are of the inverse polarity type, in that the magnetic field passes through the prominence in the inverse direction to that expected from the observed photospheric field. The classic inverse polarity model of Kuperus and Raadu (1974) assumed that the prominence lies below a region of closed magnetic field lines in the neighbourhood of an O-type neutral point and above an X-type neutral point. Since the prominence must form in a low-βcoronal plasma, the pre-prominence magnetic field must have the correct topology for an inverse polarity configuration. In this paper a wide variety of different current profiles are considered in the Grad-Shafranov equation that is used to describe the equilibrium. The results of numerical solutions to the equilibrium equation indicate that a fully developed prominence will possess an O-type, but not in general an X-type neutral point.

Magnetic Reconnection at Stressed X-Type Neutral Points

The reconnection and relaxation of two-dimensional stressed (non-potential) x-type neutral point magnetic fields are studied via solution of the nonlinear resistive 2-D MHD equations and by analytical solution of the linear eigenvalue problem. The linear dispersion relation was generalized for azimuthally nonsymmetric perturbations, and have found that for modes with azimuthal mode numbers m > 0, the relaxation can occur at a rate faster than that for n = m = 0, where n is the radial quantum'' number. One finds that for nearly azimuthally symmetric magnetic perturbations that are zero at the boundary; i.e. the frozen-in'' (sometimes called fine-tied'') boundary conditions, the fields relax incompressibly and nonlinearly to the unstressed x-type neutral point at a rate close to that predicted by linear theory. Also, fully compressible nonlinear MHD simulations have been performed, which show that the interaction between the plasma flow velocity and the magnetic field is the important physical effect, while the inclusion of thermodynamics does not affect the evolution considerably. A Lyapunov functional for the nonlinear incompressible 2-D resistive MHD equations is derived to show that the current-free x-point configuration is a global equilibrium to which general initial conditions relax.