Three-dimensional magnetic reconnection regimes: A review

The magnetic field in many astrophysical plasmas – such as the solar corona and Earth’s magnetosphere – has been shown to have a highly complex, three-dimensional structure. Recent advances in theory and computational simulations have shown that reconnection in these fields also has a three-dimensional nature, in contrast to the widely used two-dimensional (or 2.5-dimensional) models. Here we discuss the underlying theory of three-dimensional magnetic reconnection. We also review a selection of new models that illustrate the current state of the art, as well as highlighting the complexity of energy release processes mediated by reconnection in complicated three-dimensional magnetic fields.     

MHD simulations and astrophysical applications

Magnetohydrodynamics is an adequate theoretical framework to study a large variety of astrophysical flows. The generation of magnetic fields by dynamo mechanisms, the development of turbulent flows or the topological change of magnetic fields by reconnection, are just a few examples. First, we describe the basic features of the MHD framework. Second, we make a brief introduction to the physical processes listed above, namely: dynamo action, MHD turbulence, and magnetic reconnection. Finally, we show the results arising from numerical simulations of these processes, for a number of configurations of astrophysical interest.     

向阳面磁顶区可压缩涡旋诱发重联模拟研究:通量传输事件的形成和结构

本文用二维可压缩MHD模型,模拟研究了向阳面磁顶区的涡旋诱发重联过程。重联过程的结果形成了同心的磁流体涡旋。同时还对可压缩模型与不可压缩模型的异同点作了对比研究。结果表明,在同样条件下,可压缩情况的涡旋发展的增长率比不可压缩情况慢;结构特性无显著变化。本文指出,涡旋诱发重联是产生通量传输事件的一种重要机制。通量传输管可看作为磁流体涡旋管。对通量传输事件诸物理量(磁场、速度、密度、压力和温度)的分布特性作了模拟研究,可解释FTEs的主要观测特性。      

Where will efficient energy release occur in 3-D magnetic configurations?

The energy needed to power flares is thought to be stored in the coronal magnetic field. However, the energy release is efficient only at very small scales. Magnetic configurations with a complex topology, i.e. with separatrices, are the most obvious configurations where current sheets can form, and then, reconnection can efficiently occur. This has been confirmed for several flares computing the coronal field and comparing the locations of the flare loops and ribbons to the deduced 3-D magnetic topology. However, this view is too restrictive taking into account the variety of observed solar flaring configurations. Indeed, “Quasi-Separatrix Layers” (QSLs), which are regions where there is a drastic change in field-line linkage, generalize the definition of separatrices. They let us understand where reconnection occurs in a broader variety of flares than separatrices do. The strongest electric field and current are generated at, or close to where the QSLs are thinnest. This defines the region where particle acceleration can efficiently occur. A new feature of 3-D reconnection is the natural presence of fast field-line slippage along the QSLs, a process called “slip-running reconnection”. This is a plausible origin for the motions of the X-ray sources along flare ribbons.     

Numerical study of magnetic reconnection possibly occurring near heliospheric current sheet

The third-order accurate upwind compact difference scheme has been applied for the numerical study of the magnetic reconnection driven by a plasma blob impacting the heliospheric current sheet, under the framework of the two-dimensional compressible magnetohydrodynamics. The results show that the driven reconnection near the current sheet could occur in about 10–30 min for the interplanetary high magnetic Reynolds number, R_M = 2000–10,000, a stable magnetic reconnection structure can be formed in hour order of magnitude, and there appear some basic properties such as the multiple X-line reconnections, vortex structures, filament current systems, splitting and collapse of the high-density plasma blob. These results are helpful in understanding and identifying the magnetic reconnection phenomena possibly occurring near the heliospheric current sheets.     

Large-scale reconnection in a large flare

Some specific features of the large-scale magnetic reconnection in large solar flares are briefly reviewed. In particular, the large-scale structure and dynamics of the 3B/X5.7 flare on 14 July 2000 are interpreted in terms of the topological model. The role of the betatron effect in collapsing magnetic traps, that are created by reconnection in the solar corona, is considered. We discuss some possibilities to observe the collapsing trap acceleration in solar flares.     

Topological and statistical properties of nonlinear force-free fields

We use our semi-analytic solution of the nonlinear force-free field equation to construct three-dimensional magnetic fields that are applicable to the solar corona and study their statistical properties for estimating the degree of braiding exhibited by these fields. We present a new formula for calculating the winding number and compare it with the formula for the crossing number. The comparison is shown for a toy model of two helices and for realistic cases of nonlinear force-free fields; conceptually the formulae are nearly the same but the resulting distributions calculated for a given topology can be different. We also calculate linkages, which are useful topological quantities that are independent measures of the contribution of magnetic braiding to the total free energy and relative helicity of the field. Finally, we derive new analytical bounds for the free energy and relative helicity for the field configurations in terms of the linking number. These bounds will be of utility in estimating the braided energy available for nano-flares or for eruptions.     

空间等离子体压力各向异性对磁场重联的影响

基于二维时变可压缩磁流体动力学模拟,数值研究了等离子体压力各向异性对磁场重联的影响,发现一个小的压力各向异性(P_⊥=1.02P_//)即可大大加速磁场重联的发展,这可能是由于磁镜不稳定性与撕裂模不稳定性共同起作用.在P_⊥P_//的情况下,撕裂模受到抑制,电流片中不能形成大型磁岛.      

Interconnection of high-latitude and low-latitude boundary layers when IMF BY is dominant

The antiparallel merging model places the location of the reconnection region for a dominant interplanetary magnetic field (IMF) B_Y at high latitudes at the dayside magnetopause and predicts that the low-latitude boundary layer (LLBL) is located on open field lines of the magnetospheric flanks. Interball-1 data obtained in the wide local time range near the low-latitude magnetopause makes it possible to analyze the LLBL plasma population and to find a link between possible reconnection at high latitudes and LLBL occurrence. We found that no boundary layer was observed in the regions which have no topological connection with the merging site. All cases of LLBL observations are located downstream from a specific boundary. This boundary coincides with the first magnetospheric field line touching the reconnection region and can be located in a wide local time region depending on the instant IMF direction. Even the LLBL on closed field lines shows the tendency to be concentrated in the vicinity of this boundary. Thus we show that all types of observed LLBLs are linked to reconnection sites predicted by the antiparallel merging model.     

Collisionless reconnection in the magnetotail

Recent developments regarding collisionless reconnection in current sheets with a finite normal magnetic field component (B_z) are reviewed. In 2-D x, z configurations the ion tearing mode is stabilized by the electron compressibility. When the y dependence is included, cross-field current instabilities can be excited. Of these, the drift kink mode appears to be particularly important. 3-D electromagnetic particle simulations indicate that this mode can act as the precursor to the growth of tearing modes and subsequent reconnection.     

Coronal heating by reconnection

The outermost atmosphere of the Sun, called the corona, is some 200 times hotter than the surface of the Sun. The main source of energy for heating the corona is believed to be the magnetic field which dominates the corona. Magnetic reconnection is probably the most important mechanism for releasing magnetic energy and may, therefore, be important for coronal heating or micro-flaring. The best observational examples of reconnection in the corona are thought to be X-ray bright points, which are small-scale brightenings seen randomly throughout the whole corona. Theoretical models can not only explain the key observations relating to bright points, but they can also explain the complex three-dimensional structures often seen in bright points. In these models magnetic neutral points play a significant role as the centres for reconnection both in two and three dimensions.     

Short term topological changes of coronal holes associated with prominence eruptions and subsequent CMEs

We study the short-term topological changes of equatorial and polar coronal hole (CH) boundaries, such as a variation of their area and disintegration, associated to reconnection with nearby (within 15° distance) quiescent prominence magnetic fields leading to eruptions and subsequent Coronal Mass Ejections (CMEs). The examples presented here correspond to the recent solar minimum years 2008 and 2009. We consider a temporal window of one day between the CH topological changes and the start and end times of prominence eruptions and onset of CMEs. To establish this association we took into account observational conditions related to the instability of prominence/filaments, the occurrence of a CME, as well as the subsequent evolution after the CME. We found an association between short-term local topological changes in CH boundaries and the formation/disappearance of bright points near them, as well as, between short-term topological changes within the whole CH and eruptions of nearby quiescent prominences followed by the appearance of one or more CMEs.     

Analytical MHD model of three-dimensional time-dependent reconnection in a compressible plasma

We describe and analyse a model of three-dimensional time-varying reconnection in which the effect of surface waves is neglected. Reconnection is assumed to be caused by a localized decrease of the plasma conductivity inside the diffusion region. The localized dissipation gives rise to an electric field E^*, which determines the reconnection rate. As a result, the current sheet decays into a system of large-amplitude MHD waves, which propagate along the current sheet and thereby induce perturbations in the surrounding medium. Our model is applied to the case of reconnection at the magnetopause, in particular to the signatures referred to as FTEs (flux transfer events).     

On the motions of RHESSI flare footpoints

The footpoint motions of flare hard X-ray (HXR) sources are directly related to the reconnection scenario of a solar flare. In this work, we tried to extract the information of footpoint motions for a number of flares observed with RHESSI. We found that the RHESSI flare results of the footpoint motions strongly support the classification proposed from the observations of YOHKOH/HXT. Furthermore, it is found that a flare can consist of two types of footpoint motions. We discussed the connections of the footpoint motions with the two-dimensional reconnection models.     

基于能量色散特征计算磁层顶重联位置的方法研究

磁层顶磁场重联是太阳风向磁层输入能量的主要方式.重联如何触发一直是空间物理研究的难点,其机制仍然有待深入研究.由于卫星穿越磁层顶时,很难恰好穿越重联发生的区域,因此难以观测到重联的触发条件.本文利用THEMIS卫星观测,确立了反演磁层顶重联点的方法.当重联刚开始发生时,卫星能够观测到离子的能量色散特征,可利用其计算卫星到重联发生位置的距离.沿着磁力线模型追踪该距离即可反演出磁层顶发生重联的位置.与其他方法进行了对比分析,结果显示本文方法比其他方法具有更高的精度.      

3-D reconnection related to new emerging flux

We present evidences that emergence of new flux in the lower atmosphere leads to magnetic reconnection of field lines. In a first phase the phenomenon is observed in the chromosphere by the formation of dark filaments (arch filament system) which are overlaid by bright loops visible in soft X-rays. Different types of event appear according to the magnetic field configuration and the amount of energy involved. 3-D modelling of the photospheric magnetic field provides a new tool for understanding reconnection in real configurations. The observed chromospheric and coronal loops are good diagnostics for the modelling. We document our statement by examples obtained during coordinated campaigns with the H Multichannel Subtractive Double Pass spectrographs-MSDP (Pic du Midi and Tenerife) and the Yohkoh instruments.     

Magnetic reconnection configurations and particle acceleration in solar flares

Numerical simulations of two types of flares indicate that magnetic reconnection can provide environments favorable for various particle acceleration mechanisms to work. This paper reviews recent test particle simulations of DC electric field mechanism, and discusses how the flare particles can escape into the interplanetary space under different magnetic configurations.     

Numerical simulation of three-dimensional reconnection due to the instability of collisionless current sheets

Based on analytical calculations we have currently argued that spontaneous reconnection through thin collisionless current sheets is an essentially three-dimensional (3 D) process (Büchner, 1996 a, b). Since 3 D kinetic PIC codes have become available, the three dimensional nature of the collisionless current sheet decay are now illustrated by numerical simulations (Büchner and Kuska, 1996; Pritchett and Coroniti, 1996; Zhu and Winglee, 1996). While the latter two claim a coupling to a longer wavelength kink mode as a main factor, destabilizing thin current sheets in 3 D, our simulations have revealed that even shorter scale perturbations in the current direction suffice to destabilize thin sheets very quickly. Since past simulation runs, however, were limited to mass ratios near unity, the influence of the electrons was not treated adequately. We have now investigated the stability of thin collisionless current sheets including 64 times lighter negatively charged particles. We can now show that while the two-dimensional tearing instability slows down for M = M_p/m_e = 64, the three-dimensional current sheet decay is a much faster process — practically as fast as the mass ratio M = 1 3 D sheet decay, even without kinking the sheet. We further conclude that, unlike the two-dimensional tearing instability, the three-dimensional decay of thin current sheets is not controlled by the electrons. For a sheet width comparable with the ion inertial length, we also recovered signatures of the Hall effect as predicted by Vasyliunas (1975) in the mass ratio M = 64 case. The ion inertial length seems to be the critical scale at which the sheet starts to decay.     

Global Hybrid Simulation of Magnetic Reconnection in the Magnetosheath

A three-dimensional (3-D) global hybrid simulation is carried out for the generation and structure of magnetic reconnection in the magnetosheath due to interaction of an interplanetary Tangential Discontinuity (TD) with the bow shock and magnetosphere. Runs are performed for solar wind TDs possessing different initial half-widths. As the TD propagates through the bow shock toward the magnetopause, it is greatly narrowed by a two-step compression processes, a "shock compression' followed by a subsequent ``convective compression'. In cases with a relatively thin solar wind TD, 3-D patchy reconnection is initiated in the transmitted TD, forming magnetosheath flux ropes. Multiple components of ion particles are present in the velocity distribution in the magnetosheath merging, accompanied by ion heating. For cases with a relatively wide initial TD, a dominant single X-line appears in the subsolar magnetosheath after the transmitted TD is narrowed. A shock analysis is performed for the detailed structure of magnetic reconnection in the magnetosheath. Rotational Discontinuity (RD)/Time-Dependent Intermediate Shock (TDIS) are found to dominate the reconnection layer, which and some weak slow shocks are responsible for the ion heating and acceleration.      

Double null points and magnetic reconnection

2D reconnection is possible only in connection with the existence of a singularity in the magnetic field line topology, associated with a magnetic null point or a current sheet. Both of these provide an X-type structure of the magnetic field where fields of opposite polarity meet and reconnect. In 3D a similar topology is found in a null point pair, when the null points are connected by a separator line. The separator is defined as the intersection line of the two null-point fan planes. This paper reports on the topological evolution of this configuration with respect to different perturbations emerging from imposed boundary velocities, using a nonlinear numerical approach.