Spontaneous magnetic reconnection

The present review concerns the relevance of collisionless reconnection in the astrophysical context. Emphasis is put on recent developments in theory obtained from collisionless numerical simulations in two and three dimensions. It is stressed that magnetic reconnection is a universal process of particular importance under collisionless conditions, when both collisional and anomalous dissipation are irrelevant. While collisional (resistive) reconnection is a slow, diffusive process, collisionless reconnection is spontaneous. On any astrophysical time scale, it is explosive. It sets on when electric current widths become comparable to the leptonic inertial length in the so-called lepton (electron/positron) “diffusion region”, where leptons de-magnetise. Here, the magnetic field contacts its oppositely directed partner and annihilates. Spontaneous reconnection breaks the original magnetic symmetry, violently releases the stored free energy of the electric current, and causes plasma heating and particle acceleration. Ultimately, the released energy is provided by mechanical motion of either the two colliding magnetised plasmas that generate the current sheet or the internal turbulence cascading down to lepton-scale current filaments. Spontaneous reconnection in such extended current sheets that separate two colliding plasmas results in the generation of many reconnection sites (tearing modes) distributed over the current surface, each consisting of lepton exhausts and jets which are separated by plasmoids. Volume-filling factors of reconnection sites are estimated to be as large as \({<}10^{-5}\) per current sheet. Lepton currents inside exhausts may be strong enough to excite Buneman and, for large thermal pressure anisotropy, also Weibel instabilities. They bifurcate and break off into many small-scale current filaments and magnetic flux ropes exhibiting turbulent magnetic power spectra of very flat power-law shape \(W_b\propto k^{-\alpha }\) in wavenumber k with power becoming as low as \(\alpha \approx 2\). Spontaneous reconnection generates small-scale turbulence. Imposed external turbulence tends to temporarily increase the reconnection rate. Reconnecting ultra-relativistic current sheets decay into large numbers of magnetic flux ropes composed of chains of plasmoids and lepton exhausts. They form highly structured current surfaces, “current carpets”. By including synchrotron radiation losses, one favours tearing-mode reconnection over the drift-kink deformation of the current sheet. Lepton acceleration occurs in the reconnection-electric field in multiple encounters with the exhausts and plasmoids. This is a Fermi-like process. It results in power-law tails on the lepton energy distribution. This effect becomes pronounced in ultra-relativistic reconnection where it yields extremely hard lepton power-law energy spectra approaching \(F(\gamma )\propto \gamma ^{-1}\), with \(\gamma \) the lepton energy. The synchrotron radiation limit becomes substantially exceeded. Relativistic reconnection is a probable generator of current and magnetic turbulence, and a mechanism that produces high-energy radiation. It is also identified as the ultimate dissipation mechanism of the mechanical energy in collisionless magnetohydrodynamic turbulent cascades via lepton-inertial-scale turbulent current filaments. In this case, the volume-filling factor is large. Magnetic turbulence causes strong plasma heating of the entire turbulent volume and violent acceleration via spontaneous lepton-scale reconnection. This may lead to high-energy particle populations filling the whole volume. In this case, it causes non-thermal radiation spectra that span the entire interval from radio waves to gamma rays.     

Magnetic Reconnection, Turbulence, and Collisionless Shock

A short summary of recent progress in measuring and understanding turbulence during magnetic reconnection in laboratory plasmas is given. Magnetic reconnection is considered as a primary process to dissipate magnetic energy in laboratory and astrophysical plasmas. A central question concerns why the observed reconnection rates are much faster than predictions made by classical theories, such as the Sweet–Parker model based on MHD with classical Spitzer resistivity. Often, the local resistivity is conjectured to be enhanced by turbulence to accelerate reconnection rates either in the context of the Sweet–Parker model or by facilitating setup of the Pestchek model. Measurements at a dedicated laboratory experiment, called MRX or Magnetic Reconnection Experiment, have indicated existence of strong electromagnetic turbulence in current sheets undergoing fast reconnection. The origin of the turbulence has been identified as right-hand polarized whistler waves, propagating obliquely to the reconnecting field, with a phase velocity comparable to the relative drift velocity. These waves are consistent with an obliquely propagating electromagnetic lower-hybrid drift instability driven by drift speeds large compared to the Alfven speed in high-beta plasmas. Interestingly, this instability may explain electromagnetic turbulence also observed in collisionless shocks, which are common in energetic astrophysical phenomena.     

Three-Dimensional Magnetic Reconnection in Astrophysical Plasmas - Kinetic Approach

Reconnection is the most efficient way to release the energy accumulated in the tense astrophysical magnetoplasmas. As such it is a basic paradigm of energy conversion in the universe. Astrophysical reconnection is supposed to heat plasmas to high temperatures, it drives fast flows, winds and jets, it accelerates particles and leads to structure formation. Reconnection can take place only after a local breakdown of the plasma ideality, enabling a change of the magnetic connection between plasma elements. After Giovanelli first suggested magnetoplasma discharges in 1946, reconnection has usually been identified with vanishing magnetic field regions. However, for the last ten years a discussion has been going on about the structure of 3 D reconnection, e.g., whether in 3 D it is possible also without magnetic nulls or not. We first shortly review the relevant magnetostatic and kinematic fluid theory results to argue than that a kinetic approach is necessary to reveal the generic three-dimensional structure and dynamics of reconnection in collisionless astrophysical plasmas. We present results about the 3 D structure of kinetic reconnection in initially antiparallel magnetic fields. They were obtained by selfconsistently considering ion and electron inertia as well as dissipative wave-particle resonances. In this approach reconnection is a natural consequence of the instability of thin current sheets. We present the results of a nonlocal linear dispersion theory and describe the nonlinear evolution of the instability using numerical particle code simulations. The decay of thin current sheets directly leads to a configurational instability and three-dimensional dynamic reconnection. We report the resulting generic magnetic field structure. It contains pairs of magnetic nulls, connected by separating magnetic flux surfaces through which the plasma flows and along which reconnection induces large parallel electric fields. Our results are illustrated by virtual reality views and movies, both stored on the attached CD-ROM and also being available from the Internet. This revised version was published online in July 2006 with corrections to the Cover Date.     

Modeling the Resistive MHD by the Cese Method

In this paper, the Space–Time Conservation Element and Solution Element (CESE) method is applied to 2.5-dimensional resistive magnetohydrodynamics (MHD) equations in Cartesian coordinates, with the purpose of modeling the magnetic reconnection study. To show the validity and capacity of its application to MHD reconnection problem, spontaneous fast reconnection and magnetic reconnection in multiple heliospheric current sheets are studied, which show good consistency with those obtained formerly by other authors. In order to assess the ∇ ⋅ B = 0 constraint numerically, the contours and evolution of ∇ ⋅ B are analyzed. The numerical results tell us that the CESE numerical scheme not only has good numerical resolution but also can keep the divergence-free condition for magnetic fields in the reconnection problems during the evolutionary process without any special treatment.     

Dynamo theory and liquid metal MHD experiments

High values of magnetic Reynolds number R_m are characteristic not only to astrophysics, but also to other interesting objects, including liquid metal (LM) flows. Since sixties LM experiments have been performed illustrating important predictions of the dynamo theory, for example, about the existence and features of the α effect. Consideration of so called “laminar” dynamos provides a theoretical base for direct experimental realization and examination of the dynamo process. First step results, gathered at subcritical conditions, confirm the statement that self-excitation in LM experiments can be achieved practically today. In such devices as LM (sodium) cooled fast breeders R_m can reach values up to 50 and specific MHD phenomena have been observed in operating fast reactors. Cautions against crisis like processes have been expressed. It is important for the dynamo theory to understand what kind of perturbed motion is able to coexist with the generated magnetic field. Fundamentally new ideas here are issuing from the theory of 2D MHD turbulence. LM MHD served for the first direct proves, confirming, that the predicted surprising features of 2D turbulence can be observed in reality. It is worth incorporating these already not new ideas in the dynamo theory. In such a way a field for new solutions could be established.     

Observation of a Complex Solar Wind Reconnection Exhaust from Spacecraft Separated by over 1800 R E

We analyze Wind, ACE, and STEREO (ST-A and ST-B) plasma and magnetic field data in the vicinity of the heliospheric current sheet (HCS) crossed by all spacecraft between 22:15 UT on 31 March and 01:25 UT on 1 April 2007 corresponding to its observation at ST-A and ST-B, which were separated by over 1800 R _E (or over 1200 R _E across the Sun?–?Earth line). Although only Wind and ACE provided good ion flow data in accord with a solar wind magnetic reconnection exhaust at the HCS, the magnetic field bifurcation typical of such exhausts was clearly observed at all spacecraft. They also all observed unambiguous strahl mixing within the exhaust, consistent with the sunward flow deflection observed at Wind and ACE and thus with the formation of closed magnetic field lines within the exhaust with both ends attached to the Sun. The strong dawnward flow deflection in the exhaust is consistent with the exhaust and X-line orientations obtained from minimum variance analysis at each spacecraft so that the X-line is almost along the GSE Z-axis and duskward of all the spacecraft. The observation of strahl mixing in extended and intermittent layers outside the exhaust by ST-A and ST-B is consistent with the formation of electron separatrix layers surrounding the exhaust. This event also provides further evidence that balanced parallel and antiparallel suprathermal electron fluxes are not a necessary condition for identification of closed field lines in the solar wind. In the present case the origin of the imbalance simply is the mixing of strahls of substantially different strengths from a different solar source each side of the HCS. The inferred exhaust orientations and distances of each spacecraft relative to the X-line show that the exhaust was likely nonplanar, following the Parker spiral orientation. Finally, the separatrix layers and exhausts properties at each spacecraft suggest that the magnetic reconnection X-line location and/or reconnection rate were variable in both space and time at such large scales.

     

Nonlinear excitation of small-scale Alfvén waves by fast waves and plasma heating in the solar atmosphere

We study a nonlinear mechanism for the excitation of kinetic Alfvén waves (KAWs) by fast magneto-acoustic waves (FWs) in the solar atmosphere. Our focus is on the excitation of KAWs that have very small wavelengths in the direction perpendicular to the background magnetic field. Because of their small perpendicular length scales, these waves are very efficient in the energy exchange with plasmas and other waves. We show that the nonlinear coupling of the energy of the finite-amplitude FWs to the small-scale KAWs can be much faster than other dissipation mechanisms for fast wave, such as electron viscous damping, Landau damping, and modulational instability. The nonlinear damping of the FWs due to decay FW = KAW + KAW places a limit on the amplitude of the magnetic field in the fast waves in the solar corona and solar-wind at the level B/B ₀∼10⁻². In turn, the nonlinearly excited small-scale KAWs undergo strong dissipation due to resistive or Landau damping and can provide coronal and solar-wind heating. The transient coronal heating observed by Yohkoh and SOHO may be produced by the kinetic Alfvén waves that are excited by parametric decay of fast waves propagating from the reconnection sites.     

实验室模拟磁力线重联的初步结果

在中国科学技术大学的线性磁化等离子体装置上,通过对两个平行电流板施加同向电流,实现重联磁场位型的构造,进而开展实验室等离子体中磁力线重联过程的研究.利用发射探针测量了重联过程中的平行(轴向)电场,实验验证了重联电流与通行粒子的依赖关系.利用磁探针测量了磁场通量的演化,未发现通量堆积现象,与数值预言相符.     

MAGNETIC RECONNECTION IN MULTIPLE HELIOSPHERIC CURRENT SHEETS

Satellite observations of the heliospheric current sheet indicate that the internal structure of sector boundaries is a very complex structure with many directional discontinuities in the magnetic field. This implies that the heliospheric current sheet is not a single surface but a constantly changing layer with a varying number of current sheets. In this paper, we investigate magnetic reconnection caused by the resistive tearing mode instability in non-periodic multiple current sheets by using two-dimensional magnetohydrodynamic simulation. The results show that it is complex unsteady magnetic reconnection. Accompanying the nonlinear development of the tearing mode, the width of each magnetic island in multiple current sheets increases with time, and this leads to new magnetic reconnection. At the same time, the width of each current sheet increases, and the current intensity decreases gradually. Finally, the reverse current disappears, and a big magnetic island is formed in the central region. This process is faster when the separation between the current sheets is smaller. We suggest that the occurrence of multiple directional discontinuities observed at sector boundary crossings in the heliosphere may be associated with the magnetic islands and plasmoids caused by magnetic reconnection in multiple current sheets.     

An assessment of the length and variability of Mercury's magnetotail

We employ Mariner 10 measurements of the interplanetary magnetic field in the vicinity of Mercury to estimate the rate of magnetic reconnection between the interplanetary magnetic field and the Hermean magnetosphere. We derive a time-series of the open magnetic flux in Mercury's magnetosphere, from which we can deduce the length of the magnetotail. The length of the magnetotail is shown to be highly variable, with open field lines stretching between 15R_H and 850R_H downstream of the planet (median 150R_H). Scaling laws allow the tail length at perihelion to be deduced from the aphelion Mariner 10 observations.     

Decametric N Burst: A Consequence of the Interaction of Two Coronal Mass Ejections

Radio emissions of electron beams in the solar corona and interplanetary space are tracers of the underlying magnetic configuration and of its evolution. We analyse radio observations from the Culgoora and WIND/WAVES spectrographs, in combination with SOHO/LASCO and SOHO/MDI data, to understand the origin of a type N burst originating from NOAA AR 10540 on January 20, 2004, and its relationship with type II and type III emissions. All bursts are related to the flares and the CME analysed in a previous paper (Goff et al., 2007). A very unusual feature of this event was a decametric type N burst, where a type III-like burst, drifting towards low frequencies (negative drift), changes drift first to positive, then again to negative. At metre wavelengths, i.e., heliocentric distances ≲1.5R _⊙, these bursts are ascribed to electron beams bouncing in a closed loop. Neither U nor N bursts are expected at decametric wavelengths because closed quasi-static loops are not thought to extend to distances ≫1.5R _⊙. We take the opportunity of the good multi-instrument coverage of this event to analyse the origin of type N bursts in the high corona. Reconnection of the expanding ejecta with the magnetic structure of a previous CME, launched about 8 hours earlier, injects electrons in the same manner as with type III bursts but into open field lines having a local dip and apex. The latter shape was created by magnetic reconnection between the expanding CME and neighbouring (open) streamer field lines. This particular flux tube shape in the high corona, between 5R _⊙ and 10R _⊙, explains the observed type N burst. Since the required magnetic configuration is only a transient phenomenon formed by reconnection, severe timing and topological constraints are present to form the observed decametric N burst. They are therefore expected to be rare features.     

The Parker Problem and the Theory of Coronal Heating

To illustrate his theory of coronal heating, Parker initially considers the problem of disturbing a homogeneous vertical magnetic field that is line-tied across two infinite horizontal surfaces. It is argued that, in the absence of resistive effects, any perturbed equilibrium must be independent of z. As a result random footpoint perturbations give rise to magnetic singularities, which generate strong Ohmic heating in the case of resistive plasmas. More recently these ideas have been formalized in terms of a magneto-static theorem but no formal proof has been provided. In this paper we investigate the Parker hypothesis by formulating the problem in terms of the fluid displacement. We find that, contrary to Parker's assertion, well-defined solutions for arbitrary compressibility can be constructed which possess non-trivial z-dependence. In particular, an analytic treatment shows that small-amplitude Fourier disturbances violate the symmetry ∂_z = 0 for both compact and non-compact regions of the (x, y) plane. Magnetic relaxation experiments at various levels of gas pressure confirm the existence and stability of the Fourier mode solutions. More general footpoint displacements that include appreciable shear and twist are also shown to relax to well-defined non-singular equilibria. The implications for Parker's theory of coronal heating are discussed.     

Analytical theory of tachocline transport at mid latitudes

We provide a theory of magnetic diffusion, momentum transport, and mixing in the solar tachocline by considering magnetohydrodynamics (MHD) turbulence on a β plane subject to a large scale shear (provided by the latitudinal differential rotation). In the strong magnetic field regime, we find that the turbulent viscosity and diffusivity are reduced by magnetic fields only, similarly to the two-dimensional MHD case (without Rossby waves). In the weak magnetic field regime, we find a crossover scale (L_R) from a Alfvén dominated regime (on small scales) to a Rossby dominated regime (on large scales). For parameter values typical of the tachocline, L_R is larger than the solar radius so that Rossby waves are unlikely to play an important role in the transport of magnetic field and angular momentum. This is mainly due to the enhancement of magnetic back-reaction by shearing which efficiently generates small scales, thus strong currents. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Turbulence Diffusion and Energy Spectrum Analysis of Large-scale Current Sheets in Flares

Magnetic reconnection (MR) is one of the most important physical processes for many dynamical phenomena in the universe. Magnetohydrodynamical (MHD) simulation is an effective way to study the MR process and the physical pictures related to the MR. With different parameter setups, we investigate the influences of the Magnetic Reynolds number and spatial resolution on the reconnection rate, numerical dissipation, and energy spectrum distribution in the MHD simulation. We have found that the magnetic Reynolds number $R_m$ has definite impact on the reconnection rate and energy spectrum distribution. The characteristic time for entering into the non-linear phase will be earlier as the Reynolds number increases. When it comes to the tearing phase, the reconnection rate will increase rapidly. On the other hand, the magnetic Reynolds number affects significantly the Kolmogorov microscopic scale $l_{\mathit{ko}}$, which becomes smaller as $R_m$ increases. An extra dissipation is defined as the combined effect of the numerical diffusion and turbulence dissipation. It is shown that the extra dissipation is dominated by the numerical diffusion before the tearing mode instability takes place. After the instability develops, the extra dissipation rises vastly, which indicates that turbulence caused by the instability can enhance the diffusion obviously. Furthermore, the energy spectrum analysis indicates that $l_{\mathit{ko}}$ of the large-scale current sheet may appear at a macroscopic MHD scale very possibly.     

Magnetic Field Line Transport in Anisotropic Magnetic Turbulence: Anomalous, Quasilinear, and Percolative Regimes Versus the Kubo Number

The transport of plasma and of energetic particles because of magnetic turbulence is relevant to many space plasmas, ranging from the planetary magnetospheres to the solar corona and to the heliosphere. Various transport regimes for magnetic field lines can be obtained depending on the Kubo number. Here we show, by means of a numerical simulation, that the Kubo number also determines the level of chaos of the field lines. Weak chaos, closed magnetic surfaces, and anomalous transport regimes are obtained for R≪ 1; widespread chaos, destroyed magnetic surfaces, and quasilinear scaling of the diffusion coefficient for R ≳ 0.3; and global stochasticity as well as percolation scaling of the diffusion coefficient for R≫ 1. This revised version was published online in July 2006 with corrections to the Cover Date.     

Aspects of Three-Dimensional Magnetic Reconnection – (Invited Review)

In this review paper we discuss several aspects of magnetic reconnection theory, focusing on the field-line motions that are associated with reconnection. A new exact solution of the nonlinear MHD equations for reconnective annihilation is presented which represents a two-fold generalization of the previous solutions. Magnetic reconnection at null points by several mechanisms is summarized, including spine reconnection, fan reconnection and separator reconnection, where it is pointed out that two common features of separator reconnection are the rapid flipping of magnetic field lines and the collapse of the separator to a current sheet. In addition, a formula for the rate of reconnection between two flux tubes is derived. The magnetic field of the corona is highly complex, since the magnetic carpet consists of a multitude of sources in the photosphere. Progress in understanding this complexity may, however, be made by constructing the skeleton of the field and developing a theory for the local and global bifurcations between the different topologies. The eruption of flux from the Sun may even sometimes be due to a change of topology caused by emerging flux break-out. A CD-ROM attached to this paper presents the results of a toy model of vacuum reconnection, which suggests that rapid flipping of field lines in fan and separator reconnection is an essential ingredient also in real non-vacuum conditions. In addition, it gives an example of binary reconnection between a pair of unbalanced sources as they move around, which may contribute significantly to coronal heating. Finally, we present examples in TRACE movies of geometrical changes of the coronal magnetic field that are a likely result of large-scale magnetic reconnection. Supplementary material to this paper is available in electronic form at http://dx.doi.org/10.1023/A:1005248007615     

Magnetic reconnection and energy release in the solar corona by Taylor relaxation

The heating of the solar corona by resistive turbulence of coronal magnetic fields is considered. The theory of this process, based on the Taylor-Heyvaerts-Priest hypothesis and a magnetic relaxation equation, is developed. Such an approach allows one to obtain the successive magnetic reconnection configurations and energy balance of the coronal magnetic field in response to prescribed motions of the photospheric footpoints. Two specific models of the coronal magnetic configuration are investigated, namely an array of closely packed flux tubes and a two-dimensional magnetic arcade.     

Explosive reconnection in magnetars

The X-ray activity of anomalous X-ray pulsars and soft γ-ray repeaters may result from the heating of their magnetic corona by direct currents dissipated by magnetic reconnection. We investigate the possibility that X-ray flares and bursts observed from anomalous X-ray pulsars and soft γ-ray repeaters result from magnetospheric reconnection events initiated by development of the tearing mode in magnetically dominated relativistic plasma. We formulate equations of resistive force-free electrodynamics, discuss the relation of the latter to ideal electrodynamics, and give examples of both ideal and resistive equilibria. Resistive force-free current layers are unstable towards the development of small-scale current sheets where resistive effects become important. Thin current sheets are found to be unstable due to the development of the resistive force-free tearing mode. The growth rate of the tearing mode is intermediate between the short Alfvén time-scale  τ_A  and a long resistive time-scale  τ_R: Γ∼ 1/(τ_Rτ_A)^1/2  , similar to the case of non-relativistic non-force-free plasma. We propose that growth of the tearing mode is related to the typical rise time of flares, ∼10 ms. Finally, we discuss how reconnection may explain other magnetar phenomena and ways to test the model.     

Magnetic reconnection via tearing instability in a rotating viscous fluid

The resistive tearing instability of a sheet pinch, first investigated by Kuang & Roberts (1990) for the case of a rapidly rotating inviscid fluid, is studied for arbitrary rotation rate in a visco‐resistive fluid. Altogether there are three regimes of the resistive tearing instability which correspond to the particular parameter domain in the (Ω, P_m) plane. Here Ω is the angular velocity of the medium which is normalized to the Alfvén time and P_m is the magnetic Prandtl number. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)