The rate of flux pile-up magnetic reconnection in reduced MHD

The rate of two-dimensional flux pile-up magnetic reconnection is known to be severely limited by gas pressure in a low-beta plasma of the solar corona. As earlier perturbational calculations indicated, however, the pressure limitation should be less restrictive for three-dimensional flux pile-up. In this paper the maximum rate of reconnection is calculated in the approximation of reduced magnetohydrodynamics (RMHD), which is valid in the solar coronal loops. The rate is calculated for finite-magnitude reconnecting fields in the case of a strong axial field in the loop. Gas pressure effects are ignored in RMHD but a similar limitation on the rate of magnetic merging exists. Nevertheless, the magnetic energy dissipation rate and the reconnection electric field can increase by several orders of magnitude as compared with strictly two-dimensional pile-up. Though this is still not enough to explain the most powerful solar flares, slow coronal transients with energy release rates of order 10²⁵– 10²⁶ erg s^–1and heating of quiet coronal loops are within the compass of the model.     

无碰撞重联区中的混沌感应电阻

无碰撞磁场重联作为一种将磁能有效转化为等离子体动能和热能的机制,已经被广泛应用于解释太阳耀斑、地球磁暴等各类等离子体的爆发活动.然而,在无碰撞重联区中反常电阻的微观物理机制仍然是尚未解决的基本问题.在众多反常电阻的形成机制中,基于磁零点附近粒子轨道混沌性产生的混沌感应电阻,虽然不是最普遍流行的形成机制,但它的微观物理图像却是最为清晰的.回顾了无碰撞重联区中混沌感应电阻的早期研究和基本理论模型,介绍了关于混沌感应电阻研究的新进展并阐述了混沌感应电阻未来的研究方向.     

Visco-Resistive Dissipation in Strongly Driven Transient Reconnection

Solar flare energy release mechanisms often neglect the role played by viscous effects. Here we perform incompressible planar reconnection simulations, driven by the Orszag–Tang vortex, for both classical and Braginskii forms of the viscosity. We show that strongly driven “saturated” flux pile-up current layers, which lead to weak reconnection rates at small resistivities, are accompanied by invariant global viscous losses. These results support the notion that viscous dissipation in flaring plasmas can account for a significant fraction of the flare energy release.     

The Pressure Limitations on Flux Pile-up Reconnection

The problem of the plasma pressure limitations on the rapidity of flux pile-up magnetic reconnection is re-examined, following the claim made by Jardine and Allen (1998) that the limitations can be removed by relaxing the assumption of zero-vorticity two-dimensional plasma flows. It is shown that for a two-dimensional stagnation point flow with nonzero vorticity the magnetic merging rate cannot exceed the Sweet–Parker scaling in a low-beta plasma. The pressure limitation appears to be much less restrictive for weak three-dimensional flux pile-up, provided the perturbation length scale in the third dimension is much less than the global length scale. The actual reconnection rate in the latter case, however, is much lower than this upper estimate unless the current sheet width is also much less than the global scale.     

Magnetic Energy Release in Flux Pile-up Merging

The problem of pressure limitations on the rate of flux pile-up magnetic reconnection is studied. We first examine the recent suggestion of Jardine and Allen (1998) for moderating the build-up of magnetic pressure in the current sheet by considering inflows with nonzero vorticity. An analytic argument shows, however, that unbounded magnetic pressures in the limit of small resistivities can be avoided only at the cost of unphysical dynamic pressures in the plasma. Hence, the pressure limitation on the reconnection rate in a low-beta plasma cannot be avoided completely. Nevertheless, we demonstrate that reconnection can be more rapid in a new solution that balances the build-up in dynamic pressure against both the plasma and magnetic pressures. This exact MHD solution has the characteristics of merging driven by the coalescence instability. The maximum energy release rate of the model is capable of explaining a modest solar flare.     

The role of the magnetic barrier in the Solar wind-magnetosphere interaction

The magnetized solar wind carries a large amount of energy but only a small fraction of it enters the magnetosphere and powers its dynamics. Numerous observations show that the interplanetary magnetic field (IMF) is a key parameter regulating the solar wind-magnetosphere interaction. The main factor determining the amount of energy extracted from the solar wind flow by the magnetosphere is the plasma flow structure in the region adjacent to the sunward side of the magnetopause. While compared to the energy of the solar wind flow the IMF magnetic energy is relatively weak, it is considerably enhanced in a thin layer next to the dayside magnetopause variously called the plasma depletion layer or magnetic barrier. Important features of this barrier/layer are (i) a pile-up of the magnetic field with (ii) a concurrent decrease of density, (iii) enhancement of proton temperature anisotropy, (iv) asymmetry of plasma flow caused by magnetic field tension, and (v) characteristic wave emissions (ion cyclotron waves). Importantly, the magnetic barrier can be considered as an energy source for magnetic reconnection. While the steady-state magnetic barrier has been extensively examined, non-steady processes therein have only been addressed by a few authors. We discuss here two non-steady aspects related to variations of the magnetic barrier caused by (i) a north-to-south rotation of the IMF, and (ii) by pulses of magnetic field reconnection at the magnetopause. When the IMF rotates smoothly from north-to-south, a transition layer is shown to appear in the magnetosheath which evolves into a thin layer bounded by sharp gradients in the magnetic field and plasma quantities. For a given reconnection rate and calculated parameters of the magnetic barrier, we estimate the duration and length scale of a reconnection pulse as a function of the solar wind parameters. Considering a sudden decrease of the magnetic field near the magnetopause caused by the reconnection pulse, we study the relaxation process of the magnetic barrier. We find that the relaxation time is longer than the duration of the reconnection pulse for large Alfvén-Mach numbers.     

Magnetic field reconnection in a compressible plasma

An extension of Sonnerup's model for the magnetic field-line reconnection for a compressible plasma is given. The plasma is considered to be only slightly compressible so that the leading wave in Sonnerup's model can still be taken to be a thin discontinuity. The flow is assumed to occur under adiabatic conditions, and de Hoffmann-Teller jump conditions are used to connect the state variables across the shocks. The compressibility effects are found to increase the reconnection rate. The signaling problem is finally considered to study the evolution of MHD waves in a compressible, dissipative plasma so as to investigate the conditions under which the assumption of MHD waves in a compressible plasma to be thin discontinuities is valid.     

Dynamics of cosmic current layers with localized lower-hybrid-drift turbulence

A two-dimensional magnetohydrodynamic model of the dynamics of tail-like current layers caused by anomalous electrical resistivity in a plasma with lower-hybrid-drift (LHD) turbulence is considered. Additionally to the LHD-resistivity, a resistivity pulse in the magnetic neutral sheet is given initiating a magnetic reconnection process. Then the temporal and spatial evolution of the magnetic and electric fields, the plasma convection and the anomalous resistivity are obtained numerically. Taking into account more exact expressions for the LHD-resistivity in the current layer as done in former works, the LHD-turbulence is found to be excited farther from the neutral sheet, and thus, with the time, secondary current sheets are obtained in the plasma-magnetic field system. It is shown that the inductive electric field moving from the magnetic neutral sheet to the current layer periphery during the reconnection process may be considered as indicator of the plasma disturbances.     

Driven magnetic field reconnection

We consider the magnetic field reconnection in a plasma induced by perturbing the boundaries of a slab of incompressible plasma with a magnetic neutral surface inside. We assume that the boundaries of the plasma slab are perturbed at a rate which is fast compared with the hydromagnetic evolution rate; and investigate the ensuing adjustments in the plasma and the magnetic field threading through it.     

Chaos-induced resistivity of collisionless magnetic reconnection in the presence of a guide field

One of the most puzzling problems in astrophysics is to understand the anomalous resistivity in collisionless magnetic reconnection that is believed extensively to be responsible for the energy release in various eruptive phenomena. The magnetic null point in the reconnecting current sheet, acting as a scattering center, can lead to chaotic motions of particles in the current sheet, which is one of the possible mechanisms for anomalous resistivity and is called chaos-induced resistivity. In many interesting cases, however, instead of the magnetic null point, there is a nonzero magnetic field perpendicular to the merging field lines, usually called the guide field, whose effect on chaos-induced resistivity has been an open problem. By use of the test particle simulation method and statistical analysis, we investigate chaos-induced resistivity in the presence of a constant guide field. The characteristics of particle motion in the reconnecting region, in particular, the chaotic behavior of particle orbits and evolving statistical features, are analyzed. The results show that as the guide field increases, the radius of the chaos region increases and the Lyapunov index decreases. However, the effective collision frequency, and hence the chaos-induced resistivity, reach their peak values when the guide field approaches half of the characteristic strength of the reconnection magnetic field. The presence of a guide field can significantly influence the chaos of the particle orbits and hence the chaos-induced resistivity in the reconnection sheet, which decides the collisionless reconnection rate. The present result is helpful for us to understand the microphysics of anomalous resistivity in collisionless reconnection with a guide field.     

Flare-like energy release by flux pile-up reconnection

Flux pile-up magnetic merging solutions are discussed using the simple robust arguments of traditional steady-state reconnection theory. These arguments determine a unique scaling for the field strength and thickness of the current layer, namely B _s^–1/3, l^2/3, which are consistent with a variety of plasma inflow conditions. Next we demonstrate that flux pile-up merging can also be understood in terms of exact magnetic annihilation solutions. Although simple annihilation models cannot provide unique reconnection scalings, we show that the previous current sheet scalings derive from an optimized solution in which the peak dynamic and magnetic pressures balance in the reconnection region. The build-up of magnetic field in the current sheet implicit in flux pile-up solutions naturally leads to the idea of saturation. Hydromagnetic pressure effects limit the magnetic field in the sheet, yielding an upper limit on the reconnection rate for such solutions. This rate is still far superior to the Sweet–Parker merging rate, which can be derived by seeking solutions that avoid all forms of saturation. Finally we compare time dependent numerical simulations of the coalescence instability with the optimized flux pile-up models. This comparison suggests that merging driven by the relatively slow approach of large flux systems may be favored in practice.     

Optimized magnetic reconnection solutions in three dimensions

It has recently been shown that there is a well defined upper limit to the rate of magnetic merging for two-dimensional flux pile-up solutions. This rate, derived by equalizing the dynamic and magnetic pressures in the reconnection region and saturating the magnetic field in the current layer, leads to a significant enhancement of the classical Sweet–Parker merging limit. In this study we explore optimal merging rates in the case of three-dimensional fan and spine reconnection solutions. The ideas of optimization and saturation are first illustrated using an exact fan solution. We go on to show that while spine solutions seem ineffective as flare release mechanisms, optimized fan solutions have energy release characteristics typical of modest events.     

Fast magnetic reconnection with Cowling’s conductivity

The aim of the present paper is to explore the mechanism of fast Sweet–Parker’s magnetic reconnection with the Cowling’s conductivity. Cowling derived the resistivity of plasma with three components: electrons, ions and neutral particles in magnetic field theoretically after Spitzer. The resistivity is much larger than the Spitzer’s. According to the idea of partially ionized plasmas ejected into the corona as the trigger of flares, we adopt Cowling’s Conductivity to Sweet–Parker’s reconnection model in this paper. The result shows that the reconnection rate can be improved a lot in solar corona and approaches the timescale of solar flare in the absence of anomalous resistivity.     

Test particle acceleration in torsional spine magnetic reconnection

Three-dimensional (3D) magnetic reconnection is taking place commonly in astrophysical and space plasmas, especially in solar flares which are rich sources of highly energetic particles. One of the proposed mechanisms for steady-state 3D magnetic reconnection is “torsional spine reconnection”. By using the magnetic and electric fields for “torsional spine reconnection”, we numerically investigate the features of test particle acceleration with input parameters for the solar corona. We show that efficient acceleration of a relativistic proton is possible near the null point where it can gain up to 100 MeV of kinetic energy within a few milliseconds. However, varying the injection position results in different scenarios for proton acceleration. A proton is most efficiently accelerated when it is injected at the point where the magnetic field lines change their curvature in the fan plane. Moreover, a proton injected far away from the null point cannot be accelerated and, even in some cases, it is trapped in the magnetic field. In addition, adopting either spatially uniform or non-uniform localized plasma resistivity does not much influence the features of trajectory.     

Energy balance in current sheets: From Petschek to gravity driven reconnection?

It has been shown earlier that energy balance processes play a very important role in the determination of the reconnection regime in the central diffusive region of a steady Petschek flow (usually considered elsewhere as isothermal and incompressible): as a consequence of the plasma thermal properties, abrupt transitions in the reconnection regime may occur for special external conditions. The regime becomes then a dynamical one, and it was suggested that onset of plasma microturbulence may result and act as a primary triggering mechanism in solar flares.In this paper we will reexamine the problem of onset of such dynamical transition and conclude that plasma microturbulence does not appear in a straightforward way. However it is possible that the canonical Petschek regime may evolute into a new one in which the dissipative sheet is no longer infinitesimal with respect to the dimensions of the structure, and in which gravity plays an important role. Flare triggering, if related to the reconnection regime, must then proceed by more complex processes, possibly related to tearing mode dynamics, or to more global properties of the magnetic structure of the active region.     

The study of magnetic reconnection in solar spicules

This work is devoted to study the magnetic reconnection instability under solar spicule conditions. Numerical study of the resistive tearing instability in a current sheet is presented by considering the magnetohydrodynamic (MHD) framework. To investigate the effect of this instability in a stratified atmosphere of solar spicules, we solve linear and non-ideal MHD equations in the x?z plane. In the linear analysis it is assumed that resistivity is only important within the current sheet, and the exponential growth of energies takes place faster as plasma resistivity increases. We are interested to see the occurrence of magnetic reconnection during the lifetime of a typical solar spicule.     

Numerical simulation of reconnection in an emerging magnetic flux region

The resistive MHD equations are numerically solved in two dimensions for an initial-boundary-value problem which simulates reconnection between an emerging magnetic flux region and an overlying coronal magnetic field. The emerging region is modelled by a cylindrical flux tube with a poloidal magnetic field lying in the same plane as the external, coronal field. The plasma betas of the emerging and coronal regions are 1.0 and 0.1, respectively, and the magnetic Reynolds number for the system is 2 × 10³. At the beginning of the simulation the tube starts to emerge through the base of the rectangular computational domain, and, when the tube is halfway into the computational domain, its position is held fixed so that no more flux of plasma enters through the base. Because the time-scale of the emergence is slower than the Alfvén time-scale, but faster than the reconnection time-scale, a region of closed loops forms at the base. These loops are gradually opened and reconnected with the overlying, external magnetic field as time proceeds.The evolution of the plasma can be divided into four phases as follows: First, an initial, quasi-steady phase during which most of the emergence is completed. During this phase, reconnection initially occurs at the slow rate predicted by the Sweet model of diffusive reconnection, but increases steadily until the fast rate predicted by the Petschek model of slow-shock reconnection is approached. Second, an impulsive phase with large-scale, super-magnetosonic flows. This phase appears to be triggered when the internal mechanical equilibrium inside the emerging flux tube is upset by reconnection acting on the outer layers of the flux tube. During the impulsive phase most of the flux tube pinches off from the base to form a cylindrical magnetic island, and temporarily the reconnection rate exceeds the steady-state Petschek rate. (At the time of the peak reconnection rate, the diffusion region at the X-line is not fully resolved, and so this may be a numerical artifact.) Third, a second quasi-steady phase during which the magnetic island created in the impulsive phase is slowly dissipated by continuing, but low-level, reconnection. And fourth, a static, non-evolving phase containing a potential, current-free field and virtually no flow.During the short time in the impulsive phase when the reconnection rate exceeds the steady-state Petschek rate, a pile-up of magnetic flux at the neutral line occurs. At the same time the existing Petschek-slow-mode shocks are shed and replaced by new ones; and, for a while, both new and old sets of slow shocks coexist.     

Generalized analytical models of Syrovatskii’s current sheet

Two-dimensional stationary magnetic reconnection models that include a thin Syrovatskii-type current sheet and four discontinuous magnetohydrodynamic flows of finite length attached to its endpoints are considered. The flow pattern is not specified but is determined from a self-consistent solution of the problem in the approximation of a strong magnetic field. Generalized analytical solutions that take into account the possibility of a current sheet discontinuity in the region of anomalous plasma resistivity have been found. The global structure of the magnetic field in the reconnection region and its local properties near the current sheet and attached discontinuities are studied. In the reconnection regime in which reverse currents are present in the current sheet, the attached discontinuities are trans-Alfvénic shock waves near the current sheet endpoints. Two types of transitions from nonevolutionary shocks to evolutionary ones along discontinuous flows are shown to be possible, depending on the geometrical model parameters. The relationship between the results obtained and numerical magnetic reconnection experiments is discussed.     

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.     

Plasma Heating by Forced Magnetic Reconnection

A model of forced magnetic reconnection in a force-free magnetic field is considered, which allows calculation of the magnetic energy release during the current sheet reconnection. The dependence of this energy on characteristics of the magnetic configuration has been studied, and it was found that the released energy becomes very large when the field is near the marginal tearing stability. A persistent plasma heating provided by ongoing external driving and internal reconnection is also derived. It shows a typical relaxation-type dependence on the driving frequency, with dissipation becoming most efficient when the time-scales of the driving and reconnection are comparable. Possible implications of the obtained results for the problem of solar coronal heating are discussed. This revised version was published online in July 2006 with corrections to the Cover Date.