Resistive tearing mode in coronal neutral sheets

The apparent stability of coronal neutral sheets with respect to the resistive tearing mode has been attributed by previous authors to the influence of a weak normal component of the confining magnetic field. To check this hypothesis a normal mode analysis is performed applying rigorously singular perturbation technique. Allowance is made for a value of the normal component which is large measured in the appropriate units deduced from the dynamics of the one-dimensional tearing mode. The structure of the eigenmodes is completely changed: the singular layer decays into a broad band of filaments with antiparallel flow directions and spatial oscillations in the perturbed current density appear. Surprisingly, the growth rate is not changed. If parameters for a typical neutral sheet in the middle corona (0.5 solar radii) are inserted, the result is that no stabilization by a normal component occurs, if the value of the growth time predicted by the one-dimensional theory is far shorter than ten minutes - independent of the values assumed for the width of the neutral sheet or the resistivity.     

剪切流动和电阻撕裂模的相互作用

本文在细长柱位形下数值研究了具有剪切流动的电流片中电阻撕裂模不稳定性的非线性演化。结果表明，电流片附近Ｓｅｃｈ形式的剪切流动，将导致电阻撕裂模不稳定性的发展，且不稳定性增长率随着剪切参数Ｒｒ的增加而增长，导致磁岛的形成和快速的磁能释放。这种剪切流动和撕裂模的耦合过程以及超热不稳定性的相互作用，改变了磁拱中的磁场剪切强度或者说电流密度梯度，从而驱动电阻撕裂模不稳定性的发展，这种过程对于等离子体电流密     

速度切变对撕裂模不稳定性影响的初步分析

在电流片两侧的基态速度场与磁场相互平行的位形下,讨论了速度切变对撕裂模不稳定性的影响.结果表明,只有当速度场的相对变化率与磁场的相对变化率符号相同(Sign(v_0/v_0)=sign(B_0~')),|v_0~'/v_0|≥|B_0'/B_0|时,速度切变有利于不稳定增长,否则不利于不稳定增长.     

Interaction between sheared flow and resistive tearing mode

We investigate the nonlinear evolution of resistive tearing mode in a current sheet with a sheared flow in a long, thin cylinder. The results show that a hyperbolic secant (sech) flow field will lead to instability of the resistive tearing mode, formation of magnetic islands and rapid release of magnetic energy. The coupling between sheared flow and the tearing mode and interaction between suprathermal instabilities change the degree of shear in the magnetic field (the electric current gradient) and drive the development of the instability. This process may be one of the mechanisms of solar flares.     

First phase heating and particle acceleration during solar flares by fast tearing modes

We develop a simple, but physically consistent, model of heating and particle acceleration by fast tearing modes, for modeling compact loop flares or erupting prominences. It is shown that there is a slow preheating, over many e -foldings of the instability, after which a rapid heating takes place in approximately one e-folding. The role of anomalous resistivity excited by the induced electric field during tearing is discussed, and how both thermal conduction and plasma expansion may play a role in cooling. Estimates for the total number of thermal and non-thermal electrons generated by one fast tearing mode are given, and it is argued that collisional tearing modes give rise to a primarily thermal plasma.     

Radiative and reconnection instabilities: Compressible and viscous effects

Filaments and flares are prominent indicators of the magnetic fields of solar activity. These instability phenomena arise from the influence of weak transport effects (radiation and resistivity, respectively) on coronal magnetodynamics and energy flow. We have previously shown that the filament and flare (tearing or reconnection) mechanisms are resistively coupled in sheared magnetic fields of the kind existing in active regions. The present paper expands this treatment to include the effects of compressibility and viscosity, which are most prominent at short wavelengths. The results show that compressibility affects the radiative mode, including a modest increase of its growth rate, and that viscosity modifies the tearing mode, partially through a decrease of its growth rate. A comprehensive discussion of the mode structures and flows is presented. The strongest effect found is a reversal, at very long wavelengths, of the radiative cooling of the resistive interior layer of the tearing mode, caused by compressional heating.     

Tearing mode instability in the atmosphere above a sunspot

We derived the energy balance equation in steady state and made numerical calculations for 37 sets of parameter values for three layers of the atmosphere. The main results are: 1) The energy density released by tearing mode instability rapidly falls with rising temperature. It is much greater in the colmnar pinch than in the thin plate pinch. 2) The critical temperature increases with the intensity of the sheared magnetic field and decreases with its width. It is higher in the columnar pinch, and the rise time is shorter, than in the thin plate pinch. 3) At the surface of the photosphere, the energy released by tearing mode instability raises the local temperature by less than 1 K. 4) When the sheared width of the magnetic field is below a certain threshold, the local temperature is raised sharply to over (+6) K. This threshold is an increasing function of the strength of the sheared field. Our calculated results fit the observations to within one order of magnitude.     

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)     

Optimal Energy Growth in Current Sheets

In this article, we investigate the possibility of transient growth in the linear perturbation of current sheets. The resistive magnetohydrodynamics operator for a background field consisting of a current sheet is non-normal, meaning that associated eigenvalues and eigenmodes can be very sensitive to perturbation. In a linear stability analysis of a tearing current sheet, we show that modes that are damped as \(t\rightarrow \infty \) can produce transient energy growth, contributing faster growth rates and higher energy attainment (within a fixed finite time) than the unstable tearing mode found from normal-mode analysis. We determine the transient growth for tearing-stable and tearing-unstable regimes and discuss the consequences of our results for processes in the solar atmosphere, such as flares and coronal heating. Our results have significant potential impact on how fast current sheets can be disrupted. In particular, transient energy growth due to (asymptotically) damped modes may lead to accelerated current sheet thinning and, hence, a faster onset of the plasmoid instability, compared to the rate determined by the tearing mode alone.     

1986年2月4日耀斑与电流环合并不稳定性

本文收集了１９８６年２月４日大耀斑的Ｈα、微波、Ｘ射线和γ射线全波段的观测资料。利用暗条电流环模型分析了该耀斑的物理过程，测量了活动暗条的上升运动，求解了动量方程和能量方程。结果表明：（１）１９８６年２月４日的３Ｂ／Ｘ３耀斑可能是由暗条电流环之间的合并不稳定性所致；（２）电阻撕裂摸不稳定性是一种有效的耀斑前预热机制；（３）耀斑的高能观测资料进一步表明了电流环合并不稳定性是引起该大耀斑期间所有高能粒     

Excitation of high-m tearing modes at the solar flare site

It is shown that high-m drift tearing modes can be excited under the conditions prevalent at the solar flare sites. Since the growth rate of the high-m tearing modes is larger than that for low-m macroscopic tearing modes and smaller than that of microscopic ion-acoustic instability, these modes warrant accommodation in the scheme of instabilities possibly operating in the hybrid model of solar flares suggested by Spicer.     

The reason for magnetospheric substorms and solar flares

It has been proposed that magnetospheric substorms and solar flares are a result of the same mechanism. In our view this mechanism is connected with the escape, or attempted escape, of energized plasma from a region of closed magnetic field lines bounded by a magnetic bottle. In the case of the Earth, it must be plasma that is able to maintain a discrete auroral arc, and we propose that the cross-tail current connected to the arc is filamentary in nature to provide the field-aligned current sheet above the arc. A localized meander of such an intense current filament could be caused by a tearing instability in the neutral sheet. Such a meander will cause an inductive electric field opposing the current change everywhere. In trying to reduce the component of the induction electric field parallel to the magnetic field lines, the plasma must enhance the transverse or cross-tail component; this action leads to eruptive behavior, in agreement with tearing theories. This enhanced induction electric field will cause a discharge along the magnetic neutral line at the apex of the magnetic arches, constituting an impulsive acceleration of all charged particles originally near the neutral line. The products of this phase then undergo betatron acceleration for a second phase. This discharge eventually reduces the electric field along the neutral line, and thereafter the enclosed magnetic flux through the neutral line remains nearly constant. The result is a plasmoid that has definite identity; its buoyancy leads to its escape. The auroral breakup (and solar flare) is the complex plasma response to the changing electromagnetic field.     

Tearing instability in the pulsar magnetosphere

Equations governing the coupling of the scalar and vector potentials for a resistive electron-positron plasma in a strong magnetic field are derived. It is shown that in the presence of magnetic shear, a tearing instability may occur. The latter can lead to magnetic field line reconnection and the formation of magnetic islands which could affect the dynamics of the pulsar magnetosphere.     

The dynamics of the energetic proton bursts in the course of the magnetic field topology reconstruction in the earth‘s magnetotail

The paper considers the energy spectrum of particles accelerated near X-point of the magnetic field in the course of the tearing instability development in the current layer. The time dynamics of the spectrum at the linear and nonlinear stages of the instability is studied. The contribution of the particles inflowing into the vicinity of the magnetic X-point due to drift in the crossed electrical and magnetic fields was also taken into account. The dynamics of particle acceleration is numerically simulated and the results of the simulation are compared with the theoretical model. The analytical and numerical calculations are in reasonable agreement with the results of IMP satellites 7 and 8 energetic proton measurements in a wide energy interval.     

Loop models of solar flares: Revisions and comparisons

Due to developments in solar flare observations which appear to show that a particular class of solar flares result from instabilities occurring in magnetic loops we re-examine the Alfvén-Carlqvist flare model to show that it is workable and we update the Spicer loop model of a flare. It is noted that the Alfvén-Carlqvist model of necessity requires an external current driver which must maintain the current driven instability at marginal stability during the duration of the flare. In addition, it is argued that if the Alfvén-Carlqvist model is to work the current density must rise in a time shorter than an MHD or resistive tearing mode time scale. Otherwise, the dominant flare mechanism must be an ideal MHD or tearing type instability. Further, the distinctions between the two models are highlighted and a new hybrid model of the Alfvén-Carlqvist and Spicer models is introduced.     

Inertia driven tearing modes in electron-positron plasmas

It is shown that the particle inertia can cause a tearing instability in an electron-positron collisionless plasma with sheared magnetic fields. An approximate analytical expression for the growth rate is obtained. It characterizes the magnetic reconnection timescale in a magnetized electronpositron plasma.     

A hybrid simulation study of magnetic reconnection in anisotropic plasmas

The process of magnetic reconnection in anisotropic plasmas is studied numerically using a 2-dimensional, 3-component hybrid simulation. The results of the calculation show that, when the plasma pressure in the direction perpendicular to magnetic field is larger than that in the parallel direction (e.g. P/P = 1.5), instability may greatly increase, speeding up the rate of reconnection. When P is smaller than P, (e.g., when P/P = 0.6), fire hose instability appears, which will restrain the tearing mode instability and the process of magnetic reconnection.     

The 4 February, 1986 flare and flare-filament current model

In this paper, the observational data in H, radio, soft X-ray, hard X-ray, and -ray emissions for the 3B/X3.0 solar flare on 4 February, 1986 are collected. This flare is studied in detail by using the flare-filament current model. The momentum equations and the energy equations of the filament current have been solved. The influence of the highly sheared background magnetic field on the motion of the filaments is studied through numerical calculation. The results show that the resistive tearing instability is a possible pre-heating mechanism in the preflare phase, and both the rotation of the spiral sunspots and the highly sheared background field are necessary for the energy storage of this flare. The high-energy data of the flare imply that the current-loop coalescence instability is a possible eruptive mechanism.     

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.     

耀斑大尺度电流片的湍流耗散和能谱分析

磁重联在宇宙的许多动力学现象中都是非常核心的过程.磁流体动力学(MHD)数值模拟是研究磁重联过程以及相应物理图像的一种很有效的手段.通过不同的参数组合,来研究MHD数值模拟中磁雷诺数和空间分辨率对磁重联率、数值耗散和能谱分布的影响.对得到的数据进行分析后,发现磁雷诺数对磁重联率和能谱分布有一定的影响.磁雷诺数越大,磁重联过程进入非线性阶段所需的特征时间越短,磁重联率就越早发生跃升.磁雷诺数R_m对耗散开始发挥作用的Kolmogorov微观尺度l_ko有明显影响:R_m越大,l_ko就越小.研究了磁重联过程中包括数值耗散在内的额外耗散对重联过程的影响.结果表明,撕裂模不稳定性开始之前的额外耗散以纯数值耗散为主,撕裂模不稳定性出现之后,额外耗散出现同步跃升,说明不稳定性导致的湍流明显增强了耗散的效果,相当于在局部湍流区引入了超电阻.能谱分析进一步表明,大尺度电流片的l_ko完全可能出现在宏观的MHD尺度上.