Forced reconnexion by fast magnetosonic waves in a current sheet with stagnation-point flows

1983 ◽  
Vol 30 (1) ◽  
pp. 109-124 ◽  
Author(s):  
Jun-Ichi Sakai
Keyword(s):  
Current Sheet ◽  
Stagnation Point ◽  
Solar Flares ◽  
Ponderomotive Force ◽  
Magnetosonic Wave ◽  
Fast Wave ◽  
Tearing Mode ◽  
Tearing Modes ◽  
Tearing Instability ◽  
A Current

Forced reconnexion due to tearing modes driven by fast magnetosonic waves in a current sheet with stagnation-point flows is discussed. The current sheet with stagnation-point flows which is weakly unstable against tearing modes can be strongly destabilized by vortex motions due to the ponderomotive force of the fast magnetosonic wave. This forced tearing instability can be driven when the incident fast magnetosonic wave intensity, I, exceeds a critical value given by where is the Alfvén velocity, vg the group velocity of the fast wave, vo the background inflow velocity, l the thickness of the current sheet and k the wavenumber of the forced tearing mode. The growth rate is estimated. Applications to solar flares and magnetopause reconnexion processes are briefly discussed.

Resistive tearing-mode instability in a current sheet with equilibrium viscous stagnation-point flow

1991 ◽  
Vol 46 (3) ◽  
pp. 407-421 ◽  
Author(s):  
T. D. Phan ◽  
B. U.Ö. Sonnerup
Keyword(s):  
Growth Rate ◽  
Current Sheet ◽  
Stagnation Point ◽  
Solar Wind Plasma ◽  
Stagnation Point Flow ◽  
Growth Time ◽  
Tearing Mode ◽  
Long Wavelength ◽  
Tearing Modes ◽  
A Current

An analysis is presented of linear stability against tearing modes of a current sheet formed between two oppositely magnetized plasmas forced towards each other in two-dimensional steady stagnation-point flow. The velocity vector in this flow is confined to planes perpendicular to the reversing component of the magnetic field. The unperturbed state is an exact resistive and viscous equilibrium in which the resistive diffusion outwards from the current sheet is exactly balanced by the inward motion associated with the stagnation-point flow. Thus the behaviour of the tearing mode can be examined even when the resistive diffusion time is comparable to or smaller than the growth time of the instability. The linear ordinary differential equation describing the mode structure is integrated numerically. For large Lundquist number S and viscous Reynolds number Re the Furth-Killeen-Rosenbluth scaling of the growth rate is recovered with excellent accuracy. The influence of the stagnation-point flow on the tearing mode is as follows: (i) long-wavelength perturbations are stabilized so that the unstable regime falls between a short-wavelength and a long-wavelength marginal state; (ii) for sufficiently low Lundquist number (S < 12.25) the current sheet is completely stable to tearing-mode perturbations; (iii) the presence of high viscosity reduces the growth rate of the tearing instability. This effect is more important at small wavelength. Finally, application of the results from this study to the problem of solar-wind plasma flow past the earth's magnetosphere is briefly discussed.

scholarly journals Resistive Processes in the Preflare Phase of Eruptive Flares

1998 ◽  
Vol 188 ◽  
pp. 207-208
Author(s):  
T. Magara ◽  
K. Shibata
Keyword(s):  
Current Sheet ◽  
Current Density ◽  
Solar Flares ◽  
Magnetic Pressure ◽  
Anomalous Resistivity ◽  
Magnetic Island ◽  
Tearing Instability ◽  
Mhd Simulations ◽  
A Current

In this study, we perform 2.5-dimensional MHD simulations and clarify the role of perpendicular magnetic fields (which are perpendicular to the 2D plane) in a preflare current sheet of solar flares. At the first stage, a current sheet formed within a coronal magnetic structure is filled with the perpendicular fields (force-free structure). Then this sheet begins to be dissipated through the tearing instability under a uniform resistivity. As the instability proceeds, the distribution of the perpendicular fields vary in such a way that most of them gather around O-point (magnetic island) instead of X-point. Therefore, the magnetic pressure of these fields weaken in the vicinity of X-point so that they no longer suppress the inflows toward this point. These flows then make the current sheet thinner and thinner, which implies that the current density around X-point becomes high enough to cause an anomalous resistivity whose value is much larger than that of the normal collisional resistivity. In this way, the transition from a uniform resistivity to a locally-enhanced one occurs, which can make the violent energy release observed in solar flares.

scholarly journals Kinetic simulations of the coupling between current instabilities and reconnection in thin current sheets

2000 ◽  
Vol 7 (3/4) ◽  
pp. 141-150 ◽  
Author(s):  
T. Wiegelmann ◽  
J. Büchner
Keyword(s):  
Magnetic Reconnection ◽  
Current Flow ◽  
Flow Direction ◽  
Substantial Contribution ◽  
Tearing Mode ◽  
Tearing Modes ◽  
Tearing Instability ◽  
Instability Modes ◽  
Thin Current Sheet ◽  
Spatial Dimensions

Abstract. We investigate the coupling between current and tearing instability modes of a thin current sheet using the particle code GISMO. We identify pure tearing modes (kx≠ 0), instabilities in the current flow direction (ky≠ 0) and general 3D reconnection modes (kx≠ 0 and ky≠ 0). Our results give evidence that the coupling between tearing modes and current instabilities plays an important role for spontaneous magnetic reconnection. These modes give a substantial contribution to magnetic reconnection, additional to the well known 2D tearing mode. When allowing reconnection to occur in three spatial dimensions, a configuration, which was initially invariant in the current How direction, develops into a configuration with no invariant direction.

Resistive MHD stagnation-point flows at a current sheet

1975 ◽  
Vol 14 (2) ◽  
pp. 283-294 ◽  
Author(s):  
B. U. Ö. Sonnerup ◽  
E. R. Priest
Keyword(s):  
Magnetic Field ◽  
Current Sheet ◽  
Stagnation Point ◽  
Three Dimensional ◽  
Mhd Equations ◽  
Viscous Effects ◽  
Three Dimensional Flow ◽  
Merging Process ◽  
The Magnetic Field ◽  
A Current

A family of exact solutions to the MHD equations is presented for steady incompressible two- and three-dimensional flow in the vicinity of the stagnation point, which forms in a current sheet separating two colliding plasma streams. The magnetic field in each plasma is strictly parallel to the current sheet, but can have different magnitudes and directions. Resistive and viscous effects are accounted for. These flows are of considerable interest in connexion with the magnetic field merging process. They represent the limit of resistive field annihilation with zero reconnexion.

Resistive tearing-mode instability in a magnetic-field-reversing current sheet with coplanar viscous stagnation-point flow

1996 ◽  
Vol 56 (2) ◽  
pp. 265-284 ◽  
Author(s):  
Justin T. C. Ip ◽  
Bengt U. Ö. Sonnerup
Keyword(s):  
Magnetic Field ◽  
Current Sheet ◽  
Stagnation Point ◽  
Linear Growth ◽  
Field Configuration ◽  
Stagnation Point Flow ◽  
Magnetic Islands ◽  
Tearing Mode ◽  
Mode Instability ◽  
Simulation Results

The tearing-mode instability of a magnetic-field-reversing current sheet in the presence of coplanar incompressible stagnation-point flow is examined. The unperturbed equilibrium state is an exact solution of the steady-state, dissipative, incompressible magnetohydrodynamic equations; thus the analysis is valid even for small viscous and resistive Lundquist numbers Sν and Sη. The instability problem has no known analytical solution; for this reason, it is studied numerically by use of a finite-element method. Simulation results indicate stability for sufficiently small values of Sν or Sη and instability for large values. The boundary separating stable and unstable regions in the (Sν, Sη) plane is located. In the unstable regime, the simulation results show formation and subsequent convection of magnetic islands along the current sheet at about 80% of the unperturbed outflow flow speed, on average. Stretching and pinching of convecting magnetic islands are also observed. The results show the occurrence of multiple X-line reconnection at the centre of the current sheet (x = 0). Small-scale structures of vorticity and current density near the X-point reconnection sites are found to be qualitatively consistent with results obtained by Matthaeus. Normalized global linear growth rates are found to obey the approximate power law, within the ranges 20 ≦ Sν ≦ 70 and 200 ≦ Sη 1000. At least for Sν ≦ 1000, the number of magnetic islands is found to be nearly independent of Sν indicating the existence of a narrow band of dominant wavelengths in this range. The stretching of magnetic islands, which is present in this coplanar flow and field configuration, but not in the perpendicular flow and field configuration examined by Phan and Sonnerup, causes a substantial decrease in linear growth rate relative to that obtained by those authors. The stability curves obtained are qualitatively similar in both analyses, but the stable region is much larger for coplanar flow and field. Unlike most simulations of the tearing mode, no symmetry conditions are imposed on the perturbations; nevertheless, they develop in a symmetric manner.

MHD stagnation-point flows at a current sheet including viscous and resistive effects: general two-dimensional solutions

1990 ◽  
Vol 44 (3) ◽  
pp. 525-546 ◽  
Author(s):  
T. D. Phan ◽  
B. U. Ö. Sonnerup
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Current Sheet ◽  
Stagnation Point ◽  
Angle Of Incidence ◽  
Two Dimensional ◽  
Viscous Effects ◽  
Special Cases ◽  
The Magnetic Field ◽  
A Current

Exact solutions are presented of two-dimensional steady-state incompressible stagnation point flows at a current sheet separating two colliding plasmas. They describe the process of resistive field annihilation (zero reconnection) where the magnetic field in each plasma is strictly parallel to the current sheet, but may have different magnitudes and direction on its two sides. The flow in the (x, y) plane toward the current sheet, located at x = 0, may have an arbitrary angle of incidence and an arbitrary amount of divergence from or convergence towards the stagnation point. We find the most general form of the solution for the plasma velocity and for the magnetic field. For the z compenents of the flow and field, solutions in the form of truncating power series in y are found. The cases obtained in this study contain the solutions obtained by Parker, Sonnerup & Priest, Gratton et al. and Besser, Biernat & Rijnbeek as special cases. The role of viscosity in determining the flow and field configurations is examined. When the two colliding plasmas have the same viscosity and density, it is shown that viscous effects usually are important only in strongly divergent or convergent viscous flows with viscous Reynolds number of the order of unity or smaller. For astrophysical applications the viscous Reynolds number is usually high and the effects of viscosity on the interaction of plasmas of similar properties are small. The formulation of the stagnation-point flow problem involving plasmas of different properties is also presented. Sample cases of such flows are shown. Finally, a possible application of the results from this study to the earth's magnetopause is discussed briefly.

scholarly journals Effect of guide field on three-dimensional electron shear flow instabilities in electron current sheets

2015 ◽  
Vol 81 (6) ◽  
Author(s):  
Neeraj Jain ◽  
Jörg Büchner
Keyword(s):  
Shear Flow ◽  
Current Sheet ◽  
Three Dimensional ◽  
Sheet Thickness ◽  
Electron Current ◽  
Tearing Mode ◽  
Current Sheets ◽  
Tearing Modes ◽  
Guide Field ◽  
Half Thickness

We examine, in the limit of electron plasma ${\it\beta}_{e}\ll 1$, the effect of an external guide field and current sheet thickness on the growth rates and nature of three-dimensional (3-D) unstable modes of an electron current sheet driven by electron shear flow. The growth rate of the fastest growing mode drops rapidly with current sheet thickness but increases slowly with the strength of the guide field. The fastest growing mode is tearing type only for thin current sheets (half-thickness ${\approx}d_{e}$, where $d_{e}=c/{\it\omega}_{pe}$ is the electron inertial length) and zero guide field. For finite guide field or thicker current sheets, the fastest growing mode is a non-tearing type. However, growth rates of the fastest 2-D tearing and 3-D non-tearing modes are comparable for thin current sheets ($d_{e}<\text{half thickness}<2\,d_{e}$) and small guide field (of the order of the asymptotic value of the component of magnetic field supporting the electron current sheet). It is shown that the general mode resonance conditions for tearing modes depend on the effective dissipation mechanism. The usual tearing mode resonance condition ($\boldsymbol{k}\boldsymbol{\cdot }\boldsymbol{B}_{0}=0$, $\boldsymbol{k}$ is the wavevector and $\boldsymbol{B}_{0}$ is the equilibrium magnetic field) can be recovered from the general resonance conditions in the limit of weak dissipation. The conditions (relating current sheet thickness, strength of the guide field and wavenumbers) for the non-existence of tearing mode are obtained from the general mode resonance conditions. We discuss the role of electron shear flow instabilities in magnetic reconnection.

scholarly journals Effect of Sheared Flow on Resistive Tearing Instability and the Triggering of Flare

1993 ◽  
Vol 141 ◽  
pp. 443-445
Author(s):  
X.H. Deng ◽  
S. Wang ◽  
J.M. Chen ◽  
H.Q. Zhang ◽  
G.X. Ai
Keyword(s):  
Magnetic Field ◽  
Mass Flow ◽  
Solar Flares ◽  
Nonlinear Evolution ◽  
Cylindrical Geometry ◽  
Tearing Modes ◽  
Sheared Flow ◽  
Tearing Instability

AbstractThe nonlinear evolution of tearing modes in the presence of sheared mass flow is studied in the cylindrical geometry. It is demonstrated that a sufficient large sheared mass flow can destabilize the development of resistive tearing instability. It is suggested that the coupling of sheared mass flow with shear magnetic field may be a triggering of solar flares.

scholarly journals Probing Current Sheet Instabilities from Flare Ribbon Dynamics

2021 ◽  
Vol 922 (2) ◽  
pp. 117
Author(s):  
Ryan J. French ◽  
Sarah A. Matthews ◽  
I. Jonathan Rae ◽  
Andrew W. Smith
Keyword(s):  
Solar Flare ◽  
Current Sheet ◽  
Solar Flares ◽  
Spatial Scales ◽  
Tearing Mode ◽  
Scale Growth ◽  
Mode Instability ◽  
Field Lines ◽  
Flare Ribbon ◽  
High Cadence

Abstract The presence of current sheet instabilities, such as the tearing mode instability, are needed to account for the observed rate of energy release in solar flares. Insights into these current sheet dynamics can be revealed by the behavior of flare ribbon substructure, as magnetic reconnection accelerates particles down newly reconnected field lines into the chromosphere to mark the flare footpoints. Behavior in the ribbons can therefore be used to probe processes occurring in the current sheet. In this study, we use high-cadence (1.7 s) IRIS Slit Jaw Imager observations to probe for the growth and evolution of key spatial scales along the flare ribbons—resulting from dynamics across the current sheet of a small solar flare on 2016 December 6. Combining analyses of spatial scale growth with Si iv nonthermal velocities, we piece together a timeline of flare onset for this confined event, and provide evidence of the tearing mode instability triggering a cascade and inverse cascade toward a power spectrum consistent with plasma turbulence.

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