On the re-connexion of magnetic field lines in conducting fluids

1970 ◽  
Vol 4 (2) ◽  
pp. 207-229 ◽  
Author(s):  
Tyan Yeh ◽  
W. Ian Axford
Keyword(s):  
Magnetic Field ◽  
Electrical Conductivity ◽  
Two Dimensions ◽  
Neutral Point ◽  
Inviscid Fluid ◽  
Hydromagnetic Flow ◽  
Finite Electrical Conductivity ◽  
Field Lines ◽  
Two Sides ◽  
Special Case

The reconnexion of magnetic field lines is described for a special case of steady, incompressible hydromagnetic flow in two dimensions. A similarity solution is obtained which corresponds to the flow of a perfectly conducting, inviscid fluid such that magnetic field lines are carried from two sides toward, then on the other two sides away from, the centre of an X-configuration. The effects of viscosity are important in shocks which form in the vicinity of the X-lines of the configuration. The effects of finite electrical conductivity must be taken into account near the centre of the configuration which, in the symmetrical case discussed, is an X-type neutral point. From an approximate solution valid in this region it is found that the fluid must flow from the larger to the smaller wedges of the X-configuration. Hence, the reconnexion process is such that oppositely directed magnetic field lines move towards the neutral point in the larger wedges, become reconnected at the neutral point, and move away in the smaller wedges. Since the solution in the vicinity of the neutral point appears to be no more than a response to the external flow, which is in turn controlled by conditions far from the neutral point and is essentially unaffected by viscosity and finite electrical conductivity, it is tentatively concluded that the rate of re-connexion of magnetic field lines does not depend on these quantities, and that, in general, re-connexion can be expected to take place rapidly if circumstances are favourable.

On the re-connexion of magnetic lines of force

1973 ◽  
Vol 9 (3) ◽  
pp. 409-427 ◽  
Author(s):  
Shoichiro Fukao ◽  
Takao Tsuda
Keyword(s):  
Magnetic Field ◽  
Electrical Conductivity ◽  
Two Dimensions ◽  
Neutral Point ◽  
Transition Layers ◽  
Finite Electrical Conductivity ◽  
External Conditions ◽  
The Magnetic Field ◽  
Conducting Fluids ◽  
Lines Of Force

The magnetic field and flow with an X-type neutral point or stagnation point are studied numerically for the steady state of incompressible, finitely conducting, viscous fluid in two dimensions. There appear two transition layers connecting smoothly the regions on either side, each of which contains almost uniform magnetic field and flow. The electric currents are concentrated in the vicinity of the neutral point and along the transition layers. The magnetic field is regarded as almost frozen in the fluid in other current-free regions, even in the case of moderate conductivities. The current-core over the neutral point is accompanied by a remarkable shear of currents, which may contribute to reducing the local electrical conductivity effectively. Thus the re-connexion of magnetic lines of force may be possible even in very highly conducting fluids. It is shown that the re-connexion is not essentially influenced by dissipations due to finite electrical conductivity or viscosity, but definitely by external conditions such as the applied electric field in the magnetic field and flow.

Instability of a surface of discontinuity of velocity in a parallel uniform magnetic field

1963 ◽  
Vol 16 (2) ◽  
pp. 187-196 ◽  
Author(s):  
D. D. Mallick
Keyword(s):  
Magnetic Field ◽  
Secular Equation ◽  
Magnetic Reynolds Number ◽  
Wave Number ◽  
Inviscid Fluid ◽  
Dimensionless Wave Number ◽  
Electrically Conducting ◽  
Two Parameters ◽  
Two Sides ◽  
The Magnetic Field

The problem described by the title is investigated when the magnetic field is uniform and parallel to the velocity on the two sides of a surface of discontinuity of velocity in an electrically conducting inviscid fluid. The secular equation depends on two parameters β and N, where β is the ratio of magnetic Reynolds number to dimensionless wave number and N is the ratio of the magnetic to the kinetic energy of the fluid. It is found that the flow is unstable for all values of β and N.

The resistive evolution of force-free magnetic fields. Part 2. Relation to anisotropic diffusion

1979 ◽  
Vol 22 (1) ◽  
pp. 157-165 ◽  
Author(s):  
J. Reid ◽  
E. W. Laing
Keyword(s):  
Magnetic Field ◽  
Electrical Conductivity ◽  
Magnetic Fields ◽  
Anisotropic Diffusion ◽  
Free Evolution ◽  
Stationary Medium ◽  
Field Lines

We consider the diffusion of a magnetic field in a stationary medium where the electrical conductivity along field lines (σ∥) differs from that across them (σ⊥), and by showing that in the limit σ⊥/σ∥ → 0 the fields remain force-free, some unusual features of force-free evolution are clarified.

Stability of a stratified partially ionized plasma in a vertical magnetic field

1978 ◽  
Vol 19 (1) ◽  
pp. 183-191 ◽  
Author(s):  
S. L. Maheshwari ◽  
P. K. Bhatia
Keyword(s):  
Magnetic Field ◽  
Electrical Conductivity ◽  
Growth Rate ◽  
The Other ◽  
Conducting System ◽  
Vertical Magnetic Field ◽  
One Dimensional ◽  
Finite Electrical Conductivity ◽  
Partially Ionized ◽  
The Stability

The dynamic stability of a stratified layer of partially ionized compressible plasma is discussed to investigate the effects of finite electrical conductivity and ion viscosity. The prevailing magnetic field is assumed to be uniform and vertical. For a semi-infinite plasma having a one-dimensional exponential density gradient along the vertical, the dispersion relation has been obtained by variational methods. It is found that the ion viscosity and ion–neutral collisions, whether included jointly or separately, do not change the stability criterion of the perfectly conducting system. Their inclusion, however, has a tendency to reduce the growth rate of the unstable perturbations showing that they have a stabilizing influence. On the other hand the inclusion of the effects of finite resistivity and compressibility of the medium is found to be destabilizing as the wavenumber range over which the plasma would otherwise be stable, becomes unstable.

Steady transverse MHD viscous flows

1976 ◽  
Vol 54 (3) ◽  
pp. 262-267
Author(s):  
O. P. Chandna ◽  
M. R. Garg
Keyword(s):  
Magnetic Field ◽  
Electrical Conductivity ◽  
Viscous Flows ◽  
Transverse Magnetic ◽  
Incompressible Fluids ◽  
Parallel Lines ◽  
Logarithmic Spirals ◽  
Finite Electrical Conductivity ◽  
Concentric Circles ◽  
Steady Plane

Steady plane flows of viscous incompressible fluids of finite electrical conductivity in the presence of a transverse magnetic field are studied. The only flows with straight streamline pattern are shown to be those with parallel or concurrent streamlines and if the streamlines are involutes of a curve, then they are concentric circles. It is also established that if the natural net is isometric, then the streamlines are restricted to parallel lines, concurrent lines, concentric circles, or logarithmic spirals.

Geometry of magnetic field lines approaching a current sheet

2003 ◽  
Vol 69 (6) ◽  
pp. 541-550
Author(s):  
MANUEL NÚÑEZ
Keyword(s):  
Magnetic Field ◽  
Field Line ◽  
Two Dimensions ◽  
Time Of Arrival ◽  
Positive Contribution ◽  
Neutral Sheet ◽  
Spatial Function ◽  
Field Lines ◽  
The Magnetic Field ◽  
A Current

The evolution of a magnetic field line in two dimensions near a neutral sheet is analysed. It is found that the general features of this evolution are rather independent of any particular model, provided that the magnetic field is small and the current density does not vanish. The time of arrival of a field line to the neutral sheet as well as its breaking and reconnection are proved to be finite and to satisfy a simple formula whose main parameter is the resistivity, which may be a spatial function. The shape of the evolving field lines satisfies a differential equation whose solution in some simple cases is shown to agree with certain classical reconnection configurations. Hyperresistivity is found to be more often a hindrance than a positive contribution to the reconnection process.

Magnetic Field Structures for Inverse Polarity Prominences

1994 ◽  
Vol 144 ◽  
pp. 335-338
Author(s):  
A. O. Schönfelder ◽  
A. W. Hood ◽  
R. A. S. Fiedler
Keyword(s):  
Magnetic Field ◽  
Equilibrium Equation ◽  
Numerical Solutions ◽  
Neutral Point ◽  
Coronal Plasma ◽  
Photospheric Field ◽  
Shafranov Equation ◽  
Field Lines ◽  
The Magnetic Field ◽  
Correct Topology

AbstractObservations (Leroy, 1985) have shown that most large, high prominences are of the inverse polarity type, in that the magnetic field passes through the prominence in the inverse direction to that expected from the observed photospheric field. The classic inverse polarity model of Kuperus and Raadu (1974) assumed that the prominence lies below a region of closed magnetic field lines in the neighbourhood of an O-type neutral point and above an X-type neutral point. Since the prominence must form in a low-βcoronal plasma, the pre-prominence magnetic field must have the correct topology for an inverse polarity configuration. In this paper a wide variety of different current profiles are considered in the Grad-Shafranov equation that is used to describe the equilibrium. The results of numerical solutions to the equilibrium equation indicate that a fully developed prominence will possess an O-type, but not in general an X-type neutral point.

On plane flow of a gas with finite electrical conductivity in a strong magnetic field

1963 ◽  
Vol 15 (4) ◽  
pp. 577-596 ◽  
Author(s):  
M. D. Cowley
Keyword(s):  
Magnetic Field ◽  
Electrical Conductivity ◽  
Strong Magnetic Field ◽  
Shock Structure ◽  
Flow Behaviour ◽  
Structure Theory ◽  
Transition Curve ◽  
Plane Flow ◽  
Finite Electrical Conductivity ◽  
Object Of Study

The principal object of study is plane flow over bodies with a sharp apex at Mach numbers greater than unity. The magnetic field is assumed to be uniform, rectilinear, and parallel to the undisturbed stream. Flow behaviour near the apex of a wedge is investigated by the method of characteristics. It is found that for small wedge angles an attached shock attenuates initially with distance from the apex, but for larger wedge angles the shock grows stronger.The structure of a slow magneto-gasdynamic shock is investigated for the case of strong magnetic field and small electrical conductivity. The streamlines are displaced within the shock although the initial and final flow directions are the same. An ordinary gasdynamic shock may occur on the upstream side of the transition. The shock structure theory gives a solution for the flow near the apex of a certain class of bodies.For the study of slow shock structure, it is shown that the transition is described by a curve in the (F, H)-plane. F is the sum of pressure and momentum flux in the direction of variation; H is the sum of enthalpy and kinetic energy due to the velocity component in the direction of variation. General properties of the (F, H)-plane are found for a gas whose equation of state obeys the conditions of Weyl (1949). Flow behaviour on the transition curve is then determined. The theory of the (F, H)-plane can be used in the study of other one-dimensional processes in magneto-gasdynamics.

Sign in / Sign up

Export Citation Format

Share Document