Magnetic field-line reconnexion by localized enhancement of resistivity. Part 4. Dependence on the magnitude of resistivity

1979 ◽  
Vol 22 (1) ◽  
pp. 1-14 ◽  
Author(s):  
Masayuki Ugai ◽  
Takao Tsuda
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Current Sheet ◽  
Field Line ◽  
Magnetic Field Line ◽  
Theoretical Work ◽  
Magnetic Reynolds Number ◽  
Diffusion Region ◽  
Anomalous Resistivity ◽  
Set Up

The present paper quantitatively examines how the process of fast reconnexion depends on the magnitude of the local resistivity enhanced in the vicinity of the magnetic neutral point. It is shown that quasi-steady Petschek-type configurations are set up, one for each of the variously imposed local resistivity enhancements. The fundamental structure of the quasi-steady configuration is largely controlled by the initially indented value of locally enhanced resistivity. It is especially remarked that the width of the diffusion region becomes smaller as the locally enhanced resistivity becomes smaller. We find that each of the quasi-steady configurations presents nothing other than the Petschek-type configuration that corresponds to the allowable maximum reconnexion rate for the relevant magnetic Reynolds number. We also see that the magnitude of fast reconnexion rate has a weak dependence on the local resistivity in the diffusion region. All our numerical results are very consistent with previous theoretical work on the fast reconnexion problem, once the problem is reconsidered from another angle. We hence suggest that the process of fast reconnexion should be viewed as a gross instability, inherent to the current sheet system itself, that can be triggered by some local onset of anomalous resistivity.

Magnetic field-line reconnection with jets

1986 ◽  
Vol 35 (2) ◽  
pp. 333-350 ◽  
Author(s):  
A. M. Soward ◽  
E. R. Priest
Keyword(s):  
Magnetic Field ◽  
Numerical Simulations ◽  
Current Sheet ◽  
Field Line ◽  
Magnetic Field Line ◽  
Symmetry Axis ◽  
Steady State Solution ◽  
Magnetic Reynolds Number ◽  
External Boundary ◽  
Reconnection Rate

Some recent numerical simulations of driven magnetic field-line reconnection by Biskamp show no evidence of the Petschek mechanism when the reconnection rate or magnetic Reynolds number are large. Instead, an electric current sheet forms on the symmetry axis, across which a magnetic field is annihilated. The sheet terminates at a Y-point. Fluid driven into the current sheet escapes as jets along the separatrices emanating from the Y-point. This paper shows how many of the features such as the jets can be explained by a simple analytical model. Since the numerical simulations are necessarily on a bounded domain, the importance of the external boundary conditions in setting up a steady-state solution is stressed by illustrative examples.

Fast magnetic field line reconnection

1977 ◽  
Vol 284 (1325) ◽  
pp. 369-417 ◽  
Keyword(s):  
Magnetic Field ◽  
Field Line ◽  
Magnetic Field Line ◽  
Fluid Velocity ◽  
Magnetic Reynolds Number ◽  
Diffusion Region ◽  
Mathematical Basis ◽  
Similarity Type ◽  
Field Lines ◽  
The Magnetic Field

Petschek (1964) has given a qualitative model for fast magnetic field line reconnection, at speeds up to a significant fraction of the Alfven speed. It is supposed that an electrically conducting fluid is permeated by an almost uniform magnetic field which reverses direction across a plane of symmetry parallel to the field lines. An almost uniform stream flows steadily towards the plane of symmetry and is maintained by pressure forces. Magnetic field line reconnection occurs at the origin inside a small central diffusion region. The reconnected magnetic field is swept away rapidly in two thin jets aligned with the plane of symmetry. The inflow and outflow regions are separated by discontinuities at which the tangential components of the magnetic field and fluid velocity suffer abrupt changes. Sonnerup (1970) and Yeh & Axford (1970), on the other hand, have given alternative solutions for the incompressible case which include a second set of discontinuities. Their solutions are of similarity type, valid over some length scale which is much less than the overall distance between the magnetic field sources but is much greater than the size of the central diffusion region. The second set of discontinuities is, however, unacceptable for an astrophysical plasma, since they need to be generated at corners in the flow rather than at the central diffusion region. This paper presents other solutions for the incompressible case, which are locally self-similar, without discontinuities or singular behaviour at a second set of discontinuities. The solutions are valid everywhere outside the central diffusion region when the inflow Alfven Mach number M 1 (see (2.3) below) is much less than unity and are valid at large distances from the diffusion region when M 1 = 0(1). The analysis has been summarized by Priest & Soward (1976). It puts Petschek’s mechanism on a sound mathematical basis and shows that the discontinuities are not in general straight but curve away from the incoming flows. Our estimate of the maximum reconnection rate M e,max (see (10.9) below) depends weakly on the value of the magnetic Reynolds number R m,e (see (10.7) below). It decreases from 0.2 when R m,e > = 10 to 0.03 when R m,e = 10 6 .

scholarly journals First in situ evidence of electron pitch angle scattering due to magnetic field line curvature in the Ion diffusion region

2016 ◽  
Vol 121 (5) ◽  
pp. 4103-4110 ◽  
Author(s):  
Y. C. Zhang ◽  
C. Shen ◽  
A. Marchaudon ◽  
Z. J. Rong ◽  
B. Lavraud ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Field Line ◽  
Magnetic Field Line ◽  
Pitch Angle ◽  
Diffusion Region ◽  
Ion Diffusion ◽  
Angle Scattering

scholarly journals The current sheet flapping motions induced by non-adiabatic ions: case study

2018 ◽  
Author(s):  
Xinhua Wei ◽  
Chunlin Cai ◽  
Henri Rème ◽  
Iannis Dandouras ◽  
George Parks
Keyword(s):  
Magnetic Field ◽  
Current Sheet ◽  
Field Line ◽  
Magnetic Field Line ◽  
Plasma Sheet ◽  
Plasma Sources ◽  
Shear Structures ◽  
Particle Population ◽  
Alternating Bending

Abstract. In this paper, we analyzed the y-component of magnetic field line curvature in the plasma sheet and found that there are two kinds of shear structures of the flapping current sheet, i.e. symmetric and antisymmetric. The alternating bending orientations of guiding field are exactly corresponding to alternating north-south asymmetries of the bouncing ion population in the sheet center. Those alternating asymmetric plasma sources consequently induce the current sheet flapping motion as a driver. In addition, a substantial particle population with dawnward motion was observed in the center of a bifurcated current sheet. This population is identified as the quasi-adiabatic particles, and provides a net current opposite to the conventional cross-tail current.

The force on a sphere moving through a conducting fluid in the presence of a magnetic field

1961 ◽  
Vol 11 (1) ◽  
pp. 133-142 ◽  
Author(s):  
J. R. Reitz ◽  
L. L. Foldy
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Pressure Distribution ◽  
Magnetic Field Line ◽  
Potential Flow ◽  
Uniform Magnetic Field ◽  
Magnetic Reynolds Number ◽  
Conducting Fluid ◽  
Joule Dissipation ◽  
Hydrodynamic Motion

The force on a sphere moving through an inviscid, conducting fluid in the presence of a uniform magnetic field B0 is calculated for the low-conductivity case where the hydrodynamic motion deviates only slightly from potential flow. The magnetic Reynolds number is assumed small. The force on the sphere is found to consist of both a drag and a deflective component which tends to orient its motion parallel to a magnetic field line; if the sphere's velocity is V, the force may be written $\bf {R} = -AB^2_0\bf {V} + \bf C(V.B_0)B_0$ where the coefficients A and C depend on the conductivities of both sphere and fluid. The coefficients are evaluated by calculating the Joule dissipation for particular orientations of V relative to B0. In one case the force is also calculated directly from the perturbed pressure distribution in the fluid. In an analogous way, a spinning sphere in a conducting fluid experiences both resistive and gyroscopic torques.

Magnetic field-line reconnexion by localized enhancement of resistivity. Part 2. Quasi-steady process

1977 ◽  
Vol 18 (3) ◽  
pp. 451-471 ◽  
Author(s):  
Takao Tsuda ◽  
Masayuki Ugai
Keyword(s):  
Magnetic Field ◽  
Field Line ◽  
Magnetic Field Line ◽  
Evolutionary Process ◽  
Diffusion Field ◽  
Diffusion Region ◽  
Field Reversal ◽  
Ultimate Cause ◽  
Dominant Process ◽  
Field Lines

We have described previously the evolutionary process of magnetic field-line reconnexion by a localized enhancement of resistivity. In this paper, it is demonstrated by numerical experiment that the evolution is eventually checked, with the system attaining a quasi-steady state. On the basis of the quasi-steady configuration, established from an initially antiparallel magnetic field, we can now clarify the MHD properties that are characteristic of the diffusion, field reversal and external regions, respectively, and then the mutual dependence among them. Especially, the physical processes in the diffusion region are noteworthy, since the ultimate cause for the present reconnexion process is the bending of the field lines towards the magnetic neutral point, which results from the locally enhanced resistivity assumed in the diffusion region. The present numerical results generally agree with the analytical results for the steady reconnexion, although some discrepancies exist owing to the differences of the postulated basic situations between them. It is pointed out that changes in flow properties across the boundary of the field reversal region agree well with those required for a slow mode compression wave and that the dominant process in the external region corresponds to a fast mode expansion.

A re-examination of the role of magnetic field lines in electromagnetic induction

1988 ◽  
Vol 66 (3) ◽  
pp. 245-248
Author(s):  
D. H. Boteler
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Field Line ◽  
Electric Fields ◽  
Electromagnetic Induction ◽  
Magnetic Reynolds Number ◽  
Unified View ◽  
Field Lines ◽  
The Magnetic Field

By adopting a view of magnetic fields, originally proposed by Faraday, in which the magnetic field changes by a movement of field lines, it is shown that a changing magnetic field can be described by the relation [Formula: see text] where v is the velocity of the magnetic field lines. These field-line velocities are shown to be the same as material velocities in conditions of infinite magnetic Reynolds number. The "moving field-line" view provides a phenomenological model of a changing magnetic field that is useful in electromagnetic induction studies. It also allows for a unified view of electromagnetic induction in which all induced electric fields can be explained by the v × B force alone.

Magnetic field-line reconnexion by localized enhancement of resistivity: Part 1. Evolution in a compressible MHD fluid

1977 ◽  
Vol 17 (3) ◽  
pp. 337-356 ◽  
Author(s):  
Masayuki Ugai ◽  
Takao Tsuda
Keyword(s):  
Magnetic Field ◽  
Numerical Experiment ◽  
Boundary Conditions ◽  
Field Line ◽  
Magnetic Field Line ◽  
Temporal Dynamics ◽  
Magnetic Energy ◽  
Field Configuration ◽  
Global Flow ◽  
Set Up

The temporal dynamics of field-line reconnexion is studied by numerical experiment in a compressible conducting fluid. It is shown that because of localized enhancement of resistivity the reconnexion takes place in an initially antiparallel magnetic field and that an X-type field configuration develops, occupying an extended region. There is also a remarkable release of magnetic energy into kinetic and thermal energies. The global flow pattern can spontaneously be set up through the field-line reconnexion under no specially imposed boundary conditions.

scholarly journals Conjugate Conductivity Asymmetry and the Precipitation of Magnetospheric Electrons

1971 ◽  
Vol 24 (4) ◽  
pp. 881
Author(s):  
JR Catchpoole
Keyword(s):  
Magnetic Field ◽  
Field Line ◽  
Magnetic Field Line ◽  
Conjugate Point ◽  
Potential Difference ◽  
Simplified Model ◽  
Trapped Electrons ◽  
Set Up ◽  
The Magnetic Field

Using a simplified model of the atmosphere, a calculation is made of the windinduced vertical redistribution of ions derived from the 100 km level. Assuming the effect to be dissimilar in magnitude at the conjugate point, a potential difference will be set up in this way between the ends of the magnetic field line. For various values of the parameters involved, an estimate is made of the consequent precipitation to ionospheric heights of previously trapped electrons of the magnetosphere.

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