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.

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 The development of magnetic field line wander by plasma turbulence

2017 ◽  
Vol 83 (4) ◽  
Author(s):  
Gregory G. Howes ◽  
Sofiane Bourouaine
Keyword(s):  
Magnetic Field ◽  
Field Line ◽  
Magnetic Field Line ◽  
Large Scale ◽  
Magnetic Energy ◽  
Plasma Turbulence ◽  
Alfven Wave ◽  
Astrophysical Plasmas ◽  
Field Lines ◽  
The Magnetic Field

Plasma turbulence occurs ubiquitously in space and astrophysical plasmas, mediating the nonlinear transfer of energy from large-scale electromagnetic fields and plasma flows to small scales at which the energy may be ultimately converted to plasma heat. But plasma turbulence also generically leads to a tangling of the magnetic field that threads through the plasma. The resulting wander of the magnetic field lines may significantly impact a number of important physical processes, including the propagation of cosmic rays and energetic particles, confinement in magnetic fusion devices and the fundamental processes of turbulence, magnetic reconnection and particle acceleration. The various potential impacts of magnetic field line wander are reviewed in detail, and a number of important theoretical considerations are identified that may influence the development and saturation of magnetic field line wander in astrophysical plasma turbulence. The results of nonlinear gyrokinetic simulations of kinetic Alfvén wave turbulence of sub-ion length scales are evaluated to understand the development and saturation of the turbulent magnetic energy spectrum and of the magnetic field line wander. It is found that turbulent space and astrophysical plasmas are generally expected to contain a stochastic magnetic field due to the tangling of the field by strong plasma turbulence. Future work will explore how the saturated magnetic field line wander varies as a function of the amplitude of the plasma turbulence and the ratio of the thermal to magnetic pressure, known as the plasma beta.

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

Fast magnetic field-line reconnexion in a compressible fluid. Part 1. Coplanar field lines

1982 ◽  
Vol 28 (2) ◽  
pp. 335-367 ◽  
Author(s):  
A. M. Soward ◽  
E. R. Priest
Keyword(s):  
Magnetic Field ◽  
Field Line ◽  
Magnetic Field Line ◽  
Compressible Fluid ◽  
Similarity Solution ◽  
Gas Pressure ◽  
Local Similarity ◽  
Mathematical Foundation ◽  
Previous Suggestion ◽  
Field Lines

The Petschek model for incompressible reconnexion has been put on a firm mathematical foundation in an earlier paper by Soward & Priest, who discovered a ‘local’ similarity solution for the process. The present paper extends that analysis to compressible reconnexion, in which the previous Alfvén waves are replaced by slow magneto-acoustic shocks of switch-off type. By contrast with a previous suggestion, it is found unnecessary to include intermediate waves standing ahead of the slow shocks. The maximum reconnexion rate is typically half of Petschek's stated value, though faster rates are achieved when the external gas pressure is sufficiently low.

Topological analysis of a perturbed MHD equilibrium using magnetic field-line invariants

1997 ◽  
Vol 58 (3) ◽  
pp. 553-569 ◽  
Author(s):  
JASON W. BATES ◽  
H. RALPH LEWIS
Keyword(s):  
Magnetic Field ◽  
Field Line ◽  
Magnetic Field Line ◽  
Order Term ◽  
Topological Analysis ◽  
Small Perturbations ◽  
Level Curves ◽  
Mhd Equilibrium ◽  
Field Lines ◽  
Order Invariant

A procedure has previously been developed for the iterative construction of invariants associated with magnetic field-line Hamiltonians that consist of an axisymmetric zeroth-order term plus a non-axisymmetric perturbation. Approximate field-line invariants obtained with this procedure are used to examine the topological properties of magnetic field lines in a parabolic-current MHD equilibrium that was slightly perturbed from axisymmetry in the limit of a periodic cylindrical configuration. Excellent agreement between Poincaré maps and the level curves of the first-order invariant is found for small perturbations. A means of circumventing the ‘small-divisor problem’ in some cases is identified and implemented with outstanding results. These results indicate that this perturbation method can have valuable consequences for future investigations of magnetic field-line topology.

scholarly journals Uncertainties in field-line tracing in the magnetosphere. Part I: the axisymmetric part of the internal geomagnetic field

1997 ◽  
Vol 15 (2) ◽  
pp. 165-180 ◽  
Author(s):  
D. M. Willis ◽  
J. Robin Singh ◽  
J. Comer
Keyword(s):  
Magnetic Field ◽  
Field Line ◽  
Magnetic Field Line ◽  
Spherical Harmonic ◽  
Geomagnetic Field ◽  
Frame Of Reference ◽  
Standard Errors ◽  
Analytic Equation ◽  
Axisymmetric Part ◽  
Field Lines

Abstract. The technique of tracing along magnetic field lines is widely used in magnetospheric physics to provide a "magnetic frame of reference'' that facilitates both the planning of experiments and the interpretation of observations. The precision of any such magnetic frame of reference depends critically on the accurate representation of the various sources of magnetic field in the magnetosphere. In order to consider this important problem systematically, a study is initiated to estimate first the uncertainties in magnetic-field-line tracing in the magnetosphere that arise solely from the published (standard) errors in the specification of the geomagnetic field of internal origin. Because of the complexity in computing these uncertainties for the complete geomagnetic field of internal origin, attention is focused in this preliminary paper on the uncertainties in magnetic-field-line tracing that result from the standard errors in just the axisymmetric part of the internal geomagnetic field. An exact analytic equation exists for the magnetic field lines of an arbitrary linear combination of axisymmetric multipoles. This equation is used to derive numerical estimates of the uncertainties in magnetic-field-line tracing that are due to the published standard errors in the axisymmetric spherical harmonic coefficients (i.e. gn0 ± δgn0). Numerical results determined from the analytic equation are compared with computational results based on stepwise numerical integration along magnetic field lines. Excellent agreement is obtained between the analytical and computational methods in the axisymmetric case, which provides great confidence in the accuracy of the computer program used for stepwise numerical integration along magnetic field lines. This computer program is then used in the following paper to estimate the uncertainties in magnetic-field-line tracing in the magnetosphere that arise from the published standard errors in the full set of spherical harmonic coefficients, which define the complete (non-axisymmetric) geomagnetic field of internal origin. Numerical estimates of the uncertainties in magnetic-field-line tracing in the magnetosphere, calculated here for the axisymmetric part of the internal geomagnetic field, should be regarded as "first approximations'' in the sense that such estimates are only as accurate as the published standard errors in the set of axisymmetric spherical harmonic coefficients. However, all procedures developed in this preliminary paper can be applied to the derivation of more realistic estimates of the uncertainties in magnetic-field-line tracing in the magnetosphere, following further progress in the determination of more accurate standard errors in the spherical harmonic coefficients.

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.

Particle and energy transport due to magnetic field-line reconnection in a tokamak

1987 ◽  
Vol 37 (3) ◽  
pp. 335-346
Author(s):  
Satoru Iizuka ◽  
Yasujiroh Minamitani ◽  
Hiroshi Tanaca
Keyword(s):  
Magnetic Field ◽  
Field Line ◽  
Magnetic Field Line ◽  
Energy Transport ◽  
Flow Speed ◽  
Poloidal Magnetic Field ◽  
Reconnection Region ◽  
Field Lines ◽  
Plasma Flow Speed ◽  
Current Reversal

Plasma behaviour during magnetic field-line reconnection which is driven by a rapid toroidal current reversal in a tokamak is investigated by calculating plasma flow speed from the magnetohydromatic equations with variables measured in the experiment. A strong plasma acceleration appears in the outside region of the X-type separatrix formed in the poloidal magnetic field lines. The induced electric field inside the plasma is evaluated directly from Ohm's law by using the fact that the toroidal current density vanishes during the current reversal. Then, plasma resistivity is estimated in the cross-section and the resulting value of energy flow is compared with that given by Poynting's theorem. It is found that the input energy is dissipated effectively through anomalous resistivity in the reconnection region.

Peripheral Stochasticity in Tokamaks.The Martin-Taylor Revisited

1992 ◽  
Vol 47 (9) ◽  
pp. 941-944 ◽  
Author(s):  
R. L. Viana ◽  
I. L. Caldas
Keyword(s):  
Magnetic Field ◽  
Aspect Ratio ◽  
Theoretical Analysis ◽  
Field Line ◽  
Magnetic Field Line ◽  
Current Model ◽  
Large Aspect Ratio ◽  
Magnetic Surfaces ◽  
Field Lines ◽  
The Magnetic Field

Abstract We analyse the effect of an Ergodic Magnetic Limiter on the magnetic field line dynamics in the edge of a large aspect-ratio Tokamak. We model the limiter action as an impulsive perturbation and use a peaked-current model for the Tokamak equilibrium field. The theoretical analysis is made through the use of invariant flux functions describing magnetic surfaces. Results are compared with a numerical mapping of the field lines

scholarly journals A Monte Carlo simulation of magnetic field line tracing in the solar wind

2001 ◽  
Vol 8 (3) ◽  
pp. 151-158 ◽  
Author(s):  
P. Pommois ◽  
G. Zimbardo ◽  
P. Veltri
Keyword(s):  
Magnetic Field ◽  
Monte Carlo Simulation ◽  
Solar Wind ◽  
Monte Carlo ◽  
Diffusion Coefficient ◽  
Field Line ◽  
Magnetic Field Line ◽  
Magnetic Turbulence ◽  
Field Lines ◽  
The Magnetic Field

Abstract. It is well known that the structure of magnetic field lines in solar wind can be influenced by the presence of the magnetohydrodynamic turbulence. We have developed a Monte Carlo simulation which traces the magnetic field lines in the heliosphere, including the effects of magnetic turbulence. These effects are modelled by random operators which are proportional to the square root of the magnetic field line diffusion coefficient. The modelling of the random terms is explained, in detail, in the case of numerical integration by discrete steps. Furthermore, a proper evaluation of the diffusion coefficient is obtained by a numerical simulation of transport in anisotropic magnetic turbulence. The scaling of the fluctuation level and of the correlation lengths with the distance from the Sun are also taken into account. As a consequence, plasma transport across the average magnetic field direction is obtained. An application to the propagation of energetic particles from corotating interacting regions to high heliographic latitudes is considered.

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