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.

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.

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.

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

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.

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.

The development of magnetic field line wander in gyrokinetic plasma turbulence: dependence on amplitude of turbulence

2017 ◽  
Vol 83 (3) ◽  
Author(s):  
Sofiane Bourouaine ◽  
Gregory G. Howes
Keyword(s):  
Magnetic Field ◽  
Field Line ◽  
Magnetic Field Line ◽  
Plasma Turbulence ◽  
Turbulent Plasma ◽  
Nonlinearity Parameter ◽  
Time Interval ◽  
Weak Turbulence ◽  
Field Lines ◽  
The Magnetic Field

The dynamics of a turbulent plasma not only manifests the transport of energy from large to small scales, but also can lead to a tangling of the magnetic field that threads through the plasma. The resulting magnetic field line wander can have a large impact on a number of other important processes, such as the propagation of energetic particles through the turbulent plasma. Here we explore the saturation of the turbulent cascade, the development of stochasticity due to turbulent tangling of the magnetic field lines and the separation of field lines through the turbulent dynamics using nonlinear gyrokinetic simulations of weakly collisional plasma turbulence, relevant to many turbulent space and astrophysical plasma environments. We determine the characteristic time $t_{2}$ for the saturation of the turbulent perpendicular magnetic energy spectrum. We find that the turbulent magnetic field becomes completely stochastic at time $t\lesssim t_{2}$ for strong turbulence, and at $t\gtrsim t_{2}$ for weak turbulence. However, when the nonlinearity parameter of the turbulence, a dimensionless measure of the amplitude of the turbulence, reaches a threshold value (within the regime of weak turbulence) the magnetic field stochasticity does not fully develop, at least within the evolution time interval $t_{2}<t\leqslant 13t_{2}$. Finally, we quantify the mean square displacement of magnetic field lines in the turbulent magnetic field with a functional form $\langle (\unicode[STIX]{x1D6FF}r)^{2}\rangle =A(z/L_{\Vert })^{p}$ ($L_{\Vert }$ is the correlation length parallel to the magnetic background field $\boldsymbol{B}_{\mathbf{0}}$, $z$ is the distance along $\boldsymbol{B}_{\mathbf{0}}$ direction), providing functional forms of the amplitude coefficient $A$ and power-law exponent $p$ as a function of the nonlinearity parameter.

scholarly journals Relative magnetic field line helicity

2019 ◽  
Vol 624 ◽  
pp. A51 ◽  
Author(s):  
K. Moraitis ◽  
E. Pariat ◽  
G. Valori ◽  
K. Dalmasse
Keyword(s):  
Magnetic Field ◽  
Field Line ◽  
Magnetic Field Line ◽  
Solar Physics ◽  
Magnetic Helicity ◽  
Geometrical Complexity ◽  
Wide Range ◽  
Field Lines ◽  
Definition Of ◽  
The Magnetic Field

Context. Magnetic helicity is an important quantity in studies of magnetized plasmas as it provides a measure of the geometrical complexity of the magnetic field in a given volume. A more detailed description of the spatial distribution of magnetic helicity is given by the field line helicity, which expresses the amount of helicity associated to individual field lines rather than in the full analysed volume. Aims. Magnetic helicity is not a gauge-invariant quantity in general, unless it is computed with respect to a reference field, yielding the so-called relative magnetic helicity. The field line helicity corresponding to the relative magnetic helicity has only been examined under specific conditions so far. This work aims to define the field line helicity corresponding to relative magnetic helicity in the most general way. In addition to its general form, we provide the expression for the relative magnetic field line helicity in a few commonly used gauges, and reproduce known results as a limit of our general formulation. Methods. By starting from the definition of relative magnetic helicity, we derived the corresponding field line helicity, and we noted the assumptions on which it is based. Results. We checked that the developed quantity reproduces relative magnetic helicity by using three different numerical simulations. For these cases we also show the morphology of field line helicity in the volume, and on the photospheric plane. As an application to solar situations, we compared the morphology of field line helicity on the photosphere with that of the connectivity-based helicity flux density in two reconstructions of an active region’s magnetic field. We discuss how the derived relative magnetic field line helicity has a wide range of applications, notably in solar physics and magnetic reconnection studies.

Some comments on magnetic field reconnection

1975 ◽  
Vol 14 (2) ◽  
pp. 271-282 ◽  
Author(s):  
E. R. Priest ◽  
S. W. H. Cowley
Keyword(s):  
Magnetic Field ◽  
Magnetic Flux ◽  
Fluid Velocity ◽  
Neutral Point ◽  
Diffusion Region ◽  
Reconnection Rate ◽  
Field Lines ◽  
The Magnetic Field

Some comments are made about how to determine the speed with which magnetic flux is carried towards an X-type neutral point and reconnected. Conditions in the diffusion region near the neutral point are also investigated, with the conclusion that the streamlines and magnetic field lines cannot both be locally hyperbolic. Instead, two distinct modes may be possible. In the first, the magnetic field lines are straight, and the diffusion region does not differ greatly from that described by Parker (1963). In the second, the fluid velocity components increase cubically away from the neutral point with the result that, for a given reconnection rate, the diffusion region is typically five times greater than in the Parker model.

scholarly journals Comparison of the measured and modelled electron densities and temperatures in the ionosphere and plasmasphere during 20-30 January, 1993

2000 ◽  
Vol 18 (10) ◽  
pp. 1257-1262 ◽  
Author(s):  
A. V. Pavlov ◽  
T. Abe ◽  
K.-I. Oyama
Keyword(s):  
Magnetic Field ◽  
Heat Flux ◽  
Electron Temperature ◽  
Field Line ◽  
Electron Density ◽  
Magnetic Field Line ◽  
New Approach ◽  
Additional Heating ◽  
Vibrational Levels ◽  
The Magnetic Field

Abstract. We present a comparison of the electron density and temperature behaviour in the ionosphere and plasmasphere measured by the Millstone Hill incoherent-scatter radar and the instruments on board of the EXOS-D satellite with numerical model calculations from a time-dependent mathematical model of the Earth's ionosphere and plasmasphere during the geomagnetically quiet and storm period on 20–30 January, 1993. We have evaluated the value of the additional heating rate that should be added to the normal photoelectron heating in the electron energy equation in the daytime plasmasphere region above 5000 km along the magnetic field line to explain the high electron temperature measured by the instruments on board of the EXOS-D satellite within the Millstone Hill magnetic field flux tube in the Northern Hemisphere. The additional heating brings the measured and modelled electron temperatures into agreement in the plasmasphere and into very large disagreement in the ionosphere if the classical electron heat flux along magnetic field line is used in the model. A new approach, based on a new effective electron thermal conductivity coefficient along the magnetic field line, is presented to model the electron temperature in the ionosphere and plasmasphere. This new approach leads to a heat flux which is less than that given by the classical Spitzer-Harm theory. The evaluated additional heating of electrons in the plasmasphere and the decrease of the thermal conductivity in the topside ionosphere and the greater part of the plasmasphere found for the first time here allow the model to accurately reproduce the electron temperatures observed by the instruments on board the EXOS-D satellite in the plasmasphere and the Millstone Hill incoherent-scatter radar in the ionosphere. The effects of the daytime additional plasmaspheric heating of electrons on the electron temperature and density are small at the F-region altitudes if the modified electron heat flux is used. The deviations from the Boltzmann distribution for the first five vibrational levels of N2(v) and O2(v) were calculated. The present study suggests that these deviations are not significant at the first vibrational levels of N2 and O2 and the second level of O2, and the calculated distributions of N2(v) and O2(v) are highly non-Boltzmann at vibrational levels v > 2. The resulting effect of N2(v > 0) and O2(v > 0) on NmF2 is the decrease of the calculated daytime NmF2 up to a factor of 1.5. The modelled electron temperature is very sensitive to the electron density, and this decrease in electron density results in the increase of the calculated daytime electron temperature up to about 580 K at the F2 peak altitude giving closer agreement between the measured and modelled electron temperatures. Both the daytime and night-time densities are not reproduced by the model without N2(v > 0) and O2(v > 0), and inclusion of vibrationally excited N2 and O2 brings the model and data into better agreement.Key words: Ionosphere (ionospheric disturbances; ionosphere-magnetosphere interactions; plasma temperature and density)  

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