On the re-connexion of magnetic field lines in conducting fluids
TL;DR: Magnetic field lines reconnection in steady incompressible hydromagnetic two dimensional flow, formulating governing equations with cylindrical polar coordinates as mentioned in this paper, is a classic example.
Abstract: Magnetic field lines reconnection in steady incompressible hydromagnetic two dimensional flow, formulating governing equations with cylindrical polar coordinates
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TL;DR: A review of the models of magnetic field line merging is given in this paper, where the authors describe the process whereby plasma flows across a surface which separates regions including topologically different magnetic field lines.
Abstract: A review is presented of the models of magnetic field line merging defined as the process whereby plasma flows across a surface which separates regions including topologically different magnetic field lines. The models examined are characterized by uniform and antiparallel external magnetic fields. An attempt is made to simplify the presentation of the models, to clarify some doubtful mathematical points, or to extend the results to a different range of physical parameters. The models are described from a hydromagnetic point of view, with the configuration in any given case being determined by the boundary conditions. It is shown that the models developed by Sweet (1958), Parker (1957, 1963), Petschek (1964), Sonnerup (1970), and by Yeh and Axford (1970) are basically consistent, describing different aspects of the same problem; however, there is not a single model that would account for all the cases considered. The singular models and the compressible similarity models are physically not feasible.
1,310 citations
TL;DR: In this article, the power delivered by the solar wind dynamo to the open magnetosphere is calculated based on the concept of field line reconnection, independent of the MHD steady reconnection theories.
Abstract: The power delivered by the solar wind dynamo to the open magnetosphere is calculated based on the concept of field line reconnection, independent of the MHD steady reconnection theories. By recognizing a previously overlooked geometrical relationship between the reconnection electric field and the magnetic field, the calculated power is shown to be approximately proportional to the Akasofu-Perreault energy coupling function for the magnetospheric substorm. In addition to the polar cap potential, field line reconnection also gives rise to parallel electric fields on open field lines in the high-latitude cusp and the polar cap regions.
502 citations
TL;DR: In this article, the effects of turbulence on magnetic reconnection were investigated by two-dimensional spectral method magnetohydrodynamic computations and the nonlinear evolution of the periodic sheet pinch configuration was studied as an initial value problem.
Abstract: The effects of turbulence on magnetic reconnection are investigated by two‐dimensional spectral method magnetohydrodynamic computations. The nonlinear evolution of the periodic sheet pinch configuration is studied as an initial value problem. Turbulence is initiated by including a low level of broadband fluctuations in the initial data. Nonlinear features of the evolution, appropriately described as turbulence, are seen early in the solutions and persist throughout the runs. Small‐scale, unsteady coherent electric current and vorticity structures develop in the reconnection zone, resulting in enhanced viscous and resistive dissipation. Unsteady and often spatially asymmetric fluid flow develops. Large‐scale magnetic islands produced by reconnection activity, undergo internal pulsations. Small‐scale magnetic islands, or ‘‘bubbles’’ develop near the reconnection zone, prodcing multiple X points. Large‐amplitude electric field fluctuations, often several times larger than the reconnection electric field, are produced by large island pulsations and by motion of magnetic bubbles. Spectral analysis of the fluctuations show development of broad band excitations, reminiscent of inertial and dissipation range spectra in homogeneous turbulence. Two‐dimensional spectra indicate that the turbulence is broadband in both spatial directions. It is suggested that the turbulence that develops from the randomly perturbed sheet pinchbears a strong resemblence to homogeneous magnetohydrodynamic turbulence, and that analytical theories of reconnection must incorporate these effects.
456 citations
TL;DR: In this paper, it was shown that the theoretical upper limit on the electric field component parallel to the X type magnetic null line is proportional to sin squared (theta/2) when the magnetic fields on the two sides of the magnetopause have equal magnitude.
Abstract: Discussion of certain aspects of the magnetic field reconnection process at the magnetopause. It is argued that the upper limits on reconnection derived by Petschek (1964), on the one hand, and Yeh and Axford (1970) and Sonnerup (1970), on the other, may be reconciled, at least qualitatively. Further, the possibility that magnetopause reconnection proceeds at this upper limit remains a real one. It is demonstrated that under the same assumptions as those used by Petschek (1964, 1966) the theoretical upper limit on the electric field component parallel to the X type magnetic null line is proportional to sin squared (theta/2) when the magnetic fields on the two sides of the magnetopause have equal magnitude. Finally, it is shown that when the magnetic field outside the magnetopause is weaker than the field inside that surface, reconnection may cease altogether for cos theta greater than the ratio of the outside field to the inside one.
419 citations
TL;DR: In this article, a quantitative model for the electric potential arising from magnetopause reconnection is proposed, in which several approximations are made concerning configuration of the magnetosheath flow, limitations on the magnitude of the reconnection speed, and the geometry of the problem.
Abstract: A quantitative three-dimensional model is proposed for the electric potential arising from magnetopause reconnection, in which several approximations are made concerning configuration of the magnetosheath flow, limitations on the magnitude of the reconnection speed, and the geometry of the problem. These approximations are such that the model yields an upper limit for the potential. The magnitude of the polar cap ionospheric electric field computed from this model is larger than that measured on balloons by an average factor of about 3, and the model reproduces the temporal variations of the experimental data. It is concluded that magnetopause reconnection is a highly efficient process that is probably the dominant mechanism driving polar cap convection and supplying energy to the magnetosphere. It seems that the most efficient way for the solar wind to pass the magnetospheric obstacle is by magnetopause reconnection.
401 citations
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TL;DR: In this paper, it was shown that two oppositely directed sunspot fields with scales of 104 km could be merged by Sweet's mechanism, if shoved firmly together, in about two weeks; their normal interdiffusion time would be of the order of 600 years.
Abstract: Sweet's mechanism for the merging of two oppositely directed magnetic fields in a highly conducting fluid is investigated in a semi-quantitative manner. It is shown that two oppositely directed sunspot fields with scales of 104 km could be merged by Sweet's mechanism, if shoved firmly together, in about two weeks; their normal interdiffusion time would be of the order of 600 years. It is suggested that Sweet's mechanism may be of considerable astrophysical importance: It gives a means of altering quickly the configuration of magnetic fields in ionized gases, allowing a stable field to go over into an unstable configuration, subsequently converting much of the magnetic energy into kinetic energy of the fluid.
1,562 citations
TL;DR: In this paper, a systematic study of the theoretical mechanisms for diffusion, reconnection, and annihilation of magnetic fields is presented, and it is shown that there is no reason to expect runaway electrons and no effective instability unless the fields are exactly antiparallel.
Abstract: A study is presented of the observations and theory relevant to the belief that the solar-flare phenomenon is a direct consequence of the annihilation of magnetic fields on the sun. There is very little in the observations to support such views. A systematic study of the theoretical mechanisms for diffusion, reconnection, and annihilation of magnetic fields is presented. The mechanisms discussed are Joule dissipation, ambipolar diffusion, and various forms of Sweet's mechanism. It is shown that Sweet's mechanism is much more effective in a highly compressible medium if the merging magnetic fields are exactiy antiparallel. None of the known mechanisms are sufficiently rapid to account for the solar flare from the annihilation of magnetic fields. Errors and omissions in discussions of the problem are cited. Since no possible energy source other than magnetic fields is known, the question of field annihilation remains both open and pressing. The possibilities of runaway electrons and hydrodynamic instability, as means for hastening magnetic-field annihilation, are considered. It is shown that there is no reason to expect runaway electrons and no effective instability unless the fields are exactly antiparallel. (auth)
587 citations
TL;DR: In this paper, it is shown that discharges are unlikely to occur anywhere except at neutral points of the magnetic field, and that neutral points are unstable in such a way that a small perturbation will start a discharge in a time of the order of the characteristic time.
Abstract: Summary Discharges are shown to be a possible source of high energy particles, if the current density is very large. The growth of the current density is discussed using the fact that the magnetic lines of force are approximately frozen into the ionized gas. It is shown that discharges are unlikely to occur anywhere except at neutral points of the magnetic field. Neutral points are found to be unstable in such a way that a small perturbation will start a discharge in a time of the order of the characteristic time of the system. Such discharges may account for aurorae, and may also occur in solar flares and the interstellar gas.
360 citations
TL;DR: A neutral point theory of solar flares was proposed in this paper, which is consistent with the point-like nature of a flare at its onset, but does not satisfactorily explain the positions of flares relative to the components of the spot group.
Abstract: A neutral point theory of solar flares might be tenable if sunspots were formed from flux tubes protruding through the photosphere. Such a mechanism is consistent with the point-like nature of a flare at its onset, but does not satisfactorily explain the positions of flares relative to the components of the spot group.
291 citations