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Old 24th January 2012, 02:57 PM   #6135
Tim Thompson
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Lightbulb Magnetic Reconnection Defined and Described


As a preamble to an understanding of magnetic reconnection, I defined field lines & flux tubes in my previous post. Here I present several definitions and descriptions of magnetic reconnection as a physical process. Once again, I have tried to stick to unimpeachably authoritative & reliable sources. I present several, rather then just one, because the process is complicated and there are different ways to describe it. Hopefully everyone will find at least one explanation that resonates with their understanding.

I have highlighted what I think are the key points, but I have tried to cite enough language to provide proper context, as well as to avoid insufficiently brief descriptions. Any other emphasis besides the highlight is carried over from the original text. I encourage the reader to pay attention to the full text of the quotes, and to refer directly to the original sources, which I have linked to as best I can, wherever possible.

Magnetic Reconnection Defined and Described

Magnetic Reconnection
Masaaki Yamada, Russell Kulsrud and Hantao Ji; Center for Magnetic Self-Organization in Laboratory and Astrophysical Plasmas, Princeton Plasma Physics Laboratory, Princeton University
Reviews of Modern Physics 82(1): 603-664, January 2010.

Originally Posted by Yamada, Kulsrud & Ji, 2010, first two paragraphs of introduction
Magnetic fields are observed at all scales in the universe, in the Earth's dipole field, in the magnetosphere, in the solar corona, and on a larger scale from the interstellar medium to galaxy clusters. How are magnetic fields generated in the Universe? How are they involved in determining the characteristics of plasmas? Understanding magnetic reconnection, a topological rearrangement of magnetic field lines, provides a key to these questions. In magnetized astrophysical and laboratory plasmas, magnetic reconnection rearranges the magnetic field-line configurations restructuring macroscopic quantities of plasmas such as flow and thermal energy.

Magnetic reconnection is seen in the evolution of solar flares, coronal mass ejection, and interaction of solar winds with Earth's magnetosphere and is considered to occur in the formation of stars (Parker, 1979; Kulsrud, 1998; Biskamp, 2000; Priest and Forbes, 2000). It occurs as the self-organization process in current carrying fusion plasmas, typically observed in major and minor disruptions of tokamak discharges, and in relaxation processes in reversed field pinch (RFP) and spheromak plasmas (Taylor, 1986; Yamada, 1999b). Magnetic reconnection involves a topology change of a set of field lines, which leads to a new equilibrium configuration of lower magnetic energy. During this process magnetic energy is converted to kinetic energy through acceleration or heating of charged particles.

And ...

Originally Posted by Yamada, Kulsrud & Ji, 2010, Third and fourth paragraphs of Appendix A: "The Nature of Reconnection"
Any change in topology of the lines involves a change in the corresponding equilibrium and, in general, a change in the energy of this equilibrium. An abrupt change in the topology to a new topology, say by breaking magnetic field lines at some place, puts the plasma into a nonequilibrium state with generally no change in its energy. After this change the plasma will evolve with ideal plasma motions that will conserve this new topology but will lower its energy, say by viscous processes, until it reaches the new equilibrium corresponding to its new topology.

This discussion is based on the result that ideal plasma motions do not break lines or change their topology. In this manner, one sees that a sudden change in topology by a nonideal motion leads to a rapid conversion of magnetic energy into kinetic energy and then a subsequent conversion of this kinetic energy into heat, radiation, or particle acceleration by some viscous process. This abrupt change in topology is a nonideal change which magnetic reconnection can trigger. It is of considerable importance just because it can lead to a rapid conversion of magnetic energy to other forms.

Magnetic Reconnection in Astrophysical and Laboratory Plasmas
Ellen G. Zweibel and Masaaki Yamada
Annual Review of Astronomy and Astrophysics 47: 291-332 (2009)

Originally Posted by Zweibel & Yamada, 2009, abstract
Magnetic reconnection is a topological rearrangement of magnetic field that converts magnetic energy to plasma energy. Astrophysical flares, from the Earth's magnetosphere to gamma-ray bursts and sawtooth crashes in laboratory plasmas, may all be powered by reconnection. Reconnection is essential for dynamos and the large-scale restructuring known as magnetic self-organization. We review reconnection theory and evidence for it. We emphasize recent developments in two-fluid physics, and the experiments, observations, and simulations that verify two-fluid effects. We discuss novel environments such as line-tied, relativistic, and partially ionized plasmas, focusing on mechanisms that make reconnection fast, as observed. Because there is evidence that fast reconnection in astrophysics requires small scale structure, we briefly introduce how such structure might develop. Several areas merit attention for astrophysical applications: development of a kinetic model of reconnection to enable spectroscopic predictions, better understanding of the interplay between local and global scales, the role of collisionless reconnection in large systems, and the effects of flows, including turbulence.

Fundamentals of Plasma Physics
Paul M. Bellan, Bellan Plasma Group, California Institute of Technology; Cambridge University Press 2006

Originally Posted by Bellan 2006, page 410, 2nd paragraph of chapter 12, "Magnetic reconnection"
It is possible for an MHD equilibrium to be stable to all ideal MHD modes and yet not be in a lowest energy state. Because ideal MHD does not allow the topology to change, a plasma that is not initially in the lowest energy state will not be able to access this lowest energy state if the lowest energy state is topologically different from the initial state. However, the lowest energy state could be accessed by non-ideal modes, i.e., modes that violate the frozen-in flux condition, and so the available free energy could drive an instability involving these non-ideal modes. Magnetic reconnection is a non-ideal instability where the plasma is effectively ideal everywhere except at a very thin boundary layer where the ideal MHD frozen-in assumption fails so magnetic fields can leak across the plasma and change their topology. Even though this boundary layer is microscopically thin, the reconnection and associated change in magnetic topology at the boundary layer allow the configuration to relax to a lower energy state. Magnetic reconnection thus describes how a very slight departure from ideal MHD leads to important new behavior.

Magnetic Reconnection: MHD Theory and Applications
Eric Priest & Terry Forbes; Cambridge University Press, 2000

Originally Posted by Priest & Forbes, 2000, from the Preface
At present the whole field of reconnection is a huge, vibrant one that is developing along many different lines, as can be seen by the fact that a recent science citation search produced a listing of 1,069 published articles written on this subject in only the past three years. We are therefore well aware of the impossibility of comprehensively covering the whole field and apologise in advance to those who may be disappointed that we have not found space to discuss their work on reconnection. We have attempted to cover the basics of the various aspects of magnetic reconnection and to give brief accounts of the applications at the present point in time. Because of the vastness of the field and our own limited knowledge, we decided to focus only on the magnetohydrodynamic (MHD) aspects of reconnection, but those aspects do provide a foundation for treatments using kinetic theory.

Originally Posted by Priest & Forbes, 2000, from the Introduction, page 1
Like most fundamental concepts in physics, magnetic reconnection owes its appeal to its ability to unify a wide range of phenomena within a single universal principle. Virtually all plasmas, whether in the laboratory, the solar system, or the most distant reaches of the universe, generate magnetic fields. The existence of those fields in the presence of plasma flows inevitably leads to the process of magnetic reconnection. As we shall discuss in more detail later on, magnetic reconnection is essentially a topological restructuring of a magnetic field caused by a change in the connectivity of its field lines. This change allows the release of stored magnetic energy, which in many situations is the dominant source of free energy in a plasma. Of course, many other processes besides reconnection occur in plasmas, but reconnection is probably most important one for explaining large-scale, dynamic releases of magnetic energy.

Review of controlled laboratory experiments on physics of magnetic reconnection
Masaaki Yamada
Journal of Geophysical Research, Space Physics, 104(A7): 14529-14542, July 1999

Originally Posted by Yamada, 1999, First two paragraphs of the Introduction
Magnetic reconnection is the topological breaking and rearrangement of magnetic field lines in a plasma and is the most fundamental process in the interplay between plasma and magnetic field (Parker, 1979; Priest, 1984; Vasyliunas, 1975). For the past several decades, this important phenomenon has been attracting much attention in space physics research as a key process in the fast evolution of solar flares and in the Earth's magnetosphere. Magnetic reconnection always occurs during plasma formation or configuration change and is regarded as the most important self-organization process in plasmas.

In this paper we review results from the most recent experiments in which magnetic reconnection has been generated and studied in controlled laboratory settings. As a whole, research on the fundamental physics of the reconnection process and its hydromagnetic consequences has been largely theoretical. Most magnetohydrodynamic (MHD) theories of magnetic reconnection have been based on steady two-dimensional (2-D) models. Although the Sweet-Parker (Sweet, 1958; Parker, 1957) and Petschek (1964) models are well known (Sonnerup and Wang, 1987), the extensive literature describing these two-dimensional theoretical models has remained unchallenged until the most recent MHD plasma experiments. A careful comparison of experimental data in a well-controlled laboratory setting with analytical theories should reveal fundamental mechanisms of magnetic reconnection.

Nonlinear Magnetohydrodynamics
Deiter Biskamp (Max Planck Institute for Plasma Physics); Cambridge University Press 1993

Originally Posted by Biskamp, 193, Page 127, first paragraph of chapter 6, "Magnetic Reconnection"
There is hardly a term in physics exhibiting more scents, facets and also ambiguities than does magnetic reconnection or, simply, reconnection. It is even sometimes used with a touch of magic. The basic picture underlying the idea of reconnection is that of two field lines (thin flux tubes, properly speaking) being carried along with the fluid owing to the property of flux conservation until the come close together at some point, where by the effect of finite resistivity they are cut and reconnected in a different way. Though this is a localized process, it may fundamentally change the global field line connection as indicated in Fig. 6.1, permitting fluid motions which would be inhibited in the absence of such local decoupling of fluid and magnetic field. Almost all nonlinear processes in magnetized conducting fluids involve reconnection , which may be called the essence of nonlinear MHD.

Note his comment "thin flux tubes, properly speaking". Flux tubes are defined in section 2.2, "Conservation laws in ideal MHD", specifically on pages 13-14. I have used that as the definition for flux tubes in my previous post.

Relaxation and magnetic reconnection in plasmas
J.B. Taylor
Culham Laboratory, Abingdon, Oxfordshire, England
Reviews of Modern Physics 58(3): 741-763, July 1986

Originally Posted by Taylor, 1986, First two paragraphs of Introduction
In this paper a plasma is regarded as a conducting fluid having small resistivity and small viscosity. Even in this simple model interaction of the plasma with magnetic fields leads to extremely complex behavior, especially when turbulence occurs. It is therefore remarkable that one can make quantitative predictions about the plasma configuration resulting from such turbulence. This is possible because the turbulence, allied with small resistivity, allows the plasma rapid access (in a time short compared with the usual resistive diffusion time) to a particular minimum-energy state. This process, known as plasma relaxation, involves the reconnection of magnetic field lines and is a remarkable example of the self-organization of a plasma (Hasegawa, 1985). Since plasma turbulence occurs frequently, so does this relaxation process, and the theory has now been successfully applied to plasmas in many different laboratory systems (see references herein) and even to astrophysical plasmas (Heyvaerts and Priest, 1984; Konigl and Choudhuri, 1985).

An important concept in the theory is that of magnetic helicity,  \int \boldsymbol A \cdot \boldsymbol B d\tau , as an invariant of plasma motion. This was used by Woltjer (1958) and by Wells and Norwood (1969), but relaxation theory as described here began with the work of Taylor (1974a, 1975 (link is a PDF file), 1976), which explained why the total helicity alone, rather than the infinity of invariants of ideal magnetohydrodynamics, should be important and determined properties of the relaxed states of toroidal plasmas. These calculations showed that the relaxed state accounted quantitatively for many hitherto unexplained observations on toroidal pinch experiments.


As we already know, magnetic field lines are mathematical objects not physical objects. Therefore, the reconnection of magnetic field lines is, strictly speaking, a mathematical process not a physical process. This is a distinction that I have made before, on 19 November 2011 ...

Originally Posted by Tim Thompson View Post
Originally Posted by Michael Mozina View Post
Ok Tim, what do YOU PERSONALLY expect to "reconnect" in part 4, in a vacuum, *WITHOUT* plasma?
Physically: Nothing "reconnects", that's just a word we use to name the process. What physically happens is that the magnetic field changes from a higher energy state to a lower energy state, and the energy lost by the field escapes as electromagnetic photons. In the presence of a plasma, that energy will transfer to the plasma and manifest itself as an impulsive increase in plasma kinetic energy.

Mathematically: Field lines are the mathematical tool of choice to describe and analyze any field, ever since Maxwell. Mathematically, the lines of force representing the physical magnetic field literally reconnect, resulting in a change in the topology of the field. The name, "magnetic reconnection", comes from this mathematical reconnection of field lines.

That's what I, personally think.

I think my opinion then is justified by the definitions & descriptions I have posted here. The twin themes of a change on topology and a transition from a higher to a lower energy state are consistent in the definitions provided by multiple reliable sources. The change in topology is a mathematical process, the transition from higher to lower energy is a physical process. This is where the intimate relationship between mathematics and physics is well illustrated. We can pretend that the lines of force are physical, rather than mathematical, and we can likewise pretend that the reconnection of field lines is a truly physical process. If we do that, and make predictions regarding anticipated physical observations, our predictions are verified. And so one might ask, while there is a difference between the mathematics and the physics in principle, what is the real, practical difference, if the two are literally interchangeable, if the mathematical objects can be treated as if they were physical objects?

The fact remains, as demonstrated here, that magnetic reconnection is well defined, both as a physical process and a mathematical process.
The point of philosophy is to start with something so simple as not to seem worth stating, and to end with something so paradoxical that no one will believe it. -- Bertrand Russell
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