Magnetic reconnection and physical processes

[Zeuzzz]

Dare is ask why Fälthammars peer reviewed publication on the concept of moving magnetic field lines has invoked such a reaction? I find his point that belchers moving magnetic field line velocity is only valid when B × curl [B(E•B/B²)] = 0 quite satisfactory, likewise his example of a time-independent magnetic dipole field in the presence of a homogeneous electric field parallel to the dipole axis. But I am presuming you have a good reason to dismiss this?

That link appears to be dead, this one should work instead: On the Concept of Moving Magnetic Field Lines http://sprg.ssl.berkeley.edu/adminstuff/webpubs/2007_eos_169.pdf

More than 99% of the known matter in the universe is ionized into the plasma state. This cosmical plasma is generally permeated by magnetic fields. Hence, magnetic fields, and the concepts of magnetic field lines and magnetic field line motion, are of fundamental interest in the physics of space plasmas, including those that constitute the near environment of the Earth and other planets.
W. Belcher discussed the concept of magnetic field line motion as a useful tool in teaching electromagnetic theory in an article in Eos [Belcher, 2005]. However, there are some important limitations and pitfalls to this concept, none of which is mentioned in the article by Belcher

Or this one: http://scitation.aip.org/getabs/ser...00074000005000454000001&idtype=cvips&gifs=yes

Belcher and Olbert recently showed that the concept of the motion of magnetic field lines can be helpful in teaching classical electromagnetism. Although this concept holds in many situations, it has important limitations. It is shown that the most common definition, v=E×B/B2, which is the one used by Belcher and Olbert, is not appropriate when an electrostatic field is present, unless the field satisfies special conditions. In an infinitely conducting medium where the electric field has no component parallel to the magnetic field, E×B/B2 is still a meaningful definition of the motion of magnetic field lines (which follow the plasma motion as if "frozen-in"). It used to be assumed that space plasmas could be treated as infinitely conducting and therefore the concept of magnetic field line motion was used extensively. But local nonvanishing values of E·B can "cut" magnetic field lines and invalidate the frozen-in condition.

 

[Michael Mozina]

No photons needed.



The energy for the spark comes from the magnetic field. The decrease in the magnetic field that occurs after you unplug it induces an electric field, and that electric field pushes the spark across the gap, but the energy to do so was stored in the magnetic field.

How is that stored energy going to be conveyed to anything without photons?

 

[tusenfem]

I am sorry, but Karl-Gunne is just nitpicking in those two publications.
These days peeps are well aware of the breaking down of the frozen in condition, several papers have been published lately to specifically look at the breaking down of the frozen in condition Here is a paper by Rikard Lundin which concludes:

Our test suggests that ideal MHD applies in a macroscopic sense in major parts of the outer magnetosphere, for instance, in the external cusp and in the high-latitude magnetosheath. However, we also find significant departures from ideal MHD, as expected on smaller scales, but also on larger scales, near the cusp and in the magnetosphere-boundary layer. We discuss the importance of these findings.

And in the Earth's magntotail the same has been investigated by Tony Lui.

One just has to know when MHD applies and when not, that is what Fälthammar's paper is really about. Is the magnetic field moving along with the plasma or not, not whether magnetic fields can move at all or not.

So, frozen in field will not happen very near the X-point of reconnection, because first there is a region where the ions are decoupled from the field (ion diffusion region), and even further in the electrons decouple from the field (electron diffusion region).

 

[Tim Thompson]

Magnetic Reconnection Redux VII

There is much discussion of magnetic reconnection buried in the depths of several threads which do not obviously pertain to the topic, and probably should not. But in any case, I like the idea of concentrating discussion of reconnection in its own thread, if only to avoid the confusing profusion of topics in threads, not necessarily related to the OP thereof. So I will put this here and see what happens.

Regarding magnetic reconnection, Mozina as told us ...

... starting with the fact you can't even physically distinguish it from "induction" and "circuit reconnection" at the level of actual physics. The transfer of energy from the magnetic field to the charged particle is called "induction" and it has nothing to do with "magnetic reconnection".

What is "circuit reconnection"?
Let me start by pointing out that Mozina has never given any indication, at the level of real physics, as to what the words "circuit reconnection" (or "particle reconnection" as he sometimes puts it) are supposed to mean. If we simply look at simple electric currents, and assume that the currents merge, then what happens to the kinetic energy of the particles in the circuit? The total kinetic energy of the particles in the final merged current cannot exceed the total kinetic energy of the particles in the merging current, absent an influx of energy from other sources. That's why I have said (and Mozina has resolutely ignored) that "circuit reconnection" cannot be what's happening because it violates the well accepted principle of conservation of energy. My position may change, pending some more informative explanation of what "circuit reconnection" is supposed to mean. But see post #3209 by ben_m in the plasma cosmology thread for additional insight into currents & fields regarding circuit reconnection.

What is magnetic reconnection?
My authoritative source for the physics of magnetic reconnection is the book Magnetic Reconnection: MHD Theory and Applications by Eric Priest & Terry Forbes, Cambridge University Press, 2000. Let me quote from the introduction (page 1): "As we shall discuss in more detail later on, reconnection is essentially a topological restructuring of a magnetic field caused by a change in the connectivity of its field lines." And in the following paragraph we find this: "The evidence of reconnection in laboratory fusion machines such as the tokamak and the reversed field pinch is so strong that there is no longer any controversy about whether reconnection occurs, but only controversy about the way in which it occurs."

Why not induction?
Now, Mozina insists that what we are really seeing is induction. Is this a reasonable assertion? At the level of real physics it appears to be unrealistic. We know that induction is invariably constrained (or unconstrained) by the characteristic diffusion time for the magnetic field in a given environment. Remember that in the process of induction, the magnetic field move with respect to the charged particles, and it is that relative motion between field & particle that determines the transfer of energy from the magnetic field to the particles. Let me quote once again from Priest & Forbes, this time from section 1.1 ("The Origins of Reconnection Theory"), pages 6-7: "For example, solar flares release stored magnetic energy in the corona within a period of 100 s. By comparison, the time-scale for magnetic dissipation based on a global scale length of 10⁵ km is of the order of 10⁶ yrs. Typically, phenomena like the solar flare and the substorm require a significant fraction of the stored magnetic energy to be converted within a few Alfven time-scales. Such rapid time-scales are easily achieved in ideal MHD processes, but not in non-ideal ones. Although ideal MHD processes can release energy quickly, they rarely release a significant amount because of the topological constraints which exist in the absence of dissipation. In contrast, magnetic reconnection is not topologically constrained, and therefore it can release much greater amounts of energy (Kivelson and Russell, 1995)."

Are magnetic field lines physically real?
The concept of field lines was devised by Michael Faraday and adopted by James Clerk Maxwell, whom we recognize as the principle architect of classical electromagnetic theory and the more general classical field theory. Whether or not field lines are physically real is magnificently irrelevant, but a great red herring for anyone who wants to avoid the real physics. The name "magnetic reconnection" comes from the mathematical formulation (theory) for the physical process (observation). The equations use the topological reconfiguration of mathematical field lines to describe the topological reconfiguration of the magnetic field, as it is observed to happen. The point is that a physical process is seen to take place, and a mathematical formalism to describe that process is in place. In every respect, the predictions of the mathematical formalism are consistent with the observed processes. As long as the mathematics and the observed physics are mutually consistent and compatible, it is a matter of no consequence at all, whether or not the "field lines" represented in the mathematics directly correspond to physical lines of magnetism.

Here is a small list some of my own posts on the topic of magnetic reconnection, mostly from the plasma cosmology thread.

• Magnetic Reconnection Redux VI
• Magnetic Reconnection Redux V
• Reconnection is not induction
• Magnetic Reconnection Redux IV

 

[Michael Mozina]

What is "circuit reconnection"?
Let me start by pointing out that Mozina has never given any indication, at the level of real physics, as to what the words "circuit reconnection" (or "particle reconnection" as he sometimes puts it) are supposed to mean.

It's a "short circuit" between two current carrying "magnetic ropes". Is that clear enough?

 

[Michael Mozina]

I'm going to have to nibble at your posts after work Tim, but your notion of "magnetic reconnection' being a unique form of energy exchange is going down.....

 

[Zeuzzz]

Thanks tim, but if you could answer each of the questions in the OP I think that would resolve any issues far quicker than your long posts summarizing the theory.

 

[Reality Check]

Thanks tim, but if you could answer each of the questions in the OP I think that would resolve any issues far quicker than your long posts summarizing the theory.

I think that Tim's answer to all of the questions would be:
Read Magnetic Reconnection: MHD Theory and Applications by Eric Priest & Terry Forbes, Cambridge University Press, 2000.

The OP questions basically ask to give a complete explanation of every part of the theory and applications of magnetic reconnection.

 

[Zeuzzz]

RC, pontificate all you want. Questions were asked in the OP and you have not answered them. Which leads me to think that either you dont know the answer or magnetic reconnection theory is in such a confused state an answer can not be given.

Some people like Sol and Ben tackled a couple of simpler questions, but as for all the original questions as they were asked in the OP, no-one has answered completely.

 

[Reality Check]

RC, pontificate all you want. Questions were asked in the OP and you have not answered them. Which leads me to think that either you dont know the answer or magnetic reconnection theory is in such a confused state an answer can not be given.

Some people like Sol and Ben tackled a couple of simpler questions, but as for all the original questions as they were asked in the OP, no-one has answered completely.

Zeuzzz, pontificate all you want.
Questions were asked in the OP and I do not intend to answer them because it is not my area of expertise.

I know that magnetic reconection theory is in enough of a coherent state that textbooks can be written on it, e.g. Magnetic Reconnection: MHD Theory and Applications by Eric Priest & Terry Forbes, Cambridge University Press, 2000.

The complete, comprehensive answer to

I am after the whole process, from the topological change in the field lines representing the magnetic vector field around the formation of the neutral point (often respresentaed as an X type neutral line) all the way through to how the energy is physically released from the topology of the lines in this system.

is read Magnetic Reconnection: MHD Theory and Applications by Eric Priest & Terry Forbes.

The complete, comprehensive answer to

A) The difference between field lines reconnecting in the formation of a standard neutral point and what physically occurs (if anything) when this happens, and what physically occurs in magnetic reconnection used to explain various energy releasing mechanisms in astrophysics.

is read Magnetic Reconnection: MHD Theory and Applications by Eric Priest & Terry Forbes.

etc.

The short, basic and incomplete answer is (as described in this thread and others):
Magnetic field lines reconnect and the magnetic energy stored in the field is transfered to the charged particles in the plasma.

 

[Zeuzzz]

Zeuzzz, pontificate all you want.
Questions were asked in the OP and I do not intend to answer them because it is not my area of expertise.

Well thats all you need to say, RC. You cant answer the questions. Hopefully someone else will.

 

[Reality Check]

Well thats all you need to say, RC. You cant answer the questions. Hopefully someone else will.

What I said is that it is my guess that no one will because the OP basically asks for a complete description of the theory and applicaitons of magnetic reconnection.
Thus no one will answer the questions in the OP.

Other posters have handled this by stating the basics or by pointing you to other discussions, e.g.

Yes, that is the very simplified description of reconnection. However, you need to take into account that the "density of field lines" gives the magnetic field strength and in the "reconnection region" naturally the field strength goes to zero and the idea of a field line does not make sense anymore.

Apart from that "when the field lines suddenly straighten" that is caused by the magnetic tension, just like a pulled string.

For the rest, I have discussed reconnection in its simple form on BAUT and I don't feel like copy-pasting. Because there are several follow up posts. I guess I will have to put this into my "plasma physics for dummies" document, that I am producing for BAUT.

 

[DeiRenDopa]

Thanks tim, but if you could answer each of the questions in the OP I think that would resolve any issues far quicker than your long posts summarizing the theory.

Funny, I thought that the questions in the OP were each answered!

Which questions do you feel have not been answered, Z?

What parts of the answers given by various folk (tusenfem, sol, Zig, ...) did you not understand?

 

[brantc]

Are magnetic field lines physically real?
The concept of field lines was devised by Michael Faraday and adopted by James Clerk Maxwell, whom we recognize as the principle architect of classical electromagnetic theory and the more general classical field theory. Whether or not field lines are physically real is magnificently irrelevant, but a great red herring for anyone who wants to avoid the real physics. The name "magnetic reconnection" comes from the mathematical formulation (theory) for the physical process (observation). The equations use the topological reconfiguration of mathematical field lines to describe the topological reconfiguration of the magnetic field, as it is observed to happen. The point is that a physical process is seen to take place, and a mathematical formalism to describe that process is in place. In every respect, the predictions of the mathematical formalism are consistent with the observed processes. As long as the mathematics and the observed physics are mutually consistent and compatible, it is a matter of no consequence at all, whether or not the "field lines" represented in the mathematics directly correspond to physical lines of magnetism.

Isnt that an example of Newtonian thinking?

It doesnt matter how or why it happens. Only that we can measure it and calculate the results.

My question would be "Would a PIC simulation be more "realistic" than a MHD approximation"? Are frozen in fields an artifact of the MHD approximation?

 

[brantc]

Here is a small list some of my own posts on the topic of magnetic reconnection, mostly from the plasma cosmology thread.

• Magnetic Reconnection Redux VI
• Magnetic Reconnection Redux V
• Reconnection is not induction
• Magnetic Reconnection Redux IV

From V

"This is the basic equation of magnetic behavior in MHD, and it determines B once v is known. In the electromagnetic theory of fixed conductors, the electric field and electric current are primary variables with the current driven by electric fields. in such a fixed system the magnetic field is a secondary variable derived from the currents. However, in MHD the basic physics is quite different, since the plasma velocity (v) and magnetic field (B) are the primary variables, determined by the induction equation and the equation of motion, while the resulting current density (j) and electric field (E) are secondary and may be deduced from equations (1.8) and (1.10a) if required (Parker, 1996)."
Priest & Forbes, page 14.
​

The conversion of magnetic energy into a current always operates on a time-scale characteristic of the system, and that time scale is controlled by the ability of the magnetic field to move through the conductor, in order to create a dB/dt term from which the current is generated. That time-scale in a plasma is rather different than it is for a fixed conductor. Here we find the real deal once again in Priest & Forbes:

​

That is correct.... with the assumption that mechanical work is the provider of energy. The spinning of the planet for instance. Gravitational "work";-) from the beginning of the universe.

But the EU viewpoint is that there is a function that provides for electric fields that are not necessarily gravity driven. These electric fields provide that potential across plasma clouds or from the sun to form a flux tube whos job it is to equalize that potential.

So the starting assumptions are going to be different. The allowable conditions are going to be different.

You cannot model EU using MHD and say they are incorrect if the starting assumptions are different.

The energy is contained within the moving particles that create the magnetic field is the EU point of view.

From what I understand this is better modeled using PIC simulations.
This I think would show the veracity of the EU model if someone knew how to do that for show(i.e. on demand for this discussion).​

 

[Reality Check]

My question would be "Would a PIC simulation be more "realistic" than a MHD approximation"? Are frozen in fields an artifact of the MHD approximation?

What should a PIC simulation be more "realistic" than using the ideal MHD equations?
What do you mean by more "realistic"?

Frozen fields are an assumption of the ideal MHD model, i.e. that the topology of the magnetic field is fixed within the fluid.

 

[brantc]

What should a PIC simulation be more "realistic" than using the ideal MHD equations?
What do you mean by more "realistic"?

Frozen fields are an assumption of the ideal MHD model, i.e. that the topology of the magnetic field is fixed within the fluid.

Somebody said to me:

"MHD is 'smoothed out' plasma, that is, the treatment of plasma physics as fluids. There are no particle physics, electrons and ions, nor is there the concomitant radiation. Instabilities in fluids are well known, but have you ever seen them 'reconnect'?"


And well for instance, why not simulate a laser shot with MHD?

High Performance 3D PIC Code VLPL:Virtual Laser Plasma Lab
"The underlying physics is essentially kinetic and strongly nonlinear, thus precluding the use of hydrodynamic plasma models and/or raxial/quasistatic description of the laser pulse [12]. In this situation one is forced to use fully kinetic description of the plasma.
The most powerful tools for simulations of these strongly nonlinear kinetic phenomena are relativistic fully electromagnetic Particle-In-Cell (PIC) codes [13]. The PIC codes are based on fundamental equations for the particles and fields dynamics and provide the most detailed kinetic description of plasmas.
Fortunately, the super-intense laser pulses are extremely short, 100 fs – 1 ps, i.e., only tens to hundreds of laser periods for 1 m radiation wavelength. It is this short pulse duration that makes direct PIC simulations of relativistic laser-plasma interactions feasible. Two-dimensional (2D) PIC simulations have already become “a working horse” in studies of relativistic laser-plasma interactions."
http://www.billingpreis.mpg.de/hbp99/pu4hbp99.pdf

So this code would be ideal for fast events such as reconnection.
And we know that plasma has some resistance. Which means frozen in field should not exist. It is convenient to model it that way in certain situations but I would say for reconnection PIC is the way to go.
I deal with that every day. We have cold cathode gauges that strike a plasma at about 10-^3 down to 10-^6, is all our turbo/drag pump will do. I'm building a diffusion pump that will do 10-^9 with the right fluid. This gauge works by measuring the current flow which means the plasma dissipates power which means it has resistance.
At large enough time scale you can use MHD to estimate certain parameters about plasma for building a plasma device.
But as far as modeling what is really going at the smallest time scales with radiation and everything, PIC is the preferred method.

The problems is that it is computer intensive so I cant just whip out a sim on my desktop. The simulation mentioned in that paper would take a year on a single processor. Beside the code is for Cray.....

 

[Reality Check]

Somebody said to me:

"MHD is 'smoothed out' plasma, that is, the treatment of plasma physics as fluids. There are no particle physics, electrons and ions, nor is there the concomitant radiation. Instabilities in fluids are well known, but have you ever seen them 'reconnect'?"

Someone said to me "Baaa Baaa Baa". So what?


You did not answer:

• What should a PIC simulation be more "realistic" than using the ideal MHD equations?
• What do you mean by more "realistic"?

So this code would be ideal for fast events such as reconnection.

How fast is a magnetic reconnection event? Are you stating that they all take the same time? What is that time, a second, a year?

And we know that plasma has some resistance. Which means frozen in field should not exist.

And we know that plasma has some resistance. Which means frozen in field will exist when that resistance is low enough.

 

[Tim Thompson]

Where do Electric Fields Come From?

But the EU viewpoint is that there is a function that provides for electric fields that are not necessarily gravity driven.

And what function is that? You can't just invent a function out of your imagination without some basis in physics. I only know of two ways to get an electric field. One of those is through the motion of a magnetic field relative to an electric charge (which will create an effective electric field as far as the charge is concerned), or to physically separate electrically charged particles of opposite sign, so that an electric field appears between the separated charges. If you know of some other way, I am all ears.

"Gravity driven" motions in a plasma are usually not very important. More important are systematic motions (such as those induced by rotation) or turbulent motions induced by thermal effects. These systematic motions will create a relative velocity between charges and therefore generate a magnetic field, which can in turn generate an electric field by motion relative to the charges. But such motions are ineffective at creating bulk charge separation.

These electric fields provide that potential across plasma clouds or from the sun to form a flux tube whos job it is to equalize that potential.

So my problem is this: Where do these electric fields come from? As far as I can see, you are just inventing them out of "thin air".

 

[Tim Thompson]

Mhd & pic

Isn't that an example of Newtonian thinking?

Certainly not! Must it not always be true of all mathematical models that they must be consistent with observation? That's all I am really saying.

My question would be "Would a PIC simulation be more "realistic" than a MHD approximation"?

Just consider ocean water. Do I really need to know anything about the molecular nature of water to understand the dynamics of ocean waves? No, I need only consider the bulk properties of fluid water. But I do need to understand the molecular nature of water to explore surface tension, and that in turn affects how water gets into the air from the ocean. So whether or not I need to look at a kinetic model, that concentrates on the particle nature of water, or a fluid flow model that ignores particles and looks only at continuum properties, depends entirely on the specific problem at hand. Generally speaking, if the problem is large scale & macroscopic, the fluid model will do, but if the problem is small scale & microscopic, then a kinetic model is required.

The same is true for plasma. If you are considering a large scale, macroscopic phenomenon, it is not even possible to use a kinetic model (unless you know how to solve 10²³ simultaneous equations in 10²³ unknowns). So an MHD model is not only appropriate, is is simply the only thing you can ever do. On the other hand, if you are looking at a small scale, microscopic system (like the effect of the presence of the wall of a plasma chamber) then a kinetic model is really required.

I keep making reference to text books on plasma physics because sooner or later the discussion board format becomes inappropriate. Some questions just don't have simple answers and it really is necessary to hit the books and appreciate the genuinely complex nature of things. This is a case in point. Nobody can answer a question like the one you ask because it is too vague & too general.

Are frozen in fields an artifact of the MHD approximation?

Absolutely not!! an "artifact" is an artificial effect that comes from the mathematics but has no physical reality associated with it. In image processing, for instance, one can easily create "artifacts", which are not really there in the real image, but are there in the processed image. Frozen fields, on the other hand, are very physical and very real, and will manifest themselves in either type of plasma model if you do the physics right. Remember that an MHD model is the approximation to what you would get if you could solve 10²³ simultaneous equations in 10²³ unknowns. The collective energy of the particles is a physically real thing, just as the energy density of the field is a physically real thing. It should come as no surprise to anyone that the larger energy density usually rules the plasma.