Monopoles and Magnetic Reconnection

[derekmcd]

I'm currently involved in a debate elsewhere with an EU proponent involving magnetic reconnection. The debate shifted from astrophysical events to events in Tokamaks. Right now, the debate is focusing on Priests usage of the term "monopole" here:


http://books.google.com/books?id=nfQcEXpPAMoC&pg=PA472&lpg=PA472&dq=priest+monopoles&source=web&ots=ujguVpzSQW&sig=zt329H5_hEsL6QsQjJ81YLxnqh8&hl=en&sa=X&oi=book_result&resnum=9&ct=result#PPA134,M1

More specifically, this statement in the paragraph spanning pages 133 and 134:

"Thus, if the inflow field is potential, the distortion may be regarded as being produced by a series of monopole sources along the x-axis between |x|=L and |x|=Le, say."

The EU proponents argument is that monopoles don't exist and they violate Maxwell's equations, specifically Gauss' Law.

My first argument is that saying they don't exist is an extreme stance utilizing the absence of evidence fallacy. I also argue that they are not a violation... There discovery would simply mean the equations were not complete. Even with their discovery, Maxwell's equations would still be effective is explaining our everyday world. In other words, discovery of monopoles wouldn't fundamentally change what we already know concerning electromagnetism.

My second argument is that Priest and Forbes are not referring to monopole particles, but rather to some type of indirect effect due to plasma containment in a Tokamak. Another gentleman mentioned fictitious monopoles as a way to impose the boundary conditions that would create the assumed field.

I'm out of my depth concerning MHD and Tokamaks and am not sure how to approach this argument. I think it is pretty clear they are not referring to particles in the way that Dirac did and are not violating Maxwell's equation, but don't know how to properly explain what Priest and Forbes are referring to and why the usage of the term "monopole."

For the EU proponent, he is using the "AHA!" moment in that Priest and Forbes are directly violatiing Maxwell's equations by invoking non-existent particles to explain magnetic reconnection.

I'm hoping someone can dumb down, for me, Priest's reasoning for using the term "monopole". I can handle his first angle concerning monopole particles and his claim they don't exist and would be a violation, but I don't know how to show him Priest is not using "particles".

Any guidance would be much appreciated and thanks in advance.

 

[blechman]

I don't have the time to go through this carefully, but I can at least answer some of your more direct questions.

First of all, when people say, "No magnetic monopoles," what they (should) mean is that we have never seen any! In fact, there are plenty of THEORETICAL reasons why they should exist. For example, in several grand-unified theories, we predict their existence. Also Dirac has a famous argument that magnetic monopoles imply quantization of charge (however, the converse is NOT true, but it does seem to be the case that charge is quantized). So your statement about Maxwell's equations is right: they would have to be modified (in a very straightforward way) and no harm is done.

As to your second point: you are also right in that the term "monopole" can also refer to a topological point defect in your field, ANY field. So if their referring to some topology of the plasma in the tokamak, then that is a different story. However, as I already said, I haven't read the link you sent out so I don't want to say any more on this.

Anyway, hope this little bit helps to answer some of your questions.

 

[Astronuc]

Priest and Forbes are certainly familiar with Maxwell's equations.

Anyway, the reference to 'magnetic monopole' indicates a mathematical construct associated with Petschek's models. This is a simple treatment of the magnetic field at the boundaries in the 'diffusion region' between two shocks (discontinuities) in the plasma. It does not infer that magnetic monopoles exist.

I highly recommend the text by Priest and Forbes, and also's Russell Kulsrud's "Plasma Physics for Astrophysics". Also, Dieter Biskamp has a number of good books on plasma physics, including "Magnetic Reconnection in Plasmas", in the series Cambridge Monographs on Plasma Physics.

Look for references on Sweet-Parker (or Parker-Sweet) and Petschek reconnection models. These are the bases from the 1950's and 60's.

 

[derekmcd]

Thank you for your responses and reaffirming my intuition is leading me in the right direction.

Is it related to the Aharonov-Bohm effect and Berry phase? I've read a few papers on each and on the Anomolous Hall effect. Sadly, some (all) of the pdfs are a bit (way out) of my league . However, there's enough 'words' in them I can probably put together enough of a qualitative statement to make my point... I think.

I guess my goal is provide a description of a physical phenomena and show that it is not just a mathematical convenience to invoke monopoles.

If you have anything else to offer, I'd appreciate it. If not, that's ok, too. You've got me pointed in the right direction.

 

[derekmcd]

I just got through reading:

http://www.hcs.harvard.edu/~jus/0302/song.pdf"
by Jun S. Song (Song.pdf)

It was recommended in a couple other threads here. Pages five and six explained at a level clear enough, even I could understand it. Excellent paper.

In reference to the Priest/Forbes book, would it be a fair statement to say that what they recognize is the charged particles are acting in manner as if they were in the presence of a real monopole? Obviously they are not declaring a real monopole, but the conditions are such that the equations are valid to describe the particles trajectory.