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Old 28th September 2010, 10:37 PM   #4219
Tim Thompson
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Lightbulb Frozen Field Approximation I

Originally Posted by Michael Mozina View Post
No, actually that seems to be where you get yourself in trouble with MHD theory. You're using a concept Alfven applied to *DENSE NON CURRENT CARRYING PLASMA*, and you're trying to treat *LIGHT* plasma that carries current in exactly the same "frozen in" manner. It doesn't work. Alfven from Cosmic Plasma:
... The concept of `frozen-in magnetic field lines' has played a central role in plasma physics due to the fact that in several situations, but far from all, it is legitimate to use it. ... One of the requirements for using the `frozen-in' field concept is that E|| = 0. In order to satisfy this, the electric conductivity parallel to the magnetic field, \sigma||, must be infinite. If we use the classical formula (see, for example, CE, p . 149) we find that under cosmic conditions, \sigma|| is usually so large that we can regard it as infinite.
See Mozina's post for the full extent of his quote from Alfven. The assumption apparently made by Alfven, that most astrophysical plasmas do not conform to the conditions required for the frozen-field approximation, is now known to be wrong. Before I go on, remember this, from 11 February 2009:

Originally Posted by Tim Thompson View Post
Just because somebody wins the Nobel Prize does not mean they are the last & final word on the topic. Einstein was a fairly smart guy, and he won a Nobel Prize too. Then he wasted half his life in the vain pursuit of a unified field theory when he denied the validity of quantum mechanics (despite having been one of its founding fathers).

Plasma physicists today are far more knowledgeable than was Alfven, simply because they have the advantage of an extra 50 years or so to study the topic. So if you are serious, that you trust only the MHD of Alfven, then you live in yesterday's world, and adhere to yesterday's physics, and are simply being left behind while intelligence marches forward and you stand still.

Just compare Alfven's level of MHD sophistication with what we can do today. See, for instance, the text book Magnetic Reconnection: MHD Theory and Applications (Priest & Forbes, Cambridge University Press, 2000), or Nonlinear Magnetohydrodynamics (Dieter Biskamp, Cambridge Monographs on Plasma Physics, 1993). Alfven's level of sophistication is primitive by comparison, and he totally ignores the entire field of radiative transfer in plasmas (i.e., Radiation Hydrodynamics; Mihalas & Mihalas, Oxford University Press 1984; Dover reprint 1999). You can't stick with Alfven & only Alfven unless you are simply willing to abandon science altogether.
One must fully comprehend that Mozina's blind reliance on Alfven, to the exclusion of everything done in science since Alfven was active, is purely religious and has nothing at all to do with science. That kind of blind faith in any authoritative figure in science must always be rejected, no matter what the science, and no matter the qualifications of the authoritative figure. Science succeeds or fails on its own internal strengths & weaknesses, not on the declarations of authority, despite Mozina's obvious belief that authoritative imprimatur is all that science requires. Why bother with observations? Why bother with controlled laboratory experiments? What use could they possibly be, when the authority of Alfven settles everything?

It is critical to realize that astrophysical plasmas were not well explored when Alfven was active, so there was precious little factual information on which to build a science. Alfven relied mostly on his own intuition, which failed him in this case because it was built on engineering & laboratory experience that did not properly replicate the physical conditions of space & astrophysical plasma. But we must also realize that Mozina fails not only to understand plasma physics, he does not really understand Alfven either. Look again at what Alfven said: "One of the requirements for using the `frozen-in' field concept is that E|| = 0. In order to satisfy this, the electric conductivity parallel to the magnetic field, \sigma||, must be infinite." In order for a magnetic field to be literally frozen into the plasma, the conductivity has to be literally infinite, which will never happen in any physical reality, so it is a trivial observation that no magnetic field can ever be literally frozen into any physically real plasma, and literally everybody in plasma physics knows that very well.

But what else does Alfven say? He says this: "we find that under cosmic conditions, \sigma|| is usually so large that we can regard it as infinite." And what does that mean in any practical sense? It simply means that the mobility of the magnetic field lines relative to the plasma depends on the conductivity. The higher the conductivity, the slower the diffusion of the magnetic field through the plasma, and the more "practically frozen" (not of course literally frozen) it will appear to be. Now, if you are interested in physics that happens in the plasma on a time scale short compared to the diffusion time scale (set by the conductivity), then you can treat the magnetic field for that application as being "frozen". On the other hand, if you are interested in physics that happens on time scales that are long compared to the diffusion time scale of the magnetic field in the plasma, then you cannot use the "frozen" approximation at all, and must be mindful of the mobility of the magnetic field in that application. This in fact is exactly how the frozen field approximation is used in astrophysical plasma physics, and it is in fact precisely in keeping with the rules laid down by Alfven. His mistake was in his assessment of the physical characteristics of the plasma, for which he had not enough factual information at hand. But his assessment that magnetic fields are never really frozen into a plasma was correct, and modern plasma physics adheres to that assessment.

Now, with that said, allow me to repeat myself from 12 March 2009

Originally Posted by Tim Thompson View Post
Originally Posted by brantc View Post
Do magnetic fields stay frozen into a resistive (not super conducting) plasma over long time scales?
That depends on what "long time scales" mean. The mobility of the magnetic field depends on the conductivity of the plasma. The field is literally "frozen in" to the plasma only in the ideal case of zero resistivity, but of course that is not physically interesting except as an approximation. The real question you should be asking is whether or not the time scale for diffusion of the field through the plasma is long compared to the time scale of whatever physical phenomenon you are interested in. If the physical phenomenon is faster than the diffusion time scale, then the field is "frozen in" to the plasma for that case. If the the physical phenomenon is slower than the diffusion time scale, then the field is not "frozen in" to the plasma.

The "freezing" of a magnetic field in a plasma is not an all or nothing affair, like on & off, frozen or not frozen. Rather, the freezing is only an approximation, and depends entirely on the time scale of interest for any give case. The same field in the same plasma might be "frozen" for one purpose, but "not frozen" for another purpose. This is all standard plasma physics, explained in any textbook on the subject.
My quotes from over a year ago show that we are accomplishing nothing in this thread. Mozina continues to make the same tired claims, and we continue to provide the same refutations. The claims and the refutations might be cloaked in slightly different language, but the substance of both remains unchanged. Mozina himself is beyond hopeless, far too deeply engaged in his own private world of ignorance & stupidity. All we can do is repeat & repeat & repeat until one side or the other just gives up from sheer boredom. Such is our fate.

Finally, let me finish with an interesting relevant paragraph:

"The remarkable freezing of magnetic field lines into a plasma can be traced to the large induction L of a typical large scale astrophysical plasma and a correspondingly small resistance R. In electrical circuits the timescale for decay of currents is L/R and, correspondingly, the time scale during which flux freezing holds is L/R and in astrophysics is generally very large."
Plasma Physics for Astrophysics, Russell M. Kulsrud, Princeton University Press 2005, page 2.
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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