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Originally Posted by DrRocket
QUOTE=rcglinsk;1258071What if the question is not time dependent? If I measure the change in magnetic flux at points A and B for five seconds, and if the magnetic diffusion time is much longer than five seconds, then I should be able to work backward with the frozen in field line assumption to find some characteristics of point C five seconds ago with a high level of accuracy.
In this statement you have explicitly set the time frame in which you are working, and thereby made the question time dependent. Also, I think that buried in your statement is the assumption that the field that you measured was essentially constant for the five seconds, which is also a quantification of time dependence. My point is that when one makes approximations, that the conditions under which the approximation is valid need to be made explicit, and if the approximation is made under some sort of assumption regarding dynamics then the evaluation of the dependence on time is part of that exercise. An assumption of a frozen magnetic field with no qualifiers is at best misleading. Alfven, who invented the notion had many qualms about the applicatioin of it too broadly. Handwaving during mathematical derivations can lead to false conclusions, and dividing by zero can be subtle -- even Einstein blew that one on occasion.
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I would be very confused if frozen in field assumption based conversions from a measured variable to a derived variable were built into any long term plasma model, as no matter what diffusion time for the magnetic lines existed the long time scale of the model will far exceed it.
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I'm not sure what you are trying to say here. |
Is not "a small change" a qualifier?
You seem to be tripping up on generic qualifiers. The frozen in condition requires a small timescale compared to the diffusion time of the magnetic field. What is 'small' is determined when a specific problem is worked.
Alfven was right when he got worried about too broad application, but it was more because people started getting lazy about how 'small' the small changes in the field were. This was partly due to the fact that you had to do most of your work by hand, and partly due to the expansion of knowledge at the time. That lesson is now taught to new plasma physicists. Well, at least it was taught to this new plasma physicist
In the last bit rcglinsk is trying to say that frozen-in cannot be used on a long time scale. Say like stellar evolution. No matter how slow the diffusion is, there will be enough time for the field to diffuse away.