Magnetic mirrors are well known in plasma physics. In order to work, the mean free path of the charge carriers has to be at least as long as the helical paths under the influence of the B field. Therefore, magnetic mirrors exert no mirror effect on the conduction electrons in metals under usual conditions. However, ultra-pure metals at low temperature provide a mean free path of several millimeters. If the mean free path becomes longer than the dimensions of the specimen, the conduction is called ballistic.
If a magnetic mirror had the same effect on a "ballistic electron gas" as on a plasma, different electron densities in front and at the back of the mirror would result, and hence a voltage across the mirror would appear. This voltage would be built up by using the thermal energy of the electrons. Obviously, a voltage source based on thermal energy (in the absense of a temperature gradient) violates the 2nd law of thermodynamics.
I have to admit that I do not deal with details of solid state physics on a daily basis, so this is some kind of doing "armchair physics". But I would very much like to recognize the flaw in my thinking, and I didn't find publications dealing explicitely with this topic. (Usually this means that the matter is so obvious that a publication wouldn't be worthwhile.) I wrote a short paper on this subject; the quantitative result is that one could expect an open circuit voltage of the order of 200 microvolts under feasible conditions:
Preprint On the effect of magnetic mirrors on ballistic conduction
Any helpful comments will be highly appreciated!
PS The magnetic flux density is assumed to be limited to about 1 T (Fermi energy = 11.1 eV (iron), B = 0.5 T => path diameter = 45 micrometer), so the magnetic field can be provided by permanent magnets. Since ballistic transport is limited to low temperature, an alternative would be the use of superconducting coils.
In a laboratory setup, the entropy of the whole system would be increased by the means for cooling the device. Assuming for the moment that the effect under consideration occurs at all, a battery of such voltage sources would however, after initial cooling, keep itself cool, provided that both the thermal insulation and the electric load, located outside the insulation, were sufficient.
I'm not an expert on this particular experiment, but I'd argue that this is a "partial system" issue: in order to get a magnetic mirror, you require electromagnets whose maintenance requires a constant feed of electric energy, thus causing an entropy rise at the "experiment entrance" section which I would expect to compensate for the entropy loss inside the experimental setup.
Hello Jürgen Weippert ,
many thanks for your answer! I should have mentioned it in the question (I added a postscriptum now): In contrast to plasma technology, magnetic flux densities
It doesn't violate the laws of thermodynamics, necessarily. It all depends on how the mirrors are defined, in relation to the charges that are enclosed by them-how they describe the boundary conditions. The statements are too vague for a concrete answer to be possible. Just write down the equations and see what happens.
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