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From: David Jefferies
Date: 10 Nov 2001
Time: 07:07:30
Remote Name: 195.92.168.171
Frank,
On the anomalous skin effect, I can make a little progress on your "wish list".
In a perfect conductor (zero resistance, infinite conductivity) we would not expect electromagnetic fields to penetrate the material at all, and there would be enormous bulk current density confined to a surface sheet of current.
As the conductivity falls (DC resistance increases) some limited penetration of fields becomes possible; the conductor will support electric field parallel to the surface which drives currents against the inherent resistivity.
These surface-parallel E fields fall off exponentially with penetration depth; the characteristic distance required to fall to 1/e of the surface value is called the "skin depth".
The resistance of a metal surface in ohms per square may now be estimated by multiplying the bulk DC conductivity (in reciprocal ohms metres) by the skin depth in metres to get a number whose dimensions are reciprocal ohms (Siemens).
Now this is what the American Institute of Physics Handbook, edition 2, has to say on the subject of the Anomalous Skin Effect. (Page 5-160).
quote
At sufficiently low temperatures and high frequencies, the mean free path of the electrons in a good conductor becomes greater than the classically predicted skin depth, and the classical skin-effect equations break down.
[references A.B.Pippard, Proceedings of the Royal Society of London series A vol 191 pages 385-399 in 1947; and G E H Reuter and E H Sondheimer, Proc Roy Soc Lond A 195, page 336 in 1948]
Thus, the radio-frequency skin conductivity is practically independent of bulk conductivity (measured at direct current) when the mean free path of the electrons is sufficiently long. Data are given by Pippard on silver, gold, copper, tin, and aluminium.
unquote ..........................................
Note; the so-called "mean free path" is the distance an electron (regarded as a classical particle) moves, on average, between scattering events. It scatters by colliding with another electron or with a quantum of energy of a lattice vibration (called a "phonon"). As the vibrations of the lattice become less as the temperature is lowered, we find that the scattering becomes less and the mean free path longer at lower temperatures (see J M Ziman "Electrons and Phonons").
Thus we expect the transition from classical skin effect to anomalous skin effect to be both frequency and temperature dependent. There is also the issue of whether the electrons are forced into circular paths by an applied magnetic field.
It is a long time since I looked at this body of theory, so I expect that by now there is a vast literature. I can't put in numbers for you at the moment, but a search on http://google.com for "anomalous skin effect" should produce a wealth of data.
best regards
David.