ANOMALOUS SKIN EFFECT IN CYLINDRICAL SAMPLES

A description is given of the anomalous skin effect in a cylinder placed in an a.c. magnetic field parallel to the cylinder axis. The necessary nonlocal relation between current density and electric field inside the sample is established with the aid of Boltzmann’s transport equation. Results are presented in terms of the current density in the sample and its magnetic susceptibility. 1. Irztroduction. It is a well-known fact that in a metal, placed in an electromagnetic field, the internal fields are damped out rapidly due to the skin effect. The usual description of this phenomenon is based on Maxwell’s equations and Ohm’s law, leading to the introduction of the skin depth, i.e., the distance over which the field penetrates in the metal. Pippard ’ ) was the first to point out that the implicit assumption that the field may be considered as spatially constant for the purpose of calculating the current at a point, cannot be generally valid. The theory will certainly break down when the field varies appreciably over a distance of the order of the mean free path of the conduction electrons. This effect, which is observed at low temperatures where the mean free path is large, is known as the anomalous skin effect and is characterized by a further decrease of the bulk conductivity of the metal. This has been discussed at length by Reuter and Sondheimer2> and several other authors33 4, on the basis of a more general relation between current and electric field, in which the expression for the local current density involves a definite integral over the values of the field at all points in the metal. Such a relation can be derived from Boltzmann’s transport equation for the conduction electrons. The case of a cylindrical sample was first considered by Dingle’) for a wire in a homogeneous electric field in the direction of the wire. It is the purpose of the present paper to extend the theory to a case which is of particular interest from an experimental point of view, namely a cylinde