Surface Current Approximation in Certain Problems of the Classical Theory of Superconductivity

Abstract

The problems of the behavior of superconducting infinite plane-parallel plate and cylinder in an external magnetic field are solved in the approximation of the model of surface currents. The latter, in contrast to the conventional notation, enter as the currents of superconducting electrons into the boundary conditions for the magnetic induction. Surface currents are understood as the volumetric current flowing in the thickness of the near-surface layer, which is associated with the thickness of the London penetration depth of the field and currents into the thickness of the superconductor. It is shown that in this case, a jump in the magnetic quantities occurs at this thickness. The calculated average magnetization of the magnet is reduced to the strength of the external field. The proportionality coefficient, which is reasonable to call the mean magnetic susceptibility, turns out to be not exactly equal to –1, but has a slightly less value, because the field does not weaken immediately. The possibilities of experimental verification of the obtained effect are discussed.