The properties of thin-walled dual superconducting cylinders

Abstract

We deal with the properties of dual superconducting cylinders (DSC) in the limitd ₁,d ₂ ≪ δ _L (d ₁ andd ₂ are the thicknesses of the inner and outer cylinders, and δ _L is the penetration depth). The Gibbs free energy is given at this limit, and the variational equations are established. From these equations, we have found: 1) coupling between the two cylinders are determined by their screening factors, 2) the character of the phase transitions is also determined by the screening factors; and 3) the two cylinders cannot perform complete phase transition together. The critical field that suppresses the cylindrical Josephson current is also given, which is found to agree with the experiment. The field distribution over a DSC and the total magnetic moment are presented in terms of the effective areas of DSC cavities and the susceptibilities of the superconducting cylinders.