The Free Energies and Phase Transition of a Cylindrical Superconductor

Abstract

The Helmholtz and Gibbs free energies for a cylindrical superconductor of arbitrary cross section in a uniform axial magnetic field are defined carefully in terms of magnetic moment or total flux for the body as a whole. These definitions, applicable for arbitrary electrodynamic description of the superconductor, are transformed to equivalent forms with different density functions, on assuming the London equations. A general expression is obtained for change of Gibbs function when the superconducting cross section contracts and normal phase appears, which gives directly the critical current density condition of London for the phase transition. Three critical fields are defined and compared, making use of several theorems on the dependence of the boundary current density on the shape and size of the cross section. The general formulas for free energies and critical fields are illustrated for several special cross sections, including an oval shape with nonuniform boundary current density. The metastability of a superconductor described by the London equations is illustrated and discussed.