Behavior of a hollow superconducting cylinder in a magnetic field

Abstract

The behavior of a hollow superconducting cylinder of arbitrary dimensions in an external magnetic field is investigated in detail within the Ginzburg-Landau macroscopic theory. The thermodynamic potential of the system is presented in a compact form, which enables us to give a simpler description of the transitions of the system between the quantized levels in a magnetic field than in previous work on this subject. The general theory is illustrated by a number of cases, which show the dependence of the order parameter, the total flux in a cavity, and the magnetic moment of the cylinder on the magnitude of the external field and on temperature. The phase transition curves and the hysteresis boundaries are found. The tricritical points, where the difference between first- and second-order phase transitions vanishes, are established. The oscillations in a magnetic field of the specific heat of the cyclinder are investigated. The formulas are presented for the case of a thin-walled cylinder and are valid for arbitrary values of the order parameter ψ, inner and outer radii of the cylinder, external field, and temperature. The results are discussed in connection with experiment and other papers on this subject.