The current-induced critical field of a type II superconducting cylindrical filament

Abstract

The azimuthal surface nucleation field of an infinitely long type II superconducting cylindrical filament is calculated from the linearized Ginzburg-Landau equation for the order parameter. A current is thought to be passed along the axis of the filament which induces a magnetic field in the azimuthal direction. On increasing the current, the field increases to a value whereby a phase transition from the superconducting to the normal state occurs. The magnetic field lines are parallel to the surface of the cylindrical filament so that the required critical field is Hc3; the parallel surface nucleation field of a type II superconductor. The systems considered are a solid cylinder; free-standing and in a metallic matrix; and a very thin-walled hollow cylinder. The full numerical analysis is carried out only for a solid cylinder. In the case of a thin-walled cylindrical shell, the quantitative description of the superconducting- normal phase is given in terms of the limiting form of the temperature for small fields.