Superconducting tubular wires in transverse magnetic fields

The electromagnetic response of a round tubular wire of superconducting film to a transverse magnetic field is investigated theoretically. For a superconducting tubular wire (STW) in which the thickness d of the superconducting layer is much smaller than the radius R of the wire, analytical expressions for the magnetic-field and current distributions are obtained on the basis of the critical state model with constant critical current density jc. When an applied transverse magnetic field Hₐ increases monotonically from zero, the penetration of the magnetic field into an STW occurs in two stages: for 0<Hₐjcd/2 the magnetic field in the interior of an STW is shielded, whereas for Hₐ>jcd/2 the magnetic field extends into the interior. Analytical expressions of the hysteretic ac loss Qtube of an STW in a transverse ac magnetic field of amplitude H₀ are also obtained, and Qtube(H₀) is found to have an abrupt change at H₀jcd/2.