Critical state in disk-shaped superconductors

We have calculated the magnetic fields and currents occurring in a disk-shaped superconductor (radius {}thickness) in the critical state in a self-consistent way using finite-element analysis. We find that the field shielded (or trapped) in the center of the disk is roughly equal to Jcd, where d is the thickness of the disk. The shielding currents also create radial fields which are or order Jcd/2 on the disk surface. For low applied fields H_appl<Jcd these self-field effects dominate, leading to a deviation of the local field direction from the applied field, which can exceed 90 deg towards the outside perimeter of the disk. If Jcd is large, as is the case for YBa₂{Cu}₃O_7-δ single crystals at 4.2 K, self-field effects persist up to several telsa applied field. The field dependence of the calculated magnetic moment in the self-field dominated regime is independent of whether Jc is weakly or strongly ({∝}1/H) dependent on field. The calculations were validated by comparison to both magnetic and resistive measurements on a disk-shaped section in Nb₃Sn tape.