Magnetization of a Current-Carrying Superconducting Disk with B-Dependent Critical Current Density

In the frame work of the critical state model (CSM), the magnetic response of a thin type-II superconducting disk that carries a radial transport current and is subjected to an applied magnetic field have been studied. To this end, we have studied the process of the magnetic flux-penetration. For a disk initially containing no magnetic flux but carrying a radial current, when a perpendicular magnetic field is applied, magnetic flux-penetration occurs in three stages: (1) the magnetic flux gradually penetrates from the edges of the disk until an instability occurs, (2) there is a rapid inflow of magnetic flux into the disk’s central region, which becomes resistive, and (3) magnetic flux continues to enter the disk, while persistent azimuthal currents flow in an outer annular region where the net current density is equal to J _c . Also the behavior of a current-carrying disk subjected to an AC magnetic field is calculated. The magnetic flux, the current profiles and the magnetization hysteresis loops are calculated for several commonly used J _c (B) dependences. Finally, the results of the applications of the local field-dependent of the critical current density J _c (B) are compared with those obtained from the Bean model.