Magnetization and AC Susceptibility in a Thin Superconducting Disk with Field and Radius-Dependent Critical Current Density

The magnetization hysteresis loops and the ac susceptibilities of a thin superconducting disk are derived and calculated from the extended exponential critical state model, where the critical current density is assumed to be both field and radius dependent. The distributions for both the flux and current are firstly derived; later, the magnetization and ac susceptibilities are further obtained. Finally, all these quantities are numerically calculated by solving a set of coupled integral equations. Numerical results show that for a fixed maximal magnetic field, the maximal value of the magnetization and the negative real part of the ac susceptibility always decrease with the increasing of introduced radius-dependent parameter alpha, while the parameter alpha has different effects on the imagery part of the ac susceptibilities. In addition, in the increasing process of maximal applied field, the peak value of the imagery part of the ac susceptibilities decreases with the increasing of alpha. This study should be useful for the design and application of superconducting devices.