Time dependent critical state in disks and rings

The authors have developed a model to calculate the response of the current distribution in disks and rings to a time-dependent applied magnetic field. In the model, the ring (or disk) is divided into concentric segments. The segments are assumed to be inductively coupled to each other and to the applied field. A time-dependent magnetic field induces a finite electric field in the ring/disk. The induced currents will then depend on the magnitude of the electric field and the current-voltage (I-V) characteristic. The current-voltage characteristic is modeled by a nonlinear resistivity. The currents determined from AC magnetization measurements on rings and experimental I-V characteristics are compared with the results of the proposed model. It is found that the shape of the magnetization curves can be easily reproduced. However, the frequency dependence of the current in the ring shows a discrepancy. The experimental frequency dependence of the currents is much smaller than that expected on the basis of the I-V characteristics and the model calculations. A possible cause could be inhomogeneities in the sample influencing the current distribution