Critical state model for magneto-elastic problem of thin superconducting disks

Abstract

The magneto-elastic problem of a thin superconducting disk in a perpendicular magnetic field is analyzed with field-dependent critical current. We calculate numerically the body force distribution and discuss the field dependence of Jc on the magneto-elastic behavior during field ascent and descent for three critical state models: Bean, Kim, and exponential models. The results show that when considering a field dependence of Jc, the flux and remagnetization fronts have a larger moving speed towards the center of a disk relative to the Bean model. Simultaneously, the most dangerous stage of possible cracking for the disk will arrive early in the field decreasing stage. The magnetostriction loops are also presented during a full cycle of the applied field. It is interesting that the calculated magnetostriction loops for the Kim and exponential models are quite similar to the corresponding magnetostriction curves at low and high temperatures measured in the experiment.