An analytical solution for the extended critical state model

Abstract

The equations of the extended critical state model are solved analytically for the case when an external magnetic field is increased according to the law . Distributions of magnetic and electric fields in a superconductor are found to depend on the relation between characteristic times of two processes: the increase of applied external magnetic field and the diffusion of magnetic field into a superconductor. If the diffusion time is much smaller than the characteristic time of the magnetic field increase, the solution reduces to that of the classical critical state model. In the opposite case, the solution tends to the solution for normal metals. In this case, the discrepancy between the results of the expended and classical critical state models increases with time.