Response of high-Tc superconductor totime-increasing magnetic field

Abstract

Abstract Using the extended critical state model, we investigate theoretically the magnetic field penetration into a semi-infinite slab of a high-Tc superconductor in the flux flow region when an external magnetic field increases monotonically with time according to power law: H=At α . The dependencies of the flux flow resistivity and critical current density are taken to depend on magnetic field according to the generalized power law. The behavior of the solutions vs the exponent α and “amplitude” A is analyzed. It is shown that there is the critical value of the exponent α c separating the regions with different characters of the magnetic field penetration. The value of α c is determined by the exponents in the dependencies of the superconductor characteristics on magnetic field. For α α c , the electric field in a superconductor decreases with time and the magnetic field distribution tends to the one given by Bean’s critical state model. For α > α c the electric field increases with time and the pattern of magnetic field differs increasingly from Bean’s model; the behavior of a superconductor at large times is described by the model of a normal metal with the resistivity dependent on magnetic field. Thus, the response of a superconductor is described by different approximations on different stages of the process. This result is distinct from that presented in the literature. In the boundary case of α=α c , the character of the field penetration is time-independent.