The effect of the non-uniform critical current density on the magnetoelastic behavior of bulk superconductors: Case of a long cylindrical superconductor

In this paper, the effect of non-uniform critical current density on bulk superconductors is studied, the case of a long cylindrical superconductor with transport current is chose to discussed. The critical current density is distributed non-uniformly along the radius of the cylinder. Based on the Bean critical state model, the distributions of trapped magnetic flux and shielding current in the cylinder are investigated. Combined with the plane strain approach, the analytical expressions of magnetic flux pinning force and stress are obtained. The magnetostriction of the cylinder is also discussed. Results show that the non-uniform critical current density changes the distribution law of the shielding current and trapped magnetic flux in the cylinder. The increase of non-uniform parameters n leads to an obvious increase in the flux pinning force. Thus, a larger extreme value of the pinning stress is obtained, a bigger structure deformation is produced inside the superconducting cylinder. All those conclusions will provide a helpful guide for engineering application.