Numerical Simulation of Shielding Current Density in High-Temperature Superconducting Film: Influence of Film Edge on Permanent Magnet Method

A numerical method is developed for analyzing the shielding current density in a high-temperature superconducting (HTS) film. When an HTS film contains a crack, an additional boundary condition is imposed on the crack surface and it can be incorporated into the weak form. Although the weak form can be numerically solved with the essential boundary conditions, the resulting solution does not exactly satisfy Faraday's law on the crack surface. In order to resolve this problem, the following method is proposed: a virtual voltage is applied around the crack so as to make Faraday's law satisfied numerically. A numerical code for analyzing the shielding current density is developed on the basis of the proposed method and, by means of the code, the permanent magnet method is investigated numerically. Especially, the influence of a film edge or a crack on accuracy is assessed.