Virtual Voltage Method for Analyzing Shielding Current Density in High-Temperature Superconducting Film With Cracks/Holes

An accurate numerical method is proposed for calculating the shielding current density in a high-temperature superconducting film containing defects. If the initial-boundary-value problem of the shielding current density is formulated by the T -method, integral forms of Faraday´s law on defect surfaces are also imposed as natural boundary conditions. However, the conditions are not satisfied exactly by a numerical solution and their residuals develop intolerably with a decrease in the film thickness. In order to resolve this problem, the following method is proposed: virtual voltages be applied along the defect surfaces as to have the natural boundary conditions numerically satisfied. A numerical code is developed on the basis of the proposed method, and the influence of a crack on the inductive method or the permanent-magnet method is numerically investigated.