Accurate numerical calculation of shielding current density in HTS thin film: application to noncontact measurement method of critical current density

The numerical method has been developed for calculating the shielding current density in a high temperature superconducting thin film. After formulated by use of the current-vector-potential method, the behavior of the shielding current density is expressed as an integral-differential equation. When the initial-boundary-value problem of the equation is discretized with respect to time and space, improper integrals appear as coefficients of the nonlinear system. In order to evaluate the coefficients accurately, the double exponential formula is applied to the improper integrals. Consequently, the shielding current density can be determined accurately. As an application of the method, two types of the noncontact methods for measuring the critical current density jC have been simulated numerically. The results of computations show that the maximum repulsive force is roughly proportional to jC in the permanent magnet method. In addition, it is found that an error of the inductive method is not more than 3% if jC exceeds a certain lower limit