Numerical simulation of inductive method for determining spatial distribution of critical current density

The inductive method for measuring the critical current density j_C in a high-temperature superconducting (HTS) thin film has been investigated numerically. In order to simulate the method, a non-axisymmetric numerical code has been developed for analyzing the time evolution of the shielding current density. In the code, the governing equation of the shielding current density is spatially discretized with the finite element method and the resulting first-order ordinary differential system is solved by using the 5th-order Runge–Kutta method with an adaptive step-size control algorithm. By using the code, the threshold current I_T is evaluated for various positions of a coil. The results of computations show that, near a film edge, the accuracy of the estimating formula for j_C is remarkably degraded. Moreover, even the proportional relationship between j_C and I_T will be lost there. Hence, the critical current density near a film edge cannot be estimated by using the inductive method.