A parameter-free method to extract the superconductor's $J_c(B,\theta)$ field-dependence from in-field current-voltage characteristics of HTS tapes

Abstract

The estimation of the critical current ($I_c$) and AC losses of high-temperature superconductor (HTS) devices through modeling and simulation requires the knowledge of the critical current density ($J_c$) of the superconducting material. This $J_c$ is in general not constant and depends both on the magnitude ($B_{loc}$) and the direction ($\theta$, relative to the tape) of the local magnetic flux density. In principle, $J_c(B_{loc},\theta)$ can be obtained from the experimentally measured critical current $I_c(B_a,\theta)$, where $B_a$ is the magnitude of the applied magnetic field. However, for applications where the superconducting materials experience a local field that is close to the self field of an isolated conductor, obtaining $J_c(B_{loc},\theta)$ form $I_c(B_a,\theta)$ is not a trivial task. It is necessary to solve an inverse problem to correct for the contribution derived from the self field. The methods presented in the literature comprise a series of approaches dealing with different degrees of mathematical regularization, such as the use of brute force or optimization methods to fit the parameters of preconceived non linear formulas. In this contribution, we present a parameter-free method that provides excellent reproduction of experimental data and requires no human interaction or preconception of the $J_c$ dependence with respect to the magnetic field. In particular, it allows going from the experimental data to a ready-to-run $J_c(B_{loc},\theta)$ model in a few minutes.