Numerical Simulation of Critical Current in Superconducting Structures Based on Quasi-Static A- ϕ Formulation

The critical current is a key factor for the stable operation of superconducting structures. Therefore, it is imperative to employ precise and efficient numerical methods for evaluating the critical current in complex superconducting structures, thereby ensuring their operational safety and reliability. Several numerical approaches based on the finite element method have been proposed by researchers. However, when evaluating the critical current, the computational demand of the time-dependent calculation method is exceedingly high. Therefore, it is necessary to adopt a quasi-static methodology for the computation of superconducting critical currents. In this paper, it is assumed that the current in the superconductor is stable and the induced current caused by magnetic field variation has been fully dissipated. The critical current is predicted in different structures based on the quasi-static A-ϕformulation andE-Jconstitutive law. The numerical results are compared between the quasi-static A-ϕformulation and experimental data as well as the H formulation. Due to its significant computational efficiency, the quasi-static A-ϕformulation holds potential as an effective method for optimizing superconductor structures.