Numerical calculations of high temperature superconductors with the J-A formulation

Abstract One of the main challenges in superconductivity modeling stems from the strong nonlinearity of the E-J power law relationship. To overcome this difficulty, various numerical models have been developed by the superconductivity community, such as the H formulation and the T-A formulation. These models are implemented based on different state variables in Maxwell’s equations and have the advantage of efficiency and versatility. In this study, a finite element model based on the J-A formulation is further developed to enhance its accuracy and versatility. The discontinuous Lagrange shape function is employed in the J formulation to stabilize the numerical results. Meanwhile, the Lagrange multiplier method is applied to impose the transport current on the superconductors. In terms of applications, the J-A formulation can efficiently simulate the electromagnetic responses not only of superconducting films but also of superconducting bulks. Moreover, homogeneous and multi-scale strategies are introduced to simplify the model and reduce the computation cost, allowing efficient simulation of large-scale HTS systems. Finally, the three-dimensional (3D) J-A formulation is proposed to incorporate the 3D structure of HTS systems, examples including the CORC cables as well as the racetrack coils. These results reveal that the J-A formulation is an efficient and versatile numerical method for calculating the electromagnetic behavior of high temperature superconductors.