Numerical solution of nonlinear electromagnetic field problem of superconducting tape using convex optimization

Second-generation high-temperature superconducting (Re)Ba2Cu3O7-x coated conductors have great potential for applications in high-power cables and high-field superconducting magnets owing to their excellent current-carrying capacity. However, it is still a challenge to deal with nonlinear electromagnetic field problem of (Re)Ba2Cu3O7-x superconductors accurately and efficiently. In this paper, the solution of the electromagnetic response of superconductors is equivalent to a convex optimization problem. The objective function is convex, where the constraints are linear. This convex optimization problem is solved by the infeasible start Newton's method. The proposed method is used to solve the electromagnetic field problem of two-dimensional case including the infinite length parallel stacked cable and quasi-isotropic strands, and the axisymmetric case such as insulation pancake coils. Results are verified by comparing with the finite element H and T-A formulations. Whereafter, the method is extended to analyse the electromagnetic field of no-insulation pancake coils. Finally, a simplification of the algorithm and the homogenization technique are proposed to improve the computational efficiency.