Calculations of the AC losses in superconducting cables and coils: Neumann boundary conditions of the T–A formulation

Abstract Numerical techniques play an important role in the design of high-temperature superconductor (HTS) systems. In the superconductivity community, the T – A formulation of Maxwell’s equations and its homogeneous technique have become popular in recent years. The T – A formulation has the capability of simulating HTS systems and high computational efficiency. However, it is still difficult for the T – A formulation to solve some special problems. For instance, the net current is not explicitly known in each HTS tape. In the present work, the contributions of the Neumann boundary condition are studied, which represent a coupling effect between the T and the A formulations. This paper firstly describes the Neumann boundary condition in detail. Then, based on the T – A formulation and its Neumann boundary condition, the non-uniform current distribution in the cables and the current decay in the closed-loop coils are respectively analyzed. This method can solve the difficulties of the T – A formulation in calculating some specific problems, and extend the application range of the T – A formulation. Furthermore, the above supplement is also applicable to the homogeneous and the three-dimensional (3D) models.