The T-A formulation: an efficient approach to model the macroscopic electromagnetic behaviour of HTS coated conductor applications

In recent years, the T-A formulation has emerged as an efficient approach for modelling the electromagnetic behaviour of high-temperature superconductor (HTS) tapes in the form of coated conductors (CCs). HTS CCs are characterized by an extremely large width-to-thickness ratio of the superconducting layer, normally up to 1000 ∼ 6000, which in general leads to a very large number of degrees of freedom. The T-A formulation considers the superconducting layer to be infinitely thin. The magnetic vector potential A is used to calculate the magnetic field distribution in all simulated domains. The current vector potential T is used to calculate the current density in the superconducting layer, which is a material simulated with a highly nonlinear power-law resistivity. This article presents a review of the T-A formulation. First, the governing equations are described in detail for different cases (2D and 3D, cartesian and cylindrical coordinates). Then, the literature on the implementation of T-A formulation for simulating applications ranging from simple tape assemblies to high field magnets is reviewed. Advantages and disadvantages of this approach are also discussed.