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

TLDR

The T‑A formulation is an efficient method for modeling the electromagnetic behavior of high‑temperature superconductor coated conductors, which are characterized by extremely large width‑to‑thickness ratios that normally lead to a very large number of degrees of freedom. This article reviews the T‑A formulation. The T‑A formulation models the superconducting layer as infinitely thin, using the magnetic vector potential A to compute field distribution and the current vector potential T to compute current density with a nonlinear power‑law resistivity, and the governing equations are detailed for 2D/3D Cartesian and cylindrical geometries. The review discusses the advantages and disadvantages of the T‑A formulation.

Abstract

Abstract 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.