A Fast Numerical Approach Toward AC Loss and Critical Current of Large-Scale Stacked Cables

Abstract

Evaluating ac loss and critical current of large-scale high-temperature superconducting cables is one of the fundamental studies toward fusion magnet applications. In this article, a new and fast numerical method is proposed for the calculation of ac loss of large-scale stacked cables. The model consists of the $J$ integral formulation and the fast multipole method (FMM). Compared to the $T$ integral formulation, the $J$ integral formulation exhibits better nonlinear convergence. Meanwhile, the FMM successfully reduces the storage and computational complexity of dense matrices from $O(N^{2})$ to $O(N)$. This article compares the computational performance of three models through the analysis of the ac loss of a Rutherford cable consisting of ten quasi-isotropic strands. The models considered are the $T$-$A$ formulation, the $J$ integral formulation without FMM, and the $J$ integral formulation with FMM. The results show that the computational performance of the $J$ integral formulation with the FMM is significantly better than that of both the $T$-$A$ formulation and the $J$ integral formulation without FMM. Furthermore, this model can also be used for the evaluation of the critical current of the Rutherford cable.