Numerical calculations of high temperature superconductors with the J-A formulation

Abstract

One of the main challenges in superconductivity modeling stems from the strong nonlinearity of the E-J power law relationship. To overcome this difficulty, various numerical models have been developed by the superconductivity community, such as the H formulation and the T-A formulation. These models are implemented based on different state variables in Maxwell’s equations and have the advantage of efficiency and versatility. In this study, a finite element model based on the J-A formulation is further developed to enhance its accuracy and versatility. The discontinuous Lagrange shape function is employed in the J formulation to stabilize the numerical results. Meanwhile, the Lagrange multiplier method is applied to impose the transport current on the superconductors. In terms of applications, the J-A formulation can efficiently simulate the electromagnetic responses not only of superconducting films but also of superconducting bulks. Moreover, homogeneous and multi-scale strategies are introduced to simplify the model and reduce the computation cost, allowing efficient simulation of large-scale HTS systems. Finally, the three-dimensional (3D) J-A formulation is proposed to incorporate the 3D structure of HTS systems, examples including the CORC cables as well as the racetrack coils. These results reveal that the J-A formulation is an efficient and versatile numerical method for calculating the electromagnetic behavior of high temperature superconductors.

Modeling of contact resistivity and simplification of 3D homogenization strategy for the H formulation

“…The coupling form as well as the computational efficiency is close to those of the T-A formulation. As reported in [20], the use of the constant discontinuous Lagrangian shape function in the J equation can stabilize the numerical results. To further insights into the electromagnetic modeling of superconductors, a detailed review is presented in the book chapter [21].…”

“…In this context, the homogeneous strategy is proposed [62], which could significantly reduce the computational cost by an order of magnitude for large-scale HTS systems. Moreover, this modeling strategy is applicable to various models such as the H formulation [3,41], the T-A formulation [5,42,63,64] as well as the J-A formulation [20,65]. Nevertheless, the computational efficiency of 3D models still needs to be further improved.…”

FEM-Circuit co-simulation of superconducting synchronous wind generators connected to a DC network using the homogenized J–A formulation of the Maxwell equations

“…where the state variable is the current density J sc instead of current vector potential T. Thus far, the J-A formulation has been used to model superconducting tapes using a thin strip approximation [19] with zero element order in the J formulation and second order in A formulation simulating all the tapes (full model) [42]. In the present work, a new version of the J-A formulation is introduced that makes use of the homogenization technique to gain computation speed.…”