Utilizing Triangular Mesh With MMEV to Study Hysteresis Losses of Round Superconductors Obeying Critical State Model

Nature's minimum energy principle formulated in minimum magnetic energy variation (MMEV) and coupled with the Bean's critical state model (CSM) has resulted in feasible tools to model hysteresis losses in superconductors. These tools have been applied for single wires as well as for multi-turn coils in two-dimensional modelling domains. However, so far the discretization of the modelling domain has always relied on regular rectangular meshes. Therefore, the mesh representation of round filaments suffers from large discretization error if the mesh is not refined considerably more than triangular meshing would need. In this paper, we study the utilisation of triangular mesh in such a hysteresis loss modelling tool. We present the required extension to the already available knowledge that is needed to implement such a modelling tool. With our home-brewed tool, we study the convergence of the simulated transport current losses in the cross-section of a round wire represented with triangular and rectangular meshes of different types and of different densities. According to the results, triangular meshing is considerably more efficient than rectangular meshing for simulating transport current losses in the investigated situation.