Preliminary study of 3D modeling of superconductors using analytical formulae
Résumé
3D modeling with numerical software or other finite element code is usually required in order to design electrical applications using bulk High Temperature Superconductors such as machines. Several magnetic or electric behaviors can be used to model the superconductor, e.g. A = 0, µr = 0 or more classically an E(J) power law. Unfortunately, 3D modeling still involves a large amount memory, and most of the time an expensive dedicated computer. To overcome these problems, we propose to investigate 3D modeling using analytical formulae. We have developed an exact and fast computer code that is able to calculate the vector potential and the magnetic field of any structure made with current carrying conductor of rectangular cross section, i.e. rectangular beam and circular arc segment. In addition, we made the assumption of the critical state model, which means that the current density |J| = Jc in the superconductor. We have first compared our code with other numerical methods on a 2D axisymmetric case of magnetic screening. Some local and global criteria such as magnetic energy have been defined to stop the penetration of the induced currents in the superconductor's cross-section. The global criteria are closer to the physics but their used requires computing surface or volume integrals over the superconducting material which greatly increases the computing time. Finally, the magnetization of a racetrack coil is computed with our method, and compared with a 3D numerical code.