Modeling of a 3D superconducting inductor structure 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, mur = 0 or more classically an E(J) power law. Unfortunately, 3D modeling still involves a large amount of memory and, most of the time, an expensive dedicated computer. To overcome these problems, we propose to investigate 3D modeling using analytical formulae. We developed an exact and fast computer code that is able to calculate the vector potential and the magnetic field of any structure composed of current carrying conductor of rectangular cross section, i.e. rectangular beam or circular arc segment. In addition, we used the critical state model which means that the current density J is equal to +Jc, -Jc or 0 in the superconductor. 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 use requires computing surface or volume integrals over the superconducting material which greatly increases the computing time. Finally, the magnetization of a superconducting inductor of a machine is computed with our method and compared with a 3D numerical software.