J-A-$\phi$ Formulation Applied to Simulations of Linear Magnetic Bearings

The J-A-$\phi$formulation has been proposed lately. Its objective is to reduce the computational load of finite element electromagnetic simulations of superconducting devices. This formulation is the combination of the J-A approach, in which the magnetic vector potential, A, and the current density, J, are directly computed; and the use of magnetic scalar potential,$\phi$, in the current-free domains, a technique usually adopted in the H-$\phi$formulation. This work introduces how to couple the A and$\phi$fields when one of them is defined in a moving mesh. For proving the proposed methodology, this work applies the J-A-$\phi$formulation to simulations of superconducting magnetic bearings. Combined with a 2D planar approximation, the formulation is applied to the entire system, including the magnetic guideway and the superconducting domains, with linear vertical and lateral movements. The superconducting domains of choice comprise bulks and stacks of 2G tapes. Levitation and guidance forces are analyzed as results and validated against experimental data when available. This application allows for a deep observation of how the J-A-$\phi$formulation works alongside finite element mesh movement, which is of extreme importance for designs of devices such as magnetic bearings and electric machinery.