$T$-A Formulation for Calculating Induced Currents in Rotating High-Temperature Superconductor Coils

Among the numerical models based on the finite element method used to investigate the current density and magnetic field distributions inside high-temperature superconducting wires and their applications, the T-A formulation has become a widely used option. Typically, in applications with rotating parts, such as motors and generators, the superconducting wires are assumed to be in the stationary part of the geometry. In this contribution, we discuss the possibility of using the T-A formulation to model a rotating superconducting coil in a stationary magnetic field. In particular, we look at different ways of imposing the boundary conditions, in order to obtain induced currents flowing in opposite directions in each branch of the coil. First, we describe the case of an individual rotating cylinder of constant conductivity in a uniform magnetic field, for which analytical solutions exist. Then, we describe the case of a rotating superconducting coil in a uniform magnetic field, which requires the implementation of the proper conditions that ensure the correct coupling of the T and A parts. The results are validated against those obtained with the widely used H formulation for the equivalent case of a fixed coil in a rotating magnetic field.