Theoretical expressions for AC losses of superconducting coils in external magnetic field and transport current with phase difference

We propose generalized expressions for AC losses in solenoidal coils of superconducting wires without twisting, to which both alternating transport current and AC magnetic field are applied with a phase shift. We assume that the coils can be approximated by a homogeneous superconducting sheet and that the electromagnetic behavior can be described by the Bean's critical state model, in which the magnitude of local current density is equal to the critical current density or zero. The results show that the AC losses are plotted on a master curve independent of the phase shift for the maximum magnetic field applied to the coil, and that the AC loss properties for the maximum field are similar to those of transverse-field losses.