AC transport current loss in a coated superconductor in the Bean model

A new and straightforward calculation is made of the loss in a very thin superconducting strip of rectangular cross-section (e.g. the coating on a coated superconductor) carrying ac transport current in zero applied magnetic field, with a similar strip acting as the return path. The computation is made assuming only that the strip is composed of uniform material which obeys Maxwell's equations and the Bean model. An important consequence of the Bean model is the existence of a field-free region about the middle of the superconductor cross-section. The present loss calculation is novel in two respects: (1) It uses for the first time an actual computation of the shape of the field-free region rather than using qualitative assumptions, and (2) it uses a new approach for making the loss calculation, based on a rigorous solution of Maxwell's equations for this problem. The rigorous solution correctly treats the problem as three-dimensional, having a time-dependent charge on the surface of the superconductor, and having the electric field described by both a vector and a scalar potential. Loss computations are made for the ratio of peak current to critical current in the approximate range of one-half to one, where within this range the loss decreases by about two powers of 10. The most important result coming out of the present calculation (made for the case of a distant return path large compared with the conductor cross-section dimensions but small compared with the length of the conductor), is a confirmation of Norris's previously estimated loss expression which he obtained in a different way