AC Transport Current Loss in a Coated Superconductor in the Bean Model

摘要

A new and straightforward calculation is made of the loss in a very thin superconducting strip of rectangular cross section 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. A consequence of the Bean model is the existence of a field-free region about the middle of the superconductor cross-section. The loss calculation now is novel in that: 1) It uses 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. The solution treats the problem as 3-D, 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 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 is a confirmation of Norris's previously estimated loss expression.