Calculation of the surface charge on a circular type-II superconducting wire carrying transport current

Abstract

A normal uniform conductor, such as a copper wire, which carries a dc or ac transport current is subject to a surface charge consisting at a given time of a constant term plus a term which varies linearly along the conductor length. For a circular type-II superconducting wire carrying an ac transport current a similar surface charge is computed (for a dc current such a surface charge is not expected unless the critical current is exceeded). In both cases the variation of surface charge along the length produces an electric field inside the wire that allows transport current to flow through the wire. Also it is shown that in a superconducting wire obeying a Bean model the electric field distribution in the wire demanded by the model results from the electric field of the surface charge canceling part of the electric field due to the time rate of change of the vector potential. The surface charge does not change previous expressions for the ac loss but it does change the electric field outside the wire. For a circular wire a radial component of electric field exists, and a measurement of this component of external electric field can be used to investigate the current distribution inside the wire. In particular, one can examine how closely the Bean model is obeyed.