The field-free region in a coated superconductor according to the Bean model for the case of transport current

This paper is concerned with the question of whether the basic Bean model which applies for the description of transport current and its loss in ordinary superconductors can also be used for describing the ac transport current in a high-temperature coated superconductor. A corollary which goes with the Bean model is the existence of a field-free region in the interior of the conductor, and a direct computation of the loss depends strongly on an accurate knowledge of this region. A calculation of the field-free region is performed here, with the loss calculation reserved for a companion paper. The shape of the field-free region is computed for various values of transport current in zero applied magnetic field. It is found that for a ratio of peak transport current to critical current greater than about 0.46 the field-free region is described by an ellipse-like curve in a reduced plot, while in a similar plot for a ratio less than about 0.46 it has a shape that more closely resembles a rectangle. The former is similar to the field-free region assumed by Norris and this case is computed in the present analysis quite accurately for ratios of peak transport current to critical current near unity. For the case of small peak current the calculation is less accurate because of difficulties of computation near the edges. Nevertheless the result can serve as an aid to making a loss estimate.