We develop a general theory to account self-consistently for self-field effects upon the average transport critical current density Jc of a flat type-II superconducting strip in the mixed state when the bulk pinning is characterized by a field-dependent depinning critical current density Jp(B), where B is the local magnetic flux density. We first consider the possibility of both bulk and edgepinning contributions but conclude that bulk pinning dominates over geometrical edge-barrier effects in state-of-the-art YBCO films and prototype second-generation coated conductors. We apply our theory using the Kim model, JpK (B) = JpK (0)/(1 + |B|/B0), as an example. We calculate Jc(Ba) as a function of a perpendicular applied magnetic induction Ba and show how Jc(Ba) is related to JpK (B). We find that Jc(Ba) is very nearly equal to JpK (Ba) when Ba ≥ B * a , where B * a is the value of Ba that makes the net flux density zero at the strip's edge. However, Jc(Ba) is suppressed relative to JpK (Ba) at low fields when Ba < B * a , with the largest suppression occurring when B * a /B0 is of order unity or larger.
We present general solutions for the Meissner-state magnetic-field and current-density distributions for a pair of parallel, coplanar superconducting strips carrying arbitrary but subcritical currents in a perpendicular magnetic field. From these solutions we calculate (a) the inductance per unit length when the strips carry equal and opposite currents, (b) flux focusing in an applied field—how much flux per unit length is focused into the slot between the two strips when each strip carries no net current, (c) the current distribution for the zero-flux quantum state when the strips are connected with superconducting links at the ends and (d) the current and field distributions around both strips when only one of the strips carries a net current. The solutions are closely related to those found recently for the magnetic-field and current-density distributions in a thin, bulk-pinning-free, type-II superconducting strip with a geometrical barrier when the strip carries a current in a perpendicular applied field.
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