Self-field effects upon the critical current density of flat superconducting strips

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 edge-pinning 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 > Ba*, where Ba* 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 < Ba*, with the largest suppression occurring when Ba*/B0 is of order unity or larger.