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 J(c) 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 J(p)(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, J(pK) (B) = J(pK)(0)/(1 + vertical bar B vertical bar /B-0), as an example. We calculate J(c)(B-a) as a function of a perpendicular applied magnetic induction B-a and show how J(c)(B-a) is related to J(pK)(B). We find that J(c)(B-a) is very nearly equal to J(pK)(B-a) when B-a >= B*(a), where B-a(*) is the value of B-a that makes the net flux density zero at the strip's edge. However, Jc(Ba) is suppressed relative to J(pK)(B-a) at low fields when B-a < B-a(*), with the largest suppression occurring when B-a(*)/B-0 is of order unity or larger.