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

Abstract

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.

Universal self-field critical current for thin-film superconductors

“…For a very thin conductor the x -component of this self-field at the surface, B x ( x , y =± b ), is uniform across the width and of magnitude μ 0 bJ (ref. 36). Consequently, if the current I is increased until this field reaches B = B c1 , then vortices will nucleate at the flat surface in the form of closed loops around the conductor surface normal to the transport current38.…”

“…Rearranging equation (13) of Brojeny and Clem36 (or indeed equation (8) for a non-vanishingly-thin film) the y -component of the field near the edges for a uniform current distribution becomes…”

Thermodynamic Parameters of Single‐ or Multi‐Band Superconductors Derived from Self‐Field Critical Currents

“…The magnetic field, B y (x = ±a), at the film edges perpendicular to the flat surfaces was calculated using Eq. (4) of Brojeny and Clem: [11] B y (x = ±a) = ∓ (μ 0 b J c /π ) ln 2a b + 1 .…”

Current-Induced Critical State in NbN Thin-Film Structures

“…Following this model and recent works 7,8 on vortex dynamics, the density of the transport current required for penetration of magnetic vortices into a superconducting strip of the width W can be written as…”