Schematic frictional model for interacting vortices in an isotropic superconducting plate (abstract)

Abstract

In the simple model proposed, repulsive intervortex forces are balanced by containing forces produced by the external field (H) and by frictional forces representing the effects of pinning on displaced vortices. For the field-cooled (FC) state, whose vortex density is presumably uniform, the empirical fact that the average flux density (B̄) in nearly equal to H yields an operational inverse-square dependence of the intervortex force on the intervortex spacing. For both the FC and zero-field-cooled (ZFC) states, expressions are derived for B̄ vs H (including the remanences at H=0) and for the profiles of B across the sample thickness. Calculations of these properties are compared with experiment and with the macroscopically related critical-state model, revealing again that the pinning forces are strongly dependent on H. The frictional interacting-vortex model is also used in deriving the critical current as a transport property of the FC and ZFC states.