Dynamics of flat superconductors in a perpendicular magnetic field.

Abstract

The theory of flux-line motion and ac response of a thin superconducting strip or circular disk in perpendicular time-dependent magnetic field is given. Flux dynamics in general is governed by a complex nonlinear sheet resistivity \ensuremath{\rho}/d (d is the thickness). In contrast to longitudinal fields, perpendicular field changes do not obey a diffusion equation but an integral equation with singular kernel. Screening currents immediately penetrate to the strip center and at times t\ensuremath{\gg}${\mathrm{\ensuremath{\tau}}}_{0}$ decay as exp(-t/${\mathrm{\ensuremath{\tau}}}_{0}$) with ${\mathrm{\ensuremath{\tau}}}_{0}$=0.249ad${\mathrm{\ensuremath{\mu}}}_{0}$/\ensuremath{\rho} (2a is the strip width). Maximum ac losses occur at \ensuremath{\omega}${\mathrm{\ensuremath{\tau}}}_{0}$=1.11.