Dynamics of flat superconductors in a perpendicular magnetic field

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 {ρ}/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{}τ₀ decay as exp(-t/τ₀) with τ₀=0.249adμ₀/{ρ} (2a is the strip width). Maximum ac losses occur at {ω}τ₀=1.11.