Thin superconducting disk with B-dependent J(c): Flux and current distributions

The critical state in a superconducting thin circular disk with an arbitrar y magnetic field dependence of:he critical sheet current, J(c)(B), is analy zed. With an applied field B-a perpendicular to the disk, a set of coupled integral equations for the flux and current distributions is derived. The e quations are solved numerically, and flux and current profiles are presente d graphically for several commonly used J(c)(B) dependences. It is shown th at for small B-a the flux penetration depth can be described by an effectiv e Bean model with a renormalized J(c) entering the leading term. We argue t hat these results are qualitatively correct for thin superconductors of (an y shape. The results contrast the parallel geometry behavior, where at smal l B-a the B dependence of the critical current can be ignored. [S0163-1829( 99)12541-4].