Current and magnetic field distribution of disk-shaped superconducting film

When the applied field <(B)(a) over right arrow> = mu(0)<(H)(a) over right arrow> parallel to the rotation axis of a disk-shaped superconducting thin film with radius R and thickness d in a cylindrical coordinate system, and the self-field effects of the screening current <(B')over right arrow> = B'(z) (z) over cap + B-p'(p) over cap((z) over cap parallel to<(B)(a) over right arrow> perpendicular to (p) over cap) are considered, an effective method using finite-element analysis and matrix operation, to obtain the field dependent critical current function J(c)(B) from magnetic moment hysteresis loop m(B-a) in a self-consistent way, is presented. Then also in a self-consistent way, the current density J(p) and field B-z(p)= B-a + B-z'(p) distributions can be obtained, regardless whether the film being fully penetrated by the applied field or not. The effects of the radial stray field B-p(p,z) on the current cannot be neglected when B-a approximate to 0. Due to the weak self-field effects, or intense demagnetic effects of the film compared with the long cylinder-shaped superconductor, between the average values of field (B-z) and magnetization (M) there is a quantitative relation (B-z) = mu(0)[H-a + (0.8d/R)(M)] for a disk-shaped film and a qualitative relation (B-z) = mu(0)[H-a + (M)/root 1 + (2R/d)(2)] for an arbitrary cylinder-shaped superconductor under the Bean model approximation. (C) 1997 Elsevier Science B.V.