Superconductors of finite thickness in a perpendicular magnetic field: Strips and slabs

The magnetic moment, flux and current penetration, and creep in type-II superconductors of nonzero thickness in a perpendicular applied magnetic field are calculated. The presented method extends previous one-dimensional theories of thin strips and disks to the more realistic case of arbitrary thickness, including as limits the perpendicular geometry (thin long strips and circular disks in a perpendicular field) and the parallel geometry (long slabs and cylinders in a parallel field). The method applies to arbitrary cross section and arbitrary current-voltage characteristics E(J) of conductors and superconductors, but a linear equilibrium magnetization curve B = mu(0)H and isotropy are assumed. Detailed results are given for rectangular cross sections 2a x 2b and power-law electric field E(J) = E(c)(J/J(c))(n) versus current density J, which includes the Ohmic (n = 1) and Bean(n-->infinity) limits. In the Bean limit above some applied field value the lens-shaped flux- and current-free core disconnects from the surface, in contrast to previous estimates based on the thin strip solution. The ideal diamagnetic moment, the saturation moment, the field of full penetration, and the complete magnetization curves are given for all side ratios 0 < b/a < infinity.