Calculation of the magnetic flux density distribution in type-II superconductors with finite thickness and well-defined geometry

The distribution of the critical current density j(c)(r) in hard type-II superconductors depends strongly on their sample geometry. Rules are given for the construction of j(c)(r). Samples with homogeneous thickness are divided into cakelike regions with a unique current direction. The spatial magnetic flux density distribution and the magnetic polarization of such a cakelike unit cell with homogeneous current density are calculated analytically. The magnetic polarization and magnetic flux density distribution of a superconductor in the mixed state is then given by an adequate superposition of the unit cell solutions. The theoretical results show goad agreement with magneto-optically determined magnetic flux density distributions of a quadratic thin superconducting YBa2Cu3O7-x film. The current density distribution is discussed for several sample geometries.