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 ar e given for the construction of j(c)(r). Samples with homogeneous thic kness are divided into cakelike regions with a unique current directio n. The spatial magnetic flux density distribution and the magnetic pol arization of such a cakelike unit cell with homogeneous current densit y are calculated analytically. The magnetic polarization and magnetic flux density distribution of a superconductor in the mixed state is th en given by an adequate superposition of the unit cell solutions. The theoretical results show goad agreement with magneto-optically determi ned magnetic flux density distributions of a quadratic thin supercondu cting YBa2Cu3O7-x film. The current density distribution is discussed for several sample geometries.