CURRENT AND FIELD PATTERN IN RECTANGULAR AND INHOMOGENEOUS SUPERCONDUCTORS

The penetration and exit of magnetic flux in type-II superconductors i s investigated for the realistic situation where a transverse magnetic field is applied to a square or rectangular plate or film. In rectang ular specimens the pattern of the sheet current and of the density of the perpendicular flux has some common features with the one-dimension al distributions in circular disks or long strips. Other features, how ever, are characteristic for the rectangular shape, e.g., the starlike pattern of the penetrating flux and, in the fully penetrated critical state, the discontinuity Lines at which the current stream lines perf orm sharp bends and at which the perpendicular magnetic field H-z(x,y) exhibits sharp ridges. These typical features have to be calculated f rom a genuine two-dimensional theory. Such a theory based on a highly nonlinear current-voltage law is outlined. The field patterns obtained by this general theory are compared with patterns observed magnetoopt ically at the surface of square and rectangular single crystals or fil ms of high-T-c superconductors with homogeneous and inhomogeneous crit ical-current distribution. It is shown that the analysis of the curren t-discontinuity lines is essential to understand the flux dynamics in superconductors. In samples with inhomogeneous critical current densit y j(c)(r), a strong concentration of flux motion and electric field ca n occur along the lines where j(c) changes abruptly. This may trigger flux jumps.