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Bulk superconductors are used in both many applications and materialcharacterization experiments, being the bulk shape of rectangular prism veryfrequent. However the magnetization currents are still mostly unknown for thiskind of three dimensional (3D) shape, specially below the saturation magneticfield. Knowledge of the magnetization currents in this kind of samples isneeded to interpret the measurements and the development of bulk materials forapplications. This article presents a systematic analysis of the magnetizationcurrents in prisms of square base and several thicknesses. We make this studyby numerical modeling using a variational principle that enables high number ofdegrees of freedom. We also compute the magnetization loops and the saturationmagnetic field, using a definition that is more relevant for thin prisms thanprevious ones. The article presents a practical analytical fit for any aspectratio. For applied fields below the saturation field, the current paths are notrectangular, presenting 3D bending. The thickness-average results areconsistent with previous modeling and measurements for thin films. The 3Dbending of the current lines indicates that there could be flux cutting effectsin rectangular prisms. The component of the critical current density in theapplied field direction may play a role, being the magnetization currents in abulk and a stack of tapes not identical.

3D magnetization currents, magnetization loop, and saturation field in superconducting rectangular prisms