Magnetic-flux profiles of high-Tcsuperconducting granules: Three-dimensional critical-state-model approximation

Magnetic-flux penetration of high-${\mathit{T}}_{\mathit{c}}$ superconducting (HTS) granules in three dimensions is modeled using spheres and spheroids within the critical-state theory. Numerical approximations for the simplest Bean-London model overlap analytic results in the limits of small and full penetration. Examples for flux contours, initial magnetization, and magnetic hysteresis loops are calculated for the complete range of flux penetration. These results are compared with the solutions for slabs and cylinders so far used in the study of HTS materials. The differences in the flux profiles found for oblate spheroids indicate the inaccuracy of using other geometries in the analysis of HTS flakelike grains.