Calculations of the dimensional dependence of the critical state in disk-shaped superconductors

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Abstract
We present numerical calculations of the field distribution and the moment of disk-shaped superconductors in the critical state, extending earlier work of Daeumling and Larbalestier. In particular, using the Kim model for the dependence of critical current density on field, we show that a conventional model ignoring flux-line curvature predicts a nonlinear dependence of zero-field remanent moment on radius, while accounting for the curvature numerically leads to an almost linear dependence on radius, with a slope reduced from that of the Bean formula. We find an approximate analytical formula for this reduced slope.