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When an ideal (no bulk pinning) flat type-II superconducting disk is subjected to a perpendicular magnetic field H  a , the first vortex nucleates at the rim when H  a =H 0, the threshold field, and moves quickly to the center of the disk. As H  a  increases above H 0, additional vortices join the others, and together they produce a domelike field distribution of radius b. In this paper I present analytic solutions for the resulting magnetic-field and sheet-current-density distributions. I show how these distributions vary as b increases with H  a , and I calculate the corresponding field-increasing magnetization.

Geometrical Barriers and the Growth of Flux Domes in Thin Ideal Superconducting Disks