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

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.