Geometrical barriers and the growth of flux domes in thin ideal superconducting disks

TL;DR

This paper provides analytical solutions for the magnetic field and current distributions in thin ideal superconducting disks as flux domes grow with increasing magnetic field, elucidating the geometrical barriers affecting vortex behavior.

Contribution

It introduces new analytic solutions describing flux dome growth and magnetic distributions in ideal superconducting disks under perpendicular magnetic fields.

Findings

Analytic expressions for magnetic-field distributions

Descriptions of sheet-current-density variations

Calculated magnetization as flux domes expand

Abstract

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.