Superconductor disks and cylinders in an axial magnetic field. I. Flux penetration and magnetization curves

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Abstract
The current density in type-II superconductor circular disks of arbitrary thickness, or cylinders of finite length, in an axial magnetic field is calculated from first principles by treating the superconductor as a conductor with nonlinear resistivity or with linear complex resistivity, both caused by thermally activated depinning of Abrikosov vortices. From these currents follows the magnetic field inside and outside the specimen and the magnetic moment, which in its turn determines the nonlinear and linear ac susceptibilities. The magnetization loops and nonlinear ac susceptibilities are obtained directly by time integration of an integral equation for the current density, which does not require any cutoff or approximation of the magnetic field outside the cylinder. With increasing thickness the results go over from the recently obtained solutions for thin disks in a perpendicular field to the classical behavior of long cylinders in a parallel field. Here this direct method is applied to homogeneous disks with constant thickness, but it applies to any axially symmetric superconductor with arbitrary cross section and inhomogeneity.