ac permeability of defect-free type-II superconductors

Abstract

A theoretical and experimental study is presented of ac losses in the mixed state of type-II superconductors when viscous damping dominates flux line motion. The theory describes the ac response of a cylindrical superconductor in the mixed state in a dc magnetic field $H$ and a superposed parallel ac field of arbitrary frequency. The complex ac permeability is found to be related to the flux-flow resistivity ${\rho }_f\mathrm{}\left(B\right)\mathrm{}$, the differential permeability ${\mu }^{\prime }\mathrm{}\left(B\right)=\frac{dB}{dH}$, the frequency, and the sample radius. Measurements were made of the ac permeability in the frequency range 45-1000 Hz of two NbTa alloys which were prepared to minimize bulkpinning and surface losses. Values of ${\rho }_f\mathrm{}\left(B\right)\mathrm{}$ and ${\mu }^{\prime }\mathrm{}\left(B\right)\mathrm{}$ derived from the measurements agree qualitatively with the model, but ${\rho }_f\mathrm{}\left(B\right)\mathrm{}$ shows a weak frequency dependence that may arise from the presence of remnant nonviscous losses.