Nature of the ac Transition in the Superconducting Surface Sheath in Pb-2% In

The response of the superconducting sheath state of Pb-2wt% In to low-frequency (20-500 cps), smallamplitude (${10}^{-2\mathrm{}}\mathrm{Oe}<h_0<20\mathrm{} \mathrm{Oe}$) ac fields has been studied. Direct observation of the wave form shows that screening currents are developed in the sheath up to a critical value $J_c$, when the field begins to penetrate. The screening current continues to increase until a saturation value $J_s$ is reached, at which point the current in the sheath stays constant for the remainder of the half-cycle. Fourier analysis of a model wave form for which $J_m=J_c=J_s$ indicates the harmonic content, and nonlinear nature, of the response. Measurements of the real and imaginary parts of the ac permeability, ${\mu }^{\prime }$ and ${\mu }^{\prime \prime }$, at the fundamental frequency as a function of the ac field amplitude at constant dc field shows that the transition is characterized by only one parameter, dependent on the dc field, and that the model gives an excellent description of the nonlinearity. Welldefined quantitative critical-current data can be obtained for comparison with the theories of Abrikosov, Park, and Fink and Barnes. The relationship between these observations and other measurements of ${\mu }^{\prime }$ and ${\mu }^{\prime \prime }$ as a function of dc field at constant ac field amplitude is discussed. It is shown that the transition is sensitive to misalignment of the specimen relative to the dc field. The change in the transition as the frequency is changed is explored, and a preliminary conclusion is that $J_s$ is much more sensitive to frequency than $J_c$.