Low-Frequency Permeabilities of a Superconductor due to Surface Currents

Abstract

Superconductors which can carry critical persistent currents around the circumference of a specimen may dissipate energy when an alternating magnetic field ${h}_{0}cos\ensuremath{\omega}t$ is superimposed on a magnetic field ${\mathrm{H}}_{0}$ which is swept at a constant rate $\frac{d{H}_{0}}{\mathrm{dt}}$. We have calculated, for a long macroscopic superconducting cylinder, the real and imaginary parts of the permeabilities due to the surface currents alone for the first three Fourier components of the internal field. The results are complicated and depend on two parameters, namely, $\frac{(\frac{d{H}_{0}}{\mathrm{dt}})}{\ensuremath{\omega}{h}_{0}}$ and $\frac{{h}_{c}({H}_{0})}{{h}_{0}}$. The function ${h}_{c}({H}_{0})$ is a measure of the current-carrying capacity of the surface of the superconductor.