Nonlinear Properties of Fluxoids in Superconductors in a High-Speed Flux-Flow State

Abstract

The order-parameter variation and the electric current about the normal core of a fluxoid in high-speed motion in clean superconductors in the low-magnetic-field and low-temperature region are discussed on the basis of a time-dependent Ginzburg-Landau equation and a classical equation of motion for the core electrons. It is found that the normal current flow along the core electric field tends to a constant when the fluxoid velocity exceeds $(\frac{{\ensuremath{\xi}}_{0}}{\ensuremath{\tau}})(1+{\ensuremath{\omega}}_{c}^{2}{\ensuremath{\tau}}^{2})$, where ${\ensuremath{\xi}}_{0}$ is the coherence length, $\ensuremath{\tau}$ is the transport relaxation time, and ${\ensuremath{\omega}}_{c}$ is the cyclotron frequency. Expressions of the strain field associated with high-speed fluxoids are derived by the use of a modified elastic-wave equation with superconductivity parameters and are used to investigate the fluxoid velocity dependence of the flux-pinning effect. It is shown that the supersonically accelerated fluxoids radiate elastic shock wave, and that flux pinning by internal strain sources like dislocations is expected to disappear. A wave radiation and lowering of the pinning are also found when fluxoids are subjected to a high-frequency vibration.