Nonlocal diffusion of vortices in the magnetic-flux creep region inside a hard superconductor

Abstract

For describing the electrodynamics of hard superconductors, the critical-state model is widely used. According to this model, a current with a density assumed to be critical is induced in a hard superconductor as a response to any external perturbance giving rise to an electric voltage in this superconductor. For substantiating this model, the idea of pinning vortices according to which the vortex structure relaxes to the equilibrium state between the pinning and Lorentz forces acting on a vortex. In this case, the nonlocal dynamics of vortices is described by a macroscopic function, namely, the magnetic induction. This is true when the vortex density varies gradually in the spatial scale on the order of the London depth. In these cases, the evolution of the magnetic flux is a direct consequence of the collective nature of diffusion processes proceeding in hard semiconductors as a response to macroscopic perturbances of various nature. For such phenomena, the critical-state model makes it possible to investigate quasistatic properties of a hard superconductor in a simple and obvious form and to calculate both its magnetization and energy loss for remagnetization using only the equation