NONLINEAR FLUX DIFFUSION IN SUPERCONDUCTORS

A review of recent results on nonlinear diffusion of magnetic flux in high-Tc superconductors is given. Making use of a universality of thermally-activated flux diffusion, one can formulate the problem of macroscopic flux dynamics in terms of directly measured quantities. A hierarchy of flux creep time-scales and their dependence on initial and boundary conditions is considered. The essential effect of the sample geometry on the flux creep dynamics is discussed for a thin plate in a parallel and perpendicular magnetic field, which corresponds to local and nonlocal regimes of nonlinear flux diffusion, respectively. Both transient and steady-state regimes of flux creep are discussed. Instabilities of flux diffusion in anisotropic superconductors are considered which are give rise to a dissipative transition of the uniform critical state to either static macrovortex structures or magnetic flux turbulence. Manifestations of nonlinear flux diffusion in observed macroscopic electrodynamics of high-Tc superconductors are discussed.