Flux diffusion in high-T _c superconductors

Abstract

In type-II superconductors in the flux flow (J _⊥≫J _c ), flux creep (J _{c ⊥}≈J _c ), and thermally activated flux flow (TAFF) (J _⊥≪J _c ) regimes the inductionB(r,t), averaged over several penetration depths λ, in general follows from a nonlinear equation of motion into which enter the nonlinear resistivities ρ_⊥(B, J _⊥,T) caused by flux motion and ρ_‖(B, J _‖,T) caused by other dissipative processes.J _⊥ andJ _‖ are the current densities perpendicular and parallel toB,B=|B|, andT is the temperature. For flux flow and TAFF in isotropic superconductors with weak relative spatial variation ofB, this equation reduces to the diffusion equation$\dot B = (\rho _ \bot /\mu _0 ) \bar V^2 B$ plus a correction term which vanishes whenJ _‖=0 (this means Bׇ×B=0) or when ρ_⊥ − ρ_‖ = 0 (isotropic normal conductor). When this diffusion equation holds the material anisotropy may be accounted for by a tensorial ρ_⊥. The response of a superconductor to an applied current or to a change of the applied magnetic field is considered for various geometries. Such perturbations affect only a surface layer of thickness λ where a shielding current flows which pulls at the flux lines; the resulting deformation of the vortex lattice diffuses into the interior until a new equilibrium or a new stationary state is reached. The a.c. response, in particular the frequency with maximum damping, depends thus on the geometry and size of the superconductor.