Time-Dependent Theories

Abstract

Following the discovery of flux flow as a dissipative phenomenon in type-II superconductors, a number of phenomenological theories were proposed for treating this subject, namely by BARDEEN and STEPHEN [10.1], VAN VIJFEIJKEN [7.14-16], and NOZIÈRES and VINEN [10.2]. All three models assume a local superconductor and treat the core of a vortex line as being fully normal resulting in dissipation due to quasiparticle scattering by the lattice. The temperature is assumed to be much smaller than T_C such that the normal electrons outside the vortex core can be neglected. The transport current density is assumed to be small but uniform. More specific, the transport current density and the normal current densities generated by the flux motion are taken to be small compared to the supercurrent densities circulating around the vortex cores. This is equivalent to the criterion that

$${V_\varphi }\tau \ll {\xi _c}$$

(10.1)

meaning that the distance a vortex line moves in a relaxation time τ is small compared with the core radius ξ_C. Vortices are assumed to move freely without any influence of flux pinning.