Theory of the Motion of Vortices in Superconductors

The theory of the motion of vortex lines in the mixed state of type II superconductors is derived on the basis of a local model that is a generalization of the London theory. It is believed the model simulates reasonably well the behavior of relatively pure superconductors ($l>{\ensuremath{\xi}}_{0}$), giving a vortex line with a normal core. It is found that if the force on a line is produced by a uniform transport current ${\mathrm{J}}_{T}$, electric fields generated by the motion drive the current through the core, so that the total current flow is ${\mathrm{J}}_{T}+{\mathrm{J}}_{0}(\mathrm{r}\ensuremath{-}{\mathrm{v}}_{L}t)$, where ${\mathbf{J}}_{0}$(r) is the circulation of a stationary vortex and ${\mathrm{v}}_{L}$ is the velocity of the line. In part ${\mathrm{J}}_{T}$ represents superfluid flow and in part normal flow. Expressions derived for the viscosity and flow resistivity are nearly identical with empirical laws of Kim and co-workers. The Hall angle expected in the mixed state is the same as in the normal state for a magnetic field equal to that in the core.