Time dependent London approach, dissipation due to out-of-core normal excitations by moving vortices

TL;DR

This paper extends the London theory to include dissipation from normal excitations caused by moving vortices, analyzing how vortex motion affects field distribution and dissipation, with implications for vortex lattice orientation.

Contribution

It introduces a time-dependent London approach incorporating normal excitations and analyzes the resulting vortex field distribution and dissipation effects.

Findings

Vortex field distribution loses cylindrical symmetry when moving.

Contraction of vortex field is stronger along the direction of motion.

London dissipation contribution approaches Bardeen-Stephen dissipation at high velocities.

Abstract

The dissipative currents due to normal excitations are included in the London description. The resulting time dependent London equations are solved for a moving vortex and a moving vortex lattice. It is shown that the field distribution of a moving vortex looses it cylindrical symmetry, it experiences contraction which is stronger in the direction of the motion, than in the direction normal to the velocity $\bm v$. The London contribution of normal currents to dissipation is small relative to the Bardeen-Stephen core dissipation at small velocities, but approaches the latter at high velocities, where this contribution is no longer proportional to $v^2$. To minimize the London contribution to dissipation, the vortex lattice orients as to have one of the unit cell vectors along the velocity, the effect seen in experiments and predicted within the time-dependent Ginzburg-Landau theory.