Interaction between moving Abrikosov vortices in type-II superconductors

The self-energy of a moving vortex is shown to decrease with increasing velocity. The interaction energy of two parallel slowly moving vortices differs from the static case by a small term $\ensuremath{\propto}{v}^{2}$; the ``slow'' motion is defined as having the velocity $vl{v}_{c}={c}^{2}/4\ensuremath{\pi}\ensuremath{\sigma}\ensuremath{\lambda}$, where $\ensuremath{\sigma}(T)$ is the conductivity of normal excitations and $\ensuremath{\lambda}(T)$ is London penetration depth. For higher velocities, $vg{v}_{c}(T)$, the interaction energy of two vortices situated along the velocity direction is enhanced and in the perpendicular direction is suppressed compared to the static case.