Energy relaxation at a hot-electron vortex instability

At high dissipation levels, vortex motion in a superconducting film has been observed to become unstable at a certain critical vortex velocity v^* . At substrate temperatures substantially below T_C , the observed behavior can be accounted for by a model in which the electrons reach an elevated temperature relative to the phonons and the substrate. Here we examine the underlying assumptions concerning energy flow and relaxation times in this model. A calculation of the rate of energy transfer from the electron gas to the lattice finds that at the instability, the electronic temperature reaches a very high value close to the critical temperature. Our calculated energy relaxation times are consistent with those deduced from the experiments. We also estimate the phonon mean free path and assess its effect on the flow of energy in the film.