Stability of current-carrying states in narrow finite-length superconducting channels

The stability of the normal state of a narrow current-carrying superconducting channel with ends connected to normal conductors is considered. It is shown that at currents lower than some critical value (which is in turn smaller than the Ginzburg-Landau critical current) the normal state of the channel is absolutely unstable near the SN boundary with respect to formation and growth of the superconducting nucleus. The latter expands in such a way that its boundary moves into the superconductor, and after a sufficiently long time the entire channel becomes superconducting