Dynamics of resistive state in thin superconducting channels

We study theoretically how the dynamics of the resistive state in narrow superconducting channels shunted by an external resistor depends on channel's length L, the applied current j, and parameter u characterizing the penetration depth of the electric field in nonequilibrium superconductors. We show that changing u dramatically affects both the behavior of the current-voltage characteristics of the superconducting channels and the dynamics of their order parameter. Previously, it was demonstrated that when u is less than the critical value uc1, which does not depend on L, the phase slip centers appear simultaneously at different spots of the channel. Herewith, for u>uc1 these centers arise consecutively at the same place. In our work we demonstrate that there is another critical value for u. Actually, if u does not exceed a certain value uc2, which depends on L, the current-voltage characteristic exhibits the step-like behavior. However, for u>uc2 it becomes hysteretic. In this case, with increase of j the steady state, which corresponds to the time-independent distribution of the order parameter along the channel, losses its stability at switching current value jsw, and time-periodic oscillations of both the order parameter and electric field occur in the channel. As j sweeps down, the periodic dynamics ceases at certain retrapping current value jr