Instabilities in the array of phase-slip centers in superconducting filaments

The dynamics of formation and destruction of phase-slip centers (PSC) in the resistive state of a narrow superconducting channel is considered. Using the principle of minimum entropy production, stability is studied of a periodic array of PSCs with respect to their displacements from the equilibrium positions. It is shown that the periodic array of PSCs is stable only if the period is long enough. By means of numerical integration of the dynamic equations, we have considered the behavior of PSCs over times longer than the order parameter relaxation time. More specifically, we studied formation and destruction of localized and nonlocalized PSCs after variations of the current through the channel, as well as the stability of an array of PSCs as a function of its structure period. Results of the numerical integration agree well with the theoretical analysis. Moreover, we have observed numerically a new phenomenon, self-sustained oscillations in the system of PSCs. This effect consists in formation and destruction of a PSC periodically in time at certain values of the current.