Charge imbalance waves and nonequilibrium dynamics near a superconducting phase-slip center

Using a generalized two-fluid picture to describe a quasi-one-dimensional superconductor near T_c,we provide a heuristic derivation for a set of equations governing the temporal and spatial evolution of the charge imbalance (or branch imbalance) in the quasiparticles. We show that these equations are isomorphic to those that describe a simple electrical transmission line, so that charge imbalance waves may propagate in the superconductor in analogy with electrical signals that propagate down the transmission line. We propose as a model for a phase-slip center in a superconducting filament a localized Josephson oscillator coupled to the transmission line. Applying standard transmission-line theory to solve the problem, we show that the Josephson oscillations in the center generate charge imbalance waves that propagate out to a frequency-dependent distance of the order of the quasiparticle diffusion length _Q^*= (DQ^*)^1/2 before they damp out. The time-averaged behavior of the model reduces to the earlier model of Skocpol, Beasley, and Tinkham. A novel consequence of the model is a prediction of intrinsic hysteresis in the dc current-voltage relation. The model also provides a convenient framework for dealing with ac effects in phase-slip centers, including resonance and synchronization in systems of closely spaced phase-slip centers and microbridges.Research supported in part by NSF and ONR.