We analyze phase slip phenomena in one and two dimensional superconducting rings by solving the time-dependent Ginzburg-Landau equation. In the one dimensional case we show that the phase slip kinetics occurs simultaneously and consecutively depending on the dimensionless parameter u in the equation. In two dimensions there are two values of critical currents j_(c1) and j_(c2). When the local current is larger then j_(c1) the phase slip is similar to the one dimensional case. Kinetics is governed by kinematic vortices. When the local current exceeds j_(c2) value the vortex generation is governed by the Kibble-Zurek quench mechanism.
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