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The scaling of plasmoid instability maximum linear growth rate with respectto Lundquist number $S$ in a Sweet-Parker current sheet, $\gamma_{max}\simS^{1/4}$, indicates that at high $S$, the current sheet will break apart beforeit approaches the Sweet-Parker width. Therefore, a proper description for theonset of the plasmoid instability must incorporate the evolving process of thecurrent sheet. We carry out a series of two-dimensional simulations and developdiagnostics to separate fluctuations from an evolving background. It is foundthat the fluctuation amplitude starts to grow only when the linear growth rateis sufficiently large ($\gamma_{max}\tau_{A}>O(1)$) to overcome convectivelosses. The linear growth rate continues to rise until the sizes of plasmoidsbecome comparable to the inner layer width of the tearing mode. At this pointthe current sheet is disrupted and the instability enters the early nonlinearregime. The growth rate suddenly decreases, but the fluctuation amplitudecontinues to grow until it reaches nonlinear saturation. We identify importanttime scales of the instability development, as well as scalings for the lineargrowth rate, current sheet width, and dominant wavenumber at current sheetdisruption. These scalings depend on not only the Lundquist number, but alsothe initial noise amplitude. A phenomenological model that reproduces scalingsfrom simulation results is proposed. The model incorporates the effect ofreconnection outflow, which is crucial for yielding a critical Lundquist number$S_{c}$ below which disruption does not occur. The critical Lundquist number$S_{c}$ is not a constant value but has a weak dependence on the noiseamplitude.

Plasmoid Instability in Evolving Current Sheets and Onset of Fast Reconnection