Out-of-plane current density at different times shows fractal-like cascade to smaller scales via the plasmoid instability. First, the Sweet-Parker current sheet breaks up to form a chain of plasmoids connected by secondary current sheets (top panel). Secondary current sheets are Sweet-Parker like, become unstable again, and generate the next batch of plasmoids (middle panel). This cascade leads to a hierarchy of plasmoids of various sizes (bottom panel). These snapshots present a small portion of the whole simulation box from a simulation. The reader is referred to Fig. 4 of Ref. 28 for an illustration of the whole system.
(a) Cumulative distribution function and (b) distribution function of plasmoids from a simulation. The vertical dotted line denotes where .
The distribution of the leading digit of flux shows good agreement with Benford's law (for ), but deviates significantly from the prediction based on .
Stack plot of plasmoid positions along the outflow direction x during the period t = 4 to t = 6. Each dot represents a plasmoid, color coded according to its flux in logarithmic scale.
Top: On the right hand side of the panel is an example of two partially merged plasmoids, both small in size. Bottom: When the merging is completed, they become a plasmoid much larger in extent. Also there are three new plasmoids generated in the middle. Contour lines represent magnetic field lines, and plasmoids are color coded with fluxes in logarithmic scale. Note that the two panels cover different ranges in the x direction, because the whole structure is moving.
(a) Phase diagram of magnetic reconnection that shows the five phases. (b) Expanded view about and shows two history-dependent regimes.
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