# Center for Magnetic Self Organization

## in Laboratory and Astrophysical Plasmas

# Distribution of plasmoids in High-Lundquist-Number Magnetic Reconnection

In recent years, significant advances have been made in understanding the role of plasmoids (or secondary islands) in magnetic reconnection, which is believed to be the underlying mechanism of energy release for phenomena such as solar flares, magnetospheric substorms, and sawtooth crashes in fusion plasmas. Plasmoids often form spontaneously in resistive magnetohydrodynamics (MHD), Hall MHD, and kinetic particle-in-cell (PIC) simulations of large-scale systems. Evidences of plasmoids have also been found in the magnetotail and the solar atmosphere, where they are demonstrated to play a significant role in particle acceleration. In the framework of resistive MHD it has become clear that when the Lundquist number S is above a critical value Sc ~104 , the Sweet-Parker current sheet becomes unstable to the plasmoid instability, with a growth rate that increases with S. The reconnection layer changes to a chain of plasmoids connected by secondary current sheets that, in turn, may become unstable again. Eventually the reconnection layer will tend to a statistical steady state characterized by a hierarchical structure of plasmoids. The hierarchical structure suggests self-similarity across different scales, which often gives rise to power laws.

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Plasmoid distribution functions from (a) direct numerical simulations, and (b) kinetic model.
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We have carried out statistical studies of the plasmoid distribution with respect to the magnetic flux content of plasmoids, with high-Lindquist-number simulations up to S =10^7. We find that over an extended range of J , the plasmoid distribution function f(J) follows a power law f (J) ~ J−1 . We further develop a kinetic model of plasmoid dynamics that reproduces the observed distribution. Figure 5 shows plasmoid distributions from direct numerical simulations and our kinetic model.

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