Predicting Magnetic Explosions: From Plasma Current Sheet Disruption to Fast Magnetic Reconnection

Supercomputer simulations and theoretical analysis shed new light on when and how fast reconnection occurs.

Image courtesy of Yi-Min Huang, Princeton University

In each panel, the upper half shows the current density, and the lower half shows the plasma outflow velocity along the horizontal direction at special times during the simulation. Panel (a) shows the disruption of the primary reconnecting current sheet when the typical size of the plasmoids (magenta lines) exceeds the inner layer width (dashed lines). After the disruption, secondary current sheets between plasmoids become extended and thin, panel (b). In the next level of disruption, extended secondary current sheets become unstable to the plasmoid instability, panel (c). This self-similar, fractal-like process of current sheet disruption leads to a hierarchy of plasmoids of different sizes, panel (d).

The Science

Solar flares. Coronal mass ejections. Gamma-ray bursts. In the universe, many explosive events involving ionized gas, called plasma, are associated with magnetic reconnection. Reconnection “breaks” magnetic field lines and turns magnetic potential energy into kinetic energy of charged particles in the plasma. This energy conversion also causes “sawtooth crashes” in tokamaks that are potentially damaging to electricity-producing fusion devices. Scientists may have found the trigger for these explosive events and can predict when and under what conditions the events will occur.

The Impact

Magnetic reconnection starts from the formation of a current sheet, a planar structure of concentrated electric current in plasma. When the sheet becomes thin enough, plasmoid “bubbles” form. The bubbles are isolated from their surroundings by the magnetic field, just as air in soap bubbles is isolated from the external atmosphere. When large enough, the plasmoids can disrupt the current sheet, leading to fractal-like fragmentation and formation of more plasmoids. Missing in traditional theories, this feature is critical because it allows the reconnection to take place simultaneously in multiple locations and proceed more quickly. The team’s theory predicts the reconnection rate will suddenly increase when the current sheet is disrupted.

Summary

The computer simulations are fully corroborated by the theoretical predictions of a new phenomenological theory, putting the conclusions on a solid foundation. A key question is how the current sheet width, the instability growth rate, and the number of plasmoids depend on certain plasma parameters. Reconnection theories emphasize various timescales, such as how quickly the magnetic energy “spreads” or “diffuses” through space as measured by the resistive diffusion time and the travel time of “vibrations” or “oscillations” in the magnetic field—the Alfvén time. (Perturbations in the magnetic field rapidly travel along the magnetic field lines, just like vibrations in a guitar string.) The ratio between these two timescales is the Lundquist number, which is a key parameter in reconnection theories. However, previous theories could not account for the current sheet disruption and the onset of fast reconnection when the ratio of the Lundquist number was as large as it is in the solar corona, for example. The study demonstrated that the previous theoretical prediction was accurate only when the Lundquist number was moderate. At high Lundquist numbers, the current sheet disruption takes place before traditional theories predict. Moreover, the Lundquist number is not the only parameter that affects the current sheet disruption. The level of random fluctuations in magnetic field, plasma density, and so on, also influences the formation of plasmoids.

The new phenomenological theory correctly predicts the dependence on the Lundquist number and the random fluctuations obtained in state-of-the-art supercomputer simulations. The theory incorporates (1) the time evolution of the current sheet, (2) the time rate-of-changes of the sizes of plasmoids, and (3) the amount of plasma “ejected” by the reconnection outflow jets. The theory also determines the critical Lundquist number, below which the instability cannot grow large enough to disrupt the current sheet before it is transported away by the reconnection outflow jets. These results provide a fundamentally insightful understanding of the onset of fast magnetic reconnection.

Contact

Yi-Min Huang
Princeton University
[email protected]

Funding

This work is supported by the National Science Foundation and the Department of Energy, Office of Science. Simulations were performed with supercomputers at the Oak Ridge Leadership Computing Facility and the National Energy Research Scientific Computing Center, both Department of Energy Office of Science user facilities.

Publications

Y.M. Huang, L. Comisso, and A. Bhattacharjee, “Plasmoid instability in evolving current sheets and onset of fast reconnection.” Astrophysical Journal 849, 75 (2017). [DOI: 10.3847/1538-4357/aa906d]

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