Turbulent Magnetohydrodynamic Reconnection Mediated by the Plasmoid Instability

TL;DR

This paper demonstrates that three-dimensional magnetohydrodynamic reconnection with a guide field leads to turbulence driven by plasmoid instabilities, resulting in a reconnection rate comparable to two-dimensional cases but lower than some externally driven turbulent scenarios.

Contribution

It introduces 3D simulations showing how plasmoid instabilities induce turbulence and affect reconnection rates, extending previous 2D findings to more realistic 3D conditions.

Findings

Reconnection rate in turbulent state is about 1% of Alfvén speed.

Energy spectra follow power-law distributions with specific spectral indices.

Turbulence exhibits anisotropic eddies with nearly scale-independent anisotropy.

Abstract

It has been established that the Sweet-Parker current layer in high Lundquist number reconnection is unstable to the super-Alfv\'enic plasmoid instability. Past two-dimensional magnetohydrodynamic simulations have demonstrated that the plasmoid instability leads to a new regime where the Sweet-Parker current layer changes into a chain of plasmoids connected by secondary current sheets, and the averaged reconnection rate becomes nearly independent of the Lundquist number. In this work, three-dimensional simulation with a guide field shows that the additional degree of freedom allows plasmoid instabilities to grow at oblique angles, which interact and lead to self-generated turbulent reconnection. The averaged reconnection rate in the self-generated turbulent state is of the order of a hundredth of the characteristic Alfv\'en speed, which is similar to the two-dimensional result but is an order of magnitude lower than the fastest reconnection rate reported in recent studies of externally driven three-dimensional turbulent reconnection. Kinematic and magnetic energy fluctuations both form elongated eddies along the direction of local magnetic field, which is a signature of anisotropic magnetohydrodynamic turbulence. Both energy fluctuations satisfy power-law spectra in the inertial range, where the magnetic energy spectral index is in the range from $-2.3$ to $-2.1$, while the kinetic energy spectral index is slightly steeper, in the range from $-2.5$ to $-2.3$. The anisotropy of turbulence eddies is found to be nearly scale-independent, in contrast with the prediction of the Goldreich-Sridhar theory for anisotropic turbulence in a homogeneous plasma permeated by a uniform magnetic field.