Role of magnetic reconnection in MHD turbulence

TL;DR

This paper investigates how magnetic reconnection influences the smallest scales of MHD turbulence, revealing a reconnection-driven dissipation process and predicting a specific energy spectrum in the sub-inertial range.

Contribution

It introduces a new scale for reconnection importance in MHD turbulence and predicts a distinct energy spectrum, differing from traditional Kolmogorov phenomenology.

Findings

Reconnection becomes significant at a scale $oxed{ ext{}\lambda ext{}} ext{ extasciitilde} L S_L^{-4/7}$.

A sub-inertial energy spectrum $E(k_ot) ext{ extasciitilde} k_ot^{-5/2}$ is predicted.

Reconnection scale depends on magnetic Prandtl number in high-$Pm$ plasmas.

Abstract

The current understanding of MHD turbulence envisions turbulent eddies which are anisotropic in all three directions. In the plane perpendicular to the local mean magnetic field, this implies that such eddies become current-sheet-like structures at small scales. We analyze the role of magnetic reconnection in these structures and conclude that reconnection becomes important at a scale $\lambda\sim L S_L^{-4/7}$, where $S_L$ is the outer-scale ($L$) Lundquist number and $\lambda$ is the smallest of the field-perpendicular eddy dimensions. This scale is larger than the scale set by the resistive diffusion of eddies, therefore implying a fundamentally different route to energy dissipation than that predicted by the Kolmogorov-like phenomenology. In particular, our analysis predicts the existence of the sub-inertial, reconnection interval of MHD turbulence, with the Fourier energy spectrum $E(k_\perp)\propto k_\perp^{-5/2}$, where $k_\perp$ is the wave number perpendicular to the local mean magnetic field. The same calculation is also performed for high (perpendicular) magnetic Prandtl number plasmas ($Pm$), where the reconnection scale is found to be $\lambda/L\sim S_L^{-4/7}Pm^{-2/7}$.