Role of Magnetic Reconnection in Magnetohydrodynamic Turbulence

The current understanding of magnetohydrodynamic (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-sheetlike 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 subinertial, reconnection interval of MHD turbulence, with the estimated scaling of 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 $\lambda /L\sim S_L^{-4/7}P{m}^{-2/7}$.

Figure 1

Sketch of the Fourier energy spectrum (log-log scale) and the shapes of eddies as a function of $k_{\perp }\sim 1/\lambda$. The arrows indicate the direction of the magnetic field lines. For $k_{\perp }<k_{\text{cr}}\sim 1/{\lambda }_{\text{cr}}$, the turbulent eddies become progressively more anisotropic as $k_{\perp }$ approaches $k_{\text{cr}}$. For $k_{\perp }>k_{\text{cr}}$, the tearing instability is an essential part of the turbulence.