Magnetic Reconnection in Two-Dimensional Magnetohydrodynamic Turbulence

Systematic analysis of numerical simulations of two-dimensional magnetohydrodynamic turbulence reveals the presence of a large number of $X$-type neutral points where magnetic reconnection occurs. We examine the statistical properties of this ensemble of reconnection events that are spontaneously generated by turbulence. The associated reconnection rates are distributed over a wide range of values and scales with the geometry of the diffusion region. Locally, these events can be described through a variant of the Sweet-Parker model, in which the parameters are externally controlled by turbulence. This new perspective on reconnection is relevant in space and astrophysical contexts, where plasma is generally in a fully turbulent regime.

Figure 1

(a) Color map of $j$. (b) Contours of magnetic potential $a$ ($a>0$ green, $a<0$ black), with the positions of maximum (blue stars), minimum (red open squares) and $X$ points (black ×). Only one-sixth of the box is shown.

Figure 2

The reconnection rates $E_{\times }$ vs the aspect ratio of the diffusion region ${\lambda }_R$ (red dots). The power-law fit (blue line, shifted in the $y$ axis) suggests $E_{\times }\sim (\ell /\delta )$. The Gaussianized field (green squares) is shown for comparison.

Figure 3

Bottom (a) histograms of thicknesses ($\delta$, red bars) and elongations ($\ell$, green bars). Top (b) magnetic field autocorrelation function (solid blue line), the arrows (left to right) represent, respectively: dissipation scale ${\lambda }_{\mathrm{diss}}$, Taylor microscale ${\lambda }_T$, and correlation length ${\lambda }_C$. Vertical lines are average values $⟨\delta ⟩$ (red) and $⟨\ell ⟩$ (green).

Figure 4

Computed reconnection rates vs expectation from Eq. (7) [23]. Inset table gives ratio ${\lambda }_c/{\lambda }_{\mathrm{diss}}$, a measure of the extent of the inertial range, for several runs, along with grid resolution.