Factors Controlling the Statistics of Magnetic Reconnection in MHD Turbulence

Abstract

We study the statistics of dynamical quantities associated with magnetic reconnection events embedded in a sea of strong background magnetohydrodynamic (MHD) turbulence using direct numerical simulations. We focus on the relationship of the reconnection properties to the statistics of global turbulent fields. For the first time, we show that the distribution in turbulence of reconnection rates (determined by upstream fields) is strongly correlated with the magnitude of the global turbulent magnetic field at the correlation scale. The average reconnection rates, and associated dissipation rates, during turbulence are thus much larger than predicted by using turbulent magnetic field fluctuation amplitudes at the dissipation or kinetic scales. Magnetic reconnection may therefore be playing a major role in energy dissipation in astrophysical and heliospheric turbulence.

Figures (8)

• Figure 1: (a) Current density $j$ with contours of magnetic vector potential. $\lambda_c$ is the correlation length and $\lambda_\text{rec}$ is the average reconnection diffusion region thickness. Red and black arrows denote inflow and outflow directions associated with the diffusion region. (b) One-dimensional cuts of current density $j$ (solid) and reconnecting magnetic field $b_\ell$ (dashed) along the inflow direction, for the current sheet shown in panel (a), along with best fit line for $j(s)$ (dotted). Locations where $b_\text{up}$ is determined are shown by vertical dashed lines.
• Figure 2: (a) Distribution of thicknesses of diffusion regions, with vertical lines showing the average thickness $\lambda_\text{rec}$, the dissipation scale $\lambda_\text{diss}$ and the correlation scale $\lambda_\text{c}$. (b) Scatter plot of $b_{\text{up}_1}$ vs $b_{\text{up}_2}$ sampled at each reconnection site.
• Figure 3: (a) Comparison of turbulence increments and reconnection magnetic fields. PDF of transverse turbulent magnetic field increments taken with lag $\lambda_\mathrm{rec}$ sampled over entire simulation domain, $\Delta b_\perp( \boldsymbol{x}, \lambda_\mathrm{rec})$. The reconnection magnetic field is defined as $\Delta b_\mathrm{rec}/2$ for each X-point. Average values of each quantity are shown with vertical dashed lines with $\Delta b_\perp( \boldsymbol{x}, \lambda_\mathrm{rec})$ averaged over $\boldsymbol{x}$ and $\Delta b_\mathrm{rec}/2$ averaged over X-points. (b) Turbulent field increments at transverse reconnection scale, $\Delta b_\perp( \boldsymbol{x}, \lambda_\text{rec})$, near the strongly reconnecting current sheet shown in Fig. \ref{['fig:Current']}a.
• Figure 4: PDFs of transverse turbulence increments at the correlation scale compared with PDFs of reconnection fields $\Delta b_\textrm{rec}/2,$$b_1$, and $b_2$. Average values of each quantity are shown as vertical lines with matching color. The agreement of these distributions is striking, and in significant contrast with Fig. \ref{['fig:dbhist']}(a).
• Figure 5: Current density $j$ at the time of analysis ($t = 0.3$) with contours of the magnetic potential $a$ superimposed. The X-points and O-points are marked by '$\times$' and '$\square$' respectively. Insets highlight subsections of the system.