Generation and Effects of Electromotive Force in Turbulent Stochastic Reconnection

Reconnection is an important process that rules dissipation and diffusion of magnetic energy in plasmas. It is already clear that its rate is enhanced by turbulence, and that reconnection itself may increase its stochasticity, but the main mechanism that connects these two effects is still not completely understood. The aim of this work is to identify, from the terms of the electromotive force, the dominant physical process responsible for enhancing the reconnection rate in turbulent plasmas. We employ full three-dimensional numerical simulations of turbulence driven by stochastic reconnection and estimate the production and dissipation of turbulent energy and cross-helicity, the amount of produced residual helicity, and determine the relation between these quantities and the reconnection rate. We observe the development of the electromotive force in the studied models with plasma-$\beta = 0.1 - 2$ and the Lundquist number $S=10^{-5}-10^{-4}$. The turbulent energy and residual helicity develop in the large-scale current sheet, with the latter decreasing the effects of turbulent magnetic diffusion. We demonstrate that the stochastic reconnection, apart from the turbulence, can produce a significant amount of cross-helicity as well. The cross-helicity to turbulent energy ratio, however, has no correlation with the reconnection rate. We show that its sufficiently large value is not a necessary condition for fast reconnection to occur. The results suggest that cross-helicity is inherent to turbulent fields, but the reconnection rate enhancement is possibly caused by the effects of magnetic turbulent diffusion and controlled by the residual helicity.