Characterizing plasmoid reconnection by turbulence dynamics

In weakly dissipative plasmas, the plasmoid instability may lead, in principle, to fast magnetic reconnection through long current sheets. On the other hand, it is well known that weakly dissipative large-Reynolds-number plasmas easily become turbulent. We address the question of whether turbulence can enhance the reconnection rate of plasmoid-unstable current sheets by carrying out high resolution MHD simulations. Instead of resolving all scales down to dissipation, we utilize a turbulence model to investigate the influence of turbulence on the plasmoid instability. For this sake, we extend a Reynolds-averaged turbulence model expressing the energy, cross-helicity, and helicity due to the turbulence to a subgrid-scale (SGS) model of turbulence by means of a Gaussian filter. We then use the SGS turbulence model to investigate the contributions of the turbulent energy and cross-helicity to the plasmoid reconnection rate. In particular, we address the consequences of a finite guide magnetic field parallel to the reconnection electric field on the reconnection rate in terms of the residual turbulent helicity. To validate the turbulence model, we compare the SGS electromotive force with that obtained statistically from the high resolution simulations. This way, we characterize the influence of turbulence on the reconnection rate of plasmoid-unstable current sheets and attribute the plasmoid reconnection rate at large-magnetic-Reynolds-numbers to turbulence.