Topic/Type: 1.2 Fusion Plasmas (magnetic & inertial confinement), Invited

### Current sheet instability and formation of plasmoid chains

N. F. Loureiro1, D. A. Uzdensky2, A. A. Schekochihin3, R. Samtaney4, S. C. Cowley5, 6

1 Instituto de Plasmas e Fus?o Nuclear, Instituto Superior T?cnico, 1049-001 Lisbon, Portugal
2 Department of Astrophysical Sciences, Princeton University, NJ 08544, USA
3 Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford OX1 3NP, UK
4 Princeton Plasma Physics Laboratory, Princeton University, Princeton, NJ 08543, USA
5 EURATOM/UKAEA Fusion Association, Culham Science Centre, Abingdon OX14 3DB, UK
6 Blackett Laboratory, Imperial Col lege, London SW7 2BW, UK

Magnetic reconnection is a ubiquitous plasma physics phenomenon, characterized by rapid reconfiguration of the magnetic field topology. Within the simplest plasma framework ? single fluid resistive MHD ? the Sweet-Parker (SP) model provides the currently accepted description of reconnection. Famously, however, the SP model predicts reconnection rates which are orders of magnitude too slow to explain observations. It is known that fast reconnection rates can be obtained in more complex, collisionless descriptions of the plasma. However, in some situations the density is sufficiently high that the current layer is collisional and resistive MHD should apply. Can reconnection be fast in those environments? The SP model disregards two essential facts: first, that most, if not all, plasmas where reconnection takes place are likely to be turbulent; second, that the current layers predicted by SP theory are now realized to be violently unstable to plasmoid (secondary island) formation. In this talk, we discuss the eﬀects of turbulence and plasmoids in MHD reconnection. We present the first analytical theory of the instability of SP-like current sheets and formation of plasmoid chains. Results of direct numerical simulations are shown, validating the theoretical predictions and detailing the complex nonlinear evolution of this instability. These results strongly suggest that high-Lundquist-number reconnection is inherently time-dependent and hence call for a substantial revision of the standard Sweet-Parker quasi-stationary picture. When turbulence is added to the background, we obtain reconnection rates whose dependence on the plasma resistivity ($\small \eta$) is much shallower than the SP $\small \eta^{1/2}$ dependence, indicating that fast reconnection is possible whithin the resistive MHD framework.