Reconnection and the Formation of Magnetic Islands in MHD Models

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1 Reconnection and the Formation of Magnetic Islands in MHD Models N. F. Loureiro, D. A. Uzdensky, A. A. Schekochihin, R. Samtaney and S. C. Cowley Yosemite 2010 Reconnection Workshop

2 Introduction (I) In the simplest plasma description single fluid resistive MHD the accepted Sweet-Parker model of reconnection is orders of magnitude too SLOW to explain observations FAST reconnection obtained in collisionless models. Not all plasmas are collisionless! E.g., many astrophysical environments are very high density solar chromosphere, interstellar medium, inside stars and accretion disks, etc so reconnection layer is collisional and resistive MHD should apply. Can reconnection be fast in these environments? Turbulence Plasmoids

3 Introduction (II) We thought we understood MHD reconnection (Sweet- Parker --- slow, uninteresting) Actually, we don t. Current sheets are violently unstable to the formation of multiple secondary islands (plasmoids). Their effect on reconnection is not accounted for in any reconnection theory. There are hints that MHD reconnection may actually be fast in the presence of plasmoids (Lapenta PRL 08, Loureiro MNRAS 09, Bhattacharjee PoP 09, Cassak PoP 09) Plasmoids play an unknown, but ubiquitous, role in reconnection, MHD and otherwise.

4 Plasmoids in the computer MHD simulations show that Sweet-Parker current sheets for S>~10 4 are unstable to plasmoids. From Loureiro et al., PRL 05; earlier evidence in Steinolfson 84, Park 84, Biskamp 86.

5 Linear instability of SP current sheets Inside the SP current sheet, resistivity cannot be neglected anywhere. Standard tearing mode theory (FKR, Coppi) does not apply. Asymptotic theory of current sheet instability can be done in tearing mode style, except small parameter is the inverse aspect ratio of the sheet, ε ~ S 1/ 2 Cowley, PoP 07. Theory predicts --- Loureiro, Schekochihin & γ max τ A ~ S 1/ 4 k max L CS ~ S 3 / 8 Super-Alfvénic growth! Plasmoids galore!

6 Numerical simulations of CS instability Local simulations of SP-like reconnection at Lundquist numbers up to S=10 8 show CS break up. (Samtaney et al., PRL 09) Time evolution, S=10 8 Snapshots; S=10 4, 10 5, 10 6, 10 7

7 Confirmation of linear theory Numerical simulations confirm scalings predicted by linear theory. ( From Samtaney et al., PRL 09 )

8 Nonlinear plasmoid evolution - Since the linear growth rate is much larger than the inverse Alfvén time, plasmoids become nonlinear before being expelled. - Nonlinear dynamics is dictated by the competition between three timescales: plasmoid growth time, expulsion time and coalescence time (Uzdensky et al., 10) - Inter-plasmoid current sheets unstable to tertiary islands and so forth. Cascade in plasmoid sizes suggests possible turbulent scenario (Shibata& Tanuma 01; also Fermo et al., arxiv: ).

9 Nonlinear plasmoid evolution How do plasmoids affect the reconnection rate? We don t know is the short answer Two possible (non mutually exclusive) ways: 1. The plasmoid cascade eventually reaches the kinetic scales (Daughton 09, Cassak 10) 2. Within MHD itself, plasmoids may speed-up SP reconnection.

10 Nonlinear plasmoid evolution Plasmoid cascade process stops when inter-plasmoid current sheets reach the critical aspect ratio: S c = L c V A η 104 δ c 100 η V A E c 0.01B 0 V A Transition to collisionless reconnection should happen when δ < min{d i,ρ S } The existence of plasmoids implies that it is δ c, and not δ SP that matters for this transition. The implication is that non-mhd physics becomes important at lower values of S than would be expected if SP was the whole story (Daughton PoP 09, Cassak 10, Uzdensky 10)

11 Turbulent MHD reconnection Simulations of 2D magnetic reconnection in the presence of background turbulence yield reconnection rates significantly faster than laminar Sweet-Parker. From Loureiro et al., MNRAS 09; earlier numerical evidence for turbulent enhancement of the reconnection rate in 2D in Matthaeus & Lamkin, 86, and others.

12 Turbulent MHD reconnection Could this enhancement of the reconnection rate be due to plasmoids?

13 Turbulent MHD reconnection Transition occurs at u rms /V A 0.16

14 Conclusions Current sheets predicted by the SP theory are violently unstable to the formation of high wavenumber plasmoid chains. Plasmoids become nonlinear --- MHD reconnection is dynamic, bursty. SP theory needs revision. In particular, what is the reconnection rate in MHD? In the presence of background turbulence, 2D reconnection is fast. These results highlight a novel mechanism of turbulent enhancement of the reconnection which cannot be explained by any present theoretical model --- are plasmoids to blame?

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