Instability of current sheets and formation of plasmoid chains

Abstract

Current sheets formed in magnetic reconnection events are found to be unstable to highwavenumber perturbations. The instability is very fast: its maximum growth rate scales as S 1/4 LCS/vA, where LCS is the length of the sheet, vA the Alfvén speed and S the Lundquist number. As a result, a chain of plasmoids (secondary islands) is formed, whose number scales as S 3/8 .PACS numbers: 52.35. Vd, 52.35.Py, 94.30.cp, 96.60.Iv Magnetic reconnection is a plasma phenomenon in which oppositely directed magnetic field lines are driven together, break and rejoin in a topologically different configuration. It is an essential element in our understanding of the solar flares and the geotail [1,2,3], where it is directly observed [4,5], as well as of other astrophysical plasmas. On Earth, it plays a crucial role in the dynamics of magnetically confined plasmas in fusion devices [6].There are two standard reconnection models: the Sweet-Parker (SP) model [7,8], and the Petscheck model [9]. The latter is very appealing as it predicts fast reconnection rates similar to the observed ones. However, numerical simulations have consistently failed to reproduce it unless a spatially inhomogeneous anomalous resistivity is used [10] or Hall physics is invoked [3,11]. In contrast, the SP reconnection, characterized by long current sheets (∼ system size) and slow reconnection rates ∝ η 1/2 , where η is the plasma resistivity, is routinely observed both in experiments [12] and in simulations.The break up of current sheets and formation of plasmoids (secondary islands) appears to be a generic feature of reconnecting systems. Plasmoids have been observed both in solar flares [13] and in the geotail [14]. In numerical simulations, plasmoid formation has been reported in many different set ups, from fluid [15,16] to fully kinetic [17,18]. Plasmoids have been popular in theories of magnetic reconnection and related phenomena: e.g., they have been invoked as a plausible mechanism for accelerating reconnection, either by decreasing the effective length of the SP current sheet and/or by triggering anomalous-resistivity mechanisms associated with small-scale plasma effects [19]; a multiple-plasmoid scenario has been suggested to explain the production of energetic electrons during reconnection events [20]; it has been conjectured that periodic ejection of plasmoids in star-disk systems could account for the knot-like structures observed in stellar jets [21].A theoretical understanding of the mechanism whereby the plasmoids are formed has, however, been lacking. It has been believed that plasmoid formation is due to a standard tearing instability [22] of the current sheet, which implies a resistively slow instability growth rate [23]. In this Letter, we show that, while the resistivity is essential for the instability, the growth rate is, in fact, much faster even than the ideal rate.Theoretical estimates for the speed of magnetic reconnection in natural systems are usually based on the idea that a current sheet is formed (Fig. 1), whose length L C...

Review on Current Sheets in CME Development: Theories and Observations

“…Panels in Fig. 12 display LASCO C2 images of the same process that had been enhanced by the wavelet technique, which further indicates that discriminating a post-CME CS from a streamer CS is not difficult, although in both cases the tearing mode instability could take place in the same fashion (e.g., see also Einaudi et al 2001) since the occurrence of the tearing mode depends on the length to thickness ratio of the CS (e.g., see Furth et al 1963;Loureiro et al 2007;Ni et al 2010;Shen et al 2011;Bárta et al 2011aBárta et al , 2011bMei et al 2012) no matter whether the CS is stretched by the expanding solar wind, or by the disrupting coronal magnetic field.…”

“…We may also note here that Loureiro et al (2007) analyzed the relation of l to the Lundquist number in a different way. They investigated the dependence of kl on the global Lundquist number, S L , for the whole system instead of the local one, S, for the CS, as the rate of reconnection reached maximum.…”

“…Since the resistivity is small and the catastrophe takes place much faster than the dissipation at the beginning of the eruption (see discussions of Lin and Forbes 2000;Lin 2002), the CS is able to develop to a large scale, and various plasma instabilities would occur in the CS. Linear theory of the tearing mode instability indicates that the CS becomes unstable as its length exceeds 2π times its thickness (Furth et al 1963;Priest and Forbes 2000), and nonlinear investigations through numerical experiments suggest that this ratio could apparently exceed 10 and even up to 100, before the tearing mode is invoked (e.g., see Loureiro et al 2007;Ni et al 2010;Shen et al 2011;Bárta et al 2011aBárta et al , 2011bMei et al 2012). Plasma instabilities yield turbulence inside the CS that may significantly enhance the dissipation of the magnetic field, resulting in an effective resistivity that is much higher than the traditional Spitzer value (Strauss 1986(Strauss , 1988Ambrosiano et al 1988;Bhattacharjee and Yuan 1995;Shibata and Tanuma 2001;Skender and Lapenta 2010;Bárta et al 2011aBárta et al , 2011bShen et al 2011;Mei et al 2012; and references therein).…”

A current-driven resistive instability and its nonlinear effects in simulations of coaxial helicity injection in a tokamak

“…[15][16][17][18][19]24 That the resulting nonlinear dynamics have greater impact as the modeled impurity concentration is reduced and temperature increases likely reflects a smaller current-sheet width at lower resistivity, which has a role in plasmoid formation. 16,17 However, during the phase of modeled active injection, the footpoints of the current channel are distant, and the instability is not part of the reconnection process that forms closed flux on the global scale. Thus, the role of the asymmetric instability reported here is distinct from that of plasmoid formation as part of the global fluxsurface closure after injection, which is predicted in axisymmetric simulations of NSTX.…”

“…The structure is reminiscent of the current-sheet instability that underlies plasmoid instability. [15][16][17][18][19] However, unlike basic-physics studies of magnetic reconnection and simulations of axisymmetric flux closure in NSTX, 18,19 the current sheet surrounding the early evolution of the flux bubble is not associated with largescale reconnection.…”