Formation of Plasmoid Chains in Magnetic Reconnection

Introduction. Magnetic reconnection is a fundamental plasma process of rapid rearrangement of magnetic field topology, accompanied by a violent release of magnetically-stored energy and its conversion into heat and into non-thermal particle energy. It is of crucial importance for numerous physical phenomena such as solar flares and coronal mass ejections [1,2], magnetic storms in the Earth's magnetosphere [3,4,5], and sawtooth crashes in tokamaks [6,7]. Reconnection times in these environments are observed to be very short, usually only 10 to 100 times longer that the global Alfvén transit time, τ A = L/v A , where L is the characteristic system size and v A is the Alfvén speed. This is in direct contradiction with the classical Sweet-Parker (SP) [8,9] reconnection model, which employs the simplest possible non-ideal description of plasma -two-dimensional (2D) resistive magnetohydrodynamics (MHD) -and predicts a very long reconnection time scale τ rec ∼ τ A S 1/2 , where S = Lv A /η ≫ 1 is the Lundquist number, and η is the resistivity (or magnetic diffusivity) of the plasma. Both numerical simulations [10,11] and laboratory experiments [12] have confirmed the SP theory for collisional plasmas where resistive MHD with smoothly varying (e.g., Spitzer) resistivity must apply. Because of this discrepancy between the MHD picture and observations, efforts to understand magnetic reconnection have moved beyond simple resistive MHD to increasingly sophisticated and realistic plasma-physics frameworks incorporating collisionless processes such as anomalous resistivity or twofluid effects, where, indeed, fast reconnection rates have been found [13,14]. For these reasons, simple resistive-MHD reconnection has come to be viewed as well understood, uninteresting, and mostly irrelevant. However, most previous numerical studies of resistive MHD reconnection have been limited by resolution con-straints to relatively modest Lundquist numbers (S ∼ 10 4 ). The same is true for dedicated reconnection experiments. On the other hand, in most real applications of reconnection, the Lundquist numbers are much larger (e.g., S ∼ 10 12 in the solar corona, S ∼ 10 8 in large tokamaks). Thus, there is a large gap between the extreme parameter regime that we would like to understand and that accessible to the numerical and experimental studies performed so far. Asymptotically high values of S have never been probed by numerical simulations and, therefore, one cannot really claim a complete understanding of magnetic reconnection even in the simplest framework of 2D MHD with a (quasi-)uniform resistivity.

Of particular interest is the possibility that current sheets with large aspect ratios L/δ SP ∼ S 1/2 , where δ SP is the width of the SP current layer, should be unstable and break up into chains of secondary magnetic islands, or plasmoids -a phenomenon absent from the SP theory. A tearing instability of large-aspect-ratio current sheets was anticipated by Bulanov et al. [15] and Biskamp [10]. Current sheets were, indeed, found to be unstable in those numerical experiments where S ∼ 10 4 was reached (e.g. [10,16,17,18,19,20]). Current-sheet instability and plasmoid formation have also been observed in numerical reconnection studies using other physical descriptions, e.g., fully kinetic simulations [21,22,23], and there is tentative observational evidence [24,25] that they might play a key role in the dynamics of magnetic reconnection in the Earth magnetosphere and in solar flares. In fusion devices, plasmoid formation is less well diagnosed but recent results from the TEXTOR tokamak [26] suggest that they might also be present. Theoretically, plasmoid formation has been proposed as a mechanism of fast reconnection [19,27] and non-thermal particle acceleration in reconnection events [23]. Thus, plasmoids seem to be as ubiquitous as magnetic reconnection itself. However, even though their appearance has been reported by many authors, neither the plasmoid formation in the limit of asymptotically large S nor its effect on the reconnection process have been systematically investigated on any quantitative level and remains poorly understood.

As the first step towards this goal, Loureiro et al. [28] developed a linear theory of the instability of largeaspect-ratio current sheets that, unlike in the calculation of Ref. [15], emerges from a controlled asymptotic expansion in large S. Mathematically, the instability resembles a tearing instability with large ∆ ′ , leading to the formation of an inner layer with the width δ inner ∼ S -1/8 δ SP . The instability is super-Alfvénically fast, with the maximum growth rate scaling as γτ A ∼ S 1/4 ; the fastestgrowing mode occurs on a scale that is small compared to the length of the current sheet, viz., the number of plasmoids formed along the sheet scales as S 3/8 .

In this Letter, we report the next logical step towards the detailed assessment of the role of plasmoids in magnetic reconnection: the f

…(Full text truncated)…

This content is AI-processed based on ArXiv data.