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Register a new userInfluence of 3D plasmoid dynamics on the transition from collisional to kinetic reconnection
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Within the resistive magnetohydrodynamic model, high-Lundquist number reconnection layers are unstable to the plasmoid instability, leading to a turbulent evolution where the reconnection rate can be independent of the underlying resistivity. However, the physical relevance of these results remains questionable for many applications. First, the reconnection electric field is often well above the runaway limit, implying that collisional resistivity is invalid. Furthermore, both theory and simulations suggest that plasmoid formation may rapidly induce a transition to kinetic scales, due to the formation of thin current sheets. Here, this problem is studied for the first time using a first-principles kinetic simulation with a Fokker-Planck collision operator in 3D. The low-$beta$ reconnecting current layer thins rapidly due to Joule heating before onset of the oblique plasmoid instability. Linear growth rates for standard ($k_y = 0$) tearing modes agree with semi-collisional boundary layer theory, but the angular spectrum of oblique ($|k_y|>0$) modes is significantly narrower than predicted. In the non-linear regime, flux-ropes formed by the instability undergo complex interactions as they are advected and rotated by the reconnection outflow jets, leading to a turbulent state with stochastic magnetic field. In a manner similar to previous 2D results, super-Dreicer fields induce a transition to kinetic reconnection in thin current layers that form between flux-ropes. These results may be testable within new laboratory experiments.
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(abridged) Magnetic reconnection is the topological reconfiguration of the magnetic field in a plasma, accompanied by the violent release of energy and particle acceleration. Reconnection is as ubiquitous as plasmas themselves, with solar flares perhaps the most popular example. Over the last few years, the theoretical understanding of magnetic reconnection in large-scale fluid systems has undergone a major paradigm shift. The steady-state model of reconnection described by the famous Sweet-Parker (SP) theory, which dominated the field for ~50 years, has been replaced with an essentially time-dependent, bursty picture of the reconnection layer, dominated by the continuous formation and ejection of multiple secondary islands (plasmoids). Whereas in the SP model reconnection was predicted to be slow, a major implication of this new paradigm is that reconnection in fluid systems is fast (i.e., independent of the Lundquist number), provided that the system is large enough. This conceptual shift hinges on the realization that SP-like current layers are violently unstable to the plasmoid instability - implying, therefore, that such current sheets are super-critically unstable and thus can never form in the first place. This suggests that the formation of a current sheet and the subsequent reconnection process cannot be decoupled, as is commonly assumed. This paper provides an introductory-level overview of the recent developments in reconnection theory and simulations that led to this essentially new framework. We briefly discuss the role played by the plasmoid instability in selected applications, and describe some of the outstanding challenges that remain at the frontier of this subject. Amongst these are the analytical and numerical extension of the plasmoid instability to (i) 3D and (ii) non-MHD regimes. New results are reported in both cases.
Properties of plasmoid-dominated turbulent reconnection in a low-$beta$ background plasma are investigated by resistive magnetohydrodynamic (MHD) simulations. In the $beta_{rm in} < 1$ regime, where $beta_{rm in}$ is plasma $beta$ in the inflow region, the reconnection site is dominated by shocks and shock-related structures and plasma compression is significant. The effective reconnection rate increases from $0.01$ to $0.02$ as $beta_{rm in}$ decreases. We hypothesize that plasma compression allows faster reconnection rate, and then we estimate a speed-up factor, based on a compressible MHD theory. We validate our prediction by a series of MHD simulations. These results suggest that the plasmoid-dominated reconnection can be twice faster than expected in the $beta ll 1$ environment in a solar corona.
Magnetic reconnection may be the fundamental process allowing energy stored in magnetic fields to be released abruptly, solar flares and coronal mass ejection (CME) being archetypal natural plasma examples. Magnetic reconnection is much too slow a process to be efficient on the large scales, but accelerates once small enough scales are formed in the system. For this reason, the fractal reconnection scenario was introduced (Shibata and Tanuma 2001) to explain explosive events in the solar atmosphere: it was based on the recursive triggering and collapse via tearing instability of a current sheet originally thinned during the rise of a filament in the solar corona. Here we compare the different fractal reconnection scenarios that have been proposed, and derive generalized scaling relations for the recursive triggering of fast, `ideal - i.e. Lundquist number independent - tearing in collapsing current sheet configurations with arbitrary current profile shapes. An important result is that the Sweet-Parker scaling with Lundquist number, if interpreted as the aspect ratio of the singular layer in an ideally unstable sheet, is universal and does not depend on the details of the current profile in the sheet. Such a scaling however must not be interpreted in terms of stationary reconnection, rather it defines a step in the accelerating sequence of events of the ideal tearing mediated fractal cascade. We calculate scalings for the expected number of plasmoids for such generic profiles and realistic Lundquist numbers.
A set of reduced Hall magnetohydrodynamic (MHD) equations are used to evaluate the stability of large aspect ratio current sheets to the formation of plasmoids (secondary islands). Reconnection is driven by resistivity in this analysis, which occurs at the resistive skin depth $d_eta equiv S_L^{-1/2} sqrt{L v_A/gamma}$, where $S_L$ is the Lundquist number, $L$ the length of the current sheet, $v_A$ the Alfv{e}n speed, and $gamma$ the growth rate. Modifications to a recent resistive MHD analysis [N. F. Loureiro, A. A. Schekochihin, and S. C. Cowley, Phys. Plasmas {bf 14}, 100703 (2007)] arise when collisions are sufficiently weak that $d_eta$ is shorter than the ion skin depth $d_i equiv c/omega_{pi}$. Secondary islands grow faster in this Hall MHD regime: the maximum growth rate scales as $(d_i/L)^{6/13} S_L^{7/13} v_A/L$ and the number of plasmoids as $(d_i/L)^{1/13} S_L^{11/26}$, compared to $S_L^{1/4} v_A/L$ and $S^{3/8}$, respectively, in resistive MHD.
This paper discusses the transition to fast growth of the tearing instability in thin current sheets in the collisionless limit where electron inertia drives the reconnection process. It has been previously suggested that in resistive MHD there is a natural maximum aspect ratio (ratio of sheet length and breadth to thickness) which may be reached for current sheets with a macroscopic length L, the limit being provided by the fact that the tearing mode growth time becomes of the same order as the Alfv`en time calculated on the macroscopic scale (Pucci and Velli (2014)). For current sheets with a smaller aspect ratio than critical the normalized growth rate tends to zero with increasing Lundquist number S, while for current sheets with an aspect ratio greater than critical the growth rate diverges with S. Here we carry out a similar analysis but with electron inertia as the term violating magnetic flux conservation: previously found scalings of critical current sheet aspect ratios with the Lundquist number are generalized to include the dependence on the ratio $(d_e/L)^2$ where de is the electron skin depth, and it is shown that there are limiting scalings which, as in the resistive case, result in reconnecting modes growing on ideal time scales. Finite Larmor Radius effects are then included and the rescaling argument at the basis of ideal reconnection is proposed to explain secondary fast reconnection regimes naturally appearing in numerical simulations of current sheet evolution.
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