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تسجيل مستخدم جديدMagnetic reconnection: from the Sweet-Parker model to stochastic plasmoid chains
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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.
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A 2D linear theory of the instability of Sweet-Parker (SP) current sheets is developed in the framework of Reduced MHD. A local analysis is performed taking into account the dependence of a generic equilibrium profile on the outflow coordinate. The p
lasmoid instability [Loureiro et al, Phys. Plasmas {bf 14}, 100703 (2007)] is recovered, i.e., current sheets are unstable to the formation of a large-wave-number chain of plasmoids ($k_{rm max}Lsheet sim S^{3/8}$, where $k_{rm max}$ is the wave-number of fastest growing mode, $S=Lsheet V_A/eta$ is the Lundquist number, $Lsheet$ is the length of the sheet, $V_A$ is the Alfven speed and $eta$ is the plasma resistivity), which grows super-Alfvenically fast ($gmaxtau_Asim S^{1/4}$, where $gmax$ is the maximum growth rate, and $tau_A=Lsheet/V_A$). For typical background profiles, the growth rate and the wave-number are found to {it increase} in the outflow direction. This is due to the presence of another mode, the Kelvin-Helmholtz (KH) instability, which is triggered at the periphery of the layer, where the outflow velocity exceeds the Alfven speed associated with the upstream magnetic field. The KH instability grows even faster than the plasmoid instability, $gmax tau_A sim k_{rm max} Lsheetsim S^{1/2}$. The effect of viscosity ($ u$) on the plasmoid instability is also addressed. In the limit of large magnetic Prandtl numbers, $Pm= u/eta$, it is found that $gmaxsim S^{1/4}Pm^{-5/8}$ and $k_{rm max} Lsheetsim S^{3/8}Pm^{-3/16}$, leading to the prediction that the critical Lundquist number for plasmoid instability in the $Pmgg1$ regime is $Scritsim 10^4Pm^{1/2}$. These results are verified via direct numerical simulation of the linearized equations, using a new, analytical 2D SP equilibrium solution.
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.
A numerical study of magnetic reconnection in the large-Lundquist-number ($S$), plasmoid-dominated regime is carried out for $S$ up to $10^7$. The theoretical model of Uzdensky {it et al.} [Phys. Rev. Lett. {bf 105}, 235002 (2010)] is confirmed and p
artially amended. The normalized reconnection rate is $ ormEeffsim 0.02$ independently of $S$ for $Sgg10^4$. The plasmoid flux ($Psi$) and half-width ($w_x$) distribution functions scale as $f(Psi)sim Psi^{-2}$ and $f(w_x)sim w_x^{-2}$. The joint distribution of $Psi$ and $w_x$ shows that plasmoids populate a triangular region $w_xgtrsimPsi/B_0$, where $B_0$ is the reconnecting field. It is argued that this feature is due to plasmoid coalescence. Macroscopic monster plasmoids with $w_xsim 10$% of the system size are shown to emerge in just a few Alfven times, independently of $S$, suggesting that large disruptive events are an inevitable feature of large-$S$ reconnection.
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 regio
n, 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.
We present a detailed study of magnetic reconnection in a quasi-two-dimensional pulsed-power driven laboratory experiment. Oppositely directed magnetic fields $(B=3$ T), advected by supersonic, sub-Alfvenic carbon plasma flows $(V_{in}=50$ km/s), are
brought together and mutually annihilate inside a thin current layer ($delta=0.6$ mm). Temporally and spatially resolved optical diagnostics, including interferometry, Faraday rotation imaging and Thomson scattering, allow us to determine the structure and dynamics of this layer, the nature of the inflows and outflows and the detailed energy partition during the reconnection process. We measure high electron and ion temperatures $(T_e=100$ eV, $T_i=600$ eV), far in excess of what can be attributed to classical (Spitzer) resistive and viscous dissipation. We observe the repeated formation and ejection of plasmoids, which we interpret as evidence of two-fluid effects in our experiment.
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