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Register a new userOnset of fast ideal tearing in thin current sheets: dependence on the equilibrium current profile
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In this paper we study the scaling relations for the triggering of the fast, or ideal, tearing instability starting from equilibrium configurations relevant to astrophysical as well as laboratory plasmas that differ from the simple Harris current sheet configuration. We present the linear tearing instability analysis for equilibrium magnetic fields which a) go to zero at the boundary of the domain and b) contain a double current sheet system (the latter previously studied as a cartesian proxy for the m=1 kink mode in cylindrical plasmas). More generally, we discuss the critical aspect ratio scalings at which the growth rates become independent of the Lundquist number $S$, in terms of the dependence of the $Delta$ parameter on the wavenumber $k$ of unstable modes. The scaling $Delta(k)$ with $k$ at small $k$ is found to categorize different equilibria broadly: the critical aspect ratios may be even smaller than $L/a sim S^{alpha}$ with $alpha=1/3$ originally found for the Harris current sheet, but there exists a general lower bound $alphage1/4$.
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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.
This paper studies the growth rate of reconnection instabilities in thin current sheets in the presence of both resistivity and viscosity. In a previous paper, Pucci and Velli (2014), it was argued that at sufficiently high Lundquist number S it is impossible to form current sheets with aspect ratios L/a which scale as $L/asim S^alpha$ with $alpha > 1/3$ because the growth rate of the tearing mode would then diverge in the ideal limit $Srightarrowinfty$. Here we extend their analysis to include the effects of viscosity, (always present in numerical simulations along with resistivity) and which may play a role in the solar corona and other astrophysical environments. A finite Prandtl number allows current sheets to reach larger aspect ratios before becoming rapidly unstable in pile-up type regimes. Scalings with Lundquist and Prandtl numbers are discussed as well as the transition to kinetic reconnection
We present the first study of the formation and dissipation of current sheets at electron scales in a wave-driven, weakly collisional, 3D kinetic turbulence simulation. We investigate the relative importance of dissipation associated with collisionless damping via resonant wave-particle interactions versus dissipation in small-scale current sheets in weakly collisional plasma turbulence. Current sheets form self-consistently from the wave-driven turbulence, and their filling fraction is well correlated to the electron heating rate. However, the weakly collisional nature of the simulation necessarily implies that the current sheets are not significantly dissipated via Ohmic dissipation. Rather, collisionless damping via the Landau resonance with the electrons is sufficient to account for the measured heating as a function of scale in the simulation, without the need for significant Ohmic dissipation. This finding suggests the possibility that the dissipation of the current sheets is governed by resonant wave-particle interactions and that the locations of current sheets correspond spatially to regions of enhanced heating.
We study, by means of MHD simulations, the onset and evolution of fast reconnection via the ideal tearing mode within a collapsing current sheet at high Lundquist numbers ($Sgg10^4$). We first confirm that as the collapse proceeds, fast reconnection is triggered well before a Sweet-Parker type configuration can form: during the linear stage plasmoids rapidly grow in a few Alfven times when the predicted ideal tearing threshold $S^{-1/3}$ is approached from above; after the linear phase of the initial instability, X-points collapse and reform nonlinearly. We show that these give rise to a hierarchy of tearing events repeating faster and faster on current sheets at ever smaller scales, corresponding to the triggering of ideal tearing at the renormalized Lundquist number. In resistive MHD this process should end with the formation of sub-critical ($S leq10^4$) Sweet Parker sheets at microscopic scales. We present a simple model describing the nonlinear recursive evolution which explains the timescale of the disruption of the initial sheet.
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 plasmoid 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.
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