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Register a new userPlasmoid and Kelvin-Helmholtz instabilities in Sweet-Parker current sheets
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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 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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(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.
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.
Transport coefficients in highly ionised plasmas like the intra-cluster medium (ICM) are still ill-constrained. They influence various processes, among them the mixing at shear flow interfaces due to the Kelvin-Helmholtz instability (KHI). The observed structure of potential mixing layers can be used to infer the transport coefficients, but the data interpretation requires a detailed knowledge of the long-term evolution of the KHI under different conditions. Here we present the first systematic numerical study of the effect of constant and temperature-dependent isotropic viscosity over the full range of possible values. We show that moderate viscosities slow down the growth of the KHI and reduce the height of the KHI rolls and their rolling-up. Viscosities above a critical value suppress the KHI. The effect can be quantified in terms of the Reynolds number Re = U{lambda}/{ u}, where U is the shear velocity, {lambda} the perturbation length, and { u} the kinematic viscosity. We derive the critical Re for constant and temperature dependent, Spitzer-like viscosities, an empirical relation for the viscous KHI growth time as a function of Re and density contrast, and describe special behaviours for Spitzer-like viscosities and high density contrasts. Finally, we briefly discuss several astrophysical situations where the viscous KHI could play a role, i.e., sloshing cold fronts, gas stripping from galaxies, buoyant cavities, ICM turbulence, and high velocity clouds.
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.
In this paper we investigate whether Smoothed Particle Hydrodynamics (SPH), equipped with artificial conductivity, is able to capture the physics of density/energy discontinuities in the case of the so-called shearing layers test, a test for examining Kelvin-Helmholtz (KH) instabilities. We can trace back each failure of SPH to show KH rolls to two causes: i) shock waves travelling in the simulation box and ii) particle clumping, or more generally, particle noise. The probable cause of shock waves is the Local Mixing Instability (LMI), previously identified in the literature. Particle noise on the other hand is a problem because it introduces a large error in the SPH momentum equation. We also investigate the role of artificial conductivity (AC). Including AC is necessary for the long-term behavior of the simulation (e.g. to get $lambda=1/2, 1$ KH rolls). In sensitive hydrodynamical simulations great care is however needed in selecting the AC signal velocity, with the default formulation leading to too much energy diffusion. We present new signal velocities that lead to less diffusion. The effects of the shock waves and of particle disorder become less important as the time-scale of the physical problem (for the shearing layers problem: lower density contrast and higher Mach numbers) decreases. At the resolution of current galaxy formation simulations mixing is probably not important. However, mixing could become crucial for next-generation simulations.
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