Plasmoid and Kelvin-Helmholtz instabilities in Sweet-Parker current sheets

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 Alfv\'en speed and $\eta$ is the plasma resistivity), which grows super-Alfv\'enically fast (\gmax\tau_A\sim 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 Alfv\'en speed associated with the upstream magnetic field. The KH instability grows even faster than the plasmoid instability, \gmax \tau_A \sim k_{\rm max} \Lsheet\sim S^{1/2}. The effect of viscosity ($\nu$) on the plasmoid instability is also addressed. In the limit of large magnetic Prandtl numbers, $Pm=\nu/\eta$, it is found that \gmax\sim S^{1/4}Pm^{-5/8} and k_{\rm max} \Lsheet\sim S^{3/8}Pm^{-3/16}, leading to the prediction that the critical Lundquist number for plasmoid instability in the $Pm\gg1$ regime is \Scrit\sim 10^4Pm^{1/2}. These results are verified via direct numerical simulation of the linearized equations, using a new, analytical 2D SP equilibrium solution.Comment: 21 pages, 9 figures, submitted to Phys. Rev.

Fast Collisionless Reconnection Condition and Self-Organization of Solar Coronal Heating

I propose that solar coronal heating is a self-regulating process that keeps the coronal plasma roughly marginally collisionless. The self-regulating mechanism is based on the interplay of two effects. First, plasma density controls coronal energy release via the transition between the slow collisional Sweet-Parker regime and the fast collisionless reconnection regime. This transition takes place when the Sweet--Parker layer becomes thinner than the characteristic collisionless reconnection scale. I present a simple criterion for this transition in terms of the upstream plasma density (n_e), the reconnecting (B_0) and guide (B_z) magnetic field components, and the global length (L) of the reconnection layer: L < 6.10^9 cm [n_e/(10^{10}/cm^3)]^(-3) (B_0/30G)^4 (B_0/B_z)^2. Next, coronal energy release by reconnection raises the ambient plasma density via chromospheric evaporation and this, in turn, temporarily inhibits subsequent reconnection involving the newly-reconnected loops. Over time, however, radiative cooling gradually lowers the density again below the critical value and fast reconnection again becomes possible. As a result, the density is highly inhomogeneous and intermittent but, statistically, does not deviate strongly from the critical value which is comparable with the observed coronal density. Thus, in the long run, the coronal heating process can be represented by repeating cycles that consist of fast reconnection events (i.e., nanoflares), followed by rapid evaporation episodes, followed by relatively long periods (1-hour) during which magnetic stresses build up and simultaneously the plasma cools down and precipitates.Comment: 17 pages, no figures; accepted to the Astrophysical Journal; replaced to match the accepted versio

Self-Regulation of Solar Coronal Heating Process via Collisionless Reconnection Condition

I propose a new paradigm for solar coronal heating viewed as a self-regulating process keeping the plasma marginally collisionless. The mechanism is based on the coupling between two effects. First, coronal density controls the plasma collisionality and hence the transition between the slow collisional Sweet-Parker and the fast collisionless reconnection regimes. In turn, coronal energy release leads to chromospheric evaporation, increasing the density and thus inhibiting subsequent reconnection of the newly-reconnected loops. As a result, statistically, the density fluctuates around some critical level, comparable to that observed in the corona. In the long run, coronal heating can be represented by repeating cycles of fast reconnection events (nano-flares), evaporation episodes, and long periods of slow magnetic stress build-up and radiative cooling of the coronal plasma.Comment: 4 pages; Phys. Rev. Lett., in pres

Magnetic reconnection and stochastic plasmoid chains in high-Lundquist-number plasmas

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 partially amended. The normalized reconnection rate is \normEeff\sim 0.02 independently of $S$ for $S\gg10^4$. 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 $w_x\gtrsim\Psi/B_0$, where $B_0$ is the reconnecting field. It is argued that this feature is due to plasmoid coalescence. Macroscopic "monster" plasmoids with $w_x\sim 10$% of the system size are shown to emerge in just a few Alfv\'en times, independently of $S$, suggesting that large disruptive events are an inevitable feature of large-$S$ reconnection.Comment: 5 pages, 6 figures, submitted for publicatio

Reconnection in Marginally Collisionless Accretion Disk Coronae

We point out that a conventional construction placed upon observations of accreting black holes, in which their nonthermal X-ray spectra are produced by inverse comptonization in a coronal plasma, suggests that the plasma is marginally collisionless. Recent developments in plasma physics indicate that fast reconnection takes place only in collisionless plasmas. As has recently been suggested for the Sun's corona, such marginal states may result from a combination of energy balance and the requirements of fast magnetic reconnection.Comment: Revised in response to referee. Accepted ApJ. 11 pp., no figures. Uses aastex 5.0

2D Numerical Simulation of the Resistive Reconnection Layer

In this paper we present a two-dimensional numerical simulation of a reconnection current layer in incompressible resistive magnetohydrodynamics with uniform resistivity in the limit of very large Lundquist numbers. We use realistic boundary conditions derived consistently from the outside magnetic field, and we also take into account the effect of the backpressure from the flow into the separatrix region. We find that within a few Alfven times the system reaches a steady state consistent with the Sweet--Parker model, even if the initial state is Petschek-like