Fulvia Pucci

Resistive Magnetohydrodynamics Simulations of the Ideal Tearing Mode

We study the linear and nonlinear evolution of the tearing instability on thin current sheets by means of two-dimensional numerical simulations, within the framework of compressible, resistive magnetohydrodynamics. In particular we analyze the behavior of current sheets whose inverse aspect ratio scales with the Lundquist number S as S 1=3 . This scaling has been recently recognized to yield the threshold separating fast, ideal reconnection, with an evolution and growth which are independent of S provided this is high enough, as it should be natural having the ideal case as a limit for S! 1. Our simulations conrm that the tearing instability growth rate can be as fast as 0:6 A 1 , where A is the ideal Alfv enic time set by the macroscopic scales, for our least diusive case with S = 10 7 . The expected instability dispersion relation and eigenmodes are also retrieved in the linear regime, for the values of S explored here. Moreover, in the nonlinear stage of the simulations we observe secondary events obeying the same critical scaling with S, here calculated on the local, much smaller lengths, leading to increasingly faster reconnection. These ndings strongly support the idea that in a fully dynamic regime, as soon as current sheets develop, thin and reach this critical threshold in their aspect ratio, the tearing mode is able to trigger plasmoid formation and reconnection on the local (ideal) Alfv enic timescales, as required to explain the explosive aring activity often observed in solar and astrophysical plasmas. Subject headings: plasmas { MHD { methods: numerical.

THE TEARING MODE INSTABILITY OF THIN CURRENT SHEETS: THE TRANSITION TO FAST RECONNECTION IN THE PRESENCE OF VISCOSITY

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

The ideal tearing mode: theory and resistive MHD simulations

L/a\sim S^\alpha

Activation of MHD reconnection on ideal timescales

with

RECONNECTION OF QUASI-SINGULAR CURRENT SHEETS: THE “IDEAL” TEARING MODE

\alpha > 1/3

‘Ideally’ unstable current sheets and the triggering of fast magnetic reconnection

because the growth rate of the tearing mode would then diverge in the ideal limit

“Ideal” tearing and the transition to fast reconnection in the weakly collisional MHD and EMHD regimes

S\rightarrow\infty

Fast Magnetic Reconnection: “Ideal” Tearing and the Hall Effect

. 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

Triggering fast tearing: from MHD to kinetic effects

Classical MHD reconnection theories, both the stationary Sweet-Parker model and the tearing instability, are known to provide rates which are too slow to explain the observations. However, a recent analysis has shown that there exists a critical threshold on current sheets thickness, namely a/L~S^(-1/3), beyond which the tearing modes evolve on fast macroscopic Alfvenic timescales, provided the Lunquist number S is high enough, as invariably found in solar and astrophysical plasmas. Therefore, the classical Sweet-Parker scenario, for which the diffusive region scales as a/L~S^(-1/2) and thus can be up to ~100 times thinner than the critical value, is likely to be never realized in nature, as the current sheet itself disrupts in the elongation process. We present here two-dimensional, compressible, resistive MHD simulations, with S ranging from 10^5 to 10^7, that fully confirm the linear analysis. Moreover, we show that a secondary plasmoid instability always occurs when the same critical scaling is reached on the local, smaller scale, leading to a cascading explosive process, reminiscent of the flaring activity.

Fast magnetic reconnection onset for different equilibrium configurations: from analytical results to 3D simulations

Magnetic reconnection in laboratory, space and astrophysical plasmas is often invoked to explain explosive energy release and particle acceleration. However, the timescales involved in classical models within the macroscopic MHD regime are far too slow to match the observations. Here we revisit the tearing instability by performing visco-resistive two-dimensional numerical simulations of the evolution of thin current sheets, for a variety of initial configurations and of values of the Lunquist number S, up to 107. Results confirm that when the critical aspect ratio of S 1/3 is reached in the reconnecting current sheets, the instability proceeds on ideal (Alfvenic) macroscopic timescales, as required to explain observations. Moreover, the same scaling is seen to apply also to the local, secondary reconnection events triggered during the nonlinear phase of the tearing instability, thus accelerating the cascading process to increasingly smaller spatial and temporal scales. The process appears to be robust, as the predicted scaling is measured both in inviscid simulations and when using a Prandtl number P = 1 in the viscous regime.