Fast Magnetic Reconnection: Secondary Tearing Instability and Role of the Hall Term

Abstract

Magnetic reconnection provides the primary source for explosive energy release, plasma heating and particle acceleration in many astrophysical environments. The last years witnessed a revival of interest in the MHD tearing instability as a driver for efficient reconnection. It has been established that, provided the current sheet aspect ratio becomes small enough ($a/L\sim S^{-1/3}$ for a given Lundquist number $S\gg 1$), reconnection occurs on ideal Alfvén timescales and becomes independent on $S$. Here we investigate, by means of two-dimensional simulations, the \emph{ideal} tearing instability in the Hall-MHD regime, which is appropriate when the width of the resistive layer $\delta$ becomes comparable to the ion inertial length $d_i$. Moreover, we study in detail the spontaneous development and reconnection of secondary current sheets, which for high $S$ naturally adjust to the ideal aspect ratio and hence their evolution proceeds very rapidly. For moderate low $S$, the aspect ratio tends to the Sweet-Parker scaling ($a/L\sim S^{-1/2}$), in order to fulfill the condition $\delta \ll a$ necessary for the onset of a tearing instability. When the Hall term is included, the reconnection rate of this secondary nonlinear phase is enhanced and, depending on the ratio $d_i/\delta$, can be twice with respect to the pure MHD case, and up to ten times larger than the linear phase. Therefore, the evolution of the tearing instability in thin current sheets in the Hall-MHD regime naturally leads to an explosive disruption of the reconnecting site and to energy release on super-Alfvénic timescales, as required to explain astrophysical observations.

arXiv comment14 pages, 9 figures, published on ApJ

References in corpus (30)

• Instability of current sheets and formation of plasmoid chains
• Fast Reconnection in High-Lundquist-Number Plasmas Due to Secondary Tearing Instabilities
• Efficient acceleration and radiation in Poynting flux powered GRB outflows
• Plasmoid-Induced-Reconnection and Fractal Reconnection
• Dissipation in Poynting-flux Dominated Flows: the Sigma-Problem of the Crab Pulsar Wind
• Formation of Plasmoid Chains in Magnetic Reconnection
• Spectrum of Kinetic Alfven Turbulence
• Self-Feeding Turbulent Magnetic Reconnection on Macroscopic Scales
• Magnetar giant flares and afterglows as relativistic magnetized explosions
• Magnetic reconnection as a driver for a sub-ion scale cascade in plasma turbulence
• Magnetic Reconnection Onset via Disruption of a Forming Current Sheet by the Tearing Instability
• Collisionless Reconnection in Magnetohydrodynamic and Kinetic Turbulence
• Disruption of Alfvénic turbulence by magnetic reconnection in a collisionless plasma
• Plasmoid Instability in Evolving Current Sheets and Onset of Fast Reconnection
• Gamma-ray flares in the Crab Nebula: A case of relativistic reconnection?
• Fast reconnection in relativistic plasmas: the magnetohydrodynamics tearing instability revisited
• Can Hall Magnetohydrodynamics explain plasma turbulence at sub-ion scales?
• Magnetic reconnection: Self-similar current sheet collapse triggered by "ideal" tearing
• The tearing mode instability of thin current sheets: the transition to fast reconnection in the presence of viscosity
• The inner structure of collisionless magnetic reconnection: The electron-frame dissipation measure and Hall fields
• "Ideally" unstable current sheets and the triggering of fast magnetic reconnection
• Fast Magnetic Reconnection: "Ideal" Tearing and the Hall Effect
• "Ideal" tearing and the transition to fast reconnection in the weakly collisional MHD and EMHD regimes
• Onset of fast "ideal" tearing in thin current sheets: dependence on the equilibrium current profile
• Secondary fast reconnecting instability in the sawtooth crash
• The "ideal" tearing mode: theory and resistive MHD simulations
• Marginal Stability of Sweet-Parker Type Current Sheets at Low Lundquist Numbers
• Dynamic evolution of current sheets, ideal tearing, plasmoid formation and generalized fractal reconnection scaling relations
• Activation of MHD reconnection on ideal timescales
• Fast magnetic reconnection: The "ideal" tearing instability in classic, Hall, and relativistic plasmas

Cited by in corpus (10)

• Systematic construction of upwind constrained transport schemes for MHD
• Three-dimensional magnetic reconnection in particle-in-cell simulations of anisotropic plasma turbulence
• Spectral transfer and Kármán-Howarth-Monin equations for compressible Hall magnetohydrodynamics
• A $4^{\mathrm{th}}$-order accurate finite volume method for ideal classical and special relativistic MHD based on pointwise reconstructions
• Oblique tearing mode instability: guide field and Hall effect
• Multidimensional Iterative Filtering: a new approach for investigating plasma turbulence in numerical simulations
• Modification of the resistive tearing instability with Joule heating by shear flow
• Instabilities in a current sheet with plasma jet
• On the Impact of the Numerical Method on Magnetic Reconnection and Particle Acceleration -- I. The MHD case
• Three-dimensional tearing instability of flux-tube-like magnetic fields