Onset of fast "ideal" tearing in thin current sheets: dependence on the equilibrium current profile

Abstract

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 ${\Delta }^{\prime }$ parameter on the wavenumber $k$ of unstable modes. The scaling ${\Delta }^{\prime }(k)$ 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 $\alpha \ge 1/4$.

arXiv comment7 pages, 5 figures

References in corpus (17)

• Instability of current sheets and formation of plasmoid chains
• Fast Reconnection in High-Lundquist-Number Plasmas Due to Secondary Tearing Instabilities
• Nonlinear Dynamics of the Parker Scenario for Coronal Heating
• Turbulent Magnetohydrodynamic Reconnection Mediated by the Plasmoid Instability
• Role of magnetic reconnection in MHD turbulence
• Disruption of sheetlike structures in Alfvénic turbulence by magnetic reconnection
• Plasmoid and Kelvin-Helmholtz instabilities in Sweet-Parker current sheets
• Plasmoid Instability in Evolving Current Sheets and Onset of Fast Reconnection
• Nonlinear Evolution of q=1 Triple Tearing Modes in a Tokamak Plasma
• Magnetic reconnection: Self-similar current sheet collapse triggered by "ideal" tearing
• "Ideally" unstable current sheets and the triggering of fast magnetic reconnection
• "Ideal" tearing and the transition to fast reconnection in the weakly collisional MHD and EMHD regimes
• Fast Magnetic Reconnection: "Ideal" Tearing and the Hall Effect
• The magnetic field topology in the reconnecting pulsar magnetosphere
• Secondary fast reconnecting instability in the sawtooth crash
• Marginal Stability of Sweet-Parker Type Current Sheets at Low Lundquist Numbers
• The deceiving delta: on the equilibrium dependent dynamics of nonlinear magnetic islands

Cited by in corpus (13)

• Reflection-driven MHD turbulence in the solar atmosphere and solar wind
• Fast Magnetic Reconnection: Secondary Tearing Instability and Role of the Hall Term
• Kinetic models of tangential discontinuities in the solar wind
• Thermally enhanced tearing in solar current sheets: explosive reconnection with plasmoid-trapped condensations
• Coalescence Instability in Chromospheric Partially Ionised Plasmas
• Spectral signatures of recursive magnetic field reconnection
• Calculations in the theory of tearing instability
• Dynamic evolution of current sheets, ideal tearing, plasmoid formation and generalized fractal reconnection scaling relations
• Tearing instability in Alfvén and kinetic-Alfvén turbulence
• Tearing modes in partially ionized plasmas
• Effects of a Velocity Shear on Double Current Sheet Systems: Explosive Reconnection and Particle Acceleration
• Instabilities in a current sheet with plasma jet
• Current sheets, plasmoids and flux ropes in the heliosphere. Part II: Theoretical aspects