Development of tearing instability in a current sheet forming by sheared incompressible flow

• DOI: 10.1017/s002237781800017x
• Publication Date: 2018-02-21T06:35:35Z
• Authors: Elizabeth A. Tolman; Nuno F. Loureiro; Dmitri A. Uzdensky
• Keywords: Tearing; Current sheet; Incompressible Flow; Linear stability

Sweet–Parker current sheets in high Lundquist number plasmas are unstable to tearing, suggesting they will not form physical systems. Understanding magnetic reconnection thus requires study of the stability a sheet as it forms. Formation can occur due sheared, sub-Alfvénic incompressible flows which narrow sheet. Standard tearing theory (Furth et al. Phys. Fluids , vol. 6 (4), 1963, pp. 459–484, Rutherford, 16 (11), 1973, 1903–1908, Coppi Fizika Plazmy 2, 1976, 961–966) is immediately applicable such forming for two reasons: first, because flow introduces terms present standard calculation; second, changing equilibrium time dependence constant calculation, complicating formulation an eigenvalue problem. This paper adapts mode analysis confront these challenges. In initial phase when any perturbations primarily governed by ideal magnetohydrodynamics, coordinate transformation reveals that compresses and stretches perturbations. A multiple scale describes how linear be applied under flow, showing affects separable exponential growth only implicitly, making scalings dependent. nonlinear Rutherford stage, shows adapted adding stationary rates additional term strengthening field. Overall, this understanding supports use flow-free with slight modifications