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

Abstract

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

Authors:
; ;
Publication Date:
Research Org.:
Univ. of Colorado, Boulder, CO (United States); Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1538935
Grant/Contract Number:  
SC0008409; SC0016215
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Plasma Physics
Additional Journal Information:
Journal Volume: 84; Journal Issue: 1; Journal ID: ISSN 0022-3778
Publisher:
Cambridge University Press
Country of Publication:
United States
Language:
English
Subject:
Physics

Citation Formats

Tolman, Elizabeth A., Loureiro, Nuno F., and Uzdensky, Dmitri A. Development of tearing instability in a current sheet forming by sheared incompressible flow. United States: N. p., 2018. Web. doi:10.1017/s002237781800017x.
Tolman, Elizabeth A., Loureiro, Nuno F., & Uzdensky, Dmitri A. Development of tearing instability in a current sheet forming by sheared incompressible flow. United States. doi:10.1017/s002237781800017x.
Tolman, Elizabeth A., Loureiro, Nuno F., and Uzdensky, Dmitri A. Thu . "Development of tearing instability in a current sheet forming by sheared incompressible flow". United States. doi:10.1017/s002237781800017x. https://www.osti.gov/servlets/purl/1538935.
@article{osti_1538935,
title = {Development of tearing instability in a current sheet forming by sheared incompressible flow},
author = {Tolman, Elizabeth A. and Loureiro, Nuno F. and Uzdensky, Dmitri A.},
abstractNote = {Sweet–Parker current sheets in high Lundquist number plasmas are unstable to tearing, suggesting they will not form in physical systems. Understanding magnetic reconnection thus requires study of the stability of a current sheet as it forms. Formation can occur due to sheared, sub-Alfvénic incompressible flows which narrow the sheet. Standard tearing theory (Furthet al. Phys. Fluids, vol. 6 (4), 1963, pp. 459–484, Rutherford,Phys. Fluids, vol. 16 (11), 1973, pp. 1903–1908, Coppiet al. Fizika Plazmy, vol. 2, 1976, pp. 961–966) is not immediately applicable to such forming sheets for two reasons: first, because the flow introduces terms not present in the standard calculation; second, because the changing equilibrium introduces time dependence to terms which are constant in the standard calculation, complicating the formulation of an eigenvalue problem. This paper adapts standard tearing mode analysis to confront these challenges. In an initial phase when any perturbations are primarily governed by ideal magnetohydrodynamics, a coordinate transformation reveals that the flow compresses and stretches perturbations. A multiple scale formulation describes how linear tearing mode theory (Furthet al. Phys. Fluids, vol. 6 (4), 1963, pp. 459–484, Coppiet al. Fizika Plazmy, vol. 2, 1976, pp. 961–966) can be applied to an equilibrium changing under flow, showing that the flow affects the separable exponential growth only implicitly, by making the standard scalings time dependent. In the nonlinear Rutherford stage, the coordinate transformation shows that standard theory can be adapted by adding to the stationary rates time dependence and an additional term due to the strengthening equilibrium magnetic field. Overall, this understanding supports the use of flow-free scalings with slight modifications to study tearing in a forming sheet.},
doi = {10.1017/s002237781800017x},
journal = {Journal of Plasma Physics},
number = 1,
volume = 84,
place = {United States},
year = {2018},
month = {2}
}

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