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

Tolman, Elizabeth A.; Loureiro, Nuno F.; Uzdensky, Dmitri A.

doi:10.1017/s002237781800017x

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

Journal Article · Wed Feb 21 00:00:00 EST 2018 · Journal of Plasma Physics

DOI:https://doi.org/10.1017/s002237781800017x· OSTI ID:1538935

Tolman, Elizabeth A. ^[1]; Loureiro, Nuno F. ^[2]; Uzdensky, Dmitri A. ^[3]

Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States); DOE/OSTI
Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
Univ. of Colorado, Boulder, CO (United States); Inst. for Advanced Study, Princeton, NJ (United States)

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 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. Here, a multiple scale formulation describes how linear tearing mode theory 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.

View Accepted Manuscript (DOE)

Research Organization:: Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States); Univ. of Colorado, Boulder, CO (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

Grant/Contract Number:: SC0008409; SC0016215

OSTI ID:: 1538935

Journal Information:: Journal of Plasma Physics, Journal Name: Journal of Plasma Physics Journal Issue: 1 Vol. 84; ISSN 0022-3778

Publisher:: Cambridge University PressCopyright Statement

Country of Publication:: United States

Language:: English

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