Development of tearing instability in a current sheet forming by sheared incompressible flow
- 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.
- Research Organization:
- Univ. of Colorado, Boulder, CO (United States); Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC)
- Grant/Contract Number:
- SC0008409; SC0016215
- OSTI ID:
- 1538935
- Journal Information:
- Journal of Plasma Physics, Vol. 84, Issue 1; ISSN 0022-3778
- Publisher:
- Cambridge University PressCopyright Statement
- Country of Publication:
- United States
- Language:
- English
Web of Science
Onset of magnetic reconnection in a collisionless, high- plasma
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journal | February 2019 |
Scalings pertaining to current sheet disruption mediated by the plasmoid instability
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journal | September 2019 |
Scalings Pertaining to Current Sheet Disruption Mediated by the Plasmoid Instability | text | January 2019 |
Plasmoid instability in the semi-collisional regime
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journal | November 2018 |
On the growth rate of plasmoid chains during nonlinear viscoresistive evolution of the tilt instability | preprint | January 2020 |
Petschek-type reconnection in the high-Lundquist-number regime during nonlinear evolution on the tilt instability | preprint | January 2020 |
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