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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 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 duemore » 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:
 [1];  [1];  [2]
  1. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
  2. Univ. of Colorado, Boulder, CO (United States); Inst. for Advanced Study, Princeton, NJ (United States)
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:
Journal Article: 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:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; Physics; astrophysical plasmas; plasma flows; plasma instabilities

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. https://doi.org/10.1017/s002237781800017x
Tolman, Elizabeth A., Loureiro, Nuno F., and Uzdensky, Dmitri A. 2018. "Development of tearing instability in a current sheet forming by sheared incompressible flow". United States. https://doi.org/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 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.},
doi = {10.1017/s002237781800017x},
url = {https://www.osti.gov/biblio/1538935}, journal = {Journal of Plasma Physics},
issn = {0022-3778},
number = 1,
volume = 84,
place = {United States},
year = {Wed Feb 21 00:00:00 EST 2018},
month = {Wed Feb 21 00:00:00 EST 2018}
}

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Cited by: 10 works
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Works referenced in this record:

Nonlinear, three-dimensional magnetohydrodynamics of noncircular tokamaks
journal, January 1976


X -Point Collapse and Saturation in the Nonlinear Tearing Mode Reconnection
journal, November 2005


A loop-top hard X-ray source in a compact solar flare as evidence for magnetic reconnection
journal, October 1994


On the exponential flattening of current sheets near neutral X-points in two-dimensional ideal MHD flow
journal, April 1985


General theory of the plasmoid instability
journal, October 2016


Stability of a thick two-dimensional quasineutral sheet
journal, January 1982


Fast reconnection in high-Lundquist-number plasmas due to the plasmoid Instability
journal, November 2009


Neutral line model of substorms: Past results and present view
journal, June 1996


Current Sheets in the Earth Magnetotail: Plasma and Magnetic Field Structure with Cluster Project Observations
journal, February 2015


Plasmoid Instability in Evolving Current Sheets and Onset of Fast Reconnection
journal, November 2017


Nonlinear growth of the tearing mode
journal, January 1973


Adaptive Mesh Refinement for Singular Current Sheets in Incompressible Magnetohydrodynamic Flows
journal, June 1997


Reconnection of Quasi-Singular Current Sheets: the “Ideal” Tearing mode
journal, December 2013


Resistive tearing instability with equilibrium shear flow
journal, March 1990


Phase diagram for magnetic reconnection in heliophysical, astrophysical, and laboratory plasmas
journal, November 2011


Magnetic Reconnection in Astrophysical and Laboratory Plasmas
journal, September 2009


Magnetic reconnection via current sheets
journal, January 1986


Formation of Plasmoid Chains in Magnetic Reconnection
journal, September 2009


Spontaneous formation of electric current sheets and the origin of solar flares
journal, January 1988


On a plasma sheath separating regions of oppositely directed magnetic field
journal, January 1962


Nonlinear regimes of forced magnetic reconnection
journal, September 2015


Magnetic reconnection
journal, March 2010


Finite-Resistivity Instabilities of a Sheet Pinch
journal, January 1963


Magnetic Interaction Between Stars And Accretion Disks
journal, January 2004


Instability of current sheets and formation of plasmoid chains
journal, October 2007


Astrophysical Gyrokinetics: Kinetic and Fluid Turbulent Cascades in Magnetized Weakly Collisional Plasmas
journal, May 2009


Sweet's mechanism for merging magnetic fields in conducting fluids
journal, December 1957


Magnetic Reconnection Onset via Disruption of a Forming Current Sheet by the Tearing Instability
journal, March 2016


Chapter 3: MHD stability, operational limits and disruptions
journal, June 2007


Plasmoid Instability in Forming Current Sheets
journal, November 2017


Onset of the sawtooth crash
journal, May 1993


Plasmoid and Kelvin-Helmholtz instabilities in Sweet-Parker current sheets
text, January 2012


Works referencing / citing this record:

Onset of magnetic reconnection in a collisionless, high- plasma
journal, February 2019


Scalings pertaining to current sheet disruption mediated by the plasmoid instability
journal, September 2019


Plasmoid instability in the semi-collisional regime
journal, November 2018