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Title: Sausage instabilities on top of kinking lengthening current-carrying magnetic flux tubes

Abstract

We theoretically explore the possibility of sausage instabilities developing on top of a kink instability in lengthening current-carrying magnetic flux tubes. Observations indicate that the dynamics of magnetic flux tubes in our cosmos and terrestrial experiments can involve topological changes faster than time scales predicted by resistive magnetohydrodynamics. Recent laboratory experiments suggest that hierarchies of instabilities, such as kink and Rayleigh-Taylor, could be responsible for initiating fast topological changes by locally accessing two-fluid and kinetic regimes. Sausage instabilities can also provide this coupling mechanism between disparate scales. Flux tube experiments can be classified by the flux tube's evolution in a configuration space described by a normalized inverse aspect-ratio $$\bar{k}$$ and current-to-magnetic flux ratio $$\bar{λ}$$. A lengthening current-carrying magnetic flux tube traverses this $$\bar{k}$$-$$\bar{λ}$$ space and crosses stability boundaries. We derive a single general criterion for the onset of the sausage and kink instabilities in idealized magnetic flux tubes with core and skin currents. The criterion indicates a dependence of the stability boundaries on current profiles and shows overlapping kink and sausage unstable regions in the $$\bar{k}$$-$$\bar{λ}$$ space with two free parameters. Finally, numerical investigation of the stability criterion reduces the number of free parameters to a single one that describes the current profile and confirms the overlapping sausage and kink unstable regions in $$\bar{k}$$-$$\bar{λ}$$ A lengthening, ideal current-carrying magnetic flux tube can therefore become sausage unstable after it becomes kink unstable.

Authors:
ORCiD logo [1];  [1]
  1. Univ. of Washington, Seattle, WA (United States)
Publication Date:
Research Org.:
Univ. of Washington, Seattle, WA (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1465760
Alternate Identifier(s):
OSTI ID: 1361833
Grant/Contract Number:  
SC0010340; AC05-06OR23100
Resource Type:
Accepted Manuscript
Journal Name:
Physics of Plasmas
Additional Journal Information:
Journal Volume: 24; Journal Issue: 5; Journal ID: ISSN 1070-664X
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY

Citation Formats

von der Linden, Jens, and You, Setthivoine. Sausage instabilities on top of kinking lengthening current-carrying magnetic flux tubes. United States: N. p., 2017. Web. doi:10.1063/1.4981231.
von der Linden, Jens, & You, Setthivoine. Sausage instabilities on top of kinking lengthening current-carrying magnetic flux tubes. United States. doi:10.1063/1.4981231.
von der Linden, Jens, and You, Setthivoine. Mon . "Sausage instabilities on top of kinking lengthening current-carrying magnetic flux tubes". United States. doi:10.1063/1.4981231. https://www.osti.gov/servlets/purl/1465760.
@article{osti_1465760,
title = {Sausage instabilities on top of kinking lengthening current-carrying magnetic flux tubes},
author = {von der Linden, Jens and You, Setthivoine},
abstractNote = {We theoretically explore the possibility of sausage instabilities developing on top of a kink instability in lengthening current-carrying magnetic flux tubes. Observations indicate that the dynamics of magnetic flux tubes in our cosmos and terrestrial experiments can involve topological changes faster than time scales predicted by resistive magnetohydrodynamics. Recent laboratory experiments suggest that hierarchies of instabilities, such as kink and Rayleigh-Taylor, could be responsible for initiating fast topological changes by locally accessing two-fluid and kinetic regimes. Sausage instabilities can also provide this coupling mechanism between disparate scales. Flux tube experiments can be classified by the flux tube's evolution in a configuration space described by a normalized inverse aspect-ratio $\bar{k}$ and current-to-magnetic flux ratio $\bar{λ}$. A lengthening current-carrying magnetic flux tube traverses this $\bar{k}$-$\bar{λ}$ space and crosses stability boundaries. We derive a single general criterion for the onset of the sausage and kink instabilities in idealized magnetic flux tubes with core and skin currents. The criterion indicates a dependence of the stability boundaries on current profiles and shows overlapping kink and sausage unstable regions in the $\bar{k}$-$\bar{λ}$ space with two free parameters. Finally, numerical investigation of the stability criterion reduces the number of free parameters to a single one that describes the current profile and confirms the overlapping sausage and kink unstable regions in $\bar{k}$-$\bar{λ}$ A lengthening, ideal current-carrying magnetic flux tube can therefore become sausage unstable after it becomes kink unstable.},
doi = {10.1063/1.4981231},
journal = {Physics of Plasmas},
number = 5,
volume = 24,
place = {United States},
year = {2017},
month = {4}
}

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Cited by: 1 work
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Figures / Tables:

FIG. 1 FIG. 1: Analytical $\bar{k}$– $\bar\lambda$ stability spaces parameterized with core current fraction and rigidness $\delta$. (a) Stability spaces for $\epsilon$=0.1 and $\delta$= 0.1. The white region is stable, the gray region is unstable, the hatched region is kink (m=1) unstable, and the crosshatched region is unstable to both kink andmore » sausage (m=0) modes. (b) Kink stability space dependence on with $\delta$ =0. The dark red region is unstable. (c) Sausage stability space dependence on $\epsilon$ with $\delta$ = 0.7. The dark green region is unstable. (d) Sausage stability boundary dependence on $\delta$ with $\epsilon$ = 0.2. The dark green region is unstable.« less

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Works referenced in this record:

The Influence of an Axial Magnetic Field on the Stability of a Constricted Gas Discharge
journal, November 1957


Ion kinetic effect on bifurcated relaxation to a field-reversed configuration in TS-4 CT experiment
journal, July 2005


A dynamic magnetic tension force as the cause of failed solar eruptions
journal, December 2015

  • Myers, Clayton E.; Yamada, Masaaki; Ji, Hantao
  • Nature, Vol. 528, Issue 7583, p. 526-529
  • DOI: 10.1038/nature16188

Stability of a finite-length screw pinch revisited
journal, October 2004

  • Ryutov, D. D.; Cohen, R. H.; Pearlstein, L. D.
  • Physics of Plasmas, Vol. 11, Issue 10
  • DOI: 10.1063/1.1781624

Flux rope dynamics in three dimensions
journal, August 2014


Neutron Production in Linear Deuterium Pinches
journal, June 1958

  • Anderson, Oscar A.; Baker, William R.; Colgate, Stirling A.
  • Physical Review, Vol. 110, Issue 6
  • DOI: 10.1103/PhysRev.110.1375

Dynamic and Stagnating Plasma Flow Leading to Magnetic-Flux-Tube Collimation
journal, July 2005


Simulated flux-rope evolution during non-inductive startup in Pegasus
journal, February 2014


Magnetic reconnection from a multiscale instability cascade
journal, February 2012


Sheared Flow Stabilization of the m = 1 Kink Mode in Z Pinches
journal, October 1995


Appearance and Dynamics of Helical Flux Tubes under Electron Cyclotron Resonance Heating in the Core of KSTAR Plasmas
journal, October 2012


The transport of relative canonical helicity
journal, September 2012


Hydromagnetic stability of a diffuse linear pinch
journal, June 1960


Thin current sheets in collisionless plasma: Equilibrium structure, plasma instabilities, and particle acceleration
journal, February 2011


The electrodynamic 'snake' at the Galactic Centre
journal, March 1997


Coupling of sausage, kink, and magneto-Rayleigh-Taylor instabilities in a cylindrical liner
journal, March 2015

  • Weis, M. R.; Zhang, P.; Lau, Y. Y.
  • Physics of Plasmas, Vol. 22, Issue 3
  • DOI: 10.1063/1.4915520

Python for Scientific Computing
journal, January 2007


OBSERVATIONAL EVIDENCE OF SAUSAGE-PINCH INSTABILITY IN SOLAR CORONA BY SDO /AIA
journal, February 2013


Onset and Saturation of the Kink Instability in a Current-Carrying Line-Tied Plasma
journal, January 2006


The role of the nϕ=1 column mode in spheromak formation
journal, April 2009

  • Cohen, B. I.; Romero-Talamás, C. A.; Ryutov, D. D.
  • Physics of Plasmas, Vol. 16, Issue 4
  • DOI: 10.1063/1.3097909

Notes on Magnetohydrodynamics of Magnetic Reconnection in Turbulent Media
journal, October 2013


Effects of boundary conditions and flow on the kink instability in a cylindrical plasma column
journal, February 2007

  • Furno, I.; Intrator, T. P.; Lapenta, G.
  • Physics of Plasmas, Vol. 14, Issue 2
  • DOI: 10.1063/1.2435306

Why current-carrying magnetic flux tubes gobble up plasma and become thin as a result
journal, May 2003


Microphysics of Cosmic Plasmas: Hierarchies of Plasma Instabilities from MHD to Kinetic
journal, August 2013


Sheared flow stabilization experiments in the ZaP flow Z pinch
journal, May 2003

  • Shumlak, U.; Nelson, B. A.; Golingo, R. P.
  • Physics of Plasmas, Vol. 10, Issue 5
  • DOI: 10.1063/1.1558294

    Works referencing / citing this record:

      Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.