skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

This content will become publicly available on June 19, 2020

Title: Resistive stability of cylindrical MHD equilibria with radially localized pressure gradients

Abstract

As a step toward understanding 3D magnetohydrodynamic (MHD) equilibria, for which smooth solutions may not exist, we develop a simple cylindrical model to investigate the resistive stability of MHD equilibria with alternating regions of constant and nonuniform pressure, producing states with continuous total pressure (i.e., no singular current sheets) but discontinuities in the parallel current density. We examine how the resistive stability characteristics of the model change as we increase the localization of pressure gradients at fixed radii, which approaches a discontinuous pressure profile in the zero-width limit. Equilibria with continuous pressure are found to be unstable to moderate/high-m modes and apparently tend toward ideal instability in some cases. We propose that additional geometric degrees of freedom or symmetry breaking via island formation may increase the parameter space on which equilibria of our model are physically realizable, while preserving the radial localization of pressure gradients. This is consistent with the possibility of realizing, in practice, 3D MHD equilibria which support both continuously nested flux surfaces (where ∇p ≠ 0) and chaotic field regions (where ∇p = 0)

Authors:
ORCiD logo [1];  [2]; ORCiD logo [1]; ORCiD logo [1]
  1. Australian National Univ., Canberra, ACT (Australia)
  2. Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
Publication Date:
Research Org.:
Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1543151
Alternate Identifier(s):
OSTI ID: 1527064
Grant/Contract Number:  
AC02-76CH03073
Resource Type:
Accepted Manuscript
Journal Name:
Physics of Plasmas
Additional Journal Information:
Journal Volume: 26; Journal Issue: 6; 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

Wright, A. M., Hudson, S. R., Dewar, R. L., and Hole, M. J. Resistive stability of cylindrical MHD equilibria with radially localized pressure gradients. United States: N. p., 2019. Web. doi:10.1063/1.5099354.
Wright, A. M., Hudson, S. R., Dewar, R. L., & Hole, M. J. Resistive stability of cylindrical MHD equilibria with radially localized pressure gradients. United States. doi:10.1063/1.5099354.
Wright, A. M., Hudson, S. R., Dewar, R. L., and Hole, M. J. Wed . "Resistive stability of cylindrical MHD equilibria with radially localized pressure gradients". United States. doi:10.1063/1.5099354.
@article{osti_1543151,
title = {Resistive stability of cylindrical MHD equilibria with radially localized pressure gradients},
author = {Wright, A. M. and Hudson, S. R. and Dewar, R. L. and Hole, M. J.},
abstractNote = {As a step toward understanding 3D magnetohydrodynamic (MHD) equilibria, for which smooth solutions may not exist, we develop a simple cylindrical model to investigate the resistive stability of MHD equilibria with alternating regions of constant and nonuniform pressure, producing states with continuous total pressure (i.e., no singular current sheets) but discontinuities in the parallel current density. We examine how the resistive stability characteristics of the model change as we increase the localization of pressure gradients at fixed radii, which approaches a discontinuous pressure profile in the zero-width limit. Equilibria with continuous pressure are found to be unstable to moderate/high-m modes and apparently tend toward ideal instability in some cases. We propose that additional geometric degrees of freedom or symmetry breaking via island formation may increase the parameter space on which equilibria of our model are physically realizable, while preserving the radial localization of pressure gradients. This is consistent with the possibility of realizing, in practice, 3D MHD equilibria which support both continuously nested flux surfaces (where ∇p ≠ 0) and chaotic field regions (where ∇p = 0)},
doi = {10.1063/1.5099354},
journal = {Physics of Plasmas},
number = 6,
volume = 26,
place = {United States},
year = {2019},
month = {6}
}

Journal Article:
Free Publicly Available Full Text
This content will become publicly available on June 19, 2020
Publisher's Version of Record

Save / Share:

Works referenced in this record:

Equilibrium of a Magnetically Confined Plasma in a Toroid
journal, January 1958

  • Kruskal, M. D.; Kulsrud, R. M.
  • Physics of Fluids, Vol. 1, Issue 4
  • DOI: 10.1063/1.1705884

Hydromagnetic stability of a diffuse linear pinch
journal, June 1960


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

  • Furth, Harold P.; Killeen, John; Rosenbluth, Marshall N.
  • Physics of Fluids, Vol. 6, Issue 4
  • DOI: 10.1063/1.1706761

Tearing mode in the cylindrical tokamak
journal, January 1973


Resistive instabilities in a diffuse linear pinch
journal, June 1966


Resistive instabilities in general toroidal plasma configurations
journal, January 1975

  • Glasser, A. H.; Greene, J. M.; Johnson, J. L.
  • Physics of Fluids, Vol. 18, Issue 7
  • DOI: 10.1063/1.861224

Linear stability of tearing modes
journal, January 1986

  • Cowley, S. C.; Kulsrud, R. M.; Hahm, T. S.
  • Physics of Fluids, Vol. 29, Issue 10
  • DOI: 10.1063/1.865841

Hydromagnetic stability of tokamaks
journal, January 1978


Interchange instabilities in ideal hydromagnetic theory
journal, January 1968


New approach to magnetohydrodynamic stability: I. A practical stability concept
journal, January 1974


New approach to magnetohydrodynamic stability: II. Sigma-stable diffuse pinch configurations
journal, January 1974


Forced magnetic reconnection
journal, January 1985

  • Hahm, T. S.; Kulsrud, R. M.
  • Physics of Fluids, Vol. 28, Issue 8
  • DOI: 10.1063/1.865247

Stabilization of Resistive Kink Modes in the Tokamak
journal, January 1977


Analytic study on low- external ideal infernal modes in tokamaks with large edge pressure gradients
journal, March 2018


Linear stability analysis of force-free equilibria close to Taylor relaxed states
journal, September 2007

  • Tassi, E.; Hastie, R. J.; Porcelli, F.
  • Physics of Plasmas, Vol. 14, Issue 9
  • DOI: 10.1063/1.2769324

Magnetohydrodynamic stability of plasmas with ideal and relaxed regions
journal, October 2009


Relaxed MHD states of a multiple region plasma
journal, May 2009


The spectrum of multi-region-relaxed magnetohydrodynamic modes in topologically toroidal geometry
journal, February 2017

  • Dewar, R. L.; Tuen, L. H.; Hole, M. J.
  • Plasma Physics and Controlled Fusion, Vol. 59, Issue 4
  • DOI: 10.1088/1361-6587/aa5b53

Toroidal Containment of a Plasma
journal, January 1967


Existence of three-dimensional toroidal MHD equilibria with nonconstant pressure
journal, July 1996


Stepped pressure profile equilibria in cylindrical plasmas via partial Taylor relaxation
journal, December 2006


Equilibria and stability in partially relaxed plasma–vacuum systems
journal, July 2007


Variational formulation of relaxed and multi-region relaxed magnetohydrodynamics
journal, November 2015


Computation of multi-region relaxed magnetohydrodynamic equilibria
journal, November 2012

  • Hudson, S. R.; Dewar, R. L.; Dennis, G.
  • Physics of Plasmas, Vol. 19, Issue 11
  • DOI: 10.1063/1.4765691

The infinite interface limit of multiple-region relaxed magnetohydrodynamics
journal, March 2013

  • Dennis, G. R.; Hudson, S. R.; Dewar, R. L.
  • Physics of Plasmas, Vol. 20, Issue 3
  • DOI: 10.1063/1.4795739

Relaxation of Toroidal Plasma and Generation of Reverse Magnetic Fields
journal, November 1974


Relaxation and magnetic reconnection in plasmas
journal, July 1986


Relaxed Plasma Equilibria and Entropy-Related Plasma Self-Organization Principles
journal, November 2008

  • Dewar, Robert; Hole, Matthew; McGann, Mathew
  • Entropy, Vol. 10, Issue 4
  • DOI: 10.3390/e10040621

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

  • Loureiro, N. F.; Schekochihin, A. A.; Cowley, S. C.
  • Physics of Plasmas, Vol. 14, Issue 10
  • DOI: 10.1063/1.2783986

General theory of the plasmoid instability
journal, October 2016

  • Comisso, L.; Lingam, M.; Huang, Y. -M.
  • Physics of Plasmas, Vol. 23, Issue 10
  • DOI: 10.1063/1.4964481

Ideal magnetohydrodynamic theory of magnetic fusion systems
journal, July 1982


Three-dimensional magnetohydrodynamic equilibria with continuous magnetic fields
journal, July 2017


Analytic stability criteria for edge MHD oscillations in high performance ELM free tokamak regimes
journal, November 2017


Existence of three-dimensional ideal-magnetohydrodynamic equilibria with current sheets
journal, September 2015

  • Loizu, J.; Hudson, S. R.; Bhattacharjee, A.
  • Physics of Plasmas, Vol. 22, Issue 9
  • DOI: 10.1063/1.4931094

Helical bifurcation and tearing mode in a plasma—a description based on Casimir foliation
journal, August 2012


Nonlinear growth of the tearing mode
journal, January 1973