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

Title: Equilibrium β-limits in classical stellarators

Abstract

Here, a numerical investigation is carried out to understand the equilibrium β-limit in a classical stellarator. The stepped-pressure equilibrium code is used in order to assess whether or not magnetic islands and stochastic field-lines can emerge at high β. Two modes of operation are considered: a zero-net-current stellarator and a fixed-iota stellarator. Despite the fact that relaxation is allowed, the former is shown to maintain good flux surfaces up to the equilibrium β-limit predicted by ideal-magnetohydrodynamics (MHD), above which a separatrix forms. The latter, which has no ideal equilibrium β-limit, is shown to develop regions of magnetic islands and chaos at sufficiently high β, thereby providing a ‘non-ideal β-limit’. Perhaps surprisingly, however, the value of β at which the Shafranov shift of the axis reaches a fraction of the minor radius follows in all cases the scaling laws predicted by ideal-MHD. We compare our results to the High-Beta-Stellarator theory of Freidberg and derive a new prediction for the non-ideal equilibrium β-limit above which chaos emerges.

Authors:
 [1];  [2];  [1];  [1];  [1]
  1. Max-Planck-Institut fur Plasmaphysik, Greifswald (Germany)
  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:
1414936
Grant/Contract Number:  
AC02-09CH11466
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Plasma Physics
Additional Journal Information:
Journal Volume: 83; Journal Issue: 06; Journal ID: ISSN 0022-3778
Publisher:
Cambridge University Press
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; fusion plasma; plasma confinement

Citation Formats

Loizu, Joaquim, Hudson, S. R., Nuhrenberg, C., Geiger, J., and Helander, P. Equilibrium β-limits in classical stellarators. United States: N. p., 2017. Web. doi:10.1017/S0022377817000861.
Loizu, Joaquim, Hudson, S. R., Nuhrenberg, C., Geiger, J., & Helander, P. Equilibrium β-limits in classical stellarators. United States. doi:10.1017/S0022377817000861.
Loizu, Joaquim, Hudson, S. R., Nuhrenberg, C., Geiger, J., and Helander, P. Fri . "Equilibrium β-limits in classical stellarators". United States. doi:10.1017/S0022377817000861. https://www.osti.gov/servlets/purl/1414936.
@article{osti_1414936,
title = {Equilibrium β-limits in classical stellarators},
author = {Loizu, Joaquim and Hudson, S. R. and Nuhrenberg, C. and Geiger, J. and Helander, P.},
abstractNote = {Here, a numerical investigation is carried out to understand the equilibrium β-limit in a classical stellarator. The stepped-pressure equilibrium code is used in order to assess whether or not magnetic islands and stochastic field-lines can emerge at high β. Two modes of operation are considered: a zero-net-current stellarator and a fixed-iota stellarator. Despite the fact that relaxation is allowed, the former is shown to maintain good flux surfaces up to the equilibrium β-limit predicted by ideal-magnetohydrodynamics (MHD), above which a separatrix forms. The latter, which has no ideal equilibrium β-limit, is shown to develop regions of magnetic islands and chaos at sufficiently high β, thereby providing a ‘non-ideal β-limit’. Perhaps surprisingly, however, the value of β at which the Shafranov shift of the axis reaches a fraction of the minor radius follows in all cases the scaling laws predicted by ideal-MHD. We compare our results to the High-Beta-Stellarator theory of Freidberg and derive a new prediction for the non-ideal equilibrium β-limit above which chaos emerges.},
doi = {10.1017/S0022377817000861},
journal = {Journal of Plasma Physics},
number = 06,
volume = 83,
place = {United States},
year = {2017},
month = {11}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 3 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

Current sheets and nonlinear growth of the m =1 kink‐tearing mode
journal, December 1989

  • Waelbroeck, F. L.
  • Physics of Fluids B: Plasma Physics, Vol. 1, Issue 12
  • DOI: 10.1063/1.859172

Eigenvalue problems for Beltrami fields arising in a three-dimensional toroidal magnetohydrodynamic equilibrium problem
journal, May 2007

  • Hudson, S. R.; Hole, M. J.; Dewar, R. L.
  • Physics of Plasmas, Vol. 14, Issue 5
  • DOI: 10.1063/1.2722721

Stochasticity reduction
journal, January 1986

  • Cary, John R.; Hanson, James D.
  • Physics of Fluids, Vol. 29, Issue 8
  • DOI: 10.1063/1.865539

Relaxation and magnetic reconnection in plasmas
journal, July 1986


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

Stellarator and tokamak plasmas: a comparison
journal, November 2012


Development and application of HINT2 to helical system plasmas
journal, September 2006


PIES free boundary stellarator equilibria with improved initial conditions
journal, July 2005


Theory of plasma confinement in non-axisymmetric magnetic fields
journal, July 2014


Dependence of spontaneous growth and suppression of the magnetic island on beta and collisionality in the LHD
journal, June 2008


Symplectic maps, variational principles, and transport
journal, July 1992


A universal instability of many-dimensional oscillator systems
journal, May 1979


Physics of magnetically confined plasmas
journal, January 2005


Steepest-descent moment method for three-dimensional magnetohydrodynamic equilibria
journal, January 1983


Theory of pressure‐induced islands and self‐healing in three‐dimensional toroidal magnetohydrodynamic equilibria
journal, March 1995

  • Bhattacharjee, A.; Hayashi, T.; Hegna, C. C.
  • Physics of Plasmas, Vol. 2, Issue 3
  • DOI: 10.1063/1.871369

SIESTA: A scalable iterative equilibrium solver for toroidal applications
journal, June 2011

  • Hirshman, S. P.; Sanchez, R.; Cook, C. R.
  • Physics of Plasmas, Vol. 18, Issue 6
  • DOI: 10.1063/1.3597155

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

The theory of the early nonlinear stage of m =1 reconnection in tokamaks*
journal, July 1993

  • Zakharov, L.; Rogers, B.; Migliuolo, S.
  • Physics of Fluids B: Plasma Physics, Vol. 5, Issue 7
  • DOI: 10.1063/1.860735

Confirmation of the topology of the Wendelstein 7-X magnetic field to better than 1:100,000
journal, November 2016

  • Pedersen, T. Sunn; Otte, M.; Lazerson, S.
  • Nature Communications, Vol. 7, Issue 1
  • DOI: 10.1038/ncomms13493

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

Determination of Hydromagnetic Equilibria
journal, January 1961

  • Greene, John M.; Johnson, John L.
  • Physics of Fluids, Vol. 4, Issue 7
  • DOI: 10.1063/1.1706420

Minimally Constrained Model of Self-Organized Helical States in Reversed-Field Pinches
journal, July 2013


Manipulation of islands in a heliac vacuum field
journal, February 1997


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


Plasma flow healing of magnetic islands in stellarators
journal, May 2012


Elimination of stochasticity in stellarators
journal, January 1984

  • Hanson, James D.; Cary, John R.
  • Physics of Fluids, Vol. 27, Issue 4
  • DOI: 10.1063/1.864692

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