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

Title: Nonlinear neoclassical two-fluid theory of response of tokamak plasma to resonant error-field

Abstract

A nonlinear, neoclassical, two-fluid theory of the interaction of a single-helicity magnetic island chain with a resonant error-field in a quasi-cylindrical, low-β, tokamak plasma is presented. In particular, the analysis of Fitzpatrick [Phys. Plasmas 25, 042503 (2018)] is generalized to take explicit time dependence into account. Aside from the ability to more accurately treat time-varying problems, the main physical effect that is introduced into the theory by the incorporation of explicit time dependence is ion inertia. The formalism developed in the paper is used to analyze two time-varying problems. First, the interaction of a pre-existing magnetic island chain with a resonant error-field. Second, an error-field-maintained magnetic island chain. The latter problem is of direct relevance to experiments in which deliberately applied, multi-harmonic, resonant magnetic perturbations are used to suppress edge localized modes (ELMs) in tokamak plasmas. Indeed, the predictions of the theory are strikingly similar to data recently obtained from ELM suppression experiments in the DIII-D tokamak [R. Nazikian et al., Nucl. Fusion 58, 106010 (2018)].

Authors:
ORCiD logo [1]
  1. Univ. of Texas, Austin, TX (United States). Inst. for Fusion Studies, Dept. of Physics
Publication Date:
Research Org.:
Univ. of Texas, Austin, TX (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1524537
Alternate Identifier(s):
OSTI ID: 1464988
Grant/Contract Number:  
FG02-04ER54742; FG02-04ER-54742
Resource Type:
Accepted Manuscript
Journal Name:
Physics of Plasmas
Additional Journal Information:
Journal Volume: 25; Journal Issue: 8; 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

Fitzpatrick, Richard. Nonlinear neoclassical two-fluid theory of response of tokamak plasma to resonant error-field. United States: N. p., 2018. Web. doi:10.1063/1.5043203.
Fitzpatrick, Richard. Nonlinear neoclassical two-fluid theory of response of tokamak plasma to resonant error-field. United States. doi:10.1063/1.5043203.
Fitzpatrick, Richard. Fri . "Nonlinear neoclassical two-fluid theory of response of tokamak plasma to resonant error-field". United States. doi:10.1063/1.5043203. https://www.osti.gov/servlets/purl/1524537.
@article{osti_1524537,
title = {Nonlinear neoclassical two-fluid theory of response of tokamak plasma to resonant error-field},
author = {Fitzpatrick, Richard},
abstractNote = {A nonlinear, neoclassical, two-fluid theory of the interaction of a single-helicity magnetic island chain with a resonant error-field in a quasi-cylindrical, low-β, tokamak plasma is presented. In particular, the analysis of Fitzpatrick [Phys. Plasmas 25, 042503 (2018)] is generalized to take explicit time dependence into account. Aside from the ability to more accurately treat time-varying problems, the main physical effect that is introduced into the theory by the incorporation of explicit time dependence is ion inertia. The formalism developed in the paper is used to analyze two time-varying problems. First, the interaction of a pre-existing magnetic island chain with a resonant error-field. Second, an error-field-maintained magnetic island chain. The latter problem is of direct relevance to experiments in which deliberately applied, multi-harmonic, resonant magnetic perturbations are used to suppress edge localized modes (ELMs) in tokamak plasmas. Indeed, the predictions of the theory are strikingly similar to data recently obtained from ELM suppression experiments in the DIII-D tokamak [R. Nazikian et al., Nucl. Fusion 58, 106010 (2018)].},
doi = {10.1063/1.5043203},
journal = {Physics of Plasmas},
number = 8,
volume = 25,
place = {United States},
year = {2018},
month = {8}
}

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

Citation Metrics:
Cited by: 2 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

Resonant magnetic perturbation experiments on MAST using external and internal coils for ELM control
journal, February 2010


Suppression of Edge Localized Modes in High-Confinement KSTAR Plasmas by Nonaxisymmetric Magnetic Perturbations
journal, July 2012


Nonlinear error-field penetration in low density ohmically heated tokamak plasmas
journal, August 2012


Mitigation of type-I ELMs with n = 2 fields on JET with ITER-like wall
journal, June 2013


Diagnostic application of magnetic islands rotation in JET
journal, June 2016


The influence of the ion polarization current on magnetic island stability in a tokamak plasma
journal, December 2006

  • Fitzpatrick, R.; Waelbroeck, F. L.; Militello, F.
  • Physics of Plasmas, Vol. 13, Issue 12
  • DOI: 10.1063/1.2402914

A drift-magnetohydrodynamical fluid model of helical magnetic island equilibria in the pedestals of H-mode tokamak plasmas
journal, June 2010

  • Fitzpatrick, R.; Waelbroeck, F. L.
  • Physics of Plasmas, Vol. 17, Issue 6
  • DOI: 10.1063/1.3432720

Effect of Neoclassical Toroidal Viscosity on Error-Field Penetration Thresholds in Tokamak Plasmas
journal, August 2007


Locked magnetic island chains in toroidally flow damped tokamak plasmas
journal, March 2010


A first-principles predictive model of the pedestal height and width: development, testing and ITER optimization with the EPED model
journal, August 2011


Effect of flow damping on drift-tearing magnetic islands in tokamak plasmas
journal, July 2009

  • Fitzpatrick, R.; Waelbroeck, F. L.
  • Physics of Plasmas, Vol. 16, Issue 7
  • DOI: 10.1063/1.3191719

Bifurcated states of a rotating tokamak plasma in the presence of a static error-field
journal, September 1998

  • Fitzpatrick, Richard
  • Physics of Plasmas, Vol. 5, Issue 9
  • DOI: 10.1063/1.873000

Nonlinear growth of the tearing mode
journal, January 1973


Grassy-ELM regime with edge resonant magnetic perturbations in fully noninductive plasmas in the DIII-D tokamak
journal, July 2018


Linear and nonlinear response of a rotating tokamak plasma to a resonant error-field
journal, September 2014


Drift-tearing magnetic islands in tokamak plasmas
journal, January 2008

  • Fitzpatrick, R.; Waelbroeck, F. L.
  • Physics of Plasmas, Vol. 15, Issue 1
  • DOI: 10.1063/1.2829757

A four-field model for tokamak plasma dynamics
journal, January 1985

  • Hazeltine, R. D.; Kotschenreuther, M.; Morrison, P. J.
  • Physics of Fluids, Vol. 28, Issue 8
  • DOI: 10.1063/1.865255

Advances in the physics understanding of ELM suppression using resonant magnetic perturbations in DIII-D
journal, January 2015


Role of plasma response in displacements of the tokamak edge due to applied non-axisymmetric fields
journal, June 2013


Interaction of tearing modes with external structures in cylindrical geometry (plasma)
journal, July 1993


Edge stability and transport control with resonant magnetic perturbations in collisionless tokamak plasmas
journal, May 2006

  • Evans, Todd E.; Moyer, Richard A.; Burrell, Keith H.
  • Nature Physics, Vol. 2, Issue 6
  • DOI: 10.1038/nphys312

Propagation of magnetic islands in the Er=0 frame of co-injected neutral beam driven discharges in the DIII-D tokamak
journal, September 2003

  • La Haye, R. J.; Petty, C. C.; Strait, E. J.
  • Physics of Plasmas, Vol. 10, Issue 9
  • DOI: 10.1063/1.1602452

Two-fluid magnetic island dynamics in slab geometry. II. Islands interacting with resistive walls or resonant magnetic perturbations
journal, February 2005

  • Fitzpatrick, Richard; Waelbroeck, François L.
  • Physics of Plasmas, Vol. 12, Issue 2
  • DOI: 10.1063/1.1833391

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

Two-fluid magnetic island dynamics in slab geometry: Determination of the island phase velocity
journal, August 2005

  • Fitzpatrick, R.; Watson, P. G.; Waelbroeck, F. L.
  • Physics of Plasmas, Vol. 12, Issue 8
  • DOI: 10.1063/1.2001644

Two-fluid magnetic island dynamics in slab geometry. I. Isolated islands
journal, February 2005

  • Fitzpatrick, Richard; Waelbroeck, François L.
  • Physics of Plasmas, Vol. 12, Issue 2
  • DOI: 10.1063/1.1833375

Hypersonic drift-tearing magnetic islands in tokamak plasmas
journal, December 2007

  • Fitzpatrick, R.; Waelbroeck, F. L.
  • Physics of Plasmas, Vol. 14, Issue 12
  • DOI: 10.1063/1.2811928