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

Fitzpatrick, Richard

doi:10.1063/1.5043203

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:

^[1]

Univ. of Texas, Austin, TX (United States). Inst. for Fusion Studies, Dept. of Physics

Publication Date:: 2018-08-17

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.

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                    Fitzpatrick, Richard. Nonlinear neoclassical two-fluid theory of response of tokamak plasma to resonant error-field.  United States.  https://doi.org/10.1063/1.5043203

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                    Fitzpatrick, Richard. Fri .  
"Nonlinear neoclassical two-fluid theory of response of tokamak plasma to resonant error-field".  United States.  https://doi.org/10.1063/1.5043203.  https://www.osti.gov/servlets/purl/1524537.

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@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}

}

Copy to clipboard

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Works referenced in this record:

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

Kirk, A.; Nardon, E.; Akers, R.
Nuclear Fusion, Vol. 50, Issue 3
DOI: 10.1088/0029-5515/50/3/034008

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

Jeon, Y. M.; Park, J. -K.; Yoon, S. W.
Physical Review Letters, Vol. 109, Issue 3
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Nonlinear error-field penetration in low density ohmically heated tokamak plasmas
journal, August 2012

Fitzpatrick, R.
Plasma Physics and Controlled Fusion, Vol. 54, Issue 9
DOI: 10.1088/0741-3335/54/9/094002

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

Liang, Y.; Lomas, P.; Nunes, I.
Nuclear Fusion, Vol. 53, Issue 7
DOI: 10.1088/0029-5515/53/7/073036

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

Buratti, P.; Alessi, E.; Baruzzo, M.
Nuclear Fusion, Vol. 56, Issue 7
DOI: 10.1088/0029-5515/56/7/076004

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

Cole, A. J.; Hegna, C. C.; Callen, J. D.
Physical Review Letters, Vol. 99, Issue 6
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Locked magnetic island chains in toroidally flow damped tokamak plasmas
journal, March 2010

Fitzpatrick, R.; Waelbroeck, F. L.
Plasma Physics and Controlled Fusion, Vol. 52, Issue 5
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A first-principles predictive model of the pedestal height and width: development, testing and ITER optimization with the EPED model
journal, August 2011

Snyder, P. B.; Groebner, R. J.; Hughes, J. W.
Nuclear Fusion, Vol. 51, Issue 10
DOI: 10.1088/0029-5515/51/10/103016

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

Fitzpatrick, Richard
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Nonlinear growth of the tearing mode
journal, January 1973

Rutherford, P. H.
Physics of Fluids, Vol. 16, Issue 11
DOI: 10.1063/1.1694232

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

Nazikian, R.; Petty, C. C.; Bortolon, A.
Nuclear Fusion, Vol. 58, Issue 10
DOI: 10.1088/1741-4326/aad20d

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

Fitzpatrick, Richard
Physics of Plasmas, Vol. 21, Issue 9
DOI: 10.1063/1.4896244

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

Fitzpatrick, R.; Waelbroeck, F. L.
Physics of Plasmas, Vol. 15, Issue 1
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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
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Advances in the physics understanding of ELM suppression using resonant magnetic perturbations in DIII-D
journal, January 2015

Wade, M. R.; Nazikian, R.; deGrassie, J. S.
Nuclear Fusion, Vol. 55, Issue 2
DOI: 10.1088/0029-5515/55/2/023002

A neoclassical drift-magnetohydrodynamical fluid model of the interaction of a magnetic island chain with a resonant error-field in a high temperature tokamak plasma
journal, April 2018

Fitzpatrick, Richard
Physics of Plasmas, Vol. 25, Issue 4
DOI: 10.1063/1.5022685

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

Ferraro, N. M.; Evans, T. E.; Lao, L. L.
Nuclear Fusion, Vol. 53, Issue 7
DOI: 10.1088/0029-5515/53/7/073042

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

Fitzpatrick, R.
Nuclear Fusion, Vol. 33, Issue 7
DOI: 10.1088/0029-5515/33/7/I08

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

An improved neoclassical drift-magnetohydrodynamical fluid model of helical magnetic island equilibria in tokamak plasmas
journal, May 2016

Fitzpatrick, Richard
Physics of Plasmas, Vol. 23, Issue 5
DOI: 10.1063/1.4948559

Two-fluid magnetic island dynamics in slab geometry: I - Isolated islands
text, January 2004

Fitzpatrick, Richard; Waelbroeck, Francois L.
arXiv
DOI: 10.48550/arxiv.physics/0406132

Works referencing / citing this record:

Two-fluid nonlinear theory of response of tokamak plasma to resonant magnetic perturbation
journal, November 2018

Fitzpatrick, Richard
Physics of Plasmas, Vol. 25, Issue 11
DOI: 10.1063/1.5053804

Rotation reversal of tokamak plasma subject to tearing-mode under resonant magnetic perturbation
journal, May 2019

Ivanov, N. V.; Kakurin, A. M.
Physics of Plasmas, Vol. 26, Issue 5
DOI: 10.1063/1.5095703

Two-Fluid Nonlinear Theory of Response of Tokamak Plasma to Resonant Magnetic Perturbation
text, January 2018

Fitzpatrick, Richard
arXiv
DOI: 10.48550/arxiv.1808.04482

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

Abstract

Citation Formats

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

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

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

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

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

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

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

A neoclassical drift-magnetohydrodynamical fluid model of the interaction of a magnetic island chain with a resonant error-field in a high temperature tokamak plasma journal, April 2018

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

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

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

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

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

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

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

An improved neoclassical drift-magnetohydrodynamical fluid model of helical magnetic island equilibria in tokamak plasmas journal, May 2016

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Two-fluid nonlinear theory of response of tokamak plasma to resonant magnetic perturbation journal, November 2018

Rotation reversal of tokamak plasma subject to tearing-mode under resonant magnetic perturbation journal, May 2019

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Resonant magnetic perturbation experiments on MAST using external and internal coils for ELM control
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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
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Mitigation of type-I ELMs with n = 2 fields on JET with ITER-like wall
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Diagnostic application of magnetic islands rotation in JET
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The influence of the ion polarization current on magnetic island stability in a tokamak plasma
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A drift-magnetohydrodynamical fluid model of helical magnetic island equilibria in the pedestals of H-mode tokamak plasmas
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Locked magnetic island chains in toroidally flow damped tokamak plasmas
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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

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

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
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Drift-tearing magnetic islands in tokamak plasmas
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Advances in the physics understanding of ELM suppression using resonant magnetic perturbations in DIII-D
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A neoclassical drift-magnetohydrodynamical fluid model of the interaction of a magnetic island chain with a resonant error-field in a high temperature tokamak plasma
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Role of plasma response in displacements of the tokamak edge due to applied non-axisymmetric fields
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Interaction of tearing modes with external structures in cylindrical geometry (plasma)
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Edge stability and transport control with resonant magnetic perturbations in collisionless tokamak plasmas
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Propagation of magnetic islands in the Er=0 frame of co-injected neutral beam driven discharges in the DIII-D tokamak
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Two-fluid magnetic island dynamics in slab geometry. II. Islands interacting with resistive walls or resonant magnetic perturbations
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Two-fluid magnetic island dynamics in slab geometry: Determination of the island phase velocity
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Hypersonic drift-tearing magnetic islands in tokamak plasmas
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