The external kink mode in diverted tokamaks

Turnbull, Alan D.; Hanson, Jeremy M.; Turco, Francesca; Ferraro, Nathaniel M.; Lanctot, Matthew J.; Lao, Lang L.; Strait, Edward J.; Piovesan, Paolo; Martin, Piero

doi:10.1017/S0022377816000568

Title: The external kink mode in diverted tokamaks

Abstract

Here, an explanation is provided for the disruptive instability in diverted tokamaks when the safety factor at the 95% poloidal flux surface, q₉₅, is driven below 2.0. The instability is a resistive kink counterpart to the current-driven ideal mode that traditionally explained the corresponding disruption in limited cross-sections when q_edge, the safety factor at the outermost closed flux surface, lies just below a rational value. Experimentally, external kink modes are observed in limiter configurations as the current in a tokamak is ramped up and q_edge decreases through successive rational surfaces. For q_edge < 2, the instability is always encountered and is highly disruptive. However, diverted plasmas, in which q_edge is formally infinite in the magnetohydrodynamic (MHD) model, have presented a longstanding difficulty since the theory would predict stability, yet, the disruptive limit occurs in practice when q₉₅, reaches 2. It is shown from numerical calculations that a resistive kink mode is linearly destabilized by the rapidly increasing resistivity at the plasma edge when q₉₅ < 2, but q_edge >> 2. The resistive kink behaves much like the ideal kink with predominantly kink or interchange parity and no real sign of a tearing component. However, the growth rates scale with amore »« less

Authors:

Turnbull, Alan D. ^[1]; Hanson, Jeremy M. ^[2]; Turco, Francesca ^[2]; Ferraro, Nathaniel M. ^[3]; Lanctot, Matthew J. ^[1]; Lao, Lang L. ^[1]; Strait, Edward J. ^[1]; Piovesan, Paolo ^[4]; Martin, Piero ^[4]

General Atomics, San Diego, CA (United States)
Columbia Univ., New York, NY (United States)
Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
Consorzio RFX, Padova (Italy)

Publication Date:: 2016-06-16

Research Org.:: General Atomics, San Diego, CA (United States)

Sponsoring Org.:: USDOE

OSTI Identifier:: 1354788

Grant/Contract Number:: FC02-04ER54698

Resource Type:: Accepted Manuscript

Journal Name:: Journal of Plasma Physics

Additional Journal Information:: Journal Volume: 82; Journal Issue: 03; Journal ID: ISSN 0022-3778

Publisher:: Cambridge University Press

Country of Publication:: United States

Language:: English

Subject:: 70 PLASMA PHYSICS AND FUSION TECHNOLOGY

Citation Formats


                    Turnbull, Alan D., Hanson, Jeremy M., Turco, Francesca, Ferraro, Nathaniel M., Lanctot, Matthew J., Lao, Lang L., Strait, Edward J., Piovesan, Paolo, and Martin, Piero. The external kink mode in diverted tokamaks.  United States: N. p., 2016. 
Web.  doi:10.1017/S0022377816000568.

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                    Turnbull, Alan D., Hanson, Jeremy M., Turco, Francesca, Ferraro, Nathaniel M., Lanctot, Matthew J., Lao, Lang L., Strait, Edward J., Piovesan, Paolo, & Martin, Piero. The external kink mode in diverted tokamaks.  United States.  https://doi.org/10.1017/S0022377816000568

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                    Turnbull, Alan D., Hanson, Jeremy M., Turco, Francesca, Ferraro, Nathaniel M., Lanctot, Matthew J., Lao, Lang L., Strait, Edward J., Piovesan, Paolo, and Martin, Piero. Thu .  
"The external kink mode in diverted tokamaks".  United States.  https://doi.org/10.1017/S0022377816000568.  https://www.osti.gov/servlets/purl/1354788.

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@article{osti_1354788,

  title        = {The external kink mode in diverted tokamaks},

  author       = {Turnbull, Alan D. and Hanson, Jeremy M. and Turco, Francesca and Ferraro, Nathaniel M. and Lanctot, Matthew J. and Lao, Lang L. and Strait, Edward J. and Piovesan, Paolo and Martin, Piero},

  abstractNote = {Here, an explanation is provided for the disruptive instability in diverted tokamaks when the safety factor at the 95% poloidal flux surface, q95, is driven below 2.0. The instability is a resistive kink counterpart to the current-driven ideal mode that traditionally explained the corresponding disruption in limited cross-sections when qedge, the safety factor at the outermost closed flux surface, lies just below a rational value. Experimentally, external kink modes are observed in limiter configurations as the current in a tokamak is ramped up and qedge decreases through successive rational surfaces. For qedge < 2, the instability is always encountered and is highly disruptive. However, diverted plasmas, in which qedge is formally infinite in the magnetohydrodynamic (MHD) model, have presented a longstanding difficulty since the theory would predict stability, yet, the disruptive limit occurs in practice when q95, reaches 2. It is shown from numerical calculations that a resistive kink mode is linearly destabilized by the rapidly increasing resistivity at the plasma edge when q95 < 2, but qedge >> 2. The resistive kink behaves much like the ideal kink with predominantly kink or interchange parity and no real sign of a tearing component. However, the growth rates scale with a fractional power of the resistivity near the q = 2 surface. The results have a direct bearing on the conventional edge cutoff procedures used in most ideal MHD codes, as well as implications for ITER and for future reactor options.},

  doi          = {10.1017/S0022377816000568},

  journal      = {Journal of Plasma Physics},

  number       = 03,

  volume       = 82,

  place        = {United States},

  year         = {2016},

  month        = {6}

}

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Works referenced in this record:

MHD-Limits to Plasma Confinement
journal, January 1984

Troyon, F.; Gruber, R.; Saurenmann, H.
Plasma Physics and Controlled Fusion, Vol. 26, Issue 1A
DOI: 10.1088/0741-3335/26/1A/319

The Poloidal Divertor Experiment(PDX) and the Princeton Beta Experiment(PBX)
journal, September 1985

Bol, K.; Okabayashi, M.; Fonck, R.
Nuclear Fusion, Vol. 25, Issue 9
DOI: 10.1088/0029-5515/25/9/026

Toroidal effects on current driven modes in tokamaks
journal, November 1989

Turnbull, A. D.; Troyon, F.
Nuclear Fusion, Vol. 29, Issue 11
DOI: 10.1088/0029-5515/29/11/004

Direct Observation of the Resistive Wall Mode in a Tokamak and Its Interaction with Plasma Rotation
journal, May 1999

Garofalo, A. M.; Turnbull, A. D.; Austin, M. E.
Physical Review Letters, Vol. 82, Issue 19
DOI: 10.1103/PhysRevLett.82.3811

Feedback-assisted extension of the tokamak operating space to low safety factor
journal, July 2014

Hanson, J. M.; Bialek, J. M.; Baruzzo, M.
Physics of Plasmas, Vol. 21, Issue 7
DOI: 10.1063/1.4886796

Resistive wall stabilized operation in rotating high beta NSTX plasmas
journal, April 2006

Sabbagh, S. A.; Sontag, A. C.; Bialek, J. M.
Nuclear Fusion, Vol. 46, Issue 5
DOI: 10.1088/0029-5515/46/5/014

Sawtooth oscillations
journal, January 1986

Wesson, J. A.
Plasma Physics and Controlled Fusion, Vol. 28, Issue 1A
DOI: 10.1088/0741-3335/28/1A/022

Stability of ideal and resistive internal kink modes in toroidal geometry
journal, January 1987

Hastie, R. J.; Hender, T. C.; Carreras, B. A.
Physics of Fluids, Vol. 30, Issue 6
DOI: 10.1063/1.866242

Edge kink/ballooning mode stability in tokamaks with separatrix
journal, May 2006

Medvedev, S. Yu; Martynov, A. A.; Martin, Y. R.
Plasma Physics and Controlled Fusion, Vol. 48, Issue 7
DOI: 10.1088/0741-3335/48/7/003

The CHEASE code for toroidal MHD equilibria
journal, September 1996

Lütjens, H.; Bondeson, A.; Sauter, O.
Computer Physics Communications, Vol. 97, Issue 3
DOI: 10.1016/0010-4655(96)00046-X

Ideal and resistive edge stability calculations with M3D-C1
journal, October 2010

Ferraro, N. M.; Jardin, S. C.; Snyder, P. B.
Physics of Plasmas, Vol. 17, Issue 10
DOI: 10.1063/1.3492727

Investigation of peeling-ballooning stability prior to transient outbursts accompanying transitions out of H-mode in DIII-D
journal, May 2015

Eldon, D.; Boivin, R. L.; Groebner, R. J.
Physics of Plasmas, Vol. 22, Issue 5
DOI: 10.1063/1.4919942

Higher fusion power gain with profile control in DIII-D tokamak plasmas
journal, January 1997

Lazarus, E. A.; Navratil, G. A.; Greenfield, C. M.
Nuclear Fusion, Vol. 37, Issue 1
DOI: 10.1088/0029-5515/37/1/I11

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

Wall Stabilization of High Beta Tokamak Discharges in DIII-D
journal, March 1995

Strait, E. J.; Taylor, T. S.; Turnbull, A. D.
Physical Review Letters, Vol. 74, Issue 13
DOI: 10.1103/PhysRevLett.74.2483

Resistive wall stabilization of high-beta plasmas in DIII–D
journal, May 2003

Strait, E. J.; Bialek, J.; Bogatu, N.
Nuclear Fusion, Vol. 43, Issue 6
DOI: 10.1088/0029-5515/43/6/306

On the operational ideal magnetohydrodynamic limit in sawtoothing discharges
journal, November 1999

Turnbull, A. D.; Pearlstein, L. D.; Bulmer, R. H.
Nuclear Fusion, Vol. 39, Issue 11
DOI: 10.1088/0029-5515/39/11/307

Stabilization of the resistive wall mode in DIII–D by plasma rotation and magnetic feedback
journal, November 2002

Okabayashi, M.; Bialek, J.; Chance, M. S.
Plasma Physics and Controlled Fusion, Vol. 44, Issue 12B
DOI: 10.1088/0741-3335/44/12B/324

Relative instabilities in reverse shear discharges and wall stabilization on JT-60U
journal, May 2002

Takeji, S.; Tokuda, S.; Fujita, T.
Nuclear Fusion, Vol. 42, Issue 5
DOI: 10.1088/0029-5515/42/5/501

Highβ and ECRH studies in DIII-D
journal, October 1988

Stambaugh, R.; Allen, S.; Bramson, G.
Plasma Physics and Controlled Fusion, Vol. 30, Issue 11
DOI: 10.1088/0741-3335/30/11/018

Control of Neoclassical Tearing Modes by Sawtooth Control
journal, February 2002

Sauter, O.; Westerhof, E.; Mayoral, M. L.
Physical Review Letters, Vol. 88, Issue 10
DOI: 10.1103/PhysRevLett.88.105001

Overview of RFX-mod results
journal, September 2009

Martin, P.; Apolloni, L.; Puiatti, M. E.
Nuclear Fusion, Vol. 49, Issue 10
DOI: 10.1088/0029-5515/49/10/104019

Theory and Simulation Basis for Magnetohydrodynamic Stability in DIII-D
journal, October 2005

Turnbull, A. D.; Brennan, D. P.; Chu, M. S.
Fusion Science and Technology, Vol. 48, Issue 2
DOI: 10.13182/FST05-A1046

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

Interaction of external n = 1 magnetic fields with the sawtooth instability in low- q RFX-mod and DIII-D tokamaks
journal, August 2016

Piron, C.; Martin, P.; Bonfiglio, D.
Nuclear Fusion, Vol. 56, Issue 10
DOI: 10.1088/0029-5515/56/10/106012

GATO: An MHD stability code for axisymmetric plasmas with internal separatrices
journal, December 1981

Bernard, L. C.; Helton, F. J.; Moore, R. W.
Computer Physics Communications, Vol. 24, Issue 3-4
DOI: 10.1016/0010-4655(81)90160-0

The KINX ideal MHD stability code for axisymmetric plasmas with separatrix
journal, June 1997

Degtyarev, L.; Martynov, A.; Medvedev, S.
Computer Physics Communications, Vol. 103, Issue 1
DOI: 10.1016/S0010-4655(97)00037-4

Neoclassical conductivity and bootstrap current formulas for general axisymmetric equilibria and arbitrary collisionality regime
journal, July 1999

Sauter, O.; Angioni, C.; Lin-Liu, Y. R.
Physics of Plasmas, Vol. 6, Issue 7
DOI: 10.1063/1.873240

Resistive toroidal stability of internal kink modes in circular and shaped tokamaks
journal, March 1992

Bondeson, A.; Vlad, G.; Lütjens, H.
Physics of Fluids B: Plasma Physics, Vol. 4, Issue 7
DOI: 10.1063/1.860041

Validation of conducting wall models using magnetic measurements
journal, August 2016

Hanson, J. M.; Bialek, J.; Turco, F.
Nuclear Fusion, Vol. 56, Issue 10
DOI: 10.1088/0029-5515/56/10/106022

Internal Kink Modes in Toroidal Plasmas with Circular Cross Sections
journal, December 1975

Bussac, M. N.; Pellat, R.; Edery, D.
Physical Review Letters, Vol. 35, Issue 24
DOI: 10.1103/PhysRevLett.35.1638

Low-n ideal MHD stability of tokamaks: Current and beta limits
journal, April 1989

Turnbull, A. D.; Yasseen, F.; Roy, A.
Nuclear Fusion, Vol. 29, Issue 4
DOI: 10.1088/0029-5515/29/4/008

Equilibrium analysis of current profiles in tokamaks
journal, June 1990

Lao, L. L.; Ferron, J. R.; Groebner, R. J.
Nuclear Fusion, Vol. 30, Issue 6
DOI: 10.1088/0029-5515/30/6/006

Hydromagnetic stability of tokamaks
journal, January 1978

Wesson, J. A.
Nuclear Fusion, Vol. 18, Issue 1
DOI: 10.1088/0029-5515/18/1/010

Tokamak m=1 magnetohydrodynamic calculations in toroidal geometry using a full set of nonlinear resistive magnetohydrodynamic equations
journal, January 1988

Charlton, L. A.; Carreras, B. A.; Holmes, J. A.
Physics of Fluids, Vol. 31, Issue 2
DOI: 10.1063/1.866867

Stabilization of the external kink and the resistive wall mode
journal, October 2010

Chu, M. S.; Okabayashi, M.
Plasma Physics and Controlled Fusion, Vol. 52, Issue 12
DOI: 10.1088/0741-3335/52/12/123001

Erato stability code
journal, January 1981

Gruber, R.; Troyon, F.; Berger, D.
Computer Physics Communications, Vol. 21, Issue 3
DOI: 10.1016/0010-4655(81)90013-8

Tokamak Operation with Safety Factor $q_{95} < 2$ via Control of MHD Stability
journal, July 2014

Piovesan, P.; Hanson, J. M.; Martin, P.
Physical Review Letters, Vol. 113, Issue 4
DOI: 10.1103/PhysRevLett.113.045003

Works referencing / citing this record:

Kink instabilities of the post-disruption runaway electron beam at low safety factor
journal, March 2019

Paz-Soldan, C.; Eidietis, N. W.; Liu, Y. Q.
Plasma Physics and Controlled Fusion, Vol. 61, Issue 5
DOI: 10.1088/1361-6587/aafd15

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Similar Records

Title: The external kink mode in diverted tokamaks

Abstract

Citation Formats

MHD-Limits to Plasma Confinement journal, January 1984

The Poloidal Divertor Experiment(PDX) and the Princeton Beta Experiment(PBX) journal, September 1985

Toroidal effects on current driven modes in tokamaks journal, November 1989

Direct Observation of the Resistive Wall Mode in a Tokamak and Its Interaction with Plasma Rotation journal, May 1999

Feedback-assisted extension of the tokamak operating space to low safety factor journal, July 2014

Resistive wall stabilized operation in rotating high beta NSTX plasmas journal, April 2006

Sawtooth oscillations journal, January 1986

Stability of ideal and resistive internal kink modes in toroidal geometry journal, January 1987

Edge kink/ballooning mode stability in tokamaks with separatrix journal, May 2006

The CHEASE code for toroidal MHD equilibria journal, September 1996

Ideal and resistive edge stability calculations with M3D-C1 journal, October 2010

Investigation of peeling-ballooning stability prior to transient outbursts accompanying transitions out of H-mode in DIII-D journal, May 2015

Higher fusion power gain with profile control in DIII-D tokamak plasmas journal, January 1997

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

Wall Stabilization of High Beta Tokamak Discharges in DIII-D journal, March 1995

Resistive wall stabilization of high-beta plasmas in DIII–D journal, May 2003

On the operational ideal magnetohydrodynamic limit in sawtoothing discharges journal, November 1999

Stabilization of the resistive wall mode in DIII–D by plasma rotation and magnetic feedback journal, November 2002

Relative instabilities in reverse shear discharges and wall stabilization on JT-60U journal, May 2002

Highβ and ECRH studies in DIII-D journal, October 1988

Control of Neoclassical Tearing Modes by Sawtooth Control journal, February 2002

Overview of RFX-mod results journal, September 2009

Theory and Simulation Basis for Magnetohydrodynamic Stability in DIII-D journal, October 2005

Resistive instabilities in general toroidal plasma configurations journal, January 1975

Interaction of external n = 1 magnetic fields with the sawtooth instability in low- q RFX-mod and DIII-D tokamaks journal, August 2016

GATO: An MHD stability code for axisymmetric plasmas with internal separatrices journal, December 1981

The KINX ideal MHD stability code for axisymmetric plasmas with separatrix journal, June 1997

Neoclassical conductivity and bootstrap current formulas for general axisymmetric equilibria and arbitrary collisionality regime journal, July 1999

Resistive toroidal stability of internal kink modes in circular and shaped tokamaks journal, March 1992

Validation of conducting wall models using magnetic measurements journal, August 2016

Internal Kink Modes in Toroidal Plasmas with Circular Cross Sections journal, December 1975

Low-n ideal MHD stability of tokamaks: Current and beta limits journal, April 1989

Equilibrium analysis of current profiles in tokamaks journal, June 1990

Hydromagnetic stability of tokamaks journal, January 1978

Tokamak m=1 magnetohydrodynamic calculations in toroidal geometry using a full set of nonlinear resistive magnetohydrodynamic equations journal, January 1988

Stabilization of the external kink and the resistive wall mode journal, October 2010

Erato stability code journal, January 1981

Tokamak Operation with Safety Factor q 95 < 2 via Control of MHD Stability journal, July 2014

Kink instabilities of the post-disruption runaway electron beam at low safety factor journal, March 2019

MHD-Limits to Plasma Confinement
journal, January 1984

The Poloidal Divertor Experiment(PDX) and the Princeton Beta Experiment(PBX)
journal, September 1985

Toroidal effects on current driven modes in tokamaks
journal, November 1989

Direct Observation of the Resistive Wall Mode in a Tokamak and Its Interaction with Plasma Rotation
journal, May 1999

Feedback-assisted extension of the tokamak operating space to low safety factor
journal, July 2014

Resistive wall stabilized operation in rotating high beta NSTX plasmas
journal, April 2006

Sawtooth oscillations
journal, January 1986

Stability of ideal and resistive internal kink modes in toroidal geometry
journal, January 1987

Edge kink/ballooning mode stability in tokamaks with separatrix
journal, May 2006

The CHEASE code for toroidal MHD equilibria
journal, September 1996

Ideal and resistive edge stability calculations with M3D-C1
journal, October 2010

Investigation of peeling-ballooning stability prior to transient outbursts accompanying transitions out of H-mode in DIII-D
journal, May 2015

Higher fusion power gain with profile control in DIII-D tokamak plasmas
journal, January 1997

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

Wall Stabilization of High Beta Tokamak Discharges in DIII-D
journal, March 1995

Resistive wall stabilization of high-beta plasmas in DIII–D
journal, May 2003

On the operational ideal magnetohydrodynamic limit in sawtoothing discharges
journal, November 1999

Stabilization of the resistive wall mode in DIII–D by plasma rotation and magnetic feedback
journal, November 2002

Relative instabilities in reverse shear discharges and wall stabilization on JT-60U
journal, May 2002

Highβ and ECRH studies in DIII-D
journal, October 1988

Control of Neoclassical Tearing Modes by Sawtooth Control
journal, February 2002

Overview of RFX-mod results
journal, September 2009

Theory and Simulation Basis for Magnetohydrodynamic Stability in DIII-D
journal, October 2005

Resistive instabilities in general toroidal plasma configurations
journal, January 1975

Interaction of external n = 1 magnetic fields with the sawtooth instability in low- q RFX-mod and DIII-D tokamaks
journal, August 2016

GATO: An MHD stability code for axisymmetric plasmas with internal separatrices
journal, December 1981

The KINX ideal MHD stability code for axisymmetric plasmas with separatrix
journal, June 1997

Neoclassical conductivity and bootstrap current formulas for general axisymmetric equilibria and arbitrary collisionality regime
journal, July 1999

Resistive toroidal stability of internal kink modes in circular and shaped tokamaks
journal, March 1992

Validation of conducting wall models using magnetic measurements
journal, August 2016

Internal Kink Modes in Toroidal Plasmas with Circular Cross Sections
journal, December 1975

Low-n ideal MHD stability of tokamaks: Current and beta limits
journal, April 1989

Equilibrium analysis of current profiles in tokamaks
journal, June 1990

Hydromagnetic stability of tokamaks
journal, January 1978

Tokamak m=1 magnetohydrodynamic calculations in toroidal geometry using a full set of nonlinear resistive magnetohydrodynamic equations
journal, January 1988

Stabilization of the external kink and the resistive wall mode
journal, October 2010

Erato stability code
journal, January 1981

Tokamak Operation with Safety Factor $q_{95} < 2$ via Control of MHD Stability
journal, July 2014

Kink instabilities of the post-disruption runaway electron beam at low safety factor
journal, March 2019