Experimental tests of linear and nonlinear three-dimensional equilibrium models in DIII-D
Abstract
DIII-D experiments using new detailed magnetic diagnostics show that linear, ideal magnetohydrodynamics(MHD) theory quantitatively describes the magnetic structure (as measured externally) of three-dimensional (3D) equilibria resulting from applied fields with toroidalmode number n = 1, while a nonlinear solution to ideal MHD force balance, using the VMEC code, requires the inclusion of n ≥ 1 to achieve similar agreement. These tests are carried out near ITER baseline parameters, providing a validated basis on which to exploit 3D fields for plasma control development. Scans of the applied poloidal spectrum and edge safety factor confirm that low-pressure, n = 1 non-axisymmetric tokamak equilibria are determined by a single, dominant, stable eigenmode. However, at higher beta, near the ideal kinkmode stability limit in the absence of a conducting wall, the qualitative features of the 3D structure are observed to vary in a way that is not captured by ideal MHD.
- Authors:
-
- Oak Ridge Inst. for Science and Education (ORISE), Oak Ridge, TN (United States); General Atomics, San Diego, CA (United States)
- General Atomics, San Diego, CA (United States)
- Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
- Australian National Univ., Canberra, ACT (Australia)
- Columbia Univ., New York, NY (United States)
- Culham Science Centre, Abingdon (United Kingdom). Plasma Research Lab.
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
- Publication Date:
- Research Org.:
- Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States); Princeton Plasma Physics Laboratory (PPPL), Princeton, NJ (United States); General Atomics, San Diego, CA (United States). DIII-D National Fusion Facility (DIII-D)
- Sponsoring Org.:
- USDOE Office of Science (SC), Fusion Energy Sciences (FES); USDOE Office of Science (SC), Basic Energy Sciences (BES). Scientific User Facilities Division
- OSTI Identifier:
- 1295127
- Alternate Identifier(s):
- OSTI ID: 1228332; OSTI ID: 1254754; OSTI ID: 1459669
- Grant/Contract Number:
- AC05-00OR22725; FC02-04ER54698; AC05-06OR23100; AC02-09CH11466; FG02-04ER54761; AC05-00OR22725.; AC05-00OR23100; FC02-04ER5469
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physics of Plasmas
- Additional Journal Information:
- Journal Volume: 22; Journal Issue: 7; 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; Equilibrium; MHD - Toroidal; Magnetics; Tokamaks
Citation Formats
King, Josh D., Strait, Edward J., Lazerson, Samuel A., Ferraro, Nathaniel M., Logan, Nikolas C., Haskey, Shaun R., Park, Jong -Kyu, Hanson, Jeremy M., Lanctot, Matthew J., Liu, Yueqiang, Nazikian, Raffi, Okabayashi, Michio, Paz-Soldan, Carlos A., Shiraki, Daisuke, and Turnbull, Alan D. Experimental tests of linear and nonlinear three-dimensional equilibrium models in DIII-D. United States: N. p., 2015.
Web. doi:10.1063/1.4923017.
King, Josh D., Strait, Edward J., Lazerson, Samuel A., Ferraro, Nathaniel M., Logan, Nikolas C., Haskey, Shaun R., Park, Jong -Kyu, Hanson, Jeremy M., Lanctot, Matthew J., Liu, Yueqiang, Nazikian, Raffi, Okabayashi, Michio, Paz-Soldan, Carlos A., Shiraki, Daisuke, & Turnbull, Alan D. Experimental tests of linear and nonlinear three-dimensional equilibrium models in DIII-D. United States. https://doi.org/10.1063/1.4923017
King, Josh D., Strait, Edward J., Lazerson, Samuel A., Ferraro, Nathaniel M., Logan, Nikolas C., Haskey, Shaun R., Park, Jong -Kyu, Hanson, Jeremy M., Lanctot, Matthew J., Liu, Yueqiang, Nazikian, Raffi, Okabayashi, Michio, Paz-Soldan, Carlos A., Shiraki, Daisuke, and Turnbull, Alan D. Wed .
"Experimental tests of linear and nonlinear three-dimensional equilibrium models in DIII-D". United States. https://doi.org/10.1063/1.4923017. https://www.osti.gov/servlets/purl/1295127.
@article{osti_1295127,
title = {Experimental tests of linear and nonlinear three-dimensional equilibrium models in DIII-D},
author = {King, Josh D. and Strait, Edward J. and Lazerson, Samuel A. and Ferraro, Nathaniel M. and Logan, Nikolas C. and Haskey, Shaun R. and Park, Jong -Kyu and Hanson, Jeremy M. and Lanctot, Matthew J. and Liu, Yueqiang and Nazikian, Raffi and Okabayashi, Michio and Paz-Soldan, Carlos A. and Shiraki, Daisuke and Turnbull, Alan D.},
abstractNote = {DIII-D experiments using new detailed magnetic diagnostics show that linear, ideal magnetohydrodynamics(MHD) theory quantitatively describes the magnetic structure (as measured externally) of three-dimensional (3D) equilibria resulting from applied fields with toroidalmode number n = 1, while a nonlinear solution to ideal MHD force balance, using the VMEC code, requires the inclusion of n ≥ 1 to achieve similar agreement. These tests are carried out near ITER baseline parameters, providing a validated basis on which to exploit 3D fields for plasma control development. Scans of the applied poloidal spectrum and edge safety factor confirm that low-pressure, n = 1 non-axisymmetric tokamak equilibria are determined by a single, dominant, stable eigenmode. However, at higher beta, near the ideal kinkmode stability limit in the absence of a conducting wall, the qualitative features of the 3D structure are observed to vary in a way that is not captured by ideal MHD.},
doi = {10.1063/1.4923017},
journal = {Physics of Plasmas},
number = 7,
volume = 22,
place = {United States},
year = {Wed Jul 01 00:00:00 EDT 2015},
month = {Wed Jul 01 00:00:00 EDT 2015}
}
Web of Science
Works referenced in this record:
Computation of three-dimensional tokamak and spherical torus equilibria
journal, May 2007
- Park, Jong-kyu; Boozer, Allen H.; Glasser, Alan H.
- Physics of Plasmas, Vol. 14, Issue 5
Control of Asymmetric Magnetic Perturbations in Tokamaks
journal, November 2007
- Park, Jong-kyu; Schaffer, Michael J.; Menard, Jonathan E.
- Physical Review Letters, Vol. 99, Issue 19
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
A magnetic diagnostic code for 3D fusion equilibria
journal, January 2013
- Lazerson, S. A.; Sakakibara, S.; Suzuki, Y.
- Plasma Physics and Controlled Fusion, Vol. 55, Issue 2
Measurement and modeling of three-dimensional equilibria in DIII-D
journal, May 2011
- Lanctot, M. J.; Reimerdes, H.; Garofalo, A. M.
- Physics of Plasmas, Vol. 18, Issue 5
Energy principle in the Boozer model
journal, November 2005
- Pustovitov, V. D.
- Physics of Plasmas, Vol. 12, Issue 11
Tokamak magnetic islands in the presence of nonaxisymmetric perturbations
journal, September 1991
- Reiman, A. H.
- Physics of Fluids B: Plasma Physics, Vol. 3, Issue 9
Experimental imaging of separatrix splitting on DIII-D
journal, November 2012
- Shafer, M. W.; Unterberg, E. A.; Orlov, D. M.
- Nuclear Fusion, Vol. 52, Issue 12
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
Response to “Comment on ‘Energy principle in the Boozer model’ ” [Phys. Plasmas 13, 024703 (2006)]
journal, February 2006
- Pustovitov, V. D.
- Physics of Plasmas, Vol. 13, Issue 2
Calculations of two-fluid linear response to non-axisymmetric fields in tokamaks
journal, May 2012
- Ferraro, N. M.
- Physics of Plasmas, Vol. 19, Issue 5
Perturbed plasma equilibria
journal, March 1999
- Boozer, Allen H.
- Physics of Plasmas, Vol. 6, Issue 3
Comment on “Energy principle in the Boozer model” [Phys. Plasmas 12, 112504 (2005)]
journal, February 2006
- Boozer, Allen H.
- Physics of Plasmas, Vol. 13, Issue 2
An upgrade of the magnetic diagnostic system of the DIII-D tokamak for non-axisymmetric measurements
journal, August 2014
- King, J. D.; Strait, E. J.; Boivin, R. L.
- Review of Scientific Instruments, Vol. 85, Issue 8
Locked modes in DIII-D and a method for prevention of the low density mode
journal, May 1991
- Scoville, J. T.; La Haye, R. J.; Kellman, A. G.
- Nuclear Fusion, Vol. 31, Issue 5
Effect of a static external magnetic perturbation on resistive mode stability in tokamaks
journal, October 1994
- Fitzpatrick, R.; Hender, T. C.
- Physics of Plasmas, Vol. 1, Issue 10
The spectral basis of optimal error field correction on DIII-D
journal, April 2014
- Paz-Soldan, C.; Buttery, R. J.; Garofalo, A. M.
- Nuclear Fusion, Vol. 54, Issue 7
Resistive instabilities in a tokamak
journal, January 1976
- Glasser, A. H.; Greene, J. M.; Johnson, J. L.
- Physics of Fluids, Vol. 19, Issue 4
Edge localized modes and the pedestal: A model based on coupled peeling–ballooning modes
journal, May 2002
- Snyder, P. B.; Wilson, H. R.; Ferron, J. R.
- Physics of Plasmas, Vol. 9, Issue 5
Active Stabilization of the Resistive-Wall Mode in High-Beta, Low-Rotation Plasmas
journal, July 2006
- Sabbagh, S. A.; Bell, R. E.; Menard, J. E.
- Physical Review Letters, Vol. 97, Issue 4
Magnetic diagnostic system of the DIII-D tokamak
journal, February 2006
- Strait, E. J.
- Review of Scientific Instruments, Vol. 77, Issue 2
Steepest-descent moment method for three-dimensional magnetohydrodynamic equilibria
journal, January 1983
- Hirshman, S. P.
- Physics of Fluids, Vol. 26, Issue 12
Three-dimensional distortions of the tokamak plasma boundary: boundary displacements in the presence of resonant magnetic perturbations
journal, May 2014
- Chapman, I. T.; Becoulet, M.; Bird, T.
- Nuclear Fusion, Vol. 54, Issue 8
Validation of the linear ideal magnetohydrodynamic model of three-dimensional tokamak equilibria
journal, March 2010
- Lanctot, M. J.; Reimerdes, H.; Garofalo, A. M.
- Physics of Plasmas, Vol. 17, Issue 3
Full toroidal plasma response to externally applied nonaxisymmetric magnetic fields
journal, December 2010
- Liu, Yueqiang; Kirk, A.; Nardon, E.
- Physics of Plasmas, Vol. 17, Issue 12
Experiments and modelling of external kink mode control using modular internal feedback coils
journal, August 2007
- Sunn Pedersen, T.; Maurer, D. A.; Bialek, J.
- Nuclear Fusion, Vol. 47, Issue 9
Effects of resistivity and rotation on the linear plasma response to non-axisymmetric magnetic perturbations on DIII-D
journal, January 2015
- Haskey, S. R.; Lanctot, M. J.; Liu, Y. Q.
- Plasma Physics and Controlled Fusion, Vol. 57, Issue 2
Effect of resonant and non-resonant magnetic braking on error field tolerance in high beta plasmas
journal, September 2009
- Reimerdes, H.; Garofalo, A. M.; Strait, E. J.
- Nuclear Fusion, Vol. 49, Issue 11
Toroidal self-consistent modeling of drift kinetic effects on the resistive wall mode
journal, November 2008
- Liu, Yueqiang; Chu, M. S.; Chapman, I. T.
- Physics of Plasmas, Vol. 15, Issue 11
Regime of Improved Confinement and High Beta in Neutral-Beam-Heated Divertor Discharges of the ASDEX Tokamak
journal, November 1982
- Wagner, F.; Becker, G.; Behringer, K.
- Physical Review Letters, Vol. 49, Issue 19
Pedestal Bifurcation and Resonant Field Penetration at the Threshold of Edge-Localized Mode Suppression in the DIII-D Tokamak
journal, March 2015
- Nazikian, R.; Paz-Soldan, C.; Callen, J. D.
- Physical Review Letters, Vol. 114, Issue 10
Rotational stabilization in the Boozer model
journal, February 2007
- Pustovitov, V. D.
- Physics of Plasmas, Vol. 14, Issue 2
Electron thermal confinement studies with applied resonant fields on TEXT
journal, April 1989
- McCool, S. C.; Wootton, A. J.; Aydemir, A. Y.
- Nuclear Fusion, Vol. 29, Issue 4
Comparisons of linear and nonlinear plasma response models for non-axisymmetric perturbations
journal, May 2013
- Turnbull, A. D.; Ferraro, N. M.; Izzo, V. A.
- Physics of Plasmas, Vol. 20, Issue 5
Stability and dynamics of the edge pedestal in the low collisionality regime: physics mechanisms for steady-state ELM-free operation
journal, August 2007
- Snyder, P. B.; Burrell, K. H.; Wilson, H. R.
- Nuclear Fusion, Vol. 47, Issue 8
Control of the resistive wall mode with internal coils in the DIII–D tokamak
journal, November 2005
- Okabayashi, M.; Bialek, J.; Bondeson, A.
- Nuclear Fusion, Vol. 45, Issue 12
A design retrospective of the DIII-D tokamak
journal, May 2002
- Luxon, J. L.
- Nuclear Fusion, Vol. 42, Issue 5
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
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
Plasma response models for non-axisymmetric perturbations
journal, May 2012
- Turnbull, A. D.
- Nuclear Fusion, Vol. 52, Issue 5
Measurement of 3D plasma response to external magnetic perturbations in the presence of a rotating external kink
journal, October 2013
- Shiraki, Daisuke; Angelini, Sarah M.; Byrne, Patrick J.
- Physics of Plasmas, Vol. 20, Issue 10
Measurement of the Resistive-Wall-Mode Stability in a Rotating Plasma Using Active MHD Spectroscopy
journal, September 2004
- Reimerdes, H.; Chu, M. S.; Garofalo, A. M.
- Physical Review Letters, Vol. 93, Issue 13
Analyses of substantially different plasma current densities and safety factors reconstructed from magnetic diagnostics data
journal, September 2011
- Zaitsev, F. S.; Kostomarov, D. P.; Suchkov, E. P.
- Nuclear Fusion, Vol. 51, Issue 10
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
Motional Stark effect polarimetry for a current profile diagnostic in DIII‐D
journal, November 1990
- Wróblewski, D.; Burrell, K. H.; Lao, L. L.
- Review of Scientific Instruments, Vol. 61, Issue 11
Measurement of resistive wall mode stability in rotating high-β DIII-D plasmas
journal, April 2005
- Reimerdes, H.; Bialek, J.; Chance, M. S.
- Nuclear Fusion, Vol. 45, Issue 5
Observation of Plasma Toroidal-Momentum Dissipation by Neoclassical Toroidal Viscosity
journal, June 2006
- Zhu, W.; Sabbagh, S. A.; Bell, R. E.
- Physical Review Letters, Vol. 96, Issue 22
Error Field Amplification and Rotation Damping in Tokamak Plasmas
journal, May 2001
- Boozer, Allen H.
- Physical Review Letters, Vol. 86, Issue 22
Theory of plasma transport in toroidal confinement systems
journal, April 1976
- Hinton, F. L.; Hazeltine, R. D.
- Reviews of Modern Physics, Vol. 48, Issue 2
Suppression of Large Edge-Localized Modes in High-Confinement DIII-D Plasmas with a Stochastic Magnetic Boundary
journal, June 2004
- Evans, T. E.; Moyer, R. A.; Thomas, P. R.
- Physical Review Letters, Vol. 92, Issue 23
Measurement of plasma boundary displacement by n = 2 magnetic perturbations using imaging beam emission spectroscopy
journal, November 2012
- Moyer, R. A.; Van Zeeland, M. A.; Orlov, D. M.
- Nuclear Fusion, Vol. 52, Issue 12
Feedback stabilization of nonaxisymmetric resistive wall modes in tokamaks. I. Electromagnetic model
journal, September 2000
- Liu, Y. Q.; Bondeson, A.; Fransson, C. M.
- Physics of Plasmas, Vol. 7, Issue 9
Tokamak error fields and locked modes
journal, August 1991
- Reiman, A.; Monticello, D.
- Physics of Fluids B: Plasma Physics, Vol. 3, Issue 8
CORSICA: A comprehensive simulation of toroidal magnetic-fusion devices. Final report to the LDRD Program
report, March 1997
- Crotinger, J. A.; LoDestro, L.; Pearlstein, L. D.
L'inflation comme regulation
journal, July 1962
- Nicolai, André; Nicolai, Andre
- Revue économique, Vol. 13, Issue 4
Tokamak magnetic islands in the presence of nonaxisymmetric perturbations
report, July 1991
- Reiman, A. H.
Effect of a static external magnetic perturbation on resistive mode stability in tokamaks
report, March 1994
- Fitzpatrick, Richard; Hender, T. C.
Perturbed plasma equilibria
journal, October 2006
- Boozer, Allen H.; Nührenberg, Carolin
- Physics of Plasmas, Vol. 13, Issue 10
Works referencing / citing this record:
Modal analysis of the full poloidal structure of the plasma response to n = 2 magnetic perturbations
journal, July 2018
- Munaretto, S.; Strait, E. J.; Haskey, S. R.
- Physics of Plasmas, Vol. 25, Issue 7
Screening of resonant magnetic perturbation fields by poloidally varying toroidal plasma rotation
journal, August 2018
- Li, L.; Liu, Y. Q.; Loarte, A.
- Physics of Plasmas, Vol. 25, Issue 8
Effect of plasma response on the fast ion losses due to ELM control coils in ITER
journal, March 2016
- Varje, Jari; Asunta, Otto; Cavinato, Mario
- Nuclear Fusion, Vol. 56, Issue 4
Equilibrium drives of the low and high field side n = 2 plasma response and impact on global confinement
journal, April 2016
- Paz-Soldan, C.; Logan, N. C.; Haskey, S. R.
- Nuclear Fusion, Vol. 56, Issue 5
Modelling of 3D fields due to ferritic inserts and test blanket modules in toroidal geometry at ITER
journal, April 2016
- Liu, Yueqiang; Äkäslompolo, Simppa; Cavinato, Mario
- Nuclear Fusion, Vol. 56, Issue 6
ELM control with RMP: plasma response models and the role of edge peeling response
journal, October 2016
- Liu, Yueqiang; Ham, C. J.; Kirk, A.
- Plasma Physics and Controlled Fusion, Vol. 58, Issue 11
Dynamics of ideal modes and subsequent ELM crashes in 3D tokamak geometry from external magnetic perturbations
journal, November 2018
- Willensdorfer, M.; Cote, T. B.; Griener, M.
- Plasma Physics and Controlled Fusion, Vol. 61, Issue 1
Numerical survey of predicted peeling response in edge localised mode mitigated and suppressed phases on ASDEX upgrade
journal, August 2019
- Ryan, D. A.; Dunne, M.; Kirk, A.
- Plasma Physics and Controlled Fusion, Vol. 61, Issue 9
Effects of the applied magnetic fields with various toroidal phase differences on the neoclassical toroidal viscosity in JT-60SA
journal, October 2018
- Honda, M.; Satake, S.; Suzuki, Y.
- Nuclear Fusion, Vol. 58, Issue 11
Magnetic polarization measurements of the multi-modal plasma response to 3D fields in the EAST tokamak
journal, May 2018
- Logan, N. C.; Cui, L.; Wang, H.
- Nuclear Fusion, Vol. 58, Issue 7
Resistive versus ideal plasma response to RMP fields in DIII-D: roles of q 95 and X-point geometry
journal, June 2019
- Yang, Xu; Liu, Yueqiang; Paz-Soldan, Carlos
- Nuclear Fusion, Vol. 59, Issue 8
ELM control with RMP: plasma response models and the role of edge peeling response
text, January 2016
- Liu, Yueqiang; Ham, C. J.; Kirk, A.
- arXiv