Theory of ITG turbulent saturation in stellarators: identifying mechanisms to reduce turbulent transport
Abstract
A three-field fluid model that allows for general three-dimensional equilibrium geometry is developed to describe ion temperature gradient turbulent saturation processes in stellarators. The theory relies on the paradigm of nonlinear transfer of energy from unstable to damped modes at comparable wavelength as the dominant saturation mechanism. The unstable-to-damped mode interaction is enabled by a third mode that for dominant energy transfer channels primarily serves as a regulator of the nonlinear energy transfer rate. The identity of the third wave in the interaction defines different scenarios for turbulent saturation with the dominant scenario depending upon the properties of the 3D geometry. The nonlinear energy transfer physics is quantified by the product of a turbulent correlation lifetime and a geometric coupling coefficient. The turbulent correlation time is determined by a three-wave frequency mismatch, which at long wavelength can be calculated from the sum of the linear eigenfrequencies of the three modes. Larger turbulent correlation times denote larger levels of nonlinear energy transfer and hence smaller turbulent transport. The theory provides an analytic prediction for how 3D shaping can be tuned to lower turbulent transport through saturation processes.
- Authors:
-
- Univ. of Wisconsin, Madison, WI (United States). Dept. of Engineering Physics and Physics
- Publication Date:
- Research Org.:
- Univ. of Wisconsin, Madison, WI (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Fusion Energy Sciences (FES)
- OSTI Identifier:
- 1418997
- Alternate Identifier(s):
- OSTI ID: 1420362
- Grant/Contract Number:
- FG02-99ER54546; FG02-93ER54222; FG02-89ER53291
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physics of Plasmas
- Additional Journal Information:
- Journal Volume: 25; Journal Issue: 02; Journal ID: ISSN 1089-7674
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; Stellarators; Turbulent Transport; Saturation
Citation Formats
Hegna, Chris C., Terry, Paul W., and Faber, Ben J. Theory of ITG turbulent saturation in stellarators: identifying mechanisms to reduce turbulent transport. United States: N. p., 2018.
Web. doi:10.1063/1.5018198.
Hegna, Chris C., Terry, Paul W., & Faber, Ben J. Theory of ITG turbulent saturation in stellarators: identifying mechanisms to reduce turbulent transport. United States. https://doi.org/10.1063/1.5018198
Hegna, Chris C., Terry, Paul W., and Faber, Ben J. Thu .
"Theory of ITG turbulent saturation in stellarators: identifying mechanisms to reduce turbulent transport". United States. https://doi.org/10.1063/1.5018198. https://www.osti.gov/servlets/purl/1418997.
@article{osti_1418997,
title = {Theory of ITG turbulent saturation in stellarators: identifying mechanisms to reduce turbulent transport},
author = {Hegna, Chris C. and Terry, Paul W. and Faber, Ben J.},
abstractNote = {A three-field fluid model that allows for general three-dimensional equilibrium geometry is developed to describe ion temperature gradient turbulent saturation processes in stellarators. The theory relies on the paradigm of nonlinear transfer of energy from unstable to damped modes at comparable wavelength as the dominant saturation mechanism. The unstable-to-damped mode interaction is enabled by a third mode that for dominant energy transfer channels primarily serves as a regulator of the nonlinear energy transfer rate. The identity of the third wave in the interaction defines different scenarios for turbulent saturation with the dominant scenario depending upon the properties of the 3D geometry. The nonlinear energy transfer physics is quantified by the product of a turbulent correlation lifetime and a geometric coupling coefficient. The turbulent correlation time is determined by a three-wave frequency mismatch, which at long wavelength can be calculated from the sum of the linear eigenfrequencies of the three modes. Larger turbulent correlation times denote larger levels of nonlinear energy transfer and hence smaller turbulent transport. The theory provides an analytic prediction for how 3D shaping can be tuned to lower turbulent transport through saturation processes.},
doi = {10.1063/1.5018198},
journal = {Physics of Plasmas},
number = 02,
volume = 25,
place = {United States},
year = {Thu Feb 01 00:00:00 EST 2018},
month = {Thu Feb 01 00:00:00 EST 2018}
}
Free Publicly Available Full Text
Publisher's Version of Record
Other availability
Search WorldCat to find libraries that may hold this journal
Cited by: 26 works
Citation information provided by
Web of Science
Web of Science
Figures / Tables:
FIG. 1: Contours of the peak linear growth rates for the NCSX configuration as predicted by Eq. (54) as a function of kx and ky.
All figures and tables
(11 total)
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.
Works referenced in this record:
Stellarator Turbulence: Subdominant Eigenmodes and Quasilinear Modeling
journal, February 2016
- Pueschel, M. J.; Faber, B. J.; Citrin, J.
- Physical Review Letters, Vol. 116, Issue 8
Effect of Quasihelical Symmetry on Trapped-Electron Mode Transport in the HSX Stellarator
journal, November 2008
- Guttenfelder, W.; Lore, J.; Anderson, D. T.
- Physical Review Letters, Vol. 101, Issue 21
Saturation of Gyrokinetic Turbulence through Damped Eigenmodes
journal, March 2011
- Hatch, D. R.; Terry, P. W.; Jenko, F.
- Physical Review Letters, Vol. 106, Issue 11
Subdominant Modes in Zonal-Flow-Regulated Turbulence
journal, March 2014
- Makwana, K. D.; Terry, P. W.; Pueschel, M. J.
- Physical Review Letters, Vol. 112, Issue 9
Critically Balanced Ion Temperature Gradient Turbulence in Fusion Plasmas
journal, September 2011
- Barnes, M.; Parra, F. I.; Schekochihin, A. A.
- Physical Review Letters, Vol. 107, Issue 11
Effects of Collisional Zonal Flow Damping on Turbulent Transport
journal, November 1999
- Lin, Z.; Hahm, T. S.; Lee, W. W.
- Physical Review Letters, Vol. 83, Issue 18
Electron temperature gradient driven turbulence
journal, May 2000
- Jenko, F.; Dorland, W.; Kotschenreuther, M.
- Physics of Plasmas, Vol. 7, Issue 5
Nonlinear stability and instability in collisionless trapped electron mode turbulence
journal, August 2002
- Baver, D. A.; Terry, P. W.; Gatto, R.
- Physics of Plasmas, Vol. 9, Issue 8
A comparison of drift wave stability in stellarator and tokamak geometry
journal, May 2002
- Anderson, J.; Rafiq, T.; Nadeem, M.
- Physics of Plasmas, Vol. 9, Issue 5
Local three-dimensional magnetostatic equilibria
journal, January 2000
- Hegna, C. C.
- Physics of Plasmas, Vol. 7, Issue 10
Transport and isomorphic equilibria
journal, January 1983
- Boozer, Allen H.
- Physics of Fluids, Vol. 26, Issue 2
Reducing turbulent transport in toroidal configurations via shaping
journal, May 2011
- Mynick, H. E.; Pomphrey, N.; Xanthopoulos, P.
- Physics of Plasmas, Vol. 18, Issue 5
TEM turbulence optimisation in stellarators
journal, October 2015
- Proll, J. H. E.; Mynick, H. E.; Xanthopoulos, P.
- Plasma Physics and Controlled Fusion, Vol. 58, Issue 1
Zonal flows in toroidal systems
journal, July 2007
- Mynick, H. E.; Boozer, A. H.
- Physics of Plasmas, Vol. 14, Issue 7
Profile stiffness measurements in the Helically Symmetric experiment and comparison to nonlinear gyrokinetic calculationsa)
journal, May 2015
- Weir, G. M.; Faber, B. J.; Likin, K. M.
- Physics of Plasmas, Vol. 22, Issue 5
Ideal magnetohydrodynamic ballooning stability boundaries in three-dimensional equilibria
journal, May 2002
- Hegna, C. C.; Hudson, S. R.
- Physics of Plasmas, Vol. 9, Issue 5
Turbulence-driven zonal flows in helical systems with radial electric fields
journal, May 2009
- Sugama, H.; Watanabe, T. -H.
- Physics of Plasmas, Vol. 16, Issue 5
Experimental Demonstration of Improved Neoclassical Transport with Quasihelical Symmetry
journal, February 2007
- Canik, J. M.; Anderson, D. T.; Anderson, F. S. B.
- Physical Review Letters, Vol. 98, Issue 8
Dynamics of axisymmetric and poloidal flows in tokamaks
journal, January 1999
- Hinton, F. L.; Rosenbluth, M. N.
- Plasma Physics and Controlled Fusion, Vol. 41, Issue 3A
Physics issues of compact drift optimized stellarators
journal, June 2001
- Spong, D. A.; Hirshman, S. P.; Berry, L. A.
- Nuclear Fusion, Vol. 41, Issue 6
Anderson-localized ballooning modes in general toroidal plasmas
journal, June 2000
- Cuthbert, P.; Dewar, R. L.
- Physics of Plasmas, Vol. 7, Issue 6
Physics and Engineering Design for Wendelstein VII-X
journal, January 1990
- Beidler, Craig; Grieger, Günter; Herrnegger, Franz
- Fusion Technology, Vol. 17, Issue 1
Understanding nonlinear saturation in zonal-flow-dominated ion temperature gradient turbulence
journal, March 2015
- Plunk, G. G.; Navarro, A. Bañón; Jenko, F.
- Plasma Physics and Controlled Fusion, Vol. 57, Issue 4
Zonal flows in plasma—a review
journal, April 2005
- Diamond, P. H.; Itoh, S-I; Itoh, K.
- Plasma Physics and Controlled Fusion, Vol. 47, Issue 5
Inverse Energy Transfer by Near-Resonant Interactions with a Damped-Wave Spectrum
journal, December 2004
- Terry, P. W.
- Physical Review Letters, Vol. 93, Issue 23
Investigations of the role of nonlinear couplings in structure formation and transport regulation: experiment, simulation, and theory
journal, August 2003
- Holland, C.; Diamond, P. H.; Champeaux, S.
- Nuclear Fusion, Vol. 43, Issue 8
Class of Model Stellarator Fields with Enhanced Confinement
journal, February 1982
- Mynick, H. E.; Chu, T. K.; Boozer, A. H.
- Physical Review Letters, Vol. 48, Issue 5
Distinct Turbulence Saturation Regimes in Stellarators
journal, March 2017
- Plunk, G. G.; Xanthopoulos, P.; Helander, P.
- Physical Review Letters, Vol. 118, Issue 10
Dissipative trapped-electron instability in quasihelically symmetric stellarators
journal, June 2006
- Rafiq, T.; Hegna, C. C.
- Physics of Plasmas, Vol. 13, Issue 6
Drift waves in a straight stellarator
journal, January 1983
- Bhattacharjee, A.
- Physics of Fluids, Vol. 26, Issue 4
Advances in stellarator gyrokinetics
journal, April 2015
- Helander, P.; Bird, T.; Jenko, F.
- Nuclear Fusion, Vol. 55, Issue 5
Ballooning mode spectrum in general toroidal systems
journal, January 1983
- Dewar, R. L.
- Physics of Fluids, Vol. 26, Issue 10
Collisionless microinstabilities in stellarators. III. The ion-temperature-gradient mode
journal, March 2014
- Plunk, G. G.; Helander, P.; Xanthopoulos, P.
- Physics of Plasmas, Vol. 21, Issue 3
Zonal Flow Dynamics and Control of Turbulent Transport in Stellarators
journal, December 2011
- Xanthopoulos, P.; Mischchenko, A.; Helander, P.
- Physical Review Letters, Vol. 107, Issue 24
Resilience of Quasi-Isodynamic Stellarators against Trapped-Particle Instabilities
journal, June 2012
- Proll, J. H. E.; Helander, P.; Connor, J. W.
- Physical Review Letters, Vol. 108, Issue 24
Saturation scalings of toroidal ion temperature gradient turbulence
journal, January 2018
- Terry, P. W.; Faber, B. J.; Hegna, C. C.
- Physics of Plasmas, Vol. 25, Issue 1
Quasi-helically symmetric toroidal stellarators
journal, May 1988
- Nührenberg, J.; Zille, R.
- Physics Letters A, Vol. 129, Issue 2
Optimizing Stellarators for Turbulent Transport
journal, August 2010
- Mynick, H. E.; Pomphrey, N.; Xanthopoulos, P.
- Physical Review Letters, Vol. 105, Issue 9
Relation among ITG Turbulence, Zonal Flows, and Transport in Helical Plasmas
journal, January 2013
- Nunami, Masanori; Watanabe, Tomo-Hiko; Sugama, Hideo
- Plasma and Fusion Research, Vol. 8, Issue 0
Oscillations of zonal flows in stellarators
journal, April 2011
- Helander, P.; Mishchenko, A.; Kleiber, R.
- Plasma Physics and Controlled Fusion, Vol. 53, Issue 5
Loss of Second-Ballooning Stability in Three-Dimensional Equilibria
journal, June 2001
- Hegna, C. C.; Hudson, S. R.
- Physical Review Letters, Vol. 87, Issue 3
Quasi-Symmetry in Stellarator Research. 5. Status of Physics Design of Quasi-Axisymmetric Stellarators. 5.1. Physics Design of the National Compact Stellarator Experiment.
journal, January 2002
- Neilson, George H.; Zarnstorff, Michael C.; Lyon, James F.
- Journal of Plasma and Fusion Research, Vol. 78, Issue 3
Multibody Fusion Model to Explain Experimental Results
journal, January 1995
- Takahashi, Akito; Iida, Toshiyuki; Miyamaru, Hiroyuki
- Fusion Technology, Vol. 27, Issue 1
Gyrokinetic studies of trapped electron mode turbulence in the Helically Symmetric eXperiment stellarator
journal, July 2015
- Faber, B. J.; Pueschel, M. J.; Proll, J. H. E.
- Physics of Plasmas, Vol. 22, Issue 7
Toroidal drift modes driven by ion pressure gradients
journal, January 1981
- Horton, Wendell
- Physics of Fluids, Vol. 24, Issue 6
Characterization of energy confinement in net-current free plasmas using the extended International Stellarator Database
journal, November 2005
- Yamada, H.; Harris, J. H.; Dinklage, A.
- Nuclear Fusion, Vol. 45, Issue 12
Experimental determination of the magnetic field spectrum in the Helically Symmetric Experiment using passing particle orbits
journal, December 2001
- Talmadge, J. N.; Sakaguchi, V.; Anderson, F. S. B.
- Physics of Plasmas, Vol. 8, Issue 12
Collisionless damping of zonal flows in helical systems
journal, January 2006
- Sugama, H.; Watanabe, T. -H.
- Physics of Plasmas, Vol. 13, Issue 1
On the relation between neoclassical transport and turbulent transport
journal, August 2005
- Shaing, K. C.
- Physics of Plasmas, Vol. 12, Issue 8
Design studies of low aspect ratio quasi-omnigenous stellarators
journal, March 2000
- Spong, D. A.; Hirshman, S. P.; Whitson, J. C.
- Nuclear Fusion, Vol. 40, Issue 3Y
Turbulent optimization of toroidal configurations
journal, August 2014
- Mynick, H.; Xanthopoulos, P.; Faber, B.
- Plasma Physics and Controlled Fusion, Vol. 56, Issue 9
Comparison of microinstability properties for stellarator magnetic geometries
journal, October 2005
- Rewoldt, G.; Ku, L. -P.; Tang, W. M.
- Physics of Plasmas, Vol. 12, Issue 10
Reduction of Turbulent Transport with Zonal Flows Enhanced in Helical Systems
journal, May 2008
- Watanabe, T. -H.; Sugama, H.; Ferrando-Margalet, S.
- Physical Review Letters, Vol. 100, Issue 19
Role of stable modes in zonal flow regulated turbulence
journal, June 2012
- Makwana, K. D.; Terry, P. W.; Kim, J. -H.
- Physics of Plasmas, Vol. 19, Issue 6
Loss of Second-Ballooning Stability in Three-Dimensional Equilibria
text, January 2001
- Hegna, C. C.; Hudson, S. R.
- The American Physical Society
Understanding nonlinear saturation in zonal-flow-dominated ion temperature gradient turbulence
text, January 2014
- Plunk, G. G.; Navarro, A. Bañón; Jenko, F.
- arXiv
Resilience of quasi-isodynamic stellarators against trapped-particle instabilities
text, January 2015
- Proll, J. H. E.; Helander, P.; Connor, J. W.
- arXiv
Works referencing / citing this record:
A comparison of turbulent transport in a quasi-helical and a quasi-axisymmetric stellarator
journal, September 2019
- McKinney, I. J.; Pueschel, M. J.; Faber, B. J.
- Journal of Plasma Physics, Vol. 85, Issue 5
Role of stable modes in driven shear-flow turbulence
journal, December 2018
- Fraser, A. E.; Pueschel, M. J.; Terry, P. W.
- Physics of Plasmas, Vol. 25, Issue 12
Role of stable modes in driven shear-flow turbulence
text, January 2018
- Fraser, A. E.; Pueschel, M. J.; Terry, P. W.
- arXiv
Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.