How the birth and death of shear layers determine confinement evolution: from the L → H transition to the density limit
Abstract
Electric field profile structure—especially its shear—is a natural order parameter for the edge plasma, and characterizes confinement regimes ranging from the H-mode (Wagner et al. 1982 Phys. Rev. Lett.49, 1408–1412 (doi:10.1103/PhysRevLett.49.1408)) to the density limit (DL) (Greenwald et al. 1988 Nucl. Fusion28, 2199–2207 (doi:10.1088/0029-5515/28/12/009)). The theoretical developments and lessons learned during 40 years of H-mode studies (Connor & Wilson 1999 Plasma Phys. Control. Fusion42, R1–R74 (doi:10.1088/0741-3335/42/1/201); Wagner 2007 Plasma Phys. Control. Fusion49, B1–B33 (doi:10.1088/0741-3335/49/12b/s01)) are applied to the shear layer collapse paradigm (Hong et al. 2017 Nucl. Fusion58, 016041 (doi:10.1088/1741-4326/aa9626)) for the onset of DL phenomena. Results from recent experiments on edge shear layers and DL phenomenology are summarized and discussed in the light of L → H transition physics. The theory of shear layer collapse is then developed. In this work, we demonstrate that shear layer physics captures both the well known current (Greenwald) scaling of the DL (Greenwald 2002 Plasma Phys. Control. Fusion44, R27–R53 (doi:10.1088/0741-3335/44/8/201); Greenwald et al. 2014 Phys. Plasmas21, 110501 (doi:10.1063/1.4901920)), as well as the emerging power scaling (Zanca, Sattin, JET Contributors 2019 Nucl. Fusion59, 126011 (doi:10.1088/1741-4326/ab3b31)). The derivation of the power scaling theory exploits an existing model, originally developed for the L → H transitionmore »
- Authors:
-
- Univ. of California San Diego, La Jolla, CA (United States)
- Southwestern Institute of Physics, Chengdu (China)
- Univ. of California, Los Angeles, CA (United States)
- Univ. of Wisconsin, Madison, WI (United States)
- Univ. of California, San Diego, CA (United States)
- Publication Date:
- Research Org.:
- Univ. of California, San Diego, CA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Fusion Energy Sciences (FES); National Science Foundation (NSF); National Key Research and Development Program of China; National Natural Science Foundation of China (NSFC)
- OSTI Identifier:
- 1907842
- Grant/Contract Number:
- FG02-04ER54738; FG02-07ER54912; AC02-09CH11466; SC0022528; NSF PHY-1748958; 2018YFE0310300; 2022YFE03100004; U1867222; 11905050; 11875124; 2022NSFSC1791; 2020JDTD0030
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Philosophical Transactions of the Royal Society. A, Mathematical, Physical and Engineering Sciences
- Additional Journal Information:
- Journal Volume: 381; Journal Issue: 2242; Journal ID: ISSN 1364-503X
- Publisher:
- The Royal Society Publishing
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; L–H transition; turbulent transport; density limit; shear flow
Citation Formats
Diamond, Patrick H., Singh, Rameswar, Long, Ting, Hong, Rongjie, Ke, Rui, Yan, Zheng, Cao, Mingyun, and Tynan, George R. How the birth and death of shear layers determine confinement evolution: from the L → H transition to the density limit. United States: N. p., 2023.
Web. doi:10.1098/rsta.2021.0227.
Diamond, Patrick H., Singh, Rameswar, Long, Ting, Hong, Rongjie, Ke, Rui, Yan, Zheng, Cao, Mingyun, & Tynan, George R. How the birth and death of shear layers determine confinement evolution: from the L → H transition to the density limit. United States. https://doi.org/10.1098/rsta.2021.0227
Diamond, Patrick H., Singh, Rameswar, Long, Ting, Hong, Rongjie, Ke, Rui, Yan, Zheng, Cao, Mingyun, and Tynan, George R. Mon .
"How the birth and death of shear layers determine confinement evolution: from the L → H transition to the density limit". United States. https://doi.org/10.1098/rsta.2021.0227. https://www.osti.gov/servlets/purl/1907842.
@article{osti_1907842,
title = {How the birth and death of shear layers determine confinement evolution: from the L → H transition to the density limit},
author = {Diamond, Patrick H. and Singh, Rameswar and Long, Ting and Hong, Rongjie and Ke, Rui and Yan, Zheng and Cao, Mingyun and Tynan, George R.},
abstractNote = {Electric field profile structure—especially its shear—is a natural order parameter for the edge plasma, and characterizes confinement regimes ranging from the H-mode (Wagner et al. 1982 Phys. Rev. Lett.49, 1408–1412 (doi:10.1103/PhysRevLett.49.1408)) to the density limit (DL) (Greenwald et al. 1988 Nucl. Fusion28, 2199–2207 (doi:10.1088/0029-5515/28/12/009)). The theoretical developments and lessons learned during 40 years of H-mode studies (Connor & Wilson 1999 Plasma Phys. Control. Fusion42, R1–R74 (doi:10.1088/0741-3335/42/1/201); Wagner 2007 Plasma Phys. Control. Fusion49, B1–B33 (doi:10.1088/0741-3335/49/12b/s01)) are applied to the shear layer collapse paradigm (Hong et al. 2017 Nucl. Fusion58, 016041 (doi:10.1088/1741-4326/aa9626)) for the onset of DL phenomena. Results from recent experiments on edge shear layers and DL phenomenology are summarized and discussed in the light of L → H transition physics. The theory of shear layer collapse is then developed. In this work, we demonstrate that shear layer physics captures both the well known current (Greenwald) scaling of the DL (Greenwald 2002 Plasma Phys. Control. Fusion44, R27–R53 (doi:10.1088/0741-3335/44/8/201); Greenwald et al. 2014 Phys. Plasmas21, 110501 (doi:10.1063/1.4901920)), as well as the emerging power scaling (Zanca, Sattin, JET Contributors 2019 Nucl. Fusion59, 126011 (doi:10.1088/1741-4326/ab3b31)). The derivation of the power scaling theory exploits an existing model, originally developed for the L → H transition (Diamond, Liang, Carreras, Terry 1994 Phys. Rev. Lett.72, 2565–2568 (doi:10.1103/PhysRevLett.72.2565); Kim & Diamond 2003 Phys. Rev. Lett.90, 185006 (doi:10.1103/PhysRevLett.90.185006)). We describe the enhanced particle transport events that occur following shear layer collapse. Open problems and future directions are discussed.},
doi = {10.1098/rsta.2021.0227},
journal = {Philosophical Transactions of the Royal Society. A, Mathematical, Physical and Engineering Sciences},
number = 2242,
volume = 381,
place = {United States},
year = {Mon Jan 02 00:00:00 EST 2023},
month = {Mon Jan 02 00:00:00 EST 2023}
}
Works referenced in this record:
Quiescent H-mode operation using torque from non-axisymmetric, non-resonant magnetic fields
journal, June 2013
- Burrell, K. H.; Garofalo, A. M.; Solomon, W. M.
- Nuclear Fusion, Vol. 53, Issue 7
Edge shear flows and particle transport near the density limit of the HL-2A tokamak
journal, December 2017
- Hong, R.; Tynan, G. R.; Diamond, P. H.
- Nuclear Fusion, Vol. 58, Issue 1
Overview of density pedestal structure: role of fueling versus transport
journal, July 2020
- Mordijck, S.
- Nuclear Fusion, Vol. 60, Issue 8
A power-balance model of the density limit in fusion plasmas: application to the L-mode tokamak
journal, September 2019
- Zanca, P.; Sattin, F.; Escande, D. F.
- Nuclear Fusion, Vol. 59, Issue 12
Enhanced particle transport events approaching the density limit of the J-TEXT tokamak
journal, November 2021
- Long, T.; Diamond, P. H.; Ke, R.
- Nuclear Fusion, Vol. 61, Issue 12
Spatio-temporal evolution of the L → I → H transition
journal, September 2012
- Miki, K.; Diamond, P. H.; Gürcan, Ö. D.
- Physics of Plasmas, Vol. 19, Issue 9
L-mode-edge negative triangularity tokamak reactor
journal, April 2019
- Kikuchi, M.; Takizuka, T.; Medvedev, S.
- Nuclear Fusion, Vol. 59, Issue 5
I-mode: an H-mode energy confinement regime with L-mode particle transport in Alcator C-Mod
journal, August 2010
- Whyte, D. G.; Hubbard, A. E.; Hughes, J. W.
- Nuclear Fusion, Vol. 50, Issue 10
Density limits in toroidal plasmas
journal, July 2002
- Greenwald, Martin
- Plasma Physics and Controlled Fusion, Vol. 44, Issue 8
Theory of the spatiotemporal dynamics of transport bifurcations
journal, April 1997
- Lebedev, V. B.; Diamond, P. H.
- Physics of Plasmas, Vol. 4, Issue 4
A unified theory of zonal flow shears and density corrugations in drift wave turbulence
journal, January 2021
- Singh, Rameswar; Diamond, P. H.
- Plasma Physics and Controlled Fusion, Vol. 63, Issue 3
A new look at density limits in tokamaks
journal, December 1988
- Greenwald, M.; Terry, J. L.; Wolfe, S. M.
- Nuclear Fusion, Vol. 28, Issue 12
Generalization of the Heuristic Drift SOL model for finite collisionality and effect on flow shearing rate vs. interchange growth rate
journal, June 2021
- Brown, A. O.; Goldston, R. J.
- Nuclear Materials and Energy, Vol. 27
Evidence for confinement improvement by velocity-shear suppression of edge turbulence
journal, November 1990
- Ritz, Ch. P.; Lin, H.; Rhodes, T. L.
- Physical Review Letters, Vol. 65, Issue 20
Linking the micro and macro: L-H transition dynamics and threshold physics
journal, March 2015
- Malkov, M. A.; Diamond, P. H.; Miki, K.
- Physics of Plasmas, Vol. 22, Issue 3
Internal transport barrier on q =3 surface and poloidal plasma spin up in JT-60U high- discharges
journal, June 1994
- Koide, Y.; Kikuchi, M.; Mori, M.
- Physical Review Letters, Vol. 72, Issue 23
Neoclassical dielectric property of a tokamak plasma
journal, January 1984
- Hinton, F. L.; Robertson, J. A.
- Physics of Fluids, Vol. 27, Issue 5
Bifurcation of quiescent H-mode to a wide pedestal regime in DIII-D and advances in the understanding of edge harmonic oscillations
journal, June 2017
- Chen, Xi; Burrell, K. H.; Osborne, T. H.
- Nuclear Fusion, Vol. 57, Issue 8
L-H transition dynamics in fluid turbulence simulations with neoclassical force balance
journal, July 2014
- Chôné, L.; Beyer, P.; Sarazin, Y.
- Physics of Plasmas, Vol. 21, Issue 7
The H-mode density limit in the full tungsten ASDEX Upgrade tokamak
journal, November 2014
- Bernert, M.; Eich, T.; Kallenbach, A.
- Plasma Physics and Controlled Fusion, Vol. 57, Issue 1
Phase Space of Tokamak Edge Turbulence, the Transition, and the Formation of the Edge Pedestal
journal, November 1998
- Rogers, B. N.; Drake, J. F.; Zeiler, A.
- Physical Review Letters, Vol. 81, Issue 20
Ideal magnetohydrodynamic stability of the tokamak high-confinement-mode edge region
journal, May 1999
- Wilson, H. R.; Connor, J. W.; Field, A. R.
- Physics of Plasmas, Vol. 6, Issue 5
Steady-state convection and fluctuation-driven particle transport in the H -mode transition
journal, May 1992
- Tynan, G. R.; Schmitz, L.; Conn, R. W.
- Physical Review Letters, Vol. 68, Issue 20
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
Role of Zonal Flow Predator-Prey Oscillations in Triggering the Transition to H-Mode Confinement
journal, April 2012
- Schmitz, L.; Zeng, L.; Rhodes, T. L.
- Physical Review Letters, Vol. 108, Issue 15
Observation of Stable Superdense Core Plasmas in the Large Helical Device
journal, August 2006
- Ohyabu, N.; Morisaki, T.; Masuzaki, S.
- Physical Review Letters, Vol. 97, Issue 5
Influence of sheared poloidal rotation on edge turbulence
journal, January 1990
- Biglari, H.; Diamond, P. H.; Terry, P. W.
- Physics of Fluids B: Plasma Physics, Vol. 2, Issue 1
The separatrix operational space of ASDEX Upgrade due to interchange-drift-Alfvén turbulence
journal, July 2021
- Eich, T.; Manz, P.
- Nuclear Fusion, Vol. 61, Issue 8, p. 086017
Transport by intermittency in the boundary of the DIII-D tokamak
journal, May 2003
- Boedo, J. A.; Rudakov, D. L.; Moyer, R. A.
- Physics of Plasmas, Vol. 10, Issue 5
Effects of E×B velocity shear and magnetic shear on turbulence and transport in magnetic confinement devices
journal, May 1997
- Burrell, K. H.
- Physics of Plasmas, Vol. 4, Issue 5
Origin and turbulence spreading of plasma blobs
journal, February 2015
- Manz, P.; Ribeiro, T. T.; Scott, B. D.
- Physics of Plasmas, Vol. 22, Issue 2
Self-Regulating Shear Flow Turbulence: A Paradigm for the L to H Transition
journal, April 1994
- Diamond, P. H.; Liang, Y. -M.; Carreras, B. A.
- Physical Review Letters, Vol. 72, Issue 16
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
Wave-number spectrum of dissipative drift waves and a transition scale
journal, September 2015
- Ghantous, K.; Gürcan, Ö. D.
- Physical Review E, Vol. 92, Issue 3
Spatio-temporal evolution of the H → L back transition
journal, June 2013
- Miki, K.; Diamond, P. H.; Schmitz, L.
- Physics of Plasmas, Vol. 20, Issue 6
Zonal shear layer collapse and the power scaling of the density limit: old L-H wine in new bottles
journal, July 2022
- Singh, Rameswar; Diamond, P. H.
- Plasma Physics and Controlled Fusion, Vol. 64, Issue 8
Origin of Tokamak Density Limit Scalings
journal, April 2012
- Gates, D. A.; Delgado-Aparicio, L.
- Physical Review Letters, Vol. 108, Issue 16
Long-range correlations and edge transport bifurcation in fusion plasmas
journal, May 2011
- Xu, Y.; Carralero, D.; Hidalgo, C.
- Nuclear Fusion, Vol. 51, Issue 6
Gas puff fueled H-mode discharges with good energy confinement above the Greenwald density limit on DIII-D
journal, May 2001
- Osborne, T. H.; Leonard, A. W.; Mahdavi, M. A.
- Physics of Plasmas, Vol. 8, Issue 5
20 years of research on the Alcator C-Mod tokamaka)
journal, November 2014
- Greenwald, M.; Bader, A.; Baek, S.
- Physics of Plasmas, Vol. 21, Issue 11
Multiple Jets as PV Staircases: The Phillips Effect and the Resilience of Eddy-Transport Barriers
journal, March 2008
- Dritschel, D. G.; McIntyre, M. E.
- Journal of the Atmospheric Sciences, Vol. 65, Issue 3
Bounds on edge shear layer persistence while approaching the density limit
journal, June 2021
- Singh, Rameswar; Diamond, P. H.
- Nuclear Fusion, Vol. 61, Issue 7
Theoretical aspects and practical implications of the heuristic drift SOL model
journal, August 2015
- Goldston, R. J.
- Journal of Nuclear Materials, Vol. 463
Measurement and control of turbulence spreading in the scrape-off layer of TJ-II stellarator
journal, December 2018
- Grenfell, G.; van Milligen, B. Ph.; Losada, U.
- Nuclear Fusion, Vol. 59, Issue 1
Subcritical turbulence spreading and avalanche birth
journal, March 2019
- Heinonen, R. A.; Diamond, P. H.
- Physics of Plasmas, Vol. 26, Issue 3
Electrode biasing maintains the edge shear layer at high density in the J-TEXT tokamak
journal, May 2022
- Ke, R.; Diamond, P. H.; Long, T.
- Nuclear Fusion, Vol. 62, Issue 7
Correlation of the tokamak H-mode density limit with ballooning stability at the separatrix
journal, January 2018
- Eich, T.; Goldston, R. J.; Kallenbach, A.
- Nuclear Fusion, Vol. 58, Issue 3
Zonal flows and pattern formation
journal, July 2015
- Gürcan, Ö D.; Diamond, P. H.
- Journal of Physics A: Mathematical and Theoretical, Vol. 48, Issue 29
Poloidal Flow Driven by Ion-Temperature-Gradient Turbulence in Tokamaks
journal, January 1998
- Rosenbluth, M. N.; Hinton, F. L.
- Physical Review Letters, Vol. 80, Issue 4
Suppression of large edge localized modes in high confinement DIII-D plasmas with a stochastic magnetic boundary
journal, March 2005
- Evans, T. E.; Moyer, R. A.; Watkins, J. G.
- Journal of Nuclear Materials, Vol. 337-339
Particle transport in the scrape-off layer and its relationship to discharge density limit in Alcator C-Mod
journal, May 2001
- LaBombard, B.; Boivin, R. L.; Greenwald, M.
- Physics of Plasmas, Vol. 8, Issue 5
Experimental evidence of coupling between sheared-flow development and an increase in the level of turbulence in the stellarator
journal, December 2004
- Hidalgo, C.; Pedrosa, M. A.; García, L.
- Physical Review E, Vol. 70, Issue 6
A review of theories of the L-H transition
journal, December 1999
- Connor, J. W.; Wilson, H. R.
- Plasma Physics and Controlled Fusion, Vol. 42, Issue 1
A quarter-century of H-mode studies
journal, November 2007
- Wagner, F.
- Plasma Physics and Controlled Fusion, Vol. 49, Issue 12B
Spatio-temporal evolution of the L → H and H → L transitions
journal, June 2013
- Miki, K.; Diamond, P. H.; Fedorczak, N.
- Nuclear Fusion, Vol. 53, Issue 7
Mechanisms and dynamics of the external transport barrier formation in non-linear plasma edge simulations
journal, June 2015
- Chôné, L.; Beyer, P.; Sarazin, Y.
- Nuclear Fusion, Vol. 55, Issue 7
H-mode behavior induced by cross-field currents in a tokamak
journal, November 1989
- Taylor, R.; Brown, M.; Fried, B.
- Physical Review Letters, Vol. 63, Issue 21
Bifurcation in electrostatic resistive drift wave turbulence
journal, October 2007
- Numata, Ryusuke; Ball, Rowena; Dewar, Robert L.
- Physics of Plasmas, Vol. 14, Issue 10
On the dynamics of turbulent transport near marginal stability
journal, October 1995
- Diamond, P. H.; Hahm, T. S.
- Physics of Plasmas, Vol. 2, Issue 10
Generation of sheared poloidal flows via Reynolds stress and transport barrier physics
journal, May 2000
- Hidalgo, C.; Pedrosa, M. A.; Sánchez, E.
- Plasma Physics and Controlled Fusion, Vol. 42, Issue 5A
Experimental Evidence for the Intimate Interaction among Sheared Flows, Eddy Structures, Reynolds Stress, and Zonal Flows across a Transition to Improved Confinement
journal, August 2013
- Shesterikov, I.; Xu, Y.; Tynan, G. R.
- Physical Review Letters, Vol. 111, Issue 5
Dynamics of zonal shear collapse with hydrodynamic electrons
journal, June 2018
- Hajjar, R. J.; Diamond, P. H.; Malkov, M. A.
- Physics of Plasmas, Vol. 25, Issue 6
Thermal confinement bifurcation and the L‐ to H‐mode transition in tokamaks
journal, March 1991
- Hinton, F. L.
- Physics of Fluids B: Plasma Physics, Vol. 3, Issue 3
Scaling of far edge plasma turbulence and fluctuation induced particle transport in the TEXT tokamak
journal, August 1993
- Rhodes, T. L.; Ritz, C. P.; Bengtson, R. D.
- Nuclear Fusion, Vol. 33, Issue 8
Stochastic Model for Quasi-One-Dimensional Transitional Turbulence with Streamwise Shear Interactions
journal, July 2022
- Wang, Xueying; Shih, Hong-Yan; Goldenfeld, Nigel
- Physical Review Letters, Vol. 129, Issue 3
Energy confinement scaling in Tokamaks: some implications of recent experiments with Ohmic and strong auxiliary heating
journal, January 1984
- Goldston, Robert J.
- Plasma Physics and Controlled Fusion, Vol. 26, Issue 1A
Marfe: an edge plasma phenomenon
journal, August 1984
- Lipschultz, B.; LaBombard, B.; Marmar, E. S.
- Nuclear Fusion, Vol. 24, Issue 8
Zonal Flows and Transient Dynamics of the Transition
journal, May 2003
- Kim, Eun-jin; Diamond, P. H.
- Physical Review Letters, Vol. 90, Issue 18
First-Principles Density Limit Scaling in Tokamaks Based on Edge Turbulent Transport and Implications for ITER
journal, May 2022
- Giacomin, M.; Pau, A.; Ricci, P.
- Physical Review Letters, Vol. 128, Issue 18