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Title: Intrinsic rotation in axisymmetric devices

Abstract

Toroidal rotation is critical for fusion in tokamaks, since it stabilizes instabilities that can otherwise cause disruptions or degrade confinement. Unlike present-day devices, ITER might not have enough neutral-beam torque to easily avoid these instabilities. We must therefore understand how the plasma rotates 'intrinsically,' that is, without applied torque. Experimentally, torque-free plasmas indeed rotate, with profiles that are often non-flat and even non-monotonic. The rotation depends on many plasma parameters including collisionality and plasma current, and exhibits sudden bifurcations ('rotation reversals') at critical parameter values. Since toroidal angular momentum is conserved in axisymmetric systems, and since experimentally inferred momentum transport is much too large to be neoclassical, theoretical work has focused on rotation drive by nondiffusive turbulent momentum fluxes. In the edge, intrinsic rotation relaxes to a steady state in which the total momentum outflux from the plasma vanishes. Ion drift orbits, scrape-off-layer flows, separatrix geometry, and turbulence intensity gradient all play a role. In the core, nondiffusive and viscous momentum fluxes balance to set the rotation gradient at each flux surface. Although many mechanisms have been proposed for the nondiffusive fluxes, most are treated in one of two distinct but related gyrokinetic formulations. In a radially local fluxtube, appropriate for $${\rho }_{\ast }\ll 1$$, the lowest-order gyrokinetic formulations exhibit a symmetry that prohibits nondiffusive momentum flux for nonrotating plasmas in an up-down symmetric magnetic geometry with no $${\boldsymbol{E}}\times {\boldsymbol{B}}$$ shear. Many symmetry-breaking mechanisms have been identified, but none have yet been conclusively demonstrated to drive a strong enough flux to explain commonly observed experimental rotation profiles. Radially global gyrokinetic simulations naturally include many symmetry-breaking mechanisms, and have shown cases with experimentally relevant levels of nondiffusive flux. These promising early results motivate further work to analyze, verify, and validate. This article provides a pedagogical introduction to intrinsic rotation in axisymmetric devices. Finally, intended for both newcomers to the topic and experienced practitioners, the article reviews a broad range of topics including experimental and theoretical results for both edge and core rotation, while maintaining a focus on the underlying concepts.

Authors:
ORCiD logo [1]
  1. Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
Publication Date:
Research Org.:
Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1573500
Grant/Contract Number:  
AC02-09CH11466; FC02-04ER54698
Resource Type:
Accepted Manuscript
Journal Name:
Plasma Physics and Controlled Fusion
Additional Journal Information:
Journal Volume: 61; Journal Issue: 12; Journal ID: ISSN 0741-3335
Publisher:
IOP Science
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; toroidal rotation; tokamak; transport; intrinsic rotation; rotation reversal

Citation Formats

Stoltzfus-Dueck, T. Intrinsic rotation in axisymmetric devices. United States: N. p., 2019. Web. doi:10.1088/1361-6587/ab4376.
Stoltzfus-Dueck, T. Intrinsic rotation in axisymmetric devices. United States. doi:10.1088/1361-6587/ab4376.
Stoltzfus-Dueck, T. Fri . "Intrinsic rotation in axisymmetric devices". United States. doi:10.1088/1361-6587/ab4376.
@article{osti_1573500,
title = {Intrinsic rotation in axisymmetric devices},
author = {Stoltzfus-Dueck, T.},
abstractNote = {Toroidal rotation is critical for fusion in tokamaks, since it stabilizes instabilities that can otherwise cause disruptions or degrade confinement. Unlike present-day devices, ITER might not have enough neutral-beam torque to easily avoid these instabilities. We must therefore understand how the plasma rotates 'intrinsically,' that is, without applied torque. Experimentally, torque-free plasmas indeed rotate, with profiles that are often non-flat and even non-monotonic. The rotation depends on many plasma parameters including collisionality and plasma current, and exhibits sudden bifurcations ('rotation reversals') at critical parameter values. Since toroidal angular momentum is conserved in axisymmetric systems, and since experimentally inferred momentum transport is much too large to be neoclassical, theoretical work has focused on rotation drive by nondiffusive turbulent momentum fluxes. In the edge, intrinsic rotation relaxes to a steady state in which the total momentum outflux from the plasma vanishes. Ion drift orbits, scrape-off-layer flows, separatrix geometry, and turbulence intensity gradient all play a role. In the core, nondiffusive and viscous momentum fluxes balance to set the rotation gradient at each flux surface. Although many mechanisms have been proposed for the nondiffusive fluxes, most are treated in one of two distinct but related gyrokinetic formulations. In a radially local fluxtube, appropriate for ${\rho }_{\ast }\ll 1$, the lowest-order gyrokinetic formulations exhibit a symmetry that prohibits nondiffusive momentum flux for nonrotating plasmas in an up-down symmetric magnetic geometry with no ${\boldsymbol{E}}\times {\boldsymbol{B}}$ shear. Many symmetry-breaking mechanisms have been identified, but none have yet been conclusively demonstrated to drive a strong enough flux to explain commonly observed experimental rotation profiles. Radially global gyrokinetic simulations naturally include many symmetry-breaking mechanisms, and have shown cases with experimentally relevant levels of nondiffusive flux. These promising early results motivate further work to analyze, verify, and validate. This article provides a pedagogical introduction to intrinsic rotation in axisymmetric devices. Finally, intended for both newcomers to the topic and experienced practitioners, the article reviews a broad range of topics including experimental and theoretical results for both edge and core rotation, while maintaining a focus on the underlying concepts.},
doi = {10.1088/1361-6587/ab4376},
journal = {Plasma Physics and Controlled Fusion},
number = 12,
volume = 61,
place = {United States},
year = {2019},
month = {11}
}

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  • Waltz, R. E.; Staebler, G. M.; Solomon, W. M.
  • Physics of Plasmas, Vol. 18, Issue 4
  • DOI: 10.1063/1.3579481

Effect of asymmetric sources on tokamak neoclassical transport in the plateau regime
journal, September 1990

  • Solano, E. R.; Hazeltine, R. D.
  • Physics of Fluids B: Plasma Physics, Vol. 2, Issue 9
  • DOI: 10.1063/1.859431

Bulk plasma rotation in the TCV tokamak in the absence of external momentum input
journal, November 2007


Non-ambipolarity of perpendicular plasma transport and asymmetry of particle flow onto the tokamak rail limiter
journal, April 1989


Residual parallel Reynolds stress due to turbulence intensity gradient in tokamak plasmas
journal, November 2010

  • Gürcan, Ö. D.; Diamond, P. H.; Hennequin, P.
  • Physics of Plasmas, Vol. 17, Issue 11
  • DOI: 10.1063/1.3503624

Effect of the limiter position on the scrape-off layer width, radial electric field and intrinsic flows
journal, July 2014


New techniques for calculating heat and particle source rates due to neutral beam injection in axisymmetric tokamaks
journal, September 1981


Density sensitivity of intrinsic rotation profiles in ion cyclotron range of frequency-heated L-mode plasmas
journal, December 2012


Effects of poloidal variation of neutral density on Pfirsch–Schlüter transport near the tokamak edge
journal, February 2003

  • Simakov, Andrei N.; Catto, Peter J.
  • Physics of Plasmas, Vol. 10, Issue 2
  • DOI: 10.1063/1.1533065

Radial current and flows in the scrape-off layer of a tokamak
journal, March 1998


Rotation and density asymmetries in the presence of large poloidal impurity flows in the edge pedestal
journal, November 2013


Edge turbulence measurements in toroidal fusion devices
journal, June 2007


Experimental conditions to suppress edge localised modes by magnetic perturbations in the ASDEX Upgrade tokamak
journal, July 2018


Controlling edge plasma rotation through poloidally localized refueling
journal, November 2003

  • Helander, P.; Fülöp, T.; Catto, Peter J.
  • Physics of Plasmas, Vol. 10, Issue 11
  • DOI: 10.1063/1.1616014

Poloidal asymmetry of parallel rotation measured in ASDEX Upgrade
journal, July 2012


Investigation of inter-ELM ion heat transport in the H-mode pedestal of ASDEX Upgrade plasmas
journal, October 2016


On scrape off layer plasma transport
journal, May 2001


Evidence for electromagnetic fluid drift turbulence controlling the edge plasma state in the Alcator C-Mod tokamak
journal, November 2005


Measurement of flow in the scrape-off layer of TdeV
journal, December 1992


Progress in tokamak research at MIT
journal, September 1985


Asymmetric radiation-induced toroidal flow and improved confinement in tokamaks
journal, April 2006

  • Singh, R.; Kaw, P. K.; Rogister, A. L.
  • Physics of Plasmas, Vol. 13, Issue 4
  • DOI: 10.1063/1.2192509

Modeling of the parametric dependence of the edge toroidal rotation for MAST and ASDEX Upgrade
journal, June 2007


Toroidal rotation and momentum transport
journal, July 1987

  • Connor, J. W.; Cowley, S. C.; Hastie, R. J.
  • Plasma Physics and Controlled Fusion, Vol. 29, Issue 7
  • DOI: 10.1088/0741-3335/29/7/009

A unified theory of transport barriers and of subneoclassical transport
journal, January 1999


Impurity toroidal rotation and transport in Alcator C-Mod ohmic high confinement mode plasmas
journal, May 2000

  • Rice, J. E.; Goetz, J. A.; Granetz, R. S.
  • Physics of Plasmas, Vol. 7, Issue 5
  • DOI: 10.1063/1.874004

Toroidal rotation in DIII-D in electron cyclotron heating and Ohmic H-mode discharges
journal, September 2004

  • deGrassie, J. S.; Burrell, K. H.; Baylor, L. R.
  • Physics of Plasmas, Vol. 11, Issue 9
  • DOI: 10.1063/1.1778751

Inter-machine comparison of intrinsic toroidal rotation in tokamaks
journal, October 2007


Advances in understanding the generation and evolution of the toroidal rotation profile on DIII-D
journal, July 2009


Toroidal rotation in RF heated JET plasmas
journal, March 2009


Toroidicity in the tokamak SOL: effects on poloidal asymmetries, radial current and the L - H transition
journal, November 1996


Fluctuation measurements using a five-pin triple probe in the Joint European Torus boundary plasma
journal, October 2004

  • Silva, C.; Gonçalves, B.; Hidalgo, C.
  • Review of Scientific Instruments, Vol. 75, Issue 10
  • DOI: 10.1063/1.1787578

Main-Ion Intrinsic Toroidal Rotation Profile Driven by Residual Stress Torque from Ion Temperature Gradient Turbulence in the DIII-D Tokamak
journal, January 2017


Experimental evidence of edge intrinsic momentum source driven by kinetic ion loss and edge radial electric fields in tokamaks
journal, September 2016

  • Boedo, J. A.; deGrassie, J. S.; Grierson, B.
  • Physics of Plasmas, Vol. 23, Issue 9
  • DOI: 10.1063/1.4962683

Observations of toroidal plasma rotation induced by ICRH in JET
journal, May 1992

  • Eriksson, L. -G; Giannella, R.; Hellsten, T.
  • Plasma Physics and Controlled Fusion, Vol. 34, Issue 5
  • DOI: 10.1088/0741-3335/34/5/014

A possible role of radial electric field in driving parallel ion flow in scrape-off layer of divertor tokamaks
journal, July 2007


Toroidal momentum transport in a tokamak caused by symmetry breaking parallel derivatives
journal, April 2013

  • Sung, T.; Buchholz, R.; Casson, F. J.
  • Physics of Plasmas, Vol. 20, Issue 4
  • DOI: 10.1063/1.4799750

The spatial structure of edge fluctuations in the Wendelstein 7-AS stellarator
journal, July 2002


Convective transport by intermittent blob-filaments: Comparison of theory and experiment
journal, June 2011

  • D’Ippolito, D. A.; Myra, J. R.; Zweben, S. J.
  • Physics of Plasmas, Vol. 18, Issue 6
  • DOI: 10.1063/1.3594609