Skip to main content Accessibility help
×
Home
Hostname: page-component-8bbf57454-wdwc2 Total loading time: 0.294 Render date: 2022-01-22T03:51:52.873Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": true, "newCiteModal": false, "newCitedByModal": true, "newEcommerce": true, "newUsageEvents": true }

Transition to subcritical turbulence in a tokamak plasma

Published online by Cambridge University Press:  19 December 2016

F. van Wyk*
Affiliation:
Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford OX1 3NP, UK CCFE, Culham Science Centre, Abingdon OX14 3DB, UK STFC Daresbury Laboratory, Daresbury WA4 4AD, UK
E. G. Highcock
Affiliation:
Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford OX1 3NP, UK Chalmers University of Technology, Department of Physics, Göteborg SE-412 96, Sweden
A. A. Schekochihin
Affiliation:
Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford OX1 3NP, UK Merton College, Oxford OX1 4JD, UK
C. M. Roach
Affiliation:
CCFE, Culham Science Centre, Abingdon OX14 3DB, UK
A. R. Field
Affiliation:
CCFE, Culham Science Centre, Abingdon OX14 3DB, UK
W. Dorland
Affiliation:
Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford OX1 3NP, UK Department of Physics, University of Maryland, College Park, MD 20742-4111, USA
*
Email address for correspondence: ferdinand.vanwyk@physics.ox.ac.uk

Abstract

Tokamak turbulence, driven by the ion-temperature gradient and occurring in the presence of flow shear, is investigated by means of local, ion-scale, electrostatic gyrokinetic simulations (with both kinetic ions and electrons) of the conditions in the outer core of the Mega-Ampere Spherical Tokamak (MAST). A parameter scan in the local values of the ion-temperature gradient and flow shear is performed. It is demonstrated that the experimentally observed state is near the stability threshold and that this stability threshold is nonlinear: sheared turbulence is subcritical, i.e. the system is formally stable to small perturbations, but, given a large enough initial perturbation, it transitions to a turbulent state. A scenario for such a transition is proposed and supported by numerical results: close to threshold, the nonlinear saturated state and the associated anomalous heat transport are dominated by long-lived coherent structures, which drift across the domain, have finite amplitudes, but are not volume filling; as the system is taken away from the threshold into the more unstable regime, the number of these structures increases until they overlap and a more conventional chaotic state emerges. Whereas this appears to represent a new scenario for transition to turbulence in tokamak plasmas, it is reminiscent of the behaviour of other subcritically turbulent systems, e.g. pipe flows and Keplerian magnetorotational accretion flows.

Type
Research Article
Copyright
© Cambridge University Press 2016 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abel, I. G., Plunk, G. G., Wang, E., Barnes, M., Cowley, S. C., Dorland, W. & Schekochihin, A. A. 2013 Multiscale gyrokinetics for rotating tokamak plasmas: fluctuations, transport and energy flows. Rep. Prog. Phys. 76, 116201.CrossRefGoogle ScholarPubMed
Baker, D. R., Greenfield, C. M., Burrell, K. H., DeBoo, J. C., Doyle, E. J., Groebner, R. J., Luce, T. C., Petty, C. C., Stallard, B. W., Thomas, D. M. et al. 2001 Thermal diffusivities in DIII-D show evidence of critical gradients. Phys. Plasmas 8, 41284137.CrossRefGoogle Scholar
Barkley, D., Song, B., Mukund, V., Lemoult, G., Avila, M. & Hof, B. 2015 The rise of fully turbulent flow. Nature 526, 550553.CrossRefGoogle ScholarPubMed
Barnes, M., Parra, F. I., Highcock, E. G., Schekochihin, A. A., Cowley, S. C. & Roach, C. M. 2011a Turbulent transport in tokamak plasmas with rotational shear. Phys. Rev. Lett. 106, 175004.CrossRefGoogle ScholarPubMed
Barnes, M., Parra, F. I. & Schekochihin, A. A. 2011b Critically balanced ion temperature gradient turbulence in fusion plasmas. Phys. Rev. Lett. 107, 115003.CrossRefGoogle ScholarPubMed
Burin, M. J., Tynan, G. R., Antar, G. Y., Crocker, N. A. & Holland, C. 2005 On the transition to drift turbulence in a magnetized plasma column. Phys. Plasmas 12, 052320.CrossRefGoogle Scholar
Burrell, K. H. 1997 Effects of E $\times$ B velocity shear and magnetic shear on turbulence and transport in magnetic confinement devices. Phys. Plasmas 4, 14991518.CrossRefGoogle Scholar
Conway, N. J., Carolan, P. G., McCone, J., Walsh, M. J. & Wisse, M. 2006 High-throughput charge exchange recombination spectroscopy system on MAST. Rev. Sci. Instrum. 77, 10F131.CrossRefGoogle Scholar
Coppi, B., Rosenbluth, M. N. & Sagdeev, R. Z. 1967 Instabilities due to temperature gradients in complex magnetic field configurations. Phys. Fluids 10, 582587.CrossRefGoogle Scholar
Darbyshire, A. G. & Mullin, T. 1995 Transition to turbulence in constant-mass-flux pipe flow. J. Fluid Mech. 289, 83114.CrossRefGoogle Scholar
Dimits, A. M., Bateman, G., Beer, M. A., Cohen, B. I., Dorland, W., Hammett, G. W., Kim, C., Kinsey, J. E., Kotschenreuther, M., Kritz, A. et al. 2000 Comparisons and physics basis of tokamak transport models and turbulence simulations. Phys. Plasmas 7, 969983.CrossRefGoogle Scholar
Fasoli, A., Brunner, S., Cooper, W. A., Graves, J. P., Ricci, P., Sauter, O. & Villard, L. 2016 Computational challenges in magnetic-confinement fusion physics. Nat. Phys. 12, 411423.CrossRefGoogle Scholar
Field, A. R., Dunai, D., Ghim, Y.-c., Hill, P., McMillan, B. F., Roach, C. M., Saarelma, S., Schekochihin, A. A. & Zoletnik, S. 2014 Comparison of BES measurements of ion-scale turbulence with direct gyro-kinetic simulations of MAST L-mode plasmas. Plasma Phys. Control. Fusion 56, 025012.CrossRefGoogle Scholar
Field, A. R., Michael, C., Akers, R. J., Candy, J., Colyer, G., Guttenfelder, W., Ghim, Y.-c., Roach, C. M. & Saarelma, S. 2011 Plasma rotation and transport in MAST spherical tokamak. Nucl. Fusion 51, 063006.CrossRefGoogle Scholar
Fiorio, C. & Gustedt, J. 1996 Two linear time Union-Find strategies for image processing. Theor. Comput. Sci. 154, 165181.CrossRefGoogle Scholar
Fox, M. F. J., van Wyk, F., Field, A. R., Ghim, Y.-c., Parra, F. I. & Schekochihin, A. A.2016. Symmetry breaking in MAST plasma turbulence due to toroidal flow shear. Plasma Phys. Control. Fusion (submitted), arXiv:1609.08981.Google Scholar
Frieman, E. A. & Chen, L. 1982 Nonlinear gyrokinetic equations for low-frequency electromagnetic waves in general plasma equilibria. Phys. Fluids 25, 502508.CrossRefGoogle Scholar
Ghim, Y.-c., Field, A. R., Schekochihin, A. A., Highcock, E. G. & Michael, C. 2014 the MAST Team Local dependence of ion temperature gradient on magnetic configuration, rotational shear and turbulent heat flux in MAST. Nucl. Fusion 54, 042003.CrossRefGoogle Scholar
Highcock, E. G., Barnes, M., Parra, F. I., Schekochihin, A. A., Roach, C. M. & Cowley, S. C. 2011 Transport bifurcation induced by sheared toroidal flow in tokamak plasmas. Phys. Plasmas 18, 102304.CrossRefGoogle Scholar
Highcock, E. G., Barnes, M., Schekochihin, A. A., Parra, F. I., Roach, C. M. & Cowley, S. C. 2010 Transport bifurcation in a rotating tokamak plasma. Phys. Rev. Lett. 105, 215003.CrossRefGoogle Scholar
Highcock, E. G., Schekochihin, A. A., Cowley, S. C., Barnes, M., Parra, F. I., Roach, C. M. & Dorland, W. 2012 Zero-turbulence manifold in a toroidal plasma. Phys. Rev. Lett. 109, 265001.CrossRefGoogle Scholar
Kauschke, U. 1999 Observation of coherent self-organized drift structures in a turbulent DC discharge. Plasma Phys. Control. Fusion 35, 93109.CrossRefGoogle Scholar
Klinger, T., Latten, A., Piel, A., Bonhomme, G. & Pierre, T. 1997 Route to drift wave chaos and turbulence in a bounded low-beta plasma experiment. Phys. Rev. Lett. 79, 39133916.CrossRefGoogle Scholar
Kotschenreuther, M., Dorland, W., Beer, M. A. & Hammett, G. W. 1995 Quantitative predictions of tokamak energy confinement from first-principles simulations with kinetic effects. Phys. Plasmas 2, 23812389.CrossRefGoogle Scholar
Krushelnick, K. & Cowley, S. 2005 Reduced turbulence and new opportunities for fusion. Science 309, 15021503.CrossRefGoogle Scholar
Landreman, M., Plunk, G. G. & Dorland, W. 2015 Generalized universal instability: transient linear amplification and subcritical turbulence. J. Plasma Phys. 81, 905810501.CrossRefGoogle Scholar
Lao, L. L., St. John, H., Stambaugh, R. D., Kellman, A. G. & Pfeiffer, W. 1985 Reconstruction of current profile parameters and plasma shapes in tokamaks. Nucl. Fusion 25, 16111622.CrossRefGoogle Scholar
Love, N. S. & Kamath, C. 2007 Image analysis for the identification of coherent structures in plasma. Proc. SPIE 6696, 66960D. Applications of Digital Image Processing XXX.CrossRefGoogle Scholar
Mantica, P., Strintzi, D., Tala, T., Giroud, C., Johnson, T., Leggate, H., Lerche, E., Loarer, T., Peeters, A. G., Salmi, A. et al. 2009 Experimental study of the ion critical-gradient length and stiffness level and the impact of rotation in the JET Tokamak. Phys. Rev. Lett. 102, 15.CrossRefGoogle ScholarPubMed
Miller, R. L., Chu, M. S., Greene, J. M., Lin-Liu, Y. R. & Waltz, R. E. 1998 Noncircular, finite aspect ratio, local equilibrium model. Phys. Plasmas 5, 973978.CrossRefGoogle Scholar
Müller, S. H., Fasoli, A., Labit, B., McGrath, M., Pisaturo, O., Plyushchev, G., Podestà, M. & Poli, F. M. 2005 Basic turbulence studies on TORPEX and challenges in the theory-experiment comparison. Phys. Plasmas 12, 090906.CrossRefGoogle Scholar
Newton, S. L., Cowley, S. C. & Loureiro, N. F. 2010 Understanding the effect of sheared flow on microinstabilities. Plasma Phys. Control. Fusion 52, 125001.CrossRefGoogle Scholar
Reynolds, O. 1883 An experimental investigation of the circumstances which determine whether the motion of water shall be direct or sinuous, and of the law of resistance in parallel channels. Phil. Trans. R. Soc. Lond. 174, 935982.CrossRefGoogle Scholar
Riccardi, C., Xuantong, D., Salierno, M., Gamberale, L. & Fontanesi, M. 1997 Experimental analysis of drift waves destabilization in a toroidal plasma. Phys. Plasmas 4, 37493758.CrossRefGoogle Scholar
Riols, A., Rincon, F., Cossu, C., Lesur, G., Longaretti, P.-Y., Ogilvie, G. I. & Herault, J. 2013 Global bifurcations to subcritical magnetorotational dynamo action in Keplerian shear flow. J. Fluid Mech. 731, 145.CrossRefGoogle Scholar
Riols, A., Rincon, F., Cossu, C., Lesur, G., Ogilvie, G. I. & Longaretti, P.-Y.2016 Magnetorotational dynamo chimeras. The missing link to turbulent accretion disk dynamo models? Astron. Astrophys. (accepted), doi:10.1051/0004-6361/201629285.Google Scholar
Roach, C. M., Abel, I. G., Akers, R. J., Arter, W., Barnes, M., Camenen, Y., Casson, F. J., Colyer, G., Connor, J. W., Cowley, S. C. et al. 2009 Gyrokinetic simulations of spherical tokamaks. Plasma Phys. Control. Fusion 51, 124020.CrossRefGoogle Scholar
Salwen, H., Cotton, F. W. & Grosch, C. E. 1980 Linear stability of Poiseuille flow in a circular pipe. J. Fluid Mech. 98, 273284.CrossRefGoogle Scholar
Scannell, R., Walsh, M. J., Dunstan, M. R., Figueiredo, J., Naylor, G., O’Gorman, T., Shibaev, S., Gibson, K. J. & Wilson, H. 2010 A 130 point Nd:YAG Thomson scattering diagnostic on MAST. Rev. Sci. Instrum. 81, 10D520.CrossRefGoogle ScholarPubMed
Schekochihin, A. A., Highcock, E. G. & Cowley, S. C. 2012 Subcritical fluctuations and suppression of turbulence in differentially rotating gyrokinetic plasmas. Plasma Phys. Control. Fusion 54, 055011.CrossRefGoogle Scholar
Trefethen, L. N., Trefethen, A. E., Reddy, S. C. & Driscoll, T. A. 1993 Hydrodynamic stability without eigenvalues. Science 261, 578584.CrossRefGoogle ScholarPubMed
van der Walt, S., Schönberger, J. L., Nunez-Iglesias, J., Boulogne, F., Warner, J. D., Yager, N., Gouillart, E. & Yu, T. 2014 The scikit-image contributors scikit-image: image processing in Python. PeerJ 2, e453.CrossRefGoogle ScholarPubMed
Weixing, D., Huang, W., Wang, X. & Yu, C. X. 1993 Quasiperiodic transition to chaos in a plasma. Phys. Rev. Lett. 70, 170173.CrossRefGoogle ScholarPubMed
26
Cited by

Send article to Kindle

To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Transition to subcritical turbulence in a tokamak plasma
Available formats
×

Send article to Dropbox

To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

Transition to subcritical turbulence in a tokamak plasma
Available formats
×

Send article to Google Drive

To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

Transition to subcritical turbulence in a tokamak plasma
Available formats
×
×

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *