Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-16T23:05:44.417Z Has data issue: false hasContentIssue false
  • English
  • Français

Bistable turbulence in strongly magnetised plasmas with a sheared mean flow

Published online by Cambridge University Press:  03 October 2022

Nicolas Christen Open the ORCID record for Nicolas Christen [Opens in a new window] ,
M. Barnes Open the ORCID record for M. Barnes [Opens in a new window] ,
M.R. Hardman Open the ORCID record for M.R. Hardman [Opens in a new window]  and
A.A. Schekochihin Open the ORCID record for A.A. Schekochihin [Opens in a new window]
Nicolas Christen*
Affiliation:
Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford OX1 3PU, UK Lincoln College, Oxford OX1 3DR, UK
M. Barnes
Affiliation:
Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford OX1 3PU, UK University College, Oxford OX1 4BH, UK
M.R. Hardman
Affiliation:
Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford OX1 3PU, UK
A.A. Schekochihin
Affiliation:
Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford OX1 3PU, UK Merton College, Oxford OX1 4JD, UK
*
†Email address for correspondence: nicolas.christen@physics.ox.ac.uk
Get access Rights & Permissions [Opens in a new window]

Abstract

The prevailing paradigm for plasma turbulence associates a unique stationary state with given equilibrium parameters. We report the discovery of bistable turbulence in a strongly magnetised plasma with a sheared mean flow. Two distinct states, obtained with identical equilibrium parameters in first-principle gyrokinetic simulations, have turbulent fluxes of particles, momentum and energy that differ by an order of magnitude – with the low-transport state agreeing with experimental observations. Occurrences of the two states are regulated by the competition between an externally imposed mean flow shear and ‘zonal’ flows generated by the plasma. With small turbulent amplitudes, zonal flows have little impact, and the mean shear causes turbulence to saturate in a low-transport state. With larger amplitudes, the zonal shear can (partially) oppose the effect of the mean shear, allowing the system to sustain a high-transport state. This poses a new challenge for research that has so far assumed a uniquely defined turbulent state.

Keywords

fusion plasmaplasma nonlinear phenomenaplasma simulation
Type
Research Article
Information
Journal of Plasma Physics , Volume 88 , Issue 5 , October 2022 , 905880504
Check for updates
Copyright
Copyright © The Author(s), 2022. Published by Cambridge University Press

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

REFERENCES

Abel, I., Plunk, G., Wang, E., Barnes, M., Cowley, S., Dorland, W. & Schekochihin, A. 2013 Multiscale gyrokinetics for rotating tokamak plasmas: fluctuations, transport and energy flows. Rep. Prog. Phys. 76 (11), 116201.CrossRefGoogle ScholarPubMed
Artun, M. & Tang, W.M. 1992 Gyrokinetic analysis of ion temperature gradient modes in the presence of sheared flows. Phys. Fluids B 4 (5), 1102–1114.CrossRefGoogle Scholar
Barnes, M., Abel, I.G., Dorland, W., Ernst, D.R., Hammett, G.W., Ricci, P., Rogers, B.N., Schekochihin, A.A. & Tatsuno, T. 2009 Linearized model Fokker–Planck collision operators for gyrokinetic simulations. II. Numerical implementation and tests. Phys. Plasmas 16 (7), 072107.CrossRefGoogle Scholar
Barnes, M., Parra, F.I., Highcock, E.G., Schekochihin, A.A., Cowley, S.C. & Roach, C.M. 2011 Turbulent transport in tokamak plasmas with rotational shear. Phys. Rev. Lett. 106, 175004.CrossRefGoogle ScholarPubMed
Beer, M.A., Cowley, S. & Hammett, G. 1995 Field-aligned coordinates for nonlinear simulations of tokamak turbulence. Phys. Plasmas 2 (7), 2687–2700.CrossRefGoogle Scholar
Belli, E.A. 2006 Studies of numerical algorithms for gyrokinetics and the effects of shaping on plasma turbulence. PhD thesis, Princeton University.Google Scholar
Biglari, H., Diamond, P.H. & Terry, P.W. 1990 Influence of sheared poloidal rotation on edge turbulence. Phys. Fluids B 2 (1), 1–4.CrossRefGoogle Scholar
Burggraf, O.R. & Foster, M.R. 1977 Continuation or breakdown in tornado-like vortices. J. Fluid Mech. 80 (4), 685–703.CrossRefGoogle Scholar
Casson, F.J., Peeters, A.G., Camenen, Y., Hornsby, W.A., Snodin, A.P., Strintzi, D. & Szepesi, G. 2009 Anomalous parallel momentum transport due to ExB flow shear in a tokamak plasma. Phys. Plasmas 16 (9), 092303.CrossRefGoogle Scholar
Catto, P.J. 1978 Linearized gyro-kinetics. Plasma Phys. 20 (7), 719–722.CrossRefGoogle Scholar
Catto, P.J., Bernstein, I.B. & Tessarotto, M. 1987 Ion transport in toroidally rotating tokamak plasmas. Phys. Fluids 30 (9), 2784–2795.CrossRefGoogle Scholar
Chandrarajan Jayalekshmi, A. 2020 Studying the effect of non-adiabatic passing electron dynamics on microturbulence self-interaction in fusion plasmas using gyrokinetic simulations. PhD thesis, École Polytechnique Fédérale de Lausanne.Google Scholar
Christen, N., Barnes, M. & Parra, F. 2021 Continuous-in-time approach to flow shear in a linearly implicit local delta-f gyrokinetic code. J. Plasma Phys 87 (2), 905870230.CrossRefGoogle Scholar
Colyer, G.J., Schekochihin, A.A., Parra, F.I., Roach, C.M., Barnes, M.A., Ghim, Y.-C. & Dorland, W. 2017 Collisionality scaling of the electron heat flux in ETG turbulence. Plasma Phys. Control. Fusion 59 (5), 055002.CrossRefGoogle Scholar
Connor, J.W. 1998 A review of models for ELMs. Plasma Phys. Control. Fusion 40 (2), 191–213.CrossRefGoogle Scholar
Cowley, S.C., Kulsrud, R.M. & Sudan, R. 1991 Considerations of ion-temperature-gradient-driven turbulence. Phys. Fluids B 3 (10), 2767–2782.CrossRefGoogle Scholar
Diamond, P.H., Itoh, S., Itoh, K. & Hahm, T. 2005 Zonal flows in plasma—a review. Plasma Phys. Control. Fusion 47 (5), R35.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.H., et al. 2000 Comparisons and physics basis of tokamak transport models and turbulence simulations. Phys. Plasmas 7 (3), 969–983.CrossRefGoogle Scholar
Dimits, A.M., Williams, T.J., Byers, J.A. & Cohen, B.I. 1996 Scalings of ion-temperature-gradient-driven anomalous transport in tokamaks. Phys. Rev. Lett. 77, 71–74.CrossRefGoogle ScholarPubMed
Faisst, H. & Eckhardt, B. 2004 Sensitive dependence on initial conditions in transition to turbulence in pipe flow. J. Fluid Mech. 504, 343–352.CrossRefGoogle Scholar
Fox, M.F.J., van Wyk, F., Field, A.R., Ghim, Y.-C., Parra, F.I. & Schekochihin, A.A. 2017 Symmetry breaking in MAST plasma turbulence due to toroidal flow shear. Plasma Phys. Control. Fusion 59 (3), 034002.CrossRefGoogle Scholar
Frieman, E.A. & Chen, L. 1982 Nonlinear gyrokinetic equations for low-frequency electromagnetic waves in general plasma equilibria. Phys. Fluids 25 (3), 502–508.CrossRefGoogle Scholar
von Goeler, S., Stodiek, W. & Sauthoff, N. 1974 Studies of internal disruptions and $m=1$ oscillations in tokamak discharges with soft-X-ray techniques. Phys. Rev. Lett. 33, 1201–1203.CrossRefGoogle Scholar
Hammett, G.W., Dorland, W., Loureiro, N.F. & Tatsuno, T. 2006 Implementation of large scale $\boldsymbol {E}\times \boldsymbol {B}$ shear flow in the gs2 gyrokinetic turbulence code. In Poster Presented at the DPP Meeting of the American Physical Society.Google Scholar
Hastie, R. 1997 Sawtooth instability in tokamak plasmas. Astrophys. Space Sci. 256 (1), 177–204.CrossRefGoogle Scholar
Highcock, E. 2012 The zero-turbulence manifold in fusion plasmas. PhD thesis, Oxford University, UK.Google 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 (10), 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., Schekochihin, A., Cowley, S., Barnes, M., Parra, F., Roach, C. & Dorland, W. 2012 Zero-turbulence manifold in a toroidal plasma. Phys. Rev. Lett. 109 (26), 265001.CrossRefGoogle Scholar
Ivanov, P.G., Schekochihin, A.A., Dorland, W., Field, A.R. & Parra, F.I. 2020 Zonally dominated dynamics and dimits threshold in curvature-driven ITG turbulence. J. Plasma Phys. 86 (5), 855860502.CrossRefGoogle Scholar
Kotschenreuther, M., Rewoldt, G. & Tang, W.M. 1995 Comparison of initial value and eigenvalue codes for kinetic toroidal plasma instabilities. Comput. Phys. Commun. 88 (2), 128–140.CrossRefGoogle Scholar
Latter, H.N. & Papaloizou, J.C.B. 2012 Hysteresis and thermal limit cycles in MRI simulations of accretion discs. Mon. Not. R. Astron. Soc. 426 (2), 1107–1120.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, 175002.CrossRefGoogle ScholarPubMed
McMillan, B.F., Ball, J. & Brunner, S. 2019 Simulating background shear flow in local gyrokinetic simulations. Plasma Phys. Control. Fusion 61 (5), 055006.CrossRefGoogle Scholar
McMillan, B.F., Jolliet, S., Tran, T., Villard, L., Bottino, A. & Angelino, P. 2009 Avalanchelike bursts in global gyrokinetic simulations. Phys. Plasmas 16 (2), 022310.CrossRefGoogle Scholar
McMillan, B.F., Pringle, C.C.T. & Teaca, B. 2018 Simple advecting structures and the edge of chaos in subcritical tokamak plasmas. J. Plasma Phys. 84 (6), 905840611.CrossRefGoogle Scholar
Parra, F.I., Barnes, M., Highcock, E.G., Schekochihin, A.A. & Cowley, S.C. 2011 Momentum injection in tokamak plasmas and transitions to reduced transport. Phys. Rev. Lett. 106, 115004.CrossRefGoogle ScholarPubMed
Peeters, A.G., Rath, F., Buchholz, R., Camenen, Y., Candy, J., Casson, F.J., Grosshauser, S.R., Hornsby, W.A., Strintzi, D. & Weikl, A. 2016 Gradient-driven flux-tube simulations of ion temperature gradient turbulence close to the non-linear threshold. Phys. Plasmas 23 (8), 082517.CrossRefGoogle Scholar
Pueschel, M.J., Kammerer, M. & Jenko, F. 2008 Gyrokinetic turbulence simulations at high plasma beta. Phys. Plasmas 15 (10), 102310.CrossRefGoogle Scholar
Ravelet, F., Marié, L., Chiffaudel, A. & Daviaud, F. 2004 Multistability and memory effect in a highly turbulent flow: experimental evidence for a global bifurcation. Phys. Rev. Lett. 93 (16), 164501.CrossRefGoogle Scholar
Rempel, E.L., Lesur, G. & Proctor, M.R.E. 2010 Supertransient magnetohydrodynamic turbulence in Keplerian shear flows. Phys. Rev. Lett. 105, 044501.CrossRefGoogle ScholarPubMed
Rogers, B.N., Dorland, W. & Kotschenreuther, M. 2000 Generation and stability of zonal flows in ion-temperature-gradient mode turbulence. Phys. Rev. Lett. 85, 5336–5339.CrossRefGoogle ScholarPubMed
Romanelli, F. 1989 Ion temperature-gradient-driven modes and anomalous ion transport in tokamaks. Phys. Fluids B 1 (5), 1018–1025.CrossRefGoogle Scholar
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 (5), 055011.CrossRefGoogle Scholar
Schmucker, A. & Gersten, K. 1988 Vortex breakdown and its control on delta wings. Fluid Dyn. Res. 3 (1–4), 268–272.CrossRefGoogle Scholar
Shafer, M.W., Fonck, R.J., McKee, G.R., Holland, C., White, A.E. & Schlossberg, D.J. 2012 2D properties of core turbulence on DIII-D and comparison to gyrokinetic simulations. Phys. Plasmas 19 (3), 032504.CrossRefGoogle Scholar
Shtern, V. & Hussain, F. 1993 Hysteresis in a swirling jet as a model tornado. Phys. Fluids A 5 (9), 2183–2195.CrossRefGoogle Scholar
Simitev, R.D. & Busse, F.H. 2009 Bistability and hysteresis of dipolar dynamos generated by turbulent convection in rotating spherical shells. Europhys. Lett. 85 (1), 19001.CrossRefGoogle Scholar
Siren, P., Varje, J., Weisen, H. & Giacomelli, L. 2019 Role of JETPEAK database in validation of synthetic neutron camera diagnostics and ASCOT- AFSI fast particle and fusion product calculation chain in JET. J. Instrum. 14 (11), C11013–C11013.CrossRefGoogle Scholar
Snedeker, R.S. & Donaldson, C.D. 1966 Observation of a bistable flow in a hemispherical cavity. AIAA J. 4 (4), 735–736.CrossRefGoogle Scholar
Sugama, H. & Horton, W. 1998 Nonlinear electromagnetic gyrokinetic equation for plasmas with large mean flows. Phys. Plasmas 5 (7), 2560–2573.CrossRefGoogle Scholar
Synakowski, E.J., Batha, S.H., Beer, M.A., Bell, M.G., Bell, R.E., Budny, R.V., Bush, C.E., Efthimion, P.C., Hammett, G.W., Hahm, T.S., et al. 1997 Roles of electric field shear and Shafranov shift in sustaining high confinement in enhanced reversed shear plasmas on the TFTR tokamak. Phys. Rev. Lett. 78, 2972–2975.CrossRefGoogle Scholar
Waelbroeck, F.L. & Chen, L. 1991 Ballooning instabilities in tokamaks with sheared toroidal flows. Phys. Fluids B 3 (3), 601–610.CrossRefGoogle Scholar
Wagner, F., Becker, G., Behringer, K., Campbell, D., Eberhagen, A., Engelhardt, W., Fussmann, G., Gehre, O., Gernhardt, J., Gierke, G.V., et al. 1982 Regime of improved confinement and high beta in neutral-beam-heated divertor discharges of the ASDEX tokamak. Phys. Rev. Lett. 49, 1408–1412.CrossRefGoogle Scholar
Weikl, A., Peeters, A.G., Rath, F., Grosshauser, S.R., Buchholz, R., Hornsby, W.A., Seiferling, F. & Strintzi, D. 2017 Ion temperature gradient turbulence close to the finite heat flux threshold. Phys. Plasmas 24 (10), 102317.CrossRefGoogle Scholar
van Wyk, F., Highcock, E.G., Field, A.R., Roach, C.M., Schekochihin, A.A., Parra, F.I. & Dorland, W. 2017 Ion-scale turbulence in MAST: anomalous transport, subcritical transitions, and comparison to BES measurements. Plasma Phys. Control. Fusion 59 (11), 114003.CrossRefGoogle Scholar
van Wyk, F., Highcock, E.G., Schekochihin, A.A., Roach, C.M., Field, A.R. & Dorland, W. 2016 Transition to subcritical turbulence in a tokamak plasma. J. Plasma Phys. 82 (6), 905820609.CrossRefGoogle Scholar
Supplementary material: File

Christen et al. supplementary material

Christen et al. supplementary material 1

Download Christen et al. supplementary material(File)
File 9.3 KB
Supplementary material: PDF

Christen et al. supplementary material

Christen et al. supplementary material 2

Download Christen et al. supplementary material(PDF)
PDF 404.9 KB