Skip to main content
Log in

Recent progress on turbulence and multi-scale interactions in tokamak plasmas

  • Special Topics
  • Published:
Reviews of Modern Plasma Physics Aims and scope Submit manuscript

Abstract

Studies on nonlinear interactions and multi-scale physics are crucial in the physical understanding of the turbulence and transport in the complex nonlinear system of fusion plasmas. This paper reviews recent studies on the turbulence and the related transport. The prominent results are mainly from tokamaks, such as HL-2A, Tore Supra and J-TEXT. First, turbulence behaviors and its role in transport will be introduced. Critical gradients in heat and particle transports have been observed and reproduced by simulations. Turbulence modes and its role in the transport are identified using advanced diagnostics. The measured turbulence transition is consistent with the observation of particle convection reversal and the simulation prediction. In addition, the excitation of an electromagnetic turbulence by either edge self-accumulated or externally seeded impurities has been observed. The impurity-driven turbulence plays an essential role in regulating the impurity transport. Then, the effect of plasma flows on turbulence and multi-scale interactions (micro-turbulence, meso-scale fluctuations, and large scale MHD activities) will be presented. Moreover, a new meso-scale electrostatic fluctuation has been observed. The results indicate that geodesic acoustic modes and magnetic fluctuations can transfer energy through nonlinear synchronization. At last, the enhancement of nonlinear interactions by external actuators will be reported. Theoretical studies in comparisons with experimental findings will be discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2

Copyright 2013 APS

Fig. 3

Copyright 2015 IOP

Fig. 4

Reprinted from Zhong (2016a). Copyright 2016 AIP

Fig. 5

Reprinted from Zhong (2016a). Copyright 2016 AIP

Fig. 6

Copyright 2017 IOP

Fig. 7

Copyright 2016 APS

Fig. 8

Copyright 2006 APS

Fig. 9

Copyright 2015 IOP

Fig. 10

Copyright 2010 IOP

Fig. 11

Copyright 2012 APS

Fig. 12

Copyright 2018 APS

Fig. 13

Copyright 2015 APS

Fig. 14

Copyright 2015 APS

Fig. 15

Similar content being viewed by others

References

  • C. Angioni et al., Density peaking, anomalous pinch, and collisionality in tokamak plasmas. Phys. Rev. Lett. 90, 205003 (2003)

    Article  ADS  Google Scholar 

  • H. Arnichand et al., Quasi-coherent modes and electron-driven turbulence. Nucl. Fusion 54, 123017 (2014)

    Article  ADS  Google Scholar 

  • H. Arnichand et al., Discriminating the trapped electron modes contribution in density fluctuation spectra. Nucl. Fusion 55, 093021 (2015)

    Article  ADS  Google Scholar 

  • H. Arnichand et al., Identification of trapped electron modes in frequency fluctuation spectra. Plasma Phys. Control. Fusion 58, 014037 (2016)

    Article  ADS  Google Scholar 

  • L. Bardoczi et al., Modulation of core turbulent density fluctuations by large-scale neoclassical tearing mode islands in the DIII-D tokamak. Phys. Rev. Lett. 116, 215001 (2016)

    Article  ADS  Google Scholar 

  • H. Biglari, P.H. Diamond, P.W. Terry, Influence of sheared poloidal rotation on edge turbulence. Phys. Fluids B 2, 1 (1990)

    Article  ADS  Google Scholar 

  • C. Bourdelle et al., A new gyrokinetic quasilinear transport model applied to particle transport in tokamak plasmas. Phys. Plasmas 14, 112501 (2007)

    Article  ADS  Google Scholar 

  • D.L. Brower et al., Observation of a high-density ion mode in tokamak microturbulence. Phys. Rev. Lett. 59, 48 (1987)

    Article  ADS  Google Scholar 

  • L. Chen et al., On nonlinear geodesic acoustic modes in tokamak plasmas. Europhys. Lett. 107, 15003 (2014)

    Article  ADS  Google Scholar 

  • J. Cheng et al., Dynamics of low-intermediate-high-confinement transitions in toroidal plasmas. Phys. Rev. Lett. 110, 265002 (2013)

    Article  ADS  Google Scholar 

  • M.J. Choi et al., Multiscale interaction between a large scale magnetic island and small scale turbulence. Nucl. Fusion 57, 126058 (2017)

    Article  ADS  Google Scholar 

  • G.D. Conway et al., Mean and oscillating plasma flows and turbulence interactions across the L-H confinement transition. Phys. Rev. Lett. 106, 065001 (2011)

    Article  ADS  Google Scholar 

  • G.D. Conway et al., Impact of magnetic perturbation coils on the edge radial electric field and turbulence in ASDEX Upgrade. Plasma Phys. Control. Fusion 57, 014035 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  • B. Coppi et al., Drift instability due to impurity ions. Phys. Rev. Lett. 17, 377 (1966)

    Article  ADS  Google Scholar 

  • B. Coppi, C. Spight, Ion-mixing mode and model for density rise in confined plasmas. Phys. Rev. Lett. 41, 551 (1978)

    Article  ADS  Google Scholar 

  • P.H. Diamond et al., Zonal flows in plasma—a review. Plasma Phys. Control. Fusion 47, R35 (2005)

    Article  Google Scholar 

  • P.H. Diamond, T.S. Hahm, On the dynamics of turbulent transport near marginal stability. Phys. Plasmas 2, 3640 (1995)

    Article  ADS  Google Scholar 

  • R.R. Dominguez, Isotope scaling in the drift wave model. Nucl. Fusion 31, 2063 (1991)

    Article  Google Scholar 

  • R.R. Dominguez, G.M. Staebler, Impurity effects on drift wave stability and impurity transport. Nucl. Fusion 33, 51 (1993)

    Article  ADS  Google Scholar 

  • J.Q. Dong, W. Horton, Studies of impurity mode and ion temperature gradient mode in toroidal plasmas. Phys. Plasmas 2, 3412 (1995)

    Article  ADS  Google Scholar 

  • J.Q. Dong, L. Chen, F. Zonca, Study of kinetic shear Alfven modes driven by ion temperature gradient in tokamak plasmas. Nucl. Fusion 39, 1041 (1999)

    Article  ADS  Google Scholar 

  • J.R. Duff et al., Observation of trapped-electron-mode microturbulence in reversed field pinch plasmas. Phys. Plasmas 25, 010701 (2018)

    Article  ADS  Google Scholar 

  • T. Estrada et al., Transitions to improved core electron heat confinement triggered by low order rational magnetic surfaces in the stellarator TJ-II. Nucl. Fusion 47, 305 (2007)

    Article  ADS  Google Scholar 

  • S.P. Eury et al., Exact solutions of the diffusion-convection equation in cylindrical geometry. Phys. Plasmas 12, 102511 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  • A. Fujisawa et al., Identification of zonal flows in a toroidal plasma. Phys. Rev. Lett. 93, 165002 (2004)

    Article  ADS  Google Scholar 

  • X. Gao et al., Plasma density behavior in the Hefei tokamak-7. Phys. Plasmas 7, 2933 (2000)

    Article  ADS  Google Scholar 

  • X. Garbet et al., Turbulent particle transport in magnetized plasmas. Phys. Rev. Lett. 91, 035001 (2003)

    Article  ADS  Google Scholar 

  • X. Garbet et al., Gyrokinetic simulations of turbulent transport. Nucl. Fusion 50, 043002 (2010)

    Article  ADS  Google Scholar 

  • R.J. Groebner et al., Experimentally inferred ion thermal diffusivity profiles in the Doublet III tokamak: comparison with neoclassical theory. Nucl. Fusion 26, 543 (1986)

    Article  Google Scholar 

  • W.X. Guo et al., Impact of impurities on zonal flow driven by trapped electron mode turbulence. Nucl. Fusion 57, 126052 (2017)

    Article  ADS  Google Scholar 

  • A. Hasegawa, M. Wakatani, Plasma edge turbulence. Phys. Rev. Lett. 50, 682 (1983)

    Article  ADS  Google Scholar 

  • A. Hasegawa, M. Wakatani, Self-organization of electrostatic turbulence in a cylindrical plasma. Phys. Rev. Lett. 59, 1581 (1987)

    Article  ADS  Google Scholar 

  • A. Hasegawa, C.G. Maclennan, Y. Kodama, Nonlinear behavior and turbulence spectra of drift waves and Rossby waves. Phys. Fluids 22, 2122 (1979)

    Article  ADS  MathSciNet  Google Scholar 

  • R.J. Hawryluk et al., Overview of TFTR transport studies. Plasma Phys. Control. Fusion 33, 1509 (1991)

    Article  ADS  Google Scholar 

  • J.C. Hillesheim et al., Observation of a critical gradient threshold for electron temperature fluctuations in the DIII-D tokamak. Phys. Rev. Lett. 110, 045003 (2013)

    Article  ADS  Google Scholar 

  • G.T. Hoang et al., Experimental determination of critical threshold in electron transport on Tore Supra. Phys. Rev. Lett. 87, 125001 (2001)

    Article  ADS  Google Scholar 

  • G.T. Hoang et al., Particle pinch with fully noninductive lower hybrid current drive in tore supra. Phys. Rev. Lett. 90, 155002 (2003)

    Article  ADS  Google Scholar 

  • W. Horton, Drift waves and transport. Rev. Mod. Phys. 71, 735 (1999)

    Article  ADS  Google Scholar 

  • K. Ida et al., Observation of plasma flow at the magnetic island in the large helical device. Phys. Rev. Lett. 88, 015002 (2001)

    Article  ADS  Google Scholar 

  • K. Ida et al., Self-regulated oscillation of transport and topology of magnetic islands in toroidal plasmas. Sci. Rep. 5, 16165 (2015)

    Article  ADS  Google Scholar 

  • K. Ida et al., Hysteresis relation between turbulence and temperature modulation during the heat pulse propagation into a magnetic island in DIII-D. Phys. Rev. Lett. 120, 245001 (2018)

    Article  ADS  Google Scholar 

  • T. Ido et al., Geodesic acoustic-mode in JFT-2M tokamak plasmas. Plasma Phys. Controll. Fusion 48, S41 (2006)

    Article  Google Scholar 

  • A. Ishizawa, N. Nakajima, Multi-scale interactions between turbulence and magnetic islands and parity mixture—a review. Nucl. Fusion 49, 055015 (2009)

    Article  ADS  Google Scholar 

  • K. Itho et al., Excitation of geodesic acoustic mode in toroidal plasmas. Plasma Phys. Control. Fusion 47, 451 (2005)

    Article  ADS  Google Scholar 

  • S.-I. Itoh et al., Novel turbulence trigger for neoclassical tearings mode in tokamaks. Phys. Rev. Lett. 91, 045003 (2003)

    Article  ADS  Google Scholar 

  • M. Jiang et al., Localized modulation of turbulence by m/n = 1/1 magnetic islands in the HL-2A tokamak. Nucl. Fusion 59, 066019 (2019)

    Article  ADS  Google Scholar 

  • M. Jiang et al., Modulation of the trapped electron driven turbulence by m/n = 2/1 tearing mode in the core of HL-2A plasmas. Nucl. Fusion 60, 066006 (2020)

    ADS  Google Scholar 

  • Y.C. Kim et al., Digital bispectral analysis and its applications to nonlinear wave interactions. IEEE Trans. Plasma Sci. 7, 120 (1979)

    Article  ADS  Google Scholar 

  • E.J. Kim, P.H. Diamond, Zonal flows and transient dynamics of the L-H transition. Phys. Rev. Lett. 90, 185006 (2003)

    Article  ADS  Google Scholar 

  • T. Kobayashi et al., Quantification of turbulent driving forces for the geodesic acoustic mode in the JFT-2M tokamak. Phys. Rev. Lett. 120, 045002 (2018)

    Article  ADS  Google Scholar 

  • A. Krämer-Flecken et al., Long-range correlation properties of quasi-coherent modes at TEXTOR. New J. Phys. 17, 073007 (2015)

    Article  ADS  Google Scholar 

  • J.-M. Kwon et al., Gyrokinetic simulation study of magnetic island effects on neoclassical physics and micro-instabilities in a realistic KSTAR plasma. Phys. Plasmas 25, 052506 (2018)

    Article  ADS  Google Scholar 

  • P.T. Lang et al., Impact of a pulsed supersonic deuterium gas jet on the ELM behaviour in ASDEX Upgrade. Plasma Phys. Control. Fusion 47, 1495 (2005)

    Article  ADS  Google Scholar 

  • H.Y. Lee et al., Edge localized mode characteristics during edge localized mode mitigation by supersonic molecular beam injection in Korea Superconducting Tokamak Advanced Research. Phys. Plasmas 22, 122512 (2015)

    Article  ADS  Google Scholar 

  • J.A. Lee et al., Observation of electron driven quasi-coherent modes and their connection with core intrinsic rotation in KSTAR ECH and ohmic L-mode plasmas. Phys. Plasmas 25, 022513 (2018)

    Article  ADS  Google Scholar 

  • J. Li, Y. Kishimoto, Small-scale dynamo action in multi-scale magnetohydrodynamic and micro-turbulence. Phys. Plasmas 19, 030705 (2012)

    Article  ADS  Google Scholar 

  • Z. Lin et al., Turbulent transport reduction by zonal flows: massively parallel simulations. Science 281, 1835 (1998)

    Article  ADS  Google Scholar 

  • A.D. Liu et al., Characterizations of low-frequency zonal flow in the edge plasma of the HL-2A tokamak. Phys. Rev. Lett. 103, 095002 (2009)

    Article  ADS  Google Scholar 

  • S.F. Liu et al., Impurity effects on the ion temperature gradient mode in reversed-field pinch plasmas. Nucl. Fusion 51, 083021 (2011)

    Article  ADS  Google Scholar 

  • S.F. Liu et al., Gyrokinetic study of impurity mode in reversed-field pinch. Europhys. Lett. 97, 55004 (2012)

    Article  ADS  Google Scholar 

  • N.J. Lopes Cardozo et al., Tokamak transport studies using perturbation analysis. Plasma Phys. Controll. Fusion 33, 983 (1990)

    Article  ADS  Google Scholar 

  • N.J. Lopes Cardozo et al., Perturbative transport studies in fusion plasmas. Plasma Phys. Controll. Fusion 37, 799 (1995)

    Article  ADS  Google Scholar 

  • G.M. Lu et al., Kinetic shear Alfven instability in the presence of impurity ions in tokamak plasmas. Phys. Plasmas 20, 102505 (2013)

    Article  ADS  Google Scholar 

  • P. Mantica et al., 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 (2009)

    Article  ADS  Google Scholar 

  • N. Mattor, Effect of impurity density gradients on low frequency electrostatic fluctuations. Phys. Fluids B 3, 2153 (1991)

    Article  ADS  Google Scholar 

  • S. Migliuolo, Ion temperature gradient driven impurity modes. Nucl. Fusion 32, 1331 (1992)

    Article  ADS  Google Scholar 

  • T. Mizuuchi et al., Comparison between supersonic molecular-beam injection and conventional gas-puffing for plasma performance in Heliotron J. J. Nucl. Mater. 415, S443 (2010)

    Article  Google Scholar 

  • A.B. Navarro et al., Effect of magnetic islands on profiles, flows, turbulence and transport in nonlinear gyrokinetic simulations. Plasma Phys. Control. Fusion 59, 034004 (2017)

    Article  ADS  Google Scholar 

  • T. Nishizawa et al., Measurements of impurity transport due to drift-wave turbulence in a toroidal plasma. Phys. Rev. Lett. 121, 165002 (2018)

    Article  ADS  Google Scholar 

  • H. Nordman, J. Weiland, A. Jarmen, Simulation of toroidal drift mode turbulence driven by temperature gradients and electron trapping. Nucl. Fusion 30, 983 (1990)

    Article  Google Scholar 

  • M.A. Pedrosa, Evidence of long-distance correlation of fluctuations during edge transitions to improved-confinement regimes in the TJ-II stellarator. Phys. Rev. Lett. 100, 215003 (2008)

    Article  ADS  Google Scholar 

  • B. Pégourié et al., Supersonic gas injection on Tore Supra. J. Nucl. Mater. 313, 539 (2003)

    Article  ADS  Google Scholar 

  • J.E. Rice et al., Rotation reversal bifurcation and energy confinement saturation in tokamak ohmic L-mode plasmas. Phys. Rev. Lett. 107, 265001 (2011)

    Article  ADS  Google Scholar 

  • M.N. Rosenbluth, F.L. Hinton, poloidal flow driven by ion-temperature-gradient turbulence in tokamaks. Phys. Rev. Lett. 80, 724 (1998)

    Article  ADS  Google Scholar 

  • L. Schmitz et al., Role of zonal flow predator-prey oscillations in triggering the transition to H-mode confinement. Phys. Rev. Lett. 108, 155002 (2012)

    Article  ADS  Google Scholar 

  • Y. Shen et al., Impurity induced kinetic shear Alfven and kinetic ballooning instabilities in tokamak plasmas. Nucl. Fusion 58, 014004 (2018)

    Article  ADS  Google Scholar 

  • Z.B. Shi et al., A novel multi-channel quadrature Doppler backward scattering reflectometer on the HL-2A tokamak. Rev. Sci. Instrum. 87, 113501 (2016)

    Article  ADS  Google Scholar 

  • Y. Shimomura, N. Suzuki, M. Sugihara, T. Tsuda, K. Odajima, T. Tsunematsu, Japanese Atomic Energy Research Institute Report, JAERIM- 85-080 (1985)

  • P.B. Snyder, G.W. Hammett, Electromagnetic effects on plasma microturbulence and transport. Phys. Plasmas 8, 744 (2001)

    Article  ADS  Google Scholar 

  • H. Takenaga, the JT-60 Team. Particle control study towards burning plasma control in JT-60U. J. Nucl. Mater. 390:8 (2009)

  • M.Z. Tokar et al., Evidence of suppression of ITG-instability in the radiatively improved mode in TEXTOR-94. Plasma Phys. Control. Fusion 41, L9 (1999)

    Article  Google Scholar 

  • K.T. Tsang, Dissipative trapped-electron modes in the presence of impurities. Nucl. Fusion 17, 261 (1977)

    Article  ADS  Google Scholar 

  • V.A. Vershkov et al., Summary of experimental core turbulence characteristics in ohmic and electron cyclotron resonance heated discharges in T-10 tokamak plasmas. Nucl. Fusion 45, S203 (2005)

    Article  Google Scholar 

  • D. Villegas et al., Experimental electron temperature gradient dependence of heavy impurity transport in fusion devices. Phys. Rev. Lett. 105, 035002 (2010)

    Article  ADS  Google Scholar 

  • A.A. Ware, Pinch effect oscillations in an unstable tokamak plasma. Phys. Rev. Lett. 25, 916 (1970)

    Article  ADS  Google Scholar 

  • J. Weiland, A. Jarmen, H. Nordman, Diffusive particle and heat pinch effects in toroidal plasmas. Nucl. Fusion 29, 1810 (1989)

    Article  Google Scholar 

  • H. Weisen et al., Collisionality and shear dependences of density peaking in JET and extrapolation to ITER. Nucl. Fusion 45, L1 (2005)

    Article  Google Scholar 

  • N. Winsor, J.L. Johnson, J.M. Dawson, Geodesic acoustic waves in hydromagnetic systems. Phys. Fluids 11, 2448 (1968)

    Article  ADS  Google Scholar 

  • H. Xia, M.G. Shats, Inverse energy cascade correlated with turbulent-structure generation in toroidal plasma. Phys. Rev. Lett. 91, 155001 (2003)

    Article  ADS  Google Scholar 

  • W.W. Xiao et al., A method of particle transport study using supersonic molecular beam injection and microwave reflectometry on HL-2A tokamak Rev. Sci. Instrum. 81, 013506 (2010)

    Article  ADS  Google Scholar 

  • W.W. Xiao et al., Observation of a spontaneous particle-transport barrier in the HL-2A tokamak. Phys. Rev. Lett. 104, 215001 (2010b)

    Article  ADS  Google Scholar 

  • W.W. Xiao et al., ELM mitigation by supersonic molecular beam injection into the H-mode pedestal in the HL-2A tokamak. Nucl. Fusion 52, 114027 (2012)

    Article  ADS  Google Scholar 

  • M. Xu et al., Frequency-resolved nonlinear turbulent energy transfer into zonal flows in strongly heated L-mode plasmas in the HL-2A Phys. Rev. Lett. 108, 245001 (2012)

    Article  ADS  Google Scholar 

  • Z. Yan et al., Observation of the L-H confinement bifurcation triggered by a turbulence-driven shear flow in a tokamak plasma. Phys. Rev. Lett. 112, 125002 (2014)

    Article  ADS  Google Scholar 

  • L.H. Yao et al., 1993 20th EPS Conf. on Controlled Fusion and Plasma Physics (Lisboa, Portugal), vol. 17C(I) (European Physical Society, Geneva, 1993), p. 303

  • L.H. Yao et al., Plasma behaviour with molecular beam injection in the HL-1M tokamak. Nucl. Fusion 38, 631 (1998)

    Article  ADS  Google Scholar 

  • E.S. Yoon, T.S. Hahm, Transport of parallel momentum by toroidal ion temperature gradient instability near marginality. Nucl. Fusion 50, 064006 (2010)

    Article  ADS  Google Scholar 

  • K.J. Zhao et al., Toroidal symmetry of the geodesic acoustic mode zonal flow in a tokamak plasma. Phys. Rev. Lett. 96, 255004 (2006)

    Article  ADS  Google Scholar 

  • K.J. Zhao et al., Turbulence and zonal flows in edge plasmas of the HL-2A tokamak. Plasma Phys. Control. Fusion 52, 124008 (2010)

    Article  ADS  Google Scholar 

  • K.J. Zhao et al., Plasma flows and fluctuations with magnetic islands in the edge plasmas of J-TEXT tokamak. Nucl. Fusion 55, 073022 (2015)

    Article  ADS  Google Scholar 

  • K.J. Zhao et al., Synchronization of geodesic acoustic modes and magnetic fluctuations in toroidal plasmas. Phys. Rev. Lett. 117, 145002 (2016)

    Article  ADS  Google Scholar 

  • W.L. Zhong et al., Convective velocity reversal caused by turbulence transition in tokamak plasma. Phys. Rev. Lett. 111, 265001 (2013)

    Article  ADS  Google Scholar 

  • W.L. Zhong, et al., Enhancement of Nonlinear Regulation Dynamics in SMBI-stimulated L-H transition of HL-2A, 46th EPS Conference on Plasma Physics, Milan, Italy, July 8–12 (2019)

  • W.L. Zhong et al., Three dimensional measurements of Geodesic Acoustic Mode with correlation Doppler reflectometers. J. Instrum. 10, P10014 (2015a)

    Article  Google Scholar 

  • W.L. Zhong et al., Spatiotemporal characterization of zonal flows with multi-channel correlation Doppler reflectometers in the HL-2A tokamak. Nucl. Fusion 55, 113005 (2015b)

    Article  ADS  Google Scholar 

  • W.L. Zhong et al., Experimental observation of turbulence transition and a critical gradient threshold for trapped electron mode in tokamak plasmas. Phys. Plasmas 23, 060702 (2016a)

    Article  Google Scholar 

  • W.L. Zhong et al., Observation of double impurity critical gradients for electromagnetic turbulence excitation in tokamak plasmas. Phys. Rev. Lett. 117, 045001 (2016b)

    Article  ADS  Google Scholar 

  • W.L. Zhong et al., Impact of fuelling and impurity on pedestal dynamics and instabilities in the HL-2A tokamak. Plasma Phys. Control. Fusion 59, 014030 (2017)

    Article  ADS  Google Scholar 

  • W.L. Zhong et al., Impact of impurity mixture gas seeded by supersonic molecular beam injection on edge-localized modes in the HL-2A tokamak. Nucl. Fusion 59, 076033 (2019)

    Article  ADS  Google Scholar 

  • W.L. Zhong et al., Stimulated effect of SMBI on low-to-high confinement transition of tokamak plasmas. Nucl. Fusion 60, 082002 (2020)

    Article  ADS  Google Scholar 

  • F. Zonca et al., Existence of discrete modes in an unstable shear Alfvén continuous spectrum. Plasma Phys. Controll. Fusion 40, 2009 (1998)

    Article  ADS  Google Scholar 

  • X.L. Zou, et al, 2012 Proc. 24th Int. Conf. on Fusion Energy 2012 (San Diego, CA, 2012) (PD/P8-08), http://www-naweb.iaea.org/napc/physics/FEC/FEC2012/index.htm

Download references

Acknowledgements

The authors would like to thank the teams of CNNC/SWIP, CEA/IRFM and HUST for the support of the experiments and simulations. This work was supported by National Key R&D Program of China (No. 2017YFE0301106), and National Natural Science Foundation of China (Nos. 11775070 and 11922503). It was partially supported by Young Elite Scientists Sponsorship Program by CAST (No. 2016QNRC001) and Sichuan Science and Technology Program (No. 2018JY0054), and also partially supported within the framework of the cooperation between the French Commissariat à l’Energie Atomique et aux Energies Alternatives (CEA) and the China National Nuclear Corporation (CNNC).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to W. L. Zhong.

Ethics declarations

Conflict of interest

On behalf of all the authors, the corresponding author states that there is no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhong, W.L., Zhao, K.J., Zou, X.L. et al. Recent progress on turbulence and multi-scale interactions in tokamak plasmas. Rev. Mod. Plasma Phys. 4, 11 (2020). https://doi.org/10.1007/s41614-020-00047-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s41614-020-00047-5

Keywords

Navigation