First Principle Transport Modeling in Fusion Plasmas: Critical Issues for ITER

  • Yanick Sarazin
Part of the Nonlinear Systems and Complexity book series (NSCH, volume 5)


Tokamaks aim at confining hot plasmas by means of strong magnetic fields in view of reaching a net energy gain through fusion reactions. Plasma confinement turns out to be governed by small-scale instabilities which saturate nonlinearly and lead to turbulent fluctuations of a few percent. This paper recalls the basic equations for modeling such weakly collisional plasmas. It essentially relies on the kinetic, or more precisely the gyrokinetic, description, although some attempts are made to incorporate some of the kinetic properties, namely, wave-particle resonances, in fluid models by means of collisionless closures. Three main types of micro-instabilities are detailed and studied linearly, namely, drift waves, interchange, and bump-on-tail. Finally, some of the main critical issues in turbulence modeling are addressed: flux-driven versus gradient-driven models, the subsequent impact of mean profile relaxation on turbulent transport dynamics, and the role of large-scale flows, either at equilibrium or turbulence driven, on turbulence saturation and on the possible triggering of transport barriers. The significant progress in understanding and prediction of turbulent transport in tokamak plasmas thanks to first-principle simulations is highlighted.


Turbulent Transport Adiabatic Limit Transport Barrier Radial Electric Field Linear Threshold 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



It is my pleasure to acknowledge colleagues and friends who have most contributed to this paper through numerous enlightening discussions and common work on turbulence and transport for many years: X. Garbet and Ph. Ghendrih, P. Beyer, P.H. Diamond, G. Dif-Pradalier, and V. Grandgirard. Many thanks as well to the students J. Abiteboul, A. Strugarek, D. Zarzoso, and T. Cartier-Michaud. Last but not least, I wish to acknowledge C. Passeron for her precious support on numerical issues.


  1. 1.
    X. Garbet (Guest Editor), Turbulent Transport in Fusion Magnetised Plasmas, vol 6 (C.R. Physique, Amsterdam, 2006), 573–699Google Scholar
  2. 2.
    G.W. Hammett, F.W. Perkins, Phys. Rev. Lett. 64, 3019 (1990)CrossRefGoogle Scholar
  3. 3.
    M.A. Beer, Ph.D. thesis, Princeton University (1995)Google Scholar
  4. 4.
    B. Snyder, G.W. Hammett, W. Dorland, Phys. Plasmas 4, 3974 (1997)MathSciNetCrossRefGoogle Scholar
  5. 5.
    H. Sugama, T.-H. Watanabe, W. Horton, Phys. Plasmas 10, 726 (2003)CrossRefGoogle Scholar
  6. 6.
    T. Passot, P.L. Sulem, Phys. Plasmas 10, 3906 (2003)MathSciNetCrossRefGoogle Scholar
  7. 7.
    T. Chust, G. Belmont, Phys. Plasmas 13, 012506 (2006)MathSciNetCrossRefGoogle Scholar
  8. 8.
    P. Bertrand, M.R. Feix, Phys. Lett. 28A, 68 (1968)Google Scholar
  9. 9.
    P. Morel, E. Gravier, N. Besse, R. Klein, A. Ghizzo, P. Bertrand, X. Garbet, P. Ghendrih, V. Grandgirard, Y. Sarazin, Phys. Plasmas 14, 112109 (2007)CrossRefGoogle Scholar
  10. 10.
    Y. Sarazin, G. Dif-Pradalier, D. Zarzoso, X. Garbet, Ph. Ghendrih, V. Grandgirard, Plasma Phys. Control. Fusion 51, 115003 (2009)CrossRefGoogle Scholar
  11. 11.
    L.D. Landau (1946), “On the vibrations of the electronic plasma”, in Collected Papers of L.D. Landau, vol 61, ed. by D. Ter Haar (Pergamon Press, Oxford, 1965), p. 445Google Scholar
  12. 12.
    B.D. Fried, S.D. Conte, The Plasma Dispersion Function (Academic Press, New York NY, 1961)Google Scholar
  13. 13.
    A.M. Dimits et al., Phys. Plasmas 7, 969 (2000)CrossRefGoogle Scholar
  14. 14.
    Y. Sarazin, V. Grandgirard, G. Dif-Pradalier, E. Fleurence, X. Garbet, Ph Ghendrih, P. Bertrand, N. Besse, N. Crouseilles, E. Sonnendrücker, G. Latu, E. Violard, Plasma Phys. Control Fusion 48, B179–B188 (2006)Google Scholar
  15. 15.
    A.J. Brizard, T.S. Hahm, Rev. Mod. Phys. 79, 421 (2007)MathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    V. Grandgirard ans Y. Sarazin, to appear in Panoramas et Synthèses, Société Mathématique de France (2013)Google Scholar
  17. 17.
    A. Hasegawa, M. Wakatani, Phys. Rev. Lett. 50, 682 (1983)CrossRefGoogle Scholar
  18. 18.
    M. Wakatani, A. Hasegawa, Phys. Fluids 27, 611 (1984)CrossRefMATHGoogle Scholar
  19. 19.
    D. Zarzoso, X. Garbet, Y. Sarazin, R. Dumont, V. Grandgirard, Phys. Plasmas 19, 022102 (2012)CrossRefGoogle Scholar
  20. 20.
    P.H. Diamond, T.S. Hahm, Phys. Plasmas 2, 3640 (1995)CrossRefGoogle Scholar
  21. 21.
    Y. Sarazin, V. Grandgirard, J. Abiteboul, S. Allfrey, G. Dif-Pradalier, X. Garbet, Ph. Ghendrih, G. Latu, A. Strugarek, Nucl. Fusion 50, 054004 (2010)CrossRefGoogle Scholar
  22. 22.
    V. Grandgirard et al., Commun. Nonlinear Sci. Numer. Simulation 13, 81–87 (2008)CrossRefMATHGoogle Scholar
  23. 23.
    G. Dif-Pradalier, P.H. Diamond, V. Grandgirard, Y. Sarazin, J. Abiteboul, X. Garbet, Ph. Ghendrih, A. Strugarek, S. Ku, C.S. Chang, Phys. Rev. E 82, 025401(R) (2010)Google Scholar
  24. 24.
    L.N. Howard, R. Krishnamurti, J. Fluid Mech. 170, 385–410 (1986)CrossRefMATHGoogle Scholar
  25. 25.
    H. Biglari, P. Diamond, P. Terry, Phys. Fluids B 2, 1 (1990)CrossRefGoogle Scholar
  26. 26.
    T.S. Hahm, K.H. Burrell, Phys. Plasmas 2, 1648 (1995)CrossRefGoogle Scholar
  27. 27.
    R.E Waltz, G.D. Kerbel, J. Milovich, Phys. Plasmas 1, 2229 (1994)Google Scholar
  28. 28.
    A. Fujisawa, K. Itoh, H. Iguchi et al., Phys. Rev. Lett. 93, 165002 (2004)CrossRefGoogle Scholar
  29. 29.
    P.H. Diamond, M.N. Rosenbluth, F.L. Hinton et al., Plasma Physics Control Nuclear Fusion Research (IAEA, Vienna, 1998)Google Scholar
  30. 30.
    Z. Lin, T.S. Hahm, W.W. Lee, W.M. Tang, P.H. Diamond, Phys. Rev. Lett. 83, 3645 (1999)CrossRefGoogle Scholar
  31. 31.
    M.N. Rosenbluth, F.L. Hinton, Phys. Rev. Lett. 80, 724 (1998)CrossRefGoogle Scholar
  32. 32.
    F.L. Hinton, M.N. Rosenbluth, Plasma Phys. Controlled Fusion 41, A653 (1999)CrossRefGoogle Scholar
  33. 33.
    Y. Sarazin, V. Grandgirard, G. Dif-Pradalier et al., Phys. Plasmas 13, 092307 (2006)CrossRefGoogle Scholar
  34. 34.
    F. Wagner et al., Phys. Rev. Lett. 49, 1408 (1982)CrossRefGoogle Scholar
  35. 35.
    R. Moyer, K. Burrell, T. Carlstrom et al., Phys. Plasmas 2, 2397 (1995)CrossRefGoogle Scholar
  36. 36.
    H. Zohm, Plasma Phys. Control. Fusion 38, 105 (1996)CrossRefGoogle Scholar
  37. 37.
    J.W. Connor, Plasma Phys. Control. Fusion 40, 191 (1998)CrossRefGoogle Scholar
  38. 38.
    P.A. Politzer, Phys. Rev. Lett. 84, 1192 (2000)CrossRefGoogle Scholar
  39. 39.
    Y. Sarazin, M. Bécoulet, P. Beyer, X. Garbet, Ph. Ghendrih, T.C. Hender, E. Joffrin, X. Litaudon, P.J. Lomas, G.F. Matthews, V. Parail, G. Saibene, R. Sartori, Plasma Phys. Control. Fusion 44, 2445 (2002)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.CEA, IRFMSaint-Paul-Lez-DuranceFrance

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