Generic structure of externally driven tearing modes instabilities

  • E. Lazzaro
  • R. Coelho


A major limit to steady state and advanced high β p operation of tokamaks of reactor class is due to the onset of tearing modes that develop magnetic and may cause loss of energy confinement or a major disruption. Here the structure of a classical problem about the effects of external control helical fields is analysed and it is shown to offer a general paradigm of response of low order classical and neoclassical tearing modes to a wide class of external perturbations. New results of principle on the structural stability of the response model are obtained, leading to a clear interpretation of the role of “seed islands” in the onset of neo-classical tearing modes and the role of finite ion larmor radius corrections to Ohm’s law.


52.35.Py Macroinstabilities (hydromagnetic, e.g., kink, fire-hose, mirror, ballooning, tearing, trapped-particle, flute, Rayleigh-Taylor, etc.) 52.25.Fi Transport properties 52.35.Mw Nonlinear phenomena: waves, wave propagation, and other interactions (including parametric effects, mode coupling, ponderomotive effects, etc.) 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    F. Karger et al, in Proc. 5th IAEA Int., Conf. on Plasma physics and Controlled Nuclear Fusion Research. Tokyo, 1974, Influence of resonant helical fields on tokamak discharges (Vienna, 1975), Vol. 1, p. 207Google Scholar
  2. 2.
    R.J. La Have, T.C. Hender, R. Fitzpatrick, A.W. Morris, Phys. Fluids B 4, 2098 (1992).CrossRefADSGoogle Scholar
  3. 3.
    A. Santagiustina, S. Ali Arshad, D.J. Campbell, G. D’Antona, M. Debenedetti, A.M. Edwards G. Fishpool, E. Lazzaro, R.J. La Haye, A.W. Morris, R. Ostrom, L. Rossi, F. Sartori, P. Savrukhin, M. Tabellini, A. Tanga, G. Zullo, Studies of Tearing Mode Control in JET, in Proc. 22th EPS Conference on Controlled Fusion and Plasma Physics. Bournemouth, 3–7 July 1995 (Europhysics Conference Abstracts 19c IV, p. 461, European Physical Society, Geneva.Google Scholar
  4. 4.
    P. Savrukhin, S. All Arshad, D.J. Campbell, G. D’Antona, M. DeBenedetti, A.M. Edwards, G. Fishpool, R.J. La Haye, E. Lazzaro, A. Santagiustina, F. Sartori, A. Tanga, Effect of the error fields on plasma stability in JET and ITER, Proc. 23th EPS Conference on Controlled Fusion and Plasma Physics, Kiev, 26–30 July (Europhysics Conference Abstracts, European Physical Society, Geneva, 1996), Voll, p. 19.Google Scholar
  5. 5.
    H.R. Strauss, Phys. Fluids 19, 134 (1976).CrossRefADSGoogle Scholar
  6. 6.
    R.D. Hazeltine, in Plasma Confinement (Addison Wesley Publ. Co. Cambridge, 1991).Google Scholar
  7. 7.
    D.A. Monticello, R.B. White, M. Rosenbluth, Plasma Physics and Controlled Nuclear Fusion Research 1978, Proc. 1th IAEA Int, Conf Tokyo, 1978, paper IAEA-CN-37/K-3, Vol. 1, Vienna, p. 605.Google Scholar
  8. 8.
    R. White, D.A. Monticello, M. Rosenbluth, B.V. Waddell, Nucl. Fus. 20, 800 (1977).Google Scholar
  9. 9.
    R. Fitzpatrick, Phys. Plasmas 2, 825 (1995).CrossRefADSMathSciNetGoogle Scholar
  10. 10.
    P.T. Saunders, An introduction to Catastrophe Theory (Cambridge University Press, Cambridge, 1980).zbMATHGoogle Scholar
  11. 11.
    G. Nicolis, Introduction to Nonlinear Science (Cambridge University Press, Cambridge, 1995).Google Scholar
  12. 12.
    V.I. Arnold, Catastrophe Theory (Springer Verlag, Berlin, 1986).Google Scholar
  13. 13.
    C.C. Hegna, J.D. Gallen, Phys. Fluids B 4, 4072 (1992).CrossRefADSGoogle Scholar
  14. 14.
    A.I. Smolyakov et al., Phys. Plasmas 2, 1581 (1995).CrossRefADSGoogle Scholar
  15. 15.
    H.R. Wilson et al., Plasma Phys. Contr. Fus. 38, A149 (1996).Google Scholar
  16. 16.
    H. Zohm, Phys. Plasmas 4, 3433 (1997).CrossRefADSGoogle Scholar
  17. 17.
    O. Sauter et al., Phys. Plasmas 4, 1654 (1997).CrossRefADSGoogle Scholar
  18. 18.
    A.B. Mikhailovskii, B.N. Kuvshinov, V.D. Pustovitov, S.E. Sharapov, Fizika Plasmi (1999, to appear).Google Scholar
  19. 19.
    A.B. Mikhailovskii, V.D. Pustovitov, V.S. Tsypin, A.I. Smolyakov, Phys. Plasmas 7, 1214 (2000).CrossRefADSMathSciNetGoogle Scholar
  20. 20.
    X. Wang, A. Bhattacharjee, Phys. Plasmas 4, 748 (1997).CrossRefADSGoogle Scholar
  21. 21.
    F.L, Waelbroeck, R. Fitzpatrick, Phys. Rev. Lett. 78, 1703 (1997).CrossRefADSGoogle Scholar
  22. 22.
    H.R. Wilson et al., in Proceedings of 18th IAEA Fusion Energy Conference, Sorrento, Italy, Oct. l–10th, 2000, Paper IAEA-CN-77/TH3/5.Google Scholar
  23. 23.
    G. Gantenbeim et al., Phys. Rev. Lett. 85, 1242 (2000).CrossRefADSGoogle Scholar
  24. 24.
    S. Günther et al., Plasma Phys. Contr. Fus. 38, B231 (1999).Google Scholar

Copyright information

© Springer-Verlag 2002

Authors and Affiliations

  • E. Lazzaro
    • 1
  • R. Coelho
    • 2
  1. 1.Istituto di Fisica del Plasma “P.Caldirola”Consiglio Nazionale delle RicercheEuratom-ENEA-CNR AssociationMilanItaly
  2. 2.Associação EURATOM/ISTCentro de Fusão NuclearLisbon CodexPortugal

Personalised recommendations