Plasma Physics pp 326-338 | Cite as

Nonlinear Dynamics of Joule Heated Toroidal Discharges

  • Michel Cotsaftis
Part of the Nobel Symposium Committee (1976) book series (NOFS, volume 36)


A rather large and puzzling discrepancy still exists between the experimental results and the various proposed models, If ions could be almost (neo) classical, though they do not seem to switch as expected into the predicted banana regime, this is by far not the case for the electrons. For instance, numerical computations with (neo) classical MHD System produce a very strong skin effect on the electronic temperature Te taking a long time compared to the duration of the discharge to disappear, which is never observed. During the discharge also, even if one artificially eliminates the skin effect, Te does not seem to follow simple proposed laws, Moreover, the belief that the observation is the result of many antagonist effects (instabilities, impurities, neutrals) obscures again the possibility of a “theoretical” representation, as examplified by the rapidly growing numerical simulations, taking adjusted ad hoc coefficients to follow the datas, showing that classical laws are not simply verified, and limiting the theoretical arguments to pseudo qualitative ones.


Plasma Discharge Skin Effect Group Property Kink Mode Group Invariant Solution 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    F. Calogero, A. Degasperis:Il Nuovo Cimente Vol 32B Ser 11 201 (1976) and references therein.Google Scholar
  2. M. Cotsaftis: Current Thermal Instability in Sheared Systems and Skin Suppression, APS Meeting St Petersbourg Fla 5–12 Nov. 1975Google Scholar
  3. B.B. Kadomtsev, 0.P. Pogutse JETP Vol 24 n°6 p. 1172 (1967); Rev. of Plasma Physics Ed. Leontovitch Tome V Consultant Bureau (1972)Google Scholar
  4. D. Duchs NFL Report no 7340 Feb. 1972; J. Hogan g ORNL Report n° TM 51–53 Nov. 1975Google Scholar
  5. E. Hinnov PPL Report n° MATT-777 (1970)Google Scholar
  6. M, Murakami, W.R. Wing, P.H. Edmonds: Nuclear Fusion Vol 14 p. 779 (1974)CrossRefGoogle Scholar
  7. 7.
    G.W. Bit:man, J.D. Cole: Similarity Methods for Differential Equations, Springer-Verlag Applied Math. Science n° 13 (1974)Google Scholar
  8. 8.
    L.V. Ovsjannikov: Group Properties for Differential Equations, Novosibirsk (1962)Google Scholar
  9. 9.
    W.F. Ames: Nonlinear Partial Differential Equations in Engineering Academic Press New York Vol. I (1965), Vol. U (1972)Google Scholar
  10. 10.
    G. Bardotti, L. Enriques, F. Santini: Nuclear Fusion Vo1. 15 p. 621 (1975)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1977

Authors and Affiliations

  • Michel Cotsaftis
    • 1
  1. 1.ASSOCIATION EURATOM-CEAFontenay-aux-RosesFrance

Personalised recommendations