The problem of the formaton of spatially ordered structures called “coherent modes” in plasmas is of significant interest for the nonlinear theory of anomalous plasma transport. The existence of a coherent mode is expected to have a strong effect on the particle and heat transport properties in plasmas. The experimental observatios of an edge plasma turbulence in the CALTECH TOKAMAK by Zweben & Gould (1983) show a transition from turbulently unstable to stable coherent mode at high neutral filling pressure.1 There seems to be a transition between turbulent and coherent modes. We can find the large-scale vortices in the fluid turbulence and Great Red Spot in the atmosphere of Jupiter thought to be a stable monopole of nonlinear solitary vortex like a one-dimensional soliton. Let us call them roughly “ coherent (solitary)modes ”. Montgomery and his group have made an extensive study of self-organization in the relaxation process on the field of plasma physics (1978).2 Solitary vortex solutions have been extensively studied in a specific inviscid condition neglected instability; Larichev & Reznik(1976),3 Meiss & Horton(1983),4 Pavlenko & Petviashvili(1984),5 Mikhailovskii et al.(1984),6 Shukla et al.(1985),7 Morrison & Hazeltine(1985),8 and Moriguchi & Nozaki(1992).9 Makino, Kamimura and Taniuti (1981)10 numerically have shown that the stable properties of solitary vortices which are two-dimensional, localized, steady and translating solutions of the Hasegawa-Mima equation(1978).11 A localized vortex seems to comprise a self-organized state. Hasegawa reviewed a self-organization processes in the case of non-dissipative systems and discussed that the relationship between the onset of chaos and self-organization in a soliton system as well as in some localized vortex solutions (1985).12


Coherent Structure Particle Flux Vortex Solution Magnetic Shear Plasma Flux 
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.
    J. Zweben and R. W. Gould, Nucl. Fusion 123, 1625 (1983).CrossRefGoogle Scholar
  2. 2.
    D. Montgomery, L. Turner and G. Vahala, Phys. Fluid, 21, 757 (1978).ADSMATHCrossRefGoogle Scholar
  3. 3.
    V. D. Larichev and G. M. Reznik, Dokl. Akad. Nauk SSSR, 231, 1077 (1976).Google Scholar
  4. 4.
    J. D. Meiss and W. Horton, Phys. Fluids, 26, 990 (1983).ADSMATHCrossRefGoogle Scholar
  5. 5.
    V. P. Pavlenko and V. I. Petviashvili, Soviet J. Plasma Phys. 9, 603 (1984).Google Scholar
  6. 6.
    A. B. Mikhailovskii, G. D. Aburdzhaniya, O. G. Onishchenko and A. P. Chikov, Phys. Lett. 101A, 263 (1984).ADSGoogle Scholar
  7. 7.
    P. K. Shukla, M. Y. Yu and R. K. Varma, Phys. Lett. 109A, 322 (1985).ADSGoogle Scholar
  8. 8.
    P. J. Morrison and R. D. Hazeltine, Phys. Fluids 27, 886 (1984).ADSMATHCrossRefGoogle Scholar
  9. 9.
    H. Moriguchi and K. Nozaki, J. Phys. Soc. Jpn. 61, 117 (1992).ADSCrossRefGoogle Scholar
  10. 10.
    M. Makino, T. Kamimura and T. Taniuti, J. Phys. Soc. Jpn. 50, 980 (1981).MathSciNetADSCrossRefGoogle Scholar
  11. 11.
    A. Hasegawa and K. Mima, Phys. Fluids 21, 87 (1978).MathSciNetADSMATHCrossRefGoogle Scholar
  12. 12.
    A. Hasegawa, Advances in Physics 34, 1 (1985).MathSciNetADSCrossRefGoogle Scholar
  13. 13.
    K. Nozaki and N. Bekki, J. Phys. Soc. Jpn. 54, 2363 (1985).ADSCrossRefGoogle Scholar
  14. 14.
    N. Bekki and Y. Kaneda, Phys. Rev. Lett. 57, 2176 (1986).ADSCrossRefGoogle Scholar
  15. 15.
    R. D. Hazeltine, Phys. Fluids 26, 3242 (1983).ADSMATHCrossRefGoogle Scholar
  16. 16.
    R. E. Waltz, Phys. Fluids 28, 577 (1985).ADSMATHCrossRefGoogle Scholar
  17. 17.
    G. S. Patterson and S. A. Orszag, Phys. Fluids 14, 2538 (1971).ADSMATHCrossRefGoogle Scholar
  18. 18.
    C. Z. Cheng and H. Okuda, Phys. Rev. Lett. 38, 708 (1977).ADSCrossRefGoogle Scholar
  19. 19.
    R. Z. Sagdeev, V. D. Shapiro and V. I. Shevchenk, Sov. J. Plasma Phys. 4, 306 (1978).Google Scholar
  20. 20.
    N. Bekki, J. Phys. Soc. Jpn. 52, 2736 (1983).ADSCrossRefGoogle Scholar
  21. 21.
    W. Horton, B. G. Hong, T. Tajima and N. Bekki, Comm. Plasma Phys. 13, 207 (1990).Google Scholar
  22. 22.
    S. J. Zweben, PhysPluids 28, 974 (1985).ADSGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1994

Authors and Affiliations

  • Naoaki Bekki
    • 1
  1. 1.College of EngineeringNihon UniversityKoriyama, FukushimaJapan

Personalised recommendations