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Strong turbulence, self-organization and plasma confinement

  • Akira Hasegawa
  • Kunioki Mima
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  1. Plasma physics in the 20th century as told by players

Abstract

This paper elucidates the close connections between hydrodynamic models of two-dimensional fluids and reduced models of plasma dynamics in the presence of a strong magnetic field. The key element is the similarity of the Coriolis force to the Lorentz force. The reduced plasma model, the Hasegawa–Mima equation, is equivalent to the two-dimensional ion vortex equation. The paper discusses the history of the Hasegawa–Mima model and that of a related reduced system called the Hasegawa–Wakatani model. The 2D fluid ↔ magnetized plasma analogy is exploited to argue that magnetized plasma turbulence exhibits a dual cascade, including an inverse cascade of energy. Generation of ordered mesoscopic flows in plasmas (akin to zonal jets) is also explained. The paper concludes with a brief explanation of the relevance of the quasi-2D dynamics to aspects of plasma confinement physics.

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References

  1. 1.
    Biglari, H., P.H. Diamond and P.W. Terry. 1990. Influence of sheared poloidal rotation on edge turbulence. Phys. Plasmas 2: 1–4 Google Scholar
  2. 2.
    Biskamp, D., E. Schwarz and J.F. Drake. 1996. Two-dimensional electron magnetohydrodynamic turbulence. Phys. Rev. Lett. 76: 1264–1268 ADSCrossRefGoogle Scholar
  3. 3.
    Charney, J.G. 1948. On the scale of atmospheric motions, Vol. 17. Geofysiske Publikasjoner, Oslo Google Scholar
  4. 4.
    Davis, M.S., M.E. Mauel, D.T. Garnier and J. Kesner. 2014. Pressure profiles of plasmas confined in the field of a magnetic dipole. Plasma Phys. Control. Fusion 56: 095021 ADSCrossRefGoogle Scholar
  5. 5.
    Diamond, P. and Y.-B. Kim. 1991. Theory of mean poloidal flow generation by turbulence. Phys. Plasma 3: 1626–1633 Google Scholar
  6. 6.
    Diamond, P., M. Rosenbluth, E. Sanchez, et al. 2000. In search of the elusive zonal flow using cross-bicoherence analysis. Phys. Rev. Lett. 84: 4842–4845 ADSCrossRefGoogle Scholar
  7. 7.
    Diamond, P.H., S.-I. Itoh, K. Itoh and T.S. Hahm. 2005. Zonal flow – a review. Plasma Phys. Control. Fusion 47: R35 CrossRefGoogle Scholar
  8. 8.
    Diamond, P.H., A. Hasegawa and K. Mima. 2011. Vorticity dynamics, drift wave turbulence, and zonal flows: a look back and a look ahead. Plasma Phys. Control. Fusion 53: 12001 CrossRefGoogle Scholar
  9. 9.
    Fujisawa, A. 2009. A review of zonal flow plasma experiments. Nucl. Fusion 49: 013001 ADSCrossRefGoogle Scholar
  10. 10.
    Galtier, S. and A. Bhattacharjee. 2003. Anisotropic weak whistler wave turbulence in electron magnetohydrodynamics. Phys. Plasmas 10: 3065 ADSCrossRefGoogle Scholar
  11. 11.
    Hamada, Y., T. Watari, A. Nishizawa, O. Yamagishi, K. Narihara, Y. Kawasumi, T. Ido, M. Kojima, K. Toi and the JIPPT-IIU Group. 2012. Regions of kinetic geodesic acoustic modes and streamers in JIPPT-IIU tokamak plasmas. Nucl. Fusion 52: 063023 ADSCrossRefGoogle Scholar
  12. 12.
    Hasegawa, A. 1983. A test of self-organization hypothesis in Jovian and Saturnian wind systems. J. Phys. Soc. Jpn. 52: 1930–1934 ADSCrossRefGoogle Scholar
  13. 13.
    Hasegawa, A. 1985. Self-organization processes in continuous media. Adv. Phys. 34: 1–42 ADSMathSciNetCrossRefGoogle Scholar
  14. 14.
    Hasegawa, A. 1987. A dipole field fusion reaction. Comm. Plasma Phys. Control. Fusion 11: 147–151 Google Scholar
  15. 15.
    Hasegawa, A. and L. Chen. 1975. Kinetic process of plasma heating due to Alfvén wave excitation. Phys. Rev. Lett. 35: 370–373 ADSCrossRefGoogle Scholar
  16. 16.
    Hasegawa, A. and K. Mima. 1977. Stationary spectrum of strong turbulence in magnetized nonuniform plasma. Phys. Rev. Lett. 39: 205–208 ADSCrossRefGoogle Scholar
  17. 17.
    Hasegawa, A. and K. Mima. 1978. Pseudo-three-dimensional turbulence in magnetized nonuniform plasma. Phys. Fluids 21: 87–92 ADSMathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Hasegawa, A. and M. Wakatani. 1983. Plasma edge turbulence. Phys. Rev. Lett. 50: 682–686 ADSCrossRefzbMATHGoogle Scholar
  19. 19.
    Hasegawa, A. and M. Wakatani. 1987. Self-organization of electrostatic turbulence in a cylindrical plasma. Phys. Rev. Lett. 59: 1581–1584 ADSCrossRefGoogle Scholar
  20. 20.
    Hasegawa, A., C.G. Maclennan and Y. Kodama. 1979. Nonlinear behavior and turbulence spectra of drift waves and Rossby waves. Phys. Fluids 22: 2122–2129 ADSMathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Hoppensteadt, F. 2006. Predator-prey model. Scholarpedia 1: 1563 ADSCrossRefGoogle Scholar
  22. 22.
    Kawazura, Y., Z. Yoshida, M. Nishiura, H. Saitoh, Y. Yano, T. Nogami, N. Sato, M. Yamasaki, A. Kashyap and T. Mushiake. 2015. Observation of particle acceleration in laboratory magnetosphere. Phys. Plasmas 22: 112503 ADSCrossRefGoogle Scholar
  23. 23.
    Kikuchi, M. and M. Azumi. 2015. Frontier in fusion research II: introduction to modern tokamak physics. Springer International Publishing, Switzerland Google Scholar
  24. 24.
    Kolmogorov, A.N. 1941. The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers. Dokl. Akad. Nauk SSSR 30: 299–303 ADSMathSciNetGoogle Scholar
  25. 25.
    Kraichnan, R.H. 1967. Inertial range in two-dimensional turbulence. Phys. Fluids 10: 1417–1423 ADSMathSciNetCrossRefGoogle Scholar
  26. 26.
    Mazzucato,E. 1976. Small-scale density fluctuations in the adiabatic toroidal compressor. Phys. Rev. Lett. 36: 792–795 ADSCrossRefGoogle Scholar
  27. 27.
    Mima, K. and Y.C. Lee. 1980. Modulational instability of strongly dispersive drift waves and formation of convective cells. Phys. Fluids 23: 105–108 ADSCrossRefGoogle Scholar
  28. 28.
    Nagashima, Y., S.-I Ito, S. Shinohara, M. Fukao, A. Fujisawa, K. Terasaka, Y. Kawai, G.R. Tynan, P.H. Diamond, M. Yagi, S. Inagaki, T. Yamada and K. Itoh. 2009. Observation of the parametric-modulational instability between the drift-wave fluctuation and azimuthally symmetric sheared radial electric field oscillation in a cylindrical laboratory plasma. Phys. Plasmas 16: 020706 ADSCrossRefGoogle Scholar
  29. 29.
    Onsager, L. 1949. Statistical hydrodynamics. Nuovo Cim. 6: 279–287 ADSMathSciNetCrossRefGoogle Scholar
  30. 30.
    Rosenbluth, M.N. and F.L. Hinton. 1998. Poloidal flow driven ion-temperature-gradient turbulent in tokamaks. Phys. Rev. Lett. 80: 724–727 ADSCrossRefGoogle Scholar
  31. 31.
    Rossby, C.-G. 1939. Relation between variations in the intensity of the zonal circulation of the atmosphere and the displacements of the semi-permanent centers of action. J. Mar. Res. 2: 38–55 CrossRefGoogle Scholar
  32. 32.
    Sagdeev, R.Z. and A.A. Galeev. 1969. Nonlinear plasma theory (T.M. O’Neil and D.L. Book, eds.). W.A. Benjamin, New York Google Scholar
  33. 33.
    Schrödinger, E. 1944. What is life? The physical aspect of the living cell. Cambridge University Press, Cambridge Google Scholar
  34. 34.
    Slusher, R.E. and C.M. Surko. 1978. Study of density fluctuations in the absorption of oxygen on silicon. Phys. Rev. Lett. 40: 400–403 ADSCrossRefGoogle Scholar
  35. 35.
    Surko, C.M. and R.E. Slusher. 1976. Study of the density fluctuations in the adiabatic toroidal compressor scattering tokamak using CO2 laser. Phys. Rev. Lett. 37: 1747–1750 ADSCrossRefGoogle Scholar
  36. 36.
    Taniuti, T. and H. Washimi H. 1968. Self-trapping and instability of hydromagnetic waves along the magnetic field in a cold plasma. Phys. Rev. Lett. 21: 209–212 ADSCrossRefGoogle Scholar
  37. 37.
    Tynan G.R., R.A. Moyer, M.J. Burin and C. Holland. 2001. On the nonlinear turbulentdynamics of shear-flow decorrelation and zonal flow generation. Phys. Plasmas 8: 2691–2699 ADSCrossRefGoogle Scholar
  38. 38.
    Wakatani, M. and A. Hasegawa. 1984. A collisional drift wave description of plasma edge turbulence. Phys. Fluids 27: 611–618 ADSCrossRefzbMATHGoogle Scholar
  39. 39.
    Williams, G.P. 1978. Planetary circulations: 1. Barotropic representation of Jovian and terrestrial turbulence. J. Atmos. Sci. 35: 1399–1426 ADSCrossRefGoogle Scholar
  40. 40.
    Xiao, Y., I. Holod, W. Zhang, S. Klasky and Z. Lin. 2010. Fluctuation characteristic and transport properties of collisionless trapped electron mode turbulence. Phys. Plasmas 17: 022302 ADSCrossRefGoogle Scholar
  41. 41.
    Zakharov, V.E. 1972. Collapse of Langmuir waves. Sov. Phys. JETP-USSR 35: 908–914 ADSGoogle Scholar

Copyright information

© EDP Sciences and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Osaka UniversitySuita, OsakaJapan

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