Plasma Physics pp 173-204 | Cite as

Ideal Magnetohydrodynamics

  • Kyoji Nishikawa
  • Masahiro Wakatani
Chapter
Part of the Springer Series on Atoms+Plasmas book series (SSAOPP, volume 8)

Abstract

The simplest model to describe the dynamics of plasmas immersed in a magnetic field is the one-fluid magnetohydrodynamics (MHD), which treats the plasma composed of many charged particles with locally neutral charge as a continuous single fluid [10.1]. This theory does not provide information on the velocity distribution and neglects the physics relating to wave-particle interactions, as does the two-fluid theory as well. It does have the advantage that the macroscopic dynamics of the magnetized plasma can be analyzed in realistic three-dimensional geometries. From this point of view the one-fluid MHD is often more useful than the two-fluid theory.

Keywords

Vortex Assure Dition Triad Incompressibility 

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References

  1. 10.1
    J.P. Friedberg: Ideal Magnetohydrodynamics (Plenum, New York 1987)Google Scholar
  2. 10.2
    W.B. Thompson: An Introduction to Plasma Physics (Pergamon, Oxford 1962)MATHGoogle Scholar
  3. 10.3
    G. Schmidt: Physics of High Temperature Plasmas (Academic, New York 1966)Google Scholar
  4. 10.4
    V.D. Shafranov: “Plasma Equilibrium in a Magnetic Held”, in Reviews of Plasma Physics, Vol. 2 (Consultants Bureau, New York 1966) p. 103Google Scholar
  5. 10.5
    V.S. Mukovatov, V.D. Shafranov: Plasma Equilibrium in a Tokamak, Nuclear Fusion 11, 605 (1971)CrossRefGoogle Scholar
  6. 10.6
    L.S. Solov’ev, V.D. Shafranov: “Plasma Confinement in a Closed Magnetic System”, in Reviews of Plasma Physics, Vol. 5 (Consultants Bureau, New York 1970) p. 1CrossRefGoogle Scholar
  7. 10.7
    M.D. Kruskal, R.M. Kulsrud: Equilibrium of a Magnetically Confined Plasma in a Toroid, Phys. Fluids 1, 265 (1958)MathSciNetADSMATHCrossRefGoogle Scholar
  8. 10.8
    J.M. Greene, J.L. Johnson, K.E. Weimer: Tokamak Equilibrium, Phys. Fluids 14, 671 (1971)ADSCrossRefGoogle Scholar
  9. 10.9
    J.F. Clark, D.J. Sigmar: High Pressure Flux-Conserving Tokamak Equilibria, Phys. Rev. Lett. 38, 10 (1977)ADSCrossRefGoogle Scholar
  10. 10.10
    B.B. Kadomtsev: “Hydromagnetic Stability of a Plasma”, in Reviews of Plasma Physics, Vol. 2 (Consultants Bureau, New York 1966) p. 153Google Scholar
  11. 10.11
    W.A. Newcomb: Hydromagnetic Stability of a Diffuse Linear Pinch, Ann. Phys. (New York) 3, 347 (1958)MathSciNetADSMATHCrossRefGoogle Scholar
  12. 10.12
    I.B. Bernstein, E.A. Frieman, M.D. Kruskal, R.M. Kulsrud: An Energy Principle for Hydromagnetic Stability Problems, Proc. Roy. Soc. A244, 17 (1958)MathSciNetADSGoogle Scholar
  13. 10.13
    J.A. Wesson: Hydromagnetic Stability of Tokamaks, Nuclear Fusion 18, 87 (1978)ADSCrossRefGoogle Scholar
  14. 10.14
    B.R. Suydam: Stability of a Linear Pinch, IAEA Geneva Conf. 31, 157 (1958)Google Scholar
  15. 10.15
    V.D. Shafranov, E.I. Yurchenko: Condition for Flute Instability of a Toroidal-Geometry Plasma, Sov. Phys-JETP 26, 682 (1968)ADSGoogle Scholar
  16. 10.16
    G. Batemann: MHD Instabilities (Massachusetts Institute of Technology Press, Cambridge 1978)Google Scholar
  17. 10.17
    V.D. Shafranov: Hydromagnetic Stability of a Current Carrying Pinch in a Strong Longitudinal Magnetic Field, Sov. Phys. Tech. Phys. 15, 175 (1970)ADSGoogle Scholar
  18. 10.18
    J.P. Goedbloed: Lecture Notes on Ideal Magnetohydrodynamics (Rijnhuizen Report 83–145, FOM-Instituut Voor Plasmaphysica, Nederland 1983) p. 149Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Kyoji Nishikawa
    • 1
  • Masahiro Wakatani
    • 2
  1. 1.Faculty of EngineeringKinki UniversityTakaya, Higashihiroshima, HiroshimaJapan
  2. 2.Graduate School of Energy ScienceKyoto UniversityGakasho, Uji, KyotoJapan

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