Plasma Physics pp 173-204 | Cite as

Ideal Magnetohydrodynamics

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


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.


Flux Tube Magnetic Field Line Alfven Wave Magnetosonic Wave Conducting Wall 
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. 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

Personalised recommendations