Equations of Plasma Physics

  • Alan Weinstein
Conference paper
Part of the Mathematical Sciences Research Institute Publications book series (MSRI, volume 2)


A plasma is a gas of charged particles under conditions where collective electromagnetic interactions dominate over interactions between individual particles. Plasmas have been called the fourth state of matter [1]. As one adds heat to a solid, it undergoes a phase transition (melting) to become a liquid. More heat causes the liquid to boil into a gas. Adding still more energy causes the gas to ionize (i.e. some of the negative electrons become dissociated from their gas atoms, leaving positively charged ions). Above 100,000 °K, most matter ionizes into a plasma. While the earth is a relatively plasma-free bubble (aside from fluorescent lights, lightning discharges, and magnetic fusion energy experiments) 99.9% of the universe is in the plasma state (e.g. stars and most of interstellar space).


Poisson Bracket Poisson Structure Lightning Discharge Momentum Mapping Coadjoint Orbit 
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]
    W. Crookes, PhiL Trans. 1, (1879), 135.CrossRefGoogle Scholar
  2. [2]
    See e.g. Jackson, J.D., Classical Electrodynamics, 2nd edition, John Wiley and Sons Inc., New York (1975).MATHGoogle Scholar
  3. [3]
    Some general references on plasma physics are: Introductory: F. Chen, Introduction to Plasma Physics, Plenum, New York (1974). More Advanced: P.C. Clemmow and J.P. Dougherty, Electrodynamics of Particles and Plasmas, Addison-Wesley, Reading, Mass. (1969). N. Krall and A. Trivelpiece, Principles of Plasma Physics. McGraw-Hill, New York, (1973). G. Schmidt, Physics of High Temperature Plasmas, Academic Press, New York, (1979). S. Ichimaru, Basic Principles of Plasma Physics, W.A. Benjamin, Inc., Reading, Mass. (1973). R.C. Davidson, Methods in Nonlinear Plasma Theory, Academic Press, New York, (1972).Google Scholar
  4. [4]
    See e.g. S. Wollman, Comm. Pure Appl. Math 33 (1980) 173–197.MathSciNetMATHCrossRefGoogle Scholar
  5. [5]
    F. Hohl and M.R. Feix, Astrophys. J. 147, (1967), 1164. H.L. Berk, C.E. Nielson and K.V. Roberts, Phys. Fluids 13 (1970), 980.CrossRefGoogle Scholar
  6. [6]
    N.J. Zabusky, Ann, N.Y. Acad. Sci. 373 (1981), 160–170.CrossRefGoogle Scholar
  7. [7]
    V. Arnold, Annales de l’Institut Fourier 16 (1966), 319–361.CrossRefGoogle Scholar
  8. [8]
    A. Weinstein, “The local structure of Poisson manifolds”, J. Diff. Geom., to appear (1983). S. Lie, Theorie der Transformationgruppen, Zweiter Abschnitt, Teubner, Leipzig (1890).Google Scholar
  9. [9]
    F.A. Berezin, Funct, Anal. Appl 1 (1967), 91. R. Hermann, Toda Lattices. Cosymplectic Manifolds. Bäcklund Transformations, and Kinks, Part A, Math. Sci. Press, Brookline (1977). A. Lichnerowicz, J. Diff. Geom. 12 (1977), 253.MATHCrossRefGoogle Scholar
  10. [10]
    P.J. Morrison, Phys. Lett. 80A, (1980), 383.Google Scholar
  11. [11]
    A Weinstein and P.J. Morrison, Phys. Lett. 86A, (1981), 235.MathSciNetGoogle Scholar
  12. [12]
    J. Marsden and A. Weinstein, “The Hamiltonian structure of the Maxwell-Vlasov equations”, Physica D 4, (1982), 394.MathSciNetMATHCrossRefGoogle Scholar
  13. [13]
    J.E. Marsden, T. Ratiu, and A. Weinstein, “Semi-direct Products and Reduction in Mechanics”, Trans. Amer. Math. Soc., to appear, (1983).Google Scholar
  14. [14]
    G.A. Goldin, R. Menikoff and D. J. Sharp, J. Math. Phys. 21 (1980), 650.MathSciNetMATHCrossRefGoogle Scholar
  15. [15]
    C.S. Gardner, J. Math. Phys. 12 (1971), 1548. V.E. Zakharov and L.D. Faddeev, Funct. Anal. Appl. 5 (1971), 280.MATHCrossRefGoogle Scholar
  16. [16]
    J.D. Jackson, J. Nuclear Energy C 1 (1960), 171.CrossRefGoogle Scholar
  17. [17]
    L.D. Landau, J. Phys. U.S.S.R. 10, (1946), 25.Google Scholar
  18. [18]
    N.G. Van Kampen, Physica 21 (1955), 949.MathSciNetCrossRefGoogle Scholar
  19. [19]
    O. Penrose, Phys. Fluids 3 (1960), 258.MATHCrossRefGoogle Scholar
  20. [20]
    I.B. Bernstein, J.M. Greene, M.D. Kruskal, Phys. Rev. 108 (1957), 546.MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1984

Authors and Affiliations

  • Alan Weinstein

There are no affiliations available

Personalised recommendations