Skip to main content

Part of the book series: Mathematical Sciences Research Institute Publications ((MSRI,volume 2))

  • 1468 Accesses

Abstract

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).

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  1. W. Crookes, PhiL Trans. 1, (1879), 135.

    Article  Google Scholar 

  2. See e.g. Jackson, J.D., Classical Electrodynamics, 2nd edition, John Wiley and Sons Inc., New York (1975).

    MATH  Google Scholar 

  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. See e.g. S. Wollman, Comm. Pure Appl. Math 33 (1980) 173–197.

    Article  MathSciNet  MATH  Google Scholar 

  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.

    Article  Google Scholar 

  6. N.J. Zabusky, Ann, N.Y. Acad. Sci. 373 (1981), 160–170.

    Article  Google Scholar 

  7. V. Arnold, Annales de l’Institut Fourier 16 (1966), 319–361.

    Article  Google Scholar 

  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. 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.

    Article  MATH  Google Scholar 

  10. P.J. Morrison, Phys. Lett. 80A, (1980), 383.

    Google Scholar 

  11. A Weinstein and P.J. Morrison, Phys. Lett. 86A, (1981), 235.

    MathSciNet  Google Scholar 

  12. J. Marsden and A. Weinstein, “The Hamiltonian structure of the Maxwell-Vlasov equations”, Physica D 4, (1982), 394.

    Article  MathSciNet  MATH  Google Scholar 

  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. G.A. Goldin, R. Menikoff and D. J. Sharp, J. Math. Phys. 21 (1980), 650.

    Article  MathSciNet  MATH  Google Scholar 

  15. C.S. Gardner, J. Math. Phys. 12 (1971), 1548. V.E. Zakharov and L.D. Faddeev, Funct. Anal. Appl. 5 (1971), 280.

    Article  MATH  Google Scholar 

  16. J.D. Jackson, J. Nuclear Energy C 1 (1960), 171.

    Article  Google Scholar 

  17. L.D. Landau, J. Phys. U.S.S.R. 10, (1946), 25.

    Google Scholar 

  18. N.G. Van Kampen, Physica 21 (1955), 949.

    Article  MathSciNet  Google Scholar 

  19. O. Penrose, Phys. Fluids 3 (1960), 258.

    Article  MATH  Google Scholar 

  20. I.B. Bernstein, J.M. Greene, M.D. Kruskal, Phys. Rev. 108 (1957), 546.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1984 Springer Science+Business Media New York

About this paper

Cite this paper

Weinstein, A. (1984). Equations of Plasma Physics. In: Chern, S.S. (eds) Seminar on Nonlinear Partial Differential Equations. Mathematical Sciences Research Institute Publications, vol 2. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1110-5_18

Download citation

  • DOI: https://doi.org/10.1007/978-1-4612-1110-5_18

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-7013-3

  • Online ISBN: 978-1-4612-1110-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics