Advertisement

Electrostatic Waves and Instabilities in Homogeneous, Magnetized Plasmas

  • J. J. Rasmussen
Part of the CISM International Centre for Mechanical Sciences book series (CISM, volume 349)

Abstract

The linear theory of electrostatic waves in homogeneous, unmagnetized as well as magnetized plasmas will be presented. The dispersion relation for the different wave types will be derived on the basis of a fluid theory and a kinetic theory. Particular attention will be payed to ion acoustic waves and ion cyclotron waves in the low frequency regime, and to electron plasma waves (“Langmuir waves”) and electron Bernstein waves in the high frequency regime. Different instabilities leading to the excitation of these waves will be discussed. Here the emphasis will be on beam instabilities, e.g. the ion beam instability and the electron beam instability, and on the current driven instabilities, e.g. the current driven ion acoustic waves and ion cyclotron waves. The importance of the different waves and instabilities for the dynamical behaviour of the plasma will be illustrated by examples from laboratory experiments and space observations.

Keywords

Dispersion Relation Langmuir Wave Electrostatic Wave Unmagnetized Plasma Electron Plasma Wave 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    T.H. Stix, The Theory of Plasma Waves, McGraw—Hill, New York 1962; T.H. Stix, Waves in Plasmas, American Institute of Physics, 1992.Google Scholar
  2. [2]
    T.J.M. Boyd and J.J. Sanderson, Plasma Dynamics, Nelson, London 1969.Google Scholar
  3. [3]
    F.F. Chen Introduction to Plasma Physics and Controlled Fusion, Vol, 1. Second Edition, Plenum Press, New York 1984.CrossRefGoogle Scholar
  4. [4]
    D.R. Nicholson, Introduction to Plasma Theory, John Wiley and Sons, New York 1983.Google Scholar
  5. [5]
    G. Schmidt, Physics of High Temperature Plasmas, Second Edition, Academic Press, New York 1979.Google Scholar
  6. [6]
    D.G. Swanson, Plasma Waves, Academic Press, San Diego 1989CrossRefGoogle Scholar
  7. [7]
    D.C. Montgomery, Theory of the Unmagnetized Plasma, Gordon and Breach Science Publishers, New York 1971.Google Scholar
  8. [8]
    W.D. Jones, H.J. Doucet and J.M Buzzi, An Introduction to Linear Theories and Methods of Electrostatic Waves in Plasmas, Plenum Press, New York 1985.CrossRefGoogle Scholar
  9. [9]
    A.W. Trivelpiece, Slow-Wave Propagation in Plasma Waveguides, San Francisco Press, Inc. 1967.Google Scholar
  10. A.B. Mikhailovskii, Theory of Plasma Instabilities, Vol. 1, Instabilities of a Homogeneous Plasma,Consultants Bureau, New York, 1974; Theory of Plasma Instabilities, Vol. 2, Instabilities of an Inhomogeneous Plasma,Consultants Bureau, New York, 1974.Google Scholar
  11. [11]
    F.F. Cap, Handbook on Plasma Instabilities, Academic Press, New York, Vol. 1, 1976; Vol. 2, 1978.Google Scholar
  12. [12]
    A. Hasegawa, Plasma Instabilities and Nonlinear Effects, Springer-Verlag, Berlin Heidelberg New York 1975.CrossRefGoogle Scholar
  13. [13]
    D.B. Melrose, Instabilities in Space and Laboratory Plasmas, Cambridge University Press, Cambridge 1986.CrossRefGoogle Scholar
  14. [14]
    M.V. Nezlin, Physics of Intense Beams in Plasmas, Institute of Physics Publishing, Bristol 1993.Google Scholar
  15. [15]
    R.W Motley, Q-Machines, Academic Press, New York, San Francisco, London 1975.Google Scholar
  16. [16]
    H.L. Pécseli, IEEE Trans. Plasma Sci. PS-13. 53 (1985).Google Scholar
  17. [17]
    H. Okuda and J.M. Dawson, Phys. Fluids 16, 408 (1973).ADSCrossRefGoogle Scholar
  18. [18]
    P. Michelsen, Riso Report R-417, 1980.Google Scholar
  19. [19]
    H.L. Pécseli, J. Juul Rasmussen, H. Sugai and K. Thomsen, Plasma Phys. ‘Controlled Fusion 26, 1021 (1984).ADSCrossRefGoogle Scholar
  20. [20]
    P. Michelsen, H.L. Pécseli and J. Juul Rasmussen, Plasma Phys. 20, 45 (1978).ADSCrossRefGoogle Scholar
  21. [21]
    I.S. Gradshteyn and I.M. Ryzhik, Table of Integrals, Series and Products, Academic Press, New York 1980.MATHGoogle Scholar
  22. [22]
    B.D. Fried and S.D. Conte, The Plasma Dispersion Function, Academic Press, New York, 1961.Google Scholar
  23. [23]
    I.B. Bernstein, Phys. Rev. 109, 10 (1958).ADSCrossRefMATHMathSciNetGoogle Scholar
  24. [24]
    F.W. Crawford and J.A. Tataronis, J. Appl. Phys. 36, 2930 (1965).ADSCrossRefGoogle Scholar
  25. [25]
    R.J. Armstrong, J.Juul Rasmussen, R.L. Stenzel and J. Trulsen, Phys. Lett. 85A, 281 (1981).CrossRefGoogle Scholar
  26. [26]
    R.J. Armstrong, A. Frederiksen, H.L. Pécseli and J. Trulsen, Plasma Phys. Controlled Fusion 26, 703 (1984).ADSCrossRefGoogle Scholar
  27. [27]
    E. Ault and H. Ikezi, Phys. Fluids 13, 2874 (1970).ADSCrossRefGoogle Scholar
  28. [28]
    J.P.M. Schmitt, Phys. Rev. Lett. 31, 982 (1973).ADSCrossRefGoogle Scholar
  29. [29]
    O. Penrose, Phys. Fluids 3, 258 (1960).ADSCrossRefMATHGoogle Scholar
  30. [30]
    B.D. Fried and A.Y. Wong, Phys. Fluids 9, 1084 (1966).ADSCrossRefGoogle Scholar
  31. [31]
    O. Buneman. Phys. Rev.. Lett. 1, 8 (1958); Phys. Rev. 115, 503 (1959).Google Scholar
  32. [32]
    T.D. Mantei, F. Doveil, D. Grésillon, Plasma Phys. 18, 705 (1976).ADSCrossRefGoogle Scholar
  33. [33]
    J.R. Pierce, J. Appl. Phys. 15, 571 (1944).Google Scholar
  34. [34] S. Iizuka, K. Saeki, N. Sato and Y.Hatta, J. Phys. Soc. Jpn. 52, 1618 (1983).
    J. Phys. Soc. Jpn. 54, 146 (1985).CrossRefGoogle Scholar
  35. [35]
    S. Kuhn. 4th Symp. Double Layers, Innsbruck, Austria July 1992. (ed. R. Schrittwieser) World Scientific, Singapore 1993; Inv. paper Spring Meeting of the German Physical Society, Greifswald, Germany, March 1993; T.L. Crystal and S.Kuhn, Phys. Fluids 28, 2116 (1985).Google Scholar
  36. [36]
    S. Iizuka, P. Michelsen, J. Juul Rasmussen, R. Schrittwieser, R. Hatakeyama, K. Saeki and N. Sato, J. Phys. Soc. Jpn. 54, 2516 (1985).Google Scholar
  37. [37]
    D. Grésillon and F. Doveil, Phys. Rev. Lett. 34, 77 (1975).ADSCrossRefGoogle Scholar
  38. [38]
    E.G. Harris, J. Nucl. Energy, Part C, Plasma Phys. 2, 138 (1961).CrossRefGoogle Scholar
  39. [39]
    J. Juul Rasmussen and R.W. Schrittwieser, IEEE Trans. Plasma Sci. 19, 457 (1991).CrossRefGoogle Scholar
  40. [40]
    N. D’Angelo and R.W. Motley, Phys. Fluids 5, 633 (1962);ADSCrossRefGoogle Scholar
  41. R.W. Motley and N. D’Angelo, Phys. Fluids 6, 296 (1963).ADSCrossRefGoogle Scholar
  42. [41]
    J.M. Kindel and C.F. Kennel, J. Geophys. Res. 76, 3055 (1971).ADSCrossRefGoogle Scholar
  43. [42]
    D.L. Correll, N. Rynn and H. Böhmer, Phys. Fluids 18, 1800 (1975).ADSCrossRefGoogle Scholar
  44. [43]
    P. Michelsen Phys. Fluids 19, 337 (1976).ADSCrossRefGoogle Scholar
  45. [44]
    P. Michelsen, H.L. Pécseli and J. Juul Rasmussen, Phys. Fluids 20, 866 (1977).ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Wien 1994

Authors and Affiliations

  • J. J. Rasmussen
    • 1
  1. 1.Risø National LaboratoryRoskildeDenmark

Personalised recommendations