Skip to main content

Basic Features of the Kinetic Theory of Plasma Waves and of Waves-Particles Interaction

  • Chapter
Waves and Instabilities in Plasmas

Part of the book series: CISM International Centre for Mechanical Sciences ((CISM,volume 349))

  • 224 Accesses

Abstract

In the following lectures, a brief introduction into the kinetic theory of plasma waves and into the interaction of waves with plasma particles is presented.

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

Access this chapter

eBook
USD 16.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 16.99
Price excludes VAT (USA)
  • Compact, lightweight 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.

References

  1. Montgomery, D.C. and Tidman, D.A.: Plasma Kinetic Theory, MacGraw-Hill, New York 1964.

    Google Scholar 

  2. Sanderson, J.J.: Kinetic Theory, in: Plasma Physics and Nuclear Fusion Research (Ed. R.D. Gill), Academic Press, London 1981, 119–154.

    Chapter  Google Scholar 

  3. Krall, N.A. and Trivelpiece, A.W.: Principles of Plasma Physics, MacGraw-Hill, New York 1973.

    Google Scholar 

  4. Wesson, J.: Tokamaks, Oxford Science Publications, Oxford 1987.

    Google Scholar 

  5. Vlasov, A.A.: J. Phys. (USSR), 8 (1938), 25.

    Google Scholar 

  6. Landau, L.L.: J. Phys. (USSR), 10 (1946), 25.

    MATH  Google Scholar 

  7. Goldstein, H.: Classical Mechanics, Addison-Wesley, Reading, Mass. 1951.

    Google Scholar 

  8. O’Neil, T.M.: Collisionless damping of nonlinear plasma oscillations, Phys. Fluids, 8 (1965), 2255–2262.

    Article  ADS  MathSciNet  Google Scholar 

  9. Rosenbluth, M.N.: Microinstabilities, in: Plasma Physics (Seminar, Trieste, 1964 ), IAEA, Vienna 1965, 485–513.

    Google Scholar 

  10. Drummond, W.E. and Pines, D.: Nonlinear stability of plasma oscillations, Nucl. Fusion, Suppl. Pt. 3 (1962), 1049–1057.

    Google Scholar 

  11. Vedenov, A.A., Velikhov, E.P. and Sagdeev, R.Z.: Nonlinear oscillations of rarified plasma, Nucl. Fusion, 1 (1961), 82–100.

    Article  Google Scholar 

  12. Tsunoda, T.I., Doveil, F. and Malmberg, J.H.: Experimental test of quasilinear theory, Phys. Fluids, B 3 (1991), 2747–2757.

    Article  Google Scholar 

  13. T.H.Stix, Waves in Plasmas, American Institute of Physics, New York 1992.

    Google Scholar 

  14. in: Voprosy teorii plasmy 3, Gosatomizdat, Moscow 1963, 203–244.

    Google Scholar 

  15. Zaslayskii, G.M.: Stochasticity of Dynamical Systems (in Russian), Nauka, Moscow 1984.

    Google Scholar 

  16. Cary, J.R., Doxas, I., Escande, D.F. and Verga, A.D.: Enhancement of the velocity diffusion in longitudinal plasma turbulence, Phys. Fluids, B 4, (1992), 2062–2069.

    Article  Google Scholar 

  17. Laval, G. and Pesme, D.: Inconsistency of quasilinear theory, Phys. Fluids, 26 (1983), 66–68.

    Article  ADS  MATH  Google Scholar 

  18. Laval, G. and Pesme, P.: Self-consistency effects in quasilinear theory: a model for turbulent trapping, Phys. Rev. Lett., 53 (1984), 270–273.

    Article  ADS  Google Scholar 

  19. Cary, J.M., Escande, D.F. and Verga, A.D.: Nonquasilinear diffusion far from the chaotic threshold, Phys. Rev. Lett., 65 (1990), 3132–3135.

    Article  ADS  Google Scholar 

  20. Cook, I.: Plasma Turbulence, in: Plasma Physics and Nuclear Fusion Research (Ed. R.D.Gill), Academic Press, London 1981, 293–304.

    Chapter  Google Scholar 

  21. Dupreé, T.H.: A perturbation theory for strong plasma turbulence, Phys. Fluids, 9 (1966), 1773–1782.

    Article  ADS  Google Scholar 

  22. Akchiezer, A.I.: Plasma Electrodynamics (in Russian), Nauka, Moscow 1974.

    Google Scholar 

  23. Brambilla, M. and Cardinali, A.: Eikonal description of hf waves in toroidal plasmas, Plasma Physics, 24 (1982), 1187–1218.

    Article  ADS  MathSciNet  Google Scholar 

  24. Wersinger, J.M., Ott, E. and Finn, J.M.: Ergodic behavior of lower hybrid decay wave ray trajectories in toroidal geometry, Phys. Fluids, 21 (1978), 2263–2267.

    Article  ADS  Google Scholar 

  25. Bonoli P.T. and Ott, E.: Toroidal and scattering effects in lower-hybrid wave propagation, Phys. Fluids, 25 (1982), 359–375.

    Article  ADS  MATH  Google Scholar 

  26. Fisch, N.J.: Confining a tokamak plasma with rf-driven currents, Phys. Rev. Lett., 41 (1978). 873–876.

    Article  ADS  Google Scholar 

  27. Pavlo, P., Krlín L. and Thtor, Z.: Effects of magnetized alpha particles on lower hybrid heating and current drive in a reactor grade plasma, Nucl. Fusion, 31 (1991), 711–727; ITER-IL-Ph-6–9-S-23, Max-Planck-Institut fuer Plasma Physik, Garching, 1991.

    Google Scholar 

  28. Klíma, R. and Longinov, A.V.: Excitation of a stationary current in a toroidal plasma by waves with a wide spectrum, Fiz. Plazmy, 5 (1979), 496–500.

    Google Scholar 

  29. Barbato, E. and Santiti, F.: Quasi-linear absorption of lower hybrid waves by fusion generated alpha particles, Nucl. Fusion, 31 (1991), 673–685.

    Article  Google Scholar 

  30. Spada, M., Bornatici, M. and Engelmann, F.: Absorption of lower hybrid slow waves by fusion alpha particles, Nucl. Fusion, 31 (1991), 447–458.

    Article  Google Scholar 

  31. Chen, L., Vaclavik, J. and Hammet, G.W.: Ion radial transport induced by ICRF waves in tokamaks, Nucl. Fusion, 28 (1988), 389–398.

    Article  Google Scholar 

  32. Lichtenberg, A.J. and Lieberman, M.A.: Regular and Stochastic Motion, Springer, Berlin 1983.

    Book  MATH  Google Scholar 

  33. Balescu, R.: Equilibrium and Nonequilibrium Statistical Mechanics, Wiley, New York 1978.

    Google Scholar 

  34. Whiteman, K.J.: Invariants and stability in classical mechanics, Rep. Progr. Phys., 40 (1977), 1033–1069.

    Article  ADS  Google Scholar 

  35. Krlín, L.: The intrinsic stochasticity of near-integrable Hamiltonian systems, Fortschr. Phys., 37 (1989), 735–760.

    Article  MathSciNet  Google Scholar 

  36. Zaslayskii, G.M. and Chirikov, B.V.: The stochastic instability of non-linear oscillations, Uspekhi Fiz. Nauk, 105 (1971), 3–39.

    Google Scholar 

  37. Whang, K.W. and Morales, G.J.: ICRF heating and its effects on single-particle confinement in tokamaks, Nucl. Fusion, 23 (1983), 481–497.

    Article  Google Scholar 

  38. Krlín, L., Pavlo, P., Tluchor, Z. and Gâsek, Z.: On the stochastic interaction of monochromatic Alfén waves with toroidally trapped particles, Plasma Physics and Contr. Fusion, 29 (1987), 1653–1674.

    Google Scholar 

  39. Gssek, Z., Krlín, L. and Tluchor, Z.: On the stochastic interaction of toroidally trapped alpha particles with lower hybrid waves in the tokamak reactor regime, Physics Letters, 135 (1989), 284–289.

    Article  Google Scholar 

  40. Sagdeev, R.Z. and Galeev, A.A.: Nonlinear Plasma Theory, Benjamin, New York 1969.

    Google Scholar 

  41. Manley, J.M. and Rowe, H.E., Proc. IRE, 47 (1959), 2155.

    Google Scholar 

  42. Kadomtsev, B.B.: Collective Phenomena in Plasmas (in Russian), Nauka, Moscow 1976.

    Google Scholar 

  43. Davidson, R.C.: Methods in Nonlinear Plasma Theory, Academic Press, New York 1972.

    Google Scholar 

  44. Ott, E. and Dum, C.T.: Nonlinear Landau damping and beat wave trapping, Phys. Fluids, 14 (1971), 959–961.

    Article  ADS  Google Scholar 

  45. Mima, K.: Modification of weak turbulent theory due to perturbed orbit effects. II. Nonlinear Landau damping of electron plasma waves, J. Phys. Soc. Jap., 35 (1973), 261–271.

    Article  ADS  Google Scholar 

  46. Krlín, L.: Application of the theory of mixing systems to nonlinear Landau damping, J. Plasma Phys., 12, part 3 (1974), 365–379.

    Article  ADS  Google Scholar 

  47. hrlín, L.: Effect of trapped particles in the beat of two waves on the wave dynamics, Czech. J. Phys. B, 31 (1981), 383–398.

    Article  Google Scholar 

  48. Nambu, M. and Hada, T.: Conservation relations and violation of the Manley-Rowe relation for plasma-maser instability, Phys. Fluids, B 3 (1993), 743–751.

    Google Scholar 

  49. Nambu, M., Sarma, S.N. and Sarma, K.K.: Momentum source of the plasma maser, Phys. Rev., A 45 (1992), 7456–7462.

    Article  ADS  Google Scholar 

  50. Krlín, L.: On acceleration of particles trapped in the potential trough of the beat of two waves, Plasma Physics, 245 (1982), 775–781.

    Article  ADS  Google Scholar 

  51. Srivastava, S. and Morales, G.J.: Nonlinear Landau damping of resonantly excited plasma waves in a nonuniform plasma, Bull. Am. Phys. Soc., 34 (1989), 2025.

    Google Scholar 

  52. Srivastava, S., Morales, G.J. and Maggs, J.E.: Nonlinear Landau damping of resonantly excited fields in nonuniform plasmas, Bull. Am. Phy. Soc., 37 (1992), 1359.

    Google Scholar 

  53. Tajima, T. and Dawson, J.M.: Laser electron accelerator, Phys. Rev. Lett., 43 (1979), 267–270.

    Article  ADS  Google Scholar 

  54. Mikhailovskii, A.B.: Theory of Plasma Instabilities (in Russian), Atomizdat, Moscow 1970.

    Google Scholar 

  55. O’Neil, T.M. and Winfrey, J.H.: Nonlinear interaction of a small cold beam and a plasma, part II, Phys. Fluids, 15 (1972), 1514–1522.

    Article  ADS  Google Scholar 

  56. Drummond, W.E., Malmberg, J.H., O’Neil, T.M. and Thompson, J.R.: Nonlinear development of the beam-plasma instability, Phys. Fluids, 13 (1970), 2422–2425.

    Article  ADS  Google Scholar 

  57. Jungwirth, K. and Krlín, L.: Generation of an intensive stationary wave in modulated beam-plasma systems, Plasma Physics, 17 (1975), 861–873.

    Article  ADS  Google Scholar 

  58. Kruer, W.L., Dawson, J.M. and Sudan, R.N.: Trapped-particle instability, Phys. Rev. Lett., 23 (1969), 838–841.

    Article  ADS  Google Scholar 

  59. Krlín, L.: On the instability of systems with trapped particles, Plasma Physics, 19 (1977), 109–115.

    ADS  Google Scholar 

  60. Shoucri, M.: Destruction of trapping oscillations by sideband instability, Phys. Fluids, 23 (1980), 2030–2033.

    Article  ADS  Google Scholar 

  61. Riyopoulos, S. and Tang, C.M.: Chaotic electron motion caused by sidebands in free electron lasers, Phys. Fluids, 31 (1988), 3387–3402.

    Article  ADS  Google Scholar 

  62. Cohen, B.I. and Cohen, R.H.: An electromagnetic trapped-particle sideband instability, Preprint UCRL-98746, Lawrence Livermore National Laboratory, 1988.

    Google Scholar 

  63. Guss, W.C., Basen, M.A., Kreischer, K.E., Temkin, R.J., Antonsen, T.A., Cai, Jr., S.Y., Saraph, C. and Levush, B.: Sideband mode competition in a gyrotron oscillator, Phys. Rev. Lett., 69 (1992), 3727–3730.

    Article  ADS  Google Scholar 

  64. Drummond, W.E.: Quasi-Linear Theory of Plasma Turbulence, in: Plasma Physics (Seminar, Trieste, 1964 ), IAEA, Vienna 1965, 527–541.

    Google Scholar 

  65. Chen, F.F.: Introduction to Plasma Physics, Plenum Press, New York and London 1974.

    Google Scholar 

  66. Fisch, N.J.: Theory of current drive in plasmas, Rev. Mod. Phys., 59 (1987), 175–234.

    Article  ADS  Google Scholar 

  67. Pifl, V., Sunka, P., Ullschmied, J., Jungwirth, K. and Krlín, L.: Some non-linear phenomena associated with high-frequency beam-plasma instabilities, Plasma Physics and Controlled Nuclear Fusion Research (1971), IAEA, Vienna 1972, 155–163.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1994 Springer-Verlag Wien

About this chapter

Cite this chapter

Krlìn, L. (1994). Basic Features of the Kinetic Theory of Plasma Waves and of Waves-Particles Interaction. In: Cap, F. (eds) Waves and Instabilities in Plasmas. CISM International Centre for Mechanical Sciences, vol 349. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2700-1_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-7091-2700-1_2

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-211-82636-2

  • Online ISBN: 978-3-7091-2700-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics