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

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


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.


Alpha Particle Vlasov Equation Trap Particle Langmuir Wave Collision Term 
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  1. [1]
    Montgomery, D.C. and Tidman, D.A.: Plasma Kinetic Theory, MacGraw-Hill, New York 1964.Google Scholar
  2. [2]
    Sanderson, J.J.: Kinetic Theory, in: Plasma Physics and Nuclear Fusion Research (Ed. R.D. Gill), Academic Press, London 1981, 119–154.CrossRefGoogle Scholar
  3. [3]
    Krall, N.A. and Trivelpiece, A.W.: Principles of Plasma Physics, MacGraw-Hill, New York 1973.Google Scholar
  4. [4]
    Wesson, J.: Tokamaks, Oxford Science Publications, Oxford 1987.Google Scholar
  5. [5]
    Vlasov, A.A.: J. Phys. (USSR), 8 (1938), 25.Google Scholar
  6. [6]
    Landau, L.L.: J. Phys. (USSR), 10 (1946), 25.MATHGoogle Scholar
  7. [7]
    Goldstein, H.: Classical Mechanics, Addison-Wesley, Reading, Mass. 1951.Google Scholar
  8. [8]
    O’Neil, T.M.: Collisionless damping of nonlinear plasma oscillations, Phys. Fluids, 8 (1965), 2255–2262.ADSCrossRefMathSciNetGoogle Scholar
  9. [9]
    Rosenbluth, M.N.: Microinstabilities, in: Plasma Physics (Seminar, Trieste, 1964 ), IAEA, Vienna 1965, 485–513.Google Scholar
  10. [10]
    Drummond, W.E. and Pines, D.: Nonlinear stability of plasma oscillations, Nucl. Fusion, Suppl. Pt. 3 (1962), 1049–1057.Google Scholar
  11. [11]
    Vedenov, A.A., Velikhov, E.P. and Sagdeev, R.Z.: Nonlinear oscillations of rarified plasma, Nucl. Fusion, 1 (1961), 82–100.CrossRefGoogle Scholar
  12. [12]
    Tsunoda, T.I., Doveil, F. and Malmberg, J.H.: Experimental test of quasilinear theory, Phys. Fluids, B 3 (1991), 2747–2757.CrossRefGoogle Scholar
  13. [13]
    T.H.Stix, Waves in Plasmas, American Institute of Physics, New York 1992.Google Scholar
  14. [14] Vedenov, A.A.: Introduction to the Theory of a Weak-Turbulent Plasma (in Russian)
    in: Voprosy teorii plasmy 3, Gosatomizdat, Moscow 1963, 203–244.Google Scholar
  15. [15]
    Zaslayskii, G.M.: Stochasticity of Dynamical Systems (in Russian), Nauka, Moscow 1984.Google Scholar
  16. [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.CrossRefGoogle Scholar
  17. [17]
    Laval, G. and Pesme, D.: Inconsistency of quasilinear theory, Phys. Fluids, 26 (1983), 66–68.ADSCrossRefMATHGoogle Scholar
  18. [18]
    Laval, G. and Pesme, P.: Self-consistency effects in quasilinear theory: a model for turbulent trapping, Phys. Rev. Lett., 53 (1984), 270–273.ADSCrossRefGoogle Scholar
  19. [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.ADSCrossRefGoogle Scholar
  20. [20]
    Cook, I.: Plasma Turbulence, in: Plasma Physics and Nuclear Fusion Research (Ed. R.D.Gill), Academic Press, London 1981, 293–304.CrossRefGoogle Scholar
  21. [21]
    Dupreé, T.H.: A perturbation theory for strong plasma turbulence, Phys. Fluids, 9 (1966), 1773–1782.ADSCrossRefGoogle Scholar
  22. [22]
    Akchiezer, A.I.: Plasma Electrodynamics (in Russian), Nauka, Moscow 1974.Google Scholar
  23. [23]
    Brambilla, M. and Cardinali, A.: Eikonal description of hf waves in toroidal plasmas, Plasma Physics, 24 (1982), 1187–1218.ADSCrossRefMathSciNetGoogle Scholar
  24. [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.ADSCrossRefGoogle Scholar
  25. [25]
    Bonoli P.T. and Ott, E.: Toroidal and scattering effects in lower-hybrid wave propagation, Phys. Fluids, 25 (1982), 359–375.ADSCrossRefMATHGoogle Scholar
  26. [26]
    Fisch, N.J.: Confining a tokamak plasma with rf-driven currents, Phys. Rev. Lett., 41 (1978). 873–876.ADSCrossRefGoogle Scholar
  27. [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. [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. [29]
    Barbato, E. and Santiti, F.: Quasi-linear absorption of lower hybrid waves by fusion generated alpha particles, Nucl. Fusion, 31 (1991), 673–685.CrossRefGoogle Scholar
  30. [30]
    Spada, M., Bornatici, M. and Engelmann, F.: Absorption of lower hybrid slow waves by fusion alpha particles, Nucl. Fusion, 31 (1991), 447–458.CrossRefGoogle Scholar
  31. [31]
    Chen, L., Vaclavik, J. and Hammet, G.W.: Ion radial transport induced by ICRF waves in tokamaks, Nucl. Fusion, 28 (1988), 389–398.CrossRefGoogle Scholar
  32. [32]
    Lichtenberg, A.J. and Lieberman, M.A.: Regular and Stochastic Motion, Springer, Berlin 1983.CrossRefMATHGoogle Scholar
  33. [33]
    Balescu, R.: Equilibrium and Nonequilibrium Statistical Mechanics, Wiley, New York 1978.Google Scholar
  34. [34]
    Whiteman, K.J.: Invariants and stability in classical mechanics, Rep. Progr. Phys., 40 (1977), 1033–1069.ADSCrossRefGoogle Scholar
  35. [35]
    Krlín, L.: The intrinsic stochasticity of near-integrable Hamiltonian systems, Fortschr. Phys., 37 (1989), 735–760.CrossRefMathSciNetGoogle Scholar
  36. [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. [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.CrossRefGoogle Scholar
  38. [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. [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.CrossRefGoogle Scholar
  40. [40]
    Sagdeev, R.Z. and Galeev, A.A.: Nonlinear Plasma Theory, Benjamin, New York 1969.Google Scholar
  41. [41]
    Manley, J.M. and Rowe, H.E., Proc. IRE, 47 (1959), 2155.Google Scholar
  42. [42]
    Kadomtsev, B.B.: Collective Phenomena in Plasmas (in Russian), Nauka, Moscow 1976.Google Scholar
  43. [43]
    Davidson, R.C.: Methods in Nonlinear Plasma Theory, Academic Press, New York 1972.Google Scholar
  44. [44]
    Ott, E. and Dum, C.T.: Nonlinear Landau damping and beat wave trapping, Phys. Fluids, 14 (1971), 959–961.ADSCrossRefGoogle Scholar
  45. [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.ADSCrossRefGoogle Scholar
  46. [46]
    Krlín, L.: Application of the theory of mixing systems to nonlinear Landau damping, J. Plasma Phys., 12, part 3 (1974), 365–379.ADSCrossRefGoogle Scholar
  47. [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.CrossRefGoogle Scholar
  48. [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. [49]
    Nambu, M., Sarma, S.N. and Sarma, K.K.: Momentum source of the plasma maser, Phys. Rev., A 45 (1992), 7456–7462.ADSCrossRefGoogle Scholar
  50. [50]
    Krlín, L.: On acceleration of particles trapped in the potential trough of the beat of two waves, Plasma Physics, 245 (1982), 775–781.ADSCrossRefGoogle Scholar
  51. [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. [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. [53]
    Tajima, T. and Dawson, J.M.: Laser electron accelerator, Phys. Rev. Lett., 43 (1979), 267–270.ADSCrossRefGoogle Scholar
  54. [54]
    Mikhailovskii, A.B.: Theory of Plasma Instabilities (in Russian), Atomizdat, Moscow 1970.Google Scholar
  55. [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.ADSCrossRefGoogle Scholar
  56. [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.ADSCrossRefGoogle Scholar
  57. [57]
    Jungwirth, K. and Krlín, L.: Generation of an intensive stationary wave in modulated beam-plasma systems, Plasma Physics, 17 (1975), 861–873.ADSCrossRefGoogle Scholar
  58. [58]
    Kruer, W.L., Dawson, J.M. and Sudan, R.N.: Trapped-particle instability, Phys. Rev. Lett., 23 (1969), 838–841.ADSCrossRefGoogle Scholar
  59. [59]
    Krlín, L.: On the instability of systems with trapped particles, Plasma Physics, 19 (1977), 109–115.ADSGoogle Scholar
  60. [60]
    Shoucri, M.: Destruction of trapping oscillations by sideband instability, Phys. Fluids, 23 (1980), 2030–2033.ADSCrossRefGoogle Scholar
  61. [61]
    Riyopoulos, S. and Tang, C.M.: Chaotic electron motion caused by sidebands in free electron lasers, Phys. Fluids, 31 (1988), 3387–3402.ADSCrossRefGoogle Scholar
  62. [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. [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.ADSCrossRefGoogle Scholar
  64. [64]
    Drummond, W.E.: Quasi-Linear Theory of Plasma Turbulence, in: Plasma Physics (Seminar, Trieste, 1964 ), IAEA, Vienna 1965, 527–541.Google Scholar
  65. [65]
    Chen, F.F.: Introduction to Plasma Physics, Plenum Press, New York and London 1974.Google Scholar
  66. [66]
    Fisch, N.J.: Theory of current drive in plasmas, Rev. Mod. Phys., 59 (1987), 175–234.ADSCrossRefGoogle Scholar
  67. [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

Copyright information

© Springer-Verlag Wien 1994

Authors and Affiliations

  • L. Krlìn
    • 1
  1. 1.Academy of Sciences of the Czech RepublicPragueCzech Republic

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