Simulation of Kinetic Processes Involving Coulomb Interaction

  • Yuri N. Dnestrovskii
  • Dimitri P. Kostomarov
Part of the Springer Series in Computational Physics book series (SCIENTCOMP)

Abstract

At the beginning of this century, L. Boltzmann proposed a kinetic equation that plays an important role in the kinetic theory of gases and plasma. In deriving his equation, he relied on simple mechanical ideas about particle interactions through binary elastic collisions.

Keywords

Entropy Anisotropy Flare Lime Posite 

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References

  1. 2.1
    L.D. Landau: Zh. Eksp. Teor. Fiz. 7, 203 (1937)Google Scholar
  2. 2.2
    N.N. Bogoliubov: Problems of Dynamic Theory in Statistical Physics (Gostekhizdat, Moscow 1946) [in Russian]Google Scholar
  3. 2.3
    M.N. Rosenbluth, W.M. MacDonald, D.L. Judd: Phys. Rev.1071 (1957)CrossRefMATHADSMathSciNetGoogle Scholar
  4. 2.4
    B.A. Trubnikov: Zh. Eksp. Teor. Fiz.341341 (1958)Google Scholar
  5. 2.5
    B.A. Trubnikov: In Problems in Plasma Theory, Vol. 1 (Gosatomizdat, Moscow 1963) p. 98 [in Russian]Google Scholar
  6. 2.6
    M.H.A. Hassan, C.J.H. Watson: Plasma Phys.19237 (1977)CrossRefADSGoogle Scholar
  7. 2.7
    D.E. Baldwin, C.J.H. Watson: Plasma Phys.19517 (1977)CrossRefADSGoogle Scholar
  8. 2.8
    M.H.A. Hassan, C.J.H. Watson: Plasma Phys.19627 (1977)CrossRefADSGoogle Scholar
  9. 2.9
    K. Matsuda: Phys. Fluids261247 (1983)CrossRefMATHADSGoogle Scholar
  10. 2.10
    T. O’Neill: Phys. Fluids262128 (1983)CrossRefADSMathSciNetGoogle Scholar
  11. 2.11
    I.N. Inovenkov, D.P. Kostomarov, A.A. Lukyanitsa: In XVI International Conference on Phenomena in Ionized Gases (Düsseldorf, 1983) p. 40Google Scholar
  12. 2.12
    A.A. Arsen’ev, N.V. Peskov: Zh. Vychisl. Mat. Mat. Fiz.171063 (1977)MATHMathSciNetGoogle Scholar
  13. 2.13
    O.E. Buryak: Existence in the Whole of a Classical Solution of the Linearized Landau Equation (Preprint No. 119 of the Keldysh Inst. Appl. Math. USSR Acad. Sci., Moscow 1983) [in Russian]Google Scholar
  14. 2.14
    S. Ichimaru: Basic Principles of Plasma Physics: A Statistical Approach (Benjamin, Reading, MA 1973)Google Scholar
  15. 2.15
    N.B. Maslova, R.P. Chubenko: Vestn. LGU19100 (1973)Google Scholar
  16. 2.16
    N.B. Maslova, R.P. Chubenko: Vestn. LGU1390 (1976)Google Scholar
  17. 2.17
    L.A. Artsimovich: Usp. Fiz. Nauk91365 (1967)Google Scholar
  18. 2.18
    I.N. Golovin, Yu.N. Dnestrovskii, D.P. Kostomarov: In Nuclear Fusion Reactor Conference Proceedings (BNES, Culham 1970) p. 194Google Scholar
  19. 2.19
    Yu.N. Dnestrovskii, D.P. Kostomarov et al.: In VI European Conference on Controlled Fusion and Plasma Physics, Vol. 1 (Joint Institute for Nuclear Research, Moscow 1973) p. 41Google Scholar
  20. 2.20
    Yu.N. Dnestrovskii, D.P. Kostomarov (eds.): In Computational Methods in Plasma Physics (Mir, Moscow 1974) p. 483 [in Russian]Google Scholar
  21. 2.21
    J.G. Cordey, M.J. Houghton: Nucl. Fusion13215 (1973)CrossRefGoogle Scholar
  22. 2.22
    J.W. Connor, J.C. Cordey, Nucl. Fusion14185 (1974)CrossRefGoogle Scholar
  23. 2.23
    J.D. Callen, R.J. Colchin et al.: In Plasma Physics and Controlled Nuclear Fusion Research/Confer. Proc., Vol. 1, Tokyo, 1974 (IAEA, Vienna 1975) p. 645Google Scholar
  24. 2.24
    J.A. Rome, D.G. McAlees et al.: Nucl. Fusion1655 (1976)CrossRefADSGoogle Scholar
  25. 2.25
    N.V. Grishanov, Yu.N. Dnestrovskii et al.: Fiz Plazmy2260 (1976)Google Scholar
  26. 2.26
    Yu.N. Dnestrovskii, D.P. Kostomarov, A.P. Smirnov: Nucl. Fusion17433 (1977)CrossRefADSGoogle Scholar
  27. 2.27
    N.V. Karetkina: Vestn. MGU, Ser. 15. Vychisl. Mat. Kibern.341 (1978)MathSciNetGoogle Scholar
  28. 2.28
    N.V. Karetkina: Zh. Vychisl. Mat. Mat. Fiz.20236 (1980)MathSciNetGoogle Scholar
  29. 2.29
    A.A. Samarskii: The Theory of Difference Schemes (Nauka, Moscow 1977) [in Russian]Google Scholar
  30. 2.30
    I.V. Fryazinov: Zh. Vychisl. Mat. Mat. Fiz.111219 (1971)Google Scholar
  31. 2.31
    H. Dreicer: Phys. Rev.115238 (1959)CrossRefMATHADSMathSciNetGoogle Scholar
  32. 2.32
    H. Dreicer: Phys. Rev.117329 (1960)CrossRefMATHADSMathSciNetGoogle Scholar
  33. 2.33
    A.V. Gurevich: Zh. Eksp. Teor. Fiz.391296 (1960)Google Scholar
  34. 2.34
    M.D. Kruskal, I.B. Bernstein: Princeton Plasma Physics Laboratory, Report MATT-Q-20 (1962)Google Scholar
  35. 2.35
    A.N. Lebedev: Zh. Eksp. Teor. Fiz.481393 (1965)Google Scholar
  36. 2.36
    A.V. Gurevich, Yu.N. Zhivlyuk: Zh. Eksp. Teor. Fiz.49214 (1965)Google Scholar
  37. 2.37
    R.H. Cohen: Phys. Fluids19239 (1976)CrossRefADSGoogle Scholar
  38. 2.38
    J.W. Connor, R.J. Hastie: Nucl. Fusion15415 (1975)CrossRefADSGoogle Scholar
  39. 2.39
    R.M. Kulsrud, Y.C. Sun et al.: Phys. Rev. Lett.31690 (1973)CrossRefADSGoogle Scholar
  40. 2.40
    A.V. Gurevich, Ya.S. Dimant et al.: Fiz. Plasmy5777 (1979)Google Scholar
  41. 2.41
    N.D. Vinogradova, Yu.V. Esipchuk et al.: In Plasma Physics and Controlled Nuclear Fusion Research, Conf. Proc., Innsbruck, 1978 (IAEA, Vienna 1979)Google Scholar
  42. 2.42
    H. Knoepfel, D.A. Spong: Nucl. Fusion19785 (1979)CrossRefADSGoogle Scholar
  43. 2.43
    V.V. Parail, O.P. Pogutse: In Problems in Plasma Theory, Vol. 11 (Energoizdat, Moscow 1982) p. 5 [in Russian]Google Scholar
  44. 2.44
    A.V. Gurevich: Zh. Eksp. Teor. Fiz.401825 (1961)Google Scholar
  45. 2.45
    H.F. Furth, P.H. Rutherford: Phys. Rev. Lett.28545 (1972)CrossRefADSGoogle Scholar
  46. 2.46
    A.A. Vedenov, E.P. Velikhov, R.Z. Sagdeev: Nuclear Fusion 182(1961)Google Scholar
  47. 2.47
    V.L. Yakimenko: Zh. Eksp. Teor. Fiz.441534 (1963)Google Scholar
  48. 2.48
    C.F. Kennel, F. Engelmann: Phys. Fluids92377 (1966)CrossRefADSGoogle Scholar
  49. 2.49
    T.H. Stix: Nucl. Fusion15737 (1975)CrossRefADSGoogle Scholar
  50. 2.50
    J.G. Cordey: Plasma Phys. Cont. Fusion26123 (1984)CrossRefADSGoogle Scholar
  51. 2.51
    V.V. Alikaev, V.L. Vdovin et al.: Experiments on Current Drive in T-7 by Lower Hybrid Waves, Preprint Inst. Atomn. Energ. 3702/7 (Moscow 1982)Google Scholar
  52. 2.52
    S.C. Luckhardt, M. Porcolab et al.: Phys. Rev. Lett.48152 (1982)CrossRefADSGoogle Scholar
  53. 2.53
    S. Tanaka, S. Kubo et al.: In XI European Conference on Controlled Fusion and Plasma Physics, Vol. 1, ed. by S. Methfessel (European Physical Society, Aachen 1983) p. 311Google Scholar
  54. 2.54
    J.E. Stevens, S. Bernabei et al.: In III International Symposium on Heating in Toroidal Plasmas, Vol. 2 (Grenoble, 1982) p. 455Google Scholar
  55. 2.55
    N.J. Fisch: Phys. Rev. Lett.41873 (1978)CrossRefADSGoogle Scholar
  56. 2.56
    F.F. Karney, N.J. Fisch: Phys. Fluids221817 (1979)CrossRefADSGoogle Scholar
  57. 2.57
    N.J. Fisch, A.H. Boozer: Phys. Rev. Lett.45720 (1980)CrossRefADSGoogle Scholar
  58. 2.58
    F.F. Karney, N.J. Fisch: Nucl. Fusion211549 (1981)CrossRefGoogle Scholar
  59. 2.59
    V.V. Alikaev, V.L. Vdovin: Fiz. Plazmy9928 (1983)Google Scholar
  60. 2.60
    M.N. Alcock, T. Edlington et al.: In X European Conference on Controlled Fusion and Plasma Physics, Vol. 1 (Moscow 1981), Report H15Google Scholar
  61. 2.61
    D.F.H. Start, N.R. Ainsworth et al.: In X European Conference on Controlled Fusion and Plasma Physics, Vol. 1 (Moscow, 1981), Report H-16Google Scholar
  62. 2.62
    I. Fidone: In International Symposium on Heating in Toroidal Plasmas, ed. by H. Knoepfel, E. Sindoni (International School of Plasma Physics, Rome 1984) Report E-15Google Scholar
  63. 2.63
    O.C. Eldridge: ORNL/TM-7503 (1980)Google Scholar
  64. 2.64
    J.G. Cordey: Preprint UKAEA, Culham Laboratory (Abingdon 1981)Google Scholar
  65. 2.65
    V.V. Parail, G.V. Pereverzev: Fiz. Plazmy845 (1982)Google Scholar
  66. 2.66
    M. Togushi: IPPI-620 (Tokyo 1983)Google Scholar
  67. 2.67
    G.I. Budker: In Plasma Physics and Controlled Nuclear Fusion, Vol. 3, ed. by M.A. Leontovich (Izd. Akad. Nauk SSSR, Moscow 1958) p. 3 [in Russian]Google Scholar
  68. 2.68
    D.V. Sivukhin: In Problems in Plasma Theory, Vol. 5, ed. by B. Alder, S. Fernbach, M. Rotenberg (Atomizdat, Moscow 1967) p. 439 [in Russian]Google Scholar
  69. 2.69
    J. Killeen, K. Marx: In Methods in Computational Physics, Vol. 9 (Academic, New York 1970) p. 422Google Scholar
  70. 2.70
    J. Killeen, A.A. Mirin, M.E. Rensink: In Methods in Computational Physics, Vol. 16, ed. by J. Killeen (Academic, New York 1976) p. 389Google Scholar
  71. 2.71
    V.I. Pistunovich: At. Energ.3511 (1973)Google Scholar
  72. 2.72
    V.I. Pistunovich: Fiz Plazmy23 (1976)Google Scholar
  73. 2.73
    J.G. Cordey, W.G.F. Core: Nucl. Fusion15710 (1975)CrossRefGoogle Scholar
  74. 2.74
    D.L. Jussby: Nucl. Fusion1615 (1976)CrossRefADSGoogle Scholar
  75. 2.75
    D.L. Jussby: Nucl. Fusion17309 (1977)CrossRefADSGoogle Scholar
  76. 2.76
    N.V. Karetkina: At. Energ.42108 (1977)CrossRefGoogle Scholar
  77. 2.77
    J.D. Callen, J.A. Rome: Nucl. Fusion20501 (1980)CrossRefADSGoogle Scholar
  78. 2.78
    A.V. Bobylev, V.A. Chuyanov: Zh. Vych. Mat. Mat. Fiz.16407 (1976)Google Scholar
  79. 2.79
    I.F. Potapenko, V.A. Chuyanov: Zh. Vych. Mat. Mat. Fiz.20513 (1980)MathSciNetGoogle Scholar
  80. 2.80
    V.I. Volosov, M.S. Pekker: Zh. Vych. Mat. Mat. Fiz.201341 (1980)MathSciNetGoogle Scholar
  81. 2.81
    I.F. Potapenko, V.A. Chuyanov: Zh. Vych. Mat. Mat. Fiz.22751 (1982)MathSciNetGoogle Scholar
  82. 2.82
    C.F. Barnett: Atomic Data for Controlled Fusion Research, ORNL-5207 (1977)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • Yuri N. Dnestrovskii
    • 1
  • Dimitri P. Kostomarov
    • 2
  1. 1.Kurchatov Institute of Atomic EnergyMoscowUSSR
  2. 2.Department of Computer Mathematics and CyberneticsLomonosov Moscow State UniversityMoscowUSSR

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