Kinetic Equations and Linear Response Theory for Dense Coulomb Fluids

  • W. Ebeling
  • Yu. L. Klimontovich
  • W. D. Kraeft
  • G. Röpke
Part of the Experientia Supplementum book series (EXS, volume 47)


As demonstrated in the foregoing chapters the increasing interest to dense nonideal plasmas is due to its importance for many problems of practical interest as thermonuclear fusion, MEGD-generators, extreme pressure devices, highly doped or excited semiconductors, liquid metals etc. [1, 2, 3]. On the basis of the new experimental facts and the new physical models which were presented in part in chapters 1 and 2 the theoretical study of nonideal fluids with Coulombic interactions was the subject of many investigations [1–4]. The simplest model of a plasma is the one-component plasma (OOP) model [4]. The OCP-model is clearly insufficient for the study of transport properties which are mainly due to the quantum-mechanical scattering processes between electrons and ions. Therefore our investigation is based on the many component quantum plasma (MCQP) model considering the electrons as light quantum particles subject to Fermi statistics and the ions as heavy nearly classical particles. The plasma is characterized by the following Hamiltonian Chapter 4
$$ H = \sum\limits_a {\sum\limits_i {\frac{{p_i^2}} {{2ma}} + \frac{1} {2}\sum\limits_{ab} {\sum\limits_{ij} {{\Phi _{ab}}\left( {\left| {{r_i} - {r_j}} \right|} \right)} } } } $$
where the first term represents the kinetic energy while the second one is the potential part with Ф ab being the two particle interaction energy between species a and b. The summations over a, b, ... run over the species and the summations over i, j, ... run over the number of particles of the corresponding species.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Gryaznov, V. K., et al. (В. К. Грязнов, И. Л. Иосилевский, Ю. Г. Красников, Н. И. Кузнецова, В. И. Кучеренко, Г. В. Лаппо, Б. Н. Ломакин, Г. А. Павлов, Э. Е. Сон, В. Е. Фортов): Теплофизические свойства, Атомиздат, Moscow 1980.Google Scholar
  2. [2]
    Kalman, G., Carini, P. (Eds.): Strongly Coupled Plasmas. Plenum Press, New York u. a. 1978;Google Scholar
  3. [2a]
    Rice, T. M., Hensel, J. C., Philips, T. G., Thomas, G. A.: The Electron-Hole Liquid in Semiconductors. Academic Press, New York u. a. 1977.Google Scholar
  4. [3]
    Ebeling, W., Kraeft, W. D., Kremp, D.: Theory of Bound States and Ionization Equilibrium in Plasmas and Solids. Akademie-Verlag, Berlin 1976; Russian translation: Мир, Moscow 1979.Google Scholar
  5. [4]
    Baus, M., Hansen, P.: Physics Reports 59 (1980) 2.Google Scholar
  6. [5]
    Gurov, К. Р. (К. П. Гуров): Основания Кинетической Теории. Hayкa, Moscow 1966.Google Scholar
  7. [6]
    Klimontovich, Y.L., Ebeling, W.: Zh. eksp. teor. fiz. 43 (1962) 146,Google Scholar
  8. [6a]
    Klimontovich, Y.L., Ebeling, W.: Zh. eksp. teor. fiz. 62 (1972) 905.Google Scholar
  9. [7]
    Klimontovich, Yu L.. , Ebeling, W.: Wiss. Z. Univ. Rostock 11 (1962) 355.Google Scholar
  10. [8]
    Klimontovich, Yu. L. (Ю. Л.Климонтович): Кинетическая Теория Неидеального Газа и Неидеальной Плазмы. Hayкa, Moscow 1975.Google Scholar
  11. [9]
    Klimontovich, Yu. L., (Ю. Л. Климонтович): Кинетическая Теория Электромагнитных Процессов. Hayкa, Moscow 1980.Google Scholar
  12. [10]
    Silin, V. P. (В. П. Силин): Введение в Кинетическую Теорию Газов, Hayкa, Moscow 1971.Google Scholar
  13. [11]
    Balescu, R.: Statistical Mechanics of Charged Particles. Interscience Publ., London u. a. 1963;Google Scholar
  14. [11a]
    Ichimabu, S.: Basic Principles of Plasma Physics. Benjamin, New York 1973; Russian translation: Мир, Moscow 1975.Google Scholar
  15. [12]
    Ebeling, W.: Ann. Phys. (Leipzig) 33 (1976) 350.Google Scholar
  16. [13]
    Klimontovich, Yu. L., Kremp, D.: Physica 109A (1981) 517; Chapter 4. of this volume.Google Scholar
  17. [14]
    Ebeling, W., Kraeft, W. D., Kremp, D.: 13th International Conference on Phenomena in Ionized Gases. Invited Papers. Berlin 1977.Google Scholar
  18. [15]
    Spitzer, L.: Physics of Fully Ionized Gases. Wiley, New York u. a. 1962;Google Scholar
  19. [15a]
    Montgomery, D. C., Tidman, D. A.: Plasma Kinetic Theory. McGraw Hill, New York u.a. 1964;Google Scholar
  20. [15b]
    Liboff, В.: Introduction to the Theory of Kinetic Equations. Wiley, New York u. a. 1969;Google Scholar
  21. [15c]
    Ecker, G.: Theory of Fully Ionized Plasmas. Academic Press, New York u. a. 1972.Google Scholar
  22. [16]
    Prigogine, I.: Introduction to Thermodynamics of Irreversible Processes. Springfield 1955.Google Scholar
  23. [17]
    De Groot, S. R., Mazur, P.: Non-Equilibrium Thermodynamics. North Holland Publ. Comp., Amsterdam 1962.Google Scholar
  24. [18]
    Grad, H.: Principles of the Kinetic Theory of Gases (Handbuch der Physik Vol. 12). Springer-Verlag, Berlin u. a. 1957.Google Scholar
  25. [19]
    Khrapak, A. G., Yakubov, I. T. (А. Г. Храпак, И. Т. Якубов): Электроны в плотных газах и в плазме. Наука, Moscow 1981; Smirnow, В. M. (Б. M. Смирнов): Физика слабоионизованного газа. Hayкa, Moscow 1978.Google Scholar
  26. [20]
    Ebeling, W., Корке, G.: Ann. Phys. (Leipzig) 36 (1979) 429.Google Scholar
  27. [21]
    Röpke, G., Ebeling, W., Kraeft, W. D.: Physica 101A (1980) 243.Google Scholar
  28. [22]
    Kadomtsev, B. B. (Б. Б. Кадомцев): ЖЭТФ 33 (1957) 151.Google Scholar
  29. [23]
    Nernst, W.: Theoretische Chemie. Teubner-Verlag, Stuttgart 1926;Google Scholar
  30. [23a]
    Ebeling, W.: Beitr. Plasmaphysik 7 (1967) 11.Google Scholar
  31. [24]
    Falkenhagen, H.: Theorie der Elektrolyte. Hirzel-Verlag, Leipzig 1971;Google Scholar
  32. [24a]
    Ebeling, W., Feistel, R., Kelbg, G., Sändig, R.: J. Non-Equil. Thermodyn. 3 (1978);Google Scholar
  33. [24b]
    Ebeling, W., Feistel, R., Kelbg, G., Sändig, R.: J. Solution Chem. 8 (1979) 53;Google Scholar
  34. [24c]
    Justice, J. C., Ebeling, W.: J. Solution Chem. 8 (1979) 809.Google Scholar
  35. [25]
    Ebeling, W.: 15th International Conference on Phenomena in Ionized Gases. Invited Papers. Minsk 1981;Google Scholar
  36. [25a]
    Belyi, V. V., Klimontovich, Yxj. L., Nalivaiko, V. P.: 15th International Conference on Phenomena in Ionized Gazes. Contributed Papers. Minsk 1981; Preprint IZMIRAN 5A, Moscow 1981.Google Scholar
  37. [26]
    Kubo, R.: J. Phys. Soc. Japan 12 (1957) 570.Google Scholar
  38. [27]
    Zubarev, D. N. (Д. Н. Зубарев): Неравновесная статистическая термодинамика. Hayкa, Moscow 1971; German translation: Subarew, D. N., Statistische Thermodynamik des Nichtgleichgewichts. Akademie-Verlag Berlin 1976.Google Scholar
  39. [28]
    Klimontovich, Yu. L., (Ю. Л. Климонтович): Статистическая теория необратимых процессов MGU Publ., Moscow 1964.Google Scholar
  40. [29]
    Bogolyubov, N. N. (H. H. Боголюбов): Проблемы динамической теории. Го-стехиздат, Moscow 1946.Google Scholar
  41. [30]
    Hubermann, M., Chester, G. V.: Adv. Phys. 24 (1975) 489.Google Scholar
  42. [31]
    Christoph, V., Röpke, G.: phys. stat. sol. (b) 80 (1977) K117.Google Scholar
  43. [32]
    Röpke, G., Höhne, F.: Phys. stat. sol. (b) 107 (1981) 603.Google Scholar
  44. [33]
    Röpke, G., Christoph, V.: J. Phys. C8 (1975) 3615.Google Scholar
  45. [34]
    Kohler, M.: Z. Phys. 124 (1948) 772;Google Scholar
  46. [34a]
    Kohler, M.: Z. Phys. 125 (1949) 679.Google Scholar
  47. [35]
    Appel, J.: Phys. Rev. 122 (1971) 1760.Google Scholar
  48. [36]
    Meister, C. V., Röpke, G.: Ann. Physik (Leipzig) 39 (1982) 133;Google Scholar
  49. [36a]
    Meister, C. V.: Dissertation (A), Wilhelm-Pieck-Universität, Rostock 1981.Google Scholar
  50. [37]
    Palmer, R. G., Weeks, J. D.: J. Chem. Phys. 58 (1973) 4171.Google Scholar
  51. [38]
    Klyuchnikov, N. I., Triger, S.A. (H. И. Ключников, С. А. Тригер): TMФ 26 (1976) 256;Google Scholar
  52. [38a]
    Klyuchnikov, N. I., Triger, S.A. (H. И. Ключников, С. А. Тригер): TMФ 39 (1979) 368.Google Scholar
  53. [39]
    Goedsche, F., Richter, R., Vojta, G.: Phys. stat. sol. (b) 91, (1979) 581;Google Scholar
  54. [39a]
    Möbius, A., Goedsche, F., Vojta, G.: Physica 95A (1979) 294.Google Scholar
  55. [40]
    Busch, G., Güntherodt, H.-J., in: Solid State Physics, Vol.29. (Ed. H. Ehrenreich, F. Seitz, D. Turnbitll); Academic Press, New York 1974.Google Scholar
  56. [41]
    Dreirach, O., Evans, R., Güntherodt, M. J., Kunzi, H. U.: J. Phys. F2 (1972) 709.Google Scholar
  57. [42]
    Rogers, F. J.:Phys. Rev. A4 (1971) 1145;Google Scholar
  58. [42a]
    Rogers, F. J., De Witt, H. E., Boercker, D. В.: Phys. Lett. 82A (1981) 331.Google Scholar
  59. [43]
    Lie, T. J., Liboff, R. L.: Ann. Phys. 67 (1971) 349.Google Scholar
  60. [44]
    Ting, С. S., Ying, S. С., Quinn, J. J.: Phys. Rev. B14 (1976) 4439.Google Scholar
  61. [45]
    Kojima, D. Y.: Physica A39 (1978) 171;Google Scholar
  62. [45a]
    Altshuler, B. L. (Б. Л. Альтшулер): ЖЭТФ 75 (1978) 1330;Google Scholar
  63. [45b]
    Fleurov, V. N., Kozlov, A. N.: J. Phys. F8 (1978) 1899.Google Scholar
  64. [46]
    Kadanoff, L. P., Baym, G.: Quantum Statistical Mechanics. Benjamin, New York 1982.Google Scholar
  65. [47]
    Röpke, G. (Г. Рэпке): TMФ 46 (1981) 279;Google Scholar
  66. [47a]
    Röpke, G. Ann. Physik (Leipzig) 39 (1982) 35.Google Scholar
  67. [48]
    Gingrich, N. S., Heaton, L.: J. Chem. Phys. 34 (1961) 873.Google Scholar
  68. [49]
    Hubbard, J.: Proc. Roy. Soc. London A261 (1961) 371.Google Scholar
  69. [50]
    Gould, H. A., De Witt, H. E.: Phys. Rev. 155 (1967) 68;Google Scholar
  70. [50a]
    Williams, R. H., De Witt, H. E.: Phys. Fluids 12 (1969) 2326.Google Scholar
  71. [51]
    Röpke, G., Meister, С. V., Kollmorgen, К., Kraeft, W.-D.: Ann. Physik (Leipzig) 36 (1979) 377.Google Scholar
  72. [52]
    Fettee, A. L., Walecka, J. D.: Quantum Theory of Many Particle Systems, New York 1971;Google Scholar
  73. [52a]
    Stolz, H.: Einführung in die Vielelektronentheorie der Kristalle, Akademie-Verlag, Berlin 1974.Google Scholar
  74. [53]
    Kilimann, M. К.: Doctor thesis II, Rostock 1978.Google Scholar
  75. [54]
    Zimmeemann, R., Kilimann, M. K., Keaeft, W. D., Keemp, D., Röpke, G.: Phys. stat. sol. (b) 90 (1978) 175.Google Scholar
  76. [55]
    Blümlein, J., Keaeft, W. D., Meyer, T.: Ann. Physik (Leipzig) 37 (1980) 379.Google Scholar
  77. [56]
    Plakida, N. M. (H. M. Планида): ФТТ 6 (1964) 3444.Google Scholar
  78. [57]
    Blümlein, J., in preparation.Google Scholar
  79. [58]
    Ron, A., Tzoae, N.: Phys. Rev. 131 (1963) 12;Google Scholar
  80. [58a]
    Ron, A., Tzoae, N.: Phys. Rev. 131 (1963) 1943.Google Scholar
  81. [59]
    Blümlein, J., Keaeft, W. D., in preparation; Keaeft, W. D., Luft, M., Mihajlov, A. A.: Physica 120A (1983) 263Google Scholar
  82. [60]
    Keaeft, W. D., Blümlein, J., Meyee, T.: Beitr. Plasmaphysik 23 (1983) 9.Google Scholar
  83. [61]
    Kohn, W.: Phys. Rev. 123 (1961) 1242.Google Scholar
  84. [62]
    Мотт, N. F.: Proc. Camb. Phil. Soc. 32 (1936) 281.Google Scholar
  85. [63]
    Blatt, F. J.: Physics of Electronic Conduction in Solids. McGraw-Hill Book Company, New York 1968.Google Scholar
  86. [64]
    Beooks, H.: Phys. Rev. 83 (1951) 879.Google Scholar
  87. [65]
    Rogov, V.S.. С. Рогов): ТВТ 8 (1970) 689.Google Scholar
  88. [66]
    Chapman, S., Cowling, T. G.: The Mathematical Theory of Non-Uniform Gases. University Press, Cambridge 1958.Google Scholar
  89. [67]
    Fabee, T. E.: Introduction to the Theory of Liquid Metals. University Press, Cambridge 1972, p. 330.Google Scholar
  90. [68]
    Haet, G. A., Goodfeiend, P. L.: J. Chem. Phys. 53, (1970) 448.Google Scholar
  91. [69]
    Günthee, K., Lang, S., Radtke, R.: J. Phys. D., Appl. Phys. 16 (1983) 1235.Google Scholar
  92. [70]
    Ivanov, Ju. V., Mintsev, V. В., Foetov, V. E., Deemin, A. N. (Ю. В. Иванов, B. Б. Минцев, В. Е. Фортов, А. Н. Дремин): ЖЭТФ71 (1976) 216.Google Scholar
  93. [71]
    Radtke, R., Günthee, К., Popovic, S. S.: J. Phys. D9 (1976) 1131.Google Scholar
  94. [72]
    Andeeev, S. I., Gaveilova, T.V. (С. И. Андреев, Т. В. Гаврилова): ТВТ 13 (1975) 176.Google Scholar
  95. [73]
    Oguetsova, M. H., Podmoshenskh, I. V., Smirnova, V.J a. (M. H. Огурцова, И. В. Подмошенский, В. Я. Смирнова): ТВТ 12 (1974) 650.Google Scholar
  96. [74]
    Bakeev, A. A., Revinskii, R. E. (А. А. Бакеев, Р. Е. Ревинский): TBT 8 (1970) 1121.Google Scholar
  97. [75]
    Sechenov, V. A., Son, E. E., Shchekotova, O. E. (В. А. Сеченов, Е. Е. Сон, О. Е. Щекотова): Письма в ЖЭТФ 1 (1975) 891.Google Scholar
  98. [76]
    Baudeb, ГГ., et al.: Phys. Fluids 16 (1973) 2143;Google Scholar
  99. [76a]
    Günthee, К. et al.: J. Phys. D9 (1976) 1139;Google Scholar
  100. [76b]
    Günthee, К., Radtke, R.: Ergebnisse der Plasmaphysik und der Gaselektronik, Bd. 7. Akademie-Verlag, Berlin (in press);Google Scholar
  101. [76c]
    Sechenov, V. A., et al. В. А. Сеченов и др.): ТВТ 15 (1977) 411;Google Scholar
  102. [76d]
    Kulik, P. P., et al. (П. П. Кулик и др.): ТВТ 15 (1977) 415; Proc. XIII ICPIG. Berlin 1977, p. 583;Google Scholar
  103. [76e]
    Mintsev, V. В., et al. В. Б. Минцев и др.): ЖЭТФ 79 (1980) 116;Google Scholar
  104. [76f]
    Dikhtee, I. I., et al. (И. И. Дихтер и др.): ТВТ 15 (1977) 196;Google Scholar
  105. [76g]
    Ermokhin, N. V., et al. (H. В. Ермохин и др.): ТВТ 15 (1977) 695;Google Scholar
  106. [76h]
    Bushman, А. V., Foetov, V. Е. (А. В. Бушман, В. Е. Фортов): УФН 140 (1983) 177;Google Scholar
  107. [76i]
    Alekseev, V. A., Foetov, V. E. Yakubov, I. Т. (В. А. Алексеев, В. Е. Фортов, И. Т. Якубов): УФН 139 (1983) 193.Google Scholar
  108. [77]
    Langer, I. S.: Phys. Rev. 120 (1960) 714;Google Scholar
  109. [77a]
    Langer, I. S.: Phys. Rev. 124 (1961) 1003;Google Scholar
  110. [77b]
    Götze, W., Wölfle, P.: Phys. Rev. B6 (1972) 1226;Google Scholar
  111. [77c]
    Devoto, R. S.: Phys. Fluids 19 (1976) 1;Google Scholar
  112. [77d]
    Kojima, D. Y.: Physica 39A (1978) 171;Google Scholar
  113. [77e]
    Van Vliet, K. M.: J. Math. Phys. 19 (1978) 1345;Google Scholar
  114. [77f]
    Van Vliet, K. M.: J. Math. Phys. 20 (1979) 2573;Google Scholar
  115. [77g]
    Ermakov, V. V., Kalitkin, N. N. (В. В. Ермаков, H. H. Калиткин): Численные методы механики сплошной среды. Novosibirsk 1978;Google Scholar
  116. [77h]
    Noeman, G. E., Valuev, A. A.: Plasmaphys. 21 (1979) 1609;Google Scholar
  117. [77i]
    Wilhelm, H. E.: IEEE Trans. on Plasma Science PS9 (1981) 68.Google Scholar

Copyright information

© Springer Basel AG 1984

Authors and Affiliations

  • W. Ebeling
  • Yu. L. Klimontovich
  • W. D. Kraeft
  • G. Röpke

There are no affiliations available

Personalised recommendations