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On Gauss-Markov arbitrary-kinetic-level stochastic dynamics of plasmas—I

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Il Nuovo Cimento D

Summary

The paper presents the nonequilibrium statistical (kinetical) treatment of the Gauss-Markov «external» and self-consistent «intrinsic» fluctuations in an «embedded» plasma system based on the separation and decoupling of the statisticalt and stochastical τ time scales. In the frame of the generalized Gauss-Markov oscillator model, this description yields both the arbitrary kinetic-level decomposition of the statistical distributions and correlations, and Gauss-Markov evolution and momentum equations with coherent structure. The first part of the paper is concerned with both the Gauss-Markov Liouville dynamics and the Gauss-Markov propagators of this «embedded» plasma system.

Riassunto

Questo lavoro presenta il trattamento (cinetico) statistico di non equilibrio delle fluttuazioni di Gauss-Markov «esterne» e «intrinseche» autoconsistenti in un sistema di plasma incluso basato sulla separazione ed il disaccoppiamento delle scale temporali statistichet e stocastiche τ. Nell’ambito del modello di oscillatore generalizzato di Gauss-Markov, questa descrizione genera sia la scomposizione arbitraria del livello cinetico delle distribuzioni statistiche e delle correlazioni, sia le equazioni dell’impulso e di evoluzione di Gauss-Markov con struttura coerente. La prima parte di questo lavoro riguarda sia la dinamica di Gauss-Markov Liouville sia i propagatori di Gauss-Markov di questo sistema di plasma incluso.

Резюме

В этой статье предлагается неравновесное статистическое (кинетическое) рассмотрение Гауссовых-Марковских «внешних» и самосогласованных «внутренних» флуктуаций во «внедренной» плазменной системе. Предложенный подход основан на разделении и развязывании статистическогоt и стохастического τ временных масштабов. В рамках обобщенной Гауссовой-Марковской осцилляторной модели этот формализм дает разложение статистических распределений и корреляций на произвольном кинетическом уровне, а также Гауссову-Марковскую эволюцию и импульсное уравнение с когерентной структурой. Первая часть статьи посвящена Гауссовой-Марковской динамике Лиувилля, а также Гауссовым-Марковским пропагаторам для «внедренной» плазменной системы.

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References

  1. M. N. Rosenbluth andR. Z. Sagdeev (Editors):Handbook of Plasma Physics, Vol. 1 and Vol. 2 (North-Holland P.C., Amsterdam, 1983 and 1984).

    Google Scholar 

  2. R. M. Kulsrud:MHD description of plasma, inHandbook of Plasma Physics, Vol. 1, edited byM. N. Rosenbluth andR. Z. Sagdeev (North-Holland P. C., Amsterdam, 1983).

    Google Scholar 

  3. I. Gyarmati:Non-Equilibrium Thermodynamics (Springer-Verlag, Berlin, 1973).

    Google Scholar 

  4. I. Gyarmati:J. Non-Equilibrium Thermodynamics,2, 233 (1977).

    Article  MATH  Google Scholar 

  5. N. A. Krall, A. W. Trivelpiece:Principles of Plasma Physics (McGraw-Hill B.C., New York, N.Y., 1973).

    Google Scholar 

  6. A. Hasegawa:Plasma Instabilities and Nonlinear Effects (Springer-Verlag, Berlin, 1975).

    Google Scholar 

  7. T. K. Fowler:Thermodynamics of Unstable Plasmas, inAdvances in Plasma Physics, Vol. 1, edited byA.Simon andW. B.Thompson (John Wiley and Sons, New York, N. Y.).

  8. M. N. Rosenbluth andR. Z. Sagdeev (Editors):Handbook of Plasma Physics (North-Holland P.C., Amsterdam, 1983), Part 2, 3.

    Google Scholar 

  9. J. A. Krommes:Statistical descriptions and plasma physics, inHandbook of Plasma Physics, Vol. 2 edited byM. N. Rosenbluth andR. Z. Sagdeev (North-Holland P.C., Amsterdam, 1984).

    Google Scholar 

  10. R. F. Fox:Phys. Rep.,48, 179 (1978).

    Article  ADS  Google Scholar 

  11. P. Hänggi andH. Thomas:Phys. Rep.,88, 207 (1982).

    Article  MathSciNet  ADS  Google Scholar 

  12. A. G. Sitenko:Fluctuations and Nonlinear Wave Interactions in Plasmas (Pergamon Press, Oxford, 1982).

    MATH  Google Scholar 

  13. I. A. Akhiezer, Polovin, Sitenko andStepanov:Plasma Electrodynamics (Pergamon Press, Oxford, 1975).

    Google Scholar 

  14. R. G. Davidson:Methods in Nonlinear Plasma Theory (Academic Press, New York, N. Y., 1972).

    Google Scholar 

  15. D. G. Montgomery andD. A. Tidman:Plasma Kinetic Theory (McGraw-Hill B.C., New York, N. Y. 1964).

    Google Scholar 

  16. Yu. L. Klimontovich:Kinetic Theory of Nonideal Gas and Nonideal Plasma (Pergamon Press, Oxford, 1981).

    Google Scholar 

  17. G. Ecker:Theory of Fully Ionized Plasmas (Academic Press, New York, N. Y., 1972).

    Google Scholar 

  18. V. N. Tsytovich:Theory of Turbulent Plasma (Consultants Bureau, New York, N. Y., 1977).

    Google Scholar 

  19. S. Ichimaru:Basic Principles of Plasma Physics (Benjamin, London, 1973).

    Google Scholar 

  20. A. A. Galeev andR. Z. Sagdeev:Theory of weakly turbulent plasma, inHandbook of Plasma Physics, Vol. 1, edited byM. N. Rosenbluth andR. Z. Sagdeev (North-Holland P.C., Amsterdam, 1983).

    Google Scholar 

  21. W. E. Drummond:Plasma Physics (IAEA, Vienna, 1965).

    Google Scholar 

  22. B. B. Kadomtsev:Plasma Turbulence (Academic Press, London, 1965).

    Google Scholar 

  23. A. A. Galeev andR. Z. Sagdeev: inProblems in Plasma Theory, edited byM. A. Leontovich (Atomic Energy Press, Moscow, 1973).

    Google Scholar 

  24. R. Z. Sagdeev andA. A. Galeev:Nonlinear Plasma Theory (Benjamin, New York, N. Y., 1969).

    MATH  Google Scholar 

  25. V. N. Tsytovich:Introduction to the Theory of Plasma Turbulence (Pergamon Press, Oxford, 1972).

    Google Scholar 

  26. A. A. Vedenov:Theory of Turbulent Plasma, Israel Program Sc. Transl. (Jerusalem, 1966).

    Google Scholar 

  27. S. A. Kaplan andV. N. Tsytovich:Plasma Astrophysics (Pergamon Press, Oxford, 1973).

    Google Scholar 

  28. R. Z. Sagdeev:Rev. Mod. Phys.,51, 1 (1979).

    Article  ADS  Google Scholar 

  29. J. H. Misguich andR. Balescu:J. Plasma. Phys.,19, 147 (1978).

    ADS  Google Scholar 

  30. J. H. Misguich andR. Balescu:J. Plasma Phys.,13, 385 (1975).

    Article  ADS  Google Scholar 

  31. W. Horton jr. andD. Choi:Phys. Rep.,49, 273 (1979).

    Article  ADS  Google Scholar 

  32. D. Choi andW. Horton Jr.:Phys. Fluids,18, 858 (1975).

    Article  ADS  Google Scholar 

  33. D. Choi andW. Horton Jr.:Phys. Fluids,20, 628 (1977).

    Article  MathSciNet  ADS  Google Scholar 

  34. D. Choi andW. Horton Jr.:Phys. Fluids,17, 2048 (1974).

    Article  ADS  Google Scholar 

  35. D. F. DuBois:Phys. Fluids,19, 1764 (1976).

    Article  ADS  Google Scholar 

  36. D. F. DuBois andB. Bezzerides:Phys. Rev. A,14, 1869 (1976).

    Article  ADS  Google Scholar 

  37. D. F. DuBois andM. Espedal:Plasma Phys.,20, 1209 (1978).

    Article  ADS  Google Scholar 

  38. D. F. DuBois:Phys. Rev. A,23, 865 (1981).

    Article  ADS  Google Scholar 

  39. T. H. Dupree:Phys. Fluids,12, 2680 (1968).

    Article  ADS  Google Scholar 

  40. T. H. Dupree:Phys. Fluids,15, 334 (1972).

    Article  ADS  Google Scholar 

  41. T. H. Dupree:Phys. Fluids,17, 100 (1974).

    Article  MATH  ADS  Google Scholar 

  42. T. H. Dupree et al.:Phys. Fluids,18, 1167 (1975).

    Article  ADS  Google Scholar 

  43. J. A. Krommes andR. G. Kleva:Phys. Fluids,22, 2168 (1979).

    Article  MATH  ADS  Google Scholar 

  44. J. A. Krommes andP. Similon:Phys. Fluids,23, 1553 (1980).

    Article  MATH  ADS  Google Scholar 

  45. J. A. Krommes:Phys. Fluids,23, 736 (1980).

    Article  MATH  MathSciNet  ADS  Google Scholar 

  46. C. De Witt-Morett andK. D. Elworthy:Phys. Rep.,77, 123 (1981).

    Google Scholar 

  47. L. Arnold:Stochastische Differentialgleichungen (R. Oldenbourg Verlag, München-Wien, 1973).

    MATH  Google Scholar 

  48. K. Lelkes:Proceedings of International Conference on Plasma Physics, Lausanne, Switzerland, 1984.

  49. K. Lelkes:Proceedings of International Conference on Plasma Physics, Göteborg, Sweden, 1982.

  50. Pao-Liu Chow:Stochastic partial differential equations in turbulence, inProbabilistic Analysis and Related Topics, edited byA. T. Bharucha-Reid, Vol. 1 (Academic Press, New York, N. Y., 1978).

    Google Scholar 

  51. I. M. Besieris andW. Stasiak:J. Math. Phys.,17, No. 9 (1976).

Download references

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Author notes

  1. K. Lelkes

    Present address: , Keleti Károly utca 13/b, H-1024, Budapest, Hungary

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  1. Institute of Physics, Technical University of Budapest, H-1521, Budapest, Hungary

    K. Lelkes

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Lelkes, K. On Gauss-Markov arbitrary-kinetic-level stochastic dynamics of plasmas—I. Il Nuovo Cimento D 11, 1005–1023 (1989). https://doi.org/10.1007/BF02455354

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  • DOI: https://doi.org/10.1007/BF02455354

PACS 02.50

PACS 52.35.Ra

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