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New approach to statistical description of fluctuating particle fluxes

  • Turbulence and Chaos
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Abstract

The probability density functions (PDFs) of the increments of fluctuating particle fluxes are investigated. It is found that the PDFs have heavy power-law tails decreasing as x −α − 1 at x → ∞. This makes it possible to describe these PDFs in terms of fractionally stable distributions (FSDs) q(x; α, β, θ, λ). The parameters α, β, γ, and λ were estimated statistically using as an example the time samples of fluctuating particle fluxes measured in the edge plasma of the L-2M stellarator. Two series of fluctuating fluxes measured before and after boronization of the vacuum chamber were processed. It is shown that the increments of fluctuating fluxes are well described by DSDs. The effect of boronization on the parameters of FSDs is analyzed. An algorithm for statistically estimating the FSD parameters and a procedure for processing experimental data are described.

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References

  1. R. Jha, P. K. Kaw, S. K. Mattoo, et al., Phys. Rev. Lett. 69, 1375 (1992).

    Article  ADS  Google Scholar 

  2. R. Trasarti-Battistoni, D. Draghi, C. Riccardi, and H. E. Roman, Phys. Plasmas 9, 3369 (2002).

    Article  ADS  Google Scholar 

  3. N. N. Skvortsova, V. Yu. Korolev, and T. A. Maravina, Fiz. Plazmy 31, 64 (2005) [Plasma Phys. Rep. 31, 57 (2005)].

    Google Scholar 

  4. B. A. Carreras, B. van Milligen, C. Hidalgo, et al., Phys. Rev. Lett. 83, 3653 (1999).

    Article  ADS  Google Scholar 

  5. B. A. Carreras, C. Hidalgo, E. Sanchez, et al., Phys. Plasmas 3, 2664 (1996).

    Article  ADS  Google Scholar 

  6. P. Bak, C. Tang, and K. Wiesenfeld, Phys. Rev. Lett. 59, 381 (1987).

    Article  ADS  MathSciNet  Google Scholar 

  7. V. Frette, K. Christensen, A. Malthe-Sørenssen, et al., Nature 379, 49 (1996).

    Article  ADS  Google Scholar 

  8. B. A. Carreras, B. Ph. van Milligen, M. A. Pedrosa, et al., Phys. Plasmas 5, 3632 (1998).

    Article  Google Scholar 

  9. B. A. Carreras, B. Ph. van Milligen, M. A. Pedrosa, et al., Phys. Rev. Lett. 80, 4438 (1998).

    Article  Google Scholar 

  10. C. Hidalgo, Plasma Phys. Controlled Fusion 44, 1557 (2002).

    Article  ADS  Google Scholar 

  11. G. Y. Antar, G. Counsell, Yu. Yang, et al., Phys. Plasmas 10, 419 (2003).

    Article  ADS  Google Scholar 

  12. E. W. Montroll and G. H. Weiss, J. Math. Phys. 6, 167 (1965).

    Article  ADS  MathSciNet  Google Scholar 

  13. B. B. Mandelbrot, The Fractal Geometry of Nature (W. H. Freeman and Co., New York, 1982; Inst. Komp’yuternykh Issled., Moscow, 2002).

    MATH  Google Scholar 

  14. F. Bardou, J. P. Bouchaud, A. Aspect, and C. Cohen-Tannoudji, Levy Statistics and Laser Cooling (Cambridge University Press, Cambridge, 2002; Fizmatlit, Moscow, 2006).

    MATH  Google Scholar 

  15. J. R. Campanha and H. M. Gupta, Phys. A (Amsterdam) 268, 231 (1999).

    Google Scholar 

  16. M. Yu. Romanovsky, Phys. A (Amsterdam) 265, 264(1999).

    Google Scholar 

  17. G. M. Viswanathan, V. Afanasyev, S. V. Buldyrev, et al., Phys. A (Amsterdam) 282, 1 (2000).

    ADS  Google Scholar 

  18. R. Metzler and J. Klafter, Phys. Rep. 339, 1 (2000).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  19. V. V. Uchaikin, Int. J. Theor. Phys. 39, 2087 (2000).

    Article  MATH  MathSciNet  Google Scholar 

  20. A. I. Saichev and G. M. Zaslavsky, Chaos 7, 753 (1997).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  21. N. N. Skvortsova, G. M. Batanov, L. V. Kolik, et al., in Stochastic Models of Structural Plasma Turbulence, Ed. by V. Yu. Korolev and N. N. Skvortsova (MAKSPress, Moscow, 2003; VSP, Leiden, 2006), p. 63.

    Google Scholar 

  22. N. N. Skvortsova, G. M. Batanov, L. V. Kolik, et al., in Stochastic Models of Structural Plasma Turbulence, Ed. by V. Yu. Korolev and N. N. Skvortsova (MAKSPress, Moscow, 2003; VSP, Leiden, 2006), p. 37.

    Google Scholar 

  23. B. A. Carreras, V. E. Lynch, and G. M. Zaslavsky, Phys. Plasmas 8, 5096 (2001).

    Article  ADS  Google Scholar 

  24. B. Ph. van Milligen, R. Sánchez, and B. A. Carreras, Phys. Plasmas 11, 2272 (2004).

    Article  ADS  Google Scholar 

  25. R. Sánchez, B. A. Carreras, and van B. Ph. Milligen, Phys. Rev. E 71, 011 111 (2005).

  26. G. M. Batanov, V. E. Bening, V. Yu. Korolev, et al., Fiz. Plazmy 28, 128 (2002) [Plasma Phys. Rep. 28, 111 (2002)].

    Google Scholar 

  27. V. Yu. Korolev, Probabilistic-Statistical Analysis of Chaotic Processes by Using Mixed Gaussian Models: Volatility Decomposition of Financial Indices and Plasma Turbulence (IPI RAN, Moscow, 2007) [in Russian].

    Google Scholar 

  28. V. Yu. Korolev, Application of the EM Algorithm and Its Modifications to the Problem of Separation of Mixed Probability Distributions (IPI RAN, Moscow, 2007) [in Russian].

    Google Scholar 

  29. N. N. Skvortsova, G. M. Batanov, A. E. Petrov, et al., in Stochastic Models of Structural Plasma Turbulence, Ed. by V. Yu. Korolev and N. N. Skvortsova (MAKSPress, Moscow, 2003; VSP, Leiden, 2006), p. 87.

    Google Scholar 

  30. M. Kotulski, J. Stat. Phys. 81, 777 (1995).

    Article  MATH  ADS  Google Scholar 

  31. V. M. Zolotarev, Stable One-Dimensional Distributions (Nauka, Moscow, 1983; AMS, Providance, RI, 1986).

    MATH  Google Scholar 

  32. V. N. Kolokoltsov, V. Yu. Korolev, and V. V. Uchaikin, J. Math. Sci. 105, 2659 (2001).

    Article  MathSciNet  Google Scholar 

  33. J. Klafter, A. Blumen, and M. F. Shlesinger, Phys. Rev. A 35 P, 3081 (1987).

    Article  ADS  MathSciNet  Google Scholar 

  34. S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional Integrals and Derivatives: Theory and Application (Nauka i Tekhnika, Minsk, 1987; Gordon & Breach, New York, 1993).

    Google Scholar 

  35. K. B. Oldham and J. Spanier, The Fractional Calculus (Academic, New York, 1974).

    MATH  Google Scholar 

  36. K. S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations (Wiley, New York, 1993).

    MATH  Google Scholar 

  37. V. E. Bening, V. Yu. Korolev, V. N. Kolokol’tsov, et al., J. Math. Sci 123, 3722 (2004).

    Article  MATH  MathSciNet  Google Scholar 

  38. V. E. Bening, V. Yu. Korolev, T. A. Sukhorukova, et al., in Stochastic Models of Structural Plasma Turbulence, Ed. by V. Yu. Korolev and N. N. Skvortsova (MAKSPress, Moscow, 2003; VSP, Leiden, 2006), p. 175.

    Google Scholar 

  39. G. M. Batanov, O. I. Fedianin, N. K. Kharchev, et al., Plasma Phys. Controlled Fusion 40, 1241 (1998).

    Article  Google Scholar 

  40. A. I. Meshcheryakov, D. K. Akulina, G. M. Batanov, et al., Fiz. Plazmy 31, 496 (2005) [Plasma Phys. Rep. 31, 452 (2005)].

    Google Scholar 

  41. G. S. Kirnev, V. P. Budaev, S. A. Grashin, et al., Plasma Phys. Controlled Fusion 46, 621 (2004).

    Article  ADS  Google Scholar 

  42. V. Budaev, Y. Kikuchi, Y. Uesugi, and S. Takamura, Nucl. Fusion 44, S108 (2004).

    Article  ADS  Google Scholar 

  43. V. P. Budaev, S. Takamura, N. Ohno, and S. Masuzaki, Nucl. Fusion 46, S181 (2006).

    Article  ADS  Google Scholar 

  44. O. Grulke, C. Hidalgo, B. LaBombard, et al., Plasma Phys. Controlled Fusion 49, S1 (2007).

    Article  ADS  Google Scholar 

  45. C. Hidalgo, Plasma Phys. Controlled Fusion 37, A53 (1995).

    Article  ADS  Google Scholar 

  46. F. Sattin, Phys. Rev. E 72, 016407 (2005).

    Google Scholar 

  47. C. Hidalgo, M. A. Pedrosa, J. Castellano, et al., Plasma Phys. Controlled Fusion 43, A313 (2001).

    Article  ADS  Google Scholar 

  48. V. V. Uchaikin and V. V. Saenko, J. Math. Sci. 112, 4211 (2002).

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Prokhorov Institute of General Physics, Russian Academy of Sciences, ul. Vavilova 38, Moscow, 119991, Russia

    V. V. Saenko

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  1. V. V. Saenko
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Original Russian Text © V.V. Saenko, 2009, published in Fizika Plazmy, 2009, Vol. 35, No. 1, pp. 3–17.

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Saenko, V.V. New approach to statistical description of fluctuating particle fluxes. Plasma Phys. Rep. 35, 1–13 (2009). https://doi.org/10.1134/S1063780X09010012

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