Journal of Statistical Physics

, Volume 143, Issue 1, pp 148–167 | Cite as

Markov Properties of Electrical Discharge Current Fluctuations in Plasma

  • S. Kimiagar
  • M. Sadegh Movahed
  • S. Khorram
  • M. Reza Rahimi Tabar
Article

Abstract

Using the Markovian method, we study the stochastic nature of electrical discharge current fluctuations in the Helium plasma. Sinusoidal trends are extracted from the data set by the Fourier-Detrended Fluctuation analysis and consequently cleaned data is retrieved. We determine the Markov time scale of the detrended data set by using likelihood analysis. We also estimate the Kramers-Moyal’s coefficients of the discharge current fluctuations and derive the corresponding Fokker-Planck equation. In addition, the obtained Langevin equation enables us to reconstruct discharge time series with similar statistical properties compared with the observed in the experiment. We also provide an exact decomposition of temporal correlation function by using Kramers-Moyal’s coefficients. We show that for the stationary time series, the two point temporal correlation function has an exponential decaying behavior with a characteristic correlation time scale. Our results confirm that, there is no definite relation between correlation and Markov time scales. However both of them behave as monotonic increasing function of discharge current intensity. Finally to complete our analysis, the multifractal behavior of reconstructed time series using its Keramers-Moyal’s coefficients and original data set are investigated. Extended self similarity analysis demonstrates that fluctuations in our experimental setup deviates from Kolmogorov (K41) theory for fully developed turbulence regime.

Keywords

Turbulence Markov processes Plasma fluctuations 

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • S. Kimiagar
    • 1
  • M. Sadegh Movahed
    • 2
    • 3
  • S. Khorram
    • 4
  • M. Reza Rahimi Tabar
    • 5
    • 6
  1. 1.Department of Physics, Science Faculty, Tehran Central BranchIslamic Azad UniversityTehranIran
  2. 2.Department of PhysicsShahid Beheshti UniversityTehranIran
  3. 3.School of AstronomyInstitute for Research in Fundamental Sciences, (IPM)TehranIran
  4. 4.Research Institute for Applied Physics and AstronomyUniversity of TabrizTabrizIran
  5. 5.Department of PhysicsSharif University of TechnologyTehranIran
  6. 6.Fachbereich PhysikUniversität OsnabrückOsnabrückGermany

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