Markov Properties of Electrical Discharge Current Fluctuations in Plasma

TL;DR

This study applies Markovian analysis to electrical discharge current fluctuations in Helium plasma, revealing stochastic properties, correlation behaviors, and multifractal characteristics, and reconstructs the time series using derived stochastic equations.

Contribution

It introduces a comprehensive Markovian framework to analyze plasma discharge fluctuations, including deriving Fokker-Planck and Langevin equations, and explores multifractal properties of the data.

Findings

Discharge current fluctuations exhibit exponential decay in correlation functions.

Both Markov and correlation time scales increase with discharge current intensity.

Fluctuations deviate from Kolmogorov turbulence theory.

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.