Convergence of statistical moments of particle density time series in scrape-off layer plasmas

Abstract

Particle density fluctuations in the scrape-off layer of magnetically confined plasmas, as measured by gas-puff imaging or Langmuir probes, are modeled as the realization of a stochastic process in which a superposition of pulses with a fixed shape, an exponential distribution of waiting times and amplitudes represents the radial motion of blob-like structures. With an analytic formulation of the process at hand, we derive expressions for the mean-squared error on estimators of sample mean and sample variance as a function of sample length, sampling frequency, and the parameters of the stochastic process. % Employing that the probability distribution function of a particularly relevant shot noise process is given by the gamma distribution, we derive estimators for sample skewness and kurtosis, and expressions for the mean-squared error on these estimators. Numerically generated synthetic time series are used to verify the proposed estimators, the sample length dependency of their mean-squared errors, and their performance. We find that estimators for sample skewness and kurtosis based on the gamma distribution are more precise and more accurate than common estimators based on the method of moments.