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 stochastic 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.
- Authors:
-
- Department of Physics and Technology, UiT - The Arctic University of Norway, N-9037 Tromsø (Norway)
- Publication Date:
- OSTI Identifier:
- 22407998
- Resource Type:
- Journal Article
- Journal Name:
- Physics of Plasmas
- Additional Journal Information:
- Journal Volume: 22; Journal Issue: 1; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1070-664X
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; AMPLITUDES; ASYMMETRY; DENSITY; DISTRIBUTION FUNCTIONS; ERRORS; FLUCTUATIONS; LANGMUIR PROBE; PARTICLES; PLASMA CONFINEMENT; PLASMA SCRAPE-OFF LAYER; PROBABILITY; PULSES; SAMPLING; STATISTICS; STOCHASTIC PROCESSES
Citation Formats
Kube, R., E-mail: ralph.kube@uit.no, and Garcia, O. E. Convergence of statistical moments of particle density time series in scrape-off layer plasmas. United States: N. p., 2015.
Web. doi:10.1063/1.4905513.
Kube, R., E-mail: ralph.kube@uit.no, & Garcia, O. E. Convergence of statistical moments of particle density time series in scrape-off layer plasmas. United States. https://doi.org/10.1063/1.4905513
Kube, R., E-mail: ralph.kube@uit.no, and Garcia, O. E. 2015.
"Convergence of statistical moments of particle density time series in scrape-off layer plasmas". United States. https://doi.org/10.1063/1.4905513.
@article{osti_22407998,
title = {Convergence of statistical moments of particle density time series in scrape-off layer plasmas},
author = {Kube, R., E-mail: ralph.kube@uit.no and Garcia, O. E.},
abstractNote = {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 stochastic 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.},
doi = {10.1063/1.4905513},
url = {https://www.osti.gov/biblio/22407998},
journal = {Physics of Plasmas},
issn = {1070-664X},
number = 1,
volume = 22,
place = {United States},
year = {Thu Jan 15 00:00:00 EST 2015},
month = {Thu Jan 15 00:00:00 EST 2015}
}