Application of the Haar Wavelet to the Analysis of Plasma and Atmospheric Fluctuations
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DISCHARGE AND PLASMA PHYSICS
Application of the Haar Wavelet to the Analysis of Plasma and Atmospheric Fluctuations S. A. Maslova,b,*, A. A. Kharchevskyc,**, and V. A. Smirnovc,*** a
Faculty of Mechanics and Mathematics, Moscow State University, Moscow, 119991 Russia Joint Institute for High Temperatures, Russian Academy of Sciences, Moscow, 125412 Russia c Moscow Technological University (MIREA), Radio Engineering and Telecommunication Systems Institute, Moscow, 119454 Russia *e-mail: [email protected] **e-mail: [email protected] ***e-mail: [email protected] b
Received May 22, 2017
Abstract—The parameters of turbulence measured by means of a Doppler reflectometer at the plasma periphery in an L-2M stellarator and in atmospheric vortices (typhoons and tornadoes) are investigated using the wavelet methods with involvement of the Haar function. The periods of time taken for the transition (a bound of parameters) to occur in the L-2M stellarator plasma and in atmospheric processes are estimated. It is shown that high- and low-frequency oscillations of certain parameters, in particular, pressure, that occur in atmospheric vortices decay or increase at different moments of time, whereas the density fluctuation amplitudes that occur in plasma at different frequencies vary in a synchronous manner. Keywords: wavelet analysis, plasma turbulence, vortex, parameter bounds DOI: 10.1134/S1063778817110126
INTRODUCTION Wavelet analysis [1] is presently one of the techniques widely used in scientific and engineering applications. Application of special functions involving localization in space and time, called wavelets, for studying various processes lies at the heart of this technique. The capabilities of many popular signal processing methods (in particular, Fourier analysis) are limited to revealing only a set of frequencies for processes, whereas application of wavelet analysis allows a researcher to reveal the regularities of physical phenomena simultaneously in the frequency and time domains [2]; i.e., it is suitable for studying both steady and unsteady random processes. In a number of papers, their authors describe the use of wavelet analysis in astrophysics and plasma physics. This technique has become popular in the course of studying the physical properties of the external layers in the Sun’s atmosphere (solar corona) and the magnetohydrodynamic turbulence in the motion of ionized particles leaving the solar corona (the solar wind) [3, 4]. Wavelets are widely used in studying plasma (especially its edge region) in experimental installations like stellarators and tokamaks [5–8]. The turbulent transfer of particles that takes place at the edge of the plasma frequently predominates over their
directed motion, as a result of which strong fluctuations of the parameters occur [7]. Application of wavelet analysis makes it possible to reveal both frequency and time regularities of turbulence in various processes, in particular, during transitions to a mode with better confinement of plasma [7, 8]. Wavelet analysis is also succe
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