On a Spectral Analysis and Modeling of Non-Gaussian Processes in the Structural Plasma Turbulence*

Abstract

The paper presents an empirical approach to the analysis of broadband Fourier-spectra of the low-frequency structural plasma turbulence based on a priori assumptions concerning the number of processes and the Gaussian form of the spectral components. This type of turbulence in toroidal plasma devices is described by the mathematical model of non-stationary continuous-time random walk, namely compound doubly stochastic Poisson process or compound Cox process. Measurements of low-frequency (in ranges of frequencies to 5 MHz) long-wave (3..6 cm) fluctuations spectra were obtained at the plasma edge in the L-2M stellarator by the technique of Doppler reflectometry. Under some experimental conditions, the efficiency of the methodology was demonstrated. The spectra were successfully decomposed into a few components. There are more than two harmonics in broadband Fourier-spectra besides a harmonic connected with poloidal rotation of the plasma. Those additional harmonics correspond to fluctuations rotating in the directions of electron and ion drift in toroidal plasma devices. In all modes it was possible to reveal the components corresponding to the poloidal rotation of the plasma (which could be defined by a radial electric field) and phase velocity of the two types of structural turbulence (which could be defined by electron gradient and ion gradient instabilities). The suggested description of probabilistic and spectral characteristics of low-frequency plasma turbulence allow us to formulate the correct problem of characterization of structural turbulence by a system of stochastic differential equations. The equations of the system should involve stochastic processes with densities in the form of mixtures of probability distributions. Such a comprehensive approach assumes a correct comparison of different structural turbulence models (caused by drift dissipative, ion-sound, gradient instabilities, etc.) with characteristics of the obtained stochastic processes.