Empirical Similarity of Frequency Spectra of the Edge-Plasma Fluctuations in Toroidal Magnetic-Confinement Systems

Abstract

Frequency spectra of fluctuations of the ion saturation current, floating potential, and turbulent transport measured in the plasma edge of different fusion devices (tokamaks and stellarators) have been compared. All of the spectra show the same behavior over the whole frequency range investigated, which supports universality of plasma turbulence or turbulent transport. The results obtained are an indication of edge-plasma turbulence evolving into a critical state, independent of the size and plasma characteristics of the device. [S0031-9007(99)09024-9] PACS numbers: 52.55. 52.25.Gj, 52.40.Hf Many systems display universal characteristics whose experimental determination has led to insights furthering the understanding of their dynamics. An example of such a system is fluid turbulence [1]. In 1941, Kolmogorov showed that two-dimensional systems display features in spatial scales ͑k͒ leading to the well known k 25͞3 and k 23 regimes in 2D turbulence. Another broader group of dynamical systems are those thought to be described by the concept of self-organized criticality (SOC). These nonequilibrium systems often evolve naturally towards a state that is nearly critical [2,3]. The nature of this self-organized criticality may account for scale invariant phenomena in nature such as 1͞f noise [4] and fractal (self-similar) structures [5]. In SOC systems, the Fourier spectra are expected to be nearly 1͞f for a given range of frequencies. This behavior arises from the existence and random superposition of avalanches. It has been argued theoretically that transport processes in magnetically confined plasmas have some of the characteristics of self-organized critical systems [6][7][8]. Some such processes are the scaling of transport coefficients, the response to plasma perturbations [9], and the self-similar character of the electrostatic fluctuations at the plasma edge [10].The self-similar nature of fluctuations is an indication of the existence of long-range time correlations. These are characterized by algebraic "tails" (i.e., decay at large lags) of the autocorrelation function. A comparative analysis of edge fluctuations among different magnetic confinement devices gives a Hurst exponent varying between H 0.64 and 0.74 [10]. The narrow range of variation of H is an indication of the similarity of the low frequency range of the spectrum among these devices. In this Letter, we take a step further in this research and explore the properties of the complete frequency spectra of edge plasma fluctuations and turbulent transport in different tokamaks and stellarators.Even in complex systems that exhibit scale invariant fluctuations, one expects the distribution of avalanches to show finite size scaling. In a sand pile, the size of the pile, L, and the probability of dropping sand are the basic parameters of the running sand pile dynamics. Consequently, the spectral distribution, P, will depend on frequency, v, and the size of the pile, L. Techniques of finite-size scaling have been applied to interpret the data. The si...

Comparison of turbulence measurements and simulations of the low-temperature plasma in the torsatron TJ-K

“…Figure 8 shows density and transport fluctuation spectra and probability density functions (PDF) as calculated from experimental and simulated data. The measured spectra are typical of plasma turbulence [31]. Similarly to as in the simulation spectra a flat region up to about 10-20 kHz if followed by an exponential decay up to 300 kHz.…”

Auto-correlation function and frequency spectrum due to a super-position of uncorrelated exponential pulses

“…The former is possibly related to the many reports on long-range dependence of plasma fluctuations in the boundary of magnetically confined plasmas. [11][12][13][14][15] Under the assumption of self-similarity, the estimate of scaling coefficients sensitively depends on the presence of low-frequency trends and oscillations which typically are present in measurement data. It is to be noted that the stochastic model presented here obviously does not possess any self-similarity properties.…”

“…1-10 The frequency power spectra of these fluctuations are generally found to be characterized by a flat lowfrequency region and a steep high-frequency tail. [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27] In many previous works, power law scaling relationships have been inferred from experimental measurements and the results interpreted in the frameworks of scale-free inertial range cascade, self-similar processes and self-organized critical behavior. [11][12][13][14][15][16][17][18][19][20][21] By contrast, it will in this contribution be demonstrated that the auto-correlation functions and frequency spectra reported from experimental measurements can be described by a super-position of uncorrelated exponential pulses.…”

On the statistics of edge fluctuations: comparative study between various fusion devices

“…It was however soon realized that, if one goes beyond the qualitative similarity of the signal, at the quantitative level relatively large differences apparently exist between different machines (see, e.g. the lack of consensus about the analytical form of the PDF of fluctuations) [3,4,5,6,7,8]. Differences are unavoidable, since the different devices span widely differing ranges of operating conditions (geometry, magnetic field, temperature, ...).…”