Analysis of the edge plasma fluctuation in several confinement devices reveals the self-similar character of the fluctuations through the presence of long-range time correlations. These results show that the tail of the autocorrelation function decays as a power law for time lags longer than the decorrelation time and as long as times on the order of the particle diffusion time. The algebraic decay of the longrange time correlations is consistent with plasma transport characterized by self-organized criticality.

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...

The rescaled range analysis techniques are used to investigate long-range dependence in plasma edge fluctuations [Mandelbrot and Wallis, Water Resources Res. 4, 909 (1969)]. This technology has been applied to data from several confinement devices such as tokamaks, stellarators, and reversed-field pinch. The results reveal the self-similar character of the electrostatic fluctuations at the plasma edge with self-similarity parameters ranging from 0.62 to 0.72. These results show that the tail of the autocorrelation function decays as a power law for time lags longer than the decorrelation time and as long as times of the order of the confinement time. In cold plasma devices (Te<1 eV at the core), there is no evidence of algebraic tails in the autocorrelation function. Some other characteristic features of the autocorrelation function and power spectrum have been investigated. All of these features are consistent with plasma transport as characterized by self-organized criticality.

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The probability distribution function of the turbulence-induced particle flux at the plasma edge has distinct functional forms over two distinct ranges of time scales. One range corresponds to the fluctuation time scales and the other one is the mesoscale range: time scales between the turbulence decorrelation and confinement time. In the second range, the probability distribution function is selfsimilar and essentially has only the outward flux tail. This structure reflects some of the mechanisms of the underlying turbulence. PACS numbers: 52.35.Ra, From the Langmuir probe measurements in low-power Ohmically heated or electron cyclotron heated plasma discharges and for several types of confinement devices, we have concluded that the electrostatic potential and density fluctuations at the plasma edge are self-similar over a broad range of time scales [1,2]. The selfsimilarity range is, in general, for time scales longer than the turbulence decorrelation times up to times of the order of confinement time, the mesoscale range. The upper bound of the self-similarity range is difficult to determine because of the lengths of time records available and the varying plasma conditions on these longer time scales. It was found that for fluctuation measurements within the plasma confinement region the self-similarity parameter [3] varies between H 0.62 and H 0.75, a relatively small range of variation given the diversity of plasma confinement devices considered.To find out whether these properties of the plasma fluctuations have any bearing on the dynamics of plasma transport, we must investigate the properties of their induced fluxes. The relative phase between density and potential fluctuations could be such that the induced particle flux does not share the self-similarity properties. The problem with studying fluxes is the scarcity of experimental measurements. Flux measurements for core plasmas are practically nonexistent. At the plasma edge, the turbulence-induced particle flux can be inferred from the simultaneous measurement of the density and potential fluctuations. By measuring the density fluctuations at one point in the plasma,ñ 1 ñ͑r 1 , u 1 , t͒, and the electrostatic plasma potential at two nearby positions, f 1 f 2 ͑r 1 , u 1 2 d, t͒ and f 2 f 3 ͑r 1 , u 1 1 d, t͒, the instantaneous turbulence-induced particle flux at this location can be calculated, G t ñẼ u ͞B ñ 1 ͑f 2 2 f 1 ͒͑͞2r 1 dB͒. Here, B is the magnetic field and E u is the poloidal electric field. Of course, what the Langmuir probe measures is the ion saturation current, I S~n p T e , and the floating potential, V f F 2 3T e . Therefore, the flux inferred from these measurements is not necessarily equal to the particle flux. However, measurements of the temperature fluctuations at the plasma edge in some confinement devices have shown that their relative phase is such that G t calculated from I S and V f is a good estimate of the particle flux [4,5].One of the main results of the present analysis is that the self-similarity of the electrostatic pot...