Statistics of low-frequency plasma fluctuations in a simple magnetized torus

Abstract

In a toroidal plasma confined by a purely toroidal magnetic field the plasma transport is governed by electrostatic turbulence driven by the flute interchange instability on the low-field side of the torus cross section. In this paper we revisit experimental data obtained from the Blaamann torus at the University of Tromsø. On time-scales shorter than the poloidal rotation time, the time series of potential and electron density fluctuations measured on stationary Langmuir probes essentially reflect the spatial poloidal structure of the turbulent field (Taylor hypothesis). On these time scales the signals reveals an intermittent character exposed via analysis of probability density functions and computation of multifractal dimension spectra in different regimes of time scales. This intermittency is associated with the shape and distribution of pronounced spikes in the signal. On time scales much longer than the rotation period there are strong global fluctuations in the plasma potential which are shown to to be the result of low-dimensional chaotic dynamics.A useful classification of complex systems behavior should allow different behaviors to be distinguished through observation. For instance, in some cases observational spatiotemporal information is only available as fluctuations of one or more point observations, or at best as a scalar two-dimensional (2D) radiation field emitted from a system, while the internal 3D dynamics is not practically accessible to direct observation. Analysis of such fields reveals the existence of complex systems which at the same time exhibit statistical signatures that are traditionally attributed to either turbulence or selforganized critical avalanching dynamics (SOC). Examples are solar flare activity, polar aurora, fluctuations associated with anomalous transport in magnetic fusion plasma, and vortical fluid flows in ordered structures like dusty plasma quasi-crystals. For turbulent systems structure functions of the velocity field reveal an approximate scale-invariant structure, but the deviation from scaling ascribed to intermittency (or multifractality) has received a lot of attention in recent years. For a system in an SOC state local avalanche analysis reveals that the probability distributions of avalanche size and duration are approximately scale-free, but deviations from perfect scaling and their relation to the finite system size have been studied in different frameworks like finite-size scaling and multifractal scaling [1]. Appearance of intermittency has often been taken as a signature of turbulence. For instance, Consolini [2] interpreted multifractality in the time series of the auroral electrojet index as a signature that turbulence plays a major role in the magnetosphere-ionosphere interaction, and recently Govolchanskaya et al. [3] draw the same conclusion from observing spatial intermittency in auroral images. On the other hand, in the fusion literature, mono-fractal scaling with long-range time-dependence has

Statistical properties of turbulence in a toroidal magnetized ECR plasma

“…At shorter time-scales of τ = 2, 4, 6, 8 µs ( Fig. 7(a)), the four PDFs of V f are so similar that it is hard to distinguish one from another and only a slight degree of non-Gaussianity is found, which shows great similarity with K. Rapdal's work [7] but great difference from Fredriksen's [14]. The PDFs of I s at the same four time scales display a quite different image ( Fig.…”

“…Although the PDFs superposed very well, pronounced deviations from a Gaussian are observed. The non-Gaussian distribution is an extreme value distribution (EVD) which is similar to the findings in Blaamann [7]. PDFs of V f and I s under longer time scales of 256, 512, 1024, 2048 µs are shown in Fig.…”

“…Ranging only in a narrow frequency band from 8 kHz to 10 kHz, the intermediate region with an index of −1, which is predicted by the SOC theory [18][19][20], is clearly not as dominant as the other two. The much narrower frequency band of the −1 index comparing with the work of some of other devices [5,7,9,10,14,21] may undermine the existence of SOC-governed behaviors. There are sharper separations between ranges comparing with other experimental observations such as in HT-6M [9] and TEXTOR tokamak [5].…”

“…In these experiments, all of the power spectra have three distinct frequency regions, each with a characteristic power law (f 0 , f −1 , f −4 ), which implies typical SOC systems [2][3][4], and a pronounced peak of several kHz is observed in different devices [5,6]. Non-Gaussian PDFs for electron pressure fluctuations p are believed to arise from a nonlinear relationship between p and the plasma potential V p [7]. The explorations of Hurst exponents show that the values of H change in different plasmas [7][8][9][10], indicating that large scale correlations probably rely on the plasma sources, the geometrical structures of the plasmas or the positions of the observation points.…”

“…Non-Gaussian PDFs for electron pressure fluctuations p are believed to arise from a nonlinear relationship between p and the plasma potential V p [7]. The explorations of Hurst exponents show that the values of H change in different plasmas [7][8][9][10], indicating that large scale correlations probably rely on the plasma sources, the geometrical structures of the plasmas or the positions of the observation points. Among these experiments in the SMTs, hot filament or low frequency RF discharges were used.…”