# Statistical approach to bursty plasma fluctuations in toroidal and linear plasma devices

**Statistical approach to bursty plasma fluctuations in toroidal and linear plasma devices **

*S. Takamura!, N. Ohno†, H. Miyoshi!, V. Budaev!!, S. Masuzaki‡ and N. Asakura§ !Graduate School of Engineering, Nagoya University, Nagoya, 464-8603, Japan †EcoTopica Science Institute, Nagoya University, Nagoya, 464-8603, Japan !!Nuclear Fusion Institute, RRC Kurchatov Institute, 123182, Kurchatov Sq.1, Moscow, Russia ‡National Institute for Fusion Science, Toki 509-5292, Japan §Japan Atomic Energy Agency, Naka, 311-0193, Japan *

Abstract. Density fluctuation properties in the edge plasmas of magnetically confined linear and toroidal devices have been investigated by analyzing the ion saturation current Isat measured with Langmuir probes. Large positive bursty events were often observed for all devices. Statistical analysis based on probability distribution function (p. d. f.) was employed to determine the intermittent evens in the density fluctuation. In the linear plasma device NAGDIS-II, we have investigated the velocity distribution of the intermittent bursty fluctuations by using the wavelet transform with complex Morlet mother wavelet, which indicates the large intermittent bursts mainly propagate toward the wall. In the JT-60U tokamak, at the low field side of mid-plane, the skewness of Isat increases with a distance from the separatrix. It peaks around the layer, where the direction of the parallel SOL flow changed poloidally from upward to downward. In the helical device LHD, the large positive bursty events were observed near a divertor leg at which the magnetic line of force connected to the area of a low-field side with a short connection length. Keywords: density fluctuation, blobs, probability distribution function, wavelet analysis PACS: 52.25.Xz, 52.25.Fi, 52.35.Ra INTRODUCTION From experiments on magnetically confined plasma devices, there is a lot of evidences that plasma turbulence is highly intermittent[1, 2, 3, 4]. Intermittent events are well-known to play a crucial role in transport dynamics. Intermittent transport resulted from rare, large events is due to coherent structures, leading to losses above that predicted by neo-classical heat diffusive scaling. Recently, intermittent convective plasma transport, so-called “plasma blob” has been observed in the edge plasmas of several fusion devices, which is thought to play a key role for crossfield plasma transport. Intermittent bursty fluctuations of ion saturation currents I sat and/or floating potentials measured with probes are analyzed to obtain a basic property of the blobs. Comprehensive study on the fluctuation properties in the edge plasmas of linear, tokamak and helical devices is expected to give an understanding of the blobby plasma transport, because the blobby plasma transport is thought to be strongly influenced by the magnetic configuration. In this presentation, we will report the statistical analysis of the intermittent edge plasma fluctuations in the linear plasma device NAGDIS-II[5, 6, 7], JT-60U tokamak[8, 9] and the Large Helical Device (LHD)[10]. The fluctuation property has been analyzed statistically with probability distribution function (p.d.f.) and wavelet decomposition. BURSTY FLUCTUATION PROPERTY IN THE LINEAR PLASMA DEVICE Fluctuation Property in NAGDIS-II Bursty fluctuation of ion saturation currents in attached and/or detached plasmas has been investigated experimentally in the NAGDIS-II[5], which can generate high density helium plasmas with the electron density up to 10 20m.3 in steady state. The diameter of a plasma column is about 20 mm. By increasing the neutral gas pressure P in the divertor test region, we can achieve detached plasma condition. Ion saturation currents I sat and floating potential were measured with a Langmuir probe. The number of data points is 10 6 with a sampling time of 10.6s.Figure 1 shows the typical time evolution of Isat measured at different radial positions in the downstream at P of 4 mtorr, corresponding to the attached plasma condition, where r is the radial distance from the center of the plasma column. At the periphery ( r = 24 mm ) a lot of positive spikes in I sat are clearly observed. The positive spikes have the common property with the rapid positive increase and slow recovery. The I sat is analyzed with the complex Morlet wavelet decomposition. The strong intensities in the wavelet decomposition appear at a wavelet scale between 20 .sec and 100 .sec. The wavelet decompositions of I sat measured at different r show that the wavelet scale where the intensity has a peak becomes large with increasing r at the periphery, which indicates that the positive spikes tend to become wider in time. The fluctuation property has been also analyzed with probability distribution function (p.d.f.). The p.d.f. is found to be positively skewed at the periphery, meaning that large positive fluctuations are much greater than expected values from the pure random distribution (Gaussian distribution). The deviation from the Gaussian distribution function can be characterized by flatness and skewness. The skewness S is determined by: S=#x 3$/#x2$3/2 , which describes asymmetry and the flatness F = #x4$/#x2$2 measures the tail’s weight with respect to the core of the distribution. In the Gaussian distribution function, the flatness and skewness are 3 and 0, respectively. Figures 2(a) shows the radial profiles of the mean value of I sat, representing the density profile approximately, the skewness S and the flatness F at P of 4 mtorr. The skewness strongly depends on the radial position. At the central region, the skewness is found to be negative, which indicates that there are frequent negative spikes. On the other hand, the skewness becomes positive at the periphery. The flatness is slightly increasing with r. As increasing P in the divertor test region by feeding the secondary gas, the detached recombining plasmas are generated, in which the plasma density rapidly goes down along the magnetic field line mainly due to volumetric plasma recombination. Figure 2(b) shows the radial profile of the mean value of I sat, S and F in the detached plasma condition at P of 12 mtorr. The mean value of Isat becomes one fifth of that in Fig. 2(a). On the other hand, the skewness becomes positive even at the central region. This experimental result could suggest that the density bursts can propagate also along the magnetic field line when the steep density gradient exits in the detached recombining plasma. FIGURE 1. Time evolution of the ion saturation current Isat at different radial positions. Velocity Distribution of Intermittent Bursts Figure 3(a) shows the radial velocity distribution function of the density bursts at r of 9 mm and P of 5 motrr. This result clearly shows that the density bursts propagate both outward and inward across the magnetic field and the mean velocity of the bursts is calculated to be 380 m/s toward the wall. In the analysis of Fig. 3(a), all bursts with different amplitude and width in the range of the wavelet scale from 0 to 200 .sec contribute to the velocity distribution function. Figure 3(c) shows the wavelet decomposition of the I sat, which shows that the strong intensities of the wavelet decomposition are localized in the wavelet scale around 30 .sec. Figure 3(b) shows the velocity distribution function of the bursts with large amplitude located at a wavelet scale between 10 to 60 .sec. The bursts with large amplitude tend to propagate outward and the mean velocity is 810 m/s.

FIGURE 2. Radial profiles of the mean values of Isat (closed circles), the skewness (open square) and the flatness (open triangles) as a neutral pressure of (a): 4 mtorr corresponding to the attached plasma, (b) 12 mtorr to the detached plasma. FIGURE 3. Radial velocity distribution function of the density bursts at r= 9 mmand P=5 mtorr analyzed with wavelet correlation analysis for wavelet scale from (a): 0 to 200.sec, (b): 10 to 60.sec, (c):the wavelet decomposition. FLUCTUATION PROPERTY IN EDGE PLASMAS OF JT-60U AND LHD In the JT-60U tokamak, the reciprocating Mach probes are installed at the low field side (LFS) mid-plane and just below the X-point. The sampling time for Isat is 2 .s. The closed circles in Fig. 4(a) shows a profile of averaged I sat. It is found that the profile has three different e-folding lengths depending on the distance from the separatrix, d sep. The e-folding length of the averaged I sat is about 28 mm at dsep below 60 mm and 46 mm at dsep from 60 mm to 120 mm, respectively. Above dsep of 120 mm, the e-folding length becomes shorter again. Open squares in Fig. 4(b) represent Mach numbers of parallel flow velocity along the magnetic field in SOL plasma. The Mach number becomes zero around dsep of 75 mm, then the direction of the parallel SOL plasma flow changes upward to downward at this position. The small Mach number around dsep of 75 mm could be related to larger e-folding length of the averaged I sat at the dsep between 60 mm and 120 mm. Open squares in Fig. 3(a) show a radial distribution of normalized fluctuation amplitude, which monotonically increases with dsep. On the other hand, the skewness shown in Fig. 4(b) peaks around dsep = 70 mm, where the SOL plasma flow velocity is small. Large skewness indicates that positive bursty signals aredominating in the time evolution of Isat, which could be associated with the convective blobby plasma transport. Theory[1] predicts that the blobs propagate toward low field side in tokamaks because the blob motion is driven by charge separation in the scrape-off layer due to gradient B effect. On the other hand, in the LHD, the direction of the gradient in |B| is not uniform because the high-field and the low-field sides rotates poloidally along the torus in the helical system. Comparison between the intermittent bursty fluctuations in the edge plasma of tokamaks and helical devices makes it possible to understand the essential physics of the blob transport. The Large Helical Device (LHD) has a set of l = 2/m = 10 continuous helical coils and three sets of poloidal coils, producing a heliotron-type magnetic configuration[6]. Large positive bursty events were also observed near a divertor leg at which the magnetic line of force connected to the area of a low-field side with a short connection length. Condition averaging result of the positive bursty events indicates the intermittent feature is similar to the density blobs observed in tokamaks. FIGURE 4. Profiles of (a) averaged ion saturation current (closed circles) and fluctuation amplitude normalized by the averaged value (open squares), (b) skewness (closed squares) and Mach number of plasma flow along magnetic field(open squares). SUMMARY We have investigated density fluctuation properties in the edge plasmas of magnetically confined linear and toroidal devices. Radial velocity distribution function of the intermittent bursty fluctuations in the NAGDIS-II, has been analyzed by a sophisticated wavelet cross-correlation technique with complex Morlet mother wavelet. In the JT-60U, at LFS mid-plane, it was found that the positive bursty events appeared most frequently at a distance from separatrix dsep = 40-80 mm, and a kind of flat far SOL was formed in outer flux surfaces. Positive bursty events were seen in a wide SOL radii only at LFS mid-plane, where the flow reversal of the SOL plasma was observed. Influences of the radial transport of the convective blobby plasma on the SOL formation and the flow reversal were investigated. In the helical device LHD, the bursty fluctuations were also observed near a divertor leg at which the magnetic line of force connected to the area of a low-field side with a short connection length. REFERENCES 1. S. I. Krasheninnikov, Phys. Letters A, 283, 368 (2001). 2. D. A. D’Ippolito et al., Phys. Plasma 9, 222(2002). 3. G. Y. Antar et al. Phys. Rev. Lett. 87, 065001-1(2001). 4. J. A. Boedo, D. Rudakov et al. Phys. Plasmas, 8, 4826 (2001). 5. N. Ohno, D. Nishijima, S. Takamura, Y. Uesugi et al. Nucl. 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