1. Workshop on Edge Transport in Fusion Plasmas, Kraków 1 Evidence of edge turbulence structures in RFX-mod virtual shell discharges with Gas Puffing Imaging Diagnostic P. Scarin M. Agostini, R. Cavazzana, F. Sattin, G. Serianni, N. Vianello Consorzio RFX, Associazione Euratom-ENEA sulla Fusione, corso Stati Uniti 4, Padova, Italy

2. Workshop on Edge Transport in Fusion Plasmas, Kraków 2 In the Reversed Field Pinch eXperiment RFX-mod (R=2 m, a=0.46 m) a Gas Puffing Imaging Diagnostic (GPID) is being used to investigate the dynamical structures of plasma edge turbulence in different plasma conditions The GPID measures the radiation emitted from He gas puffed in H discharges and allows the investigation of edge plasma properties with high time and space resolution at high plasma current during the entire discharge. The characterization of edge turbulence has been carried out in terms of power spectrum, cross-correlation and toroidal velocity of structures. The toroidal characteristic length of intermittent structures at different time scales has been determined by applying the conditional average technique on the structures identified by the Continuous Wavelet Transform (CWT). PDF of GPI signals show a fit with 2 Gamma functions O u t l i n e

3. Workshop on Edge Transport in Fusion Plasmas, Kraków 3 RFX-mod Virtual Shell 4 (poloidally)  48 (toroidally) saddle coils, each with its own independent power supply The control of the magnetic field at the boundary can be achieved by a feedback system cancelling the local radial field measured by a set of coils on the shell Improvement of plasma temperature and confinement (up to twofold), pulse length (threefold) and effective mitigation of plasma wall interaction and mode locking are recorded The “virtual shell” operation produces also “reproducible conditions” for internal MHD plasma dynamics

4. Workshop on Edge Transport in Fusion Plasmas, Kraków 4 32 chords ( 16 + 8 + 8 ) HeI (668nm) emission Focal dept:  50mm Beam diameter:  3 mm Spatial resolution: 5 mm View area: 70mm x 30 mm Flux  10 19 ÷ 10 20 atoms/s Cloud Density n o  5 ·10 18 m - 3 Bandwidth: 2 MHz Sampling: 10 MSamples/s Gas Puffing Imaging Diagnostic

5. Workshop on Edge Transport in Fusion Plasmas, Kraków 5 Plasma and GPI signals 10 μs n/n G =0.35 n/n G =0.2 without puffing n G =10 20 ·I  (MA)·(  ·a 2 ) -1

6. Workshop on Edge Transport in Fusion Plasmas, Kraków 6 Toroidal velocity of emission fluctuations v  from cross-correlation analysis high-intensity “bursts” emerge from the background turbulence similar pattern shifted in time, propagating toroidally from chord 1 to 16, in the direction opposite to plasma current, the same of the E  B drift flow. The maximum of the cross-correlation function presents a linear dependence of the chord position with the delay time, from which it is possible to calculate the toroidal velocity v  of fluctuations, that can be interpreted as a flow velocity. The average cross-correlation length L co  v  ·  a  40÷100 mm -10 -5 0 5 10 lines of sight t(μs) lines of sight 155.60 155.65 155.70 t(ms) # 17705

7. Workshop on Edge Transport in Fusion Plasmas, Kraków 7 n/n G Experimental scaling of v  with n/n G mm n/n G =0.35 v  (km/s) n/n G The comparison of v  at different density regimes displays a saturation at about -20km/s for n/n G > 0.35 while for lower density | v  | increases Each point of the scaling is an average over 10 ms taken during the current flat-top working ranges: I   (0.3 ÷ 1) MA  (1 ÷ 5) 10 19 m -3 The trend of v  vs n/n G is obtained from a data-base of different plasma regimes: Reversal parameter F = B  (wall)/  - 0.06 ÷ - 0.3 Effective Scrape-Off Layer Depth:  SOL ( ,  )  - 20 ÷ - 4 mm P. Scarin et al., 17th PSI Conf., Hefei, 2006, p 3-28

8. Workshop on Edge Transport in Fusion Plasmas, Kraków 8 Power spectrum: decay index α depends from Power spectrum: decay index α depends from n/n G k the power–law ƒ -α in the frequency range 300÷700 kHz is considered a scaling of decay index α with n/n G is obseved 2 regions can be recognized: n/n G < 0.35 α decreases from -2 to about -3 n/n G > 0.35 α displaies a saturation at about -3 At lower frequency (ƒ < 100 kHz) the power spectra is dominated by MHD activity. ƒ [kHz] n / n G n/n G =0.35 decay index α

9. Workshop on Edge Transport in Fusion Plasmas, Kraków 9 Wavenumber/Frequency Spectrum S(k,ƒ) from 2 point spetral analysis The behaviour of k(ƒ) =  (ƒ)/  is linear until ƒ > 500kHz (frozen turbulence) The most of power content is due to fluctuations with |k| < 100 m -1 and ƒ < 500 kHz.  ( cross-correlation ) The average dispersion yields a mean phase velocity 2  ƒ/|k| consistent with v  ( cross-correlation ) At spectral width  k (ƒ)  25÷50m -1 corresponds a characteristic length L ch   k -1  20÷40 mm of turbulence structures consistent with cross-correlation length L co ƒ [kHz] k [m -1 ]  (ƒ) Coherence

10. Workshop on Edge Transport in Fusion Plasmas, Kraków 10 The statistical properties of fluctuations at different time- scales  = 1/ƒ are study with CWT A set of wavelet coefficients C  (t) is obtained for each time series C  (t) represents the time behaviour of characteristic fluctuations at each time-scale  The PDFs of the normalized wavelet coefficient fluctuations  C  /   are accounted The scaling of PDF flatness  x 4  /  x 2  2 with  is considered to weight the PDF tails Wavelet Analysis of HeI emission

11. Workshop on Edge Transport in Fusion Plasmas, Kraków 11 Intermittency from PDF flatness scaling At higher density (n/n G  0.35) the flatness increases at low time-scale (increase the tails) for 1μs<  <10μs, the process is not self-similar and exhibits an intermittent character At lower density (n/n G  0.15) the shape of PDF does not change with time-scales  but non-Gaussian behaviour (flatness > 3) has been recorded For the analysis of PDFs, the flatness for all 16 LoS is evaluated in a time window of 20ms and then the average of 16 LoS ensemble is computed for each time-scale.

12. Workshop on Edge Transport in Fusion Plasmas, Kraków 12 Toroidal width scaling of HeI emission structures Spatial features of intermittent bursts is carried out with conditional average technique A CWT has applied at reference signal to allow the detection of events on different  From the measurements of the burst intensity it is possible to put together ensemble data for all LoS at each time scale  and so to reconstruct the toroidal pattern of structure A best fit exp[-(x/  ) 2 ] has been superimposed to the average pattern of the structure, where 2  is the toroidal width of the structures A non-linear increase from 15mm to 45mm in the range 1 μs <  < 10 μs is observed

13. Workshop on Edge Transport in Fusion Plasmas, Kraków 13 Number of structures scaling The structures recognized at different  can be counted The number of structures N S per unit length is obtained after a normalisation to the measurement time portion  t and the toroidal propagation velocity v  The scaling N S vs  for two density regimes (n/n G ) is shown. There is an increase of N S at small time scales (  < 5  s) and the increase is particularly emphasized at the higher density regimes. This increase of N S corresponds at a frequency ƒ >200 kHz that is the range where the power spectra presented a power-law scaling.

14. Workshop on Edge Transport in Fusion Plasmas, Kraków 14 PDF of GPI signals: a fit with 2 Gamma functions A first empirical analysis suggests that PDF of GPI signals in RFX-mod may be interpolated with a linear combination of 2 Gamma functions This suggests the simultaneous presence of different mechanism driving respectively coherent bursts and background turbulence. It may be stressed the identification between low / high value of N, M parameters with coherent-structures / incoherent turbulence The evidence is that improved confinement regimes (Virtual Shell) appear related to a reduction of the low-N,M fluctuations. Conversely the high-N,M contribution, that in standard discharges has a small weight, gains relative importance in Virtual Shell operation. no VS N = 6.5, M = 9.8 PDF(N) = 86% PDF(M) = 14% VS N= 14.7, M = 10.5 PDF(N) = 55% PDF(M) = 45% F. Sattin et al., PPCF 48 (2006) 1033

15. Workshop on Edge Transport in Fusion Plasmas, Kraków 15 Correlation between the “coherent” fraction of the signal and the linear density of bursts A convincing test that low-N, M fraction is related to coherent part of fluctuations comes from the explicit comparison with the number of intermittent events counted through a wavelet technique. There appears a fairly good correlation between the “coherent” fraction of the signal measured through the PDF analysis (blue squares) and the linear density of bursts standing out of the background turbulence (red circles). The “coherent” fraction is conventionally set to zero when both N, M > 10, meaning that a true low-dimensional fraction of the PDF could not be recovered and when both N, M < 10 the coherent fraction is set to one. F. Sattin et al., 33th EPS Conf., Roma, 2006, p 5.093 linear density of bursts [m -1 ] coherent fraction [%]

16. Workshop on Edge Transport in Fusion Plasmas, Kraków 16 Imaging of Emission Structures Different inversion techniques have been applied to the data in order to obtain a 2D tomographic reconstruction of the light emission pattern from the line integrals. Emission structures (blobs), that move along the ExB flow, emerge from the background turbulence. The high time resolution allows to obtain a 2D image every 0.1  s.

17. Workshop on Edge Transport in Fusion Plasmas, Kraków 17 Summary A scaling v  versus n/n G of HeI emission fluctuations has been observed with a saturation at about -20km/s for higher density ( n/n G  0.35 ) From the emission power spectra a scaling of decay index α versus n/n G (in the range 300÷700 kHz) is observed Analysis of fluctuations at different time scales gives distributions with non Gaussian tails for 1 μs <  < 10 μs and more intermittent bursts at higher density From the spatial resolution of emission structures a width 15 mm < 2  < 45 mm for time scales 1 μs <  < 10 μs has been observed and their numbers N s increases at  ≤ 5 μs, particularly at higher density

18. Workshop on Edge Transport in Fusion Plasmas, Kraków 18 HeI emission Bursts compared with MHD dynamics F NSNS The internal MHD dynamic of a RFP is monitored from oscillatory behaviour of the toroidal field and is related to the cyclical process of magnetic diffusion and flux generation, which takes place in the core region (Dynamo Relaxation Event) An interesting correlation between this MHD dynamics and the edge turbulence has been observed: intermittent events are found to cluster during the toroidal field oscillations (DRE). The time behaviour of the number of structures N S at different time scale  are compared with the reversal parameter F and electron temperature inside the plasma In correspondence to DRE there is a cluster of the structures for  ≤ 5μs After DRE the electron temperature inside the plasma increases M. Agostini et al., 33th EPS Conf., Roma, 2006, p 5.094

19. Workshop on Edge Transport in Fusion Plasmas, Kraków 19 Scaling of fluctuations velocity v  with power spectrum decay index α A experimental scaling of toroidal velocity of fluctuations v  with the decay index α of power spectrum is recognized: at lower velocity corresponds a higher spectrum slope whereas at higher velocity the slope decreases to α  -2 ÷ -1.4 mm decay index α v  (km/s) The trend of v  vs α is obtained from a data-base of different plasma regimes selecting with: Reversal parameter F = B  (wall)/  -0.08 ÷ -0.2 Effective Scrape-Off Layer Depth  SOL ( ,  )  -20 ÷ -4 mm

20. Workshop on Edge Transport in Fusion Plasmas, Kraków 20 Tentative intrepretation of n/n G experimental scaling v  vs n/n G This scaling corresponds to different values of dimensionless ratio ci / ei ranging from below to above unity ci  3·Ip /a (in the edge of a RFP) ei  5·10 -11 · n ·Te -3/2 (mks units, Te in eV) ci / ei  a·Te 3/2 ·(500·n/n G ) -1 at critical density n/n G  0.35 Te  50 eV (in the edge) ci / ei  1

21. Workshop on Edge Transport in Fusion Plasmas, Kraków 21 Vacuum vessel Fan 1 Fan 2 Fan 3 Fan1Fan2Fan3  A high temporal resolution can be reached: an image every 0.1 μs  All the discharge duration is covered Back Projection Reconstruction

22. Workshop on Edge Transport in Fusion Plasmas, Kraków 22 2D Spatial Fourier Expansion k: “wave vector” along the toroidal direction q: “wave vector” along the radial direction Unknowns: coefficients C kq, D kq, E kq, F kq The linear system is underdetermined and it is solved with the Singular Value Decomposition technique

23. Workshop on Edge Transport in Fusion Plasmas, Kraków 23 % Decay index α Scaling of rms vs n/n G and rms vs decay index α of edge emission line The rms  I/ of HeI line (668nm) ranges 30% ÷ 50% and increases with the density and with the slope of power spectrum At higher values of rms corresponds a higher coherent-structures component

24. Workshop on Edge Transport in Fusion Plasmas, Kraków 24 Effective Scrape-Off Layer Depth  SOL ( ,  ) identified as the local displacement of the plasma column from the wall, by linear overlapping of m = 1 and m = 0 poloidal modes wall plasma GPI  SOL  (rad) Displacement of plasma column (m)

25. Workshop on Edge Transport in Fusion Plasmas, Kraków 25 Probability Distribution Functions of HeI Fluctuations In the case of self-similar process, the PDF of normalized fluctuation does not change its shape at different time scales. This reflect a constant flatness at all the scales, whereas if the PDF of normalized fluctuations varies with the scales with a increasing of the tails of distribution at smaller scales the process is not self-similar and exhibits an intermittent character. This obviously implies an increase of flatness at smaller time scales. The solid line indicates a fit exp(-b|X|  (  ) ).

26. Workshop on Edge Transport in Fusion Plasmas, Kraków 26 v  = f 1 (n/n G,  SOL ) toroidal velocity of emission fluctuations P( ƒ )  ƒ -   = f 2 (n/n G, F,  SOL ) power spectrum Flatness (  ) Statistical properties from the PDF of Wavelet Transform 2  (  ) =15 ÷ 45 mm 1  s<  <10  s structures toroidal width N s  n/n G  < 5  s edge structures number / unit length PDF of GPI signals show a fit with 2 Gamma functions Summary (2)