Universal extreme statistical properties (of plasma edge transport)

Transcription

1 Universal extreme statistical properties (of plasma edge transport) Ingmar Sandberg 1,2 1 2 National Observatory of Athens D. del-castillo Castillo-Negrete,, S. Fututani, S. Benkadda, X. Garbet,, G. Ropokis and K. Hizanidis

2 Outline Motivation Introduction Experimental/observational results Introducing an extreme stochastic process w(t) Basic properties of PDF(w) Comparisons with observations Conclusions

3 Motivation Understand statistical properties of plasma transport in the edge of tokamaks, stellarators, spheromaks etc. Explain the observed universality Use generic properties of plasma turbulence

4 Transport in plasma edge In plasma edge: Cross-field transport is known to be dominated by large radial transport bursty events Turbulent diffusion is nearly absent: bursty convective transport accounts for the totality of the plasma that survived parallel transport

5 Blobs, avaloids, filaments.. Interchange instability Electron motion cannot cancel the space-charge separation Blobs are convected outwards Graves, et al PPCF 47 L1-L9 (2005) Garcia et al PRL (2004)

6 Plasma edge fluctuations n Antar et al PoP 10 (2) 419 (2003)

7 Anomalous transport in laboratory n Antar et al PoP 10 (2) 419 (2003)

8 Anomalous transport on Cygnus-X1 accretion disk R. Dendy, this conference, Monday

9 High order moments K ( X X ) ( X X ) 4 3 μ μ = 3 = -3 S = = σ σ σ σ k k 2 ( ), 2 ( ) μ = X X σ = μ = X X 2

10 Scaling between K and S of density fluctuations F=K+3 TORPEX K = (1.502±0.015)S 2 (0.226±0.019) Labit et al PRL 98, (2007)

11 Scaling between K and S of SST variability K = 1.5S 2 Sura and Sardeshmukh, J. Ph. Ocean. 639 (2008)

12 Extreme statistics: Bursts attributed to the strongest coupling of turbulent fields Sea of Gaussian fluctuations

13 Stochastic process Let us construct the simplest stochastic process that accounts strongly coupled turbulent fields: given by the sum of a Gaussian and a non-gaussian: wt ( ) = z (t)+ γz (t) G where the non-gaussian is attributed to quadratic non-linearity: ng w ng (t)= z ()- t z () t 2 2 G G σ 2 0

14 Bursty behavior: recovered! wt () wt () wt () Labit, PRL 98, (2007)

15 Calculation of PDF(w) Cut off! Asymmetry induced

16 PDF(w)

17 Scaling of Kurtosis and Skewness 2 2 z ()- t z () t wt ( ) = z (t)+ G G G γ σ 2 0

18 K-S scaling w () t = γ z () t z () t Γ Γ 1G 2G wt ( ) = z (t)+ γ G z ()- t z () t 2 2 G G σ 2 0

19 K-S scaling: recovered

20 Universal PDF: recovered Antar et al PoP (2003)

21 Conclusions A stochastic process w(t) for the description of bursty fluctuations based on generic properties of quadratic non-linearities was introduced The associated PDF(w) recovers observed features of extreme processes The analytic form of PDF(w) can be used as a diagnostic tool Do relaxation processes in convective systems lead to a state of extreme intermittency?

22 Thank you!

23 White noise spectra nt ( ) = n (t)+ γn (t) G ng n ng (t)= n ()- t n () t 2 2 G G σ 2 0 White noise (non-gaussian) type Signal does not change in time, H=0 Absence of correlations Extreme bursty behavior