Device type Spherical tokamak Heliotron-type stellaratorMajor radius, R 0.85m 3.9mMinor radius, a 0.65m 0.65m

Typical magnetic field strength 0.5T 2.5TProbe type Reciprocating probe Reciprocating probe

Probe location Outboard midplane MidplaneSampling frequency 500kHz 1000kHz

Typical length of time series 50ms / 25,000 samples 1s / 250,000 samplesShot numbers 14219, 14222 76566, 77659

Statistical properties of edge turbulence in MAST spherical tokamak and LHD stellarator

J.M. Dewhurst1, B. Hnat1, N. Ohno2,3, R.O. Dendy4,1, S.Masuzaki3, T. Morisaki3, A. Komori3, B.D. Dudson5, G.F. Counsell4, A. Kirk4 and the MAST team4

1 Centre for Fusion, Space and Astrophysics, University of Warwick, Coventry U.K.;2 EcoTopica Science Institute, Nagoya University, Nagoya 464-8603, Japan;

3 National Institute for Fusion Science, Toki 509-5292, Japan;4 Euratom/UKAEA Fusion Association, Culham Science Centre, Abingdon, Oxfordshire OX14 3DB, U.K.;

5 Physics Department, University of York, YO10 5DD, U.K

1. IntroductionTurbulence in the scrape-off layer (SOL) and divertor region of magnetically confined plasmas is bursty and intermittent. Intermittent events, associated with density blobs (filaments), have been linked with increased cross-field transport and are therefore a subject of much study. Recent experimental evidence suggests that this edge turbulence has generic statistical properties which emerge in the functional forms of the probability density functions (PDFs) and the scaling of their higher moments [1-3]. The extent of this universality across a range of confinement systems and operational regimes is an important but unresolved issue. Here, we focus on the statistical properties of measurements of the ion saturation current jsat from the edge region of the Mega-Amp Spherical Tokamak (MAST) and the Large Helical Device (LHD) stellarator [4-6]. We utilise modern statistical techniques which provide constraints on models and theory.

3. Statistical methods [7,8]

Fluctuations on time scale τ given by: Scaling of absolute moments:

Probability density function (PDF) on time scale τ: PDFs are fitted with three model distributions [9]:

• Log-Normal:

• Gamma:

• Generalised Extreme Value:

2. Data sets Ion saturation current, jsat, collected by Langmuir probe in the mid-

plane of the device LHD data are stationary for much longer then MAST data Power spectrum was used to select data with clean high frequency

regions No low pass filter during data collection, so some aliasing is possible Ion saturation current is defined as: jsat signals from MAST Discharge 14222 and LHD discharge 76566

( , )satP I

'

( ( ') ) /t

sat sat satt t

I j t j

, sound speedsat e s sj en c c

( )( , ) m mm sat satS I I

2

2

ln( )( | , , ) ( 2 exp

2sat

LN sat sat

IP I I

1 1( | , , ) ( ( )) exp( )a a satG sat sat

IP I a b b a Ib

1 11( )1( | , , , ) exp 1 1k ksat sat

GEV sat

I IP I k k k

For k>0 PGEV represents Fréchet distribution of maxima selected from the setof realizations of the process with diverging second moment.For k=0 PGEV represents Gumbel distribution of maxima selected from the setof realizations of the process with converging second moment

4. Autocorrelation function and skewness• Autocorrelation is related to power spectrum via Fourier transform• Skewness measures the asymmetry of statistics, S=0 for the gaussian process• Skewness is often thought of as a measure of nonlinear interactions and in turbulent system can be related to the energy transfer rate

5. Absolute moment analysis [10]

• All discharges show two distinct scaling regions• We define following temporal scales:

• τac where the autocorrelation function falls below the threshold of ~0.1• τm which separates two distinct scaling regions of the absolute moments

• For MAST discharges: τac≈τm≈30-50 μs; for LHD these are shorter τac≈τm≈10-20 μs• Region I with scaling of ~1 is consistent with scaling of coherent signal• Temporal scale , τm , is similar to the observed lifetime of MAST [11]6. Probability distribution Function

MASTτ ≈ 4 μs

LHDτ ≈ 4 μs

MASTτ ≈ 64 μs

LHDτ ≈ 64 μs

• PDF of aggregates, Isat(τ), is non-Gaussian on all temporal scales, but evolves toward more symmetric and Gaussian-like form for large values of τ• Extreme value distributions appear to provide a generic model for the PDFs, while other functions (log-normal and gamma) fit only particular temporal scales

8. Conclusions

References:[1] B Ph van Milligen, R Sánchez, B A Carreras et al., Phys Plasmas 12, 052507 (2005)

[2] G Y Antar, G Counsell, Y Yu, B Labombard and P Devynck, Phys Plasmas 10, 419 (2003)

[3] R O Dendy and S C Chapman, Plasma Phys Control Fusion 48, B313 (2006)

[4] N Ohno, S Masuzaki, H Miyoshi, S Takamura, V P Budaev, T Morisaki, N Ohyabu and A Komori, Contrib Plasma Phys 46, 692 (2006)

[5] N Ohno, et al., 21st IAEA Fusion Energy Conference, Chengdu, China, Oct 16-21, 2006, EX/P4-20

[6] S Masuzaki, T Morisaki, N Ohyabu, A Komori et al., Nucl Fusion 42, 750 (2002)

[7] J M Dewhurst, B Hnat, N Ohno, R O Dendy, S Masuzaki, T Morisaki and A Komori, Plasma Phys. Control. Fusion 50 No 9, 095013 (2008)

[8] B D Dudson, R O Dendy, A Kirk, H Meyer and G F Counsell, Plasma Phys Control Fusion 47, 885 (2005)

[9] D. Sornette, Critical Phenomena in Natural Sciences; Chaos, Fractals, Selforganization and Disorder: Concepts and Tools, Springer-Verlag, 2000!.

[10] B Hnat, B D Dudson, R O Dendy, G F Counsell, A Kirk and the MAST team, Nucl Fusion 48, 085009 (2008)[11] A Kirk, N Ben Ayed, G Counsell, B Dudson et al., Plasma Phys Control Fusion 48, B433 (2006)

• Statistically, MAST and LHD Isat aggregates are different, but some generic features are present• PDFs are non-Gaussian and can be modelled by extreme value distributions• Differences in statistics are related to the size/shape of coherent structures

7. Averaged peak shape

• Observed statistical features can be related to the average peak shape for MAST and LHD datasets.• MAST peaks (blobs, filaments) are broader and more asymmetric as compared to these from LHD

Green-MASTBlue-LHD