workshop on edge transport in fusion plasmas, kraków 1 evidence of edge turbulence structures in...

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


• 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


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


• 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 1019 ÷ 1020 atoms/s

• Cloud Density no 5 ·1018

m-3

• Bandwidth: 2 MHz• Sampling: 10 MSamples/s

Gas Puffing Imaging Diagnostic


Plasma and GPI signals

10 μs

n/nG=0.35

n/nG=0.2

without puffing

nG=1020·I(MA)·(·a2) -1


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 EB 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 Lco v· a 40÷100 mm

-10 -5 0 5 10

line

s o

f si

gh

t

t(μs)

line

s o

f si

gh

t

155.60 155.65 155.70t(ms)

# 17705


Experimental scaling of v with n/nn/nGG

mmn/nn/nGG=0.35=0.35

v

(km

/s)

n/nG

• The comparison of v at different density regimes displays a saturation at about -20km/s for n/nG > 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 <ne> (1 ÷ 5) 1019 m-3

The trend of v vs n/nG is obtained from a data-base of different plasma regimes:

• Reversal parameter F = B(wall)/<B> - 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


Power spectrum: decay index Power spectrum: decay index αα depends from depends from n/nG

k

• the power–law ƒ-α in the frequency range 300÷700 kHz is considered

• a scaling of decay index α with n/nG is obseved

• 2 regions can be recognized: n/nG< 0.35 α decreases from -2 to about -3

n/nG> 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 / nG

n/nG=0.35

deca

y in

dex

α


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.

• The average dispersion yields a mean phase velocity 2ƒ/|k| consistent with v((cross-correlationcross-correlation))

• At spectral width k(ƒ) 25÷50m-1 corresponds a characteristic length Lch k-1 20÷40

mm of turbulence structures consistent with cross-correlation length Lco

ƒ [kHz]

ƒ[kH

z]

k [m-1]

(ƒ)

Coh

eren

ce


• 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 x4 / x2 2 with is considered to weight the PDF tails

Wavelet Analysis of HeI emission


Intermittency from PDF flatness scaling

•At higher density (n/nG 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/nG 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.


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


Number of structures scaling

• The structures recognized at different can be counted

• The number of structures NS per unit length is obtained after a normalisation to the measurement time portion t and the toroidal propagation velocity v

• The scaling NS vs for two density regimes (n/nG ) is shown.• There is an increase of NS at small time scales ( < 5s) and the increase is particularly emphasized at the higher density regimes.• This increase of NS corresponds at a frequency ƒ >200 kHz that is the range where the power spectra presented a power-law scaling.


PDF of GPI signals: a fit with 2 Gamma functions

MnDnNnCnnP MNfit expexp)( 11

• 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 = 10.5PDF(N) = 55% PDF(M) = 45%

F. Sattin et al., PPCF 48 (2006) 1033


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

linea

r de

nsity

of b

urst

s [m

-1]

cohe

rent

frac

tion

[%]


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.


Summary

• A scaling v versus n/nG of HeI emission fluctuations has been observed

with a saturation at about -20km/s for higher density ( n/nG 0.35 )

• From the emission power spectra a scaling of decay index α versus n/nG

(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 Ns increases at ≤ 5 μs, particularly at higher density


HeI emission Bursts compared with MHD dynamics

F

NS

• 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 NS 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


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 ÷ -1.4mm

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)/<B> -0.08 ÷ -0.2

• Effective Scrape-Off Layer Depth SOL(,) -20 ÷ -4 mm


Tentative intrepretation of

experimental scaling v vs n/nn/nGG

• 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·Te3/2·(500·n/nG ) -1

•at critical density n/nG 0.35

• Te 50 eV (in the edge)

• ci / ei 1


Vacuum vessel

Fan 1

Fan 2

Fan 3

Fan1•Fan2•Fan3

A high temporal resolution can be reached: an image every 0.1 μs

All the discharge duration is covered

Back Projection Reconstruction


2D Spatial Fourier Expansion

k: “wave vector” along the toroidal direction

q: “wave vector” along the radial direction

Unknowns: coefficients Ckq, Dkq, Ekq, Fkq

The linear system is underdetermined and it is solved with the Singular Value Decomposition technique


% %

Decay index α

Scaling of rms vs n/nG and rms vs decay index α of edge emission line

• The rms I/<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


Effective Scrape-Off Layer Depth SOL(,)

identified as the local displacement of the plasma column from the identified as the local displacement of the plasma column from the wall, by linear overlapping of m = 1 and m = 0 poloidal modeswall, by linear overlapping of m = 1 and m = 0 poloidal modes

wallwall

plasma

GPI

SOL

(rad)

Dis

plac

emen

t of

plas

ma

colu

mn

(m)


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| ( ) ).


• v= f1(n/nG, SOL) toroidal velocity of emission fluctuations

• P( ƒ ) ƒ - = f2 (n/nG , F, SOL ) power spectrum

• Flatness ( ) Statistical properties from the PDF of Wavelet Transform

• 2 () =15 ÷ 45 mm 1s<<10s structures toroidal width

• Ns n/nG < 5 s edge structures number / unit length

• PDF of GPI signals show a fit with 2 Gamma functions

Summary (2)

workshop on edge transport in fusion plasmas, kraków 1 evidence of edge turbulence structures in...

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