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Turbulence and coherent structuresTurbulence and coherent structuresin the HT-7 Tokamakin the HT-7 Tokamak

Guo Sheng Xu (Guo Sheng Xu (徐国盛徐国盛 ))

B.N. Wan, W. Zhang, S.Y. Ding, J.F. Chang, Y.D. LiB.N. Wan, W. Zhang, S.Y. Ding, J.F. Chang, Y.D. Li

Institute of Plasma Physics, Chinese Academy of Sciences, Hefei, ChinaInstitute of Plasma Physics, Chinese Academy of Sciences, Hefei, China

gsxu@ipp.ac.cngsxu@ipp.ac.cn

Hang Zhou meeting Sept. 25, 2007Hang Zhou meeting Sept. 25, 2007

systemssystems

Plasma edge region:Langmuir probe arrays

Questions presented for discussion

1. Evidence for ballooning structures of plasma turbulence in HT-7

2. Zonal flows measurements in HT-7

3. Electrostatic coherent mode in HT-7

4. Multi-scale coherent structure in plasma turbulence

5. Open questions

toroidallinearmodecoupling

实验中测量到的湍流，显然是充分发展的非线性饱和状态的结果。我们看到的不是一个线性的单模，而是多模叠加并充分演化的最终状态。非线性湍流模拟提供了一个和实验比较以及理解实验结果的平台。

Ballooningstructures

Zonal flows break the global eigenmode structure in ITG turbulence more isotropic in direction

In a torus linear mode couplingballooning structuresToroidal global eigenmode

kr

02

0

sk

qnkr

tirqintr n 0expˆ,,,~

k

single mode structure

Li

qR

mnqk

//

qnd

1

At plasma edge turbulence propagate in theelectron diamagnetic direction and alsopropagate in the radial direction

02

0

sk

qnkr

dr

dq

q

rs

r

A movie shows the intermittently occurring coherent structure in HT-7

r

r

HT-7上发现湍流的实频依赖于当地参数。Turbulence frequency was found increase with TePropagate in the electron diamagnetic direction

In plasma core measured byCO2 collective scattering

0 250 500 750 1000 1250 1500 1750 20000.0

0.2

0.4

0.6

0.8

1.0

No

rma

lize

d P

ow

er

Sp

ect

ra

Frequency ( kHz )

CO2 laser scattering

HT-7 Shot 81705200 ~ 750 ms

k = 11.4 cm-1

k = 20 cm-1

0 200 400 600 800 10000.0

0.2

0.4

0.6

0.8

1.0

No

rma

lize

d P

ow

er

Sp

ect

ra

Frequency ( kHz )

Measured byLangmuir probe

= 0.6 = 0.78 = 0.9

In plasma edge measured byLangmuir probe

ks = 1 ~ 5

In plasma core frequency band10 kHz ~ 1 MHz/ci = 0 ~ 6%

ks = 0 ~ 1

In plasma edge frequency band10 kHz ~ 300 kHz/ci = 0 ~ 2%

ee

e Tdr

dn

eBn

Tk~*

020406080

01020304050

010203040

0 20 40 60 80 1000

10

20

0 20 40 60 80 1000 20 40 60 80 100

ne

f

( 2 )r = 0.5 cm

( 3 )r = 0 cm

( 4 )r = -0.5 cm

( 5 )r = -1 cm

( 6 )r = -1.5 cm

( 7 )r = -2 cm

( 8 )r = -2.5 cm

( 9 )r = -3 cm

( 10 )r = -3.5 cm

( 1 )r = 1 cm

( 11 )r = -4 cm

( 12 )r = -4.5 cm

Aut

o p

ower

spe

ctra

S(f

)

f ( kHz )

In plasma edge measured by Langmuir probe

ne0 ~ 1.51019m-3

ee

e Tdr

dn

eBn

Tk~*

Questions presented for discussion

1. Evidence for ballooning structures of plasma turbulence in HT-7

2. Zonal flows measurements in HT-7

3. Electrostatic coherent mode in HT-7

4. Multi-scale coherent structure in plasma turbulence

5. Open questions

ks = 0 ~ 1

/ci = 0 ~ 2%

Zonal flowsspectrumThere are generally three components in

the measured fluctuation spectra:1. broad band turbulence2. zero-mean-frequency zonal flows3. low frequency coherent mode

Zero-mean-frequency zonal-flow modeStudy on the HT-7 tokamak

Zonal flows pattern

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-3-2-10123

-3-2-10123

-3-2-10123

0 20 40 60 80 100-3-2-10123

0 20 40 60 80 1000 20 40 60 80 100

( 2 )r = 0.5 cm

( 3 )r = 0 cm

( 4 )r = -0.5 cm

( 5 )r = -1 cm

( 6 )r = -1.5 cm

( 7 )r = -2 cm

k (f

) (

ra

d/c

m )

( 8 )r = -2.5 cm

( 9 )r = -3 cm

( 10 )r = -3.5 cm

( 1 )r = 1 cm

( 11 )r = -4 cm

f ( kHz )

( 12 )r = -4.5 cm

ion

ele

Poloidal dispersion relations measured at 12 radial locationsPoloidal dispersion relations measured at 12 radial locations

Ed

ge

SOL

Questions presented for discussion

1. Evidence for ballooning structures of plasma turbulence in HT-7

2. Zonal flows measurements in HT-7

3. Electrostatic coherent mode in HT-7

4. Multi-scale coherent structure in plasma turbulence

5. Open questions

Langmuir probe

magnetic coils

Low frequency coherent mode in HT-7

10~20 kHz electrostatic coherent mode was frequently observed in the plasma edge region of the HT-7 tokamak. Our special designed new experiments clearly demonstrated that this coherent mode is strongly correlated with tearing mode activity in the plasma core region.

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Tearing mode

10 kHz

17 kHz

P2

P1

Mirnov coils

Cross section

MHD spectrumMeasured byMirnov coils

9 kHz 18 kHz

MHD spectrumMeasured byMirnov coils

Potential fluctuation spectrameasured by Langmuir probeat plasma edge

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Correlation between two potential signals toroidally separated by about 90°Turbulence is almost completely decorrelated, while MHD perturbations have strong correlation in long distance.

tnmim

mnmn

rer

rbB

1

1

tnmim

mnmnr

rer

ribB

1

1

0

1

0

1

**

**

*

0~

02

3

2

3

0

n

n

T

e

mnpenmnmn

pnTTnnTTn

nn

e

gt

RBtt

t

uuBBuEuuuu

uuuuuu

uu

Global magnetic field perturbations induced by rotating islands of tearing mode

Coupling of the global magnetic field perturbations with the local electron drift mode large-scale electrostatic perturbations

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Poloidal rake probe

MHD spectrumMeasured byMirnov coils

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Questions presented for discussion

1. Evidence for ballooning structures of plasma turbulence in HT-7

2. Zonal flows measurements in HT-7

3. Electrostatic coherent mode in HT-7

4. Multi-scale coherent structure in plasma turbulence

5. Open questions

m

immrnqtinirt expˆexp,,,~

Different mode number overlapping

4 cm inside the LCFS, averaged lifetime of turbulence eddies is around 25 s.lifetime of the largest turbulence eddy is about 100 s, beyond this time scale the fluctuation is completely decorrelated.

long correlation tailfrom 12.5 to 100 s

Turbulence structureat plasma edge

Intermittently occurring large-scale coherent structuresmainly in low frequency region

a

tts

attsaW as

1

,, ,

Two dimension FFTDispersion relation Vph = 2 km/s

Typical drift-wave dispersion relation

Turbulence propagates in the electron diamagnetic direction with phase velocityVph ~ 2 km/s.

Turbulence concentrates in low frequency and long wavelength region.Decay towards high frequency and short wavelength region.

Large-scale coherent structure : poloidal scale > 6 cm, time scale > 50 sSmall-scale coherent structure : poloidal scale < 1 cm, time scale < 10 sCoiflet wavelets (a biorthogonal wavelet) are used to extract these structures

Structures self-similarity Intermittency

Use singular value decomposition method to seethe multi-scale structures of plasma turbulence

Sort according tosignal magnitude

Large-scale

Large-scale structures have long lifetime up to 100 s

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1. Which mode is responsible for plasma turbulence at tokamak edge? Particular instability at plasma edge or spreading from the core region?

2. Plasma turbulence structure in tokamaks is ballooning or not?

3. Besides zonal flows, local parameters (n, T, p) changing (with r) is also a possible reason for breaking the global enginemode structure and the presence of mesoscale ballooning structures.

4. Big eddy not necessarily implies big contribution to transport. The traditional fluid picture of convection transport need to be reconsidered. Particles scattering by wave diffusive transport

Open questions

Li

Thanks for your attention.

Filamentary structures or blob structures in plasma turbulence were observed in some tokamaks recently by imaging: TFTR, ASDEX, Alcator C-Mod, DIII-D, NSTX. // >> 1 m (qR~10 m), = 1~10 cm. beam emission spectroscopy (BES)gas-puff imaging (GPI)

NSTXMaqueda, Wurden, ZwebenRev. Sci. Instrum. 72, 931 (2001)

Alcator C-ModGrulke, Terry, LaBombard, ZwebenPhys. Plasmas 13, 012306 (2006)

Not ELMy !

Alcator C-ModTerry, LaBombard, Zweben, http://www.pppl.gov/~szweben/index.html

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