Intermittency Studies in DIII-D

Intermittency Studies in DIII-D

Presented by J. Boedo

For

D. Rudakov, R. Moyer, S. Krasheninnikov, G. McKee, D. Whyte, S. Allen, D. Colchin, T. Evans, A. Leonard, A. Mahdavi, G. Porter, P.

Stangeby, J. Watkins, X. Xu and the DIII-D Team.

Motivation

•Recent results from ALCATOR C-MOD [La Bombard, APS2000] have indicated that strong recycling occurs at the main chamber wall.•DIII-D research [D. Whyte] has determined that the walls are a large source of carbon.

•What is then the mechanism that brings plasma to the walls?

•Previous results in DIII-D [Moyer, 96] indicated that transport in the far SOL was stronger than thought.•Profiles in the far SOL of various tokamaks [Boedo 98, Heller 99]feature flat profiles in the far SOL => diffusion?•Intermittency has been identified as a significant source of transport in various devices

•Tokamaks: Heller 99 (CASTOR), others•Linear: Nielsen 96, Lehmer 96, Antar 2001

Intermittency in DIII-D Apparent in Short Time Scale (1ms)

Rprobe- Rsep 0.5cm Rprobe- Rsep 5cm Rprobe- Rsep 10cm

Is

Vf2

E

IsE

0.0 100

5.0 104

1.0 105

1.5 105

2.0 105

2.5 105

3.0 105

1.00 1.10 1.20 1.30 1.40

Jsat

(A/cm2) vs Ψ

Jsat

Ψn

= 2* (-( 0- 3)/ 4)y m exp M m m

ErrorValue1.9302 +10e1.416 +05e2 m

187260.966633 m0.00363280.137614 m

NA8.0843 +11eChisqNA0.89858R

Thomson scattering Is Shows similar behavior

0.0

50.0

100.0

150.0

200.0

1.00 1.10 1.20 1.30 1.40

Te (eV) vs Ψ

n

_ _TS EV THOM

Ψn

= 2* (-( 0- 3)/ 4)y m exp M m m

ErrorValue2.947 +07e92.7592 m

355400.992573 m0.00367150.112114 m

NA9.7566 +05eChisqNA0.87116R

Relative Flcutuation level increases with radius

0.00

0.05

0.10

0.15

0.20

0.25

0.30

1.00 1.10 1.20 1.30 1.40

ne (m-3 ) vs Ψ

n

_20_NE THOM

Ψn

= 2* (-( 0- 3)/ 4)y m exp M m m

ErrorValue406180.166592 m822360.970133 m

0.00782570.337514 mNA0.42668ChisqNA0.87967R

Do Intermittent Structures Originate at the LCFS?

Are they reduced/eliminated during H-mode?

C-Mod

DIII-D

Experimental Arrangement on DIII-D

Separatrix

R sep

Probe

ThomsonScattering

Vf1

Vf2

Te or Isat

Doubleprobe

Probe head layout

Poloidal electric field is estimated as:E (Vf2- Vf1) /a

a

The total in-and-out (plunge) time is about 0.2 s

The total plunge length is about 15 cm

Rsep is the major radius of the separatrix (calculated by EFIT) at the probe location

One Tool: Conditional Averaging

Threshold

t

•Conditional averaging tools allow us to extract pulsed or intermittent information from a signal

•Features that are correlated can be brought out

•Used by Fillipas (TEXT), Nielsen, Heller (CASTOR)

Reference Signal

Reference Signal

Search in L and H Mode Discharges

Edge/SOL Profiles L-H Comparison

0

5

10

15

0 2 4 6 8 10 12 14

L and H Mode

L-ModeH-Mode

L-Mode

H-Mode

ELM

R-Rsep

(cm)

0

10

20

30

40

50

60

70

80

0 2 4 6 8 10 12 14

L and H Mode

L-ModeH-Mode

L-Mode

ELM

H-Mode

R-Rsep

(cm)

Ne Bursts vs R in L and H-mode

100

101

102

0.0 20 40 60 80 1.0 102

cond105191_2500_2505.tab;1

Ne (x10^18m-3)Ne (x10^18m-3)Ne (x10^18m-3)Ne (x10^18m-3)Ne (x10^18m-3)Ne (x10^18m-3)Ne (x10^18m-3)

t (mks)

100

101

102

103

0.0 20 40 60 80 1.0 102

cond105188_2500_2505.tab;1

Ne (x10^18m-3)Ne (x10^18m-3)Ne (x10^18m-3)Ne (x10^18m-3)Ne (x10^18m-3)Ne (x10^18m-3)Ne (x10^18m-3)

t (mks)

Skewness and Event Count Suggests Creation at LCFS

-40

-30

-20

-10

0

10

20

30

40

-2 0 2 4 6 8 10

Positive, H-modeNegative, H-modeTotalPositive, H-modeNegative, H-modeTotalPositive, L-modeNegative, L-modeTotal L-Mode

R-Rsep

(cm)

Negative events dominate inside LCFS and positive events from LCFS to the wallDifference between L and H mode!!!

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

-2 0 2 4 6 8 10

L-ModeH-Mode

R-Rsep

(cm)

Probe

BES

A Simple Interpretative Model: Sergei Krasheninnikov’s

• High density plasma structures detach from the bulk plasma due to turbulence effects resulting in plasma stratification in the region around separatrix.

• These structures extended along the magnetic field lines.

• Propagate to the outer wall due to plasma polarization and associated drift.

VE

+

-

VExB~ C s i

R

wall

plasma blob

From Sergei’s APS’00 poster and 2001 PRA

r

r B ×∇B

r E ×

r B

Shot#96346 reversed Bt Shot#96329 normal Bt

Reversal of Bt results in reversed object polarization

The GradB drift polarization mechanism is supported!!

What can we learn quantitatively from these measurements?

rr Vt ≈

Vr can be calculated as E /B as per Sergei’s model and simple ExB force

t

Rprobe- Rsep (cm) t (s) E (V/m) Vr(m/s) r(cm)

LCFS 0.5 1.510-5 4000 2000 3

5 210-5 1500 750 1.5

Wall 10 1.510-5 500 250 0.37

The radial size of the objects can be calculated at ~2 cm at LCFS!The bursts are slowing down, decaying and thinning as they move outThere about 104 of these per s!

Probes are essential instruments for these studies due to their dense datasets and high bandwidth

Poloidal Velocity is significant in L and H Mode

-12000

-10000

-8000

-6000

-4000

-2000

0

2000

-2 0 2 4 6 8 10 12 14

V ( / )m s

105191 L105188 H

-R Rsep

( )cm

Vf2

Vf1

•Vf1 is lagging behind Vf2 by 1-1.5s

•For the tip separation of 5.2mm: V = 5.2e-

3/1.2e-6 4300 m/s

•Cross-Correlation measurements yield V =

5.2e-3/3.0e-6 1733 m/s•This velocity is directed down, towards X-

point, same direction as VrB

•Poloidal size at LCFS is ~ 2cm!!

Various Diagnostics Indicate Structures Exist

D, Colchin ORNL,D. Whyte UCSD

QuickTime™ and a decompressor

are needed to see this picture.



G. McKee, UW





BES Data Confirms Presence of Structures and Size





6 cm

5 cm

G. McKee, UW (2001)

•Structures move poloidally at ~5km/s at the LCFS •The size near the LCFS is 2x2 cm •In agreement with probes!!

-1 103

0 100

1 103

2 103

3 103

4 103

5 103

-2 0 2 4 6 8 10 12 14

Vpol vs R

VExB

Vdel

Vcross-corr

NPosition

Flux vs R, L and H-mode

0 100

1 104

2 104

3 104

4 104

5 104

6 104

0 20 40 60 80 100

cond105195_4460_4465_744

Γ r (m2s-1

) 10x

18

(t )s0 100

1 104

2 104

3 104

4 104

5 104

6 104

0 20 40 60 80 100

cond105188_2465_2470_769

Γ r (m2s-1

) 10x

18

(t )s

H-Mode L-Mode

0 100

4 104

8 104

1 105

2 105

0 20 40 60 80 100

cond105188_2465_2470_769

Γ r (m2s-1

) 10x

18

(t )s

ExB Flux is much higher at LCFS and falls rapidly with R (within 0.5 cm)

Flux is much higher in L-mode in the SOL

Te Bursts vs R, L and H-Mode

1.0

10.0

100.0

0.0 20 40 60 80 1.0 102

cond105191_2500_2505.tab;1

Te (eV)Te (eV)Te (eV)Te (eV)Te (eV)Te (eV)Te (eV)

t (mks)

1.0

10.0

100.0

0.0 20 40 60 80 1.0 102

cond105188_2500_2505.tab;1

Te (eV)Te (eV)Te (eV)Te (eV)Te (eV)Te (eV)Te (eV)

t (mks)

Spikes >2.5 rms are ~ 50% of total ExB transport

(IsE -< IsE >)/ (IsE))rmsRelative spike amplitude:

Not much difference between H and L modes

0.0

0.2

0.3

0.5

0.7

0.8

1.0

0 1 2 3 4 5 6

Relative FLux vs Event Size

H-mode 1.6cmH-mode 2cmL-mode 0.7cmL-mode 2cm

Γ/Γ_s

Intermittent ExB transport already accounted for

Γ⊥tot =D⊥∇n

NEOCLASSICAL+

1Bϕ

˜ n ̃ E θ

“Diffusive”classical and neoclassical

losses “Turbulent”driven by wide-band

elecrostatic turbulence

“Convective”Blobs

SCALE?

•However, the dynamics of these blobs is quite different•Instead of diffusing, they convect.

1Bϕ

˜ n ̃ E θBROADBAND

+1Bϕ

˜ n ̃ E θINTERMITTENT

Broadband Turbulence Particle Flux L-H Mode

-1 1017

-5 1016

0 100

5 1016

1 1017

2 1017

2 1017

3 1017

3 1017

-2 0 2 4 6 8 10 12 14

Γr L and H Mode

Γ r cm-2s

-1

-R Rsep

( )cm

0

0.5

1

1.5

2

L modeELM-free H mode

EFIT separatrix

shot 82830

-1

-0.5

0

0.5

1

1.5

2

-2 -1 0 1 2 3 4 5

ohmicohmic H-mode

EFIT separatrixshot 77739

0

0.5

1

1.5

2

-1.0 0 1.0 2.0 3.0 4.0 5.0 6.0

ELMing H modeVH mode

( )R cm

87504 & 83231shots EFIT separatrix

R. Moyer 92-95

€

Deff =˜ Γ

∇n

Effective diffusion coefficient flattens or increases in the SOL

L Mode ne scan Comparison Discharges

FourDensityPlateaus

Edge/SOL Profiles ne Scan

0

10

20

30

40

50

0 2 4 6 8 10 12 14

Discharges 105194_95

5.54.53.52.5

R-Rsep

(cm)

0

2

4

6

8

10

0 2 4 6 8 10 12 14

Discharges 105194_95

5.5

4.5

3.5

2.5

R-Rsep

(cm)

Broadband Turbulence Particle Flux Ne Scan

0 100

1 1017

2 1017

3 1017

4 1017

5 1017

0 2 4 6 8 10

Γr L Mode N

e Scan

5.54.53.52.5

-R Rsep

( )cm

Ne=5.5 1013 cm-3

Ne=2.5 1013 cm-3

•Flux Increases with density

• Flux roughly accounts for particle inventory

Skewness Shows Trend with Density

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 2 4 6 8 10

Skewness vs R, Ne Scan

Ne=2.5Ne=3.5Ne=5.5Ne=4.5

R-Rep (cm)

Higher ne Pulses for higher averaged ne

0

5

10

15

20

25

30

0 20 40 60 80 100

cond105195_4450_4455.tab;1

t ( )s

0

5

10

15

20

25

30

0 20 40 60 80 100

cond105194_3255_3260.tab;1

t ( )s

Intermittent Flux Increases with Density

0.0 100

1.0 104

2.0 104

3.0 104

4.0 104

5.0 104

6.0 104

0 20 40 60 80 100

Flux 105194_2

Γ r (m2s-1

) 10x

18

(t )s0 100

1 104

2 104

3 104

4 104

5 104

6 104

0 20 40 60 80 100

Flux 105195_2

Γ r (m2s-1

) 10x

18

(t )s

Conclusions

•Intermittency exists in DIII-D in L and H-mode

•The structures are created near the LCFS

•They propagate poloidally in the ExB direction (faster than ExB?)

•In the framework of Krasheninnikov’s model:•GradB polarization is responsible for radial motion•So far evidence supports the mechanism•Then a radial velocity can be calculated

•Structures shrink from 2 cm at the LCFS to 0.5 cm at the wall•Structures slow down as they move radially

•Poloidally from 5 km/s to ~0.1-0.2 km/s•Radially from 2 km/s to 0.2 km/s

•Other diagnostics show similar behavior (BES, D_alpha, etc)

This is NOT new. All the elements were available before 2000

• Edge density profiles in DIII-D TEXTOR and PISCES can show

different decay lengths in near and far SOL with that in far SOL often

being much longer (Watkins et al J. Nucl. Mater. 1992, Boedo et al

RSI 1998)

• Turbulent EB transport is considerable in far SOL (Moyer et al J.

Nucl. Mater. 1997, Boedo, et al. 1999, 2000)

• Isat PDFs are usually positively skewed while those of Vf are negatively

skewed or Gaussian (Bora, 92, Turney, Moyer et al APS’9, Carreras)

• While Isat near the separatrix has skewed PDF, PCI and BES show

Gaussian PDFs for the density fluctuations (Rost et al APS’00)

• A. V. Filippas, et al (TEXT 95), A. H. Nielsen et al (96), Heller

(CASTOR 99) etc etc.

0.1

1.0

10.0

100.0

224 226 228 230 232 234 236 238 240

Jsat vs R

isat 103004_1isat 103004_2

Rlp (cm)

y = m2*exp(-(M0-m3)/m4)

ErrorValue

8.8523e+063.806m2

1.4463e+07226.13m3

0.535666.2745m4

NA15.199Chisq

NA0.92805Ry = m2*exp(-(M0-m3)/m4)

ErrorValue

1.0594e+074.5251m2

1.436e+07227.63m3

0.47246.1905m4

NA28.703Chisq

NA0.94222R

L-ModeUSNHigh TriangularityIp~ 1 MANe~ 4.5 1019

Isat=6 cm !!!

Intermittency-Dominated Transport is NOT Always Present

Which explains why it has not been emphasized before!

L-ModeUSN-DNMedium Triangularity

Isat= 2.5 cm !!!

0.1

1.0

10.0

100.0

225 230 235 240

Jsat vs R

isat 102025isat 102024isat 102022isat 102021isat 102020

Rlp

y = m2*exp(-(M0-m3)/m4)

ErrorValue

1.0318e+074.6658m2

5.3005e+06225.56m3

0.143812.4529m4

NA3.9978Chisq

NA0.98351R

Significant Spikeness is NOT common in DIII-D

Statistical Moments Help Evaluate Intermittency

Variance =σ 2 =1N

Xj −N / 2 −X ( )2

j=0

N−1

∑

Mean =X =1N

Xj−N / 2j=0

N−1

∑

Skewness=S=1N

Xj−N / 2 −X

σ

⎛

⎝ ⎜

⎞

⎠ ⎟

3

j=0

N−1

∑

Kurtosis =K =1N

Xj −N / 2 −X

σ

⎛

⎝ ⎜

⎞

⎠ ⎟

4

j=0

N−1

∑

Mean value,SMOOTH in IDL

Square of RMS amplitude

Measure of flatness of the PDF;for Gaussian PDF K = 3

Measure of asymmetry of the PDF; for Gaussian PDF S = 0

Negative

Positive

PositiveNegative

Intermittency Studies in DIII-D

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