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.
QuickTime™ and a decompressor
are needed to see this picture.
G. McKee, UW
QuickTime™ and a decompressor
are needed to see this picture.
QuickTime™ and a decompressor
are needed to see this picture.
BES Data Confirms Presence of Structures and Size
QuickTime™ and a decompressor
are needed to see this picture.
QuickTime™ and a decompressor
are needed to see this picture.
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