j. horacek: interchange turbulence simulation describes experiment 1 understanding sol plasma...
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J. Horacek: Interchange turbulence simulation describes experiment1
Understanding SOL plasma turbulence by interchange motions
J. Horacek1, O.E. Garcia2, R.A. Pitts3, A.H. Nielsen2, W. Fundamenski4, J.P. Graves3, V. Naulin2, J.J. Rasmussen2
1 Institute of Plasma Physics, Prague, Czech Republic 2 Risø National Laboratory, Roskilde, Denmark
3 CRPP EPFL, Lausanne, Switzerland 4 UKAEA, Abingdon, United Kingdom
1. TCV & fast probe
2. ESEL simulation based on interchange motions
3. Statistics of density, temperature, flux and potential
4. Conclusions
Workshop on Edge Transport in Fusion Plasmas, 11-13.9.2006, Kraków, Poland
J. Horacek: Interchange turbulence simulation describes experiment2
• Reciprocating Langmuir probe• Pins measure at 6MHz
sampling– floating potential
Vfl=-3Te
potential – temperature Te (1-120kHz)
– ion saturation current
IsatneTe1/2
density ne
– Radial particle flux:
r(Vfl1-Vfl
4)Isat
– Assuming Te/Te is small
Map SOL 3D →1D
Probe head
4mm
B-field
Vfl
1
Vfl
4
Is,Te
2-3
cm
Experimental set-up for diagnosing edge turbulence in tokamak TCV
J. Horacek: Interchange turbulence simulation describes experiment3
Density statistics
• [Graves PPCF 2005]• [J. Horacek CJP 2004]• Various discharges
(ne,B<>0,Ip, L/H-mode, D/He)
• Statistics confirms many observations by others e.g. [Boedo]
• Fixed-shape PDF not possible
• Found some universalities but it is impossible to understand without a model
A=saturates
J. Horacek: Interchange turbulence simulation describes experiment4
The ESEL model•Electrostatic 2D fluid (*>>10) model solves selfconsistently turbulence in n,Te,. No neutrals.
•Simplifications: parallel losses by linear damping, drift approximation, finite Li effects neglected, thin layer approximation (n/n<<1,T/T<<1), only LFS.
xxB
B
z
tdt
d
y
D(nT)dt
d
TT(n)n
T(T)
T)(
T
dt
dT
nnD(nT))(ndt
dn
nn
nn
1
1)(,,,
3
2
3
7
3
2
2
2
22
2
-C
C
CCC
CC
Curvature operator, Advective derivative, s/R0, =a/R0.
TTD TT 2
Particle conservation n
Energy conservation
Vorticity conservation
SinksParallel
dampingDiffusion -A.H. Nielsen, Monday 16:10. O.E. Garcia, Tuesday 14:40
J. Horacek: Interchange turbulence simulation describes experiment5
Dissipation and parallel loss estimates
Just 5 scalar measurable inputs: TLCFS,nLCFS,BLCFS,R+a,L|| determine the simulation [Fundamenski, Phys. Plasmas 2006]:
• neo-classical collisional perpendicular transport: D┴n~D┴T~D┴~10-3m2s-1.
• classical parallel transport determines parallel particle loss-time: T~n=~Lc/cs~1/250s
Taken as constants in space and time with abrupt changes at LCFS and wall
J. Horacek: Interchange turbulence simulation describes experiment6
ESEL simulation geometry
J. Horacek: Interchange turbulence simulation describes experiment7
ESEL simulation geometry
Linear damping
edge LCFS SOL wall shadow
Periodic
assuming statistical homogeneity in poloidal direction =>
Inner boundary
constant level of n, T and
=0 => no boundary convection
Outer boundary
Flat n and T profiles
No poloidal velocity
=0 => no boundary convection
Radial ~3cm
Po
loid
al
J. Horacek: Interchange turbulence simulation describes experiment8
Radial
Po
loid
al
2~3cm
J. Horacek: Interchange turbulence simulation describes experiment9
ESEL simulation rvpol generated at LCFS due turbulence itself (via Reynolds stress=Tilting instability)
•Blobs are generated at LCFS (due rvpol and rp ?)
•Blobs then propagate due (rBxB)xB
•Qualitatively consistent with all experimental observations and theoretical concepts.
LCF
S
wal
l
30mm
30m
m
ESEL 116, particle density
S.J. Zweben et al, Nucl. Fusion 44,134 (2004)
O +
X *
J. Horacek: Interchange turbulence simulation describes experiment10
Density fluctuations in the SOL
= -0.2
= +0.6
J. Horacek: Interchange turbulence simulation describes experiment11
Gamma PDF match best TCV & ESEL
Gamma: S=2/A
Log-Normal S=3/A+A-3
BHP: S=0.9
Gumbel: S=1.14
Gaussian: S=0
Skewness Kurtosis
A = <n>/n
AT = <T>/T DensityDensityTemperatureTemperatureTe correlated with ne at a fixed position
Functional dependence of statistical moments
defines a particular PDF.
[Graves PPCF 2005], [J. Horacek CJP 2004][J. Horacek EPS Tarragona 2005]
J. Horacek: Interchange turbulence simulation describes experiment12
Coherently averaged density bursts match
• Isolate large bursts, normalize, average them and fit by
exp(-t/)• Time-scales and
asymmetry match• Inter-burst period
match => even blob generation is well modelled => no additional mechanism needed
• BTW, [Kirnev Tuesday 11:40] sees 100s.
J. Horacek: Interchange turbulence simulation describes experiment13
Density
• Gradients, time-scales, turbulence levels and statistical moments match
• [O.E. Garcia, PPCF L1 2006]
J. Horacek: Interchange turbulence simulation describes experiment14
Flux• Cross-field
turbulence-driven ExB particle flux
• Gradients, turbulence levels and statistical moments match for flux
• In absolute levels!
• [O.E. Garcia, PSI, China, 2006]
Inside LCFS experiment
not reliable due pins separation
too large
J. Horacek: Interchange turbulence simulation describes experiment15
Potential structure amplitude and dimension
• Correlation on 2 pins poloidally separated is a measure of structure dimensions
• Level of potential fluctuations much stronger in ESEL
• Potential profile
J. Horacek: Interchange turbulence simulation describes experiment16
Turbulence-driven (ballooning) flow• Idea: radially propagating blob
generates localised pressure increase, i.e. ||p which drives M|| [Fundamenski, Nucl. Fusion 2006]
• Turbulence-driven flow given by relative time proportion of high pressure events
• In ESEL: p=nT. For TCV: assuming nT, p Isat
4/3
• Compare with B-field-independent flow measured by Mach probe
• Conclusion: absolute magnitudes roughly match
t
paptMM bckgballoon
)(
||||
J. Horacek: Interchange turbulence simulation describes experiment17
Summary• We demonstrated that a 2D fluid
turbulence simulations quantitatively agree with a high-density TCV discharge everywhere in midplane SOL in nearly all studied statistical characteristics
• => interchange motions driven by (BxB)xB drifts in p at LFS, dominated by rare convective blobs of ~2cm size and vr~2km/s [J. Horacek, PhD-thesis, EPFL, Switzerland, 2006]
• In progress:– ESEL density scan
– Varying damping and diffusion coefficients in space and time
J. Horacek: Interchange turbulence simulation describes experiment18
Reserve slides
J. Horacek: Interchange turbulence simulation describes experiment19
Density scan
• Matched one discharge, what about others?
• Confirmed square dependence of ne and r at wall [LaBombard, IAEA Sorrento, 2000]
• Simulations on the way
J. Horacek: Interchange turbulence simulation describes experiment20
Motivation
• Turbulence is claimed to be responsible for anomalous transport but no model was demonstrated yet to really quantitatively agree with experiment, or even have a predictive capability for radial transport
J. Horacek: Interchange turbulence simulation describes experiment21
ESEL does describe the anomalous transport, on question over decades!
Why now?
• Gradual development of models based on better experimental observations
• Analytic treatment (Endler) in 1995 but due to poor computers, only orders of magnitude predictions
• The Danes picked up the right physics, e.g. no sheath dissipation
• Good quality diagnostic, fast data acquisition, removing properly noise
• Close collaboration between theorists, modellers and experimentalists
J. Horacek: Interchange turbulence simulation describes experiment22
Interchange turbulenceCurvature and BxB drift
vertical charge separation (Ez)
EzxB drift outwards
Unstable at LFS due p
2D fluid ESEL model [Garcia Tuesday 14:40] based on interchange motions.
Risø run the simulations, CRPP the experiment.
+
-
BEz
+
-
r
r
J. Horacek: Interchange turbulence simulation describes experiment23
• Autocorrelation function ACF(c,). Time-scales match
• Self-organized critical system yields self-similar power spectra f –, well defined only in wall shadow.
Detail temporal characteristics
= -0.2
= +0.6
J. Horacek: Interchange turbulence simulation describes experiment24
Temperature statistics
J. Horacek: Interchange turbulence simulation describes experiment25
Gamma distribution describes density PDF
Graves et al., PPCF 47, L1 (2005)
J. Horacek et al. CJP (2004)
Two-parameter Gamma PDF: <n> and A = <n>/n
A determines the shape
TCV experiment ESEL model
J. Horacek: Interchange turbulence simulation describes experiment26
Various analytical distributions determined by mean and STD
1. Gamma: in systems with clustering, e.g. sand-piles with avalanches [Graves PoP 2002]
2. Lognormal: for Boltzmann-distributed electrons, neexp(-/Te) and Gaussian [Sattin, PoP 2004]
3. BHP: describes self-organized critical systems [van Milligen, PoP 2005]
4. Gumbel: PDF of extreme value systems5. Gaussian: most frequent in nature, sum of independent random processes
Gamma
Lognormal
A=
J. Horacek: Interchange turbulence simulation describes experiment27
Analogy with a sandpile
Two-parameter Gamma PDF:
• mean <n>
• fluctuation level A = <n>/n
A determines the shape
radial
density
Local sandpile height
Sandpile Tokamak edge
Sandpile slope rp
Sand grains Individual ions on Larmor orbits
Force of gravity Curvature and rBxB
Static friction Threshold to start an instability (Kelvin-Helmholtz?)
Dynamic friction Dissipation at small scales and velocity shear
Gamma distribution describes
1. Sandpile [Graves, PoP’02]
2. Density PDF in experiment
3. Density PDF in ESEL everywhere in tokamak edge
Horacek et al. Czech J. Phys. (2004)
Graves et al. PPCF 47, L1 (2005)
J. Horacek: Interchange turbulence simulation describes experiment28
Edge turbulence terminology
Dimension Name Observation Characteristic
0D (+ time) Intermittent event, burst
Langmuir probe Non-Gaussian
1D radial Avalanche, streamer, density finger
Sandpile modelfluid model (Sarazin, Ghendrih)
Clustering, SOC, self-similarity, marginal stability (Hidalgo)
1D parallel Filaments Langmuir probe and camera
Long correlations (>20m, Endler)
2D poloidal x radial
Theory
Blob, eddy (vortex) Models of isolated blobs (Krasheninnikov, Bian, Garcia)
Propagation dynamics due (BxB)xB
2D Experiment plasmoid, avaloid, IPO
Fast cameras, LP matrix (CASTOR, DIII-D)
1x2cm2, 1km/s, …
Too many terms for those coherent structures, perhaps result of a unique phenomena! What phenomena?
J. Horacek: Interchange turbulence simulation describes experiment29
Absolute level of flux match
• Perfect match, independent from normalisation
%75200
1%65.2
1
1
ms
kms
• Large blobs (>) with velocity ~1km/s are rare (6%). With average flux ~200m/s, these blobs carry large part (75%) of all particles
J. Horacek: Interchange turbulence simulation describes experiment30
=1.0
Turbulence-driven (ballooning) flow
• Idea: radially propagating blob generates localised pressure increase, i.e. ||
p which drives M||. [Fundamenski, Nucl. Fusion 2006]
• Jhfund.m
t
paptMM bckgballoon
)(
||||
=1.5=2.0
J. Horacek: Interchange turbulence simulation describes experiment31
Explaining overestimation of Te from swept Langmuir probe?
• Use the fluctuating (,t), Te(,t), ne(,t) to generate swept VI-characteristics of a Langmuir probe in the experimental bandpath < 125kHz.
• Fit it in the way the experimental data are fitted.
Applied Voltage [V]Co
llect
ed
Cur
ren
t [A
]
=0.8=0
#24530
. ESEL data
- Quiet plasma
- Fit
J. Horacek: Interchange turbulence simulation describes experiment32
Effect of fluctuations
• profiles well reproduced inside LCFS
• Fast sweep is better
• Te is indeed overestimated which might explain the experiment!
Run 129
J. Horacek: Interchange turbulence simulation describes experiment33
Potential profile matches
• Vf from the swept lower than from DC Vf-measurement as expected
• Profiles correspond well to ESEL
J. Horacek: Interchange turbulence simulation describes experiment34
Basic characteristics of SOL
Various discharges (ne,B<>0,Ip, L/H-mode,Z, D/He)