j. horacek: interchange turbulence simulation describes experiment 1 understanding sol plasma...

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


• 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


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


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


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


ESEL simulation geometry


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


Radial

Po

loid

al

2~3cm


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 *


Density fluctuations in the SOL

= -0.2

= +0.6


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]


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.


Density

• Gradients, time-scales, turbulence levels and statistical moments match

• [O.E. Garcia, PPCF L1 2006]


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


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


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

)(

||||


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

http://library.epfl.ch/theses/?nr=3524


Reserve slides


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


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


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


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


• 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


Temperature statistics


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


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=


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)


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?


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


=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


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


Effect of fluctuations

• profiles well reproduced inside LCFS

• Fast sweep is better

• Te is indeed overestimated which might explain the experiment!

Run 129


Potential profile matches

• Vf from the swept lower than from DC Vf-measurement as expected

• Profiles correspond well to ESEL


Basic characteristics of SOL

Various discharges (ne,B<>0,Ip, L/H-mode,Z, D/He)

j. horacek: interchange turbulence simulation describes experiment 1 understanding sol plasma...

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