TTF 2002 1M. Ottaviani

Euratom TORE SUPRA

Overview of progress in transport theory and in the understanding of the scaling

laws

M. OttavianiEURATOM-CEA, Cadarache

Acknowledgements: B. Labit, G. Manfredi

TTF 2002 2M. Ottaviani

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Outline

• Brief review of transport studies, scaling laws, similarity experiments, difficulties.

• The gyroradius scaling problem• Beta dependence issues• Electron heat transport. ETG?• Profile effects, stiffness, safety factor (current) dependence• Conclusions

TTF 2002 3M. Ottaviani

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Scaling laws, ITER

TTF 2002 4M. Ottaviani

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Difficulties with the scaling laws

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Similarity experiments

• Similarity experiments (espec. DIII-D), that vary one adimensional parameter at a time, shed some light but do not resolve the issue.

• The scaling of the ion conductivity from power balance changes from Bohm (or worse) in L-mode to g-Bohm in H-mode

• Electrons always gyro-Bohm (different physics?)• Measured turbulence microscopic characteristics

essentially gyro-Bohm (DIII-D, IAEA 2000)

Limitations as in 0-D scaling apply (espec. error bars 30%)

TTF 2002 6M. Ottaviani

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Gyroradius scaling

TTF 2002 7M. Ottaviani

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Global ITG fluid simulations (Manfredi-Ottaviani)

TTF 2002 8M. Ottaviani

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ITG correlation functions and pol. spectraRho-star=1/50,1/100,1/200.Gyro-Bohm scalingPeak of the corr. funct. at around 0.3

TTF 2002 9M. Ottaviani

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ITG gyrokinetic simulations, Lin et al.

Recent (2002) gyrokinetic simulations also convergeto gyro-Bohm scaling at sufficiently small rho-star.Microscopic features sameas in fluid simulations

TTF 2002 10M. Ottaviani

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Convergence to gyro-Bohm: a possible explanation

TTF 2002 11M. Ottaviani

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Gyroradius scaling: conclusions

• Numerical simulations of ITG tubulence now agree that convergence to gyro-Bohm scaling occurs in the limit of small gyroradius.

• Recent ETG simulations (Labit-Ottaviani) also show the same behaviour, although convergence is more difficult due to the radial extension of ETG vortices.

• Thus:

TTF 2002 12M. Ottaviani

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BETA: not a scaling parameter

Alfven ITG (AITG) from Zonca et al. (1998): new e.m. branch. The maximum growth rate depends on beta.

TTF 2002 13M. Ottaviani

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AITG: global gyrokinetic eigenvalue analysis

(Falchetto-Vaclavik, EPS 2002)

TTF 2002 14M. Ottaviani

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Nonlinear results

From Scott, NJP (2002)Beta scan from the DALFTIModel (drift-Alfven with iontemperature dynamics)

TTF 2002 15M. Ottaviani

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FWEH in Tore Supra

0

0.5

1

1.5

2

0 0.5 1 1.5 2 2.5 3 3.5 4

0.2 0.3 0.4 0.5 0.6 0.7 0.8

Rel

ativ

e de

viat

ion

Normalized radius

Rel

ativ

e de

viat

ion

r/a = 0.20

0.65

0.70

0.60

a)

c)

1 / LTe - 1 / Lc (m-1)

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0 1 2 3 4 5 6 7 8

q e /

Te3/

2 (M

W /

m2 ,

keV

)

b)

0.20 Š r:a Š 0.75

0

0.5

1

1.5

2

The Tore Supra FW transport database is optimally represented by an offset linear formula, independent of the density

 qe ne T

e (1/ LTe-1/ Lc) ,with 1.5, = 0, andR / Lc = 5 ( 1) + 10 ( 2) |s| / q

TTF 2002 16M. Ottaviani

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Renewed interest in ETG

TTF 2002 17M. Ottaviani

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ETG transport resuscitated

From Jenko et al, 2000. Gyrokinetic flux tube simulations of ETG tubulence show enhancement of at least an order of magnitude over the equivalent ITG transport. This is enough to compensate the reduction due to the mass ratio

The ETG adiabatic responsedoes not allow strong zonalflow generation:STREAMERS

TTF 2002 18M. Ottaviani

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ETG fluid simulations (Labit-Ottaviani)

Phenomenology:Contour plots and2D correlation

functions

TTF 2002 19M. Ottaviani

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Fluid ETG: beta scan

• Weak dependence on beta• Transport from the

magnetic flutter negligible• Not a definite scaling

TTF 2002 20M. Ottaviani

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Fluid ETG: power(gradient) scan

Transport somewhatbelow the required level to matchobservations

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Test particles in model streamers

Zero frequency: ballistic transport.Bohm timescale

With typical frequency, inthe rest frame of the wave:ZERO TRANSPORT

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Beta scaling: conclusions

• Beta: not a scaling parameter. Not a power-law dependence

• Expect degradation near the ideal limit, otherwise the dependence is probably weak

TTF 2002 23M. Ottaviani

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Profile effects: resiliency, stiffness

0

0.1

0.2

0.3

0.4

0 1 2 3 4 5 6 7 8

r/a = 0.2

r/a = 0.4

r/a = 0.6

Elec

tron

heat

flux

(MW

/ m

2 )

1 / LTe (m -1)

Tore Supra (left), Asdex (right). Almost-independence of the temperature gradient scale-length on the input power

TTF 2002 24M. Ottaviani

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Automatic stiffness model

TTF 2002 25M. Ottaviani

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Stiffness ?

• Stiffness as seen from power balance analysis can be the consequence of the dominance of a specific physics in a certain region of the discharge

• Criticality effects better seen by tailoring the power deposition profiles

• Also from pulse propagation/modulation, but interpretation more problematic

TTF 2002 26M. Ottaviani

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More on profile effects

TTF 2002 27M. Ottaviani

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Conclusions

• Gyro-Bohm scaling finally well established numerically. It remains to be clarified why it does not turn out in certain experiments (Not enough asymptotic + profile/flow effects? Proximity to threshold?)

• Possible action: force gyro-Bohm scaling in transport analysis. Adds a constraint to the exponents. Reduce uncertainty?

• Beta not a scaling parameter. Degradation near the ballooning limit from Alfvenic dynamics.

• ETG perhaps a good explanation for electron heat transport. Pluses: independence of the electron transport on the mode of operation; exptl. threshold matches theory. More work needed to understand the size of the ETG transport.

• Current scaling not a true scaling, comes from threshold• Stiffness of the temperature scalelength can come from the dominance

of a given physics in the transport region, not from threshold.