(I) Microturbulence in magnetic fusion devices –
New insights from gyrokinetic simulation & theory
F. Jenko, C. Angioni, T. Dannert, F. Merz, A.G. Peeters, and P. Xanthopoulos
IPP, Garching and Greifswald
(II) Theoretical understanding of
core transport phenomena in ASDEX Upgrade
C. Angioni, R. Dux, A. Manini, A.G. Peeters, F. Ryter, R. Bilato, T. Dannert,
A. Jacchia, F. Jenko, C.F. Maggi, R. Neu, T. Pütterich, J. Schirmer,
J. Stober, W. Suttrop, G. Tardini, and the ASDEX Upgrade team
IPP, Garching
21st IAEA Fusion Energy Conference, Chengdu/China, 16-21 October 2006
A rough outline of this talk
Complex
phenomena
PART I
Quasilinear models
Nonlinear gyrokinetic
simulations
All nonlinear gyrokinetic simulations shown in this talk
have been performed with the continuum code GENE.
Adiabatic ITG turbulence in a simple tokamak
Reference case for core turbulence simulations:
• “Cyclone base case” – also serves as standard paradigm of turbulence
• idealized physical parameters; adiabatic electrons; s-α model equilibrium
Key findings:
• saturation via zonal flows
• ion heat flux is offset-linear
• nonlinear upshift of threshold
GENE data
What about all the other transport channels?
How generic is the adiabatic ITG s-α scenario?
Microturbulence in stellarators
An example: Wendelstein 7-X
W7-X is minimized with respect to
neoclassical losses:
Role of turbulent transport in
(optimized) stellarators?
Effect of magnetic geometry on
turbulence (tokamak edge etc.)?
A = R/a > 10
Field-aligned, Clebsch-type coordinates
[Xanthopoulos and Jenko, PoP 2006]. Still:
N>100 parallel grid points
Adiabatic ITG turbulence in the stellarator W7-X
increasing R/LTi
linear threshold:
R/LTi ≈ 9
(a/LTi ≈ 1)
Nonlinear upshift of critical temperature gradient by some 20%.
Very low transport levels due to strong zonal flow activity (ωE»γ).
TEM turbulence in tokamaks
Basic properties of TEM turbulence
Systematic gyrokinetic study of TEM turbulence:
1. Relatively weak zonal flow activity
2. Formation of radial structures
3. Structures appear to be remnants of linear modes
ky
Φ vs. np
Φ vs. T
w/ ZFs
α
α
α
Φ vs. T
w/o
ZFs
α
[Dannert & Jenko ‘05]
Φ vs. nt
Nonlinear saturation in TEM turbulence
For the transport-dominating modes, the ExB
nonlinearity is well represented by a diffusivity:
transport
dominating
regime
transport
dominating
regime
Nonlinear saturation in TEM turbulence (cont’d)
Dressed test mode approach in the spirit of renormalized perturbation theory
explains nonlinear saturation and serves as basis for a transport model.
Dressed test mode approach:
Parallel weighting:
weighting function
A novel quasilinear transport model
Qi and Γ from QL ratios
weighted w.r.t. parallel mode structure
NL GK simulation
QL model
This model is able to capture key features of TEM turbulence
and can be used to predict TEM-induced transport.
An empirical critical gradient model
• Many dedicated experiments with dominant electron heating
• Transport is dominated by TEM turbulence (low Ti → ETG modes stable)
• Interpretation via an empirical critical gradient (CG) model:
[F. Imbeaux et al., PPCF 2001]
[X. Garbet et al., PPCF 2004]
• Confirmed by nonlinear gyrokinetic simulations with GENE:
R/Ln = 0
R/LTe dependence for ‘large’ density gradients
R/Ln > 2.5
Conventional (quasi-)linear models:
no critical gradient (density gradient drive)
electron/ion heat flux
Nonlinear simulations and new quasilinear model:
effective critical gradient
electron heat flux has offset-linear scaling
GENE
vs.
QL model
• similar as in adiabatic ITG case
• implies Te profile stiffness
• coupling of particle and electron heat flux
q dependence of TEM-induced transport
Conventional QL theories predict a relatively weak dependence on q, but:
Part of the q scaling is provided by the q dependence of the threshold:


Eddy size (ky)
scales with q

model
[Jenko & Dannert ‘05]
simulation
results
States of zero particle flux in ITG-TEM turbulence
Observation of a particle
pinch (Γ < 0) for low values
of R/Ln (ITG regime).
ν=β=0
TEP theory
(Isichenko
et al. 1995)
GK/QL
(GS2)
GF/QL
(GLF23)
[Jenko, Dannert & Angioni ‘05]
Nonlinear and quasilinear gyrokinetics show good agreement, while both
the GF model and TEP theory predict smaller values of the marginal R/Ln.
Main reason: Model adjusts ky value, and transition point depends on ky.
Experimental identification of TEM features
Existence of a threshold in R/LTe
•
•
AUG L-mode plasmas
[0.8 MW ECRH, little OH)
gradual reduction of central
ECRH, balanced by increase
of off-axis heating
[F. Ryter et al., PRL 2005]
ETG stable
Te
2
Ti
Threshold behavior is observed directly; power balance and transient
transport consistent with both linear gyrokinetics and CG model.
Collisional stabilization of TEMs
Density ramp in AUG L-mode plasmas and quasilinear analysis
With increasing collisionality, the R/LTe dependence of the electron heat
flux decreases. Eventually, the dominant mode changes from TEM to ITG.
Impurity transport in the core
Experimental observations in AUG
General finding:
No central impurity accumulation when
central heat transport is anomalous!
Example:
W accumulation is suppressed by
0.8 MW of central ECRH during a
high density phase with 5 MW of NBI
[R. Neu et al., JNM 2003]
Quasilinear gyrokinetic study of an impurity trace
R / Ln = -R V / D
#15524 (ECRH phase; mid radius)
nominal parameters & R/LTz=R/LTi (ITG)
R/LTe  & collisionality  (TEM)
W ionization stage (Z=46, A=184; ITG)
A=2Z
In confinement region, impurity transport is likely to be turbulent.
High-Z limit is well behaved – in contrast to neoclassical theory.
Momentum and ion heat transport
Effects of electron heating on ion heat transport
• In very low density H-mode plasmas, one finds a strong
confinement degradation in response to central ECRH
• Related R/LTi drop due to increase of Te/Ti (implies reduction
of ITG threshold) and reduction of vtor (decrease of ωE)
[A. Manini et al., NF submitted]
Coupling of momentum and ion heat transport
• Strong correlation between
Ti and vtor
• Consistent with constant ratio
of χΦ / χi
• Power balance analysis
(ASTRA,
yields
a ratio of ~ 1 at mid radius
FAFNER, TRANSP, TORIC)
• Promising agreement with both
quasilinear and nonlinear
GK studies of ITG modes
[A. Peeters et al., PoP ’05 & PPCF submitted]
Insights and conclusions
Specific insights:
• The adiabatic ITG paradigm is not universal (see, e.g., TEM)
• QL models can be quite successful when used with care
• Experimental TEM studies can be related to NL gyrokinetics
• Different transport channels tend to be strongly coupled
General conclusions:
• No real predictive capability without deeper understanding
• There is room for more synergy between theory, modelling,
and experiment
See posters: EX / 8-5Ra & EX / 8-5Rb