(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 21 st IAEA Fusion Energy Conference, Chengdu/China, October 2006

Complex phenomena Quasilinear models Nonlinear gyrokinetic simulations All nonlinear gyrokinetic simulations shown in this talk have been performed with the continuum code GENE. A rough outline of this talk PART I PART II

Adiabatic ITG turbulence in a simple tokamak Reference case for core turbulence simulations: “Cyclone base case” – also serves as standard paradigm of turbulence “Cyclone base case” – also serves as standard paradigm of turbulence idealized physical parameters; adiabatic electrons; s-α model equilibrium idealized physical parameters; adiabatic electrons; s-α model equilibrium Key findings: saturation via zonal flows saturation via zonal flows ion heat flux is offset-linear ion heat flux is offset-linear nonlinear upshift of threshold 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 N>100 parallel grid points Field-aligned, Clebsch-type coordinates [Xanthopoulos and Jenko, PoP 2006]. Still: 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

Adiabatic ITG turbulence in the stellarator W7-X Nonlinear upshift of critical temperature gradient by some 20%. Very low transport levels due to strong zonal flow activity (ω E »γ). linear threshold: R/L Ti ≈ 9 (a/L Ti ≈ 1) increasing R/L Ti

TEM turbulence in tokamaks

w/ ZFs w/oZFs 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 [Dannert & Jenko ‘05] Φ vs. n t Φ vs. n p Φ vs. T  Φ vs. T  α ααα kykykyky

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 weighted w.r.t. parallel mode structure Q i and Γ from QL ratios This model is able to capture key features of TEM turbulence and can be used to predict TEM-induced transport. QL model NL GK simulation

An empirical critical gradient model Many dedicated experiments with dominant electron heating Many dedicated experiments with dominant electron heating Transport is dominated by TEM turbulence (low T i → ETG modes stable) Transport is dominated by TEM turbulence (low T i → ETG modes stable) Interpretation via an empirical critical gradient (CG) model: Interpretation via an empirical critical gradient (CG) model: Confirmed by nonlinear gyrokinetic simulations with GENE: Confirmed by nonlinear gyrokinetic simulations with GENE: R/L n = 0 [F. Imbeaux et al., PPCF 2001] [X. Garbet et al., PPCF 2004]

R/L n > 2.5 R/L n > 2.5 Conventional (quasi-)linear models: no critical gradient (density gradient drive) Nonlinear simulations and new quasilinear model: effective critical gradient electron heat flux has offset-linear scaling R/L Te dependence for ‘large’ density gradients similar as in adiabatic ITG case similar as in adiabatic ITG case implies T e profile stiffness implies T e profile stiffness coupling of particle and electron heat flux coupling of particle and electron heat flux electron/ion heat flux GENE vs. QL model

q dependence of TEM-induced transport Conventional QL theories predict a relatively weak dependence on q, but:   simulationresults [Jenko & Dannert ‘05] model Eddy size (k y ) scales with q Part of the q scaling is provided by the q dependence of the threshold:

GK/QL (GS2) GF/QL (GLF23) TEP theory (Isichenko et al. 1995) Nonlinear and quasilinear gyrokinetics show good agreement, while both the GF model and TEP theory predict smaller values of the marginal R/L n. Main reason: Model adjusts k y value, and transition point depends on k y. States of zero particle flux in ITG-TEM turbulence Observation of a particle pinch (Γ < 0) for low values of R/L n (ITG regime). [Jenko, Dannert & Angioni ‘05] ν = β = 0

Experimental identification of TEM features

AUG L-mode plasmasAUG L-mode plasmas [0.8 MW ECRH, little OH) gradual reduction of central ECRH, balanced by increasegradual reduction of central ECRH, balanced by increase of off-axis heating Existence of a threshold in R/L Te [F. Ryter et al., PRL 2005] ETG stable 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/L Te 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 / L n = -R V / D A = 2 Z #15524 (ECRH phase; mid radius) In confinement region, impurity transport is likely to be turbulent. High-Z limit is well behaved – in contrast to neoclassical theory. nominal parameters & R/L Tz =R/L Ti (ITG) R/L Te  & collisionality  (TEM) W ionization stage (Z=46, A=184; ITG)

Momentum and ion heat transport

Effects of electron heating on ion heat transport In very low density H-mode plasmas, one finds a strong In very low density H-mode plasmas, one finds a strong confinement degradation in response to central ECRH Related R/L Ti drop due to increase of Te/Ti (implies reduction Related R/L Ti drop due to increase of Te/Ti (implies reduction of ITG threshold) and reduction of v tor (decrease of ω E ) [A. Manini et al., NF submitted]

Coupling of momentum and ion heat transport Strong correlation between Strong correlation between  T i and  v tor Consistent with constant ratio Consistent with constant ratio of χ Φ / χ i Power balance analysis (ASTRA, Power balance analysis (ASTRA, FAFNER, TRANSP, TORIC) yields a ratio of ~ 1 at mid radius Promising agreement with both 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) The adiabatic ITG paradigm is not universal (see, e.g., TEM) QL models can be quite successful when used with care QL models can be quite successful when used with care Experimental TEM studies can be related to NL gyrokinetics Experimental TEM studies can be related to NL gyrokinetics Different transport channels tend to be strongly coupled Different transport channels tend to be strongly coupled General conclusions: No real predictive capability without deeper understanding No real predictive capability without deeper understanding There is room for more synergy between theory, modelling, and experiment There is room for more synergy between theory, modelling, and experiment See posters: EX / 8-5Ra & EX / 8-5Rb