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(I) Microturbulence in magnetic fusion devices –

(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

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(I) Microturbulence in magnetic fusion devices –

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  1. (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

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

  3. 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?

  4. Microturbulence in stellarators

  5. Field-aligned, Clebsch-type coordinates [Xanthopoulos and Jenko, PoP 2006]. Still: N>100 parallel grid points 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

  6. 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).

  7. TEM turbulence in tokamaks

  8. Φ vs. nt Φ vs. np Φ vs. T Φ vs. T ky α α α α w/ ZFs w/o ZFs Basic properties of TEM turbulence • Systematic gyrokinetic study of TEM turbulence: • Relatively weak zonal flow activity • 2. Formation of radial structures • 3. Structures appear to be remnants of linear modes [Dannert & Jenko ‘05]

  9. 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

  10. 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

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

  12. 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: • Confirmed by nonlinear gyrokinetic simulations with GENE: [F. Imbeaux et al., PPCF 2001] [X. Garbet et al., PPCF 2004] R/Ln = 0

  13. R/LTe dependence for ‘large’ density gradients GENE vs. QL model electron/ion heat flux R/Ln > 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 • similar as in adiabatic ITG case • implies Te profile stiffness • coupling of particle and electron heat flux

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

  15. TEP theory (Isichenko et al. 1995) GF/QL (GLF23) GK/QL (GS2) 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. 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 [Jenko, Dannert & Angioni ‘05]

  16. Experimental identification of TEM features

  17. 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 Threshold behavior is observed directly; power balance and transient transport consistent with both linear gyrokinetics and CG model.

  18. 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.

  19. Impurity transport in the core

  20. 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]

  21. Quasilinear gyrokinetic study of an impurity trace #15524 (ECRH phase; mid radius) nominal parameters & R/LTz=R/LTi (ITG) R/LTe & collisionality  (TEM) W ionization stage (Z=46, A=184; ITG) R / Ln = -R V / D A = 2 Z In confinement region, impurity transport is likely to be turbulent. High-Z limit is well behaved – in contrast to neoclassical theory.

  22. Momentum and ion heat transport

  23. 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) andreduction of vtor (decrease of ωE) [A. Manini et al., NF submitted]

  24. Coupling of momentum and ion heat transport • Strong correlation between • Ti and vtor • Consistent with constant ratio • of χΦ / χi • Power balance analysis (ASTRA, • FAFNER, TRANSP, TORIC) yields • a ratio of ~ 1 at mid radius • Promising agreement with both • quasilinear and nonlinear • GK studies of ITG modes [A. Peeters et al., PoP ’05 & PPCF submitted]

  25. 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

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