Improving Predictive Transport Model

1. Improving Predictive Transport Model C. Bourdelle 1), A. Casati 1), X. Garbet 1), F. Imbeaux 1), J. Candy 2), F. Clairet 1), G. Dif-Pradalier 1), G. Falchetto 1), T. Gerbaud 1), V. Grandgirard 1), P. Hennequin 3), R. Sabot 1), Y. Sarazin 1), L. Vermare 3), R. Waltz 2) 1) CEA, IRFM, F-13108 Saint-Paul-lez-Durance, France 2) General Atomics, P.O. Box 85608, San Diego, California 92186-5608, USA 3) Laboratoire de Physique et Technologie des Plasmas, CNRS-Ecole Polytechnique, 91128 Palaiseau Cedex, France

2. Guideline • Goal: To improve predictions on turbulent fluxes need physics based transport models • Context: • Nonlinear gyrokinetic electromagnetic simulations still too costly in terms of computing tim • Interestingly, quasi-linear approximation seems to retain the relevant physics • Work on quasi-linear fluxes in two parts: • quasi-linear weight : phase and amplitude, follows well non-linear predictions • electrostatic potential: based on both non-linear simulations and turbulence measurements • Integrated in QuaLiKiz where flux agrees with non-linear one when ranging from Ion Temperature Gradient (ITG) to Trapped Electron Modes (TEM)

3. general approach for quasi-linear model, QuaLiKiz[Bourdelle PoP07] • fluctuating distribution function linearly responds to the fluctuating electrostatic potential through Vlasov equation computed by eigenvalue code Kinezero [Bourdelle NF02] • Example for particle flux: • No information on the saturation of the fluctuating electrostatic potential in terms of its amplitude or on its spectral shape versus the wave number and the frequency

4. Accounting for the « non-resonant terms » • Resonance Broadening Theory: non negligible finite +i0+=+in linked to irreversibility through mixing of the particles orbits in the phase space. Moreover in the limit n→0 the particle fluxes are not ambipolar • intrinsic frequency spectral shape of the fluctuating potential • In QuaLiKiz, n=0+ and : equivalent to RBT where n=gk and • Nevertheless shape and width choices arbitrary. ongoing measurements vs nonlinear simulations

5. Frequency spectrum: non-linear simulations vs measurements Dwk = gk + Cst*kqawith a~1-2 reproduce widths of the frequency spectra observed from GYRO simulations and measurements. Ongoing… GYRO Backscattering on Tore Supra a=2.3 a=2.2 Antar PPCF 1999

6. Saturation rule: mixing length • In QuaLiKiz, flux = sum over all unstable modes each weighted by corresponding gk as [Jenko, Dannert, Angioni 2005] adding a

7. kr spectrum: non-linear simulation vs measurements • nonlinear GYRO compared with fast-sweeping reflectometer [Casati TTF08] #39596, r/a=0.7 ar,exp = -2.8 ar,sim = -3.0

8. kq spectrum: non-linear simulations vs measurements • nonlinear GYRO compared with Doppler reflectometer [Casati TTF08] #39596, r/a=0.7

9. k spectrum isotropy • Isotropy found in some GYRO simulations Ongoing… • Apparent (kq,kr) anisotropy due to Doppler instrumental integration domain • Hence, actual choice: from 0 to kmax: and from kmax to infinity:

10. quasi-linear weights • in the case of an eigenvalue approach, the fluxes can not be unequivocally divided by Therefore, discussion limited to most unstable mode • no simple tool allowing testing the validity of the quasi-linear approach for subdominant modes yet developed

11. Amplitude of the weight: QL/NL~1.5 • local and global simulations : systematic over-prediction QL vs NL around 1.5 • QL/NL ratio stays reasonably constant when changing plasma parameters, especially at low kq scales • Reason of this over prediction to be assessed adiabatic electrons, r/a=0.4, R/LTi=8.28, *=1/256

12. Phase of the weight: OK for ITG, fails for ITG-TEM • Test introduced for TEM by [Jenko 2005-2008] extended to ITG and ITG-TEM cases • Good QL/NL phase matching for ITG cases: particle and energy • But close to ITG/TEM transition QL phase from most unstable mode fails for particle whereas energy OK R/LTi=9 R/LTe=9 R/Ln=3 R/LTi=6 R/LTe=9 R/Ln=3

13. quasilinear fluxes vs nonlinear predictions • test quasi-linear fluxes computed by actual version of QuaLiKiz versus nonlinear GYRO ion and electron energy fluxes and particle fluxes for various parameter scans ranging from ITG to TEM dominated cases • only one renormalisation factor, C0, has been used in order to get the best fit to the nonlinear fluxes

14. R/LT scan Ion energy electron energy particle effective diffusivities GYRO (diamonds) QuaLiKiz (lines) for R/LTi=R/LTe scan with R/Ln=3

15. n* scan Based on Tore Supra n* experiment In agreement with experimental obs. GYRO (diamonds) QuaLiKiz (lines) Ion energy electron energy particle r/a=0.5 R/LTi=8 R/LTe=6.5 R/Ln=2.5

16. Ti/Te scan DIII-D Ti/Te scan PRL Petty 99 Qualitative agreement with experiment GYRO (diamonds) QuaLiKiz (lines) Ion energy electron energy particle r/a=0.3 R/LTi=6.5 R/LTe=4.6 R/Ln=1.4

17. Summary • Assuming a linear response of the transported quantities to the fluctuating potential works rather well:phase OK if one unstable mode, amplitude over-estimated • Moreover, when coupling the choices for electrostatic potential with the quasi-linear response, find quasi-linear fluxes agreeing well to nonlinear predictions for energy and particle fluxes over a wide range of parameters, from ITG to TEM dominated cases

18. Discussion • A number of challenging issues remain to be tackled: • quasi-linear approach known to fail : far from the threshold, onset of zonal flows, etc. Hence, domain in which it can be applied should be better understood • choices for the electrostatic potential deserve more comparisons with nonlinear simulations and experimental measurements. In Tore Supra, presently comparing density fluctuations k and frequency spectra from Doppler and fast-sweeping measurements versus GYRO and GYSELA • Finally, only integration of QuaLiKiz in a transport code such as CRONOS will allow testing in situ the predictive capabilities

19. R/LTi=9 R/LTe=9 R/Ln=3 R/LTi=6 R/LTe=9 R/Ln=3