1. 11 Role of Non-resonant Modes in Zonal Flows and Intrinsic Rotation Generation Role of Non-resonant Modes in Zonal Flows and Intrinsic Rotation Generation Joint US-EU Transport Taskforce Workshop TTF 2011 April 6-9, 2011 San Diego, California Sumin Yi, J.M. Kwon, T. Rhee, P.H. Diamond [1], and J.Y. Kim WCI Center for Fusion Theory, NFRI, Korea [1] CMTFO and CASS, UCSD, USA

2. 22 Introduction and Motivation In gyrofluid and gyrokinetic simulations, qualitatively different transport phenomena were observed for different non-resonant mode configurations of the fluctuation spectrum. A transport barrier is found to develop in the gap region if non-resonant modes are artificially suppressed in the simulation (Garbat et al PoP 2001, Kim et al NF submitted, Sarazin et al J. Phys.: Conf. Ser. 2010). Finite non-resonant modes were observed in numerical studies of the reversed shear plasmas (Idomura 2002 and Candy 2004). We study role of non-resonant modes in the self regulating dynamics of turbulence and zonal flows.

3. 33 Central Theme Radial propagation of turbulence by nonlinear mode coupling affects 〈 k r 〉 of Turbulence Spectrum & Reynolds Stress Zonal Flows Turbulence Level Temperature Profile 〈 k θ 〉 of Turbulence Spectrum Parallel Asymmetry & Toroidal Flow

4. 44 gKPSP : global gyrokinetic δf PIC code Simulation code: gKPSP [Kwon IAEA2010]  Global δf PIC gyrokinetic simulation code  δf Coulomb collision operator (W.X. Wang et al PPCF’99)  No external heat source → turbulence intensity front by profile relaxation  General equilibrium from EFIT data Quasi-ballooning representation of fluctuating potential Q i (ψ) and Q j (θ) : quadratic spline centered at ψ i and θ j for periodicity in θ

5. 55 Quasi-ballooning representation of fluctuating potential modes with m/n = q include modes with m/n ≠ q m n modes with m/n = q modes with m/n ≠ q Proper resolution of “amplitude” part ϕ n (ψ,θ) is important for modes with m/n ≠ q, so called non-resonant modes Usually, enough number of grid points in poloidal direction is used N θ ≥ 32 In this work, this feature is utilized to study the role of non-resonant modes i.e. we compare N θ = 32 and N θ = 6 cases

6. 66 Suppression of Non-resonant Modes By artificially restricting the poloidal extent N θ, non-resonant modes are suppressed → Scattering in spectral space through mode-mode interaction is reduced Monotonic q-profile (Cyclone case) q = 0.8 - 3.0 (s = 0.84 at r/a=0.5) W/O non-resonant modes With non-resonant modes Non-resonant mode contribution

7. 77 Zonal Flow Evolution When non-resonant modes are included, zonal flow (ZF) becomes stronger and continues to grow in radially outward. At certain radius, the direction of ZF becomes opposite due to excitation of the non-resonant modes. W/O non-resonant modes With non-resonant modes

8. 88 Turbulence Spectrum in k r and k θ Without non-resonant modes, RS is produced by fluctuations with Inclusion of non-resonant modes provides -fluctuations with -and compensates the asymmetry in spectrum -leads to sign change in RS at later time Why additional positive k r from non-resonant modes ? -from radial propagation/spreading of turbulence by enhanced non- linear mode coupling W/O non-resonant modes With non-resonant modes

9. 99 Difference in Reynolds Stress (Diamond and Kim, Phys. Fluids B1991) RS is computed from turbulence spectrum Difference in RS is consistent with ZF drive and evolution By including non-resonant modes: -Reduce shear in RS and ZF -Change ZF drive and direction Reynolds Stress t=1300-1400t=1400-1500 Zonal Flow Drive t=1300-1400t=1400-1500

10. 10 Difference in Poloidal Flow Evolution By including non-resonant modes, The sign of RS changes  The direction of E  B poloidal flow becomes opposite at certain radius  This opposite poloidal flow affects toroidal flow generation r=0.170 r=0.163-0.180

11. 11 Difference in Turbulence Intensity Without non-resonant modes asymmetry in fluctuation spectrum enhanced RS and ZF drive become stronger turbulence regulation becomes stronger Non-resonant mode contribution

12. 12 Difference in Temperature Profile Without non-resonant modes turbulence regulation becomes stronger temperature gradient becomes steeper → prelude to ITB formation? consistent trend with previous gyrofluid (Garbet PoP’01, SS Kim submitted NF) and gyrokinetic simulations (Sarazin J.Phys’10)

13. 13 Toroidal Rotation and Parallel Wave Number Without non-resonant modes, strong toroidal flow is generated and persists after non- linear saturation With non-resonant modes, parallel wave number asymmetry becomes weakened and toroidal flow decreases W/O non-resonant modes With non-resonant modes

14. 14 Asymmetry in Parallel Wave Number In early phase of non-linear evolution,. It determines parallel wave number asymmetry in fluctuation spectrum in both cases W/O non-resonant modes With non-resonant modes

15. 15 Asymmetry in Parallel Wave Number (cont’d) In later phase of non-linear evolution, by including non-resonant modes, asymmetry in decays due to the excitation of +θ propagating modes (+θ directional ZF in inner radii) W/O non-resonant modes With non-resonant modes

16. 16 Mode rational surface By suppressing non-resonance modes, the radial scattering/propagation of turbulence is restricted turbulence spectrum becomes quite stationary in the nonlinear saturation phase so 〈 k || 〉 and toroidal flow persists longer into the nonlinear phase With non-resonant modes, → Enhanced radial scattering of the +  directional modes. Decay of Parallel Wavenumber Asymmetry

17. 17 SummarySummary By suppressing non-resonant modes, ▶ spurious asymmetry in fluctuation spectrum appears ▶ radial scattering/propagation of fluctuation intensity is hindered and turbulence spectrum becomes stationary ▶ RS and ZF drives are enhanced ▶ turbulence suppression is enhanced ▶ asymmetry in fluctuation spectrum persists and leads to stronger toroidal rotation ▶ artificially promotes ITB formation? By allowing non-resonant modes, ▶ asymmetry in fluctuation spectrum is weakened ▶ RS and ZF shears formation are delayed and weakened ▶ radial scattering of fluctuation intensity becomes stronger ▶ toroidal flow becomes weaker ▶ ITB?