Role of Non-resonant Modes in Zonal Flows and Intrinsic Rotation Generation

1. Role of Non-resonant Modes in Zonal Flows and Intrinsic Rotation Generation SuminYi, 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 Joint US-EU Transport Taskforce Workshop TTF 2011 April 6-9, 2011San Diego, California

2. 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. Central Theme Radial propagation of turbulence by nonlinear mode coupling affects 〈kr〉 of Turbulence Spectrum & Reynolds Stress Zonal Flows Turbulence Level 〈kθ〉of Turbulence Spectrum Temperature Profile Parallel Asymmetry & Toroidal Flow

4. 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 Qi(ψ) and Qj(θ) : quadratic spline centered at ψi and θj for periodicity in θ

5. Quasi-ballooning representation of fluctuating potential include modes with m/n ≠ q modes with m/n = q n modes with m/n ≠ q • Proper resolution of “amplitude” part ϕn(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 Nθ ≥ 32 • In this work, this feature is utilized to study the role of non-resonant modes i.e. we compare Nθ = 32 and Nθ = 6 cases m modes with m/n = q modes with m/n ≠ q

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

7. Zonal Flow Evolution W/O non-resonant modes With non-resonant modes • 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.

8. Turbulence Spectrum in kr and kθ • 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 kr from non-resonant modes ? • from radial propagation/spreading of turbulence by enhanced non-linear mode coupling With non-resonant modes W/O non-resonant modes

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

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

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. Toroidal Rotation and Parallel Wave Number W/O non-resonant modes With non-resonant modes • 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

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

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

16. Decay of Parallel Wavenumber Asymmetry • With non-resonant modes, • → Enhanced radial scattering of • the + directional modes. • 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 Mode rational surface

17. Summary • 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?