1. Y. Kishimoto 1,2), K. Miki 1), N. Miyato 2), J.Q.Li 1), J. Anderson 1) 21 st IAEA Fusion Energy Conference IAEA-CN-149-PD2 (Post deadline paper) October 16-21, 2006, Chengdu, China Turbulent transport associated with GAM dynamics near critical gradient regime 1) Graduate School of Energy Science, Kyoto University, Japan 2) Fusion Research and Development directorate, JAEA, Japan

2. Understanding the transport nature near critical gradient (CG) is important since fluctuations and associated confinement degradation are triggered when we try to increase the pressure gradient crossing the point. Motivation : Critical Phenomena Different plural states with different physical process coexist and the time scale of the phenomena is prolonged, i.e. “critical slowing down”, in order to determine the state from plural states, which state I should be. ○ ○ Enhancement of fluctuation, such as intermittency and bursts, takes place which affect on the crossing and/or transition dynamics. ￮ ￮ Small perturbation drastically changes the dynamics near CG by the transition among the states. “Zonal flow” is one of key factors near the CG. critical region profile evolution Gradient

3. Quench of turbulence by zonal flow near CG region Motivation : Zonal flow and intermittent dynamics ○ ○Nonlinear up-shift of CG (no dissipation limit) [Dimits et al., PoP, 00’, Parker et al., PoP] Maternal fluctuation Reynols stress Zonal flow Intermittent dynamics Nonlinear up-shift Small dissipation trigger intermittent and bursting dynamics near critical gradient Collisional damping Lin et al.,99’, PRL Li-Kishimoto, 02’, PRL ○ ○ Collisional ZF damping in ITG turbulence [Lin et al., PRL, ’99, Markov et al., PoP, ’01] ○ ○ Different scale fluctuation works as a dynamical dissipation through nonlinear mode coupling, causing intermittency near CG region Different scale fluctuation [Li-Kishimoto, PRL, ’02]

4. Two zonal flow states in toroidal system (1) Geodesic Acoustic mode (GAM) ○ ○ Turbulence simulation (edge and core) : [Hallatschek st al., PRL, ’01, Scott, Phys.Lett. A,’03] ○ ○ Experiments McKee, et al., PoP, ’03, Fujisawa et al., IAEA, ’06) Oscillatory counterpart of ZF coupled with pressure perturbation GAM Maternal fluctuation Zonal flow Collisional damping Landau damping q=2 : state (A) Oscillatory ZF for high-q value state (B) state (A) q=1 : state (B) Stationary ZF for low-q value time radius

5. Two zonal flow states in toroidal system (2) Global Landau fluid simulation Heat flux Zonal flow energy Stationary ZF Oscillatory ZF (GAM) Transition region state (B) state (A) GAM Maternal fluctuation Zonal flow Collisional damping Landau damping state (A) state (B) Miyat et al., PoP, ’04, IAEA-TH/P2-11, ’06 time State (A) State (B)

6. Two zonal flow states and critical gradient Near linear CG Far from marginal Transition dynamics between nonlinear Dimits-shift region dominated by stationary ZF and above critical region dominated by turbulence with GAM Transition region Stationary ZF Oscillatory ZF with GAM state (B) state (A)

7. Transport dynamics near critical gradient regime Global Landau fluid ITG Toroidal simulation near CG regime ○ ○Single toroidal mode (n=17) with n=0 Mixing length  i a/  i 2 v ti ￮ ￮ Quenching with single burst, lading to steady state ZF (state A) ○ ○ ZF energy is higher than that of GAM

8. Intermittent dynamics near critical gradient regime ￮ ￮ Bursting behavior survives above nonlinear CG ￮ ￮ Multiple bursts with gradual increase of ZF, leading to quench of turbulence ￮ ￮ Intermittent bursts with an increase of R/L T, showing a tight coupling between ZF and GAM. ￮ ￮ Period of intermitency,  b, decreases with R/L T, and finally shorter than that or GAM, leasing to a steady state turbulence.  i a/  i 2 v ti

9. Intermittent burst and GAM damping Phase 1 : Linear increase of turbulence : State (A) Phase 2 : Abrupt growth due to excitation of GAM : State (B) Phase 3 : Damping of GAM with residual un-damped steady state ZF Accumulation of residual ZF in each burst

10. (I) Propagating GAM mode (1) (II)(III) p(1,0) turbulence (I) (III) zonal flows (II) ￮ ￮ No sign of reflection of the emitted GAM, indication a propagation mode ￮ ￮ Turbulence energy is transferred to GAM, which propagates in radial direction (mainly outward) suffering damping. phase velocity : group velocity : ( inward) (outward)

11. Local turbulence energy is transferred out over wide radial region as GAMs. (cf. turbulent diffusion, Lin-Hahm, PoP, ’04) Propagating GAM mode (2)

12. Passing of GAM Turbulence quenched Non-local ZF generation due to propagating GAM Accumulation of residual zonal flows triggered by GAM emission r/a=0.645 Local turbulence energy GAM excitation Propagation of GAM with damping Damping ZF generation

13. Interference of GAMs and Intermittency Similar intermittent behavior is observed, but exhibiting complex interference pattern among different bursts triggered at different spaces and times. Multi-mode simulation zonal flows p(1,0) turbulence

14. Minimum model of GAM Intermittency Turbulence energy :Zonal flow :Parallel flow :Pressure perturbation :

15. Summary : GAM Intermittency   A new type of intermittency near CG, i.e., GAM Intermittency, due to emission and damping of spatially propagating GAMs was found in global Landau-fluid ITG turbulence simulation. An extended minimum model including dynamical GAM damping qualitatively describes the GAM intermittency.   The intermittent burst is triggered by the onset of GAM when the turbulence energy exceed a critical value.   Accumulation of un-damped residual part of theGAM energy increases the stationary zonal flow and quench the turbulence, dynamically leading to a nonlinear up-shift of critical gradient.   The period becomes shorter with R/L T and comparable to that of GAM, leading to a quasi-steady state turbulent transport. GAM intermittency non-locally transfers and/or convects local turbulence energy to wide radilal region as that of steady state ZF through GAM propagation and damping.