1. HL-2A 1 Roles of Turbulence Induced Zonal Flow and Diamagnetic Flow in L-I-H Transitions J.Q. Dong, J. Cheng, L.W. Yan, Z.X. He, K. Itoh, H. S. Xie, Y. Xiao, K. J. Zhao, W.Y. Hong, Z.H. Huang, L. Nie, S.-I. Itoh, W.L. Zhong, D.L. Yu, X.Q. Ji, Y. Huang, X.M. Song, Q.W. Yang, X.T. Ding, X.L. Zou, X. R. Duan, Yong Liu and HL-2A Team Southwestern Institute of Physics, Chengdu, China Institute for Fusion Theory and Simulation, ZJU, Hangzhou, China National Institute for Fusion Science, Toki, Japan University of Science and Technology of China, Hefei, China WCI Center for Fusion Theory, Daejeon, Korea Kyushu University, Kasuga, Japan CEA, IRFM, Cadarache, France March 22-25, 2015 The Third Theory and Simulation Workshop Hefei, China

2. HL-2A 2 Outline 1.Motivation 2. Experimental results 3. Summary and discussion

3. HL-2A 1. Motivation Identification of the key plasma parameters, which control/determine the L-H transition and reveal its mechanism in tokamaks, has been a long term focus of investigation and a topic of interest. Limit cycle oscillations (LCO) were observed when heating power was close to L-H transition power threshold. Study on dynamics of LCO with expansion of time scale provides opportunity to investigate the subject quantitatively. The LCO has been studied theoretically with predator-prey and bifurcation models, respectively. In experiment, spontaneous LCOs were observed on JET, JFT-2M, AUG, DIII-D, EAST, H-1 and TJ-II stellarators, and NSTX. The roles of turbulence induced zonal flow and diamagnetic drift flow in LCO & L-I-H transitions are investigated in HL-2A experiment. [Cheng, Dong & Itoh et al., PRL 110, 265002 (2013) ] [Dong, Cheng & Yan et al., 25 th IAEA FEC, oral talk(2014) ] 3

4. HL-2A 4 H- 模物理研究：功率阈值 0 0.5 1 1.5 2 2.5 23456789 ECH H-NBI ECH D-NBI P thres [MW] 4 He plasmas D plasmas n e [10 19 m -3 ]

5. HL-2A 5 Sampling rate = 1 MHz Spatial resolution= 3 mm Diameter of tips is 1.5 mm. Height of tips is 3 mm. 3D Langmuir probe arrays PP TSLP Parameters measured simultaneously: etc. at a few radial and poloidal positions in two poloidal sections; The most complete data of edge turbulence in tokamak plasmas.

6. HL-2A 6 The poloidal and toroidal symmetries, measured simultaneously, for LFZF and GAM. AT Coexistence of intensive LFZFs and GAMs K. J. Zhao, J. Q. Dong, L. W. Yan, Plasma Phys. Control. Fusion 52, 124008 (2010). (a) Radial wave vector-frequency and (b) wave vector spectra of LFZF and GAM potential fluctuations,

7. HL-2A Modulation of turbulence by zonal flows (a) Poloidal and toroidal coherency spectra of turbulence envelopes. (b) Corresponding phase shift spectra. (c ) Radial wave number-frequency spectra of turbulence envelopes, (d,e) The radial wave number spectra for the LFZF, GAM and envelopes of same frequencies.

8. HL-2A 8 2. Experimental results Shot I with L-I-H transitions Bt=1.4 T Ip=180 kA P NBI =1.0 MW Shot II with L-I-L transitions Bt=1.4 T Ip=185 kA P NBI =1.0 MW In the I-phases, all the fluctuations oscillate at same frequency of f LCO ~ 2-3 kHz which is identified to be close to the local ion-ion collision frequency.

9. HL-2A LCO in L-I-H transitions 9 Type-J Type-Y Type-J E r (a.u.)

10. HL-2A 10 LCO in L-I-L transitions Type-Y

11. HL-2A LCO in L-I-H & L-I-L transitions 11 t= 536-536.5 ms, t=538.5-539 ms, t=543-543.5 ms. t=506-506.5 ms, t=510-510.5 ms, t=518-518.5 ms, t=525-525.5 ms. [Cheng & Dong et al., PRL 110, 265002 (2013) ] ee

12. HL-2A [1] S.-I. Itoh, et al., Phys. Rev. Lett. 67, 2485 (1991). [2] H. Zohm, Phys. Rev. Lett. 72, 222 (1994). [3] S. J. Zweben et al., Phys. Plasmas 17, 102502 (2010). [4] G. D. Conway et al., Phys. Rev. Lett. 106, 065001 (2011). [5] G. S. Xu et al., Phys. Rev. Lett. 107, 125001 (2011). [6] L. Schmitz, et al., Phys. Rev. Lett. 108 155002 (2012). [7] G.R. Tynan et al., IAEA 2012, EX/10-3 [8] J. Cheng, et al., PRL. 110, 265002 (2013). [9] K. J. Zhao, et al.: IAEA 2012, EX/7–2Ra. [10] T. Kobayashi, et al.: PRL. 111, 035002 (2013). [11] T. Estrada, et al EPL 92 (3) (2010). [12] A. Fujisawa, et al. Phys. Rev. Lett. 81 (1998) 2256. [13] A. Fujisawa, et al.: Plasma Phys. Contr. Fus. 48 (2006) S205. [14] J. Cordey et al., Nucl. Fusion 35, 505 (1995). Observations of LCO - Varieties JET[14](95)

13. HL-2A Predator-prey model for LCO Near H-mode power threshold ， LCO appears in turbulence and shear flow Phase shift between turbulence and flow: ： turbulence precedes shear flow 90 degrees ； then phase shift becomes 180 degrees. LCO Theory E r bifurcation model for LCO flux mean parameter CCW CW [S-I. Itoh, et al., PRL 67, 2485 (1991).] [Kim & Diamond et al., PRL 90, 185006, (2003).]

14. HL-2A 14 Oscillation of radial electric field (ZF) propagates inwards Radial electric field(ZF) lags density fluctuation [ PRL 108, 155002 (2012) ] DIII-D Miki et al., PoP 19,092306 (2012) Force balance equation of ions

15. HL-2A 15 蓝 - 红背景对比 Bicoherence analysis (a-c)Squared auto- bicoherence contour, (d) summed auto bicoherence in the periods of time for the L-I-H transition.

16. HL-2A Spatio-temporal evolutions of fluctuations 16 The fluctuations of floating potentials, radial electric fields and electron density of frequency f~ 2-3 kHz.

17. HL-2A Spectrum of Mirnov coil signals ∂B θ /∂t 17 (a)The time evolution of the spectrum of Mirnov coil signals ∂B θ /∂t, (b) the coherence γ and (c) phase shift spectra between ∂B θ /∂t and fluctuations of the gradient of electron pressure ∂p e /∂r, respectively, in the frequency range of 2 − 3 kHz

18. HL-2A Plausible loops for LCOs and I-H transition 18 (a) ε, V zf and N as functions of Q=0.01 t, (b) the Lissajous diagrams for ε versus V zf (CW) (c) ε versus N (CCW) yellow for I-H transition Green for CW LCO, red for CCW LCO, yellow for I-H transition

19. HL-2A Limit Cycle discharge provides laboratory to test L-H physics –Turbulence induced flow insufficient to sustain H mode –H-mode locked in by rise in ion diamagnetic flow –See ∇ P term start to lead drive to  ExB rotation Measured L-mode seed flow shear consistent with upturn in L-H threshold H Mode Access: Measurements Confirm Role of Ion Diamagnetic Flow in L-H Transition L mode H-mode Limit Cycle Oscillations Rise in diamagnetic flow Time Correlation ms 0 4 8 12 -4 16 20 ∇ P leads  : contributes to ∇ P lags  : not cause of  ExB t – t LCO (ms)  ExB Schmitz  ExB dia 0 3 6 Promising foundation for physics based L-H prediction Before L-LCO transition

20. HL-2A 20 3. Summary and discussion Two types of LCOs were observed in L-I-H and L-I-L transitions. Three plausible loops of zonal flow vs. turbulence and turbulence vs. pressure gradient are proposed for the LCOs and I-H transition. The dominant roles (balancing Er, acceleration etc.) played by the diamagnetic drift flow in I-phase and I-H transition are demonstrated The rates of energy transfer from the diamagnetic drift and turbulent Reynolds stress E B flow in L-I-H transitions are compared. The triggering mechanism and conditions for L-I and I-H transitions are discussed. Much more theoretical and experimental investigations are expected.

21. HL-2A 21 Thank you for your attention!

22. HL-2A LCOs of plasma parameters in L-I-H transitions 22 The temporal evolutions of (a) D α emission, (b) inverse of the electron pressure gradient scale length 1/L pe, (c) the radial electric field E r, and (d) the Reynolds stress R s. Negative peaks of E r | and R s at L-I transition 1/L pe and |E r | gradually increase; their oscillations are in phase R s is in /out of phase with |E r | in early/late LCO phase,

23. HL-2A Time averaged E B and diamagnetic flows 23 Force balance equation of ions ( V E -V dim )/V E > 50% in L-mode & early I-phase but <10% prior to I-H transition. Evolutions of ∂ V dim / ∂ t and V E and V dim are strongly correlated. No evident correlations between ∂ R s /∂ r and V E are observed in I-phase.

24. HL-2A Rates of energy transfer 24 The temporal evolutions of (a) the energy transfer rates from pressure gradient drive P dim, (b) from Reynolds stress drive P RS, (c) the power of ambient turbulence P AT, (d) the ratio of P RS / P AT, P dim (P RS )fast increases prior to theI-H (L-I) transition. P RS is positive, negative, then positive and keeps increasing with time, P AT increases and decreases, respectively, when P RS is negative and positive. The ratio of P RS /P AT has a peak prior to the I-H transition.

25. HL-2A Triggering condition for I-H transition 25 The time evolutions of soft X-ray (a), inverses of the scale lengths of electron temperature and density (b), and pressure (c), the ion-ion collision frequency and the growth rate of the diamagnetic drift flow (d), the E B flow shearing rate and the turbulence decorrelation (e) for two shots. (1) the I-phase has type-J LCOs, (2) the plasma pressure gradient scale length is less than a critical value (~ 1.7 cm) (3) the E B flow shearing rate is higher than a critical value (~10^6/ s) and the turbulence decorrelation rate (4x10^5 /s), (4) the growth rate of the diamagnetic drift flow is equal to or slightly higher than the ion-ion collision frequency. The conditions for I-H transition:

26. HL-2A Formation of density ETB 26 The evolutions of (a) ion saturation current I s ~n e, (b) particle flux Γ, (c) the phase relations between the turbulent particle flux and the electron pressure gradient scale length in LCO. The density increases/decreases at Δr = -6 mm/-3 mm The turbulent particle flux is negative/positive at Δr=-6 mm/-3 mm The density gradient scale length at Δr = -6 mm is in/out of phase with the particle flux Γ at Δr = -6 mm/ /-3 mm The diffusion in this region is dominated by pressure gradient induced turbulence which leads to inward particle pinch in the process of particle ETB formation.