Formation and Back Transition of Internal Transport Barrier in Reversed Shear Plasmas

Transcription

1 Formation and Back Transition of Internal Transport Barrier in Reversed Shear Plasmas S. S. Kim [1], Hogun Jhang [1], P. H. Diamond [1,2], [1] WCI Center for Fusion Theory, NFRI [2] CMTFO and CASS, UCSD, USA Acknowledgements: X. Garbet, L. Terzolo, S. Yi, T. S. Hahm J. Y. Kim, J. M. Kwon, S. Ku, F. L. Hinton, O. Gurcan, G. Dif-Pradalier 1 st Asia-Pacific Transport Working Group Meeting, June 14-17, 2011, NIFS, Japan 1

2 Questions and Issues Intrinsic rotation in RS ITB: Strongly coupled to ITB evolution [Kim et.al. NF 11] Mean flow shear & Reynolds stress, which are involved in intrinsic rotation, are key players in ITB dynamics. Reynolds stress changes significantly before/during ITB formation and back transition. Is there any hidden player? What drives the Reynolds stress change? Instability as a candidate? High free energy source, low magnetic shear in ITB PSFI Role of PSFI in ITB dynamics? 2

3 Outline Simulation model & power ramp simulation Parallel shear-flow-driven instability (PSFI) Linear growth rates Onset of PSFI in RS ITB plasmas ITB formation and back transition Momentum redistribution due to PSFI Mean flow shear evolution Cross interactions at q min position Nonlocal interactions of fluctuations via ZFs Reynolds stress bursts Back transition mechanism 3

4 Simulation model & power ramp simulation Global gyrofluid simulations using modified TRB code (Garbet et. al. PoP 01) ITG turbulence with heat source. Only resonant modes are retained. Fixed density and q-profile with reversed shear No-slip boundary condition on V Flux driven, self-consistently evolving profiles Power ramp simulation [Kim et.al. NF 11] Forward transition Back transition 4

5 Several positions are important in ITB dynamics We found that 4 radial positions are important in ITB dynamics: r=0.57 (ITB shoulder), r=0.6 (q min ), r=0.61 (ITB foot), r=0.63 (most unstable) Physical quantities at these positions are nonlocally coupled to each other. r= r=

6 Linear growth rates Linear growth rates for global modes are calculated by solving eigenvalue equation. The growth rate evolves smoothly due to the absence of rational surface inside strong gradient region. 6

7 Onset of parallel shear flow instability In the power ramp simulation, several peaks in <dv 2 > (at r=0.63) are observed when the ExB shearing rate at the region of maximal V (r=0.57) is below the linear growth rate. This implies the excitation of parallel shear-flow-driven instability (PSFI). r=

8 Momentum redistribution due to PSFI PSFI onset is followed by a Reynolds stress change and drives a momentum redistribution. Forward transition occurs when V profile changes from a bimodal to unimodal one. Reynolds stress Instability (PSFI) Free energy source ( V at r=0.57) r=0.57 8

9 Mean flow shear evolution Forward transition Back transition ExB shearing rate more closely tracks V than T i curvature at q min position [Kim et. al. NF 11, Fiore et.al. APS 10]. The dramatic change of V at the q min position (r=0.6) plays an important role in both the ITB formation and back transition. The forward transition occurs as mean flow shear develops. 9

10 10 In reversed shear plasmas, resonant modes with same rational q appear in pairs. Cross interactions between them play an important role in ITB dynamics near the q min position. Cross interactions at q min position r i r i r i r i r i V p V p V p V p pv Q Forward transition Back transition rational q

11 Cross phase shift during ITB transition Cross phase between 1 and 2 modes shifts from positive to negative during forward transition, while reverse process prevails in back transition. before transition after transition 11

12 Forward transition mechanism The radial profile change of V during ITB formation induces strong mean flow shear at q min position, which drives cross phase shifts for the inner and outer mode interactions. Reynolds stress change triggers ITB formation? Reynolds stress change by PSFI V profile change Increase of mean ExB flow shear Positive Feedback Cross phase shift T i profile steepening 12

13 Nonlocal interactions of fluctuations via ZFs After ITB formation, zonal flow shear at r=0.61 is correlated with <dv 2 > at r=0.63. Stronger fluctuations at r=0.63 suppress weaker fluctuations at r=0.6, via induction of ZFs: seesaw mechanism [Itoh et.al. JPFRS 09] T i increases in spite of the reduction of g E. 13

14 Reynolds stress bursts Reynolds stress bursts appear after PSFIs. RSBs, just prior to back transition, induce the direction change of momentum flux from inward to outward. similar to MTE [Osborne et. al. NF 95] [Kim et. al. NF 11] Flat Spot Back transition 14

15 Back transition mechanism Outward RSBs decrease (increase) of V inside (outside) ITB suppression of PSFI Nonlocal interactions via ZFs T i changes small in spite of the large reduction of V (i.e. g E ) during t 7 <t<t 8 ; suppression of PSFI significant relaxation of T i profile. 15

16 Conclusions Linear analysis showed that parallel shear-flow-driven instability (PSFI) can be onset in reversed shear ITB plasmas. PSFI onset is followed by a Reynolds stress change and drives a momentum redistribution. The momentum redistribution significantly affects V and resultingly mean flow shear at q min position. Forward transition occurs with increase of mean flow shear. Cross interactions between inner and outer modes at q min position are important in ITB dynamics and affected significantly by the mean flow shear. Outward Reynolds stress burst (RSB) appears after PSFI and results in the reduction of both mean and zonal flow shears, which triggers back transition. Nonlocal interactions via ZF induction between fluctuations at different positions are observed, which play an important role in back transition together with RSB. 16