1. Interaction between vortex flow and microturbulence Zheng-Xiong Wang （王正汹） Dalian University of Technology, Dalian, China West Lake International Symposium on Plasma Simulation April 18-20, 2012 ， Hangzhou

2. Outline Introduction: Background & Motivation Model and equations Simulation results:  Linear stabilization of ITG mode by vortex flows (VFs)  Nonlinear dynamics of ITG turbulence w/o zonal flows  Characteristics of Zonal flows in the presence of VFs  Transport structure Summary

3. Motivation

4. Vortex flow m=1 pattern Formation of ITB

5. Background Interactions in multiple T-S scales Zonal structures Interaction between a large spatial scale vortex flow and ion-scale micro-turbulence Turbulent transport due to ITG instability is crucially important for improved operation!

6. Background Mean flows (MFs)  toroidally and poloidally symmetric  suppress turbulence by radial flow shear effects  lead to internal transport barriers MFs  driven by external momentum source or by neoclassic effect x y x y (a) (b) eddy eddies Flow shearing Mode coupling Spectral scattering

7. Background Vortex flows (large scale VFs)  Varying in both radial and poloidal directions VFs  Often observed in natural and laboratory plasmas  Inevitable due to the inherent poloidal asymmetry of equilibrium pressure or magnetic field anisotropy  Induced by numerous plasma instabilities, such as Kelvin–Helmholtz (KH) or tearing mode, Moderate scale VFsLarge scale VFs Observation in experiments M.G. Shats et al., PRL, 2007 KH induced vortex in simulations Pegoraro et al., JoP, conference, 2008

8. Background purpose In comparison with MFs What are the roles of VFs in ITG evolution?  Linear stabilization of ITG mode by VFs  Direct interaction between VFs and ITG turbulence  Multiple interactions among turbulence, zonal flows, and VFs Understanding of these fundamental processes is crucially desirable

9. Model and equations A stationary large scale VF may be represented Streamer-like flows(SF) The VFs may then be understood as a combination of MF and SF structures. ---poloidal wave number ---flow strength

10. Model and equations: ITG with imposed VFs MF effect, SF effect Satisfying wave matching condition Multiplied Effect!!! Global ITG !!!

11. Model and equations: ITG with imposed VFs An initial value code with simulation box and In equations, for ZF component and for ITG fluctuations. Finite difference method in x direction with periodic boundary condition Fourier decomposition in y direction. ParametersNormalization

12. Linear growth rate of ITG modes versus amplitude of flows 2-dimensional linear calculations VFs show strong stabilization effect in comparison with MFs and SFs Numerical results

13. Linear growth rate of ITG modes versus amplitude of flows growth rate versus MF MFs Wang, Diamond, Rosenbluth, 1992 growth rate of Hamiltonian number L Mechanism MFs couple the modes with different radial scale The results of MFs agree with the previous works Hamaguchi and Horton, PoF B, (1992) Wang, Diamond, Rosenbluth, PoF B, (1992) 2-dimensional linear calculations Numerical results

14. 2-dimensional linear calculations Linear growth rate of ITG modes versus amplitude of flows SF Linear evolution of each poloidal mode Growth rate of each SFs couple together all the poloidal modes and lead to a global ITG mode with an identical, greatly reduced growth rate usual ITGWith SF Numerical results

15. Linear growth rate of ITG modes versus amplitude of flows VF Growth rate of each Normalized spectra in linear ITG modes Multiplied effect of MF and SF Growth rate versus VF wave number Numerical results

16. Effects of magnetic shear s Decreasing s reduces the stabilizing roles of MS, SF, and VF Numerical results

17. Effects of magnetic shear s on role of MFs ITG structures s=0.4 s=0.1 Decreasing s enlarges the width of ITG linear structure beyond the effective shear region of MFs MFs does not change mode width With MFs W/o MFs s=0.1 Numerical results

18. Effects of magnetic shear s on role of SFs Streamer-like flows(SF) W/o SFsWith SFs s=0.1 ITG structures L number for each poloidal mode Numerical results

19. When s becomes small, the increasing of L number is a destabilizing Effect, counteracting the stabilizing effect of poloidal mode coupling induced by SF Effects of magnetic shear s on role of SFs Growth rate of L with magnetic shear s Hamaguchi Horton, 1990 Terry, et al 1988 Growth rate of L with different s Small s large s Numerical results

20. Effects of magnetic shear s on role of VFs s=0.1 W/o VFs With VFs ITG structures VFs structure Numerical results

21. 3-dimensional nonlinear simulations w/o ZFs Contours of electric potential (a) w/o VF and (b) w VF (a) (b) Ion heat conductivity: Radial profile of conductivity in the quasisteady state. (a) For and (b) for <> the average in y and z directions and in time VFs can suppress turbulent transport more effectively than MFs with same amplitude Numerical results

22. 3-dimensional nonlinear simulations w/o ZFs Turbulent heat flux Profiles of electric potential fluctuations (EPF), pressure fluctuations (PF), and cross phase factor (CPF) for VFs Suppression by VFs is due mainly to synergetic decreases of EPF and CPF rather than PF This trend is similar to the results of MFs in toroidal simulations by Benkadda and Garbet X. Garbet, et al., PoP (2002). C.F. Figarella, et al., PRL (2003). Numerical results

23. 3-dimensional nonlinear simulations with ZFs ZF equation Reynolds stress Coupling of VF and ITG Viscosity term low frequency finite frequency Three wave resonance condition Assumption of zero frequency VF  Numerical results Z.X. Wang, et al., PRL, 2009 Z.X. Wang, et al., POP, 2011

24. 3-dimensional nonlinear simulations with ZFs Numerical results Conductivity profile Time history of ZF profile Region (I) suppression by VFs Region (II) suppression by VFs is reduced due to finite frequency w/o ZF Region (III) suppression by ZFs Frequency spectra of ZF and ITB Z.X. Wang, et al., PRL, 2009 Z.X. Wang, et al., POP, 2011

25. Vortex flow m=1 pattern Formation of ITB

26. Summary  VFs can stabilize linear ITG mode more effectively than MFs due to multiplied effect.  VFs can suppress turbulent transport more strongly than MFs with same amplitude.  An oscillatory ZF is found due to the interaction between VFs and ITG turbulence.  The resultant transport structure is consistent with that of ITBs observed experimentally.