Dynamics of ITG driven turbulence in the presence of a large spatial scale vortex flow

1. Dynamics of ITG driven turbulence inthe presence of a large spatial scale vortex flow Zheng-Xiong Wang,1J. Q. Li,1 J. Q. Dong,2 andY. Kishimoto1 1 Graduate School of Energy Science, Kyoto University, Japan 2 Southwestern Institute of Physics and Zhejiang University, China

2. outline • Introduction:Background • 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 Effects of magnetic island on ITG evolution

3. Background Interactions in multiple T-S scales 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! Zonal structures

4. Background Internal transport barrier (ITB) A inner region of reduced anomalous transport Radial profile of conductivity Radial profile of pressure • A key factor for ITBs • EXB shear flows often lead to ITB formation

5. y y x x 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 • Flow shearing • Mode coupling • Spectral scattering eddies eddy (b) (a)

6. 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, Observation in experiments KH induced vortex in simulations Moderate scale VFs Large scale VFs M.G. Shats et al., PRL, 2007 Pegoraro et al., JoP, conference, 2008

7. 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 but seldom

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

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

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

11. Numerical results 2-dimensional linear calculations Linear growth rate of ITG modes versus amplitude of flows VFs showstrong stabilizationeffect in comparison with MFs and SFs

12. Numerical results 2-dimensional linear calculations Wang, Diamond, Rosenbluth, 1992 MFs Mechanism growth rate versus MF growth rate of Hamiltonian number L Linear growth rate of ITG modes versus amplitude of flows • 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)

13. Numerical results 2-dimensional linear calculations Linear evolution of each poloidal mode usual ITG With SF SF Linear growth rate of ITG modes versus amplitude of flows SFs couple together all the poloidal modes and lead to a global ITG mode with an identical, greatly reduced growth rate Growth rate of each Li and Kishimoto PoP(2008)

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

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

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

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

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

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

20. Numerical results 3-dimensional nonlinear simulations w/o ZFs Ion heat conductivity: (a) (b) Radial profile of conductivity in the quasisteady state. Contours of electric potential (a) w/o VF and (b) w VF (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

21. Numerical results 3-dimensional nonlinear simulations w/o ZFs Turbulent heat flux 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). Profiles of electric potential fluctuations (EPF), pressure fluctuations (PF), and cross phase factor (CPF) for VFs

22. Numerical results 3-dimensional nonlinear simulations with ZFs Reynolds stress Coupling of VF and ITG Viscosity term ZF equation low frequency finite frequency Three wave resonance condition Assumption of zero frequency VF 

23. Numerical results 3-dimensional nonlinear simulations with ZFs w/o ZF Conductivity profile Region (I) suppression by VFs Region (III) suppression by ZFs ITB Region (II) suppression by VFs is reduced due to finite frequency Frequency spectra of ZF and Time history of ZF profile

24. 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.

25. Ｅｆｆｅｃｔ　ｏｆ　ｉｓｌａｎｄｓ Island structure ITG mode structure

26. Ｅｆｆｅｃｔ　ｏｆ　ｉｓｌａｎｄｓ Equations:

27. Ｅｆｆｅｃｔ　ｏｆ　ｉｓｌａｎｄｓ Poloidal wave number of island Coupling mechanism: parallel compressibility or acoustic wave

28. Ｅｆｆｅｃｔ　ｏｆ　ｉｓｌａｎｄｓ 2D linear calculation w/o island with island Time evolution of poloidal modes

29. Ｅｆｆｅｃｔ　ｏｆ　ｉｓｌａｎｄｓ 2D linear calculation ITG growth rate versus island width Island can stabilize linear ITG mode Linear spectra of ITG mode in different island width

30. Ｅｆｆｅｃｔ　ｏｆ　ｉｓｌａｎｄｓ 2D nonlinear simulation without ZFs Time evolution of heat conductivity in the whole system The presence of island will increase heat transport

31. Ｅｆｆｅｃｔ　ｏｆ　ｉｓｌａｎｄｓ 2D nonlinear simulation without ZFs Magnetic field Contour of potential Fluctuation Contour of pressure Fluctuation Contour of conductivity O X Conductivity is enhanced around X point but O point of island

32. Further work • Ｅｆｆｅｃｔ　ｏｆ　ｉｓｌａｎｄｓ • Dynamics of ZFs in the presence of islands (2d/3d simulation) • Combined effects of vortex flows and islands

33. Thank you very much!