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Interaction between vortex flow and microturbulence

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

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Interaction between vortex flow and microturbulence

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

  6. 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)

  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, 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

  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) ---poloidal wave number ---flow strength The VFs may then be understood as a combination of MF and SF structures.

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

  11. 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

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

  13. 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)

  14. 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

  15. 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

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

  17. 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

  18. 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 numberfor each poloidal mode

  19. 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

  20. 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

  21. 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

  22. 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

  23. 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  Z.X. Wang, et al., PRL, 2009 Z.X. Wang, et al., POP, 2011

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

  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.

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