1. Rotation driven by local rf forces in tokamaks 陈佳乐 中科院等离子体物理研究所 高喆 清华大学

2. Subject Rotation change due to local rf forces benefits: –Explore ways to externally control rotation –Estimate the other forces or torques from experiments Drives induced by rf waves ? Intrinsic mechanisms or instabilities global fluxes caused by rf Local rf forces Scope: Core rotation affected by LHRF ， ICRF

3. Subsonic flows Momentum equation in the steady state: Toroidal angular momentum equation : Parallel momentum equation:

4. Local rf forces to bulk ions Most of local rf forces on a flux surface act on resonant particles

5. 平行磁场方向作用力 对共振粒子的垂直动量注入导致共振粒子在不均匀方向上 漂移，从而产生伴随的平行动量的流 更完整的形式请见： Jiale Chen and Zhe Gao. Physics of Plasmas: 2014,21,062506 共振有质动力 RPF

6. 垂直磁场方向作用力 径向梯度导致的极向力共振有质动力 与径向共振扩散流有关： 共振有质动力 共振加热导致的压强梯度 唯一的非共振力沿 不均匀方向

7. Local rf forces to bulk ions Most of local rf forces on a flux surface act on resonant particles Forces transfer to bulk ions through collision and screening –Collision: –Screening: with radial flows Steady state: –Energy transport cancels heating then –“Poloidal force” effect reappears in

8. Poloidal flow Controversy: “Para-Perp” VS “Para-Para” (Assumption)Parallel diffusion == Toroidal diffusion supports “Para-Perp” (Myra et al 2002) But this argument is doubtable.

9. D|| different from D Φ The LFS-HFS asymmetry of stress makes that e.g.(neoclassical stress, see Kim and Hinton 1992) e.g. ITG is stronger at LFS, No rigorous conclusion can be obtained without the calculation of turbulence momentum transport.

10. Cases free from the controversy Order of magnitude of poloidal flow driven by is free from the controversy if ： (IBW, ICW) ， or (LHW) 。 “Para-Perp” (Myra et al) “Para-Para” (Wang 2011) Neoclassical parallel viscosity * Due to theta-parallel projection,

11. Poloidal flows by LHCD (C-Mod) Neither Para-Para nor Para-Perp gives noticeable poloidal flows. Banana regime In contrast to Guan et al (2013) 2km/s per MW

12. Poloidal flows by LHCD (EAST 2011) Poloidal flow obtained through Para-Para is larger than that through Para-Perp in this case. Banana regime Smaller in experiments in future for higher density

13. Poloidal flow due to RPF Steady state: –Energy transport cancels heating then –“Poloidal force” effect reappears in Neoclassical flow (Jaeger et al 2000b) The rise of diamagnetic drift due to perpendicular heating (Chen et al 2000) e.g., MCICW (Lin 2009 C-Mod), ~1km/s for /3MW and is not dipolar.

14. Toroidal rotation A phenomenological momentum diffusion and pinch is required to calculate the profile. Wang 2011, Guan 2013, LHCD (C-Mod) –30km/s per MW MCICW (C-Mod) –Symmetry spectrum –Shear toroidal force –Without the need for up-down asymmetry

15. Para RPF by MCICW Fullwave code produce the information about the field.(TORIC) Only calculate the ICW regime

16. Para RPF by MCICW Force (1MW, ) Only calculate the ICW regime Toroidal Flow ( ) Uniform D D ∝ q

17. Conclusion Using perpendicular force or parallel force to balance with neoclassical parallel viscosity yields poloidal rotation velocity to the same order for LHW. Perpendicular RPF does not appear at the steady state momentum function directly but affects the rotation by change the temperature and pressure profile. Using the full wave code TORIC we demonstrate that the parallel RPF can drive a considerable toroidal flow. More couple with wave codes is on going to evaluate the driving ability of local rf forces.