1. Nonlinear plasma-wave interactions in ion cyclotron range of frequency N Xiang, C. Y Gan, J. L. Chen, D. Zhou Institute of plasma phsycis, CAS, Hefei J. R. Cary University of Colorado and Tech-X corp

2. outline Motivation Benchmark with linear theory Parametric decays of ICRF Induced particle transport Summary

3. Motivation (1) ICRF wave heating has been widely used and proved to be an efficient way to heat plasma, especially for EAST tokamak, key for long pulse H-mode (up to 6MW ICRF heating power). (2) Experiments observed many nonlinear processes of ICRF, especially parametric decay, affect wave absorption. This is beyond the capability of mainstream codes. (3) Particle momentum transport induced by RF waves. Hot topic but theoretical work is very limited.

4. Linear theory of mode transform (conversion) of ICRF An electron plasma wave (EPW) can mode-transformed to an ion Bernstein wave (IBW) (Ono,93) Near lower hybrid resonance (LHR) (B ~0), Ex reaches its maximum Nonlinear effects could be strongest near LHR.

5. Simulation model Full-PIC simulation in the framework of VORPAL(Chet & Cary 2004). Fully kinetic ions and electrons. Density gradient in x (radial), external magnetic field in y (toroidal). Simulation model. Antenna is on the left side. Plasma density is along x-direction.

6. Simulations confirm theoretical predictions Mode-transform confirmed Simulated IBWs satisfy the linear dispersion relation

7. Parametric decays induced by mode conversion Decay channels of an IBW,  0 =  1 +  2 1) IBW (  0 ) -> IBW (  1 ) + ICQM (  2 ~ m  i ) (non-resonant) 2) IBW (  0 ) -> IBW (  1 ) + EQM (  2 ~ k // V te ) 3) IBW (  0 ) -> IBW (  1 ) + IBW(  2 ) (resonant) Experimental results on HT-7 (J.Li et al 01) (1) and (2) were observed. Particles can be heated via nonlinear Landau damping (Pokolab 72, Xiang 11)

8. PDI for H-D plasma with  = 1.2  H Possible decay channels 1)IBW (  ) -> IBW (  -  D ~0.56  )+ ICQM(  D ~0.44  ) 2)IBW (  ) -> IBW (  +  D ~1.44  )+ ICQM(  D ~0.44  ) 3)IBW (  ) -> IBW (  -  D ~-0.3  )+ ICQM(3  D ~1.3  ) 4) IBW (  ) -> QM (  -  H ~ 0.18  )+ ICQM(  H ~0.8  ) 5) IBW (  ) -> IBW (  +  H ~ 1.8  )+ ICQM(  H ~0.8  ) 6)IBW (  ) -> IBW (  -  H ~ -0.6  )+ ICQM(2  H ~1.6  ) 7) IBW (  ) -> IBW (  k // V te ~ 1.06  )+ EQM(k // V te ~0.06  )

9. Simulations confirm predicted PDI Spectra of Ex, Pattern (1),(3),(4) and (6) are observed. Two ion-species plasma (n H /n D = 0.05/0.95)

10. Consequence of PDI: ion heating Hydrogen and Deuterium ions are heated via NLD Channels (1)-(3) for D, (4)-(6) for D.

11. Decay channels decrease for pure H- plasma For pure hydrogen plasma, only decay channels (4)- (7) are possible. (5) and (6) observed. H ions are heated.

12. Decay channels increase for pure D plasma For pure deuterium plasma, in addition to decay channels (1)-(6), decay into ICQM with 4  D is observed. D ions are heated

13. Asymmetric distribution in poloidal direction is observed As ion heated, particle distribution in V x (radial) direction is nearly symmetric, but asymmetric in V z (poloidal) direction -> ion poloidal flow.

14. Ion flow induced by RF waves RF induced poloidal flow predicted by theories (Wang et al 94, Jaeger et al 99, Myra et al 04) comes from the balance of momentum equation in z direction. Reynolds stress electromagnetic force Simulations indicate that poloidal flow is mainly produced by the force in x direction when neglecting collision terms. Reynolds stress electromagnetic force

15. Simulations show ion flow shear is induced near LHR Time-averaged poloidal velocity

16. Contributions of Reynolds stress and electromagnetic force Reynolds stress causes charge separation near LHR which in turn produces a radial electric field. Contribution of electromagnetic force mainly comes from radial electric field and is comparable to the Reynolds stress in the region around LHR.

17. Summary –PIC simulations are performed to study nonlinear effects during ICRF heating. –Simulations agree with the linear theory for small input power. –Parametric decays of IBWs are observed and ion are heated via nonlinear Landau damping near LH resonance. –Poloidal ion shear flow is produced due to the ion heating. Electric force mainly comes from the radial electric field due the charge separation and it is comparable to Reynolds stress near the LHR.

18. Thanks for your attention