1. INTRODUCTION OF WAVE-PARTICLE RESONANCE IN TOKAMAKS J.Q. Dong Southwestern Institute of Physics Chengdu, China International School on Plasma Turbulence and Transport August 16 – 18, 2007, Chengdu, China

2. Outline Introduction Tokamak magnetic configuration Charged particle motion in tokamaks Wave-particle resonance due to parallel motion of particles Wave-particle resonance due to drift motion of particles Wave-particle resonance due to rotation of particles Summary

3. Plasmas are affluent in collective oscillations and waves Wave-particle interaction is an important part of magnetic fusion plasma science:  Excitation of turbulent flows and fluctuations leads turbulent mass, momentum and energy transport  Effects of external waves on plasma particles include trapping of particles in waves, chaotic behavior in particle orbits, particle acceleration,  plasma heating and current drive Resonance is an efficient way for collisionless energy transfer between particles and waves Introduction

4. Tokamak magnetic configuration Equilibrium magnetic field ： Toroidal field Poloidal field

5. Charged particle motion in tokamaks Parallel (lognitudinal) motion: Rotation: Drifts of guiding center i) Electric field drift:

6. ii) magnetic gradient ( ) drift ： iii) magnetic curvature drift ：

7. iv)trapping, bounce and toroidal drift a) Particle trapping b) Bounce period of the trapped particles c) Toroidal drift of trapped particles

8. Diamagnetic drift of plasma fluids It is in the vertical direction; It induces charge separation and then plasma outward motion.

9. Wave-particle resonance due to parallel motion of particles

10. Landau damping & bump on tail instability Vlasov equation: Linearization: Langmuir wave: Consider the parallel motion of the electrons only

11. Poison equation Dispersion equation Landau damping: for Maxwellian distribution

12. Instability: for bump on tail distribution

13. Lower hybrid current drive Electron velocity distribution functions with different trapping effects under LHCD

14. Bump-on-tail problem with the presence of energetic particles Discrete Alfven eigenmodes Energetic particle modes

15. Destabilization of shear Alfven waves via wave-particle resonance Dispersion relation of shear Alfven wave Destabilization mechanism (universal drive) Wave particle resonance at For the right phase, particle will lose energy going outward and gaining energy going inward. As a result, particles will lose energy to waves. Energetic particle drive Spatial gradient driveLandau damping Due to velocity space gradient

16. Shear Alfven spectrum, continuum damping, and discrete modes Shear Alfven wave dispersion relation in tokamaks Continuum spectrum Initial perturbation decays due to phase mixing at time scale of Driven perturbation at  is resonantly absorbed at  continuum damping Phase mixing and resonant absorption has exact analogy with Landau damping for Vlasov plasma.

17. Mode coupling between m and m+1 induces a continuum gap Continuum spectrum is modified by toroidicity. at

18. Example of Discrete AE: Toroidal Alfven Eigenmode (TAE) TAE mode frequencies are located inside the toroidcity-induced Alfven gaps; TAE modes peak at the gaps with two dominating poloidal harmonics. C.Z. Cheng, L. Chen and M.S. Chance 1985, Ann. Phys. (N.Y.) 161, 21

19. Bump-on-tail problem: saturation with damping, source and sink Collisions tend to restore the original unstable distribution. Balance of nonlinear flattening and collisional restoration leads to mode saturation. It can be shown that the linear growth rate is reduced by a factor of. Thus, the mode saturates at H.L. Berk and B.N. Breizman 1990, Phys. Fluids B 2, 2235

20. H.L. Berk et al, Phys. Plasmas 2, 3007 (1995).

21. . Multiple unstable modes can lead to resonance overlap and stochastic diffusion of energetic particles H.L. Berk et al, Phys. Plasmas 2, 3007 (1995).

22. First observation of TAE in TFTR K.L. Wong, R.J. Fonck, S.F. Paul, et al. 1991, Phys. Rev. Lett. 66, 1874.

23. Discrete Alfven Eigenmodes versus Energetic Particle Modes Discrete Alfven Eigenmodes (AE): Mode frequencies located outside Alfven continuum (e.g., inside gaps); Modes exist in the MHD limit; energetic particle effects are often perturbative. Energetic Particle Modes (EPM): Mode frequencies located inside Alfven continuum and determined by energetic particle dynamics; Energetic effects are non-perturbative; Requires sufficient energetic particle drive to overcome continuum damping.

24. Wave-particle resonance due to drift motion of particles

25. Fishbone Instability Induce by injection of high energy neutral beam Due to interaction between the injected particles and the m=1,n=1 MHD mode Resonance between the toroidal wave velocity of the mode and toroidal drift of the trapped particles

26. Fishbone dispersion relation L. Chen, R.B. White and M.N. Rosenbluth 1984, Phys. Rev. Lett. 52, 1122

27. Electron fishbone instability

29. HL-2A results need further explanation

30. Wave-particle resonance due to rotation of particles ECRH, ICRH, ECE

31. Summary Wave-particle resonance is a basic and important mechanism for wave-particle interaction in tokamak plasmas Externally launched waves may be absorbed and heat plasma or drive current in plasma by wave- particle resonance Waves may be driven by particle motion through wave-particle resonance in plasmas There are quite a few observations on wave excitation in plasmas need explanation