1. Nonlinear Simulations of Energetic Particle-driven Modes in Tokamaks Guoyong Fu Princeton Plasma Physics Laboratory Princeton, NJ, USA In collaboration with J. Breslau, J. Chen, S. Jardin, W. Park (PPPL) H.R. Strauss (NYU) L.E. Sugiyama (MIT)

2. Outline Introduction M3D code Energetic particle-driven fishbone Energetic particle-driven Alfven modes Conclusions Important issues for future

3. Introduction In a tokamak fusion reactor, fusion product alpha particles have a birth speed comparable to Alfven phase velocity, thus can destabilize Alfven waves via resonant interaction. The alpha-driven Alfven instability can cause alpha particle loss which may lead to degradation in heating efficiency and damage in the reactor’s first wall. In this work, we investigate nonlinear dynamics of energetic particle-driven instabilities via Particle/MHD hybrid simulations using M3D code.

4. M3D Code M3D is a 3D extended nonlinear MHD code with multiple level of physics: resistive MHD two fluids Particle/MHD hyrid

5. M3D XMHD Model

7. M3D code: numerical method M3D uses finite elements in poloidal planes and finite difference in toroidal direction. M3D is implicit for resistive MHD model. M3D runs on massively parallel super-computers.

8. 3D numerical grids

9. Nonlinear kink (NSTX) Sawteeth (NSTX)Internal kink (ITER) RSAE (D3D) Current hole (JET) TAE (NSTX) ELM (ITER)

10. M3D hybrid simulations of fishbone: Brief review of fishbone Fishbone instability was first discovered on the PDX tokamak. The instability was named for its characteristic magnetic signal ( K. MCGuire et al, Phys. Rev. Lett., 1983). The instability was later observed in others tokamaks and stellarators. The instability has characteristic bursting behavior with strong chirping. The instability was explained as a n/m=1/1 kink mode resonantly destabilized by trapped energetic ions: precessional branch:  ~  d (L. Chen et al, P.R.L., 1984)  * branch:  ~  * (B. Coppi et al, P.R.L., 1985)

11. Experimental observation of fishbone instability in PDX

12. Excitation of Fishbone at high  h

13. Mode Structure: Ideal Kink v.s. Fishbone

14. Linear mode structure and dependence of mode frequency and growth rate on energetic particle beta

15. Nonlinear evolution of mode structure and mode amplitude

16. Saturation amplitude scale as square of linear growth rate

17. Simulation of fishbone shows distribution fattening and strong frequency chirping distribution

18. Simulations of Beam-driven Alfven Modes in the National Spherical Torus Experiment (NSTX). Recent NSTX experimental observations show rich beam-driven instabilities: fishbone, TAEs etc and associated fast particle losses. M3D simulations show beam-driven Alfven instability with mode frequency consistent with measurement. Nonlinear simulations show strong nonlinear interaction among different modes.

19. The bursting modes are in the TAE frequency range (NSTX) Multiple modes burst at the same time. Toroidal mode number, n, ranges from 2 - 5 with the dominant mode being n=2 or 3. Mode frequencies in reasonable agreement with expected TAE frequencies. E. Fredrickson

20. NSTX Parameters and Profiles NSTX shot #108530 at t=0.267sec: R=87cm, a=63cm, B=0.43T, n e (0)=2.5e13, Ti=1.7kev, Te=1.4kev; q(0)=1.82, q(a)=12.9, weakly reversed;  (0)=21%,  beam (0)=13%; v beam /v Alfven = 2.1,  beam /a =0.17

21. t=0.0t=336. Nonlinear evolution of single n=2 mode in NSTX

25. Conclusions Hybrid simulations of energetic particle-driven fishbone instability in a circular tokamak show dynamic mode saturation as the particle distribution is flattened and mode frequency is reduced strongly. MHD nonlinearity reduces the mode saturation level. Hybrid simulation of energetic particle-driven Alfven modes in NSTX shows rich nonlinear dynamics: frequency chirping, nonlinear interaction between multiple modes and nonlinearly driven modes.

26. Important Energetic Particle Issues Linear Stability: basic mechanisms well understood, but lack of a comprehensive code which treats damping and drive non-perturbatively Nonlinear Physics: single mode saturation well understood, but lack of study for multiple mode dynamics Effects of energetic particles on thermal plasmas: needs a lot of work