1. Nonlinear Frequency Chirping of Alfven Eigenmode in Toroidal Plasmas Huasen Zhang 1,2 1 Fusion Simulation Center, Peking University, Beijing 100871, China 2 Department of Physics and Astronomy, University of California, Irvine, CA92697, USA In collaboration with Z. Lin, I. Holod, GTC team, and GSEP team Supported by ITER-CN Project and GSEP West Lake Simulation International Symposium April 18-April 20, 2012 Hangzhou

2. Outline 1. Background 2. Fast repetitive chirping of BAE 3. Coherent structures in phase space 4. Nonlinear particle dynamics 5. Summary

3.  Repetitive chirping  Period in sub-millisecond  90 o phase shift  Transport enhanced Universal mechanism? Various chirping events in tokamaks NBI-driven TAE on MAST(Pinches, ppcf2004) NBI-driven TAE on NSTX (pppl4719,Podesta, NF2011) GAE burst on NSTX (Fredrickson, POP2006) Energetic particle produced by fusion reaction and auxiliary heating attracts many attentions because we want to use them to heat the plasmas. Meanwhile, large lose of EP by transport may cause damage to the fusion devices. MHD modes driven by EP are often associated with frequency chirping.

4. Chirping study by theory and simulation  One-dimensional analytic model recovers many kinds of chirping events. (Berk, PRL1992)  Single burst of chirping is recovered by hybrid MHD simulation with source and sink (Lang, POP2010)  In our work, we use Gyrokinetic simulation with realistic toroidal geometry Chirping events are intensively studied by theory and simulation

5. Gyrokinetic Turbulence Approach for EP Simulation Fully self-consistent simulation of EP turbulence and transport in burning plasmas must incorporate kinetic effects of thermal particles and coupling to microturbulence Large dynamical ranges of spatial-temporal processes require simulation codes efficient in utilizing massively parallel computers at petascale and beyond Therefore, studies of EP physics in ITER burning plasmas call for a new approach of global nonlinear gyrokinetic simulation [http://phoenix.ps.uci.edu/gsep]

6. Gyrokinetic Toroidal Code (GTC) Confinement and stability properties of fusion plasmas depend on nonlinear interaction of multiple physical processes ► Microturbulence, energetic particle (EP), magnetohydrodynamic (MHD) modes, heating/current drive using radio-frequency (RF), …. GTC Physics Integration Goal: first-principles simulations of microturbulence + EP + MHD + RF ► General geometry & experimental profiles ► Kinetic electrons & electromagnetic fluctuations ► Gyrokinetic or fully kinetic ions ► Equilibrium current ► Scalable to 100 thousand cores; GPU acceleration [http://phoenix.ps.uci.edu/GTC]

7. GTC Simulations of TAE, RSAE, BAE Verified Using identical geometry and profile data of DIII-D shot # 142111, GTC, GYRO, and TAEFL observed similar transition of RSAE to TAE, frequency up- sweeping, and mode structures in good agreement with experiments. [W. Deng, Z. Lin, I. Holod, Z. Wang, Y. Xiao, and H. Zhang, Nuclear Fusion 52, 043006 (2012)] [Verification and validation of gyrokinetic simulation of Alfvén eigenmodes in the DIII-D tokamak, D. A. Spong, et al, 2012] GTC simulation with real geometry & kinetic electron

8. Outline 1. Background 2. Fast repetitive chirping of BAE 3. Coherent structures in phase space 4. Nonlinear particle dynamics 5. Summary

9. Linear BAE simulation and verification EP excitation of n=3 BAE at q=3 surface. Thermal ion and EP are governed by gyrokinetic equation. Collisionless simulation

10. Nonlinear simulation: Fast and repetitive chirping TAE observation on NSTX (Podesta2012) No source and sink

11. Thermal ion dominates the saturation level  Thermal ion nonlinearity determines the BAE saturation level  EP nonlinearity is responsible for frequency chirping Green: NL thermal & NL EP Black: L thermal & NL EP Red: NL thermal & L EP

12. Nonlinear modification of BAE mode structure Mode width decrease: Thermal ion interacts with BAE through:  mode coupling (fine sale structures)  enhanced Landau damping by chirping Thermal ion can’t be represented by effective damping rate. Mode shifts slightly outward

13. Outline 1. Background 2. Fast repetitive chirping of BAE 3. Coherent structures in phase space 4. Nonlinear particle dynamics 5. Summary

14. Barely passing particles: Deeply trapped particles: (,E) phase space shows multi-resonance Precessional resonance contributes most.

15. Chirping induced by coherent structure evolution A.Linear structures form B.Coherent structures downshift ~15% C.Negative structures upshift D.Linear-like structures form

17. Outline 1. Background 2. Fast repetitive chirping of BAE 3. Coherent structures in phase space 4. Nonlinear particle dynamics 5. Summary

18. Coherent structures controlled by particle dynamics Island width  mode width Radial variation -> free streaming Island stretch & phase-mixing

19. Coherent structure controlled by particle dynamics

20. Summary Wave frequency exhibits a fast and repetitive chirping Sub-millisecond chirping period 90 o phase shift of amplitude and frequency Frequency chirping is induced by evolution of coherent structures in EP phase space Coherent structures are controlled by the nonlinear particle dynamics Nonlinear gyrokinetic simulation of BAE find that: Simulations provide a new paradigm to understand the fast, repetitive chirping and nonlinear wave-particle interaction.

21. Marginal saturation region Our simulation Current simulation: Deviation from marginality More relevant to experiment More important for transport Green: thermal & EP NL Red: thermal NL only Black: EP NL only

22. Phase space structure comparison Strongly driven BAE, weakly driven BAE and 1D Landau damping Strongly driven: particles are scattered to different islands Weakly driven: little scattering, no rotation