HAGIS Code

1. HAGIS Code Lynton Appel … on behalf of Simon Pinches and the HAGIS users EURATOM/CCFE Fusion Association, Culham Science Centre, Oxon, UK CCFE is the fusion research arm of the United Kingdom Atomic Energy Authority

2. HAGIS Description1 • Self-consistently models the nonlinear interaction between spectrum of linear eigenfunctions and fast particle distribution function • Weakly damped global Alfvén Eigenmodes (AE) could be driven unstable by fusion-born -particles • Straight field-line equilibrium • Boozer coordinates • Hamiltonian description of particle motion • Fast ion distribution function • f method • Evolution of waves • Wave eigenfunctions computed by CASTOR/MISHKA/CAS-3D and held invariant throughout system evolution 1SD Pinches, LC Appel et al., Comput. Phys. Commun. 111 131 (1998)

3. Boozer Coordinates

4. Evolution of Energetic Particles

5. Equations of Motion • Derived from total system Hamiltonian

6. Fast Particle Orbits z [m] R [m] • ICRH ions in JET deep shear reversal • On axis heating: = B0/E = 1 • E = 500 keV

7. Calculation of AE Eigenfunctions

8. Wave Evolution

9. Wave Equations • Linear eigenstructure assumed invariant • Introduce slowly varying amplitude and phase: • Gives wave equations as: • where Additional mode damping rate, d

10. Delta f Method - νeff δf

11. Quiet Start Method

12. Conservation of Particles

13. Applications Mode saturates at B/B~10-3 np = 52,500 • AE linear growthrates and nonlinear saturation amplitudes • Determination of • fast particle re-distribution • Fast particle losses d/0=2.7% Fast ion redistribution Wave-particle trapping

14. TAE Amplitude Determination 140 MAST #5568 120 Frequency [kHz] 100 80 64 68 70 66 72 Time [ms] Chirping modes exhibit frequency sweeping, /0~ 20% • Frequency sweeping observed when damping rate ~ linear growth rate and holes/clumps form in particle phase space • Modelling with HAGIS allows determination of experimental internal mode amplitudes from observed frequency sweeping • Particle trapping frequency determined using HAGIS 1.2 1.1 Frequency [0] 1.0 0.9 0.8 0.7 0 100 150 50 Time [Lt]

15. Fast Ions in MAST • High performance MAST plasmas achieved with off-axis NBI • Off-axis NBI current drive used to tailor current profile • Fast ion distribution very different with on and off axis injection • Changes to current profile with off-axis beams studied in MAST

16. Transport Code Modelling Sn TRANSP Experiment Difference • Discrepancy in neutron rate coincident with observation of fast particle driven modes • Fishbones • Can be explained by introducing an anomalous fast ion diffusion, D~0.5 m2/s

17. Fast Particle Simulations • Fishbones simulated in HAGIS to study effect on fast ion population and calculate an effective fast ion diffusion

18. Comparison with Experiment • Levels of anomalous fast ion diffusion found in simulations consistent with those required in transport codes to explain observations: • Neutron rate • Stored energy • Current profile

19. HAGIS code performance 6000 1/n scaling 5000 Linux Cluster 4000 Run time [s] 3000 2000 1000 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Number of processors, # • HAGIS code parallelises very well • relatively low level of inter-processor communication traffic Wall clock time to calculate TAE linear growthrate in ITER