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

2. The HAGIS code - ANU, Australia May 2010 HAGIS Description 1 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 1 SD Pinches, LC Appel et al., Comput. Phys. Commun. 111 131 (1998)

3. The HAGIS code - ANU, Australia May 2010 Boozer Coordinates

4. The HAGIS code - ANU, Australia May 2010 Evolution of Energetic Particles

5. The HAGIS code - ANU, Australia May 2010 Equations of Motion Derived from total system Hamiltonian

6. The HAGIS code - ANU, Australia May 2010 Fast Particle Orbits ICRH ions in JET deep shear reversal –On axis heating:  =  B 0 /E = 1 –E = 500 keV R [m] z [m]

7. The HAGIS code - ANU, Australia May 2010 Calculation of AE Eigenfunctions

8. The HAGIS code - ANU, Australia May 2010 Wave Evolution

9. The HAGIS code - ANU, Australia May 2010 Linear eigenstructure assumed invariant Introduce slowly varying amplitude and phase: Gives wave equations as: where Additional mode damping rate,  d Wave Equations

10. The HAGIS code - ANU, Australia May 2010 Delta f Method - ν eff δf

11. The HAGIS code - ANU, Australia May 2010 Quiet Start Method

12. The HAGIS code - ANU, Australia May 2010 Conservation of Particles

13. The HAGIS code - ANU, Australia May 2010 Applications AE linear growthrates and nonlinear saturation amplitudes Determination of –fast particle re-distribution –Fast particle losses  d /  0 =2.7% Mode saturates at  B/B~10 -3 n p = 52,500 Wave- particle trapping Fast ion redistribution

14. The HAGIS code - ANU, Australia May 2010 TAE Amplitude Determination 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 80 70 72 64 68 66 Time [ms] 140 120 100 Frequency [kHz] MAST #5568 0100 50 150 Time [  L t] Frequency [  0 ] 0.7 0.8 0.9 1.0 1.1 1.2 Chirping modes exhibit frequency sweeping,  /  0 ~ 20%

15. The HAGIS code - ANU, Australia May 2010 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. The HAGIS code - ANU, Australia May 2010 Transport Code Modelling SnSn 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 m 2 /s

17. The HAGIS code - ANU, Australia May 2010 Fast Particle Simulations Fishbones simulated in HAGIS to study effect on fast ion population and calculate an effective fast ion diffusion

18. The HAGIS code - ANU, Australia May 2010 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. The HAGIS code - ANU, Australia May 2010 HAGIS code performance HAGIS code parallelises very well –relatively low level of inter-processor communication traffic Wall clock time to calculate TAE linear growthrate in ITER