1. Hefei, China/ August 2012 / 2nd LectureValentin Igochine 1 Physics and control of fast particle modes Valentin Igochine Max-Planck Institut für Plasmaphysik EURATOM-Association D-85748 Garching bei München Germany

2. Hefei, China/ August 2012 / 2nd LectureValentin Igochine 2 Outline Motivation Physics of Fast Particles Fast particles in tokamak Alfven waves Influence of the geometry and kinetic effects Different types of modes Control and active study of fast particle modes Excitation of the modes by fast particle Possibilities for control of fast particle modes Summary

3. Hefei, China/ August 2012 / 2nd LectureValentin Igochine 3 Redistribution / Loss of Fast Particles Loss of bulk plasma heating –Unacceptable for an efficient power plant –May lead to ignition problems Damage to first wall –Can only tolerate fast ion losses of a few % in a reactor

4. Hefei, China/ August 2012 / 2nd LectureValentin Igochine 4 Toroidal direction Ion gyro-motion Fast ion trajectory Poloidal direction Projection of poloidally trapped ion trajectory Fast Ion Orbits Various natural frequencies associated with particle motion ωφωφ ωθωθ ω ci

5. Hefei, China/ August 2012 / 2nd LectureValentin Igochine 5 Burning Plasmas New physics element in burning plasmas: –Plasma is self-heated by fusion alpha particles v Ti << v A < v α << v Te v Ti = 0.9  10 6 m/s v A = 8  10 6 m/s v α = 12  10 6 m/s v Te = 59  10 6 m/s ITER parameters + + + Deuterium + Tritium Energy + + Helium Neutron

6. Hefei, China/ August 2012 / 2nd LectureValentin Igochine 6 Alfvén waves and αs Alfvén wave is very weakly damped by background plasma α 3.5 MeV e 10 keV i Fusion products (αs) interact with Alfvén waves much better than thermal plasma

7. Hefei, China/ August 2012 / 2nd LectureValentin Igochine 7 Ideal MHD, linearized force balance Boyd, Sanderson, The Physics of Plasma Alfvén waves

8. Hefei, China/ August 2012 / 2nd LectureValentin Igochine 8 Alfvén waves Incompressible. Produce neither density nor pressure fluctuations. This mode is usually driven unstable by geometrical effects or finite current Perpendicular plasma kinetic energy (i.e. inertial effects) Line bending magnetic energy (i.e. field line tension)

9. Hefei, China/ August 2012 / 2nd LectureValentin Igochine 9 Alfvén waves fast magnetosonic (compression Alfven) slow magnetosonic (sound wave) All three solutions are real and the waves propagate without growth or decay. There is neither dissipation to cause decay nor free energy (currents) to drive instabilities.

10. Hefei, China/ August 2012 / 2nd LectureValentin Igochine 10 r r Alfvén waves in cylinder No wave packet of finite size across the magnetic field can persist for a long time since each slice moves with different velocity and in a different direction (phase mixing)

11. Hefei, China/ August 2012 / 2nd LectureValentin Igochine 11 Alfvén waves in cylinder No wave packet of finite size across the magnetic field can persist for a long time since each slice moves with different velocity and in a different direction (phase mixing) Kinetic effects modify the dispersion relation reduced kinetic limit: mode conversion to the kinetic Alfven wave (mode conversion) Result: Modes are strongly damped! P.Lauber LIGKA results

12. Hefei, China/ August 2012 / 2nd LectureValentin Igochine 12 Alfvén waves in torus CylinderTorus P.Lauber LIGKA results

13. Hefei, China/ August 2012 / 2nd LectureValentin Igochine 13 Alfvén waves in torus CylinderTorus Toroidal geometry removes the crossing points of two neighboring continuum branches (m and m+1) and generates gaps The global modes are only weakly damped by Landay damping within the gaps. No continuum damping! P.Lauber LIGKA results

14. Hefei, China/ August 2012 / 2nd LectureValentin Igochine 14 Alfvén waves in torus P.Lauber LIGKA results

15. Hefei, China/ August 2012 / 2nd LectureValentin Igochine 15 Alfvén waves in tokamak P.Lauber LIGKA results Toroidal Alfven Eigenmodes (m, m+1) Ellipticity induced Alfven Eigenmodes (m, m+2) Non-up-down-symmetric Alfven Eigenmodes (m, m+3) Kinetic TAEs: two kinetic alfven waves that propagate towards each other and form a standing wave between two continuum intersections at a given frequency

16. Hefei, China/ August 2012 / 2nd LectureValentin Igochine 16 Fast Particle Modes as they are seen by diagnostics Temperature perturbations due to fast particle modes [P. Piovesan, V. Igochine et.al., NF, 2008] fast ions

17. Hefei, China/ August 2012 / 2nd LectureValentin Igochine 17 Alfvén cascades JET Cascades The mode is highly localized

18. Hefei, China/ August 2012 / 2nd LectureValentin Igochine 18 Alfvén Cascades Reversed magnetic shear scenarios have an off-axis extremum in the magnetic helicity –New type of AE associated with point of zero magnetic shear q 0 =2.920 q 0 =2.875 q 0 =2.860 q 0 =2.850 AC TAE q min decreasing in time m=12 Time evolution of n = 4 Alfvén continuum q min = 3.0, 2.9,…2.4  1, 2,...7 Radius Frequency [v A /R 0 ] Radius Mode structure,  m=11,12 B.N. Breizman et al., Phys. Plasmas 10 (2003) 3649

19. Hefei, China/ August 2012 / 2nd LectureValentin Igochine 19 Diagnostic Potential Fitting dispersion relation provides a powerful diagnostic for determining evolution of safety factor profile –Can be used monitor scenario development Alfvén Grand Cascade q min Frequency [kHz] Time [s] MHD spectroscopy TAEs

20. Hefei, China/ August 2012 / 2nd LectureValentin Igochine 20 New diagnostic capabilities for fast particle modes

21. Hefei, China/ August 2012 / 2nd LectureValentin Igochine 21 New diagnostic capabilities for fast particle modes

22. Hefei, China/ August 2012 / 2nd LectureValentin Igochine 22 Overview:modes that can be driven by energetic particles toroidal mode number n Frequency of the mode EPM, BAE coupling between shear Alfven, acoustic, drift modes Cascades (n=3-8) TAEs, KTAEs, KAWs: shear Alfven,electromagnetic JET(n=1,2...) AUG(n=4-7) ITER(n=7-12)

23. Hefei, China/ August 2012 / 2nd LectureValentin Igochine 23 Excitation and control of fast particle modes

24. Hefei, China/ August 2012 / 2nd LectureValentin Igochine 24 A simple picture for the interaction of fast particles with MHD modes An effective interaction between a wave and particles is possible only in case of a resonance (v particle ~ v wave ), i.e. the particle always feels the same phase of the wave and thus constant force In the frame moving with the wave (and the particle) an additional electric field occurs The electric field perturbation gives rise to an ExB drift:

25. Hefei, China/ August 2012 / 2nd LectureValentin Igochine 25 Radial drift of particles due to wave-particle interaction   BrBr  v wave. B BrBr E*E* vrvr. B BrBr E*E* vrvr

26. Hefei, China/ August 2012 / 2nd LectureValentin Igochine 26 Particles moving outwards loose energy BrBr  v wave. B BrBr E*E* vrvr. B BrBr E*E* vrvr  E p >0  E p <0 Particle gains energy during inward motion Particle loses energy during outward motion This drift motion corresponds to a change in the particle energy:

27. Hefei, China/ August 2012 / 2nd LectureValentin Igochine 27 Landau damping and fast particle modes Energy exchange between a wave with phase velocity v ph and particles in the plasma with velocity approximately equal to v ph, which can interact strongly with the wave. accelerateddecelerated wiki During this process particle gains energy from the wave without collisions. More slower particles

28. Hefei, China/ August 2012 / 2nd LectureValentin Igochine 28 Landau damping and fast particle modes Energy exchange between a wave with phase velocity v ph and particles in the plasma with velocity approximately equal to v ph, which can interact strongly with the wave. accelerateddecelerated wiki During this process particle gains energy from the wave without collisions. But if the distribution function different the result could be opposite! Waves (instabilities) will gain energy from the fast particles. This produces fast particle driven mode. More faster particles

29. Hefei, China/ August 2012 / 2nd LectureValentin Igochine 29 Drive by fast particles only if resonance condition fulfilled Particles always see the same phase if: primary resonance at never fulfilled on ASDEX Upgrade (only weak drive by NBI v NBI ~v A /3) For passing particles (TAE modes): vAvA v A /2 v A /3 3v A /5 Velocity Distribution EAE TAE NAE TAE

30. Hefei, China/ August 2012 / 2nd LectureValentin Igochine 30 Drive by fast particles only if resonance condition fulfilled Particles always see the same phase if: primary resonance at never fulfilled on ASDEX Upgrade (only weak drive by NBI v NBI ~v A /3) For passing particles (TAE modes): For trapped particles: Resonance with multiples of the bounce frequency possible relevant for fishbones relevant for TAEs (driven by ICRH)

31. Hefei, China/ August 2012 / 2nd LectureValentin Igochine 31 f TAE f meas  damp BB Active Excitation Antenna Allows measurement of proximity to instability Drive stable AE and measure plasma response –AE damping rate n=1 TAE damping vs. plasma shape TriangularityElipticity JET TAE antenna [D Testa et al.] One of the main questions: How strong the mode is damped?

32. Hefei, China/ August 2012 / 2nd LectureValentin Igochine 32 Effect of plasma shape ITPA Energetic Particles Topical Group code- experiment comparison –n = 3 TAE in JET –Excellent agreement with frequency & mode structure [THW/P7-08, IAEA FEC (2010)] Elongation scan n = 3 #77788 But…this damping measurements sensitive to distance between vessel wall and plasma. (This should be done carefully.)

33. Hefei, China/ August 2012 / 2nd LectureValentin Igochine 33 Close Alfvén frequency gaps! Engineer Alfvén continuum so gaps aren’t open! –Centre of frequency gap ~ v A /(2qR) –So make q 2 n a strong function of radius How? –Current drive and fuelling (pellets)

34. Hefei, China/ August 2012 / 2nd LectureValentin Igochine 34 Damping Mechanisms Continuum damping –Phase-mixing occurs where mode intersects continuum –Depends upon alignment of frequency gaps and thus profiles: ω AE ~ v A /qR ~ 1/q√n Thermal ion Landau damping –γ d ~ q 2 and depends upon β i –For T th,T = T th,D, v th,T < v th,D, D provides stronger LD than T Radiative damping –FLR corrections lead to finite radial group velocity

35. Hefei, China/ August 2012 / 2nd LectureValentin Igochine 35 Radius Energy [MeV] Fast Particle Drive Collective instabilities –Fast particle gradients act as source of free energy Non-Maxwellian distribution –  ~   f/  E - n  f/  –Negative radial gradient  Drive (n>0) –Negative energy gradient  Damping

36. Hefei, China/ August 2012 / 2nd LectureValentin Igochine 36 Alpha particles Tailor Fast Particle Distribution? Alpha particles peaked on-axis Use off-axis beams to change drive-damping balance? Radius Distribution Function NBI df/dr < 0  strong alpha drive df/dr > 0  strong beam damping

37. Hefei, China/ August 2012 / 2nd LectureValentin Igochine 37 Effect of β on existence of TAE Increasing β Alfvén continuum in START –Modes move out of gap as thermal pressure increases CSCAS [Gryaznevich & Sharapov, PPCF 46 (2004)] No modes!

38. Hefei, China/ August 2012 / 2nd LectureValentin Igochine 38 Overlap of the modes is a potential danger While single toroidal Alfven eigenmodes (TAE) and Alfven cascades (AC) eject resonant fast ions in a convective process, an overlapping of AC and TAE spatial structures leads to a large fast-ion diffusion and loss.

39. Hefei, China/ August 2012 / 2nd LectureValentin Igochine 39 Fast particle losses from core BAEs Non-Alfvenic character! Driven by radial gradient of ICRH-heated ions low-frequency gap in Alfven continuum induced by ion compressibility m=4;n=4;5 mode follows dispersion relation(B- field dependence cancels) BAE

40. Hefei, China/ August 2012 / 2nd LectureValentin Igochine 40 Different mechanisms for particle losses Linear dependence of the coherent losses at the TAE n=3 frequency on the MHD fluctuation amplitude Quadratic dependence of the incoherent losses on the TAE n=5 fluctuation amplitude M. Garcia-Munoz et al., EPS 2010 transient losses, due to resonant drift motion across the orbit-loss boundaries in the particle phase space of energetic particles which are born near those boundaries diffusive losses above a stochastic threshold, due to energetic particle stochastic diffusion in phase space and eventually across the orbit-loss boundaries.

41. Hefei, China/ August 2012 / 2nd LectureValentin Igochine 41 Different mechanisms for particle losses Quadratic dependence of the incoherent losses on the TAE n=5 fluctuation amplitude diffusive losses above a stochastic threshold, due to energetic particle stochastic diffusion in phase space and eventually across the orbit-loss boundaries. Due to the large system size, mainly stochastic losses are expected to play a significant role in ITER. Stochastic threshold single mode multiple modes

42. Hefei, China/ August 2012 / 2nd LectureValentin Igochine 42 What should be done next? Considered situation Real situation mode fast particle mode background plasma (turbulence, flows, etc.) fast particle + nonlinear evolution of the system

43. Hefei, China/ August 2012 / 2nd LectureValentin Igochine 43 Fast particle physics summary Alfven modes are typically strongly damped by continuum damping Toroidal geometry, ellipticity and other effects lead to gaps in the continuum where the modes are weakly damped Fast particle (gradients in energy and velocity space and gradient of the distribution function) could drive these modes to unstable regimes Big drive from fast particles could even overcome continuum damping (Energetic particle modes, EPM) Overlap of the modes leads to bigger particle losses. This could be a potential danger for future scenarios in ITER.

44. Hefei, China/ August 2012 / 2nd LectureValentin Igochine 44 Fast particle control summary Affect stability/existence of Alfvén eigenmodes –Plasma conditions: density, safety factor, beta, isotope mix (mass density), magnetic field, introduce flow (rotation) Tailor fast particle distribution to change drive –Alphas: Fuelling –NBI: Beam geometry, injection energy –ICRF: Resonance layer –Field topology: Ripple, 3D field coils, aspect ratio Avoid mode overlap if possible

45. Hefei, China/ August 2012 / 2nd LectureValentin Igochine 45 Interesting papers

46. Hefei, China/ August 2012 / 2nd LectureValentin Igochine 46