Physics and control of fast particle modes

1. Physics and control of fast particle modes Valentin Igochine Max-Planck Institut für Plasmaphysik EURATOM-Association D-85748 Garching bei München Germany

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. 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 toleratefast ion losses of afew % in a reactor

4. Projection of poloidally trapped ion trajectory Toroidal direction Fast ion trajectory Poloidal direction Ion gyro-motion Fast Ion Orbits ωφ ωθ ωci Various natural frequencies associated with particle motion

5. Deuterium Helium Energy Tritium + + + Neutron + + + vα = 12106 m/s vTi = 0.9106 m/s vTe = 59106 m/s vA = 8106 m/s Burning Plasmas • New physics element in burning plasmas: • Plasma is self-heated by fusion alpha particles vTi << vA < vα << vTe ITER parameters

6. 3.5 MeV 10 keV i α e 10 keV Alfvén waves and αs Alfvén wave is very weakly damped by background plasma Fusion products (αs) interact with Alfvén waves much better than thermal plasma

7. Alfvén waves Ideal MHD, linearized force balance Boyd, Sanderson, The Physics of Plasma

8. Alfvén waves Incompressible. Produce neither density nor pressure fluctuations. This mode is usually driven unstable by geometrical effects or finite current Line bending magnetic energy (i.e. field line tension) Perpendicular plasma kinetic energy (i.e. inertial effects)

9. Alfvén waves slow magnetosonic (sound wave) fast magnetosonic (compression Alfven) 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. 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) r r

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. Alfvén waves in torus Cylinder Torus P.Lauber LIGKA results

13. Alfvén waves in torus Cylinder Torus 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. Alfvén waves in torus P.Lauber LIGKA results

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

16. fast ions Fast Particle Modes as they are seen by diagnostics Temperature perturbations due to fast particle modes [P. Piovesan, V. Igochine et.al., NF, 2008]

17. Alfvén cascades The mode is highly localized JET Cascades

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 AC Time evolution of n = 4 Alfvén continuum qmin = 3.0, 2.9,…2.4  1, 2, ...7 q =2.920 0 m=12 q =2.875 0 qmin decreasing in time Mode structure,  q =2.860 0 Frequency [vA/R0] q =2.850 0 TAE m=11,12 Radius Radius B.N. Breizman et al., Phys. Plasmas 10 (2003) 3649

19. Diagnostic Potential Fitting dispersion relation provides a powerful diagnostic for determining evolution of safety factor profile • Can be used monitor scenario development qmin Alfvén Grand Cascade TAEs Frequency [kHz] MHD spectroscopy Time [s]

20. New diagnostic capabilities for fast particle modes

21. New diagnostic capabilities for fast particle modes

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

23. Excitation and control of fast particle modes

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 (vparticle ~ vwave), 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.  vwave Br E* B . . Radial drift of particles due to wave-particle interaction  vr  vwave vr E* Br Br B 

26.  vwave Br E* B . . Particles moving outwards loose energy This drift motion corresponds to a change in the particle energy: Ep>0 vr Particle gains energy during inward motion  vwave Ep<0 vr E* Particle loses energy during outward motion Br Br B

27. Landau damping and fast particle modes Energy exchange between a wave with phase velocity vph and particles in the plasma with velocity approximately equal to vph, which can interact strongly with the wave. More slower particles During this process particle gains energy from the wave without collisions. wiki accelerated decelerated

28. Landau damping and fast particle modes Energy exchange between a wave with phase velocity vph and particles in the plasma with velocity approximately equal to vph, which can interact strongly with the wave. More faster particles 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. wiki accelerated decelerated

29. primary resonance at never fulfilled on ASDEX Upgrade (only weak drive by NBI vNBI~vA/3) TAE Distribution EAE NAE TAE vA/3 3vA/5 Velocity vA vA/2 Drive by fast particles only if resonance condition fulfilled Particles always see the same phase if: For passing particles (TAE modes):

30. primary resonance at never fulfilled on ASDEX Upgrade (only weak drive by NBI vNBI~vA/3) Drive by fast particles only if resonance condition fulfilled Particles always see the same phase if: For passing particles (TAE modes): For trapped particles: relevant for fishbones relevant for TAEs (driven by ICRH) Resonance with multiples of the bounce frequency possible

31. fTAE gdamp dB fmeas Active Excitation Antenna n=1 TAE damping vs. plasma shape • Allows measurement of proximity to instability • Drive stable AE and measure plasma response • AE damping rate Triangularity Elipticity JET TAEantenna [D Testa et al.] One of the main questions: How strong the mode is damped?

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

33. Close Alfvén frequency gaps! • Engineer Alfvén continuum so gaps aren’t open! • Centre of frequency gap ~ vA/(2qR) • So make q2n a strong function of radius • How? • Current drive and fuelling (pellets)

34. Damping Mechanisms • Continuum damping • Phase-mixing occurs where mode intersects continuum • Depends upon alignment of frequency gaps and thus profiles: ωAE~ vA/qR ~ 1/q√n • Thermal ion Landau damping • γd ~ q2 and depends upon βi • For Tth,T = Tth,D, vth,T < vth,D, D provides stronger LD than T • Radiative damping • FLR corrections lead to finite radial group velocity

35. 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 Radius Energy [MeV]

36. Alphaparticles NBI Tailor Fast Particle Distribution? • Alpha particles peaked on-axis • Use off-axis beams to change drive-damping balance? df/dr < 0 strong alpha drive df/dr > 0 strong beam damping Distribution Function Radius

37. Effect of β on existence of TAE • Alfvén continuum in START • Modes move out of gap as thermal pressure increases Increasing β No modes! CSCAS [Gryaznevich & Sharapov, PPCF 46 (2004)]

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. 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. Different mechanisms for particle losses Quadratic dependence of the incoherent losses on the TAE n=5 fluctuation amplitude Linear dependence of the coherent losses at the TAE n=3 frequency on the MHD 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. Different mechanisms for particle losses Quadratic dependence of the incoherent losses on the TAE n=5 fluctuation amplitude • Due to the large system size, mainly stochastic losses are expected to play • a significant role in ITER. • Stochastic threshold • single mode • multiple modes diffusive losses above a stochastic threshold, due to energetic particle stochastic diffusion in phase space and eventually across the orbit-loss boundaries.

42. What should be done next? Considered situation Real situation mode mode background plasma (turbulence, flows, etc.) fast particle fast particle + nonlinear evolution of the system

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. 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. Interesting papers