1. Interplay between energetic-particle-driven GAMs and turbulence D. Zarzoso 15 th European Fusion Theory Conference, Oxford, September 23-26 CEA, IRFM, F-13108 Saint-Paul-lez-Durance, France Y. Sarazin, X. Garbet, R. Dumont, J.B. Girardo, A. Strugarek, T. Cartier-Michaud, G. Dif-Pradalier, Ph. Ghendrih, V. Grandgirard, C. Passeron, O. Thomine A. Biancalani, A. Bottino, Ph. Lauber, E.Poli, J. Abiteboul Max-Planck-Institut für Plasmaphysik, EURATOM Association, Boltzmannstr. 2, 85748 Garching, Germany

2. D. Zarzoso2 Outline Motivation Towards the control of turbulence by energetic particles or Interaction between GAMs and turbulence and experimental observation of energetic-particle-driven GAMs → EGAMs Bump-on-tail model: from GAMs to EGAMs Electrostatic gyrokinetic simulations –EGAMs with GYSELA without turbulence –Interaction between EGAMs and turbulence Electromagnetic gyrokinetic simulations  EGAMs with NEMORB Summary and open questions

3. Radial shearing as a control of turbulence Confinement time  E ~  * -3 → Towards bigger machines Turbulence reduces confinement time (  exp ~ m 2 /s ~  tur ) CONTROL OF TURBULENCE IS ESSENTIAL Efficient mechanism of turbulence reduction: poloidal rotation ↔ E r shearing CONTROL OF TURBULENCE ↔ CONTROL OF E r D. Zarzoso3   ZF/eq  ≈ 0  ac  ≈ c S /R ≈ 10 4 Hz Radial force balance: - Fuelling (  n) - Heating (  T) - Parallel momentum Zonal flows Reynolds Stress Autoregulation [Diamond – 2005] Geodesic Acoustic Modes - Efficiency? - Excitation? (Landau damping) [Hallatschek – 2001, Itoh – 2001, Conway - 2011] ~ a ~ 10  i

4. Oscillatory flows to control turbulence 4 Time   ac  ≈ c S /R ≈ 10 4 Hz  ZF/eq  ≈ 0 Can GAMs be externally excited? Limit-cycle behavior in AUG [Conway: PRL 2011] D. Zarzoso

5. 5 Energetic GAMs in different devices ICRF driven GAMs in JET [Berk: NucFus 2006] Counter-NBI driven EGAMs in DIII-D [Nazikian: PRL 2008] Off-axis co-NBI driven GAMs in AUG [Lauber: IAEA TM 2013] GAMs excited by energetic electrons in HL-2A [Chen: PhysLettA 2013]

6. From EPs to control of turbulence D. Zarzoso6 TURBULENCE ENERGY CONFINEMENT TIME SHEARED FLOWS Zonal Flows GAMs Radial Force Balance ENERGETIC PARTICLES E

7. Kinetic description is essential 7 ExB drift velocity Curvature drift velocity Quasi-neutrality equation  : adiabatic invariant Kinetic description Low collisionality regimes → wave – particle interaction EPs cannot be described by fluid approach (F ≠ FM) Gyro-kinetic equation (adiabatic limit) Adiabatic electrons (GYSELA) Kinetic electrons (NEMORB) D. Zarzoso

8. Physics of GAMs: three ingredients D. Zarzoso8 Axisymmetric (n=0) and up-down asymmetric perturbation (m=1) Resonance + Curvature + Gradient in energy Vlasov equation: Poisson equation: Energy from particles to mode

9. Bump-on-tail: from GAMs to EGAMs D. Zarzoso9 q r Positive slope in energy essential for GAM excitation [McKee – 2006, Conway – 2008, Vermare – 2012] Axisymmetric (n=0) and up-down asymmetric perturbation (m=1) 9 Im(  ) Re(  ) EGAM GAM n EP /n i = 0.02n EP /n i = 0.05 n EP /n i = 0.001 n EP /n i = 0.005n EP /n i = 0 n EP /n i = 0.1 Solving D(  )=0 No radial structure considered!! n EP /n i = 0.01 [D. Zarzoso et al Phys. Plasmas 19, 022102 (2012)]

10. Gyrokinetic simulations of EGAMs → GYSELA 10 Instability  Equilibrium evolution needed for saturation → Full-f: no scale separation between equilibrium and fluctuations Nonlinear regime → flux-driven to excite the mode in steady-state –S th bulk heating (flux-driven simulations) [Sarazin: NucFus2011] –S EP energetic particles (energy source) [Zarzoso: PRL2013] Global plasma geometry Gysela 5D code [Grandgirard: ComNonLin2008, Sarazin: NusFus2010] Electrostatic limit, adiabatic electrons and circular cross-sections. Number of grid points ~ 20·10 9 (~ 10 3 procs. → HPC simulations) Typical time for simulations > 2·10 6 CPU-h  * ≈ 6·10 -3 ≈ 3·  * ITER (number of grid points ~  * -3 ), * = 0.02 (low coll.) D. Zarzoso

11. EGAMs without turbulence in GYSELA Implementation of bump-on-tail in GYSELA → Density scan →  and  EGAMs excited (  EGAM ≈ 0.5  GAM ) [Fu: PRL 2008, Qiu: PPCF 2010] Growth rate increases with EP concentration D. Zarzoso11 + Flat profiles + without ITG (filter) Linear growth rate Frequency [D. Zarzoso et al Phys. Plasmas 19, 022102 (2012)]  ZF/eq  ≈ 0  ac  ≈ c S /R ≈ 10 4 Hz  EGAM ≈  GAM /2

12. 12 TURBULENCE (ITG) SHEARED FLOWS Zonal Flows GAMs Radial Force Balance ENERGETIC PARTICLES E SEP - Radial profiles - Collisions - Flux-driven D. Zarzoso

13. 13 Energetic particles source in GYSELA E xternal source to create bump on the tail: 3 free parameters Source of parallel energy only (no injection of momentum nor particles) v 0 =0 → Without EPs → ∂ E F eq < 0 → no EGAMs v 0 =2 → With EPs → ∂ E F eq > 0 → EGAMs D. Zarzoso

14. Comparing simulations with/without EGAMs Two flux-driven simulations: S = S th + S EP Only difference: S EP such that Same heating power D. Zarzoso14 No energetic particles Energetic particles → EGAMs?

15. EP source successful at exciting EGAMs S EP effectively inverts the slope in the outer radial positions (r/a > 0.5) Observation of  ~ sin  and n=0 at  ≈ 0.4  GAM → Consistent with simulations without turbulence EGAMs present in linearly stable regions D. Zarzoso15

16. EPs → EGAMs → Impact on turbulence D. Zarzoso16 S EP switched on Quench of turbulence at r/a > 0.5 (due to the source…) EGAMs not excited yet EGAMs are excited Turbulence is re-excited Complex interplay EGAMs – Turbulence with modulation of turbulent transport [D. Zarzoso et al Phys. Rev. Lett. 110, 125002 (2013)] Turbulent diffusivity

17. EGAMs → Increase and modulation of  turb Axisymmetric perturbations as important as non-axisymmetric ones. but Axisymmetric modes do not increase the transport. Excitation of EGAMs and increase of  turb correlated. No modification observed w/o EPs Possible EPs – turbulence interaction via EGAMs. Oscillating sheared electric field does not suppress turbulence but Modulation of  turb at  EGAM Time-averaged  turb D. Zarzoso17

18. (m,n=0) modes grow… … until saturation What’s going on here? D. Zarzoso18 S EP = Injection of energy Particles Energy Wave Feedback One single mode  Wave-particle trapping Different modes which do not interact with each other  Quasi-linear diffusion ≈ 0 … with background of (m,n) coupled modes? Ok without turbulence, but… Wave 1 Wave 3 Wave 2 Relaxation in v- space Possible three-wave interaction (parametric instability). Analogous to the phenomenon described in [Zonca&Chen: EPL-2008] EGAM (m=1,n=0,  EGAM ) ITG 1 (m,n,   )ITG 2 (m-1,n,  EGAM -   )  Some constraints on the radial structure of the EGAM  Propagative character of ITG ~ avalanches

19. 19 TURBULENCE SHEARED FLOWS Zonal Flows GAMs Radial Force Balance ENERGETIC PARTICLES E SEP - Radial profiles - Collisions - Flux-driven Adiabatic electrons Electrostatic simulations Circular cross-section Open questions D. Zarzoso

20. Multiple ion species? Modification of  and  in standard GAMs [Ye: PoP 2013] Elongation, triangularity? From sin  to cos  [Robinson: PPCF 2012, PoP 2013] EGAMs with magnetic islands [Chen: PLA 2013] ? Comparing impacts on turbulence Fully kinetic electrons? Damping/excitation of GAMs by electrons [Zhang&Lin: PoP 2010] Solving Ampère’s law? Component m=2 of EGAM [Berk: NucFus 2006] and interaction with Alfvén modes [Chen: PLA 2013] → more interactions between EP and turbulence are possible! Threshold modified by finite-  effects? NEMORB: Towards electromagnetic EGAMs D. Zarzoso20 NEMORB [Bottino: PPCF 2011] global gyrokinetic electromagnetic PIC code Benchmark results in the electrostatic limit + adiabatic electrons –Implementation of bump-on-tail without turbulence (parametric distribution function [Di Troia: PPCF 2012] ) → EGAMs? Trapped kinetic electrons Fully kinetic electrons in electromagnetic simulations

21. Growth rate decreased by trapped electrons Bump-on-tail successfully implemented in NEMORB → two ion species –Thermal (Centered Maxwellian) –Energetic (Shifted Maxwellian) EGAMs observed beyond a threshold with no turbulence and flat profiles. Frequency agrees with theory, but growth rate overestimated by theory (due to FLR effects) Trapped electrons damp GAMs due to resonance with bounce frequency [Zhang&Lin: Pop 2010] (  be ~  GAM ) We expect that trapped electrons satisfying  be ~  EGAM will add extra damping. Growth rate of EGAMs significantly reduced with trapped electrons. Frequency is not modified. 21D. Zarzoso

22. 22 Electromagnetic EGAMs → Alfven wave Standard GAMs observed in low finite-  (  =10 -4 ) simulations w/o EPs, together with Alfven waves. No turbulence + flat profiles. Without EPs → damped GAMs With EPs → EGAMs (  EGAM  0.5  GAM ) EGAMs excited beyond a threshold n EP /n i ~ 0.1 (as with trapped electrons electrostatic simulations) The amplitude of Alfven wave is increased with EPs → possible excitation of Alfven waves by the bump-on-tail? Scan towards increasing  needed to determine if the threshold is decreased. D. Zarzoso

23. Summary Turbulence and energetic particles: two ubiquitous elements in magnetic fusion plasmas → analysis of their interplay is essential! Importance of kinetic approach to analyse wave-particle interaction → gyrokinetic codes (GYSELA, NEMORB) Bump-on-tail in GYSELA and NEMORB → EGAMs without turbulence With turbulence → NEW source in GYSELA → EGAMs with turbulence Complex interaction EGAM – turbulence observed →  turb increased in the presence of EGAMs but modulated → Possible three wave interaction? Many open questions, ongoing work in electromagnetic simulations → energetic particles in electromagnetic simulations with NEMORB → excitation of both EGAMs and Alfven waves. Ongoing work: towards increasing  → Threshold for EGAMs decreased? D. Zarzoso23

24. GYSELA: first EGAMs in gyrokinetic simulations GYSELA [Grandgirard 2008, Sarazin 2010] (CPU time ~ 4·10 6 h) gyrokinetic, full-f, flux-driven, global geometry electrostatic limit, adiabatic electrons, circular cross-sections Implementation of bump-on-tail in GYSELA → Density scan →  and  EGAMs excited (  EGAM ≈ 0.5  GAM ) [Fu: PRL 2008, Qiu: PPCF 2010] Growth rate increases with EP concentration + ∂ E F → 0 during saturation D. Zarzoso24 + Flat profiles + without ITG (filter) Linear growth rate Frequency [D. Zarzoso et al Phys. Plasmas 19, 022102 (2012)]  eq  = 0  ZF  ≈ 0  ac  ≈ c S /R ≈ 10 4 Hz  EGAM ≈  GAM /2