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Interplay between energetic-particle-driven GAMs and turbulence

Interplay between energetic-particle-driven GAMs and turbulence. D. Zarzoso. 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. CEA, IRFM, F-13108 Saint-Paul-lez-Durance, France.

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Interplay between energetic-particle-driven GAMs and turbulence

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  1. Interplay betweenenergetic-particle-driven GAMsandturbulence D. Zarzoso 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 CEA, IRFM, F-13108 Saint-Paul-lez-Durance, France A. Biancalani, A. Bottino, Ph. Lauber, E.Poli, J. Abiteboul Max-Planck-Institut für Plasmaphysik, EURATOM Association, Boltzmannstr. 2, 85748 Garching, Germany 15th European Fusion Theory Conference, Oxford, September 23-26

  2. D. Zarzoso 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 tE~r*-3 → Towards bigger machines Turbulence reduces confinement time (cexp ~ m2/s ~ ctur) CONTROL OF TURBULENCE IS ESSENTIAL Efficient mechanism of turbulence reduction: poloidal rotation ↔ Er shearing CONTROL OF TURBULENCE ↔ CONTROL OF Er D. Zarzoso wZF/eq≈ 0 wac≈ cS/R ≈ 104 Hz w l ~ a l ~ 10ri Geodesic Acoustic Modes - Efficiency? - Excitation?(Landau damping) [Hallatschek – 2001, Itoh – 2001, Conway - 2011] Radial force balance: - Fuelling (n) - Heating (T) - Parallel momentum Zonal flows Autoregulation Reynolds Stress [Diamond – 2005]

  4. Oscillatory flows to control turbulence Limit-cycle behavior in AUG [Conway: PRL 2011] Time wZF/eq≈ 0 wac≈ cS/R ≈ 104 Hz w Time Can GAMs be externally excited? D. Zarzoso

  5. D. Zarzoso 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 ENERGETIC PARTICLES Zonal Flows Radial Force Balance GAMs E SHEARED FLOWS TURBULENCE ENERGY CONFINEMENT TIME D. Zarzoso 6

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

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

  9. Bump-on-tail: from GAMs to EGAMs q Axisymmetric (n=0) and up-down asymmetric perturbation (m=1) Positive slope in energy essential for GAM excitation r [D. Zarzoso et al Phys. Plasmas19, 022102 (2012)] [McKee – 2006, Conway – 2008, Vermare – 2012] nEP/ni = 0.01 nEP/ni = 0.005 nEP/ni = 0 nEP/ni = 0.05 nEP/ni = 0.02 nEP/ni = 0.1 nEP/ni = 0.001 EGAM GAM Solving D(w)=0 Im(w) No radial structure considered!! Re(w) D. Zarzoso 9

  10. Gyrokinetic simulations of EGAMs → GYSELA • 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 • Sth bulk heating (flux-driven simulations) [Sarazin: NucFus2011] • SEP 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 ~ 20·109 (~ 103 procs. → HPC simulations) • Typical time for simulations > 2·106 CPU-h • r* ≈ 6·10-3 ≈ 3· r*ITER (number of grid points ~ r*-3), n* = 0.02 (low coll.) D. Zarzoso

  11. EGAMs without turbulence in GYSELA Implementation of bump-on-tail in GYSELA → Density scan → w and g EGAMs excited (wEGAM≈ 0.5wGAM) [Fu: PRL 2008, Qiu: PPCF 2010] Growth rate increases with EP concentration D. Zarzoso + Flat profiles + without ITG (filter) [D. Zarzoso et al Phys. Plasmas19, 022102 (2012)] Linear growth rate Frequency wEGAM ≈ wGAM/2 wZF/eq≈ 0 wac≈ cS/R ≈ 104 Hz

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

  13. Energetic particles source in GYSELA • External source to create bump on the tail: 3 free parameters • Source of parallel energy only (no injection of momentum nor particles) v0=0 → Without EPs → ∂EFeq < 0 → no EGAMs v0=2 → With EPs → ∂EFeq > 0 → EGAMs D. Zarzoso

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

  15. EP source successful at exciting EGAMs • SEP effectively inverts the slope in the outer radial positions (r/a > 0.5) • Observation of f ~ sinq and n=0 at w≈ 0.4wGAM → Consistent with simulations without turbulence • EGAMs present in linearly stable regions D. Zarzoso 15

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

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

  18. What’s going on here? (m,n=0) modes grow… … until saturation SEP = Injection of energy Energy One single mode  Wave-particle trapping Particles Wave 3 Wave Wave 1 Different modes which do not interact with each other  Quasi-linear diffusion Feedback Wave 2 Ok without turbulence, but… Relaxation in v-space ≈ 0 … with background of (m,n) coupled modes? • Possible three-wave interaction (parametric instability). • Analogous to the phenomenon described in [Zonca&Chen: EPL-2008] • Some constraints on the radial structure of the EGAM • Propagative character of ITG ~ avalanches EGAM (m=1,n=0,wEGAM) ITG1 (m,n,w1) ITG2 (m-1,n, wEGAM-w1) D. Zarzoso 18

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

  20. NEMORB: Towards electromagnetic EGAMs • Multiple ion species? Modification of w and g in standard GAMs [Ye: PoP 2013] • Elongation, triangularity? From sinq to cosq[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-b effects? • 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 D. Zarzoso 20

  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] (wbe ~ wGAM) • We expect that trapped electrons satisfying wbe ~ wEGAM will add extra damping. • Growth rate of EGAMs significantly reduced with trapped electrons. • Frequency is not modified. D. Zarzoso 21

  22. Electromagnetic EGAMs → Alfven wave • Standard GAMs observed in low finite-b (b =10-4) simulations w/o EPs, together with Alfven waves. • No turbulence + flat profiles. • Without EPs → damped GAMs • With EPs → EGAMs (wEGAM 0.5wGAM) • EGAMs excited beyond a threshold nEP/ni ~ 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 b 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 → cturb 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 b→ Threshold for EGAMs decreased? D. Zarzoso 23

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