Interplay betweenenergetic-particle-driven GAMs

andturbulence

D. Zarzoso

15th 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. AbiteboulMax-Planck-Institut für Plasmaphysik, EURATOM Association,

Boltzmannstr. 2, 85748 Garching, Germany

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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

Radial shearing as a control of turbulence

• Confinement time E~*-3 → Towards bigger machines

• Turbulence reduces confinement time (exp ~ m2/s ~ tur)

CONTROL OF TURBULENCE IS ESSENTIAL

• Efficient mechanism of turbulence reduction: poloidal rotation ↔ Er shearing

CONTROL OF TURBULENCE ↔ CONTROL OF Er

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ZF/eq≈ 0 ac≈ cS/R ≈ 104 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 ~ 10i

Oscillatory flows to control turbulence

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Time

Time

ac≈ cS/R ≈ 104 HzZF/eq≈ 0

Can GAMs be externally excited?

Limit-cycle behavior in AUG [Conway: PRL 2011]

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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]

From EPs to control of turbulence

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TURBULENCE

ENERGY CONFINEMENT TIME

SHEARED FLOWS

Zonal FlowsGAMs

Radial Force Balance

ENERGETIC PARTICLES

E

Kinetic description is essential

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ExB drift velocity Curvature drift velocity

Quasi-neutrality equation : adiabatic invariant

Kinetic descriptionLow 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)

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Physics of GAMs: three ingredients

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Axisymmetric (n=0) and up-down asymmetric perturbation (m=1)

Resonance+ Curvature + Gradient in energy

Vlasov equation:

Poisson equation:

Energy from particles to mode

Bump-on-tail: from GAMs to EGAMs

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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)

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Im(

)

Re()

EGAM GAM

nEP/ni = 0.02nEP/ni = 0.05nEP/ni = 0.001nEP/ni = 0.005nEP/ni = 0nEP/ni = 0.1

Solving D()=0

No radial structure considered!!

nEP/ni = 0.01

[D. Zarzoso et al Phys. Plasmas 19, 022102 (2012)]

Gyrokinetic simulations of EGAMs → GYSELA

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• 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

• * ≈ 6·10-3 ≈ 3· *ITER (number of grid points ~ *-3), * = 0.02 (low coll.)

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EGAMs without turbulence in GYSELA

• Implementation of bump-on-tail in GYSELA → Density scan → and • EGAMs excited (EGAM ≈ 0.5GAM) [Fu: PRL 2008, Qiu: PPCF 2010]

• Growth rate increases with EP concentration

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+ Flat profiles + without ITG (filter)

Linear growth rate

Frequency

[D. Zarzoso et al Phys. Plasmas 19, 022102 (2012)]

ZF/eq≈ 0 ac≈ cS/R ≈ 104 HzEGAM ≈ GAM/2

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TURBULENCE (ITG)

SHEARED FLOWS

Zonal FlowsGAMs

Radial Force Balance

ENERGETIC PARTICLES

E

SEP

- Radial profiles

- Collisions

- Flux-driven

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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

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Comparing simulations with/without EGAMs

• Two flux-driven simulations: S = Sth + SEP

• Only difference: SEP such that

• Same heating power

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No energetic particles

Energetic particles → EGAMs?

EP source successful at exciting EGAMs

• SEP effectively inverts the slope in the outer radial positions (r/a > 0.5)

• Observation of ~ sin and n=0 at ≈ 0.4GAM → Consistent with simulations without turbulence

• EGAMs present in linearly stable regions

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EPs → EGAMs → Impact on turbulence

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SEP 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

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

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(m,n=0) modes grow…

… until saturation

What’s going on here?

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SEP = Injection of energy

ParticlesEnergy 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 1Wave 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)

ITG1 (m,n,) ITG2 (m-1,n, EGAM-)

Some constraints on the radial structure of the EGAM

Propagative character of ITG ~ avalanches

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TURBULENCE

SHEARED FLOWS

Zonal FlowsGAMs

Radial Force Balance

ENERGETIC PARTICLES

E

SEP

- Radial profiles

- Collisions

- Flux-driven

• Adiabatic electrons• Electrostatic simulations• Circular cross-section

Open questions

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• 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

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• 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

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

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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 0.5GAM)

• 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 needed to determine if the threshold is decreased.

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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?

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