Interaction between EGAMs andturbulence in full-f gyrokinetic

simulations

David Zarzoso1

X Garbet1, Y Sarazin1, V Grandgirard1, J Abiteboul1, A Strugarek1,2, GDif-Pradalier1, R Dumont1, G Latu1 and Ph Ghendrih1

1 CEA, IRFM, F-13108 Saint-Paul-lez-Durance, France.2 Laboratoire AIM Paris-Saclay, CEA/Irfu Universite Paris-Diderot

CNRS/INSU, 91191 Gif-sur-Yvette, France

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Towards the control of turbulence?

I Efficient mechanism of turbulence reduction

Poloidal rotation ⇔ Er shearing Biglar-1990

I Control of Er

GAMs (due to geodesic curvature) Landau damped γL ∼ −e−q2.

How to excite GAMs in steady state?Interaction with turbulence?

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Towards the control of turbulence?

I Efficient mechanism of turbulence reduction

Poloidal rotation ⇔ Er shearing Biglar-1990

I Control of Er

I GAMs (due to geodesic curvature) Landau damped γL ∼ −e−q2.

I How to excite GAMs in steady state?I Interaction with turbulence?

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Fast particles excite GAMs → EGAMs

I GAMs unstable due to fast particles (e.g. bump-on-tail):∂EFeq|v‖=vres > 0→ EGAMs

I Theoretically Fu-2008, Berk-2010, Qiu-2010I Experimentally Nazikian-2008I Numerically Zarzoso-2011 to be submitted and Poster on Friday, P2.16

I EGAM: new mode ωEGAM + radial structure determined byI GAM continuum (∇T ) and FLR effects Fu-2008I Radial structure of the fast particles source (Sfp) Qiu-2010,2011

Simulations with Gysela

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Fast particles excite GAMs → EGAMs

I GAMs unstable due to fast particles (e.g. bump-on-tail):∂EFeq|v‖=vres > 0→ EGAMs

I Theoretically Fu-2008, Berk-2010, Qiu-2010I Experimentally Nazikian-2008I Numerically Zarzoso-2011 to be submitted and Poster on Friday, P2.16

I EGAM: new mode ωEGAM + radial structure determined byI GAM continuum (∇T ) and FLR effects Fu-2008I Radial structure of the fast particles source (Sfp) Qiu-2010,2011

Simulations with Gysela

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EGAMs simulations with Gysela code

I Gysela code: global full-f 5D gyrokinetic code to modelelectrostatic turbulence Grandgirard-2008, Sarazin-2010, Abiteboul et al.

this afternoon (A4.3)

I GK equation + quasineutrality Brizard-2007

B∗‖∂tF +∇ ·(B∗‖ xG F

)+ ∂vG ,‖

(B∗‖ vG ,‖ F

)= C(F ) + Sbulk + Sfp

e

Te,eq(φ− 〈φ〉)− 1

neq∇⊥.

(mineqeB2

∇⊥φ)

=nG − neq

neq

I Adiabatic electrons

I C (F ) collisions operator Dif-Pradalier-2011

I Sbulk bulk heating (flux-driven simulations) Sarazin-2011

I Sfp fast particles energy source

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Fast particles source implementation

I EGAM excitation ⇔ ∂EFeq|v‖=vres > 0⇔ Resonance in v‖.

Need to invert the slope

∂EFeq|v‖=vres < 0 v0 6= 0→ ∂EFeq|v‖=vres > 0

I Sbulk and Sfp do not inject particles.

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Comparing simulations with/without EGAMs

I Two flux driven simulations S = Sbulk + Sfp. Only difference: Sfpwith v0 = 0 and v0 = 2. Same heating power.

I Total heating such that ∇T ≡∫S Ed3vχneo

< ∇Tcrit ⇒ No expectedITG turbulence.

I ρ∗ = 1/64 (ρ∗ITER = 2 · 10−3), ν∗ = 0.1 (banana regime)

I Nr = 128, Nθ = 128, Nϕ = 64, Nv‖ = 128, Nµ = 16⇒ Nproc = 512

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New source successful at exciting EGAMs

I When v0 = 0: ∂EFeq < 0→ Landau damped GAMs.

I When v0 = 2: ∂EFeq > 0→ EGAMs excited at ωEGAM ≈ ωGAM/2.

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EGAMs lead to improved confinement!

I EGAMs ⇒ Temperature gradient locally increased

I Core temperature increases with EGAMs → Improved confinement

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Improved confinement ⇒ ITG turbulence

I Improved confinement → ∇T > ∇Tcrit⇒ ITG turbulenceI Destabilization of resonant modes k‖ = m + nq = 0.I Broad turbulent spectrum

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EGAMs modify neoclassical transport

I EGAMs ⇒ Positive shearing rate, ωE×B ∼ φ′′ > 0 (ωE×B < 0without fast part.)

I Present understanding: Berk-1967, Hazeltine-1989, Shaing-1992,Kagan-2010 ⇒ Modification of neoclassical transport through orbit

squeezing factor Sorb = 1 + q2

ε2φ′′ ⇒ χneo = χ0

neoSαorb

I φ′′ > 0⇒ Sorb > 1⇒ χneo < χ0neo

I φ′′ < 0⇒ Sorb < 1⇒ χneo > χ0neo

I Our simulations are in qualitative agreement with this explanationI With EGAMs → Sorb ≈ 1.5 Without EGAMs → Sorb ≈ 0.5

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Saturation of EGAMs

Without turbulenceI Wave-particle trapping as a mechanism

for nonlinear saturation ofI bump-on-tail instability O’Neil-1965,

Berk-1992.I EGAMs (recently invoked in Qiu-2011,

Zarzoso-2011)⇒ 2nd harmonic.

I Wave-particle trapping ⇒ ∂EF → 0

With turbulence∂EF starts decreasing only when turbulencesaturates. Turbulence contributes toEGAM saturation.Wave-particle trapping is not excluded.

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Saturation of EGAMs

Without turbulenceI Wave-particle trapping as a mechanism

for nonlinear saturation ofI bump-on-tail instability O’Neil-1965,

Berk-1992.I EGAMs (recently invoked in Qiu-2011,

Zarzoso-2011)⇒ 2nd harmonic..

I Wave-particle trapping ⇒ ∂EF → 0

With turbulence

I ∂EF starts decreasing only whenturbulence saturates. Turbulencecontributes to EGAM saturation.

I Wave-particle trapping is not excluded.

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Conclusion and perspectives

I EGAMs efficiently excited in full-f GK simulations by means of aconvenient external source.

I A mechanism of energy transfer from energetic particles toturbulence has been identified

I (1) EGAMs ⇒↑ ωE×B.I (2) ↑ ωE×B ⇒ decreased neoclassical transport and increased

temperature gradient → Improved confinementI (3) Improved confinement → ITG turbulence.I (4) EGAM saturation occurs only when turbulence saturates.

I Analysis to understand the role of turbulence in progress.

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