interaction between egams and turbulence in full-f gyrokinetic...
TRANSCRIPT
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?
2 / 15
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?
3 / 15
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
4 / 15
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
6 / 15
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.
7 / 15
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
8 / 15
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
12 / 15
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.
13 / 15
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.
15 / 15