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
D. Zarzoso 2
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
D. Zarzoso 3
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
4
Time
Time
ac≈ cS/R ≈ 104 HzZF/eq≈ 0
Can GAMs be externally excited?
Limit-cycle behavior in AUG [Conway: PRL 2011]
D. Zarzoso
D. Zarzoso 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]
From EPs to control of turbulence
D. Zarzoso 6
TURBULENCE
ENERGY CONFINEMENT TIME
SHEARED FLOWS
Zonal FlowsGAMs
Radial Force Balance
ENERGETIC PARTICLES
E
Kinetic description is essential
7
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)
D. Zarzoso
Physics of GAMs: three ingredients
D. Zarzoso 8
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
D. Zarzoso 9
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
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
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
– 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.)
D. Zarzoso
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
D. Zarzoso 11
+ 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
12
TURBULENCE (ITG)
SHEARED FLOWS
Zonal FlowsGAMs
Radial Force Balance
ENERGETIC PARTICLES
E
SEP
- Radial profiles
- Collisions
- Flux-driven
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
Comparing simulations with/without EGAMs
• Two flux-driven simulations: S = Sth + SEP
• Only difference: SEP such that
• Same heating power
D. Zarzoso 14
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
D. Zarzoso 15
EPs → EGAMs → Impact on turbulence
D. Zarzoso 16
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
D. Zarzoso 17
(m,n=0) modes grow…
… until saturation
What’s going on here?
D. Zarzoso 18
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
19
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
D. Zarzoso
• 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. Zarzoso 20
• 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
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 0.5GAM)
• 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.
D. Zarzoso
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. Zarzoso 23
Top Related