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
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
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
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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
wZF/eq ≈ 0
l~a
Radial force balance:
- Fuelling (n)
wac ≈ cS/R ≈ 104 Hz
w
l ~ 10ri
Zonal flows
Autoregulation
- Heating (T)
Reynolds Stress
- Parallel momentum
[Diamond – 2005]
Geodesic Acoustic Modes
- Efficiency?
- Excitation? (Landau damping)
[Hallatschek – 2001, Itoh – 2001,
Conway - 2011]
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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?
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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
GAMs excited by energetic electrons in HL-2A
[Lauber: IAEA TM 2013]
[Chen: PhysLettA 2013]
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From EPs to control of turbulence
ENERGETIC PARTICLES
E GAMs
Zonal
Flows
Radial Force
Balance
SHEARED
FLOWS
TURBULENCE
ENERGY
CONFINEMENT TIME
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Kinetic description is essential
Kinetic description
Low collisionality regimes → wave – particle interaction
EPs cannot be described by fluid approach (F ≠ FM)
Gyro-kinetic equation (adiabatic limit)
ExB drift velocity
Curvature drift velocity
Quasi-neutrality equation
m: adiabatic invariant
•
•
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Adiabatic electrons
(GYSELA)
Kinetic electrons
(NEMORB)
7
Physics of GAMs: three ingredients
Vlasov equation:
Resonance
+ Curvature
+ Gradient in energy
Axisymmetric (n=0) and up-down
asymmetric perturbation (m=1)
Poisson equation:
Energy from
particles to mode
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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. Plasmas 19, 022102 (2012)]
[McKee – 2006, Conway – 2008, Vermare – 2012]
0.005
0.01
0.02
0.05
0
nEP/ni = 0.1
0.001
EGAM
GAM
Im(w)
Solving D(w)=0
No radial structure
considered!!
Re(w)
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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.)
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EGAMs without turbulence in GYSELA
+ Flat profiles + without ITG (filter)
• 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 et al Phys. Plasmas 19, 022102 (2012)]
Linear growth rate
Frequency
wZF/eq ≈ 0
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wEGAM ≈ wGAM/2 wac ≈ cS/R ≈ 104 Hz
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ENERGETIC PARTICLES
EGAMs
Zonal
Flows
SEP
Radial Force
Balance
SHEARED
FLOWS
- Radial profiles
- Collisions
- Flux-driven
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TURBULENCE
(ITG)
12
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
No energetic particles
•
Only difference: SEP such that
Energetic particles → EGAMs?
•
Same heating power
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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
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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
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EGAMs → Increase and modulation of 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
Time-averaged cturb
but
•
Modulation of cturb at wEGAM
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What’s going on here?
(m,n=0) modes grow…
SEP = Injection of energy
Particles
Energy
… until saturation
Wave
Feedback
One single mode  Wave-particle trapping
Wave 3
Different Wave
modes which
do not interact with each
1
other  Quasi-linear diffusion
Wave 2
Ok without turbulence, but…
Relaxation in v≈
0
… with background of (m,n) coupled
space
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
ITG2 (m-1,n, wEGAM-w1)
~ avalanches
EGAM (m=1,n=0,wEGAM)
ITG1 (m,n,w1)
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ENERGETIC PARTICLES
EGAMs
SEP
• Adiabatic electrons
• Electrostatic simulations
Zonal
Radial Force
• Circular cross-section
Flows
Balance
Open questions
SHEARED
FLOWS
- Radial profiles
- Collisions
TURBULENCE
- Flux-driven
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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
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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.
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Electromagnetic EGAMs → Alfven wave
• Standard GAMs observed in low finiteb (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.
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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 → 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?
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