1pppl g. giruzzi association euratom-cea tore supra 6/10/2003 non-linear oscillations and synergy...
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6/10/2003 1PPPL G. Giruzzi
AssociationEuratom-Cea TORE SUPRA
Non-linear oscillations and synergy effects in non-inductive plasma regimes
on Tore Supra
G. Giruzzi
Association Euratom-CEA sur la Fusion
CEA/DSM/DRFC, CEA/Cadarache (FRANCE)
Acknowledgements:J.F. Artaud, A. Bruschi, R. Dumont, G. Granucci, F. Imbeaux, J.L. Ségui,and the Tore Supra Team
6/10/2003 2PPPL G. Giruzzi
AssociationEuratom-Cea TORE SUPRAPhysics of discharges at E||~ 0
• Discharges at vanishing Ohmic field. Requirements:
– a powerful non-inductive CD system
– implementation of long-pulse technology on PFC
– discharges much longer than the full resistive time
• Discharges at vanishing Ohmic field. Main properties:
– particle transport: no Ware pinch
( Hoang et al., Phys. Rev. Lett. 90, 155002 (2003))
– absence of the strong Ohmic constraint on current profile
q profile is dominated by non-linearities
in wave-plasma interaction, bootstrap current, heat
transport, interplay with MHD ....
control of non-inductive discharges
6/10/2003 3PPPL G. Giruzzi
AssociationEuratom-Cea TORE SUPRASummary of the talk
Illustration of the physics at E|| ~ 0
by two noticeable examples on Tore Supra experiments:
– Non-linear Te oscillations: discovery of the O-regime
( Giruzzi et al., Phys. Rev. Lett. 91, 135001 (2003))
– ECCD experiments in LHCD plasmas: synergy effects
6/10/2003 4PPPL G. Giruzzi
AssociationEuratom-Cea TORE SUPRA
Non-linear temperature oscillations:the O-regime
6/10/2003 5PPPL G. Giruzzi
AssociationEuratom-Cea TORE SUPRAWhat is the O-regime ?
(ECE)
6/10/2003 6PPPL G. Giruzzi
AssociationEuratom-Cea TORE SUPRAThese oscillations are not MHD
Magneticaxis
• low frequency (~ 10 Hz)• no helical structure (m=0, n=0, from soft X-ray tomography)• no correlation with MHD signals (Mirnov coils)
Te
6/10/2003 7PPPL G. Giruzzi
AssociationEuratom-Cea TORE SUPRAThe best shots are in the O-regime
30414
Injected energy record shot:• 0.75 GJ• 4 min. 25 s
6/10/2003 8PPPL G. Giruzzi
AssociationEuratom-Cea TORE SUPRA
nl (1019 m-2)
PLH (MW)
Te(= 0 - 0.1) (keV)
Oscillations during LH ramp-up
6/10/2003 9PPPL G. Giruzzi
AssociationEuratom-Cea TORE SUPRA
nl (1019 m-2)
PLH (MW)
Te(= 0) (keV)
nl (1019 m-2)
Te(= 0) (keV)
… or during density ramp-up
6/10/2003 10PPPL G. Giruzzi
AssociationEuratom-Cea TORE SUPRA
nl (1019 m-3)
PLH (MW)
Te(= 0) (keV)
Vloop (V)
An "anomalous" case (Vloop 0)
Vloop ~ 175 mV n|| = 1.5
6/10/2003 11PPPL G. Giruzzi
AssociationEuratom-Cea TORE SUPRA
0
0.2
0.4
0.6
0.8
1
5 10 15 20
ΔTe ( )keV
( )frequency Hz
n|| ≈ 1.8 no ECRH
Oscillations amplitude vs frequency
6/10/2003 12PPPL G. Giruzzi
AssociationEuratom-Cea TORE SUPRA
ΔTe peaked<Vloop> = 62.2 mV
ΔTe hollow<Vloop> = 9.3 mV
Oscillations amplitude vs Vloop
0
0.2
0.4
0.6
0.8
1
-50 0 50 100 150 200
ΔTe ( )keV
V loop ( )mV
n|| = 1.5
ICRH
6/10/2003 13PPPL G. Giruzzi
AssociationEuratom-Cea TORE SUPRA
Vloop (V)PEC (MW)
PLH (MW)
Vloop ≠ 0
Transition to O-regime by co-ECCD
Te(= 0 - 0.2) (keV)
Vloop (V)PEC (MW)
PLH (MW)
Te(= 0 - 0.2) (keV) Vloop = 0
6/10/2003 14PPPL G. Giruzzi
AssociationEuratom-Cea TORE SUPRA... or by counter-ECCD at = 0.2
nl (1019 m-2)
PLH (MW)
Te(= 0) (keV)
ECRH phase
PEC = 0.4 MW
6/10/2003 15PPPL G. Giruzzi
AssociationEuratom-Cea TORE SUPRAA short ECCD trigger is sufficient
Te (keV)ECE
ECCD
PLH (MW)
6/10/2003 16PPPL G. Giruzzi
AssociationEuratom-Cea TORE SUPRA
q(r)
Te(r)
Te0 (keV)
EC phase
Current diffusion analysis (CRONOS)
• link with the q profile (shear and/or rational surface)• link with confinement• oscillations regime of intermediate confinement
6/10/2003 17PPPL G. Giruzzi
AssociationEuratom-Cea TORE SUPRA
– appearance after a long time
( E|| diffusion)
– appearance during transient phases
(LH or density ramp-up)
– link with Vloop level and n|| of LH waves
– link with the hard X-ray profile width
Te(0) (keV)
Hard X-rayprofile
Te oscillations are linked with j(r)
– link with q profile and confinement:
the O-regime is an incomplete
transition to improved confinement
6/10/2003 18PPPL G. Giruzzi
AssociationEuratom-Cea TORE SUPRA
• Lotka-Volterra equations
• Used for modelling populations in ecosystems
• 2 coupled nonlinear equations, periodic solutions
• J = predator; T = prey ?
∂tJ =−ν J J 1−νJT
ν JT
⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟ =−ν J J +νJT JT
∂tT =+νTT 1−νTJ
νTJ
⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟ =+νTT −νTJ TJ
Predator-prey systems
6/10/2003 19PPPL G. Giruzzi
AssociationEuratom-Cea TORE SUPRA
μ0∂ J∂ t
=1r
∂∂r
r∂∂r
η(T )(J −J LH ( j,T )−J bs( j,T ))( )
n∂T∂ t
=PLH ( J ,T )+1r
∂∂r
r nχ(J ,T )∂T∂r
⎛
⎝ ⎜
⎞
⎠ ⎟ +losses+coupling with ions
χ(J ,T )∝ c1+c2H(s), s=shear, η resistivity
When current chases temperature
1r
∂∂r
r∂∂r
η(J −J LH −J bs)( ) → −ν J J (1−bT )
1r
∂∂r
r nχ(J ,T )∂T∂r
⎛
⎝ ⎜
⎞
⎠ ⎟ → νTT(1−aJ )
dJdt
=−ν J J (1−bT ) dTdt
= νTT(1−aJ )
Resistive diffusion and heat transport equations:
... have similarities with the Lotka-Volterra equations:
6/10/2003 20PPPL G. Giruzzi
AssociationEuratom-Cea TORE SUPRAOscillations reproduced by CRONOS
coupled resistive and heat diffusion equationshave periodic solutions if:
• jLH(r) j(r)Te(r)• e is a function of j (e.g., improved confinement for negative shear)
Outputs of the CRONOS code
• resistive diffusion• heat transport• self-cons. equilibrium• jLH(r) j(r)Te(r)
6/10/2003 21PPPL G. Giruzzi
AssociationEuratom-Cea TORE SUPRAProfiles during an oscillation
q()
Te()
s()
6/10/2003 22PPPL G. Giruzzi
AssociationEuratom-Cea TORE SUPRAConclusions on O-regime
• A new tokamak plasma regime
• Predator-prey system with a distinctive feature:
non-linearity in a diffusive term
• Challenging application for the CRONOS code
• Can this be useful ?
(e.g.: periodic q profile movements could
prevent MHD)
6/10/2003 23PPPL G. Giruzzi
AssociationEuratom-Cea TORE SUPRAAssociationEuratom-Cea TORE SUPRA
Combined Electron Cyclotron and Lower Hybrid Current Drive Experiments on Tore Supra:
the Synergy Effect
6/10/2003 24PPPL G. Giruzzi
AssociationEuratom-Cea TORE SUPRAAssociationEuratom-Cea TORE SUPRAWhy to combine LH and EC waves ?
LH waves:• best CD efficiency• limited control capability (multi-junction launcher)
EC waves:• much lower CD efficiency (waiting for reactor Te)• good control capability (localized absorption)
Combination of the two suggested since the early '80sI. Fidone et al., Phys. Fluids 27 (1984) 2468
Successful current ramp-up experiments with LH+ECWT-2: A. Ando et al., Phys. Rev. Lett. 56 (1986) 2180JFT-2M: T. Yamamoto et al., Phys. Rev. Lett. 58 (1987) 2220WT-3: T. Maekawa et al., Phys. Rev. Lett. 70 (1993) 2561
Kinetic calculations point out a possible synergyI. Fidone et al., Nuclear Fusion 27 (1987) 579
6/10/2003 25PPPL G. Giruzzi
AssociationEuratom-Cea TORE SUPRAAssociationEuratom-Cea TORE SUPRAWhat is the synergy ?
A definition: ILH+EC > ILH + IEC
Simple physical picture:
1) EC waves heat electrons at the lower end of the LH tail (~ 3vth)
2) LH waves push them to high parallel energies
3) As a result, v|| >> 3vth CD
efficiency improved
LH controls the efficiencyEC controls the j profile
parallel distribution
6/10/2003 26PPPL G. Giruzzi
AssociationEuratom-Cea TORE SUPRAAssociationEuratom-Cea TORE SUPRAAttempts to demonstrate synergy
WT-3 and JFT-2M ramp-up experiments:• effect of E|| and hot conductivity
• transient regimes• fast electron confinement issue
synergy cannot be assessed or quantified
Steady CD experiments:• Versator- II (J. Colborn et al., Nucl. Fusion 38 (1998) 783)
• TdeV (Côté et al., 25th EPS Conf. 22C (1998) 1336)
inconclusive or negative results
6/10/2003 27PPPL G. Giruzzi
AssociationEuratom-Cea TORE SUPRAAssociationEuratom-Cea TORE SUPRAExploiting long shots on TS
Te(0) (keV)
transformer flux (Wb)
PLH (MW)
nl (1019 m-2)Ip (MA)
LHCD plasma target:
Vloop = 0
(transf. flux kept constant)
Ip kept constant
(feedback by LH power)
density kept constant(feedback by gas puff)
6/10/2003 28PPPL G. Giruzzi
AssociationEuratom-Cea TORE SUPRAAssociationEuratom-Cea TORE SUPRAPLH decreases during ECCD phase
Te(0) (keV)
PLH (MW)
nl (1019 m-2)
Te(=0.1) (keV)
Te(=0.25) (keV)
ECCD phase
PEC = 0.7 MW (two gyrotrons), toroidal angle +24°
LH and EC waves absorbed at same location
2 improvements:• core confinement• ECCD efficiency
6/10/2003 29PPPL G. Giruzzi
AssociationEuratom-Cea TORE SUPRAAssociationEuratom-Cea TORE SUPRACore confinement improved
after ECCD
before ECCD e (m2/s)
before ECCD
after ECCD
q()
before ECCD
after ECCD
6/10/2003 30PPPL G. Giruzzi
AssociationEuratom-Cea TORE SUPRAAssociationEuratom-Cea TORE SUPRAPLH=0.5 MW replaced by PEC=0.7 MW
PLH (MW)
transformer flux (Wb)
line-int. density(1019 m-2)
plasma current (MA)
ECCD phase
ΔPLH ≈ 0.5 MW
6/10/2003 31PPPL G. Giruzzi
AssociationEuratom-Cea TORE SUPRAAssociationEuratom-Cea TORE SUPRAProof of synergy effect
ΔI = (Ip-Ibs)ΔPLH/ PLH ΔPLH = 0.5 MW ΔI ≈ 80 kA
predicted IEC = 22 kA.
Enhancement of LHCD efficiency LH. Possible effects:
• LH increases with Ip.
Here, Ip constant
• LH increases with <Te>.
Here, <Te> in the EC phase
increases by 5 % only with respect to the phase after EC• enhancement of Ibs.
NEOCLASS computations yield negligible difference
LH+EC phaseLH phase, post-EC
6/10/2003 32PPPL G. Giruzzi
AssociationEuratom-Cea TORE SUPRAAssociationEuratom-Cea TORE SUPRAVariations of EC power deposition
Variations of:• toroidal angles• poloidal angles
Result in variations of:• EC = rEC/a
(EC power deposition location)• <Te>
(Te averaged over EC
power deposition)
PLH (W/cm3)
6/10/2003 33PPPL G. Giruzzi
AssociationEuratom-Cea TORE SUPRAAssociationEuratom-Cea TORE SUPRAΔI well beyond computed IEC
0
20
40
60
80
100
120
0.05 0.15 0.25 0.35
Iec (kA)
Δ ( )I kA
EC
linear current (computed)synergy current (measured)
tor= +28°,+25°
tor= +24°,+24°
6/10/2003 34PPPL G. Giruzzi
AssociationEuratom-Cea TORE SUPRAAssociationEuratom-Cea TORE SUPRAECCD theory is reliable
ECCD theory in excellent agreement with DIII-D experiments
(Petty et al., Nucl. Fus. 42 (2002) 1366)
6/10/2003 35PPPL G. Giruzzi
AssociationEuratom-Cea TORE SUPRAAssociationEuratom-Cea TORE SUPRASynergy factor: Fsyn = ΔI/IEC
0
1
2
3
4
5
0.05 0.15 0.25 0.35
Fsyn (exp)
EC
Comparison with kinetic theory (3-D Fokker-Planck code G. Giruzzi, PPCF 35 (1993) A123 )
0
1
2
3
4
5
0.05 0.15 0.25 0.35
Fsyn (exp)Fsyn (the)
EC
6/10/2003 36PPPL G. Giruzzi
AssociationEuratom-Cea TORE SUPRAAssociationEuratom-Cea TORE SUPRADLH+DEC in the u||-u plane
Overlap of the two interactions in both real and momentum space is a necessary condition for synergy
Fsyn ~ 4 Fsyn ~ 1
6/10/2003 37PPPL G. Giruzzi
AssociationEuratom-Cea TORE SUPRAAssociationEuratom-Cea TORE SUPRAEC absorbed power in u||-u space
with LH
Fsyn ≈ 1
Fsyn ≈ 4
without LH
6/10/2003 38PPPL G. Giruzzi
AssociationEuratom-Cea TORE SUPRAAssociationEuratom-Cea TORE SUPRAConclusions on LH+EC experiments
• LH power replaced by EC power of the same
order: an experimental fact
• Improvement of CD efficiency difficult to explain
by other effects than synergy
• Kinetic calculations of the synergy factor in
excellent agreement with experiments
• Dependence of the synergy factor on physical
parameters still to be explored and understood
6/10/2003 39PPPL G. Giruzzi
AssociationEuratom-Cea TORE SUPRAAssociationEuratom-Cea TORE SUPRAProspects
• Characterization of the O - regime dedicated experimental studies
mathematical properties
use properties of the O-regime to constrain transport models
• Control of LHCD discharges at Vloop = 0 by ECCD
experimental study of system non-linearities
feedback control of q and Te
• Establishment and control of electron ITB regimes