1pppl g. giruzzi association euratom-cea tore supra 6/10/2003 non-linear oscillations and synergy...

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


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


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



Non-linear temperature oscillations:the O-regime


AssociationEuratom-Cea TORE SUPRAWhat is the O-regime ?

(ECE)


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


AssociationEuratom-Cea TORE SUPRAThe best shots are in the O-regime

30414

Injected energy record shot:• 0.75 GJ• 4 min. 25 s



nl (1019 m-2)

PLH (MW)

Te(= 0 - 0.1) (keV)

Oscillations during LH ramp-up



nl (1019 m-2)

PLH (MW)

Te(= 0) (keV)

nl (1019 m-2)

Te(= 0) (keV)

… or during density ramp-up



nl (1019 m-3)

PLH (MW)

Te(= 0) (keV)

Vloop (V)

An "anomalous" case (Vloop 0)

Vloop ~ 175 mV n|| = 1.5



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



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



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


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


AssociationEuratom-Cea TORE SUPRAA short ECCD trigger is sufficient

Te (keV)ECE

ECCD

PLH (MW)



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



– 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



• 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



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:


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)


AssociationEuratom-Cea TORE SUPRAProfiles during an oscillation

q()

Te()

s()


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)


AssociationEuratom-Cea TORE SUPRAAssociationEuratom-Cea TORE SUPRA

Combined Electron Cyclotron and Lower Hybrid Current Drive Experiments on Tore Supra:

the Synergy Effect


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


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


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


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)


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


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


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


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


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)


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°


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)


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


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


AssociationEuratom-Cea TORE SUPRAAssociationEuratom-Cea TORE SUPRAEC absorbed power in u||-u space

with LH

Fsyn ≈ 1

Fsyn ≈ 4

without LH


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


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

1pppl g. giruzzi association euratom-cea tore supra 6/10/2003 non-linear oscillations and synergy...

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