QTYUIOP

byM.S. Chu*

Presented at the21st IAEA Fusion Energy ConferenceChengdu, China

October 16–21, 2006

Maintaining the Quasi-steady State Central Current Density Profile in Hybrid Discharges

277-06/MSC/jy

for D.P. Brennan,† V.S. Chan,* M. Choi,* R.J. Jayakumar,‡ L.L. Lao,* R. Nazikian,¶ P.A. Politzer,* H.E. St. John,*

A.D. Turnbull,* M.A. Van Zeeland,* R.B. White,¶

*General Atomics, San Diego, California†Univeristy of Tulsa, Tulsa, Oklahoma‡Lawrence Livermore National Laboratory, Livermore, California¶Princeton Plasma Physics Laboratory, Princeton, New Jersey

2 Chu IAEA 2006

The Hybrid Scenario is an AttractiveOption for ITER Operation

• Good confinement, nearly steady state

• Projected ITER performance at or aboveQfusion=10

• Robustly achievable over wide rangeof discharge parameters

• Compatible with sustained ignitionscenario in ITER

• Can operate near the high stability limit

• Reduced or eliminated occurrence ofsawtooth

3.22.8-4.7q95

2.82.6-3.3N

2.42.3-2.7H89p

2.0 m0.6 ma

12.9N/AQ

1500 s9.5 sTdur

5.3 T1.1-1.9 TBT

6.2 m1.75 mR

13.9 MA1.2 MAIp

ITERDIII-D

Hybrid Discharge Parameters

Wade Nuclear Fusion 2005

3 Chu IAEA 2006

NTM-MHD Mode is Key to Maintainingq0 1 and Avoiding Sawteeth

• In DIII-D hybrids, rotating 3/2 or 4/3 NTM islands observed.

• Magnetic islands prevent development of sawteeth - q0 ~ 1+

• There is a current deficit – possibility of negative current drive insideneoclassical island surface

Explore the Relation of NTM Island and Current Deficit

Politzer EPS05

012345

No 3/2mode

With 3/2mode

Sawteethn = 1 B rms (G)

~n = 2 B rms (G)

~

012345

3.0 4.0 5.0Time (s)

6.0 7.0

Jayakumar APS04

DIII-D

I -50 kA

n=1

n=2

5/25/20054 Chu IAEA 2006

Outline

• Rotating island provides rotating magnetic perturbation andacts as antenna, emitting Alfvén waves into the surroundingplasma

• Particle drifts due to Alfv én waves produce charge separationand effectively drive counter current

– Polarization drift could give rise to mode conversion

– Curvature drift produces side band electric fields

• The wave can scatter NBI ions and reduce efficiency of NBIcurrent drive

5 Chu IAEA 2006

Rotating Magnetic Island Emits AlfvénWave and Redistributes Fast Ions

• Alfvén waves drive current throughmodification of plasma drifts andexcitation of

– Polarization drift and subsequentmode conversion to kinetic Alfvenwave(kAW) excites

– Magnetic curvature drift causescharge accumulation and drives

• Magnetic field perturbation fromNTM island can redistribute densityof energetic ions and reduce NBIcentral current drive

E||

E||

E||

6 Chu IAEA 2006

Current Drive by Alfvén Wave Is StrongCandidate to Explain Counter Current Drive

Rotating3/2-NTMisland

2/2 sideband near q0=1

Mainharmonic

Polarizationdrift

Magnetic curvaturedrift, electrostatic sideband

Magneticperturbations

Modify densitydistribution ofenergetic particles

3/2

Countercurrentdrive

ORBITCODE

DKE, Charge Neutrality, Fisch-Karney CD Theory

Alfvénwave

2 /2

3/2

Strong

strong

Mod

erate

KAW

Moderate

Modeconversion

7 Chu IAEA 2006

Current Drive by Alfvén Wave Is StrongCandidate to Explain Counter Current Drive

Rotating3/2-NTMisland

2/2 sideband near q0=1

Mainharmonic

Polarizationdrift

Magnetic curvaturedrift, electrostatic sideband

Magneticperturbations

Modify densitydistribution ofenergetic particles

Countercurrentdrive

ORBITCODE

DKE, Charge Neutrality, Fisch-Karney CD Theory

Alfvénwave

3/2

weak

KAW

8 Chu IAEA 2006

Established F-K Current Drive Theory Requires

Parallel Electric Field to Drive Current• Phase velocity important for current drive

• Electrons Landau damp on therefore Pd

depends on

• required to drive J

J /en0vtePd /men0 evte

2=8xa

+ 2+1.4 xa( )2

J =n0 e3

(2 )1/2me2

3/2

vte3

e

E||2

k||2exp(

xa2

2) 8+ 2xa +1.4xa

3[ ]

xa = 3/2

e

k||vtePhase velocity

Parallel electric field

E||E||

E||

Current density

Powerdissipation

9 Chu IAEA 2006

Perpendicular Electric Field Excites Parallel ElectricField through Particle Drifts

• Kinetic theory determines electron and ion densityresponses to perturbing electric fields

• Quasineutrality condition then determines the relationshipbetween the electric fields,

TeTss1+ sZ s

0( )[ ] 1 s*

3/2i

=TeZ s

0( )Ts 2k||vtss

3/2i

s2 2 + D

s

1 s

*

3/2i

FLRcurvaturedrift

E = ||Electric field

Parallel potential Perpendicular potential

Polarization drift

is rotation frequency of 3/2 island w.r.t. local thermal ions3/2i (r)

10 Chu IAEA 2006

Total Alfvén Wave Driven Current Depends onDetails of Electron and Ion Dynamics

J = JMHD f f|| JMHD =2 3/2

02

e ln3/2e ( 3/2

i )2B2 2

k2

Electron dynamics determines , ion dynamics determines

0 2 4 60

10

20

xa

Changing the wave speed relative to the electron thermal speed does notgrossly modify the current drive efficiency so long as xa is less than 3

xa =3/2e

k||vte

Kinetic Alfvénwave

DrivenAlfvén

oscillationParallel phase speed of perturbation relative toelectron thermal speed

vA vte

Alfvénresonancef||

f|| f

11 Chu IAEA 2006

Polarization Drift Due to Alfvén Wave Contributesto Current Drive

Rotating3/2-NTMisland

2/2 sideband near q0=1

Mainharmonic

Polarizationdrift

Magnetic curvaturedrift, electrostatic sideband

Magneticperturbations

Modify densitydistribution ofenergetic particles

Countercurrentdrive

ORBITCODE

Alfvénwave

2 /2

3/2

strong

strong

weak

KAW

Moderate

modeconversion

12 Chu IAEA 2006

Without Mode Conversion or Sideband CouplingTotal Driven Current is Small = 0.3 - 3.0 kA

• Polarization drift induced ƒ = ƒ1

• Estimate based on typical DIII-D hybriddischarge parameters

• Assume central current drive region to cover

only 0.10 m radius

q = q0 + (q3/2 q0 )r 2

r = r /r3/2

r3/2 = 0.3 m

3/2 =1.05•105 / s

i = 4.2•10 3m

= .1 m , JMHD = 3.56•107A /m2 , f|| =13,

f =1.5•10 5 , Area = .044 m2 , I = Area•J = .3kA

1.5

2.0

2.0

2.5

2.5

3.0

3.0

4.0

4.0

4.0

4.0

4.0

1.5

2.0

2.0

2.5

2.5

3.0

3.0

4.0

4.0

4.0

4.0

4.0

f 1 = i4 TeTik2(1 i

*

3/2i)

2

13 Chu IAEA 2006

Mode Conversion to KAWCan Amplify Driven Current

Rotating3/2-NTMisland

2/2 sideband near q0=1

Mainharmonic

Polarizationdrift

Magnetic curvaturedrift, electrostatic sideband

Magneticperturbations

Modify densitydistribution ofenergetic particles

Countercurrentdrive

ORBITCODE

Alfvénwave

2 /2

3/2

strong

Strong

weak

KAW

weak

Modeconversion

14 Chu IAEA 2006

Mode Conversion to Kinetic Alfvén WaveFacilitated by Polarization Drift (FLR Effect)

(r-rs)/L0-20 20

Alfvén resonance

Kinetic Alfvén wave

Driven MHDoscillation

Completely reflectingboundary condition

Er

f 1 = i4 TeTik2(1 i

*

3/2i)

2

A=Amplification factorobtained only from solutionof mode conversion equation

f 1 = i4 /3A2

dq

drTeTi

+34

3/2i

2n A

4 /3

TeTi(1 i

*

3/2i)

2Mode conversion

Plasma centerPlasma center3/2 surface

Mode conversion greatly shortens perpendicular wave length and increases f 1

E

15 Chu IAEA 2006

Total Driven Current Large at ResonancesDue to Large Amplification Factor

10 kA

0.1 kATot

al D

rive

n C

urre

nt

2 3 4

• Normalized to at• Large current drive equilibria are associated with special solutions of the

mode conversion equation which are the KAW eigenstates!!

2 / 2 =1 cm r3/2

1000 kA

q

4

3

2

0.996 0.998 1.000 1.002 1.004q0

Green 1 kABlue 10 kARed 102 kA

q

q0=1.002

MHDKinetic q = q0 + (1.5 q0 )(rr3/2

) q

Experimentalrange

16 Chu IAEA 2006

Magnetic Curvature Drift Produces SidebandElectric Fields and Drives Current Effectively

Rotating3/2-NTMisland

2/2 sideband near q0=1

Mainharmonic

Polarizationdrift

Magnetic curvaturedrift, electrostatic sideband

Magneticperturbations

Modify densitydistribution ofenergetic particles

3/2

Countercurrentdrive

ORBITCODE

Alfvénwave

3/2

Strong

strong

weak

KAW

weak

modeconversion

17 Chu IAEA 2006

Magnetic Curvature Drift due to AlfvénWave Induces Electrostatic Sidebands

± = is1

esBR1 s

*

Isi

12k||±vts

Z s±( )m ±1r

mr

s1Ts1+ s±Z s±( )[ ] 1 s±

*

Isi

Induced parallel potential

Perpendicularpotential ofAlfvén wave(MHD)

• + upper sideband, - lower sideband• Scales with as or ,• purely toroidal effect

R( )2

f 2 = Di 2 Te

Ti 3/2i(1 i

*

3/2i)

2

|B| Contour

R (m)Z

(m

)

0.8

0.4

0

–0.4

–0.8

1.2 1.6 2.0

iondrift

electiondrift

Di 2

18 Chu IAEA 2006

Electrostatic Sidebands Due to Magnetic CurvatureDrift Drive Significant Amount of Current

• Purely toroidal effect• Current driven mainly by lower sideband

q = q0 + (1.5 q0 )(rr3/2

) q

q

1.0

1.5

0.0 1.00.5

q=2

q=4

r/r3/2

19 Chu IAEA 2006

Magnetic Perturbation Due to NTM IslandModifies Distribution of NBI Current Drive

Rotating3/2-NTMisland

2/2 sideband near q0=1

Mainharmonic

Polarizationdrift

Magnetic curvaturedrift, electrostatic sideband

MagneticPerturbations

Modify densitydistribution ofenergetic particles

Countercurrentdrive

ORBITCODE

Alfvénwave

strong

strong

Mod

erate

KAW

weak

modeconversion

20 Chu IAEA 2006

ORBIT Code Results Show Energetic ParticleDensity Modified Moderately by NTM Island

• New equilibrium reached within a few particle transit times

• Independent of energetic particles energy

• Account for 10%-20% of missing current

120 160 200

−100

−60

−20

20

60

100z

x

Poincare Energetic particle density

Perturbationamplitudemultiplier

0.0

1.0

2.0

(cm)

(cm

)

˜

2.5

2.0

1.5

1.0

0.5

0.00.0 0.5 1.0

5/25/200521 Chu IAEA 2006

Discussion: Possible Tests of Theory and Extensions

1. Current deficit independent ofplasma rotation

2. Broadening of energetic particledensity profile

Excites other mode(s)

(TAEs, ELMs?) to worksynergistically with NTM

energetic particleredistribution

1. Same as above

2 a) b) Same as above

3. less effective at larger A

1. rotation shear ofisland w.r.t centralplasma

2. q(0) ~ 1

3. aspect ratio A

curvature drift

current drive

1. More current deficit ifrotation is higher

2. a) low q(0) less accessibleb) less current deficit if q(0)higher

c) evolution path to low q(0) hasintermittent hesitation

1. Rotation shear ofisland w.r.t. centralplasma

2. q(0) ~1

KAW mode

conversion current

drive

Possible observationsVariablesMechanism

5/25/200522 Chu IAEA 2006

Conclusion: Magnetic Curvature Drift and KAW ModeConversion Can Explain Observed Current Deficit

Three mechanisms for driving negative current by therotating NTM are investigated:

• Polarization drift gives rise to mode conversion whicheffectively drives counter current

• Magnetic curvature drift produces sideband electricfields which effectively drives counter current

• The wave scatters NBI ions and reduces efficiency ofNBI current drive to account for 10-20% of negativecurrent