Fast-Ion Physics: What, Where, and Why

W.W. HeidbrinkUC Irvine

What What do we understand? Not understand?

Where What scale experiment is most likely todeliver understanding?

Why Will the tokamak burning plasma experi-ment work? Will we learn anything applicable to other concepts?

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1) Experimental review by Heidbrink and Sadler, Nucl. Fusion 34 (1994) 535.2) ITER review by Putvinskii et al., Nucl. Fusion 39(1999) 2471.3) TFTR DT review by Strachan, Plasma Phys. Cont.Fusion 39 (1997) B103.4) TFTR alpha review by Zweben et al., Nucl. Fusion 40 (2000) 91.5) TAE review by Wong, Plasma Phys. Cont. Fusion41 (1999) R1.

Coulomb deceleration accurate to within ~10%.

Pitch-angle scattering and energy diffusion less certain but probably OK.

Modified Stix formula for ICRF accelerationagrees well with measurements for minority heating.

More acceleration experiments desirable.

Alpha deceleration understood for burningtokamak--applicable to other concepts.

Velocity Distribution Function

0

1

2�

3� ICRF

D NB 100 keV

1 MeV D loss a t θ=45

ICRF Source and AccelerationMinority HeatingModified Stix formula for ICRF acceleration agrees towithin ~10% with measurements.

Spatial position of the tail is approximately correct ifnon-standard orbits and Doppler shifts are included.

Higher harmonic minority heatingA

�cceleration OK but less rigorously tested.

Mode conversionEnergy diffusion much greater than expected.

Detailed RF fieldand fast-ion measure-ments in small-to-J

�ET scale devices.

Minority heatingis reliable for aburning tokamak.

TIME (s)

�

Orbits in Static Fields

Loss boundaries are accurately known.

Ripple losses accurately calculated. Stochastic rippleboundary roughly verified.

Error fields unimportant.

Burning tokamak projections reliable.

Burning tokamak does not address key issues forother concepts.

Small machine could study ripple boundary.

Turbulent Transport of Fast Ions

Observed transport in MHD-quiescent plasmasis barely detectable. Plausible explanation is gyro-averaging over background fluctuations.Test explanation on a small machine.

Alpha diffusion will be small in a burning tokamak.

Little contribution to other concepts.

RF-induced transport hardly measured. Moreexperiments at both small and JET scale.

Transport by plasma MHD

Sawteeth cause transport if the crash time is shortcompared to characteristic orbit times.

Tearing modes cause transport when island overlapoccurs in orbit phase space.

Test selective transport of fast ions by propagatinglong wavelength modes in a small-to-moderatescale device. (Alpha ash removal & channeling)

Given the MHD characteristics, can predict alphatransport.

Little contribution to other concepts.

Sawtooth and Fishbone Stability

A plausible but complicated theory exists. Roughcomparisons exist but detailed confirmation islacking.

Comparisons in existing tokamaks with accuratelymeasured plasma parameters and well knownfast-ion populations are needed. A well-diagnosedburning tokamak experiment is useful.

Estimates for ITER indicate that alpha particles should lengthen the sawtooth period but maydrive fishbones unstable.

Little contribution to other concepts.

TAE Physics

The gyrokinetic PENN code matches measureddamping rates better than theories based onperturbative MHD.

Perturbative MHD does give rough agreement withalpha-driven TAEs in TFTR.

The most unstable toroidal mode scales approximatelywith RBT.

Calculated eigenfunctions vary enormously butmeasurements are inaccurate.

Simplified models explain qualitative features ofsaturation phenomena but no quantitative comparisons.

• Core localization of most unstable alpha driven mode confirmed on TFTR

• Expect core localized modes in a burning plasma

Alpha-Driven TAEs Appear After NBI:Beam Damping Dominates in Plasma Core

TFTR

PRINCETON PLASMA PPPLTIME(s)

NBI off

-3

BB

~n=4

n=5n=3

n=2

2.8 2.9 3.00

6 x10-9

103101

2.00

PNBI(MW)

βα(0)0

Neutral Beam Injection

10

x10-2

2.5TIME(s)

3.00

25β(0)“Damping”

“Drive”

“Response”

wall

T

PHASEFLUCTUATION

LEVEL(rad.)

n=40

&.06

0&

-1.0 0&

1.0(R-Ro' )/a

( )

TAE Physics (continued)

Better eigenfunction measurements on existing tokamaks.

Further JET stability studies with accurate q profile.

Since higher n numbers and more unstable modesare anticipated, stability and saturation behavior fora burning tokamak are valuable.

A burning tokamak could be unstable.

The results are relevant to other toroidal concepts.

Energetic Particle Modes +

Fast-ion driven modes with f < fTAE are common.They are called EPM, RTAE, BAE, KBM, chirping....

A plausible theoretical explanation is that theyare energetic particle modes (not normal modesof the background plasma). Comparisons arerudimentary.

Instability is predicted for some burning plasmascenarios.

Need detailed comparisons on existing devices,including the eigenfunction.

Transport by Fast-Ion Driven MHD

Fishbone transport inPDX well understood.

No detailed comparisonsin larger devices.

Transport by Alfveninstabilities poorlyunderstood.

Need measurementsof the Alfven eigenfunctionand fast-ion transportin existing tokamaks.Must also study in a large RBT device.

Can calculate fishbonetransport in a burningtokamak. We do not knowwhat Alfven modes will do.

The results are relevant to the viability of all toroidalreactors.

Understand?SourceFusion Products yes Beam yesRF mostly

Velocity Coulomb yesRF acceleration mostly

TransportDrift orbit yesRipple yesFluctuations probablyRF-induced possiblyMHD yesFishbone yesTAE not yet

StabilitySawtooth/Fishbone probablyTAE somewhatEPM no

Small/Existing/Burning

E

S E

SS

E E

E B E B E B

Extrapolate Other

yes yes yes

yes yes

yes yes yes yes yes yes no toroidal

probablymaybe toroidal no ?

0 0 0 0 0 0 0 0 0 0 34 5 7 9 ; = > > 9 > 5 B 7 D F ; ; J F > 9 = O 7 9 R T R 9 ; 9 B 7 = 7 F 5 B Z

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