Fast Ion Transport and Instabil ities:RecentProgressand Outstanding

IssuesW.W. HeidbrinkUniversityof California,

Irvine

1. Measuringthe Fast-ionDistribution Func-tion

2. Transportin Large-scaleMagneticandElec-tric Fields

3. NonlinearPhaseof CoherentModes

4. Alfv enTurbulenceandFast-ionTransport

5. BeneficialManipulationof theDistributionFunction

1

50 ms

25 ms

1 ms

ENERGY (keV)

v || /

v

Distribution Function f(v,r)

Gyroangle ignorable

NORMALIZED RADIUS

βt (%)

βf (%)

2

GammaRayTomography

Different species: p, d, t,�He,

�He

Different reactions someenergy reso-lution

V.G. Kipti ly et al., Nucl. Fusion42 (2002)999.

3

Collective ThomsonScattering

ωi , ki ωi , ki

ω s , k

s ω , k

v� f

λ

λD

H. Bindslev et al., FusionEng.Design53 (2001)105.

4

D � Light from ReneutralizedBeamIons(Hydrogen CER)

15 R0

330 R0

HaloInjected

3�

00 Neutral Beam

Edge

Beam Ion

0

2

4

6

8

10

Beam Ion

Halo

Background

Net

S

IGN

AL

(a.u

.)

#115549

651 652 6�

53 6�

54 6�

55WAVELENGTH (nm)

unsh

ifted

line

to injected

W.W. Heidbrinket al., PlasmaPhys.Cont.Fusion(2004)submitted.

5

Fast-ionSources

NNBI in JT60U (super-Alfvenic, high � ,anisotropicpopulation).K. Shinoharaet al., Nucl.Fusion

42 (2002)942.

MeV alphapopulationin JET(perpendicu-lar ICRF tail distribution). M.J. Mantsinenet al., Phys.

Rev. Lett. 88 (2002)105002.

What’sneeded?A compact, collimatedsourcethatcanselectively populatephasespace.

6

Fast-ionConfinement

If we knew B andE and � , we canusetheLorentzforcelaw, F E v B .

Needto verify orbit topologyandreducedmodels(e.g.,stochasticripple diffusion).

7

NTM andIntrinsic Orbit Stochasticity

Tearingmodemakes a is-landchain.

Circulatingfastionshave aorbit shift.

Beatingcausessecondary islandchains,e.g.,.

If theislandsoverlap,theorbitsbecomestochas-tic.

E.M. Carolipioet al., Nucl. Fusion42 (2002)853.

8

Fastion interactionwith MHD Modes

E.D. Fredrickson,Phys.Plasmas9 (2002)548.

9

TAE Transport is LargerThanExpected

E.M. Carolipio et al., Phys.Plasmas8 (2001) 3391; Y. Todo et al., Phys.

Plasmas10 (2003)2888.

10

TAE Eigenfunction is Uncertain

IDEAL MHD GYROFLUID GYROKINETIC

DIII-D Beam-Driven TAE Eigenfunctions

Carolipio et al., Phys. Plasmas 8 (2001) 3391

Needto measureeigenfunction!E.M. Carolipioet al., Phys.Plasmas8 (2001)3391.

11

ModeCouplingAltersTAE Eigenfunction

Very weakshearin coreallows couplingtodrift kineticmodes;verystrongshearin edgecouplesto kineticAlfv en waves.

12

Gyrokineticcalculationsagreewith JETan-tennaexperimentsfor mass,gyroradius,andshapingdependencies. A. Fasoli et al., Phys.Plasmas7

(2000)1816;D. Testaet al., Nucl. Fusion43 (2003)479; D. Testaet al.,

Nucl. Fusion43 (2003)724.

Gyrokineticcalculationsagreebestwith DIII-D eigenfunctionmeasurements. E.M. Carolipio et

al., Phys.Plasmas8 (2001)3391.

13

FastIonsCreateNew Modes

Normal Mode nfast << ne Wave exists w/o fast ions. Re(ω) unaffected by fast ions. Fast ions resonate with mode, altering Im(ω).

Energetic Particle Mode βfast ~ β Fast ions create a new wave branch. Re(ω) depends on βfast. Fast ions resonate with mode, altering Im(ω).

L. Chen,Phys.Plasmas1 (1994)1519;N.N. Gorelenkov andW.W. Heidbrink,

Nucl. Fusion42 (2002)150.

14

RapidFrequency Chirpingis CommoninTokamaks,Stellarators,andSpherical

Tokamaks

ChirpsNarrow Line

Broader Line

TIME (ms)

FR

EQ

UE

NC

Y (

kHz)

MA

GN

ET

ICS

(a.

u.)

100 120 140 160 180 2�

00

15

Berk-BreizmanModel ExplainsManyPhenomena

H.L. Berk et al., Phys.Plasmas6 (1999)3102; D. Maslovsky et al., Phys.

Plasmas10 (2003)1549.

16

f

v

Initial

Hole-Clump Pair

γD

γ D

γL /

ν eff

ν eff

/ = γ

Sta

ble

Chirp

Explosive

Stochastic

17

JETPhenomenaconsistentwith B-B Stages

As drive increases,progresses throughin-stability, pitchforksplittling,perioddoubling,andfinally chaotic saturation.

R.F. Heeteret al., Phys.Rev. Lett. 85 (2000)3177.

18

IncreasedCollisionsSuppressChirpinginDipole Experiment

D. Maslovsky et al., Phys.Plasmas10 (2003)1549.

19

Feedback Loop for WavesandFast-ionDistribution

G. Vlad et al. (2003).

20

TurbulentWavefieldsareAnticipatedinBurningPlasmas

W.W. Heidbrinket al., PlasmaPhys.Cont.Fusion45 (2003)983;N.N. Gore-

lenkov et al., Nucl. Fusion43 (2003)594.

21

ICRF

A�

lphas Beams

0 5

100

5

10

NSTX

DIII-D

EX

PE

RIM

EN

TAL

n max

THEORETICAL nmax

5�

10 150�

0�

.5

1

1.5

2

2.5

3�

3�

.5

4�

γ α,α+

NNBI/

γ damp

Unstable

Stable

α� -particles only α� -particles and 1MeV NNBI

TOROIDAL MODE NUMBER

(a)

(b)

kθ ρα

ALP

HA

DR

IVE

ω∗α increasing

g� yroradius > mode width

Theory

22

Theoretical Frontiers

3D codesfor stellarators

Modecouplingeffects

Energeticparticlemodes

High

– Compressional modes

– Thermal ion effects

Turbulencewith multiple modesand cou-pledfast-ionnonlinearities

Stellarator Tokamak

G.Y. Fu (2003).

23

BeneficialManipulationof theFastIons

Ions

e� lectron t�ransport

Conventional Reactor Power Flow

Electrons

Ions

e� lectron t�ransport

Fisch's Channeling Dream

Electrons

A�

lphas

Alphas

W�

aves

Drive current Damp on ions

Make transport barrier

fusi

onfu

sion

N. Fischet al., Phys.Rev. Lett. (1992).

24

ICRF PinchControlsProfilein JET

The changein toroidal angularmomentumdependson thewave spectrum, � � .Ionspinchinwardor outwarddependingon

� .

M.J.Mantsinenet al., Phys.Rev. Lett. 89 (2002)115004.

25

Beam-ionRedistributionSustainsCurrentProfilein DIII -D��� ��� ��� ��� ��� � � � � �

�� � ! ��"�"#�

! ��"�"�"

! ��"�"��

$&%�'

$)(*'

$)+,'

$)-*'

��

.0/1231456789:; �� �

�#

�� � �# ��<0� =?>A@CB $&D�'

! ��"�"��! ��"�"�"

! ��"�"��

��< E ��<AF

GIH � H �H �H �

GJH �GIH �

���<A ��<0���<A ��<0�K $ '

� � �=?>A@CB $&D�'K.L. Wonget al. (2004).

26

Discussion#1: Fast-ionDiagnosticsandSources

Gamma-ray tomography

CollectThomsonscattering

D-alphabeam-ion diagnostic

Desirea compactsourceto populatephasespaceselectively

27

Discussion#2: Fast-ionTransport

Wherethefieldsareknown, it isunderstood.

Verificationof orbit topologyin stellarators,FRC’s, ... is needed.

TAE’shavesurprisinglystrongradialtrans-port.

Needeigenfunctionmeasurements.

28

Discussion#3: NonlinearEvolutionofCoherent Modes

Rapidfrequency chirpingiscommonin manydevices.

Berk-Breizmanmodeloftenexplainsquali-tative featuresof nonlinearevolution.

More testsareneeded.

29

Discussion#4: TheoreticalFrontiers

Complex interactionof waveswith fastionsarealready modelled.

Many modesareanticipatedin burningplas-mas.

New directionsinclude3D, high , kineticthermalions, drift-Alf ven couplings,ener-getic particleimpacton eigenfunction, andAlfv enturbulence.

30

Discussion#5: BeneficialManipulationofFastIons

ICRFexperimentsprovesomecontrolispos-sible.

DIII-D experimentsprovemanipulationcanbebeneficial.

New control techniques?Are any of thesepractical?

31