Impact of Energetic-Ion-Driven
Global Modes on
Toroidal Plasma Confinements
Kazuo TOICHS & LHD Experimental Group
National Institute for Fusion ScienceToki 509-5292, Japan
Special contributions from:* CHS Exp. Gr.: M. Takechi(JAERI), M. Isobe, S. Takagi, G. Matsunaga,
M. Sasao, J. Kotani* LHD Exp. Gr.: S. Yamamoto, S. Ohdachi, S. Sakakibara, M. Osakabe,
N. Nakajima
Presented at 12th International Toki Conf. ,Dec. 11-14, 2001, Toki, Japan

Outline
1. Introduction*Motivation & Objectives* Energetic ion driven Alfven eigenmodes

2. Excitation of Alfven eigenmodes by energetic ions* in tokamaks and helical devices

3. Effects of energetic ion driven AEs on energetic
ion confinement* in tokamaks and helical devices

4. Summary and future plan

Introduction
109

VA: Bt =5T, ni=1020 m-3 , DT

108
Particle Speed (m/s)♣ In DT burning plasmas,
energetic α-particles
dominantly heat electrons
through slowing-down
process. In the course ofslowing down, the speed of
α-particles will match theAlfven speed . These αparticles will resonantlyinteract with shear Alfven
waves, and excite Alfveneigenmodes inside the shear
Alfven spectral gaps.

VtheVA

107

VA/3

610VHVα105

104
0.010.1

1
10 100 1000 104
Particle energy (keV)Motivation & Objectives♣ It is important to predict impacts of energetic-ion-driven MHD
modes such as Alfven eigenmodes (AEs) in ITER like burning
plasma.
♣ It is crucial to clarify the damping rate of AEs and their effecton energetic ion transport in such burning plasmas.
♣ In major tokamaks these subjects are intensively investigatedusing NBI and/or ICRF heating, and alpha particles generated
in DT plasmas.
♣ In helical devices, that is, W7-AS, CHS and LHD, these studies
are also performed.
In this presentation, we summarize experimental results onenergetic ion driven AEs from CHS and LHD, comparing
with those in tokamaks and W7-AS.

Excitation of AEs by energetic
ions such as α-particles• Shear Alfven spectral gaps in toroidal plasmas
magnetic field strength:

N(field period number)=10 in LHD

B/ Bo= 1+ ¦ ε µB,ν (ψ ) cos(µθ−νNφ )µ,ν

• two cylindrical Alfven branches intersect andgenerate gaps:
ω= k//m,nVA= - k //m+µ,n+νNVAµ=1,ν
ν=0: TAE µ=2,νν=0: EAE µ=3,νν=0: NAE ,…
µ=2,ν
ν=1: HAE21 µ=1,νν=1: HAE11 µ=2,νν=2: HAE22 ,…

gap frequency :f(µ,ν)= | Nνq* - µ|VA/ (4πRq*)

gap position :q*=(2m+µ)/(2n+νN)
gap half-width : ∆f~ |ε(µν)B-ε(µν)g/2| f(µ,ν)
resonance condition : Vb///VA=1/[1±2/(νNq*-µ)]Experimental conditions forenergetic ion experiments*Electron Landau damping*Continuum damping*Radiative damping*Ion Landau damping

NSTXLHD1<β hot > (%)• Parameter space forstudies of energetic
driven MHD modes@Resonant condition@Energetic ion driveγ/ωο=9/4β hot [f*hot/fo- 0.5 ]F(VA/V hot)@Damping mechanisms

DIII-D
ITER
0.1

JT-60U

JET

TFTR
CHS

W7-AS

0.01
00.5

1

1.5

2

2.5

3

V hot /V A

<ββ hot>, Vhot/V A, f*hot : important parameters• Helical devices havedifferent 1/q-profile fortokamaks.
• 3D-configuration• Non-uniformity ofmagnetic field can be
introduced by various
Fourier components.

Rotational Transform 1/q

Radial profile of rotational transformin major helical devices
Heliotron/Torsatron
Shearless Stellarator
Standard Tokamak
Reversed Shear Tokamak

1.5
1.2
0.9
0.6
0.3
00

0.2

0.4
0.6
r/<a>

0.8

Shearless stellarator (W7-AS) : GAEs, TAEs, EPMs
Heliotron/torsatron (CHS, LHD) : TAEs, EPM, n=0 GAE, ...

1

Excitation of Alfven Eigenmodes
by Energetic Ions

Various AEs driven byenergetic ions in a tokamak plasma♣ Toroidicity-induced AE(TAE) and core-localized
TAE (CLM)♣ Kinetic TAE (KTAE)♣ Ellipticity induced AE(EAE)♣ Triangularity induced AE(NAE)♣ Energetic paricle(continuum) mode (EPM)or resonant TAE(R-TAE)
ITER Phys. Basis, NF (1999)

Typical example of AEs observedin reversed shear plasmas of JET♣ Alfven spectra exhibit quasiperiodic pattern with mainly
upward frequency sweeping(Alfven cascade).
♣ Time evolution of frequency
clearly reflects that of qmin.
Alfven cascade phenomena
can be used for a diagnostic
tool of qmin in the reversedshear configuration.
♣ The similar observation wasdone in ICRF plasma of JT60U.

H.L. Berk et al., PRL (2001)

Measurement of internal structureof AEs♣ Information about internalstructure of TAEs isimportant to identify them,comparing theoreticalresults.
♣ Internal structure of TAEs
was measured byreflectometer in TFTR andother tokamaks.
♣ The data clearly indicateda core-localized type ofTAEs.

R. Nazikian et al., PoP, 1998

Excitation of EPM in tokamaks♣ EPMs are also observed inmany tokamaks when
instability drive is trongenough.
♣ EPM and TAEs often
couple each other.
In TFTR, TAE can be
excited by the radialtransport of energetic ionsby EPM.
♣ EPM often play a key rolein enhanced enegetic-ionloss.

TAEEPM

S. Bernabei et al., PoP (1999)

TAEs & EPMs in tangential NBI
heated plasmas of LHD#24612, Bt=1.3 T, Rax=3.6 m, H, PNBI~2 MW, ENBI~150 keV
fTAE (m/n=2~3/1)

120

2log10(P) contour

Nf=1 shear Alfven spectrum (2D) (#24612,t=070s)
Nf=1:n=1t = 0.7s

(1,1)

(3,1)

(2,1)

100

R-TAE(m/n~2/1)

40
100

TAEs (m/n~2/1)
64

50

201.2
0.8
0.40.0321020NBI(ctr.)

04

PNBI (MW)60[ / A(0)]2R-TAE
80 (m/n~2/1)

1

fexp
84kHz
79kHz
sidebandexcitation(TAE)
40 < f < 140 kHz
RMS

022

1

100.6

0.7
Time (sec)

0.8

0.0

0.2

0.4

0.6

0.8

1.0

In LHD or CHS, TAE gap frequency increases toward theplasma edge. This TAE may be a core-localized type TAE.

0ne (x1019m-3)

b /Bt (x10-7)

vb// /vAne (1019m-3)

wp (kJ)

Frequency (kHz)140

Internal structure of TAE & EPM inCHS
SX fluctuation diagnostics
2<f<10kHz (84-86ms)
10<f<50kHz (83.5-84.5ms)
90<f<110kHz (84-86ms)

12#73144 Bt=1.2T

Phase (rad.)1

δI

SX(a.u.)

1.5

••
•
•
•

0-0.5

0.5

0-1

0.5

-1-0.5

0r/a

0.5

1-1

-0.5

0r/a0.5

1

EPM is localized inside the q=2 rational surface.
TAE is localized near the plasma center. ---> Core localized type TAE
LF has a peak near the q=2 surface, indicating interchange mode.
EPM as well as TAE exist near the innermost TAE gap.
m~3/n=2 EPM has a similar internal structure to that of m~2/n=1 EPM.

Excitation of EPM & TAE in CHS
Rax=0.92m, Bt=1.2 T

magnetic Fluc.

80

90

Soft X-RayTAE

TAE

FB (EPM)FB (EPM)100

110
Time(ms)

120

Rax

130

80

90

100110120

130Time (ms)* Fishbone-like burst modes FB ( EPM ): strong frequency chirping* n=1TAE is interrupted by m~2/n=1 EPM.
* Time evolution of amplitudes of FBs and TAEs can be explained by thetemporal change in Pfasti or ∇ Pfasti.

GAEs in low shear plasmas of W7-AS

Due to low magnetic shear, low n GAEs can be destabilized at
the fairly low beam velocity due to side-band excitation.
The small shear enables the exciation of TAEs in W7-AS.
A. Weller et al., PRL (1994).

Variety of various AEs
observed at low Bt in LHD
250#27233, Bt=0.5 T, Rax=3.6 m, H, =1.25, Bq=100 %t=1.38 s240
220

Frequency (kHz)

200200180

150

4 180 < f (kHz) < 220

100-7b /Bt(x10 )

20800

5030 < f (kHz) -7< 120b /Bt(x10 )

080
406420#1 P=0.91 (MW)E=129 (keV)#2 P=1.7 (MW)E=137 (keV)#3 P=2.1 (MW)
E=148 (keV)

NBI P=3.8 (MW)

00.0

0.5

1.5
1.0
Time (sec)

2.0

NBI (MW)Wp (kJ)

400
0

1.0

1.4
Time (sec)

1.8

2.5

Helicity induced Alfven eigenmode (HAE) has a frequency by
about Nq-times higher than TAE-frequency.
At low Bt<0.7T, f HAE< 500 kHz in LHD.
Observed fluctuations may be HAE.

Nonlinear effects of energetic iondriven AEs(1) Bursting amplitude
modulation: TAEs, EPMs
in CHS, LHD, ...
(2) Fast frequency chirping:TAEs, EPMs
in CHS, LHD, ...
(3) Frequency spectrum
splitting: in CHS(similar to that in JET)

400

300

200

1000204080
100
Time (ms)

1.2 10 -10
PSD (a.u.)120

8 10 -11
6 10 -11
4 10 -11
2 10 -11060

140Spectrum
Splittingin CHSTAE

1 10 -10

These nnonlinear phenomenaclosely link to energeticion transport.

6080100120f (kHz)K. Toi et al., Nucl. Fusion (2000)

Summary of excitation condition ofTAEs and EPMs in LHD
not observed
observed (w/ burst)
observed (w/o burst)

TAE

1< b//> (%) classic

1< b//> (%) classic

not observed
observed

EPM

0.1

0.01
02

1vb// / vA

3

0.1

0.01
02

1vb// / vA

TAEs: 0.01 < <ββb//> <3 %, 0.3 < Vb///VA < 1.7 ;At higher <ββb//> , TAE becomes bursting.
EPMs: 0.08 < <ββb//> <3 %, 0.1 < Vb///VA < 1.6 ; EPM is usually bursting3

Effects of energfetic ion driven
AEs on energetic ion transport

Typical example of energetic ion
loss in tokamak plasmas• TAEs sometimes
enhance loss ofenergetic ions, orredistribution ofenergetic ion profiles.
• Multiple TAEs ,bursting TAE andEPMs often enhanceradial transport ofenergetic ions.
H. Kimura et al.Nucl. Fusion (1998)

Particle Orbit Classes in CHS (LHD)

Guiding center orbit• Banana orbit in a tokamak does not exist in CHS ( LHD) configuration.
Usual fishbones observed in tokamaks would not be excited.
• In CHS (LHD), the initial pitch angle of most ions will be in the range of
χ=20-50°° because of tangential injection.

Hit Points of Lost Energetic Ions on
the Vacuum Vessel Surface in CHS
Rax=0.92 m; ρstart=0.3 & 0.5; E=40 keV• Transient loss of fast ions wasdetected only in the outwardshifted plasmas.
• Orbit calculations haverevealed that energetic ions arelost in poloidally and toroidally
localized zone for both inward
and outward shifted
configurations.
• Detectors of lost ions should beplaced at this narrow zone
where lost fast ions wouldarrive.

360
ρ=0.3
ρ=0.5
270

180

900-180-90

0toroidal angle φ90

180

80

85

200
150
100
50
095 100 105 110 115 120
Time(ms)

90

40
Step function like30

δΓi ~ (b θ _rms ) 5

20
100-1005 10 -6

1 10 -5 1.5 10 -5bθ _rms (T)2 10 -5

Γ i (a.u.)#69908
Rax=99.5 cm, Bt=0.88 T
χ = 40-50 deg.

2 10 -5
1 10 -50-5-1 10-2 10 -5δΓi (a.u.)• Relation between ion lossflux and fluctuation level:δΓi∝ (bfluc) s
s=1: Resonant convec. loss
s=2: Diffusive transports>2: Destruction ofmagnetic surface• For fast ions in χ=40-50 deg.
s > 5 orδΓi∝ u(bθ-bcrit): threshold
This may link to loss cone.

bθ (T)

Dependence of energetic ion loss flux
on fluctuation amplitude (CHS)Transient Decrease in Shafranov
Shift due to m~2/n=1 EPM (CHS)• Magnetic axis position
derived from SX-emission
profile is transiently
changed by each fishboneburst.
• The transient decrease of
the Shafranov shift may be
attributed to the flatteningof the energetic ion profile,because of no change in<bbulk> .

Shafranof shift ∝ βb//(0)+ββdia(0)S. Takagi et al., Rev. Sci. Instrum. 2001

Energetic ion loss due to bursting
TAEs in LHD
Frequency (kHz)* Note:Just after the each burst,
Wp is increased beyond theprevious level, reducing Halight and increasing ne &SX-emission.

200SX(a.u.)
IIS(a.u.)
B (µT)
dW/dt(W)IIS(a.u.)
H (a.u.)B (µT)* Strong bursting TAEs
(n=1 + n=2) transientlyreduce Wp (i.e.,dWp/dt<0), whichsuggests enhanced lossof energetic ions.
~ 15 % loss of P NBI#25950, Bt=0.6T, Rax=3.6 m, H, PNBI~3 MW, ENBI~150 keV
250

0150
100
50
400
0-600
100-10
15
0-15
1.0
0.5
0.0
0.8
0.4
0.0
1.4
1.0
0.1
0.6

T
TAEs
dW/dt

B (25-150kHz)

B (0-25kHz)

0.0
1.25

1.35

1.45

Time(sec)

S. Yamamoto et al., this conf.

Energetic ion loss in W7-AS plasma• Bursting AEs enhanceenergetic ion loss, ofwhich modes arem=3/n=1 GAE orEPM.
• High freq. burstingmodes (TAE?) alsoenhance the loss.
• These modes reducethe bulk plasmaenergy too.
A. Weller et al.,PoP (2001)

Impact of EPM on Bulk Conf. (CHS)
0.0002m~2/n=1
Low freq.
mode#68837b (T)0.0001θ

0-0.0001
b (T)0.0002-0.0002θ

0-0.0002-0.0004

0.5
Soft X-ray Intensity (a.u.)#68837

ρ =0.00.4

ρ =‑0.04
ρ =‑0.14
ρ =‑0.25

0.3

ρ =‑0.35
ρ =‑0.46

0.2
0.1
08
ne1.5

Ip14
Wp0.52en (106080

0100120time(ms)140

I p (kA)-3pm ), W (kJ)219

• Bulk plasma confinement isappreciably affected by m~2/n=1EPM.
• The suppression of the EPM leads
to the increase in Wp & neby ~20 %.
• The suppression of EPM as well as
low frequency(LF) modes is notdue to the removal of q=2 surface
by the rise of Ip.
• The suppression occurs in thecertain range of <ββb//> (=0.25 0.35%). This phenomenon does
not always take place.
• Suppression mechanism is stillunclear and under investigation.

m~2/n=1
EPM

Summary and Future Plan
♣ Studies on energetic ion induced MHD modes such as Alfven eigenmodes
have intensively been performed in three helical devices LHD, CHS andW7-AS as well as in major tokamaks.
♣ A lot of information about Alfven eigenmodes excited by energetic ions areobtained, that is, TAEs, EAEs, EPMs and so on were identified, as arepredicted by MHD theories including energetic ions.
However, quantitative comparison between experiments and theories is still
preliminary.
♣ In helical devices such as CHS and LHD, very wide parameter range can beexplored without suffering current disruptions. These researches cancontribute to improved understanding of Alfven eigenmode in toroidal
plasmas, as well as need for physics design of a helical device reactor.
♣ As future studies in CHS and LHD,
to experimentally obtain shear Alfven spectra through Alfven spectroscopy.
to clarify physics related to interaction between MHD modes and energeticions.