ISHW+ITC17, Seratopia in Toki(Jpn), Oct. 18, 2007

Confinement study on the reactor
relevant high beta LHD plasmas
K.Y. Watanabe, S. Sakakibara, H. Funaba, S. Ohdachi,
K.Tanaka, I. Yamada, L. Garciaa, Y. Narushima,
C. Michel, H. Yamada, Y. Suzuki, N. Nakajima,
K. Narihara, T.Tokuzawa, K. Kawahata
and LHD experimental group

LHD(Large Helical
Device)2.0
NIFS,β=0%Japanax

National Institute for Fusion ScienceaUniv. Carlos III

1% β~(1-ρ 2 )2%

1.5

rotationaltransform

1.0

Special Thanks the LHD technicalstaff for their support of the experiments.

0.5

0.0

0

0.2

1

0.4
0.6
0.8
Minor Radius ρ1

Buck ground65
4

LHD (JPN)
CHS (JPN)
W7AS (BRD)
ATF (USA)
HeliotronE (JPN)

32
101985 1990 1995 2000 2005

Year

Progress of achievement ofmax. beta in helical devices<β>=5%;
A targeted value of LHD
project from the design phase# For an economical fusion
reactor, <β>~5% is necessary.
# Mainly by increasing theheating capabilities andoptimizing configurations,
heating efficiency of NBI.
# Last exp. campaign in LHD,
the 5.0% beta plasma is
obtained.
# Analysis of the plasma
properties like the beta
dependence up to the reactor
relevant high beta regimes
become possible.
2 /21

Contents# Progress of high beta operation in LHD# Characteristics of LHD high beta plasmas with β~5%
# Effects of global MHD instability (low-n,m modes)
on LHD high beta plasmas
Through comparison between achieved pressure
gradients and linear MHD numerical analyses# Confinement properties of LHD high beta plasmas
Through comparison between experimentallyobtained thermal conductivities and sometheoretically predictions
3

Recent results of ext. of operational β range in LHD<β>=4.5% up to last IAEA conf.(2006)
Quasi-steady (only gas-puffing and parallel NBI);<β>=4.8%; Increase //NBI power (~1.8MW up; tot.13.8MW)
Transient (pellet inj.);<β>=5.0%; Improve heating efficiency of ⊥NBI(6.9MW)
due to Suppression of Shafranov shift by pellet and //NBI modulation
20

Transient

5

15

4

Achieved <β>

(%) 3

10

Quasi-steady2

NBI//port_throu

(MW)
5

1
0

0
1998

2000

2002

Fiscal Year

2004

Optimized Config.
pre-set Rax=3.6m,
Ap=6.6,
B0=0.425 T

2006

4

Transient (pellet inj.) high-β dischrage I
tduration>90% ~10 τE

pellet inj.
6

~5.0%

10

4
5

2

2<βe-kin>

0
0 .6

0

# Shafranov shift is suppressed bypellet and //NBI power modulation
ΔRax/aeff ~ 0.4 => ~0
Increasing heating efficiency of⊥NBI(6.9MW)=> <βdia>=5.0%

0 .4

Δ R a x/a p

0 .2
0 .0

0

#1 +2+3

10

#4

5

NBI

⊥

p o r t - te m p

0
0 .5

//

1
t im e ( s )

0
1 .5

1.0

Time
evolution
of Te

667ms
700
800
834
867
900

0.5

0.0

-0.5
2.5

3.0

3.5
4.0
R(m)

4.5

Heating efficiency of⊥NBI (=>1.5T) Preliminary 5

Transient (pellet inj.) high-β dischrage II
tduration>90% ~10 τE

pellet inj.
6

~5.0%

# Just after pel. inj. for ~10 τE, highbeta plasma, <βdia>=5.0% istransiently achieved.

10

4
5

2

2<βe-kin>

0
0 .6

0

# Te and ne profiles at max βalmost same with Quasi-steady

0 .4

Δ R a x/a p

0 .2
0 .0

0

#1 +2+3

10

#4

5

NBI
0
0 .5

p o r t - te m p//

1
t im e ( s )

T
T e

0.4

⊥

#69910@t=1.23s

74835@t=0.9s
4

e

0.4

T

n

e

0
1 .5

Quasi-steady6

0.5

0.5

0.3

n

e-TS

(AU)

4

0.3

ne

e-TS

0.2

2

0.2
2
0.1

0.1
0

0
0

0.2

0.4
a (m)
eff

0.6

0
0

0
0.2

0.4
a (m)
eff

0.6

6

Characteristics of MHD stability in LHD high β conf.
(%)<βdia >

Ap=6.2, p~(1-ρ2)(1-ρ8)

Mag. Well

Hill

Rotaional transform 2/3

1.5

vac
3/4
~1%
<β>
(%)
~2%
~3%

1.0

Low order m/n=2/1,
rational
3/2,1/1(,2/2,3/3),
surface
3/4,2/3m<=3

1/1(,2/2,3/3)
0.5
0

0.2

0.4 ρ 0.6

0.8

In high beta regime,
magnetic hill still exists inperipheral region=>
Peripheral MHD
instabilities (pressure
driven) are important inhigh beta regime.

1

7

Quasi-steady high-β dischrage

tduration>90% >80 τE<β>=4.8 %# No disruptive high beta plasma is
maintained during more than 80τE
# Large shafranov shift Δ/ap ~ 40%# Low-n,m MHD activities- No observation of core resonant modes.
- Only resonating mode with peripheral
surf. (m/n = 2/3 and 1/1) appear# Global confinement property is almost
same with ISS95 scaling.

0.6
0.4

ΔR /a

0.2

ax

p

0.0

0

1 .5

1 .0
0 .5

τE/τE-ISS95

τ /τ
E

E _ IS S 9 5

0 .0

ι=1 bθ/B0[10-5] 10
8

ι=1.5

69910t1.23s

βdia

No large β
flattening enoughto affect a global
confinement
0

(%)

6
4
2

ι=2

0
3

3.5

4

4.5

R(m)

τE~13.3ms

Small flattening and asymmetric structures areobserved

8

S (Reinolds#) dependence of MHD mode
Saturation of peripheral MHD
mode strongly depends on S
parameter.
By a simple model,~
w ~ bθ Bt
S dependence of w is close tothat predicted by linear theoryof resistive interchange mode (w∝ β1/6S-1/3).

S-0.69DI < 0.2
DR > 0Commonly observed modes in
LHD high beta operation=>
resistive (interchange) modes
92Comparison between peripheral pressure gradientand the prediction of linear MHD stability analysis

Rotaional Transform
1.5

1

A ~6.3(γ=1.22)p

0.5(Terpsichore code)00

0.2 0.4 0.6 0.8

r/a

1

1.2

m/n=1/1 unstableρ=0.9 (ι~1)-2
dβ kin/dρ γ/ω A =10p

12

δ/ap~3% (Ideal)~5%(S=106) consistent with exp.
1.0
Ideal

0.3x10-2

0.5

8

Mercier

0.0

4

0.7
0

0

1

2

3

4

<β > (%)
dia

Observed kinetic beta gradients anda contour of growth rate of low-n
ideal MHD mode

No strong reduction ofgradients

S=10

6

S=10

5

Calc. byFAR3D

ξ(m/n=1/1)
0.8

ρ

0.9

1.0

Radial structure of low-n
ideal and resitive MHD mode
In <βdia> ~4% plasmas, the global
MHD mode is predicted unstable, but
its radial mode width is narrow (~5%of ap/ growth rate γ/ωA~10-2)# The gradients are averaged for Δρ=0.1.
even in the mode is even in the mode is expected linearly unstable, when the mode
width is narrow, the effect on the confinement is quite small

10

No fatal effect of “global” mode on the helical plasma?
Helcal coil of LHD
consists of 3 layers.
By changing the current
ratio in the 3 layers,
plasma aspect ratio,
mag.shear and mag. hill
hight are controlled.

High aspect configuration (a special
config.) has low magnetic shear andhigh magnetic hill in LHD=> Interchange mode is more unstable
Magnetic curvature

Rotaional transform6

κn (m-1)

1.5

ι
High-aspect config.
A =8.34p

A =8.3

1

p

2

6.3

6.3
0.5

HC-O
HC-M
H-M
HC-I

Plasma

0

0.6

ρ

0.8

1

0.6

High-β (mid.
aspect.) config.
ρ

0.8

1

The magnetic shear of high aspect. conf. is muchsmaller than that of midium aspect. conf., and κn inboth aspect ratio is almost same at the m/n=1/1
rational surface.
11

m/n = 1/1 mode in high aspect config. (low shear/high hill)# 55397, Ap=8.34|dβ/dρ|(%)

3

collapse
occursρ=0.9 (ι~1.3)

2
10ρ=0.7 (ι~1)

-1
(%)

1.5

0.84s
0.87s
0.90s

2.0

0.93s
0.97s

Te(keV)<β dia >#55397

1.0

1.0
0.5

0.0

<βdiaP
> (%)

0.0

2.8

3.2

NB

0

0.5

1 (s) 1.5
time (s)

3.6
R(m)

4

4.4

2

Br11/B0 non-rotating
A collapse occurs in a high aspect plasma
Before the collapse occurs, stability condition of global MHD mode isstrongly violated.

12

m/n = 1/1 mode in high aspect config. (low shear/high hill)# 55397, Ap=8.34|dβ/dρ|(%)

3

collapse
occursρ=0.9 (ι~1.3)

1.0#55397(t=0.84s)

0.8

2

0.6

1

0.4

0

ρ=0.7 (ι~1)

-1

(%)
1.5

ΔTe/|dTe/dρ|<β dia >

0.2
0.0
1.0

#553971.0

δ/ap>10%(ξ(0);finite)γ/ωA~10-2

Ideal
S=10

0.0

ξ(m/n=1/1)

0.5<βdiaP
> (%)

0.0

NB

0

0.5

1 (s) 1.5
time (s)20.0Br11/B0

6

0.5

0.2

0.4

ρ

0.6

0.8

1.0

Predicted mode width
before collapse by FAR3D

A collapse occurs in a high aspect plasma
Before the collapse occurs, stability condition of global MHD mode isstrongly violated.
Mode width is much important

13

for the effect on confinement!

Dependence of the global confinement on the beta valueτE normalized by ISS95 scaling
RaxV=3.6m, Ap=6.3

2
1.5
1
0.5

H

H

ISS-kin001ISS-dia2<β > (%)
dia

3

4

A disruptive
degradation has notbeen observed up to
high-β regime,
in both τE based on
the diamagnetic
energy and the
kinetic energy.

τ ISS 95 ∝ a 2.21 R 0.65 P −0.59 ne 0.51 B 0.83ι2 / 30.4
ISS95 scaling(International Stellarator Scaling 1995)

However, the enhancement factors aregradually
reducedas betaon the diamagnetic
plasma increases.
energy.
HISS-dia is based
HISS-kin are based on Te and ne profile measurements under theassumption of Zeff=1 and Ti=Te.

14

Beta dependence of peripheral local transport
χ/χGRB in peripheral region increases
with β in more than 1%.

χ GRB ∝ β ν p* ρ χ B
0

0

1
*

100

χeff/χGRB @ρ=0.9

(ι~1)

10

~β1

1

0.1
0.2

# χ dependence on β is similar with aprediction based on MHD (resistive
interchange mode) driven
turbulence.

χ GMTe ∝ β 1ν p*0.67 ρ*0.33 χ B
RaxV=3.6m, Ap=6.3
0.5

1

2

<βdia> (%)

3

proposed by Carreras et al. (PoF B1
5(1989))# Resistive interchange (g-) mode isNormalized thermal conductivity byalways unstable in the peripheral
GB (Gyro-reduced Bohm) model
region of LHD finite beta.
（Global property of GB is quite=> high m,n MHD modes would affectsimilar with ISS95)
it!
Not important!!
Other possibilities:# Invasion of stochastic region with beta is predicted See P2-043 by Y.Suzuki
See P2-049 by H.Funaba
15# Configuration effect as proposed in ISS04 scalingEffect of resistive interchange mode on peripheral transport
Thermal conductivity based on resistive
interchange (g) mode turbulence(induced through the magnetic field
diffusion)
Today’s Model

8

1

12 10

0.8

10 107
8

0.6

150

6

10

R κ

eff n

200

S

6
5

0.4

4/3

10

-7/3 2(R κ ) /(ιs^)

r

eff n

4

ιs^

GGMTe

0.2
0

Λ; Renormalization factor
γ; Linear growth rate
W; mode width of g-mode

50

4

10

2

Rdβ/dρ

3

10

0

β

0

100

0

1

2

3

4

<β > (%)
dia

GGMTe
χ ∝

(κ n R 0 )

q
sˆ

4
3

a eff

2

⎛ β R0 ⎞
⎟
⎜
⎜ L ⎟
⎝ p ⎠

4
3

S

−

2
3

v Te
R0

refs. B.A.Carrears et al. Phys.Fluids 30, 1388 (1987)
B.A.Carreras et al. Phys.Fluids B1, 1011 (1989)
100

Normalized thermal conductivity
by g-mode turbulence model isconstant in a high beta regime
with β>1%.

χ /χ
eff

GMTe

@ρ=0.910

RaxV=3.6m, Ap=6.3
1

0.1
0

[ref] H.Funaba et al, Fusion Sci. Tech. to be publised in 2006,
Proc. in 15th Int. Stell. WS in Madrid (2005).

12
3<β > (%)
dia

4

16

0

Collateral evidence
Density fluctuation amplitude with relatively long wavelength
increases with β

nLtilde/NL (A.U.)
at R=3.669m

3 10

-5

2 10

-5

1 10

-5

0 10

Beta dependence of the density
fluctuation amplitude withrelatively long wavelength,λ>~30mm(m<100)# Sight line passes the relatively peripheral
region0100# Inflection point of thermal
conductivity looks
synchronized with that of thedensity fluctuation amplitudewith relative long wave lengthχeff/χGRB @ρ=0.9

(ι~1)

10

1

0.1
0.2

RaxV=3.6m, Ap=6.3
0.5

1

2

<βdia> (%)

3

5

17

Effect of g- mode turbulence on confinement of reactor
Contour of pred. χ basedon g-mode turbulence
Reactor0.3 χ =1
S
gmt
3
7

10

10

10

6

5

0

10

<β >
dia
<1%
~2%
~3%
~4%
20

Depend. on geometric param.
4 aq(κ n R0 )3 eff
χ GMTe ∝
sˆ
R0

S

−

2
3

vTe aeff

Depend. on plasma param.

30

40
R dβ/dr (%)⎛ β R0 ⎞
⎟
⎜
⎜ L ⎟
⎝ p ⎠

4
3

60 A =6.3 config. ρ=0.9

Increases
Decreasespeff

LHD high beta plasmas are obtained under low mag. field operations. Then S is
reduced as beta increases.
=> The prediction of large value of χ in high beta regimes.
In a reactor, B0 and ne are larger by 10 times, and vTeaeff is by 15~20 times than LHD
high beta operations. => S would be larger by 300-400 times.
18=> χ~1m2/s (Not negligible but not large)

Summary# LHD transiently achieved the 5% beta and the 4.8 % beta inquasi-steady
Improving the heating efficiency of ⊥NBI due to the suppression of the
Shafranov shift
In addtion to the increment of the //NBI power and the optimization of theconfiguration.

# No observation of disruptive phenomena in LHD high beta
discharges would result from the radial localization of thepredicted global MHD modes
Through comparison between achieved pressure gradients and linear MHD
numerical analyses in 2 different configurations# Degradation of peripheral local transport with beta is observed.
But for a fusion reactor, that would not be strong obstacle.
The above degradation is is fairly consistent with an anomalous transport model
based on a g-mode turbulence (GMT) model . For the fusion reactor, GMT
would not be strong obstacle because it is significantly reduced in the highmagnetic Reynolds number comparatively with a reactor.
19

Options

20

Observed b profile andPoincare map by HINT
calculation for <βdia>=4.8%
plasmasInvasion of stochastic
region up to ρ~0.9 surf.
is not predicted.

LCFS in vac.

present def.
of ρ=1ρ=1 suf. passes the torus
outboard side of LCFS of vac. at
holizontally elongated crosssection.
21

See P2-043 by Y.Suzuki

Collateral evidence 1
Peripheral transport properties in another configuration
100

10

10

1

1

χ /χ
eff

GRB

χ GMTe ∝ β 1ν p*0.67 ρ*0.33 χ B~β0

GMT (g-mode
turbulence) model is more
5 consistent withexperimental thermal
conductivity in a highbeta range than GB(Gyro-reduced Bohm)
model.

@ρ=0.9

0.1

0.1

0.5

1

2

3

0.2

5

0.5

1

2

3

Ap=6.3 (lower
mag. hill)
100

100

χeff/χGRB @ρ=0.9

χeff/χGMTe @ρ=0.9

~β1

10

10

1

1

0.1

0.1

0.2

χ ISS 95 ∝ β 0.16ν p*0.04 ρ*0.71 χ B ,χeff/χGMTe @ρ=0.9

~β1

0.2

χ GRB ∝ β 0ν p*0 ρ*1χ B ,Ap=8.3 (low shear and highmag. hill)
100

0.5

1

2

<βdia> (%)

3

5

0.2

(The dispersion of data in ahigh aspect config. is fairly
large.)

~β0

0.5

1

2

3

5

<βdia> (%)

Normalized thermal conductivity by GB model and GMT model

22

grenχ=χeff/χISS04
See P2-049 by H.Funaba

23

Why is the predicted χGMTe (χ induced by g-mode turbulence)of a high aspect (Ap=8.3) plasma much large??
GGMTe

4

Peripheral Rdβ/dρ both in Ap=8.3 and 6.3 arealmost same.
=> p@ρ=0.9 in Ap=8.3 < p@ρ=0.9 in Ap=6.3=> T@ρ=0.9 in Ap=8.3 < T@ρ=0.9 in Ap=6.3 if ne
is same.(Reason not clear)=> S@ρ=0.9 in Ap=8.3 > S@ρ=0.9 in Ap=6.3
Peripheral S in Ap=8.3 is smaller by ~10times than Ap=6.3.

4
⎛
⎞3 −2
q
(κn R0 )3 aeff 2 ⎜⎜ βR0 ⎟⎟ S 3 vTeχ∝sˆ
R0⎝ Lp ⎠
8200

10Ap=8.3

S

7

10

150

6

10

100
5

10

50

4

10

Rdβ/dρ

3

10

0

1

2

3

71

12

0
4

8

200

10

0.8

R κ

0.6

(R κ ) /(ιs^)

10

eff n

4/3

GGMTe
8

-7/3 2

eff n

r

6

Ap=6.3

7

10

0.4

150

6

10

S

5

10

Ap=8.3

ιs^

0.2

0

1

12

100

Ap=6.30.8

50

4Rdβ/dρ

3

10

0

1

2

3

eff n

0.4

4/3

8
6

-7/3 2(R κ ) /(ιs^)
eff n

4

10

R κ

r

GGMTe

4

ιs^

0.2

0

2

0

0.6

10

4

0
0

β

Geometric factor of g-mode
turbulence model (GGMTe);
GGMTe in Ap=8.3 is larger by
2~2.5 times than Ap=6.3.

20<β > (%)
dia

Beta dependence of plasma parameter andgeometric facter determining χGMTe

GGMTe; 2~2.5=> χGMTe; 2~2.5
S; ~1/10=> χGMTe; ~4.5=> χGMTe; ~10 times larger
24

Port-through power //NBI 13.8MW<βdia> ; 4.8% (βperp~3.2)<βkin> ; 4.3% (=2*<βkin-e>)<βbeam>; 1.5% (Cal. by FIT code)<βdia> ; based on the diamagnetic measurement.
defined as (2Wdia/3Vp0)/ (Bav02/2μ0).
Bav0 and Vp0 are based on a vacuum calculation.
<βkin>; based on the Te and ne profile measurements
Zeff=1 and Ti=Te are assumed.
(When Zeff=2.5, <βkin>~3.6%(βperp~2.45), <βbeam> perp~0.75%, <βbeam>ara~0.75%)<βbeam> ; based on the calculation
with Monte Carlo technique and the steady state Fokker-Plank solution. 25

RaxV=3.6m, Ap=5.8

Loss particle ratio based on HINT data
B = 3 T, β = 0 %
1.0

no CX
1017 m-3
1018 m-3
no re-ent

0.8
0.6

LOSS PARTICLE RATIOLOSS PARTICLE RATIO

1.0

B = 0.5 T, β = 3.2 %

0.4
0.2
0.0

0.6

no CX
1017 m-3
1018 m-3
no re-ent

0.4
0.2
0.0

3.0

3.5

4.0
R (m)

LCFS

4.5

LCFS

0.95 ◎◎■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■◎◎
0.90 ◎◎■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■◎◎
0.85 ◎◎■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■◎◎
0.80 ◎◎■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■◎◎
0.75 ◎◎◎◎■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■◎◎◎◎
0.70 ◎◎◎■◎◎■◎■■■■■■■■■■■■■■■■■■■■■◎◎◎◎◎◎◎◎◎
0.65 ◎◎■■■■■■■■■■■■■■■■■■■■■■◎◎◎■◎◎■■◎◎◎◎◎◎
0.60 ◎◎■■■■■■■■■■■■■■■■◎■◎◎■■■■◎■■■■■■■■■◎◎
0.55 ■◎◎◎■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■◎◎
0.50 ■■◎■■■■■■■■■■■■■■■■■◎■■■■■■■■■■■■■■◎◎■
0.45 ■■◎◎■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■◎◎◎
0.40 ■■◎■■■■■■■◎■■■■■■■■■■■■■■■◎■■■■■■■◎◎◎◎
0.35 ■■■◎■■◎◎◎■■■■■■■■■■■■■■■■■◎◎◎◎◎◎◎◎◎◎◎■
0.30 ■■◎■◎◎◎■■■■■■■■■■■■■■■■■■■■■■■■■◎◎◎◎◎■
0.25 ■■■◎◎■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■◎◎◎
0.20 ■◎◎◎■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■◎◎
0.15 ■◎◎◎■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■◎◎
0.10 ■◎◎◎■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■◎◎
0.05 ◎◎◎◎■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■◎◎
2.7
3.0
3.3
3.6
3.9
4.2
4.5

通過
バナナ

0.8

カオス
即損失

損失

3.0

LCFS

3.5

4.0
R (m)

4.5

LCFS

0.95 ◎◎◎◎◎◎◎■■■■■■■■■■■■■■■■■■■■■■◎◎◎◎◎◎■■■
0.90 ◎◎◎◎◎◎◎■■■■■■■■■■■■■■■■■■■■■■◎◎◎◎◎◎■■■
0.85 ◎◎◎◎◎◎◎■■■■■■■■■■■■■■■■■■■■■■◎◎◎◎◎◎■■◎
0.80 ◎◎◎◎◎◎◎■■■■■■■■■■■■■■■■■■■■■■◎◎◎◎◎◎◎■■
0.75 ■◎◎◎◎◎◎■■■■■■■■■■■■■■■■■■■■■◎◎◎◎◎◎◎■■◎
0.70 ■■◎■◎◎◎■■■■■■■■■■■■■■■■■■■■◎◎◎◎◎■◎■■■■
0.65 ■◎◎◎◎◎■◎◎■■■■■■■■■■■■■■■■■◎◎■◎■◎■■■■■■
0.60 ■■■◎◎◎◎■◎◎◎◎■◎◎◎◎■■■◎◎■■■■■◎◎◎◎◎◎◎◎◎■ ■0.55 ■■■■■◎◎■■■■◎◎■◎◎◎◎◎◎◎◎◎◎◎■■■■■■◎◎◎■■■■
0.50 ■■■■■■◎◎◎■■■◎◎◎◎◎■◎◎◎◎◎◎◎◎◎◎◎◎◎■■■■■■■
0.45 ■■■■■■■◎◎◎◎◎◎◎◎◎■■■■◎◎◎◎■■■◎◎■■■■■■■■■
0.40 ■■■■■■■■■◎◎◎◎■■■◎■◎◎◎◎◎◎◎■■■■■■■■■■■■■
0.35 ■■■■■■■■■■◎◎◎■◎◎◎◎◎◎◎◎◎■■■■■■■■◎■■■■■■
0.30 ■■■■■■■■■■◎◎◎◎◎◎◎◎◎◎◎◎■■■■■■■■■■◎◎◎◎■■
0.25 ■■■■■■■◎◎◎◎◎◎◎◎◎◎◎◎◎◎◎■■■■■■■■■■◎◎◎◎◎◎
0.20 ■■■■◎■◎◎◎◎◎◎◎◎◎◎◎◎◎◎◎◎■■■■■■■■■■■◎◎◎◎◎
0.15 ■■■■■■◎◎◎◎◎◎◎◎◎◎◎◎◎◎◎■■■■■■■■■■■■◎◎◎◎◎
0.10 ■■■■■■◎◎◎◎◎◎◎◎◎◎◎◎◎◎◎■■■■■■■■■■■■◎◎◎◎◎
0.05 ■■■■■■◎◎◎◎◎◎◎◎◎◎◎◎◎◎◎■■■■■■■■■■■■◎◎◎◎◎
2.7
3.0
3.3
3.6
3.9
4.2
4.5

26

Summary# By improving the heating efficiency of ⊥NBI due to the suppression of
the Shafranov shift and the NBI power modulation, in addition to theincrement of the parallel NBI power, LHD transiently achieved the 5%beta value.
# According to the numerical analysis of the g-mode for a typical highbeta discharge, the radial mode width is quite narrow, Δ/ap~5%. This
fact supports that we have never observed disruptive phenomena in the
LHD high beta discharges because the predicted MHD instabilities arequite localized.
# According to the transport properties on beta, the gradual degradationof the local transport with beta comparing with GB (Gyro-Bohm) model
is observed. The above degradation is is fairly consistent with ananomalous transport model based on a g-mode turbulence (GMT)
model .
# For the fusion reactor, the anomalous transport based on the GMT isstill important, but it would not be strong obstacle for the production of
the high performance plasmas because it is significantly reduced in the27high magnetic Reynolds number comparatively with a reactor.

他の配位での検証は?
Helcal coil of LHD
consists of 3 layers.
By changing the curennt
ratio in the 3 layers,
plasma aspect ratio,
mag.shear and mag. hill
hight are controlled.

High aspect configuration has low
magnetic shear and high magnetic hillin LHD
Rotaional transform

Magnetic curvature6κn (m-1)

1.5

ι
High-aspect config.
A =8.34p

A =8.3

1

p

2

6.3

6.3

High-β config.

0.5
0
HC-O
HC-M
H-M
HC-I

0.6

ρ

0.6

1

ρ

0.8

1

GGMTe

12

1

Ap=6.30.8
0.6

Plasma

0.8

10

0.4

4/3

12

0.8

R κ

0.6

(R κ ) /(ιs^)

4/3

eff n

6
-7/3 2(R κ ) /(ιs^)
eff n

r

4

0
0

β

8

-7/3 2r

6
0.4

Ap=8.3

ιs^

0.2

10

eff n

8

R κ

eff n

71

2

0.2

0

0

ιs^

0

β

4
2
0

28

垂直NBIの高ベ－タ領域拡大への寄与
5

20
~0.5%

⊥NBI;6.9MW(ポートスルー)=> Δ<βdia>~0.5%@<βdia>~4.4%/ペレット入射直後
電子温度がコア領域で上昇。
密度はほとんど変化なし

4
10
3

#4

2
0.6

0

0.4

//NBIパワーモジュレーションによるベータの押し上げ効果は小さい( Δ<βdia>~0.1%)

ΔR /a

0.2

ax

p

0.0
0.5

1.5

#74827

0.5

T

0.4

平成17年度LHD実験成果
報告会資料(池田/高Ti)5nt=0.63s
0.67s

Te(keV)

4

e

e

1

0.5

0.3

3

0.2

(AU)

(keV)

1
time (s)

0

0.83s

2

t=0.87s
0.90s

-0.5

0.1

1

#74824 w ⊥NB#74827 w/o ⊥NB

0
0

0.2

r

eff

(m)

0.4

2.5

0
0.6

3

3.5

4
R(m)

4.5

29

⊥NBIの加熱効率(真空/>1.5T)

Discussion I What is a good index for the limitationof the operational regime in stellarator/heliotron?
Periphery

ρ=0.9 (ι~1)(Ap=6.3)12

dβ /dρ

Though the observed pressure gradients are in nonlinear saturation phases, a linear MHD theory could
be a reference for more complicated non-linear
analyses, and/or a criterion for a reactor design.

γ/ω A =10-2

kin

0.3x10-2
8

Mercier
4

0

0

1

12

dβ/dρ (%)

3

4

ρ=0.5 (ι~1/2)

Core(Ap=5.8)kin

2dβ kin/dρ
Mercier8
currentless
m/n=2/1 unstable
γ/ωA=10-2

For further verification, we need to extend theabove comparative analyses between theexperimental results and the theoreticalprediction based on a linear theory to a wide
range of magnetic configurations in LHD!!

4
1.5x10-20012<β dia> (%)

Peripheral region:
the maxima of the achieved
Peripheralregion
region:region the maxima of the achievedpressure gradients are less than γlow-n/ωA= 10-2-2.
pressure gradients are less than γlow-n/ωA= 10 .
Core region; the maxima of the achieved pressureCore region;
the maxima
of theachieved
pressure
gradients
saturateagainst thecontourof γlow-n/ωA=-2 insaturate/ω =gradients
againstcontour of γ
1.5x10
the rangeof <βthedia> = 1~1.8%. low-n A
1.5x10-2 in the range of <βdia> = 1~1.8%.
-2
Roughly speaking, γlowlow-n/ωA= 1~1.5x10 isconsidered a good index to determine thecondition that the global ideal MHD instability
limits the LHD operational regime.

3

30

3

0.3

2

0.2

1

0.1

10
10
10

4.4

4.5

4.6

4.7

4.8

0
4.9

OMFS in Vac．
0.1
p /p
e

e0

0.01
1-W /Wpe

0.001

pe100%

Stochastic
ap@Wpe=99%

0.0001
0.55

OMFS in Vac．

ρ=0.9

0.6

ρ=1

0.65
a (m)

0.7

ap@pe=0eff

Predicted magnetic field structure by HINT and observed pressure profile ina high beta LHD discharge with RaxV=3.6m, B0=0.5T and <βdia>~2.9%.
31

LHD

Wave formof highphenomena
beta discharge
Disruptive
havewith
not been observed<β>=4.5in%high beta operation with <βdia> >4%

5

CHS
W7AS
ATF
HeliotronE

4
3
2
1
0
1985

1990

1995

Year

2000

t2005
duration >> 10tE

# Achieved max. averaged beta : 4.8 %# Long sustainment of 4 % plasma# Shafranov shift D/aeff ~ 0.25
# Low-n,m activities- No observation of core resonant modes.
- m/n = 2/3 and 1/2 modes (peripheral
resonant surfaces, Resonances arelocated outside ρ ~ 0.9) appear (< 4 %),but behave intermittently withincreasing beta.
- Mercier criterion DI < 0.2 @ι=1/ρ~0.9
0.5

6.0

0.4

T (keV)e19-3n (10 m )

0.3

4.0

e

0.2

2.0

0.1

Though some flattening and asymmetric structures areobserved in the Te profile, they are not large enough to affecta global confinement.

0

3

3.5

4
R(m)

4.5

0.0

32 /21

S (Reinolds#) dependence of MHD mode
15

dβ/dρ (%)γ /ω A = 1 0 -2

10

0 .3 x1 0-2

M e rc ie r

5

0

0

1

2

3

< β dia> (%)

4

Saturation of peripheral MHD mode
strongly depends on S parameter. If w ~(bθ/Bt)1/2, S dependence of w is close tothat predicted by linear theory of
resistive interchange mode (w ∝ β1/6S-1/3).
=>
Commonly observed modes in LHD=> resistive (interchange) modes
CHS: S=103 ~105

LHD: S=106 ~108

Amplitudes in LHD(high-S) are muchsmaller than that in
CHS (low-S).

DI < 0.2
DR > 0<βdia> (%)

33 /18

Summary (Cont.)
4. In higher aspect config. with lower magnetic shear and higher magnetic hillcompared with high-β config., a minor collapse occurs. Before the collapse
occurs, stability condition of ideal global MHD mode is strongly violated.
The predicted mode width and growth rate are δ/ap=15~25% andγ/ωA~0.5~1x10-2. The observed magnetic fluctuation is not rotating. It isobserved more easily as S is larger. The above facts suggest that the observed
modes in the collapse is the ideal interchange mode.
5. From Aabove results suggest a possibility that the ideal low-m,n MHD
instability with large mode width affects the large effect of on theconfinement in heliotron devices.
6. Both the observed modes in high beta plasmas and in a minor collapse canbe suppressed by using the external resonant field. However, the mechanism
has not been clear. The non-linear calculation of the MHD instability in wide
range of S is necessary taking static error fields into account.

34 /21

35

Buck ground
For an economical fusion reactor,
achievement and sustainment of highbeta plasma (β~5%) is necessary.

654

LHD (JPN)
CHS (JPN)
W7AS (BRD)
ATF (USA)
HeliotronE (JPN)

32
101985 1990 1995 2000 2005

Year

Progress of achievement ofmax. beta in helical devices

In order to predict the behavior ofreactor plasma with β~5%, we need theextension of the operational beta regime,
and the analysis of the properties of thehigh beta plasmas like the beta
dependence.
The <β>=5% is a targeted value in the
LHD projects from the design phase.
We have made big effort aimed atachieving <β>=5% by increasing theheating capabilities and optimizing theoperational conditions like configurations
and so on.
The achieved beta value is increasing
yearly, and last exp. campaign of LHD
36 /21 wetransiently had the 5.0% beta plasma.

Contents# Progress of high beta operation in LHD# Characteristics of LHD high beta plasmas with β~5%.
# Effects of global MHD instability (low-n,m modes)
on LHD high beta plasmas
Through comparison between achieved pressure
gradients and linear MHD numerical analyses# Confinement properties of LHD high beta plasmas
Through comparison between experimentallyobtained thermal conductivities and sometheoretically predictions
37

Progress of ext.
of operational β range in LHD

Better Pabs,τE,
Orbit

MHD stability(~F.Y.2005/9th exp.campaign)<β>max (Ap, B0, (Rax))~FY’02 (Rax; opt.
: 3.2 % (5.8, 0.5 T, (3.6m))
B0;reduc., PNB;inc.)
FY’03 (Ap;reduc.): 4.1 % (6.2, 0.5 T)

FY’04 (Ap;opt.): 4.3 % (6.6, 0.45T)

FY’05 (B0;opt.): 4.5 % (6.6, 0.425 T)

5

20

4

15

Achieved <β>
3

10

(%) 2
NBI port_throu (MW)
1
0
2000

2002

Fiscal Year

2004

RaxV=3.6m
optimized.

Better MHD stability

Pabs,
Orbit

Ap --> increase
Rax in high-β --> decrease

5

0
1998

Rax in vac. --> increase
Rax in high-β --> increase

Ap=6.6
optimized.

2006

38

Characteristics of MHD stability in LHD high beta conf.
(%)<βdia >

Ap=6.2, p~(1-ρ2)(1-ρ8)

Mag. Well

Hill

Rotaional transform 2/3

1.5

m/n=1/1(,2/2,3/3),3/4,2/3,,,, .

vac
3/4
~1%
~2% <β> (%)
~3%

1.0

1/1(,2/2,3/3)

Low order m/n=2/1,
rational
3/2,1/1(,2/2,3/3),
surface
3/4,2/3m<=3m/n=3/2
2/1

0.5
0

0.2

0.4 ρ 0.6

0.8

In high beta regime,
magnetic hill exists in the
peripheral region=>
MHD instabilities (interchange/pressure driven) resonated with
peripheral rational surface would
be important in high beta regime.

139

Summary# By improving the heating efficiency of ⊥NBI due to the suppression of
the Shafranov shift and the NBI power modulation, in addition to theincrement of the parallel NBI power, LHD transiently achieved the 5%beta value.
# According to the numerical analysis of the g-mode for a typical highbeta discharge, the radial mode width is quite narrow, Δ/ap~5%. This
fact supports that we have never observed disruptive phenomena in the
LHD high beta discharges because the predicted MHD instabilities arequite localized.
# According to the transport properties on beta, the gradual degradationof the local transport with beta comparing with GB (Gyro-Bohm) model
is observed. The above degradation is is fairly consistent with ananomalous transport model based on a g-mode turbulence (GMT)
model .
# For the fusion reactor, the anomalous transport based on the GMT isstill important, but it would not be strong obstacle for the production of
the high performance plasmas because it is significantly reduced in the40high magnetic Reynolds number comparatively with a reactor.

Minor collapse due to m/n = 1/1 mode in high aspect config.
Minor collapse due toabrupt profilefattening near m/n =1/1 resonance
Growth of radial
component of m/n =1/1 mode (Nonrotate)
No observation ofclear precursor

Predicted ideal MHD mode
width before collapse
1.0

FAR3D

Ideal
6

0.5

S=10

0.0

ξ(m/n=1/1)

Profile flattening

DI > 0.2 even incurrentless plasma

0.0

0.2

0.4

ρ

0.6

0.8

1.0

δ/ap>10%(ξ(0);finite)γ/ωA=0.6~1.1x10-2
A collapse occurs in a high aspect plasma with low magnetic shear andhigh magnetic hill. Before the collapse occurs, stability condition of global
ideal MHD mode is stromgly violated. Mode width is much important
41
for the effect on confinement.

Quasi-steady high-β dischrage

tduration>90% >80 τE<β>=4.8 %# No disruptive high beta plasma is
maintained during more than 80τE
# Large shafranov shift Δ/ap ~ 40%# Low-n,m MHD activities- No observation of core resonant modes.
- Only resonating mode with peripheral
surf. (m/n = 2/3 and 1/1) appear# Global confinement property is almost
same with ISS95 scaling.

0.6
0.4

ΔR /a

0.2

ax

p

0.0

0

1 .5

1 .0
0 .5

τ /τ
E

E _ IS S 9 50 .0

bθ/B0[10-5] 10

ι=1

8

ι=1.5

69910t1.23s

β

dia

(%)

No large β flattening
enough to affect a
global confinement

6
4
2

ι=2
τE~13.3ms

0

0
3

3.5

4

4.5

R(m)

Small flattening and asymmetric structures areobserved

42

Transient (pellet inj.) high-β dischrage
tduration>90% ~10 τE

pellet inj.

# Just after pel. inj. for ~10 τE, highbeta plasma, <βdia>=5.0% istransiently achieved.

6

~5.0%

10

4
5

2

2<βe-kin>

0

0 .6# Shafranov shift is suppressed bypellet and //NBI power modulation
ΔRax/aeff ~ 0.4 => ~0
Increasing heating efficiency of⊥NBI(6.9MW)=> <βdia>=5.0%

0

0 .4

Δ R a x/a p

0 .2
0 .0

0

#1 +2+3

10

#4

5

NBI
0
0 .5

p o r t - te m p

//
0.5

⊥

1
t im e ( s )

0.5

1 .5

6

#69910@t=1.23s

74835@t=0.9s

0

0.4

T

0.4

T

4

e

n

e

e-TS

(AU)

4

0.3

ガスパフ
4.8%

0.2

0.3

2

n

0.1

e-TS

0.2

2

0
0

0
0.2

0.4

0.6

a (m)
eff

0.1

⊥NBIの加熱効率(真空/>1.5T)

0

0
0

0.2

0.4
a (m)
eff

0.6

電子密度、温度分布はガスパフ時とほとんど変わらず 43