effects of global mhd instability on operational high beta-regime in lhd

Effects of global MHD instability on Effects of global MHD instability on operational high beta-regime in LHDoperational high beta-regime in LHD

0.0

0.5

1.0

1.5

2.0

0 0.2 0.4 0.6 0.8 1

Rotational Transform R

ax=3.6m, currentless

=0%1%2%

Minor Radius

~(1-2)

EX3/3 IAEA FEC2004, Vilamoura, Nov.3, 2004IAEA FEC2004, Vilamoura, Nov.3, 2004

LHD(Large Helical (Large Helical Device)Device)NIFS, JapanNIFS, Japan

rotational transform

K.Y.Watanabe1), S.Sakakibara1), Y.Narushima1), H.Funaba1), K.Narihara1), K.Tanaka1), T.Yamaguchi2), K.Toi1), S.Ohdachi1), O.Kaneko1), H.Yamada1), Y.Suzuki3), W.A.Cooper4), S.Murakami5), M.Yokoyama1), N.Nakajima1), I. Yamada1), K.Kawahata1), T.Tokuzawa1), A.Komori1) and LHD experimental group

1) National Institute for Fusion Science, 322-6 Oroshi, Toki, 509-5292, Japan2) The Graduate University for Advanced Studies, Toki 509-5292, Japan3) Graduate School of Energy Science, Kyoto Univ., Kyoto, 606-8224, Japan4) Centre de Recherches en Physique des Plasmas, Association Euratom / Confederation Suisse, EPFL, 1015 Lausanne, Switzerland5) Department of Nuclear Engineering, Kyoto Univ., Kyoto 606-8501, Japan

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

Background I Background I --- --- ideal MHD effects on the beta limit ----ideal MHD effects on the beta limit ----

# A Heliotron device is a probable candidate of thermonuclear fusion # A Heliotron device is a probable candidate of thermonuclear fusion reactor under steady-state operation.reactor under steady-state operation.

However, a disadvantage with respect to pressure driven MHD However, a disadvantage with respect to pressure driven MHD instabilities is theoretically predicted. instabilities is theoretically predicted.

# How do MHD instabilities limit the operational regime in high beta # How do MHD instabilities limit the operational regime in high beta plasmas? It is very important issue in heliotron devices. plasmas? It is very important issue in heliotron devices.

# Tokamaks; well known # Tokamaks; well known The operational beta limits are quite consistent The operational beta limits are quite consistent

with theoretical predictions of ideal linear MHD with theoretical predictions of ideal linear MHD theory.theory.

Profile and shape dependence of N in JT-60U.

[Kamada et al, 16th IAEA proc.]

# Stellarator/helotrons; there were a few # Stellarator/helotrons; there were a few experimental studiesexperimental studies

The ideal MHD effects on the beta limit (the The ideal MHD effects on the beta limit (the operational regime) were not clear.operational regime) were not clear.

1. In Core region,1. In Core region, Comparison between observed dComparison between observed d/d/d and the theoret and the theoret

ical ideal MHD stability analysis, ical ideal MHD stability analysis, =>=> The observed dThe observed d/d/d are limited by the ideal global are limited by the ideal global

MHD instability in the intermediate beta range.MHD instability in the intermediate beta range.[[WATANABE, K.Y., et al, Fusion Sci. Tech. 2004WATANABE, K.Y., et al, Fusion Sci. Tech. 2004 ]]

0 1 2 3

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0.09

0.12

dki

n/d

(%)

0

8

12

4

<dia> (%)

0 1 2 30

0.04

0.08

0.12

0.0

4.0

8.0

12.0

ddi

a/d

(%)

0

8

12

4

=0.5 (~1/2)

Mercier

<dia> (%)

/A=10-2

currentless m/n=2/1 unstable

1.5x10-2

d/d

(%)

dkin/d

Background II Background II --- Related previous study in LHD --- Related previous study in LHD --------

2. When only core resonant magnetic fluctuation 2. When only core resonant magnetic fluctuation disappears, the plasma stored energy gains. disappears, the plasma stored energy gains. However, the gain is ~5% of WHowever, the gain is ~5% of Wpp. . [[SAKAKIBARA, S., Nucl. Fusion 2001SAKAKIBARA, S., Nucl. Fusion 2001 ]]

3. On the global energy confinement time, 3. On the global energy confinement time, a disruptive degradation of the improvement a disruptive degradation of the improvement

factor had not been observed up to <factor had not been observed up to <diadia> ~3%> ~3% Normalized Normalized E E by ISS95 by ISS95

vs vs [[YAMADA, H., et al., Plasma Phys. Control. Fusion 2001YAMADA, H., et al., Plasma Phys. Control. Fusion 2001]]

OutlineOutline0. Background0. Background1. On a typical discharge in 1. On a typical discharge in the extended beta range up to ~the extended beta range up to ~

4% in the LHD4% in the LHD2. Effect of the global confinement on the beta value2. Effect of the global confinement on the beta value3. Relationships between predicted global ideal MHD modes 3. Relationships between predicted global ideal MHD modes

and transport analysisand transport analysis4. Discussion4. Discussion--- Index for the limitation of an operational regime --- Index for the limitation of an operational regime

in the LHD (as a stellarator/heliotron device)in the LHD (as a stellarator/heliotron device)--- Beam pressure effects on the pressure driven MHD instability--- Beam pressure effects on the pressure driven MHD instability

5. Summary5. Summary

Topics of TalkTopics of TalkIn order to make clear the effectsIn order to make clear the effects of the global ideal MHD of the global ideal MHD instabilities on the operational regimes in stellarator/ instabilities on the operational regimes in stellarator/ heliotrons, the MHD analysis and the transport analysis are heliotrons, the MHD analysis and the transport analysis are done in a high beta range up to ~4% in the LHD.done in a high beta range up to ~4% in the LHD.

On a typical discharge in On a typical discharge in the extended beta range (I)the extended beta range (I)

Wave form for a high discharge

Beam pressure is Beam pressure is fairly large. fairly large.

When <When <diadia> reaches 4%,> reaches 4%,

NBI Power NBI Power Port through ; 11.2MWPort through ; 11.2MW Deposition ; 6.2MW(Cal.)Deposition ; 6.2MW(Cal.) <<kinkin> ; > ; 3.3%3.3%

<<beambeam> ; > ; 1.5%1.5% (Cal.)(Cal.)

<dia> ; based on the diamagnetic measurement.

defined as (2Wdia/3Vp0)/ (Bav02/20).

Bav0 and Vp0 are based on a vacuum calculation.

<kin>; based on the Te and ne profile measurements

Zeff=1 and Ti=Te are assumed.

(When Zeff=2.5, <kin>~2.8%, <beam> perp~0.8%, <beam> para~0.7%)

<beam> ; based on the calculation

with Monte Carlo technique and the steady state Fokker-Plank solution.

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wp_fir@47724 4:45:02 2004/10/24

betad nl3669/1.8 btkin btb_tot btdia

nbpw_pth

ne(10

19m

-3)

time(s)

<dia

> (%)<

kin>

<beam

>

NBI

0.45T, RaxV=3.6m, Ap=6.3

Heating Efficiency

dia

Shafranov shift

StandardStandardAApp=5.8=5.8 AApp=6.3=6.3

high high

Tangential radius of NBI

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wp_fir@47724 4:45:02 2004/10/24


nbpw_pth

ne(10

19m

-3)

time(s)

<dia

> (%)<

kin>

<beam

>

NBI

High-aspect ratio Config. for High 0.45T, Rax

V=3.6m, Ap=6.3

On a typical discharge in On a typical discharge in the extended beta range (II)the extended beta range (II)

High-aspect ratio config.=> high , Reduced shafnanov shift=> Retains a good heating efficiency

in high beta discharges

The config. is unfavorable for MHD stability<= reduces the formation of magnetic well in high beta regimes..

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wp_fir@47724 4:45:02 2004/10/24


nbpw_pth

ne(10

19m

-3)

time(s)

<dia

> (%)<

kin>

<beam

>

NBI

On a typical discharge in On a typical discharge in the extended beta range (III)the extended beta range (III)

Magnetic fluctuation and ...

The m/n=1/1 and 2/3 modes are dominantly observed. (peripheral region )

Though some structures with the Though some structures with the flattening and the asymmetry are flattening and the asymmetry are observed in the Tobserved in the Tee profile at the profile at the

peripheral resonant surfaces, they are peripheral resonant surfaces, they are not large enough to affect a global not large enough to affect a global confinement.confinement.

It has not been clear what produces the fine structure.Due to equilibrium current and/or MHD activity??

t=t@max

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200

400

600

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3 3.5 4 4.5

te_io@47724t1175-1275_2.QPC

R (m)

Te(eV)

=1 Te profile

Effect of the global confinement on the beta Effect of the global confinement on the beta valuevalue

E normalized by ISS95 scaling

0

0.5

1

1.5

2

0 1 2 3 4

HISS-kin

HISS-dia

<dia

> (%)

ISS95 scaling(International Stellarator Scaling 1995)

HISS-dia is based on the diamagnetic plasma energy.

HISS-kin are based on Te and ne profile measurements under the

assumption of Zeff=1 and Ti=Te.

A disruptive degradation has not been observed up to <dia> ~4%,

in both E based on the diamagnetic energy and the kinetic energy .

However, the enhancement factors are gradually reduced as beta increases.

How about the ideal MHD effects?! How about the ideal MHD effects?!

Instability in the peripheral region is more unstable.The instability might limit the operational beta range.

Ideal MHD stability in peripheral region

As the becomes higher,,,,,,

Relationships between predicted global ideal MHD modes and transport analysis (I)Relationships between predicted global ideal MHD modes and transport analysis (I)

Here =0.9 (~1) surface is focused to analyze the relationships between observed beta gradients and the prediction of ideal MHD instability.

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0 0.2 0.4 0.6 0.8 1 1.2

Ap~6.3(=1.22)

r/ap

Rotaional Transform

=0.9 =0.9 ((~1)~1)

0

4

8

12

0 1 2 3 4

<dia

> (%)

Mercier


0.3x10-2

=0.9 (~1) /A =10-2

Contours of low-n ideal MHD mode growth rate in <>-d/d diagram

Ideal MHD unstable region in peripheral region

0

4

8

12

0 1 2 3 4

<dia

> (%)

Mercier


/A =10-2

0.3x10-2

=0.9 (~1)d

kin/d

Kinetic beta gradients are plotted on a contour of low-n ideal MHD mode

Kinetic beta gradients are estimated under the assumption Zeff=1 and Te=Ti.

Position of experimental region

Though beta value and its gradients reach the Though beta value and its gradients reach the global mode unstable region where the global mode unstable region where the predicted radial width of the ideal MHD mode predicted radial width of the ideal MHD mode reaches reaches /a/app=5%, the disruptive degradation of =5%, the disruptive degradation of

global confinement has not been observed. global confinement has not been observed.

0

0.7 0.8 0.9 1

S46755T1675

m1n1 m2n1 m3n1 m4n1 m5n1

Radial structure of ideal MHD modecalculated by TERPSICHORE code

/ap~5%

Relationships between predicted global ideal MHD modes and transport analysis (II)Relationships between predicted global ideal MHD modes and transport analysis (II)

0

0.5

1

1.5

2

0 1 2 3 4

HISS95-kin

<dia

> (%)

Enhancement factor Enhancement factor based on kinetic energy based on kinetic energy

vs vs beta valuebeta value

Ideal MHD effects on global confinement

Relationships between predicted global ideal MHD modes and transport analysis (III)Relationships between predicted global ideal MHD modes and transport analysis (III)

In In the global MHD the global MHD mode unstable regmode unstable region (ion (=3~4%),=3~4%),

No disruptive No disruptive degradation!!degradation!!

0.3x10-2

/A =10-2

0

4

8

12

0 1 2 3 4

<dia

> (%)

Mercier


/A =10-2

0.3x10-2

=0.9 (~1)d

kin/d

Ideal MHD effects on local transport

Relationships between predicted global ideal MHD modes and transport analysis (IV)Relationships between predicted global ideal MHD modes and transport analysis (IV)

1

10

0 1 2 3 4

X/GRB

<dia

> (%)

=0.9 (=0.9 (~1)~1) For study the ideal mode effects on a local d/d. We introduce a parameter, X,

Q/S is the heat flux normalized by a unit area. When ne is constant, X=> a heat conductivity.GRB: Gyro-Reduced Bohm heat conductivity.

0

2

9.09.0 2

BrS

QX kin

0.3x10-2

/A =10-2

0

4

8

12

0 1 2 3 4

<dia

> (%)

Mercier


/A =10-2

0.3x10-2

=0.9 (~1)d

kin/d

0

2

9.09.0 2

BrS

QX kin

No disruptive degradation No disruptive degradation in in the global mode unstablthe global mode unstabl

e region!!e region!!

X/X/GRBGRB gradually increases in gradually increases in

Mercier unstable region.Mercier unstable region.

High-n and/or low-n localized High-n and/or low-n localized ideal interchange modes affect a ideal interchange modes affect a local transport!?local transport!?

Kinetic beta gradients plotted with growth rate contours of low-n ideal

MHD mode

0

4

8

12

0 1 2 3 4

<dia

> (%)

Mercier


/A =10-2

0.3x10-2

=0.9 (~1)d

kin/d

In typical LHD high beta operations, the beam pressure is fairly large. We need the beam pressure effect on the ideal interchange mode.

How does beam pressure affect How does beam pressure affect the pressure driven MHD instability ?the pressure driven MHD instability ?

Discussion Discussion

In order to estimate the beam effect In order to estimate the beam effect on MHD modes as the 1st step,on MHD modes as the 1st step,We apply assumptions;We apply assumptions;ddbeambeam//dd is proportional to d is proportional to dkinkin//dd<<diadia -< -<kinkin>> => < => <beambeam

Assumption;Assumption;ddbeambeam//dd is proportional to d is proportional to dkinkin//dd<<diadia -< -<kinkin>> => < => <beambeam

0

4

8

12

0 1 2 3 4

<dia

> (%)

Mercier


/A =10-2

0.3x10-2

=0.9 (~1)d

dia/d

1.5x10-2

Including a beam Including a beam pressure effectpressure effect

Predicted maximum growth rate Predicted maximum growth rate exceeds exceeds low-nlow-n//AA= 1.5x10= 1.5x10-2-2 .

Growth rate is fairly large!!

To make clear the beam effects, we need more detail analysis.=> Future subject

SummarySummary

1. In LHD, the operational highest beta value has been expanded 1. In LHD, the operational highest beta value has been expanded from 3.2% to 4% in last two years by increasing the heating from 3.2% to 4% in last two years by increasing the heating capability and exploring a high aspect configuration.capability and exploring a high aspect configuration.

2. In order to make clear the effect of the global ideal MHD 2. In order to make clear the effect of the global ideal MHD instabilities on the operational regimes, the MHD analysis and instabilities on the operational regimes, the MHD analysis and the transport analysis are done in the high beta range up to 4%. the transport analysis are done in the high beta range up to 4%.

# In a high beta range of more than 3%, the maxima of the # In a high beta range of more than 3%, the maxima of the observed peripheral thermal pressure gradients are marginally observed peripheral thermal pressure gradients are marginally unstable to a global ideal MHD instability. unstable to a global ideal MHD instability.

# Though a gradual degradation of both the peripheral local # Though a gradual degradation of both the peripheral local transport and the global confinement has been observed as beta transport and the global confinement has been observed as beta increases, a disruptive degradation does not appear in the beta increases, a disruptive degradation does not appear in the beta range up to ~4%.range up to ~4%.

3. There is a possibility that the beam pressure gradient effect on t3. There is a possibility that the beam pressure gradient effect on the operational limits will be a key issue for a further extension ohe operational limits will be a key issue for a further extension of the beta range in LHD. f the beta range in LHD.

[J. Miyazawa et al, J.Plasma Fus. Res. (2004).]

0

0.5

1

1.5

2

0 1 2 3 4

HSudo

<0.5

HSudo

=0.5~0.7

HSudo

>0.7

E~n

0.51=>n

0.28

HISS95-kin

<dia

> (%)

=> In a low beta regimeIn a low beta regime, the scattering of the data is reduced.In a high beta regimeIn a high beta regime, the gradual degradation of the global confinement on still remains.

0

0.5

1

1.5

2

0 1 2 3 4

HISS95-kin

<dia

> (%)

Effect of ideal MHD mode on the global confinement (II)Effect of ideal MHD mode on the global confinement (II)

0

0.5

1

1.5

2

0 1 2 3 4

HSudo

<0.5

HSudo

=0.5~0.7

HSudo

>0.7

<dia

> (%)

HISS95-kin

How about the ideal MHD effects?! How about the ideal MHD effects?!

The high beta discharges with >3% are done near a density limit, HSudo>0.7.

HSudo=ne/ne_lim, ne_lim~(PabsB/V)0.5.

[S.Sudo et al. Nucl. Fusion 1990]According to a recent transport study in the LHD high collisional regime,EE scales as n scales as n

ee0.280.28

(In the ISS95 scaling, E~ne0.51)

Applying the above collection near a density limit

Predicted high n ballooning modes are as unstable as Predicted high n ballooning modes are as unstable as ideal interchange modes in high beta range of ideal interchange modes in high beta range of =3~4%.=3~4%.

Example of ideal ballooning Example of ideal ballooning stability analysis in high stability analysis in high range range

Radial structure of ideal MHD mode 0

0.7 0.8 0.9 1

S46755T1675

m1n1 m2n1 m3n1 m4n1 m5n1

/ap~5%

0

0.05

0.1

0

0.05

0 0.2 0.4 0.6 0.8 1

10%up(<>, dd)

(<>,d/d)=(3.4%,10.0%)

/A of high-n ballooing

0

4

8

12

0 1 2 3 4

<dia

> (%)

Mercier


/A =10-2

0.3x10-2

=0.9 (~1)d

kin/d

Kinetic beta gradients are plotted on a contour of low-n ideal MHD mode

Discussion IVDiscussion IV

0 1 2 3 40

5

10

15

0 1 2 3 40

5

10

15

d/d

(%

)

0.01000

0.04373

0.1913

0.8365

3.658

16.00

<dia

> (%)

d/d

(%

)

<dia

> (%)

0.01000

0.04373

0.1913

0.8365

3.658

16.00

Mercier

/A =10-2

0.3x10-2

(%)

The m/n=1/1 mode is observed even in the Mercier stable region.Amplitude of the m/n=1/1 mode increases as beta and the gradients increase.

Discussion III Discussion III

b/Bb/B00 on d on d/d/d and global ideal MHD unstable region and global ideal MHD unstable region~

Amplitude of b/B00 of m/n=1/1 mode~

No disruptive degradation is observed in the global ideal MHD modes, <dia>=3-4%.

There high-n ideal ballooning and resistive interchange/ballooning modes might be also unstable. A future subject!!

Discussion VDiscussion V

Ideal MHD effects on Electron thermal transport (II)

1

10

0 1 2 3 4

X/GRB

<dia

> (%)

1

10

chi_list_rho09_01

0 1 2 3 4

/GRB

<dia

> (%)

=0.9 (=0.9 (~1)~1)

Maxima of Maxima of //GRBGRB increases when the beta increases when the beta

gradients are in Mercier unstable region.gradients are in Mercier unstable region.High-n and/or low-n localized ideal interchange High-n and/or low-n localized ideal interchange modes affect a local transport!?modes affect a local transport!?

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0 0.2 0.4 0.6

2pe_ne_io@47724t1175-1275_ohp1

ap (m)

p[kJ/m3]

ne[1019m-3]

t=t@max

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

What is a good index for the limitation What is a good index for the limitation of the operational regime in stellarator/heliotron?of the operational regime in stellarator/heliotron?

Discussion II Discussion II

For further verification, we need to extend the above comparative analyses between the experimental results and the theoretical prediction based on a linear theory to many magnetic configurations in LHD!!

Core region;Core region; the maxima of the achieved pressure gradients saturate against the contour of low-n/A=

1.5x10-2 in the range of <dia> = 1~1.8%.

0 1 2 3

0.0

2.0

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12.0

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0.03

0.06

0.09

0.12

dki

n/d

(%)

0

8

12

4

<dia> (%)

0 1 2 30

0.04

0.08

0.12

0.0

4.0

8.0

12.0

ddi

a/d

(%)

0

8

12

4

=0.5 (~1/2)

Mercier

<dia> (%)

/A=10-2


1.5x10-2

d/d

(%)

dkin/dCore Core (A(App=5.8)=5.8)

0

4

8

12

0 1 2 3 4

<dia

> (%)

Mercier


/A =10-2

0.3x10-2

=0.9 (~1)d

kin/d

PeripheryPeriphery

(A(App=6.3)=6.3)

Peripheral regionPeripheral region: the maxima of the achieved pressure gradients are less than low-n/A= 10-2.

Peripheral regionPeripheral region: the maxima of the achieved pressure gradients are less than low-n/A= 10-2.

Core region;Core region; the maxima of the achieved pressure gradients saturate against the contour of low-n/A=

1.5x10-2 in the range of <dia> = 1~1.8%.

Roughly speaking, Roughly speaking, low-nlow-n//AA= 1~1.5x10= 1~1.5x10-2-2 is is

considered a good index to determine the condition considered a good index to determine the condition that the global ideal MHD instability limits the that the global ideal MHD instability limits the LHD operational regime.LHD operational regime.

Aspect ratio of plasma can be optimized by the control of the central position of HC current.

Poloidal Coils

Plasma

H-M

HC-OHC-MHC-I

Helical Coil

- Aspect-ratio of 5.8 ~ 8.3 is available in the Rax

V = 3.6 m configuration.

- High aspect-ratio configuration has high rotational transform which suppresses.

Aspect-ratio Control in LHD

5

6

7

8

9

10

0

0.2

0.4

0.6

0.8

1.15 1.2 1.25

Ap

0

Rax

V = 3.6 m

(the parameter of the HC current center)

high- Standard

effects of global mhd instability on operational high beta-regime in lhd

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