density limit studies in lhd b. j. peterson, j. miyazawa, k. nishimura, s. masuzaki, y. nagayama, n....

Density Limit Studies in LHDB. J. Peterson, J. Miyazawa, K. Nishimura, S. Masuzaki, Y. Nagayama, N. Ohyabu, H. Yamada,

K. Yamazaki, T. Kato, N. Ashikawa, R. Sakamoto, M. Goto, K. Narihara, M. Osakabe, K. Tanaka, T. Tokuzawa, M. Shoji, H. Funaba, S. Morita, T. Morisaki, O. Kaneko, K. Kawahata, A. Komori,

S. Sudo, O. Motojima and the LHD Experiment Group

National Institue for Fusion Science, Toki, Japan

20th IAEA Fusion Energy Conference

November 4, 2004Vilamoura, Portugal

Topics

• Motivation

• Comparison with Sudo scaling

• Maximum achieved densities

• Gas puff

• H2 pellet

• Effect of boronization

• Confinement degradation

• Summary

B.J. Peterson et al. NIFS 20th IAEA FEC EX6-2 2004.11.4 [email protected] page 1

• Limitation by Radiative Collapse

• Evolution of radiative collapse

• Radiated fraction threshold

• Critical edge temperature

• Edge behavior

• Radiation asymmetry

mailto:[email protected]

0.0

0.5

1.0

1.5

2.0

0.0 0.5 1.0 1.5 2.0

low Bhigh B

<N

e>ex

p. (

1020

m-3

)

<Ne>Sudo scaling

(1020

m-3

)

0.25*(PB)0.5(a2R)-0.5

@ Wp-max

0.0

0.5

1.0

1.5

2.0

0.0 0.5 1.0 1.5 2.0

low Bhigh B

<N

e>ex

p. (

1020

m-3

)

<Ne>Sudo scaling

(1020

m-3

)

0.25*(PB)0.5(a2R)-0.5

@ Wp-max

figure by K. Nishimura

Motivation• Fusion reaction rate goes as density squa

red 　　 RDT ~ n2<>

• Tokamak density is limited by current di

sruption and scales with plasma current de

nsity:

nTok ~ Ip/a2 (Greenwald) but

has weak power dependence

• Helical devices have radiative density li

mit which scales with square root of input

power:

nH-E ~ (PB/V)0.5 (Sudo) nW7AS ~ (P/V)0.4 B0.32 (Gianonne-Itoh)

• LHD has a density limit which is more th

an 1.6 times the Sudo limitB.J. Peterson et al. NIFS 20th IAEA FEC EX6-2 2004.11.4 [email protected] page 2


0

5

10

15

20

<n e>

1019

m-3

Gas

s pu

ff (

a.u.

)

Time (s)

<ne>

gass puff

#46289

0

5

10

15

PN

BIs (

MW

)

Gas

s pu

ff (

a.u.

)

Time (s)

0.00.20.40.60.81.0

CII

I, O

V (

a.u.

)

Gas

s pu

ff (

a.u.

)

Time (s)

CIII

OV

0

0.2

0.4

0.6

0.8

0.0

2.0

4.0

6.0

8.0

0.0 0.5 1.0 1.5 2.0 2.5

Wp (

MJ)

Pra

d (M

W)

Time (s)

Wp

Prad

Rax = 3.75 m, B = 2.64 T

by K. Nishimura

Peak Sustained Density

• With He gas puffing

• line-averaged densities of 1.

6 x 1020/m3

• ne = 1.36 ne-Sudo

• sustained for > 0.7 s

• Pin ~ 11MW (3 NBI, -ion, 1

60-180 keV)

• Prad/Pin < 25%

• Plasma collapses after reduc

tion of beam power




05

10152025

<n e>

1019

m-3

Gas

s pu

ff (

a.u.

)

Time (s)

<ne>

gass puff

#47492

0

5

10

15

PN

BIs (

MW

)

Gas

s pu

ff (

a.u.

)

Time (s)

0.0

0.5

1.0

1.5

2.0

CII

I, O

V (

a.u.

)

Gas

s pu

ff (

a.u.

)

Time (s)

CIII

OV

0.00.20.40.60.81.0

0.02.04.06.08.0

10.0

0.0 0.5 1.0 1.5 2.0 2.5

Wp (

MJ)

Pra

d (M

W)

Time (s)

Wp

Prad

by K. Nishimura

Higher densities with H2 pellets

• H2 pellet into He gas puffing

• Core fuelling @ ~0.7

• transient line-averaged densitie

s of > 2.2 x 1020/m3

• Pin ~ 10.5 MW (3 NBI, -ion, 16

0-180 keV)

• Prad/Pin < 35%

• Wp begins to decay then collap

ses after reduction of beam powe

r

Rax = 3.6 m, B = 2.75 T




Boronization raises density and reveals carbon as dominant radiating impurity

• Using 3 nozzles in LHD

• 60% coverage of vacuum v

essel with diborane (B2H6)

• Effective in wall conditioni

ng leading to extension of de

nsity range


• OV radiation decreases by a factor of >10

• While CIII radiation decreases by factor of 2.5

• Similarly, radiation decreases by factor of 1.5

• Therefore carbon should be dominant light impurity

K. Nishimura et al., J. Plasma Fusion Res. 79 1216 (2003)

Pin = 6 MW

• Wp saturates and drops more rapidly due to confinement degradation at high density

• Density and radiation peak as plasma collapses at density limit

• Radiated power is approximately 30% of input at onset of thermal instability

• First OV then CIII increase rapidly at onset of TI

• Edge temperature degrades after TI onset

• Density profile is maintained well beyond onset of TI

Evolution at Radiative Collapse

figure by J. Miyazawa

0

4

8

0

200

400

n e (10

19 m

-3) W

p_dia (kJ)

#43383 : H2, R

ax = 3.6 m, B

0 = 1.5 T

(a)

0

2

4

0

2

4

Pra

d (M

W) P

abs (MW

)

(b)

0

1

0

1

CII

I / n

e (ar

b.) O

V / n

e (arb.)

(c)

0

1

2

0

0.2

0.4T e0

(ke

V) T

e09 (keV)

(d)

0

2

4

0

2

4

1.8 1.9 2 2.1 2.2 2.3

(Pra

d'/ P

rad)

/ (n

e' / n

e) Ne L

(3669

) / Ne L

(411

9)

time (s)

(e)



Collapse

No collapse

mixed

In LHD Radiative Collapse occurs above a certain Radiated Power Fraction

• Collapse occurs for Prad/Pabs> 30%

• Prad does not include divertor radiati

on which is hard to estimate due to he

lical asymmetry.

•Prad/Pabs = 100% in cases with large c

ore radiation from metallic impurities


figure by Yuhong Xu


• Impurity radiation can be written as:

• Assuming that nz and Te have some dependence on ne

• The radiated power can be expressed as having a certain p

ower dependence on density

　 Prad nex = c ne

x

　　 and an expression for x can be derived as 　

　　　 x = (Prad’/ Prad) / (ne’ / ne)

　　※ this is called the density exponent

• During the steady state portion x = 1

• Increases to > 3 after the onset of the thermal instability

• Define onset of thermal instability at x = 3

0.01

0.1

1

10

0.1 1 10P

rad (

MW

)

ne (1019 m-3)

#43383 (t = 0.75 - 2.20 s)

Prad

~ ne

1

Prad

~ ne

3

43383_ne_Prad.QPC

t = 0.8 s

t = 2.1 s

t = 2.2 s

Quantification of thermal instability onset


dVTLnnP eZeZZ )(


○ Therefore a certain edge threshold

temperature exists for the onset of the thermal

instability (but not necessarily at = 0.9)

0

0.1

0.2

0.3

0.4

0 2 4 6

x = 3#43357 NB#3#43360 NB#2#43383 NB#2 + NB#3#43385 NB#2 + NB#3#43401 NB#2 + NB#3

T e09 (

keV

)

ne (1019 m-3)

Te09

~ 0.15 keV

th_360m150T_ne_Te09.QPC

Rax = 3.6 m,

B0 = 1.5 T, H

0.0

0.2

0.4

0.6

0.8

1.0

0 2 4 6 8 10

H2, R

ax = 3.60 m, B

0 = 1.5 T, = 0.1

H2, R

ax = 3.60 m, B

0 = 1.5 T, = 0.9

He, Rax

= 3.60 m, B0 = 1.5 T, = 0.1

He, Rax

= 3.60 m, B0 = 1.5 T, = 0.9

He, Rax

= 3.75 m, B0 = 1.5 T, = 0.1

He, Rax

= 3.75 m, B0 = 1.5 T, = 0.9

T e (ke

V)

ne (1019 m-3)

D:\PV-WAVE\LHD_7th\2003-10-01\data\th_360m150T.QPC

Rax

= 3.6 m

Rax

= 3.75 m

wh

en x

= 3

Edge Temperature threshold for density-limiting radiative collapse in LHD

B. J. Peterson, J. Miyazawa et al. B.J. Peterson et al. NIFS 20th IAEA FEC EX6-2 2004.11.4 [email protected] page 9

○ x = 3 is correlated with Te09 （ = 0.

9) = 150 eV independent of the input pow

er, density (right plot), magnetic configur

ation and gas (left plot)

= 0.1H

He

= 0.9

figures by J. Miyazawa


• Divertor radiation increases after thermal instability begins and is less dramatic

• Ion saturation current in divertor decreases

• Thermal instability begins first in OV

• CIII coincident with Prad

•Indicates C as dominant impurity

Evolution of Impurity Radiation and Divertor Plasma during Thermal Instability and Collapse

• Radiation asymmetry accompanies onset of thermal instability

Radiation asymmetry begins

Divertor radiation begins to grow

Inboard channel

Outboard channel

Divertor leg channel

Onset of thermal instability Prad ~ n3



• Initially hollow

• Slight increase in core radiation

• Extremely hollow during collapse at 2.19 s

• Estimated power density for 3% C, ne = 7 x 1019, L = 10-33Wm3 is 150kW/m3

Evolution of Radiation Profile during Thermal Instability and Collapse

Onset of thermal instability Prad ~ n3

Peak moves in as temperature drops

And second peak appears



up

down

up

down

up

down

inboard

outboard

outboard

Tangen

tial view T

op view

Imaging Bolometers show radiative collapse that is:poloidally asymmetric, toroidally symmetric

Symmetric Hollow Profile

by Peterson and Ashikawa


Experimental data


up

down

up

down

up

down

up

down

inboard

outboard

inboard

outboard

outboard

Tangen

tial view T

op view

)(),( SS


Symmetric Hollow Profile



Experimental data

0

0.04

0.08

0.12

0.16

0 0.5 1 1.5

Radi

atio

n po

wer d

ensit

y (a

rb.)

Model

S()

up

down

up

down

up

down

up

down

inboard

outboard

inboard

outboard

inboard

outboard

Tangen

tial view T

op view

)(),( SS


Symmetric Hollow Profile Asymmetric Collapse



Experimental data

0

0.04

0.08

0.12

0.16

0 0.5 1 1.5

Radi

atio

n po

wer d

ensit

y (a

rb.)

Model

S()

0)( F Experimental data

up

down

up

down

up

down

up

down

inboard

outboard

inboard

outboard

inboard

outboard

inboard

outboard

Tangen

tial view T

op view

)](1[)(),( FSS

500 2/))cos(1()( F


Symmetric Hollow Profile Asymmetric Collapse



Experimental data

0

0.04

0.08

0.12

0.16

0 0.5 1 1.5

Radi

atio

n po

wer d

ensit

y (a

rb.)

Model

S()

0)( F Experimental dataModel 1500

Sym

metric radiation

with gas puff

AXUV Diode Arrays in semi-tangential cross-section

Reconstructed 2-D Images(tomography courtesy Y.Liu, SWIPP, China)

Asym

metric

collapse

out in

in out

in out

Gas PuffPeterson et al., PPCF 45 (2003) 1167.


2-D tomography with AXUV diodes also indicates poloidally asymmetric, toroidally symmetric

0.4

0.6

0.8

1.0

1.2

1.4

0.01 0.1 1 10

E

exp /

E

ISS9

5

p* ( = 0.9)

Rax

= 3.6 m, B0 = 1.5 T, H

2

0.1

1

10

0.1

1

10

0.2 0.4 0.6 0.8 1

eeff (

m2 /s

)

p*

Te (keV)

~ Te

4.5

~ Te

1.5

~ Te

0.5

Rax

= 3.6 m, B0 = 1.5 T, H

2 = 0.5

Confinement degradation at high density

E compared with ISS95 declines in high-density (high-collisionality) re

gime, however eeff still is lower in this regime (yellow band).

This “confinement limit” appears at lower density than the operational density limit by radiative collapse and leads to an earlier saturation of and accelerated decay of Wp and thus Te as ne increases.

Shallow penetration of heating beams at high density is not sufficient to explain degradation.

The effective thermal diffusivity shows weaker temperature dependence of e

eff Te0.5 at low Te (corresponds to E ne

1/3).

As temperature increases, temperature dependence becomes stronger, gyro-Bohm (blue) and/or neo-classical theory (green).

Degradation from ISS95 in high-density regime attributed to change in temperature dependence of thermal diffusivity.

Weaker temperature dependence is less favorable (and thus leads to lower density limit) as higher temperature dependence inhibits collapse by giving weaker transport as temperature drops.

However, higher power is expected to raise temperature returning to regime of favorable density and temperature dependences.


Summary• Maximum line-averaged densities of 1.6 x 1020 /m3 have been sustained in LHD which is 1.36 times the value expected from scaling laws for smaller helical devices.

• Boronization of 60% of vacuum vessel effectively conditions wall and can lead to lower radiation and higher density limits.

• LHD plasmas are limited at high density by a radiative thermal instability leading to radiative collapse of the plasma when core radiated power fraction is > ~30%.

• Onset of the radiative thermal instability at a certain edge temperature indicates temperature threshold.

• Comparison of CIII and OV signals with Prad before and after boronization and during radiative collapse indicate C is dominantly radiating impurity.

• A poloidally asymmetric, toroidally symmetric radiation structure accompanies the collaspse of the plasma similar to a MARFE in tokamak.

• Degradation from ISS95 in high-density regime due to weak temperature dependence of thermal diffusivity should accelerate the decrease in the electron temperature leading to a lower density limit at the collapse.B.J. Peterson et al. NIFS 20th IAEA FEC EX6-2 2004.11.4 [email protected] page 15

Loss of edge profile stiffness at high density

In the high density range, the scale length of the electron pressure gradient is sustained except at the periphery where it increases with density in the shaded region.

Pressure itself is found to increase with Pabs, pe Pabs0.51

The electron pressure profile can be fitted with a model equation in the plateau regime: pe

plt

() = 3.4Pabs0.51exp(-(1.52+1.510))

This can be integrated over to give Weplt

At low B the dgradation of the We kin compared to themodel in the P-S regime is due to deterioration in the edge as seen above.

At high B hovevfer the deterioration happens at lower collisionaltiy and occurs in the core.

Loss of profile stiffness at high collisionality should limit the density which can be obtained before the raditive collapse


0

2

4

6

8

10

12

0 1 2 3 4 5 6 7 8

= 0.6 = 0.8 = 0.9

(-d

p e / d

) /

p e

ne (1019m-3)

H2, R

ax = 3.6 m, B

0 = 1.5 T

figures by J. Miyazawa

0

0.5

1

1.5

2

0.01 0.1 1 10

Weki

n / W

eplt

p* ( = 0.9)

H2, R

ax = 3.6 m

(2.75/1.5)

1/ Plateau P.S.

2.75 T

1.5 T

Role of electric field on radiative collapse

0.0

0.5

no radiation collapse

radiation collapseT

i(keV

) (d)

0.15keV

0

1

2

3

<ne>

(10

19m

-3)

Gas Puffing

(a)

150ms

180ms200ms

0

1

2no radiation collapseradiation collapse

P rad /n

e(MW

/10

19m

-3)

(b)

Prad

~ ne

1 Prad

~ ne

3

-10

-5

0

5 radiation collapse

radiation collapseE

r(kV

/m) (c)

positive Er

negative Er

0

50

100

150

0.0 0.5 1.0 1.5 2.0

no radiation collapseradiation collapse

Inte

nsity

(a.

u.)

time (sec)

(e)

positive radial electric field contributes to avoid radiation collapses

10% Increase Ne puff

increase Ne and ne

More negative Er

decrease Te

increase b*

Recombining impurity

increase Prad

first loop ~ 0.5 sec

second loop~ 0.1 sec

Radiation collapse

increase cooling rate


density limit studies in lhd b. j. peterson, j. miyazawa, k. nishimura, s. masuzaki, y. nagayama, n....

Documents