Density Limit Studies in LHDDensity Limit Studies in LHD B. J. Peterson, J. Miyazawa, K. Nishimura,...

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 ConferenceNovember 4, 2004

Vilamoura, Portugal

Topics

• Motivation

• Comparison with Sudo scaling

• Maximum achieved densities

• Gas puff

• H2 pellet

• Effect of boronization

• Confinement degradation

• Summary

• Limitation by Radiative Collapse

• Evolution of radiative collapse

• Radiated fraction threshold

• Critical edge temperature

• Edge behavior

• Radiation asymmetry

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

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

<Ne>

exp.

(1020

m-3

)

<Ne>Sudo scaling

(1020m-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

<Ne>

exp.

(1020

m-3

)

<Ne>Sudo scaling

(1020m-3)

0.25*(PB)0.5(a2R)-0.5

@ Wp-max

figure by K. Nishimura

Motivation• Fusion reaction rate goes as density squared RDT ~ n2<σν>

• Tokamak density is limited by current disruption and scales with plasma current density:

nTok ~ Ip/a2 (Greenwald) but has weak power dependence

• Helical devices have radiative density limit 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 than 1.6 times the Sudo limitB.J. Peterson et al. NIFS 20th IAEA FEC EX6-2 2004.11.4 [email protected] page 2


Peak Sustained Density

05

101520

<ne>

1019

m-3

Gas

s puf

f (a.

u.)

Time (s)

<ne>

gass puff

#46289

05

1015

P NB

Is (M

W)

Gas

s puf

f (a.

u.)

Time (s)

0.00.20.40.60.81.0

CII

I, O

V (a

.u.)

Gas

s puf

f (a.

u.)

Time (s)

CIII

OV

00.20.40.60.8

0.02.04.06.08.0

0.0 0.5 1.0 1.5 2.0 2.5

Wp (M

J)

P rad (M

W)

Time (s)

Wp

Prad

Rax = 3.75 m, B = 2.64 T

by K. Nishimura

• 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, 160-180 keV)

• Prad/Pin < 25%

• Plasma collapses after reduction of beam power




Higher densities with H2 pellets

05

10152025

<ne>

1019

m-3

Gas

s puf

f (a.

u.)

Time (s)

<ne>

gass puff

#47492

05

1015

P NB

Is (M

W)

Gas

s puf

f (a.

u.)

Time (s)

0.00.51.01.52.0

CII

I, O

V (a

.u.)

Gas

s puf

f (a.

u.)

Time (s)

CIIIOV

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 (M

J)

P rad (M

W)

Time (s)

Wp

Prad

by K. Nishimura

• H2 pellet into He gas puffing

• Core fuelling @ ρ ~0.7

• transient line-averaged densities of > 2.2 x 1020/m3

• Pin ~ 10.5 MW (3 NBI, -ion, 160-180 keV)

• Prad/Pin < 35%

• Wp begins to decay then collapses after reduction of beam power

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 vessel with diborane (B2H6)

• Effective in wall conditioning leading to extension of density 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

figure by J. Miyazawa

Evolution at Radiative Collapse

0

4

8

0

200

400

n e (1019

m-3

) Wp_dia (kJ)

#43383 : H2, R

ax = 3.6 m, B

0 = 1.5 T

(a)

0

2

4

0

2

4

P rad (M

W) P

abs (MW

)

(b)

0

1

0

1

CII

I / n

e (arb

.) OV

/ ne (arb.)

(c)

0

1

2

0

0.2

0.4T e0

(keV

) Te09 (keV

)

(d)

0

2

4

0

2

4

1.8 1.9 2 2.1 2.2 2.3

(Pra

d'/ P ra

d) / (n

e' / n

e) Ne L (3669) / N

e L (4119)

time (s)

(e)



In LHD Radiative Collapse occurs above a certain Radiated Power Fraction

Collapse

No collapse

mixed

• Collapse occurs for Prad/Pabs> 30%

• Prad does not include divertorradiation which is hard to estimate due to helical asymmetry.

•Prad/Pabs = 100% in cases with large core 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 power 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 ra

d (MW

)

ne (1019 m-3)

#43383 (t = 0.75 - 2.20 s)

Prad

~ ne1

Prad

~ ne3

t = 0.8 s

t = 2.1 s

t = 2.2 s

Quantification of thermal instability onset


∫= dVTLnnP eZeZZ )(


Edge Temperature threshold for density-limiting radiative collapse in LHD

○ Therefore a certain edge threshold temperature exists for the onset of the thermal

instability (but not necessarily at ρ = 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 (k

eV)

ne (1019 m-3)

Te09

~ 0.15 keV

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

T e (keV

)

ne (1019 m-3)

Rax

= 3.6 m

Rax

= 3.75 m

whe

nx

= 3

○ x = 3 is correlated with Te09 （ρ = 0.9)= 150 eV independent of the input power, density (right plot), magnetic configuration and gas (left plot)

ρ = 0.1H

He

ρ = 0.9

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



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

• Radiation asymmetry accompanies onset of thermal instability

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

• Ion saturation current in divertordecreases

• Thermal instability begins first in OV

• CIII coincident with Prad

•Indicates C as dominant impurity

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

Divertor Leg

Main Plasma

1

16

Vacuumvessel wall

0.5 m

Bolometerchords

ρ = 1

Ergodic region

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

Tangential view

Top 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

Tangential view

Top view

)(),( ρθρ SS =


Symmetric Hollow Profile

by Peterson and AshikawaB.J. Peterson et al. NIFS 20th IAEA FEC EX6-2 2004.11.4 [email protected] page 12

Experimental data

0

0.04

0.08

0.12

0.16

0 0.5 1 1.5

ρRadiation power density (arb.)

Model

S(ρ)


up

down

up

down

up

down

up

down

inboard

outboard

inboard

outboard

inboard

outboard

Tangential view

Top view

)(),( ρθρ SS =


Symmetric Hollow Profile Asymmetric Collapse


Experimental data

0

0.04

0.08

0.12

0.16

0 0.5 1 1.5

ρ

Radiation power density (arb.)

Model

S(ρ)

0)( =θF Experimental data


up

down

up

down

up

down

up

down

inboard

outboard

inboard

outboard

inboard

outboard

inboard

outboard

Tangential view

Top view

)](1[)(),( θρθρ FSS +⋅=

( )500 2/))cos(1()( θθθ −+=F


Symmetric Hollow Profile Asymmetric Collapse


Experimental data

0

0.04

0.08

0.12

0.16

0 0.5 1 1.5

ρ

Radiation power density (arb.)

Model

S(ρ)

0)( =θF Experimental dataModel °−= 1500θ


Symm

etric radiationw

ith gas puff

AXUV Diode Arrays in semi-tangential cross-section

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

Asym

metric

collapse

outin

in out

in out

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

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

[email protected]. Peterson et al. NIFS 20th IAEA FEC EX6-2 2004.11.4 page 13


0.4

0.6

0.8

1.0

1.2

1.4

0.01 0.1 1 10

τ Eexp /τ

EISS9

5

νp* (ρ = 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

χ eeff (m

2 /s)

νp*

Te (keV)

~ Te4.5

~ Te1.5

~ Te0.5

Rax

= 3.6 m, B0 = 1.5 T, H

2 ρ = 0.5

Confinement degradation at high densityτE compared with ISS95 declines in high-density (high-collisionality)

regime, however χeeff 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 χe

eff ∝ Te0.5 at low Te (corresponds to τE ∝ 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 returningto 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:

peplt(ρ) = 3.4Pabs

0.51exp(-(1.5ρ2+1.5ρ10))

This can be integrated over ρ to give Weplt

At low B the dgradation of the We kin compared to themodelin 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

ρ = 0.6 ρ = 0.8ρ = 0.9

(-d

p e / d

ρ) /

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

νp* (ρ = 0.9)

H2, R

ax = 3.6 m

(2.75/1.5)

1/ν 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(k

eV) (d)

0.15keV

0

1

2

3

<ne>

(1019

m-3)

Gas Puffing

(a)

150ms

180ms200ms

0

1

2no radiation collapseradiation collapse

P rad /n

e(MW

/1019

m-3)

(b)

Prad

~ ne

1 Prad

~ ne

3

-10-505 radiation

collapseradiation collapseE r(k

V/m

) (c)positive Er

negative Er

050

100150

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 νb*

Recombining impurityincrease Prad

first loop~ 0.5 sec

second loop~ 0.1 sec

Radiation collapse

increase cooling rate



Density Limit Studies in LHDDensity Limit Studies in LHD B. J. Peterson, J. Miyazawa, K. Nishimura,...

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Transcript of Density Limit Studies in LHDDensity Limit Studies in LHD B. J. Peterson, J. Miyazawa, K. Nishimura,...