density limit studies in lhd b. j. peterson, j. miyazawa, k. nishimura, s. masuzaki, y. nagayama, n....
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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 peterson@LHD.nifs.ac.jp page 1
• Limitation by Radiative Collapse
• Evolution of radiative collapse
• Radiated fraction threshold
• Critical edge temperature
• Edge behavior
• Radiation asymmetry
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 peterson@LHD.nifs.ac.jp 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
B.J. Peterson et al. NIFS 20th IAEA FEC EX6-2 2004.11.4 peterson@LHD.nifs.ac.jp page 3
figure by K. Nishimura
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
B.J. Peterson et al. NIFS 20th IAEA FEC EX6-2 2004.11.4 peterson@LHD.nifs.ac.jp page 4
figure by K. Nishimura
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
B.J. Peterson et al. NIFS 20th IAEA FEC EX6-2 2004.11.4 peterson@LHD.nifs.ac.jp page 5
• 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)
B.J. Peterson et al. NIFS 20th IAEA FEC EX6-2 2004.11.4 peterson@LHD.nifs.ac.jp page 6
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
B.J. Peterson et al. NIFS 20th IAEA FEC EX6-2 2004.11.4 peterson@LHD.nifs.ac.jp page 7
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
B.J. Peterson et al. NIFS 20th IAEA FEC EX6-2 2004.11.4 peterson@LHD.nifs.ac.jp page 8
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 peterson@LHD.nifs.ac.jp 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
B.J. Peterson et al. NIFS 20th IAEA FEC EX6-2 2004.11.4 peterson@LHD.nifs.ac.jp page 10
• 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
B.J. Peterson et al. NIFS 20th IAEA FEC EX6-2 2004.11.4 peterson@LHD.nifs.ac.jp page 11
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
B.J. Peterson et al. NIFS 20th IAEA FEC EX6-2 2004.11.4 peterson@LHD.nifs.ac.jp page 12
Experimental data
up
down
up
down
up
down
up
down
inboard
outboard
inboard
outboard
outboard
Tangen
tial view T
op view
)(),( SS
Imaging Bolometers show radiative collapse that is:poloidally asymmetric, toroidally symmetric
Symmetric Hollow Profile
by Peterson and Ashikawa
B.J. Peterson et al. NIFS 20th IAEA FEC EX6-2 2004.11.4 peterson@LHD.nifs.ac.jp page 12
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
Imaging Bolometers show radiative collapse that is:poloidally asymmetric, toroidally symmetric
Symmetric Hollow Profile Asymmetric Collapse
by Peterson and Ashikawa
B.J. Peterson et al. NIFS 20th IAEA FEC EX6-2 2004.11.4 peterson@LHD.nifs.ac.jp page 12
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
Imaging Bolometers show radiative collapse that is:poloidally asymmetric, toroidally symmetric
Symmetric Hollow Profile Asymmetric Collapse
by Peterson and Ashikawa
B.J. Peterson et al. NIFS 20th IAEA FEC EX6-2 2004.11.4 peterson@LHD.nifs.ac.jp page 12
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.
B.J. Peterson et al. NIFS 20th IAEA FEC EX6-2 2004.11.4 peterson@LHD.nifs.ac.jp page 13
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.
B.J. Peterson et al. NIFS 20th IAEA FEC EX6-2 2004.11.4 peterson@LHD.nifs.ac.jp page 14
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 peterson@LHD.nifs.ac.jp 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
B.J. Peterson et al. NIFS 20th IAEA FEC EX6-2 2004.11.4 peterson@LHD.nifs.ac.jp page 17
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
B.J. Peterson et al. NIFS 20th IAEA FEC EX6-2 2004.11.4 peterson@LHD.nifs.ac.jp page 18
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