電場と回転の能動的制御小形ヘリアック装置でのバイアス実験から

C01-3
｢プラズマ燃焼のための先進プラズマ計測｣シンポジウム 2005/2/2
電場と回転の能動的制御
< 小型ヘリアック装置でのバイアス実験から >
東北大学大学院工学研究科
北島純男
Introduction
背景
! H モード遷移理論によると、L-H 遷移においてポロイダルマッハ数 -Mp = 1 - 3 近
傍でのイオン粘性の極大値が重要な役割を担っている。
! ポロイダルマッハ数 -Mp = 1 近傍での電場と回転の詳細を調べることによって、
L-H 遷移におけるトカマクおよびステラレータ共通の性質を研究することがで
きる。
目的
! 東北大学ヘリアック装置での電極バイアスプラズマの特徴の調査
! 電極電流制御によるポロイダル回転速度の能動的制御の可能性
! ポロイダル回転のための J x B 駆動力より、イオン粘性を見積もる
! 実験により見積もられたイオン粘性と理論値（新古典輸送理論）との比較
Tohoku University Heliac (TU-Heliac)
Machine and Plasma Parameters
Number of field periods
4
Major radius
48 cm
Average radius of the last closed
flux surface rLCFS
7 cm
0.3 T
Magnetic field on axis B0
Rotational transform
1.54 - 1.71
Well depth
3%
18.8 kHz
RF frequency fRF
35 kW
RF output power PRF
Residual gas pressure
~ 5 x 10-6 Pa
Bird's-eye view of the Tohoku University Heliac
Experimental set-up
Working gas
He (1.2×10-2 Pa)
Electron density on axis Ne0
6×1011 cm-3
Electron Temperature on axis Te0
~ 25eV
RF frequency fRF
18.8 kHz
The hot cathode is inserted horizontally from the low field side.
Negative bias voltage is applied against to the vacuum vessel.
0
E
(a)
-0.2
0
(b)
-3
E
Typical time evolution of the plasma
parameters with a constant voltage biasing
I (A) V (kV)
Characteristics of biased plasma with Constant Voltage (1)
E (kV/m)
r
cm )
0.39
3 (d)
2
1
0
30
20 (e)
10
0
0.4
0.2 (f)
-2
e
n l
(10
s
s
(a.u.)
H0
n
The biased plasma shows the same characteristics
as the H-mode in large tokamaks and stellarators.
_
~
I /I
f
_
~
eV /T
e
! Normalized impurity light emission (Hα) decreased.
0.65
13
! Fluctuation level of floating potential eVf / Te
Fluctuation level of saturation current Is / Is
Suppressed.
0.75
-2
e
! Line density increased by a factor of 2 ~ 3.
ρ = 0.85
-1 (c)
T (eV)
! Strong negative Er and Er shear were formed.
0
0
0.2
(g)
0.1
0
2 (h)
1
0
0
2
ρ = 0.39
ρ = 0.39
ρ = 0.39
4
6
Time (m s)
8
10
Characteristics of biased plasma with Constant Voltage (2)
! The linear gradient after the transition was
about twice larger than that before the
transition.
This suggests the energy confinement time
increases by a factor of 2.
-2
Before Transition
After Transition
eV cm
5
4
14
e
e
# The electrode voltage actively changed.
# The stored energy: the product of the density and
the electron temperature.
# The input power: the product of the electrode
voltage and electrode current.
# The input power of the low frequency joule heating
was kept constant.
n L T ( 10
The stored energy was plotted against the hot
cathode input power.
)
Dependence of the stored energy on the input power through the hot cathode
3
2
0
500
1000
1500
V I (W )
E
E
PInput = PJoule heating + PHot Cathode
PJoule heating = constant
This observation also indicates the same characteristics as the H-mode in large
tokamaks and stellarators.
Characteristics of biased plasma with Current Sweep
Typical time evolution of the plasma parameters with current sweep
-2.5
-120
-110
-100
VE (V)
-90
(b)
H
I (A)
E
E (kV/m )
0.67
-2
-2
cm )
r
0.28
3
13
f
B
A
ρ = 0.87
0.80
0
e
(d)
(10
n l
L
Transition
E
V (V)
H-mode
(c)
e
H-mode
L-mode
-200
s s
I /I
-2
~
A
ramp down
-2
-100
eV /T
B
~ -
I E (A)
-1.5
(a)
-4
0
e
! The electric fields in outer region decreased
gradually according to the electrode current IE.
! The improved mode continued until ~7 msec
# The line density was sustained high level.
# The floating potential fluctuation level
The saturation current fluctuation level
suppressed.
! Plasma shows negative resistance between A
and B.
! The electrode current IE bifurcates to an
electrode voltage VE. -1
L-mode
0
T (eV)
The electrode current IE was kept constant at ~ 4 ampere from
0 to 5 msec and then ramped down from 5 to 10 msec
0
20
10
0
0.4
0.2
0
0.2
0.1
0
(e)
(f)
ρ = 0.54
(g)
ρ = 0.54
0
2
4
6
Time (ms)
8
10
Feasibility study of active control of driving force
with current sweep (1)
Dependence of radial electric field Er on the electrode current IE
Negative resistance region
-2
-1
H mode
L mode
r
This indicates the capability of active control
of the driving force for the poloidal rotation.
-3
E (kV/m)
! Radial electric field Er (except around the
magnetic axis) was almost linearly
proportion to the electrode current IE in
both the current ramp up and ramp down
cases.
L-H transition
H-L transition
ρ = 0.56
0
0
-1
-2
I (A)
E
-3
Feasibility study of active control of driving force
with current sweep (2)
Measurements of the fluctuation level of ion saturation currents by
a multi-Langmuir probe
Demonstration of active control of the J × B driving force for the poloidal rotation
by externally controlled electron injection
! The frequency range spread from 80 kHz to 130 kHz.
! All signals were kept a similar time evolution and had a phase shift according to the
poloidal locations.
! The estimation of the poloidal rotation velocities from the phase shift
The rotation velocities were widely changed by the actively controlled electrode current
sweep and agreed with the E × B drift velocities.
(km/s)
15
10
V
ph
This also indicates the capability of active control of the
driving force for the poloidal rotation.
probe 2
5
s
probe 3
I
probe 4
0
probe 5
0
10
20
30
Time ( µ s)
40
50
0
5
10
15
-E /B (km/s)
r
This discrepancy can be eliminated
by the ion diamagnetic drift velocity.
Estimation of ion viscous damping force (1)
! Momentum Balance Equation in steady state
(1) J x B
(2) viscosity
(3) friction
IE
(1) < J ρ > B0 ⇒ B0 I E pi −1ε −2 , < J ρ >=
2π < r > L
π 2πL
r
t
π
<
B
⋅
∇
⋅
i >
(2)
⇒ M p ( M p + 2 M p2 + 2M p4 ) exp( − M p2 ) ;
ΘB0
Rozhansky model(1)
2
ν in R0 q
q
2
1
+
2
(3) (1 + 2q )ni miν inVθ ⇒
M p;
2
π q
vth
2
Dam ping force
r
t
< B ⋅ ∇ ⋅π i >
< J ρ > B0 = −
− (1 + 2q 2 ) ni miν inVθ
ΘB0
6
4
Ion viscosity + Friction
2
Friction
Ion viscosity
0
0
-2
-4
M
-6
-8
p
local maximum exists for Mp
proportional to Mp
t
< Jρ > ; surface averaged radial current density, B0 ; magnetic field on axis, π i ; ion viscosity stress tensor, Θ =
Bθ / Bφ, q ; safety factor, νin = < σcxui > nn, Vθ ; surface averaged poloidal flow velocity, L ; length of the magnetic
axis, ε ; toroidal ripple, Mp = Vθ / Θvth, vth = (2Ti / mi)1/2, R0 ; major radius
(1) V. Rozhansky and M. Tendler: Phys. Fluids B 2 (1992) 1877.
Estimation of ion viscous damping force (2)
The ion viscous damping force opposing to the poloidal rotation was estimated from the
externally controlled driving force for the J x B poloidal rotation, and compared with the
neoclassical predictions.
! The measured damping force had a local maximum at the poloidal Mach number
Mp ~ - 1.5 and agreed well with the neoclassical predictions.
(We assumed that the ion temperature Ti = 0.2Te.)
! The plasma showed the negative resistance characteristics (closed symbol )
in the region where the ion viscous damping force had a local maximum.
T = 1 eV
i
6
Driving force at the
negative
resistance
region
20 eV
4
Experim ent
2
r (m m) T (eV)
i
100
3.71
-1.5
-2
-2.5
-120
0
0
-2
-4
M
L-mode
-1
1/2
2π L
e
π
B
0
E
-1
I p ε
t
-2
i
4 eV
I E (A)
T = 0.2T
-6
p
-8
-10
H-mode
-110
-100
VE (V)
-90
Estimation of ion viscous damping force (3)
Effect of collisionality to the damping force
In the high Mp region (-Mp > 3), the dominant damping force to the poloidal rotation is the
friction to neutral particles.
! The negative resistance region can be seen at all filling gas pressure cases.
! The measured viscous damping forces had a local maximum at -Mp ~ 1.5 at all cases
and agreed well with the neoclassical predictions at low pressures, i.e., in case of lower
collisionality.
! Regions of the negative resistance (1< -Mp< 2) are independent on collisionality,
although the electrode parameters were quite different.
T = 0.2T
i
8
-1 -2
-2
Pa)
0.7
1.2
2.7
5.4
-3
(b)
1.2
p=0.7x10
-2
2π L
E
6
4
1/2
B
0
p (10
2.7
-2
p (10 Pa) T (eV)
π
E
I (A)
-2
5.4
I p ε
-1
(a)
e
i
0.7
1.2
2.7
5.4
2
negative
resistance
ρ = 0.54
-4
-140 -120 -100 -80
V (V)
E
-60
0
0
-2
-4
M
p
-6
3.7
3.7
3.1
2.8
-8
ま
と
め
! 東北大学ヘリアック装置において、定電圧、電流走引、両バイアスモードで
閉じ込め改善モードへの遷移に成功した。
! 電極電流走引バイアスによりポロイダル回転のための J × B 駆動力を制御
することができた。
$ 電極電流電圧特性曲線に負性抵抗領域が観測された。
! ポロイダル回転のための J x B 駆動力より、イオン粘性を見積もった。
$ イオン粘性(実験値)はポロイダルマッハ数 - Mp ~ 1.5 で極大値を持ち
（衝突周波数に依存しない）、理論値（Rozhansky model）と一致する
$ イオン粘性(実験値)の極大値近傍でプラズマは負性抵抗性を示す。
以上より、L-H 遷移はイオン粘性の極大値付近で起きていることが示唆されて
いる。
Dependence of the measured ion viscous damping force
on the poloidal Mach number
Estimation of ion viscous damping force
Subtraction of the friction from the measured driving force
! The solid line: the ion viscous damping force of the
!
!
!
4
T = 0.2T
i
e
experiments
negative resistance
Rozhansky
Shaing
ρ = 0.5
3
Viscosity
!
Rozhansky1) model without the friction term
The broken line: the ion viscous damping force of the
Shaing2) model which includes a gradient of ion
temperature and that of pressure and helical ripples
These viscosities had a local maximum in the region
1 < -Mp < 3.
The measured viscous damping forces had a local
maximum at -Mp ~ 1.5 and agreed well with the
neoclassical predictions.
The
plasma
showed
negative
resistance
characteristics (closed symbols) in the region where
the ion viscous damping force had a local maximum
in 1 < -Mp < 3.
2
1
0
0
-2
-4
M
-6
p
This suggested that the L-H transition occurred near the local maximum in ion
viscosity which originates from a toroidal ripple and the local maxima which
originate from helical ripples may not affect the L-H transition.
[1] V. Rozhansky and M. Tendler, Phys. Fluids B 4, 1877 (1992).
[2] K. C. Shaing, Phys Fluids B 5, 3841 (1993).
-8
Effect of the Fourier components on the ion viscosity (1)
εmn (r / R0 = 0.05)
Well
rax
(cm)
a
10
Z (cm )
Magnetic configurations in Heliac can be changed
widely by selection of coil current ratio.
! Magnetic Fourier components
(0,1)
(%)
(1,0)
(1,1)
-0.99
-0.09
-0.051
-0.060
7.5
6.6
-0.11
-0.11
-0.049
-0.056
7.9
6.8
2.3
-0.13
-0.040
-0.051
8.4
6.2
4.1
-0.16
-0.039
-0.050
1
axis
7.7 cm
o
(c-1) Standard
(c-1) Outw ard
8
8.5
Magnetic axis position (cm)
(c-2) O utward
5
0
-5
-15
-15 -10 -5
7.5
(b-2) Standard
axis
7.9 cm
Hot C athode
axis
8.4 cm
0
5
r (cm )
0
o
-5
-10
0.5
θ = 90
0
10
Z (cm )
-2
Viscosity peak (10 )
axis position
1.5
θ = 180
15
-15
! Dependence of viscosity peak on the magnetic
o
5
-10
These Configurations have similar profile for rotational transform.
θ = 270
-5
15
-15
Z (cm )
6.3
θ =0
Inw ard
o
0
10
7.3
(a-1) Inw ard
5
-10
depth
(cm)
Center Conductor
C oil (a-2)
15
10 -15
15 -10 -5
0
5
r (cm )
10 15
Effect of the Fourier components on the ion viscosity (2)
Estimation of poloidal ion viscosity
1.5
0.5
F
F
0
CAL
1
EXP
Rax
Rax
Rax
Rax
(b)
-2
(10 )
2
F
-2
Viscosity peak (10 )
F
EXP
-2
(10 )
Rax = 7.7 cm
Subtraction of the friction term from the poloidal driving force
Rax = 7.9 cm
5
Rax = 8.4 cm
! The theoretical ion viscosities and the
(a)
Inward
measured ion viscosities had local maxima
4 negative
ρ = 0.53
resistance
on all configurations.
Standard
3 region
0.54
! Negative resistance characteristics (closed
2
symbols) around the ion viscosity
Outward
0.52
peaks.The estimated peak values of
1
viscosity agreed well with theoretical
0
predictions.
1.5
7.3cm
7.5cm
7.9cm
8.4cm
1
0.5
M = 2.4
CAL
7.5
=
=
=
=
8
8.5
Magnetic axis position (cm)
0
p
0
-2
-4
M
-6
p
-8
-10

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