PPT

磁力管合体における磁気ヘリシティー保存性に関する実
験的検証
小野靖, 河森栄一郎 TS-3 & 4 グループ
東京大学・高温プラズマ研究センター
1. Ion particle
effect on
rec. speed
2. Anomalos
ion heating
hz (t) [mWm]
Progress in TS-3/4 Merging ST Exp.
3
Bz /B//0 =0.5
Bz /B//0 =1.0
Bz /B//0 =1.6
2
Bz /B//0 =2.2
Bz /B//0 =2.7
Bz /B//0 =3.2
1
0
0
1
2
3
4
[d/ri ](t)
High-ß ST
ramp-up
3. Plasmoid
ejection
5
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6
Clear evidence of ion heating by outflow!
Loop top hard X-ray sources
Masuda et al. 1994
Shibata et al. 1995
CONTENTS
Helicity effect of two colliding force-free toroids
Helicity control by co / counter-helicity merging.
1) Global Helicity Effect
----Global bifurcated relaxations (Nucl. Fusion ‘99)
● Taylor relxation to low-ß force-free state.
● New kinetic relaxations
to high-ß state
● Helicity conservation /
annihilation /energy release
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Yokoyama, Shibata Nature ‘95
Shimizu, Tsuneta, Astrophys. J. 93
What will the merging spheromaks with varied K relax to ?
The counterheilcity merging varied K from zero to KTaylor.
Total
helicity
K=0
Large K
K=KTaylor
K／W Scan Experiment
ヘリシティーのバランスしない２個のスフェロマックの合体を用いると（ＭＨＤ
不安定の問題なく）プラズマ全体の磁気ヘリシティーＫ／磁気エネルギーＷを
（０付近でも）自由に設定できる。
スフェロマック＃１（Taylor 状態） K1／W1= a
スフェロマック＃２（Taylor 状態） K2／W2= a
合体プラズマの磁気ヘリシティー
K = K1 - K2 （Counter-helicity Merging のため)
合体プラズマの磁気エネルギー
W = W1 + W2 （ Merging のタイプに無関係）
Tayl or
K /W
(K1  K2) /(W1  W2) 1 K2 /K1 1 a 2




0
(K /W )Tayl or
K1 /W1
1 W2 /W1 1 a 2
２個の初期スフェロマックの磁気ヘリシティー比 K2/ K1
（磁束比F2/ F1=a）を０から１まで変化させれば、 K/W値は
０からTaylor 状態の値 = aの範囲で自由に設定することができる。
Global Effect : How do the merging toroids relax?
Force-Free Loop (Spheromak) vs. High-ß Loop (FRC)
Spheromak
Taylor State
low-ß state
FRC
High-ß
state
Bifurcated Relaxations to Non-Tayor State (FRC)
and to Taylor State: Spheromak
a) Merging spheromaks with Kc>K>0 relax to a Non-Taylor state:
high-ß FRC.
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Bifurcated Relaxations to Non-Tayor State (FRC)
and to Taylor State: Spheromak
b) Merging spheromaks with KTaylor>K>Kc relax to a Taylor state:
spheromak
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KTaylor>K>Kc ⇨ K/W approaches (K/W)Taylor
------ Tayor Relaxation
Kc>K>0 ⇨ K/W approaches 0
------ Non-Tayor Relaxation
K/W (m)
0.08
Taylor State
(spheromak)
Taylor Relaxation to another spheromak
0.06
0.04
Non-Taylor Relaxation
(Annihilation of helicity)
0.02
0
10
(c)
20
30
40
Time (µsec)
Large Increase in Ti ⇨ Relax to High-ß FRC
No Increase in Ti ⇨ Relax to Taylor State Spheromak
Relaxation to an FRC
Relaxation to another spheromak
The largest magnetic energy
release of counterhelicity
reconnection.
If toroidally symmetric and
kinetic (fusion plasma),
relaxation to an FRC.
Energy Loss
Flux conversion
toroidal
magnetic
energy
Spheromak (ß=0-0.1)
If not (solar coronas etc.),
the most violent energy
release to space.
See Y. Ono et al. Phys. Rev. Lett.
76, 3328, ‘99.
How does the merging causes large energy-release?
If merging toroids have Knorm>0.4, relaxation to
min. energy state causes energy loss W(const.)-K.
However, if Knorm<0.2, they relax to another stable state.
If rBt>>ri, Taylor relxation
loses huge energy because
K:conserved, W: relax to K.
Wloss
Magnetic energy of
produced spheromak
huge energy loss
Relaxation to
Spheromak?
W=const., K is varied.
Knorm
Possible Mechanism for the Bifurcated Relaxations:
Poloidal current Ip was maintained or annihilated
depending on Ip loop radius rBt>ri or rBt<ri .
Relaxation to
FRC (high-ß)
Relaxation to
spheromak
(force-free)
Knorm=(K/W) /(K/W) Taylor
Mechanisms for Taylor and new high-ß relaxations
Low-ß relaxation
High-ß relaxation
H
0.6
0.4
0.2
Taylor relaxation
0
-0.2
1
Large i
0.8
K/KTaylor
Time evolutions of normalized
eigenvalues K/KTaylor of
merging spheromaks with
varied initial helicities
(K/KTaylor =1: Taylor state)
p/ Taylor
K/K
Taylor
The regime for FRC
relaxation is wider in Ar
discharge with larger i,
while that for the Taylor
relxation is wider in H
discharge with smaller i.
Small i
0.8
p/ Taylor
TS-4 large ri (~i ) exp.:
RTS-4≈3RTS-3
1
Ar
Taylor relaxation
0.6
0.4
FRC relaxation
0.2
0
-0.2
0
10
20
time [ s]
30
40
(a)
Taylor状態へ緩和
K/KTaylor
0.8
0.6
 /
0
テーラー状態へ緩和する限
界となる境界値/ 
は
S*が大きいほど広範囲.
Taylor
1
0.4
FRCへ
緩和
0.2
0
回転が止まる範囲と
Taylor 緩和する範囲が一致
V / VA
：緩和前の固有値(j/B)
 y
：緩和前の固有値
(=jp/Bp)
S*：プラズマ径/イオンスキン長
10
n= 1
n= 2
n= 3
1
(b)
V / a
=0.1k V A
n=3
n=2
0.1
n=1
0.01
0
2
4
6
S*
8
10
CONCLUSIONS
Helicity Effects on Reconnection/Merging
were studied using co/ counterhelicity merging
with varied K but equal W
Global Effect ------- Bifurcated relaxations
1) Two merging force-free plasmas relax either to
another force-free plasmas or to high-ß FRC,
depending on whether initial K>Kc or K<Kc .
2) The threshold value Kc is dermined by that where
ri=rBt, indicating the high-ß relaxation is caused
by some kinetic effect.
3) The largest energy release was observed in
counterhelicity reconnection with ri < <rBt.
TS-4 ST/ FRC Merging Device
Operation:
1) FRC merging formation
2) High-ß ST formation by FRC
3) Boundary study of CTs/STs
R=0.4-0.55m, A=1.2-1.9,
Bt0<3-5kG, Ip≈300kA

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