Joint Conference of 12th International Toki Conference and 3rd General Scientific Assembly of Asia Plasma Fusion Association(ITC-12 & APFA’01)
in Toki, JAPAN, December 11-14, 2001

Study of Time Evolution of Toroidal current in LHD
Kiyomasa Y. Watanabea, Satoru Sakakibaraa, Hajime Sasaob, Michael Yakovleva,
Kiyohiko Nishimuraa, Sadayoshi Murakamia, Noriyoshi Nakajimaa, Hiroshi Yamadaa,
Kazushige Nariharaa, Ichihiro Yamadaa, Kazuo Kawahataa, Tokihiko Tokuzawaa,Kenji Tanakaa, Katsumi Idaa, Shigeru Moritaa, Osamu Kanekoa, Katsuyoshi Tsumoria,Katsunori Ikedaa, Yoshirou Narushimaa, Tomohiro Morisakia, Akio Komoria, LHD
experimental groupa and LHD device engineering groupaa) National Institute for Fusion Science, Toki, Gifu 509-5292, Japanb) Japan Atomic Energy Research Institute, Naka, Ibaragi, 311-0193, Japan

Tangential View of LHD

Toroidal Current --- Observation ---ITC-12 & APFA’01 WATANABE K.Y. et al

In principle
Toridal current for plasma confinement
is not necessary in Heliotron devices!!

Observation in LHD
In NBI discahrge
More than 100kA of toroidal current isobserved.
B0=0.75~2.9T, H2, RaxV=3.6/3.75m,
Ip= -30~110kA, ∆ι(a) = -0.04~0.1.

No active control of one turn voltage

Toroidal current affects MHD equilibrium, stability and Transportin Heliotron devices
Determination of Driving Mechanism; Important!!
Candidates of Current Driving Mechanism;
Ohkawa Current & Bootstrap Current

ITC-12 & APFA’01 WATANABE K.Y. et al

Outline of talk
1. Properties of Bootstrap Current in Heliotron devices
2. Experimental Observation of Bootstrap current in LHD(including comparison results between experimental dataand theoretical prediction)
3. Observation of MHD activity and rational surface(A MHD activity indicates information of centralrotational transform)
Î Information leads to determination of the current
profileITC-12 & APFA’01 WATANABE K.Y. et al

Properties of Bootstrap Current in Heliotron devices (1)- profile TOKAMAK vs LHD (Heliotron) LHD

IBSC-LHD/IBSC-TOK~0.5

equiv. TOKAMAK

22

3.5

3.5
1.5

bs

1.5
(f /f )Gt cbsqBS

0.5
GLHDbs1bs

2t c

TOKAMAK(f /f )G , Gbst cbs(f /f )G , G22.5qGt c

1

10.5

t c

t c

f /f , q

2.5
f /f

3

1.5

3f /f , q

1.5

00

0.2

0.4

0.6

1

1.5
0.5

1(f /f )Gt c

0.5

bs

0.5

f /ft c

bs

0.8

1

0

0

0

0.2

0.4

0.6

0.8

10r

r

0
1.4

2

-0.5

0

0.2

0.4

0.6

0.8

1jBS ~ (ft/fc)*Gbs*dP/ds
in banana(1/ν)-regime
e0.8

ne

1

0.6e

･ BS current profile in LHD is much broader than
TOKAMAKcomes fromDifference of Radial profile of q and geometricalfacter between TOKAMAK and LHD

1Te

0.4

0.5

0.2
000.2

0.4

0.6
r

0.8

10-dP/ds

ρ (minor radius)

1.2-dP/ds

1.5
T , n (A.U.)

j (A.U.)424

ITC-12 & APFA’01 WATANABE K.Y. et al

Properties of Bootstrap Current in Heliotron devices (2)- Dependence on Magnetic Axis Configuration jBS ~ (ft/fc)*Gbs*P*(n'/n+a1Ti'/Ti+a2Te'/Te)
a1, a2 ~O(+0.1), Gbstok=Ip/2πι
0.8
tokbs

0.6

bs

Geometric factor, G /G

Geometric Factor (BS current)
strongly depends
on Magnetic Axis Position!!

ρ =0.5

0.4
0.2

Note!!

0-0.2
-0.4
3.5

Magnetic Axis goes
torus-outwardly =>Device center
3.6

3.7

3.8

3.9

4

Magnetic axis position, Rax

V

4.1

(m)

Geometrical Factor for LHD in 1/ν-regime
Standard configuration

Geometric factor significantly
decreases and changes the sign.

ITC-12 & APFA’01 WATANABE K.Y. et aldt

+ ∑ M iP
idI idt

MeasureIp: observed plasma current
INI: non-inductive plasma current
Vloop: one-turn voltage(self-induced part isdominant in LHD.
When dIp/dt=0, Vloop~0)
Ii: increment of current in helicalcoils, vacuum vessel and so on.
Mip: Mutual inductance between icomponent and plasma.
Lp: self-inductance of Plasma
Rp: resistance of plasma(Tokamak neoclassical used here )

50
40
30
20
100-10I

V0.2
voltage (V)dI p

L dI /dtloopp

Ip

NI

sum M dI /dt

p

i-P

i

0.1
0-0.1
-0.2

sum M dI /dtiM

MdI /dt

Mi-P

0.2
voltage (V)Vloop = − L pHI-P0.1

dIHM-P

HI/dt

HM

dI

HO-P/dt

HO0-0.1

Helical coil

-0.2
0.2
voltage (V)R p I p = Vloop + R p I NI

Calculatetoroidal current (kA)Time evolution of toroidal current
and the estimation of non-inductive current

M

0.1

dI /dtIV-P

IVM

dI /dtIS-P

M

IS0-0.1

Poloidal coil

-0.2
00.5

1

1.5

2 2.5time(s)3dI /dt

OV-P

3.5

4OV

ITC-12 & APFA’01 WATANABE K.Y. et al

Experimental result for non-inductive current (1)- Wp and collionality dependence in NB balanced injection ν < 0.7 @ ρ=0.8*eν = 1.5 @ ρ=0.835

10ν @ ρ=0.8*e*e30plateau-regime

25

Collisionality

Non-Inductive current (kA)

40

20
15

11/ν-regime

10
5
00.1

050

100

150200

250

050

100

150

200

W (kJ)p

W (kJ)
pR

Vax=3.75m, 1.5/1.52T, Hydrogen∆ι(a)˜0.02(20kA@1.5T)

NB balanced Inj. Total NBI power = 2~3.7MW

Observed toroidal current
increases with Wp increasing.
Collisionalty increses=> Observed current decreases

Probable candidate of current driving mechanism;
Bootstrap Current

250

ITC-12 & APFA’01 WATANABE K.Y. et alComparison result with theoretical prediction- Wp dependence Experiment
Theo. Pred.(LHD config.)
Theo. Pred.(equil. LHD A , q same)p
Theo. Pred.(equil. straight hel. ε , q same)

Theoretical calculation of BS current
1. SPBSC code (ref K.Y.WATANABE et al,

2. ne-bar and Te are used by measurement.

ne profile is assumed as ~(1-ρ8)
3. Zeff=2, Te = Ti are assumed.

40h3020pI (kA)

Nuclear Fusion 35 (1995) 335)
･ BS current calculation with the consistent
MHD equilibrium･ Connection formula from 1/ν to P-S collisional
regime･ BS current is estimated based on momentum
method for asymmetricdevices proposed by K.C Shaing et al.
( Phys. Fluids 26(1983)3315,
Phys. Fluids 29(1986)521 )

100-10050

100

150200250

W (kJ)
pR

Vax=3.75m, 1.5T, Hydrogen

NBI balanced Inj. Total NBI power = 3.5~3.7MW･ Calculated result agrees with experimental data in Wp dependence.
･ Direction and Amplitude of theoretical prediction also agrees.

ITC-12 & APFA’01 WATANABE K.Y. et al

Experimental result for non-inductive current (2)- Magnetic axis configuration dependence in NB “balanced” injection 1035

Istedy(kA)

25

3.75m
3.9m
4.0m
4.05m

νe* @ ρ=0.8

30

3.75m
3.9m
4.0m
4.05m

120
15
100.1
05

0.5

1
n0-5
00.5

1
n1.5

219-3

2.5

T (10 m keV)e_bar e03

∼β

Co-Injected power is larger
by 20% than Cntr-one.
Co/ 2.0MW, Cntr/ 1.6MW

1.5

219-3

2.5

T (10 m keV)e_bar e0RaxObservation･ Rax goes torus-outwardly =>･ Observed toroidal current
decreases･ NB injection Condition
keeps same during above experiment sequence in magnetic axis changing.

3

ITC-12 & APFA’01 WATANABE K.Y. et alComparison result with theoretical prediction- Magnetic Configuration dependence Pick up data with almost same
beta value
β=0.33~0.41%()
0.8~1.9e19m-3, Te0=0.8~1.6keV

35(10 m )15stedy5I00.51n1.5219-3

2.5T (10 m keV)e_bar e0

31.5

101

1

0.5

0.1
1/ν-regime-3
1910

e_bare_bar(kA)

stedy

I

20

25

15-50nExperimental ResultBS Theory

30

20

100

100
3.7

5

Observation･ Rax goes torus-outwardly=> toridal current decreasesν @ρ=0.8
e*

3.8

3.9

40.01
4.1

R (m)

0-5
3.7

ν*(kA)

25

3.75m
3.9m
4.0m
4.05m

n30

235ax

3.8

3.9
R (m)

44.1ax=> ･ Agrees with BS behavior predicted in theory.

･ Cntr-Direction current not observed clearly!!
Theoretically predicted in torus outward magnetic axis shift configuration

ITC-12 & APFA’01 WATANABE K.Y. et al

MHD activity and rational surface (1)In LHD “Magnetic axis torus-inwardshift” configuration (Rax=3.6m),
Even in low beta regime (β>0.3%),m/n=2/1(Magnetic fluctuation)
is observed generally.
m: Poloidal mode number
n: Toroidal mode number
Rational surface of ι=1/2 is located at
ρ=0.5 in Rax=3.6m config.(vacuum).

Remark!!
In high beta discharge with highpositive toroidal current(0.75T, Rax=3.6m, β~2%, δι(a)~0.04
due to Ip)

m/n=2/1(Magnetic fluctuation)
suddenly disappears.

ITC-12 & APFA’01 WATANABE K.Y. et al

MHD activity and rational surface (2)m/n=2/1 mode
100~-5b /B (10 )
θp

500ι

0D

I

0.4
0.2
0-0.2
-0.4

D @ι=0.5(ρ~0.5)
I

0.7
0.6
currentless is assumed
0.5
0.4
0.3
0.2
1.4 1.6 1.8 2 2.2 2.4 2.6 2.8time(s)3Theoritical Analysis withCurrentless assumption(MHD equilibrium is calculated usingpressure profile obtained bymeasurement)･ iota=1/2 surface exists (ι0<0.5)
both before and after disappearance of
2/1 mode.
･ The plasma after disappearance of
2/1 mode is more Mercier unstable
than that before disappearance of
2/1 mode
Most probable explanation of 2/1 mode
disappearance･ Rational Surface (ι=1/2)
disappears.

Compare between time trace of central rotational transform
based on calculation and MHD activity

ITC-12 & APFA’01 WATANABE K.Y. et al

Basic Equation for Time Evolution Analysis of toroidal current profile

BS current; calculated by SPBSC code
Ohkawa current; cal. by MCNBH code (considering orbit and CX loss)

ITC-12 & APFA’01 WATANABE K.Y. et al

Calculation result of toroidal current evolution
302004#16964
w

p

100

n2T (0)

1e50

e000

1234

･ Co dominant-NB Injected･ Non inductive current is almost
same with time.
･ Ohkawa current is decreasing
ne gradually increases･ BS current is increasing with time.
Wp gradually increases,
central ne profile hollow => flat
central Te profile => peaked

Ip-exp

IBS+Iohkawa

3Current(kA)

150

Ip-cal

25
20
15
105
000.5

1

1.5

2t(s)

2.5

Ohkawa-current
70

3.5

4BS-current
70

1.4s
2.2s
2.6s
3.0s

60
50
40

60

40
30

20

20

10

10

0

00

0.2

0.4

0.6

0.8

1.4s
2.2s
2.6s
3.0s

50

30

-10

3

1-10

0

0.2

0.4

0.6

0.8

1

ITC-12 & APFA’01 WATANABE K.Y. et alComparison between time traces of m/n=2/1 magnetic
fluctuation and calculated central rotational transform
70

0.7m/n=2/1 mode
0.6~-5b /B (10 )

0ι0ι

0
0.7
0.6
0.5
0.4
Cal. result
0.3
with toroidal curret
0.2
0.7
0.6
currentless is assumed
0.5
0.4
0.3
0.2
1.4 1.6 1.8 2 2.2 2.4 2.6 2.8time(s)ιp50

Result!

current density

100
θ

1.2s
2.2s
2.6s
3.0s

60

0.5
1.4s
2.2s
2.6s
3.0s

0.4

0.3

350
40
30
20
100-10

0

0.1

0.2

0.3

ρ

0.4

0.5

0.6

0

0.2

0.4

0.6

0.8

1ρ

1.2s<t < 1.8s
･ peaked current profile due to Iohkawa
1.8s < t <2.7s･ flat current profile (Iohkawa decreases, IBS increases)=> ι=1/2 surface appears
2.8s < t･ peaked current profile due to IBS (peaked pressureprofile) => ι=1/2 surface disappears

Timing, when m/n=2/1 disappears, is close to theoretically
predicted timing when ι=1/2 rational surface disappears.

ITC-12 & APFA’01 WATANABE K.Y. et al

Summary
We analyze the non-inductive toroidal current in LHD experiments withbalanced NB-Injection.
1. We experimentally obtain the dependence of non-inductive current on
Wp and Rax.
2. Wp and Rax dependence agree with theoretical prediction based on
BS current for Heliotron devices.
We analyze the MHD activity behavior in high beta LHD experiment withhigh toroidal current (β>2%, ∆ι(a) due to Ip > 0.05) and time evolution oftoroidal current profile.
1. The possibility of determination of current profile (central rotationaltransform) by measuring existence of m/n=2/1 in LHD.
2. Timing, when m/n=2/1 disappears, agrees with theoretically prediction
when ι=1/2 rational surface disappears based on BS-current andOhkawa current.