study of time evolution of toroidal current in lhd · 2013. 10. 1. · katsunori ikedaa, yoshirou...

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 groupa

a) National Institute for Fusion Science, Toki, Gifu 509-5292, Japanb) Japan Atomic Energy Research Institute, Naka, Ibaragi, 311-0193, Japan

Study of Time Evolution of Toroidal current in LHD

Tangential View of LHD

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

Toroidal Current --- Observation ---

In NBI discahrge More than 100kA of toroidal current is observed.No active control of one turn voltage

Observation in LHD

Toroidal current affects MHD equilibrium, stability and Transportin Heliotron devices

Determination of Driving Mechanism; Important!!

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

B0=0.75~2.9T, H2, RaxV=3.6/3.75m,

Ip= -30~110kA, ∆ι (a) = -0.04~0.1.

In principle

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 data and theoretical prediction)

3. Observation of MHD activity and rational surface

(A MHD activity indicates information of central rotational transform)

Information leads to determination of the current profile


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

-0.5

0

0.5

1

1.5

2

0 0.2 0.4 0.6 0.8 1

j BS(A

.U.)

ρ (minor radius)

TOKAMAK

LHD 0

0.5

1

1.5

2

0

0.5

1

1.5

2

2.5

3

3.5

4

0 0.2 0.4 0.6 0.8 1r

(f t/f c)Gbs

, Gbs

(ft/f

c)G

bs

Gbs

ft /fc , q

ft/f

c

q

0

0.5

1

1.5

2

0

0.5

1

1.5

2

2.5

3

3.5

4

0 0.2 0.4 0.6 0.8 1r

Gbs

(ft/f

c)G

bs ft/f

c

q

(f t/f c)Gbs

, Gbs ft /fc , q

0

0.5

1

1.5

2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 0.2 0.4 0.6 0.8 1

-dP/ds

r

T e, ne (A

.U.)

ne

Te

-dP/ds

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

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

IBSC-LHD/IBSC-TOK~0.5 equiv. TOKAMAKLHD


jBS ~ (ft/fc)*Gbs*P*(n'/n+a1Ti'/Ti+a2Te'/Te) a1, a2 ~O(+0.1), Gbs

tok=Ip/2πι

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

Magnetic Axis goestorus-outwardly =>Geometric factor significantly decreases and changes the sign.

Geometrical Factor for LHD in 1/ν-regime

Properties of Bootstrap Current in Heliotron devices (2)- Dependence on Magnetic Axis Configuration -

-0.4

-0.2

0

0.2

0.4

0.6

0.8

3.5 3.6 3.7 3.8 3.9 4 4.1

ρ =0.5

Geo

met

ric fa

ctor

, Gbs

/Gbs

tok

Magnetic axis position, Rax

V (m)

Device center

Standard configuration

Note!!


Time evolution of toroidal current and the estimation of non-inductive current

Ip: observed plasma currentINI: non-inductive plasma currentVloop: one-turn voltage

(self-induced part is dominant in LHD. When dIp/dt=0, Vloop~0)

Ii: increment of current in helical coils, vacuum vessel and so on.

Mip: Mutual inductance between i-component and plasma.

Lp: self-inductance of PlasmaRp: resistance of plasma (Tokamak neoclassical used here ) -0.2

-0.1

0

0.1

0.2

0 0.5 1 1.5 2 2.5 3 3.5 4

volta

ge (V

)

time(s)

MOV-P

dIOV

/dtMIS-P

dIIS

/dtMIV-P

dIIV

/dt

-0.2

-0.1

0

0.1

0.2

volta

ge (V

)

MHM-P

dIHM

/dt

MHI-P

dIHI

/dt

sum Mi-P

dIi/dt

MHO-P

dIHO

/dt

-0.2

-0.1

0

0.1

0.2

volta

ge (V

)

LpdI

p/dtV

loop sum Mi-P

dIi/dt

NIplooppp IRVIR +=

tIM

tI

LV i

iiP

pploop d

dd

d∑+−=

Calculate

Helical coil

Poloidal coil

-100

1020304050

Ip

INI

toro

idal

cur

rent

(kA)

Measure


Experimental result for non-inductive current (1)- Wp and collionality dependence in NB balanced injection -

Observed toroidal currentincreases with Wp increasing.

Collisionalty increses=> Observed current decreases

0

5

10

15

20

25

30

35

40

0 50 100 150 200 250W

p(kJ)

Non

-Indu

ctiv

e cu

rrent

(kA)

Rax

V=3.75m, 1.5/1.52T, HydrogenNB balanced Inj. Total NBI power = 2~3.7MW

ν*e

= 1.5 @ ρ=0.8ν

*e < 0.7 @ ρ=0.8

0.1

1

10

0 50 100 150 200 250W

p(kJ)

Col

lisio

nalit

y

ν*e

@ ρ=0.8

1/ν-regime

plateau-regime

∆ι (a)̃0.02([email protected])

Probable candidate of current driving mechanism;Bootstrap Current


Comparison result with theoretical prediction- Wp dependence -

Theoretical calculation of BS current1. SPBSC code (ref K.Y.WATANABE et al,

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 asymmetric devices proposed by K.C Shaing et al.( Phys. Fluids 26(1983)3315,

Phys. Fluids 29(1986)521 )

2. ne-bar and Te are used by measurement.ne profile is assumed as ~(1-ρ8)

3. Zeff=2, Te = Ti are assumed.

･ Calculated result agrees with experimental data in Wp dependence.･ Direction and Amplitude of theoretical prediction also agrees.

-10

0

10

20

30

40

0 50 100 150 200 250W

p(kJ)

I p(kA)

Rax

V=3.75m, 1.5T, HydrogenNBI balanced Inj. Total NBI power = 3.5~3.7MW

Experiment

Theo. Pred.(equil. straight hel. εh, q same)

Theo. Pred.(equil. LHD Ap, q same)

Theo. Pred.(LHD config.)


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

Observation･ Rax goes torus-outwardly =>･ Observed toroidal current

decreases Co-Injected power is larger

by 20% than Cntr-one.Co/ 2.0MW, Cntr/ 1.6MW

0.1

1

10

0 0.5 1 1.5 2 2.5 3

3.75m3.9m4.0m4.05m

ne_bar

Te0

(1019m-3keV)

ν e*

@ ρ

=0.8

Rax-5

0

5

10

15

20

25

30

35

0 0.5 1 1.5 2 2.5 3

3.75m3.9m4.0m4.05m

ne_bar

Te0

(1019m-3keV)

I sted

y (kA)

･ NB injection Conditionkeeps same during above experiment sequence in magnetic axis changing.

∼β


Comparison result with theoretical prediction- Magnetic Configuration dependence -

Observation･ Rax goes torus-outwardly=> toridal current decreases

=> ･ Agrees with BS behavior predicted in theory.

Pick up data with almost same beta value β=0.33~0.41%

-5

0

5

10

15

20

25

30

35

0 0.5 1 1.5 2 2.5 3

3.75m3.9m4.0m4.05m

ne_bar

Te0

(1019m-3keV)

I sted

y (kA)

0

0.5

1

1.5

2

0.01

0.1

1

10

100

3.7 3.8 3.9 4 4.1

ne_bar

Rax

(m)

n e_ba

r(1019

m-3

)

ν*

νe*

@ρ=0.8

1/ν-regime

･ Cntr-Direction current not observed clearly!!

-5

0

5

10

15

20

25

30

35

3.7 3.8 3.9 4 4.1

I sted

y (kA)

Rax

(m)

( )0.8~1.9e19m-3, Te0=0.8~1.6keV

Experimental ResultBS Theory

Theoretically predicted in torus outward magnetic axis shift configuration


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

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

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 numbern: Toroidal mode number

Rational surface of ι=1/2 is located at ρ=0.5 in Rax=3.6m config.(vacuum).

Remark!!


Theoritical Analysis withCurrentless assumption

(MHD equilibrium is calculated using pressure profile obtained by measurement)･ iota=1/2 surface exists (ι0<0.5)both before and after disappearance of2/1 mode.･ The plasma after disappearance of2/1 mode is more Mercier unstable than that before disappearance of2/1 mode

Most probable explanation of 2/1 mode disappearance ･ Rational Surface (ι=1/2)

disappears.

MHD activity and rational surface (2)

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

-0.4-0.2

00.20.4

DI@ι=0.5(ρ~0.5)

DI

0.20.30.40.50.60.7

1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3

currentless is assumed

ι 0

time(s)


0

50

100b

θ/B

p (10-5)

~

m/n=2/1 mode

Basic Equation for Time Evolution Analysis of toroidal current profile

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


Calculation result of toroidal current evolution

0

50

100

150

200

0

1

2

3

4

0 1 2 3 4

#16964

wp n

e

Te(0)

･ 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 => flatcentral Te profile => peaked -10

0

10

20

30

40

50

60

70

0 0.2 0.4 0.6 0.8 1

1.4s2.2s2.6s3.0s

-10

0

10

20

30

40

50

60

70

0 0.2 0.4 0.6 0.8 1

1.4s2.2s2.6s3.0s

BS-currentOhkawa-current

0

5

10

15

20

25

30

0 0.5 1 1.5 2 2.5 3 3.5 4

Ip-cal Ip-exp

Cur

rent

(kA)

t(s)

IBS+Iohkawa


0

50

100b

θ/B

p (10-5)

~

m/n=2/1 mode

0.20.30.40.50.60.7

1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3

currentless is assumed

ι 0

time(s)

0.20.30.40.50.60.7

Cal. result with toroidal curret

ι 0Comparison between time traces of m/n=2/1 magnetic fluctuation and calculated central rotational transform

ρ

curre

nt d

ensi

ty

-10

0

10

20

30

40

50

60

70

0 0.2 0.4 0.6 0.8 1

1.2s2.2s2.6s3.0s

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

1.2s<t < 1.8s･ peaked current profile due to Iohkawa1.8s < 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 pressure profile) => ι=1/2 surface disappears

0.3

0.4

0.5

0.6

0.7

0 0.1 0.2 0.3 0.4 0.5 0.6

1.4s2.2s2.6s3.0s

ι

ρ

Result!


Summary

We analyze the non-inductive toroidal current in LHD experiments with balanced 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 with high toroidal current (β>2%, ∆ι (a) due to Ip > 0.05) and time evolution of toroidal current profile. 1. The possibility of determination of current profile (central rotational

transform) 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 and Ohkawa current.


study of time evolution of toroidal current in lhd · 2013. 10. 1. · katsunori ikedaa, yoshirou...

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