1

Plasma Current Ramp-up by the Vertical Field and Heating Power in the CTF Device

Sep. 29-Oct. 1, 2004 ST Workshop 2004 at Kyoto University

O. Mitarai Kyushu Tokai University, Kumamoto, Japan

M. Peng PPPL, Princeton University, New Jersey, USA

Contents 1. Recent progress of CS-less operation in Japan 2. Formula [1] Plasma circuit equation with vertical field and divertor coils [2] 0-D particle and energy balance equations with control algorithm 3. Calculated results [1]. Equivalent circuit method

[2]. Separate coil current method with E=min{ NA, IPB98} [3]. Separate coil current method with E= IPB98 4. Summary

2

1. Recent progress of CS-less operation in Japan [1] In TST-2 spherical tokamak, the plasma current up to 10 kA has been

achieved by the vertical field and ECRH.

O. Mitarai, Y. Takase A. Ejiri, S. Shiraiwa, H. Kasahara, T. Yamada, S.Ohara, TST-2 Team, K. Nakamura, A. Iyomasa, M. Hasegawa, H. Idei, M. Sakamoto, K. Hanada, K. N. Satoh H. Zush), TRIAM Group and N. Nishino

“Plasma Current Start-up by ECW and Vertical Field in the TST-2 Spherical Tokamak” Journal of Plasma and Fusion Research 80 No.07 (2004) RC0083

[2] Recently, in the CS-less operation without any inner VT coil, the plasma

current up to 110 kA has been achieved by ECRH and vertical field in JT60-U. (Takase, Mitarai, Ide, Suzuki et al) Model calculation predicted 140 kA.

(a)

(b)

(c)

(d)

#302405

(e)

V L01 (outboard)

IPF3(kA/turns)

P RF (kW)

Ip (kA)

IPF2-5(KA/turns)

-3

-2

-1

0

1

I PF

3(k

A)

0

2

4

6

8

10

I p(k

A)

-202468

10

VL(V

olt

s)

-2

-1

0

1

I PF

25(k

A)

-0.2

-0.1

0

0.1

0.2

-0.2

-0.1

0

0.1

0.2

Rp-0.38 Zp

0.137 0.139 0.141 0.143 0.145 0.147

Rp(m

)

Zp(m

)

Time (s)

0

50

100

150

200

Prf(k

W)

3

2. Formula for calculation [1] Plasma circuit equation with vertical field and divertor coils (for initial start-up phase)

Lp

dIp

dt Rp (I p ICD IBS ) MPV

dIV

dt MPsh

dIsh

dt MPdiv

dIdiv

dt

ICD CD

nRo

PCD , CD = 1.25x1019 [Am-2W-1], fBS IBS / I p CBS p

CBS = 0.6, Rp NC2 R a2

[2]. Equivalent plasma circuit method (for overall knowledge) div = Idiv/Ip and sh = Ish/IV,

Lpeff

dIp

dt Rpeff I p

MPV MPsh sh

BzoV Bzosh sh

dBVE

dt Lpeff Lp MPdiv MPV MPsh sh

BzoV Bzosh sh

Bzodiv

div

Lp =0.580x10-6 H, Lpeff =0.595x10

-6 H.

[3]. Separate coil current method (for second, divertor coil activation phase)

Lp

dIp

dt Rpeff I p

MPV MPsh sh

BzoV Bzosh sh

dBVE

dt MPdiv

MPV MPsh sh

BzoV Bzosh sh

Bzodiv

dIdiv

dt

BVE BzoV IV Bzosh Ish BzodivIdiv

4

Poloidal coil layout in CTF and simple magnetic surface for Ip=10 MA.

The total current of the divertor coil is +72 MA, and the total current of the shaping and vertical field coil are -8 MA, respectively

5

2.3．0-D particle and energy balance equations with control algorithm

dnT(0)

dt = 1 + n ST(t) - (1 + n) nD(0)nT(0) < v>DT(x) -

nT(0)

T*

dnD(0)dt

= 1 + n SD(t) - (1 + n) nD(0)nT(0) < v>DT(x) - nD(0)

D*

dn (0)

dt = (1 + n) nD(0) nT(0) < v>DT(x) -

n (0)*

dTi(0)

dt = 1 + n + T

1.5 e fD+ fT + 1/ i + f ne(0) PEXT /Vo + P + Poh - PL + Pb + PS

-

Ti(0) fD+fT+1/ i+ f ne(0)

1+ 1 i 1 - (1+ n)Zfimp

dnD(0)

dt + 1+ 1

i 1 - (1+ n)Zfimp dnT(0)

dt + 1 + 2

i 1 - (1+ n)Zfimp dn (0)

dt

Confinement time

IPB(y,2)

s = HH

0.0562 Ai0.19 Ip

0.93 MA n190.41

[x1019m-3] R1.97 m 0.58 m x

0.78 Bt0.15 T /PHT

0.69 MW

NA

[s] = 7.1 10-22 n cm- 3 R2.04[cm] a1.04 [cm] q(a)

[1] E=min{ NA, IPB98} (First part) [2] E= IPB98 (Second part) [3] 1/ E

2 =1/ NA

2 +1/ IPB98

2 (Not in use here)

6

(1) External heating power (Mainly preprogram in this study) PEXT HL [W] = MHL0(t)x106 Pthresh - Poh + P - Pb - Ps Vo

with H-mode power threshold MHL0=15

Pthresh [MW] = 2.84 n 0.58 [1020 m -3] Bt0.82 [T] R1.0[m] a0.81 / A i

(2) Current drive power (PI control Tint=5 sec)

PCD(Ip) =100x106GPCD eIP,n +1

TIPinteIP(i T) T•

i = 0

n-1

eIP(t) = 1 -

Ip(t)

Ipo(t) The actual heating/current drive power PCD is determined by the maximum value PCD = max {PEXT(HL), PCD(Ip)}

(3) Fueling control (PID control Tint=3 sec, Td=0.01~1 sec)

SDT(t) =SDT0GSDT(t) ePf(n T) +1

TDTintePf(i T) T•

i = 0

n-1

+TDTd

TePf(n T) - ePf((n-1) T

ePf(t) = 1 -

Pf(t)

Pfo(t)

7

Table 1. CTF assumed plasma parameters Major radius: R= 1.2 m Enhancement factor: HH=0.6 ~2.2 (IPB98(y,2)) Minor radius: a = 0.8 m Peak electron density: n(0) ~ 3.6 x1020 m-3 Aspect ratio: A = 1.5 Greenwald density limit1: nGW ~ 6.8x1020 m-3 (for Ip = 10 MA) Toroidal field: Bt = 2.5 T Peak temperature: Ti(0) ~ 15 keV Elongation: = 3 Effective ion charge: Zeff ~ 1.3 Internal inductance i = 0.5 Confinement time E ~ 0.6~0.7 s Plasma current: Ip ~ 10 MA Fusion power Pf=300 MW Temperature ratio: i = Ti / Te= 0.95 Density profile: n = 0.5 Temperature profile: T = 1.0

Plasma inductance ( = 3) Lp ~ 0.589 H

Mutual inductance between PF3 coil and plasma: MPV = 6.08x10-6 H/A, BzoV =1.33x10-6 T/A

Mutual inductance between PF2 coil and plasma: MPsh = 2.91x10-6 H/A, Bzosh = 0.631x10-6 T/A

Mutual inductance between PF1 coil and plasma: MPdiv =0.132x10-6 H/A, Bzodiv = 0.0272x10-6 T/A

8

3. Calculated results 3.1. Equivalent circuit model ( E=min{ NA, IPB98}) For CD = 0 [Am-2W-1], the external heating power of 37 MW together with the fusion power up to 300 MW increases the plasma current up to 10 MA. As the non-inductive driven current does not exist in this case and the bootstrap current is ~80 % (for CBS=0.6), the plasma current is slowly reduced after peak of 10 MA.

0

2 1020

4 1020

6 1020

0 100

2 104

4 104

6 104

NE0NE0GW

T

n(0

) (m

-3)

Ti(0

) (e

V)

00.010.020.030.040.05

0 1001 1082 1083 1084 1085 108

FALPHA

PFPF0

f alp

ha

Pf (

W)

-1

0

1

-2

-1

0

1

2

VLOOP

BV

Vlo

op(V

)

BV(T

)

0

0.5

1

1.5

2

0

0.2

0.4

0.6BETAP

BETAABet

ap

<Bet

a>

0

5 107

1 108

02 1064 1066 1068 1061 107

WPV

PNFLUX

Wp(J

)

n(M

W/m

2)

0

1 107

2 107

0 100

1 107

2 107

IP ICDIBS

I p (

A)

I CD

(A)

01 1072 1073 1074 1075 107

0 100

1 1020

2 1020

3 1020

4 1020

0 20 40 60 80 100

PEXT

SSDT

PE

XT

(W)

SD

T(m

-3/s

)

Time (s)-1 108

-5 107

0

5 107

1 108

-1 108

-5 107

0 100

5 107

1 108

IPF3T

IPF1T

0 20 40 60 80 100

I PF

3(A

)

I PF1(A

)

Time (s)

9

When the heating power is slightly decreased to 35 MW, the operating point can be reached but the oscillation in plasma parameters takes place.

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

0

2 1020

4 1020

6 1020

0 100

2 104

4 104

6 104

NE0NE0GW

T

n(0

) (m

-3)

Ti(0

) (e

V)

00.010.020.030.040.05

0 1001 1082 1083 1084 1085 108

FALPHA

PFPF0

f alp

ha

Pf (

W)

-1

0

1

-2

-1

0

1

2

VLOOP

BV

Vlo

op(V

)

BV(T

)

-1 108

-5 107

0

5 107

1 108

-1 108

-5 107

0 100

5 107

1 108

IPF3T

IPF1T

0 20 40 60 80 100

I PF

3(A

)

I PF1(A

)

Time (s)

0

0.5

1

1.5

2

0

0.2

0.4

0.6BETAP

BETAABet

ap

<Bet

a>

0

5 107

1 108

02 1064 1066 1068 1061 107

WPV PNFLUX

Wp(J

)

n(M

W/m

2)

0

1 107

2 107

0 100

1 107

2 107

IP ICDIBS

I p (

A)

I CD

(A)

01 1072 1073 1074 1075 107

0 100

1 1020

2 1020

3 1020

4 1020

0 20 40 60 80 100

PEXT

SSDTP

EX

T(W

)

SD

T(m

-3/s

)

Time (s)

10

When the heating power is further decreased to 33 MW, the steady operating point cannot be obtained because the plasma parameter oscillation grows and the discharge is eventually terminated.

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

0

2 1020

4 1020

6 1020

0 100

2 104

4 104

6 104

NE0NE0GW

T

n(0)

(m-3

)

T i(0) (

eV)

00.010.020.030.040.05

0 1001 1082 1083 1084 1085 108

FALPHAPFPF0

f alph

a

Pf (W

)-1

0

1

-2

-1

0

1

2

VLOOP

BV

V loop

(V)

BV(T

)

-1 108

-5 107

0

5 107

1 108

-1 108

-5 107

0 100

5 107

1 108

IPF3T

IPF1T

0 20 40 60 80 100

I PF3(A

)

I PF1(A

)

Time (s)

0

0.5

1

1.5

2

0

0.2

0.4

0.6BETAP

BETAABet

ap

<Bet

a>

0

5 107

1 108

02 1064 1066 1068 1061 107

WPV PNFLUX

Wp(J

)

n(MW

/m2 )

0

1 107

2 107

0 100

1 107

2 107

IP ICDIBS

I p (

A)

I CD

(A)

01 1072 1073 1074 1075 107

0 100

1 1020

2 1020

3 1020

4 1020

0 20 40 60 80 100

PEXT

SSDT

PEX

T(W

)

SD

T(m

-3/s

)

Time (s)

11

The reason of these oscillations and termination is understood using POPCON. As the height of the contour line during accessing the operating point is high for NA, it is difficult to reach the operating point with the smaller heating power.

0

2 1020

4 1020

6 1020

8 1020

1 1021

0 5000 1 104

1.5 104

2 104

n e(0

)(m-3

)

T(keV) Operation path

POPCON for fash =0.012

12

When the non-inductive current drive efficiency with CD = 1.25x1019 [Am-2W-1] exists, the same plasma current should be obtained by the smaller heating power than 37 MW. However, the discharge is terminated with PEXT=37 MW and needs 40 MW. This is in contradiction to our intuition.

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

0

2 1020

4 1020

6 1020

0 100

2 104

4 104

6 104

NE0NE0GW

T

n(0)

(m-3

)

T i(0) (

eV)

00.010.020.030.040.05

0 1001 1082 1083 1084 1085 108

FALPHA

PFPF0

f alph

a

Pf (W

)-1

0

1

-2

-1

0

1

2

VLOOP

BV

V loop

(V)

BV(T

)

0

1 107

2 107

0 100

1 107

2 107

IP ICDIBS

I p (

A)

I CD

(A)

01 1072 1073 1074 1075 107

0 100

1 1020

2 1020

3 1020

4 1020

0 20 40 60 80 100

PEXT

SSDT

PEX

T(W

)

SD

T(m

-3/s

)

Time (s)

0

5 107

1 108

02 1064 1066 1068 1061 107

WPV

PNFLUX

Wp(J

)

n(MW

/m2 )

-1 108

-5 107

0

5 107

1 108

-1 108

-5 107

0 100

5 107

1 108IPF3T

IPF1T

0 20 40 60 80 100

I PF3

(A)

I PF1

(A)

Time (s)

0

0.5

1

012345

TAUIPBTNA

GHH

E(s

)

HH

Reason: During discharge, the Neo-Alcator scaling is dominant. Therefore, the larger plasma current decreases the confinement time through the Neo-Alcator scaling with q0.5 (q is the safety factor), leading to necessity of larger heating /current drive power.

13

3.2. Separate coil current method with E=min{ NA, IPB98}, The null point is created when the coil current ratio is maintained. In the outward region of this null point, the normal vertical field for equilibrium is generated. (No vacuum chamber current effect). The null point moves inward with time.

The magnetic field vector in the breakdown phase;

(a) IPF1=+80 kA total, IPF2=-6.4 kA total, and IPF3=0 kA, (b) IPF1=+80 kA total, IPF2=-6.626 kA total, and IPF3=-0.215 kA total, (c) IPF1=+80 kA total. IPF2=-6.85 kA total, and IPF3=-0.429 kA total

14

[1] Initial phase controlled by PF1, PF2 and PF3 coils. The plasma current is ramped up to ~0.67 MA when IPF1(total) =+80 kA is maintained, IPF2 (total) = -6.4 kA -320 kA IPF3 (total) = 0 kA -320 kA

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

-0.1

-0.05

0

0.05

0.1

-0.1

-0.05

0

0.05

0.1

BVCOIL

BV BV

CO

IL(T

)

BV(T

)

01 10192 10193 10194 10195 1019

0 1002 1034 1036 1038 1031 104

NE0NE0GW

T

n(0

) (m

-3)

Ti(0

) (e

V)

-5

0

5

-0.2

-0.1

0

0.1

0.2VLOOP

BV Vlo

op(V

)

BV(T

)

-1 106

-5 105

0

5 105

1 106

-1 106

-5 105

0

5 105

1 106

IPF3TIPF2T

IPF1T

0 0.1 0.2 0.3 0.4 0.5 0.6

I PF

3(A

)

I PF1

(A)

Time (s)

0

5 105

1 106

02 1064 1066 1068 1061 107

WPV

PNFLUX

Wp(J

)

n(M

W/m

2)

0

5 105

1 106

0 100

5 105

1 106

IP

ICDIBS

I p (

A)

I CD

(A)

01 1072 1073 1074 1075 107

0 100

1 1020

2 1020

3 1020

4 1020

0 0.1 0.2 0.3 0.4 0.5 0.6

PEXT SSDT

PE

XT

(W)

SD

T(m

-3/s

)

Time (s)

0

0.02

0.04

0

0.5

1

1.5

2

TAUIPB･TNA

GHH

E(s

)

HH

@ Initial phase is determined by IPB(y,2) scaling.

15

[2] Divertor coil activation phase E=min{ NA, IPB98},

When the divertor coil current Idiv reaches divIp, it is now set to be proportional to the plasma current with div= 1.8. Reverse induction by divertor coil is not large.

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

Fig. 8

0

2 1020

4 1020

6 1020

0 100

2 104

4 104

6 104

NE0NE0GW

T

n(0)

(m-3

)

T i(0) (

eV)

00.010.020.030.040.05

0 1001 1082 1083 1084 1085 108

FALPHAPFPF0f al

pha

Pf (W

)-1

0

1

-2

-1

0

1

2

VLOOP

BV

V loop

(V)

BV(T

)

-1 107

-5 106

0

5 106

1 107

-1 108

-5 107

0

5 107

1 108

IPF3TIPF2T

IPF1T

0 5 10 15 20

I PF3

(A)

I PF1

(A)

Time (s)

0

0.4

0.8

0

1

2

3

4TAUENA

GHH

E(s

)

HH

0

5 107

1 108

02 1064 1066 1068 1061 107

WPV

PNFLUXWp(J

)

n(MW

/m2 )

0

1 107

2 107

0 100

1 107

2 107

IP ICDIBS

I p (

A)

I CD

(A)

01 1072 1073 1074 1075 107

0 100

1 1020

2 1020

3 1020

4 1020

0 5 10 15 20

PEXT SSDTP

EXT

(W)

SD

T(m

-3/s

)

Time (s)

16

[3] The long time behavior up to 100 s (PEXT= 45 MW, CD = 0 [Am-2W-1], E=min{ NA, IPB98},) The plasma current of 10 MA is finally obtained. (We should note that the slower ramp rate

of the fusion power can reduce the heating power to the operating point with PEXT =43 MW and

tramp=200 sec.)

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

0

2 1020

4 1020

6 1020

0 100

2 104

4 104

6 104

NE0NE0GW

T

n(0)

(m-3

)

T i(0) (

eV)

00.010.020.030.040.05

0 1001 1082 1083 1084 1085 108

FALPHA

PFPF0

f alph

a

Pf (W

)

-1

0

1

-2

-1

0

1

2

VLOOP

BV

V loop

(V)

BV(T

)

-1 107

-5 106

0

5 106

1 107

-1 108

-5 107

0

5 107

1 108

IPF3TIPF2T

IPF1T

0 20 40 60 80 100

I PF3(A

)

I PF1(A

)

Time (s)

0

5 107

1 108

02 1064 1066 1068 1061 107

WPV

PNFLUXWp(J

)

n(MW

/m2 )

0

1 107

2 107

0 100

1 107

2 107

IP ICDIBS

I p (

A)

I CD

(A)

01 1072 1073 1074 1075 107

0 100

1 1020

2 1020

3 1020

4 1020

0 20 40 60 80 100

PEXT SSDT

PEX

T(W

)

SD

T(m

-3/s

)

Time (s)

0

0.4

0.8

0

1

2

3

4TAUENA

GHH

E(s

)

HH

17

3.3. Separate coil current method with E= IPB98 [1] CD = 0 [Am-2W-1], PEXT=45 MW, HH=1.9, (Td=0.5 s, Tint=3 s)

When no current drive exists, 45 MW is needed to obtain 10 MA. (Note: Density and temperature has no steady state.)

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

0

2 1020

4 1020

6 1020

0 100

2 104

4 104

6 104

NE0NE0GW

T

n(0

) (m

-3)

Ti(0

) (e

V)

00.010.020.030.040.05

0 1001 1082 1083 1084 1085 108

FALPHA

PFPF0

f alp

ha

Pf (

W)

-1

0

1

-2

-1

0

1

2

VLOOP

BV

Vlo

op(V

)

BV(T

)

-1 107

-5 106

0

5 106

1 107

-1 108

-5 107

0

5 107

1 108

IPF3TIPF2T

IPF1T

0 20 40 60 80 100

I PF

3(A

)

I PF1

(A)

Time (s)

0

0.4

0.8

0

1

2

3

4TAUEIPB

GHH

E(s

)

HH

0

5 107

1 108

02 1064 1066 1068 1061 107

WPV

PNFLUXWp(J

)

n(M

W/m

2)

0

1 107

2 107

0 100

1 107

2 107

IP ICDIBS

I p (

A)

I CD

(A)

01 1072 1073 1074 1075 107

0 100

1 1020

2 1020

3 1020

4 1020

0 20 40 60 80 100

PEXT SSDTP

EX

T(W

)

SD

T(m

-3/s

)

Time (s)

18

[2] CD = 1.25x1019 [Am-2W-1], PEXT=30 MW, HH=1.9, (Td=0.1 s, Tint=3 s) On the other hand, if the current drive capability exists, the heating/current drive

power can be reduced to 30 MW for 10 MA ramp-up. IPB(y,2) scaling provides reasonable results with respect to the plasma current.

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

0

2 1020

4 1020

6 1020

0 100

2 104

4 104

6 104

NE0NE0GW

T

n(0)

(m-3

)

T i(0) (

eV)

00.010.020.030.040.05

0 1001 1082 1083 1084 1085 108

FALPHA PFPF0

f alph

a

Pf (W

)

-1

0

1

-2

-1

0

1

2VLOOP BV

V loop

(V)

BV(T

)

-1 107

-5 106

0

5 106

1 107

-1 108

-5 107

0

5 107

1 108

IPF3TIPF2T

IPF1T

0 20 40 60 80 100

I PF3

(A)

I PF1

(A)

Time (s)

0

0.4

0.8

0

1

2

3

4TAUEIPB

GHH

E(s

)

HH

0

5 107

1 108

02 1064 1066 1068 1061 107

WPV

PNFLUXWp(J

)

n(MW

/m2 )

0

1 107

2 107

0 100

1 107

2 107

IP ICDIBS

I p (

A)

I CD

(A)

02 1074 1076 1078 1071 108

0 100

1 1020

2 1020

3 1020

4 1020

0 20 40 60 80 100

PEXT

SSDTPEX

T(W

)

SD

T(m

-3/s

)

Time (s)

19

[3] Second phase is unstable for IPB(y,2) scaling. Careful adjustment of the PID parameter in fueling control is necessary.

CD = 0 [Am-2W-1], PEXT=45 MW, HH=1.9, (Td=0 s, Tint=3 s)

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

0

2 1020

4 1020

6 1020

0 100

2 104

4 104

6 104

NE0NE0GW

T

n(0)

(m-3

)

T i(0) (

eV)

00.010.020.030.040.05

0 1001 1082 1083 1084 1085 108

FALPHAPFPF0

f alph

a

Pf (W

)-1

0

1

-2

-1

0

1

2VLOOP BV

V loop

(V)

BV(T

)

-1 107

-5 106

0

5 106

1 107

-1 108

-5 107

0

5 107

1 108

IPF3TIPF2T

IPF1T

0 5 10 15 20

I PF3

(A)

I PF1

(A)

Time (s)

0

0.4

0.8

0

1

2

3

4TAUEIPB

GHH

E(s

)

HH

0

5 107

1 108

02 1064 1066 1068 1061 107

WPV

PNFLUX

Wp(J

)

n(MW

/m2 )

0

1 107

2 107

0 100

1 107

2 107

IP ICDIBS

I p (

A)

I CD

(A)

01 1072 1073 1074 1075 107

0 100

1 1020

2 1020

3 1020

4 1020

0 5 10 15 20

PEXT

SSDT

PEX

T(W

)

SD

T(m

-3/s

)

Time (s)

20

[4] Steady state of 10.5 MA after 100 sec is maintained by the feedback control of the non-inductive drive power.

CD = 1.25x1019 [Am-2W-1], HH=1.9, PEXT=30 MW to 70 MW, (Td=0.1 s, Tint=3 s)

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

0

2 1020

4 1020

6 1020

0 100

2 104

4 104

6 104

NE0NE0GW

T

n(0)

(m-3

)

T i(0) (

eV)

00.010.020.030.040.05

0 1001 1082 1083 1084 1085 108

FALPHA PFPF0

f alph

a

Pf (W

)

-1

0

1

-2

-1

0

1

2VLOOP BV

V loop

(V)

BV(T

)

-1 107

-5 106

0

5 106

1 107

-1 108

-5 107

0

5 107

1 108

IPF3TIPF2T

IPF1T

0 50 100 150 200

I PF3

(A)

I PF1(A

)

Time (s)

0

0.4

0.8

0

1

2

3

4TAUEIPB

GHH

E(s

)

HH

0

5 107

1 108

02 1064 1066 1068 1061 107

WPV

PNFLUXWp(J

)

n(MW

/m2 )

0

1 107

2 107

0 100

1 107

2 107

IP ICDIBS

I p (

A)

I CD

(A)

02 1074 1076 1078 1071 108

0 100

1 1020

2 1020

3 1020

4 1020

0 50 100 150 200

PEXT

SSDTPEX

T(W

)

SD

T(m

-3/s

)

Time (s)

21

4. Summary and further issues

[1] The plasma current ramp up to 10 MA is possible with the heating power of 30~45 MW in the CTF device without the central solenoid for these scalings.

[2] It is confirmed that the equivalent circuit equation model and separate poloidal

coil circuit model provide the similar results with 0-D equation. [3] The plasma current of ~600 kA could be obtained in the initial phase by outer

poloidal coil activation. [4] Discharge behaviors based on the minimum selection of the confinement time

of NA and IPB provides the contradictory results. IPB scaling provides the reasonable behaviors except for the second phase.

(Careful choice of the derivative time for fueling is necessary in the second phase.)

[5] For steady state operation, more heating/current drive power is required.

Further optimization would be necessary to reduce the power.

22