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 Kyushu Tokai University, Kumamoto, Japan O. Mitarai 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 1
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. #302405 1 IPF2-5(KA/turns) (a) I PF25 (kA) 0 O. Mitarai, Y. Takase A. Ejiri, S. Shiraiwa, H. Kasahara, T. -1 -2 Yamada, S.Ohara, TST-2 Team, K. Nakamura, A. Iyomasa, M. 1 IPF3(kA/turns) PF3 (kA) 0 ) , (b) Hasegawa, H. Idei, M. Sakamoto, K. Hanada, K. N. Satoh H. Zush -1 -2 I TRIAM Group and N. Nishino -3 10 8 L (Volts) (c) 6 4 V L01 (outboard) 2 V 0 “Plasma Current Start-up by ECW and Vertical Field in the TST-2 -2 10 Ip (kA) 8 Spherical Tokamak” (d) I p (kA) 6 4 Journal of Plasma and Fusion Research 80 No.07 (2004) RC0083 2 0 200 P RF (kW) (e) rf (kW) 150 100 P 50 0 0.2 0.2 Zp Rp-0.38 0.1 0.1 Z p (m) R p (m) 0 0 -0.1 -0.1 -0.2 -0.2 0.137 0.139 0.141 0.143 0.145 0.147 Time (s) [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. 2
2. Formula for calculation [1] Plasma circuit equation with vertical field and divertor coils (for initial start-up phase) dI p dI V dI sh dI div L p dt R p ( I p I CD I BS ) M PV dt M Psh dt M Pdiv dt -1 ], f BS I BS / I p C BS p CD 19 [Am -2 W I CD P CD , CD = 1.25x10 nR o 2 R C BS = 0.6 , R p NC a 2 [2]. Equivalent plasma circuit method (for overall knowledge) div = I div /I p and sh = I sh /I V , B B zoV I V B zosh I sh B zodiv I div VE dI p M PV M Psh dB VE sh L peff dt R peff I p M PV M Psh sh B zoV B zosh dt sh L peff L p M Pdiv B zodiv div B zoV B zosh sh L p =0.580x10 -6 H, L peff =0.595x10 -6 H . [3]. Separate coil current method (for second, divertor coil activation phase) dI p M PV M Psh dB VE M PV M Psh dI div sh sh L p dt R peff I p M Pdiv B zodiv dt B zoV B zosh dt B zoV B zosh sh sh 3
Poloidal coil layout in CTF and simple magnetic surface for I p =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 4
2.3． 0-D particle and energy balance equations with control algorithm dn T (0) = 1 + n S T (t) - (1 + n ) n D (0)n T (0) < v> DT (x) - n T (0) T* dt dn D (0) = 1 + n S D (t) - (1 + n ) n D (0)n T (0) < v> DT (x) - n D (0) D* dt dn (0) = (1 + n ) n D (0) n T (0) < v> DT (x) - n (0) * dt dT i (0) 1 + n + T = 1.5 e f D + f T + 1/ i + f n e (0) P EXT /V o + P + P oh - P L + P b + P S dt T i (0) dn D (0) dn T (0) dn (0) 1 1 2 - f D +f T +1/ i + f n e (0) 1+ + 1+ + 1 + i 1 - (1+ n )Zf imp dt i 1 - (1+ n )Zf imp dt i 1 - (1+ n )Zf imp dt Confinement time 0.41 [x10 19 m -3 ] R 1.97 m 0.58 m x 0.78 B t 0.69 MW 0.19 I p 0.93 MA n 19 0.15 T /P IPB(y,2) s = HH 0.0562 A i HT NA [s] = 7.1 10 -22 n cm - 3 R 2.04 [cm] a 1.04 [cm] q(a) [1] E =min{ NA , IPB98 } (First part) [2] E = IPB98 (Second part) [3] 1 / E 2 =1/ NA 2 + 1 / 2 (Not in use here) IPB98 5
(1) External heating power (Mainly preprogram in this study) P EXT HL [W] = M HL0 (t)x10 6 P thresh - P oh + P - P b - P s V o with H-mode power threshold M HL0 =15 P thresh [MW] = 2.84 n 0.58 [10 20 m -3 ] B t 0.82 [T] R 1.0 [m] a 0.81 / A i (2) Current drive power (PI control T int =5 sec) n-1 1 CD (I p ) =100x10 6 G PCD • P e IP,n + e IP (i T) T T IPint i = 0 I p (t) e IP (t) = 1 - I po (t) The actual heating/current drive power P CD is determined by the maximum value P CD = max {P EXT (HL), P CD (I p )} (3) Fueling control (PID control T int =3 sec, T d =0.01~1 sec) n-1 T DTd 1 • S DT (t) =S DT0 G SDT (t) e Pf (n T) + e Pf (i T) T + e Pf (n T) - e Pf ((n-1) T T DTint T i = 0 P f (t) e Pf (t) = 1 - fo (t) P 6
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 x10 20 m -3 Aspect ratio: A = 1.5 Greenwald density limit1: n GW ~ 6.8x10 20 m -3 (for I p = 10 MA) Toroidal field: B t = 2.5 T Peak temperature: T i (0) ~ 15 keV Elongation: = 3 Effective ion charge: Z eff ~ 1.3 Internal inductance i = 0.5 Confinement time E ~ 0.6~0.7 s Plasma current: I p ~ 10 MA Fusion power P f =300 MW Temperature ratio: i = T i / T e = 0.95 Density profile: n = 0.5 Temperature profile: T = 1.0 Plasma inductance ( = 3) L p ~ 0.589 H Mutual inductance between PF3 coil and plasma: M PV = 6.08x10 -6 H/A, B zoV =1.33x10 -6 T/A Mutual inductance between PF2 coil and plasma: M Psh = 2.91x10 -6 H/A, B zosh = 0.631x10 -6 T/A Mutual inductance between PF1 coil and plasma: M Pdiv =0.132x10 -6 H/A, B zodiv = 0.0272x10 -6 T/A 7
3. Calculated results 3.1. Equivalent circuit model ( E =min{ NA , IPB98 }) -2 W -1 ], the external heating power of 37 MW together with the fusion power For CD = 0 [Am 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 C BS =0.6), the plasma current is slowly reduced after peak of 10 MA. 6 10 20 6 10 4 2 0.6 BETAP NE0 T i (0) (eV) n(0) (m -3 ) 1.5 NE0GW 4 10 20 4 10 4 0.4 <Beta> Betap 1 2 10 20 2 10 4 BETAA 0.2 0.5 T 0 10 0 0 0 0 1 10 8 1 10 7 5 10 8 0.05 WPV 8 10 6 PF 4 10 8 n (MW/m 2 ) 0.04 PF0 W p (J) 6 10 6 FALPHA 3 10 8 0.03 5 10 7 f alpha P f (W) 4 10 6 2 10 8 0.02 2 10 6 1 10 8 0.01 PNFLUX 0 0 0 10 0 0 2 10 7 2 10 7 1 2 IP ICD 1 BV IBS V loop (V) I CD (A) B V (T) p (A) 1 10 7 1 10 7 0 0 I -1 VLOOP 0 10 0 0 -1 -2 4 10 20 5 10 7 1 10 8 1 10 8 PEXT 4 10 7 IPF3T 3 10 20 S DT (m -3 /s) P EXT (W) 5 10 7 5 10 7 3 10 7 I PF3 (A) IPF1T 2 10 20 I PF1 (A) 0 10 0 0 2 10 7 SSDT 1 10 20 1 10 7 -5 10 7 -5 10 7 0 10 0 0 -1 10 8 -1 10 8 0 20 40 60 80 100 0 20 40 60 80 100 Time (s) Time (s) 8
When the heating power is slightly decreased to 35 MW, the operating point can be reached but the oscillation in plasma parameters takes place. 2 0.6 6 10 20 6 10 4 (e) BETAP NE0 (a) 1.5 T i (0) (eV) n(0) (m -3 ) 0.4 4 10 20 4 10 4 <Beta> Betap NE0GW 1 0.2 BETAA 2 10 20 2 10 4 0.5 T 0 0 0 10 0 0 1 10 8 1 10 7 5 10 8 0.05 (f) 8 10 6 WPV PNFLUX 4 10 8 n (MW/m 2 ) 0.04 (b) W p (J) 6 10 6 FALPHA 3 10 8 0.03 5 10 7 f alpha P f (W) 4 10 6 2 10 8 0.02 PF 2 10 6 1 10 8 PF0 0.01 0 0 0 10 0 0 2 10 7 2 10 7 1 2 (g) ICD IP BV 1 IBS V loop (V) I CD (A) p (A) B V (T) 1 10 7 1 10 7 0 0 I -1 VLOOP (c) 0 10 0 0 -1 -2 4 10 20 1 10 8 1 10 8 5 10 7 IPF3T PEXT 4 10 7 (h) (d) 5 10 7 5 10 7 3 10 20 S DT (m -3 /s) P EXT (W) I PF3 (A) IPF1T 3 10 7 I PF1 (A) 2 10 20 0 10 0 0 SSDT 2 10 7 1 10 20 -5 10 7 -5 10 7 1 10 7 0 10 0 -1 10 8 -1 10 8 0 0 20 40 60 80 100 0 20 40 60 80 100 Time (s) Time (s) 9
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. 6 10 20 6 10 4 2 0.6 (e) BETAP (a) NE0 T i (0) (eV) 1.5 n(0) (m -3 ) 4 10 20 NE0GW 4 10 4 0.4 <Beta> Betap 1 2 10 20 2 10 4 0.2 BETAA 0.5 T 0 10 0 0 0 0 1 10 8 1 10 7 5 10 8 0.05 (f) 8 10 6 WPV 4 10 8 0.04 PF PNFLUX n (MW/m 2 ) (b) W p (J) 6 10 6 FALPHA PF0 3 10 8 0.03 5 10 7 f alpha P f (W) 4 10 6 2 10 8 0.02 2 10 6 1 10 8 0.01 0 0 0 10 0 0 2 10 7 2 10 7 1 2 ICD IP (g) 1 IBS V loop (V) I CD (A) BV B V (T) p (A) 1 10 7 1 10 7 0 0 I -1 VLOOP (c) 0 10 0 0 -1 -2 1 10 8 1 10 8 5 10 7 4 10 20 IPF3T (d) PEXT 5 10 7 5 10 7 4 10 7 (h) 3 10 20 S DT (m -3 /s) P EXT (W) I PF3 (A) IPF1T 3 10 7 I PF1 (A) 0 10 0 0 2 10 20 2 10 7 SSDT -5 10 7 -5 10 7 1 10 20 1 10 7 -1 10 8 -1 10 8 0 10 0 0 0 20 40 60 80 100 0 20 40 60 80 100 Time (s) Time (s) 10
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. 1 10 21 8 10 20 -3 ) 6 10 20 n e (0)(m 4 10 20 2 10 20 0 4 4 4 0 5000 1 10 1.5 10 2 10 Operation path T(keV) POPCON for f ash =0.012 11
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