A. Fukuyama

K. Itoh

M. Yagi

S.-I. Itoh

Y. Fuji

Fukuyama,  A.

Fuji,  Y.

Itoh,  S.-I.

Yagi,  M.

Itoh,  K.

NIFS-Repository (National Institute for Fusion Science)

§30. Self-Organized Dynamics and Thermal Instability in Steady State Tokamaks A. Fukuyama, Y . Fuji (Okayama Univ.) S. -1. ltoh, M. Yagi (Kyushu Univ.) K . Itoh . lmJX)rtant role of current profile on the Improved confinement has been recognized these days. Based on the self-sustained turbulence, it has been shown that a new link is generated between the profiles of the pressure, current and x. causing the improved confinement such as the PEP and high-(\ mode [1]. The analysis is extended to the burmng plasma and new dynamics is found [2]. The energy confinement time for the high-~ mode was theoretically predicted as 't = [ 2·5 L 1 12 T-1.5 (1 + A4 )0·5 where the E t p Pp plasma volume is replaced by L3. (we choose the approximation n0 = nT = n/2). The temperature dependence of the cross section is written as < av > = < crv > g(T). The dimensionless function g(f) is normalized to unity at the temperature T = T*, where the condition dg/dT = 2.5g/T holds. The steady state solution is written as ( 1) where~ and Cr are the coefficients, <;, = (8Jt2~0 1a2 n)4 , C.r = 4 /f;·s nLQr< av >0. Equation ( 1) predicts new branch in the ignition curve as is shown in Fig.l. In the limit ~ = 0, the prediction by the L-mode confinement law holds. When the confinement improvement by the Bootstrap current is effective (i.e.,~ is finite), there appears new branches. The asymptotic form of the left hand side of Eq.(1) behaves as ~ T21~2 in the low current limit. This allows a solution of the form I P ~ c[t2t;- 114 T- 114g(T) 112 This solution gives the low temperature branch and the high temperature branch for the fixed plasma current. These two branches merge, in the small~ limit, at the temperature T = T* *• where the condition dg/dT = g/2T holds. 168 30 > (lJ cs 20 ~ 10 I I I I I I . I T •• t::--------l ~ \ :I !:"'. j \ /<")7 . \ ..-.·':/" III/c~)~)~}-·' II Tc I I I. o~~~~~~~~~~ 0.0 0.5 1.0 1 . 5 2.0 Fig.l Phase diagram in the ignited plasma. The stationary solution (solid line) is compared to that of the L-mode plasma (dashed line). (a) 1. 0 p~~~~~~~~-~~ :Z O. 8 : · ··"-..·' · ·/ -....._./-.'-..,.~ .. J'-....._.f· ·'-..:r- ., "_........ Iss ::s 0. 6 rr·f oJ :.:- o . 4 1, 0. 2 :,'-·'\:-./\·/·--------------- leo o. o IJ ~ ' / ' /' ~ /\ /, / ' 5 ~ 4 =- 3 f-< 2 - "' ~ ~ IoH 0 10 20 30 40 50 60 l [s] -~~~~~~~~~ 10 20 30 ~0 50 60 l [s] Te0 Too < T. > <To> Fig.2 Self-generated oscillation in the steady state plasma with improved confinement. Figure 2 predicts the self-generated oscillation in the steady-state plasma in present-day- large tokamaks. The total current is chosen as 1MA. (The central heating power is taken as 13.5MW. The central current drive power is 0.5MW and the off-axis current drive power is 1MW. The Bootstrap current is dominant due to the lower plas~a current.) The spatial-temporal evolution of this self-generated oscillation is investigated. These analyses provide a new picture for the ?ynamics in burning plasmas and identify the Issue related to thermal instability . It illuminates that the transport analysis of the steady state and ignited plasma is the key issue in the fusion research. 1) A. Fukuyama et al., Plasma Phys. Contr. Fusion 36 ( 1994) 1385. 2) A. Fukuyama, et al., Nucl. Fusion 35 (1995) 1669. --

Self-Organized Dynamics and Thermal Instability in Steady State Tokamaks

Self-Organized Dynamics and Thermal Instability in Steady State Tokamaks

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