H." Sugama

N. Nakajima

O. "Yamagishi

T.-H. Watanabe

Y. Nakamura

National Institute for Fusion Science (NIFS-Repository)

§9. Short Wavelength ITG Modes with Toroidal and Trapped Particle Effects Yamagishi, 0., Watanabe, T.-H., Nakajima, N., Nakamura, Y. (Kyoto Univ.), Sugama, H. The ion temperature gradient (JTG) mode is one of the drift instabilities and it is regarded as a candidate to cause the anomalous transport. It is well known that the ion FLR effects can stabilize the linear ITG modes when wavelength of the modes becomes short. Thus it is conventional to investigate the ITG at k e P <h;<- I. However, recently the ITG modes have been found at relatively short wavelength region, ke P <h;>1[1,2]. In these papers, the ITG modes were treated with some assumptions; the adiabatic electrons are assumed, and the trapped particles dynamics and the toroidal effects are neglected. Here we include these effects formally based on Ref.[3]. The basic parameters used are cyclone base: s=0.78, a =O(zero {l thus electrostatic limit), m;lm,,=3670, T,IT;=I, q=1.4, , ,=r1Ro=0.18, and the ballooning angle e k=O. The remaining parameters k e P thi, and two of (RofLm RoiLT, TJ =L,/LT) are changed in the following. Here L,=-nl( dnldr) and Lr=-T/(dT/dr) are scale length ofn and T respectively. In Fig. I, the ITG frequencies are shown as a function ofk, P,h;, which are normalized as w/(v",;lqR,,)=w/[w., X (L,/qR,,) / k e P <h;] to eliminate the parameter dependence relevant to X-axis in the diamagnetic frequency. Here ~ =5 is fixed and some RdLn values are taken into account. In the R,,/L,=2 case, the modes are stabilized at about k, P <h;= I, while in the higher R,,/L, cases the modes remain unstable at higher k e P ,h;' A case of R,,/L,= I 0 with adi~batic electrons is also shown by squares, and it can be con finned that the non-adiabatic electrons are not necessary for the short wavelength ITG. In the case of Ro/Ln=4 or 10, there is a local minimum of growth rates at near ke P ",;-1, as in Ref.[1,2]. The eigenfunctions for k, P ",;=0.6, 1.0, and 2.0 are shown in Fig.2 for R,,/L,=IO. It can be seen that the modes with ke P thi=2.0 is more broad, that is kl/ - a / a e is more small. This is not the case for usual ITG as can be seen from the cases ofk, P <h;=0.6 and 1.0, and thus the local minimum of the real frequencies also exits through the k"vlI resonance in Fig.I. We next show frequencies of short. wavelength ITG as a function OfRJLT in Fig.3, where ke P thi=1.6 is assumed and the value of R,,/L,=2 and 10 are taken into account. There is a cut-off of instabilities at slightly above R,,/L, I 0 for R,,/L,=2. The case of RoIL,=2 is unstable although that value is stable in Fig.1. Thus the high R,,/L, value itself may not be necessary for instabilities but the high R"iLr is necessary. At the marginal stability, the value of ~ is 6 for R,,/L,=2 while ~ <- I for R,,/L,= 10. Thus ~ itself seems also not to be essential. We can find the similar tendency of short wavelength ITG modes to that reported in Ref.[I,2]' Thus the short wavelength ITG modes are essentially slab-like (parallel resonance is dominated), and the non-adiabatic electrons (including trapped electrons) are incidental. The value of RJLr I 0 gives an estimate of normalized temperature gradient as IdT/d P IIT-IO(afRo). This value is high but seems to be sustained in the transport barrier or plasma edge region. In these cases, there is a possibility that the ITG modes with short wavelength may limit the temperature gradient. 10 ill I v y L,,= D " II II o 2 Fig. I. Frequencies of ITG as a function of k, P <h; for R,,/L,=2,4, and 10. R, . \\ /1 \\ i I \ :"! \ \. , , , , , , , , °f···~~=-_,c",1,..1 \, ,_ ·2 o 2 8/rr Fig. 2. Eigenfunctions at k, P ,h;.=0.6 (solid), 1.0 (dashed) and 2.0 (dotted) for R,,/L,= 10. oJ! , 5 y o ---------------------·5 ·'0 OJ, o 20 RdlT 40 Fig. 3. ITG frequencies with k, P ,h;=1.6 as a function of R,,/LT, for R,,/Ln=2(squares) and 10(circles). Reference [I] Gao. Z., et. aI., Phys. Plasmas 10, (2003) 2831 [2] Smolyakov, A.I., et. aI., Phys. Rev. lett. 89, (2002) 125005-1 [3] Rewoldt. G., et. aI., Phys. Fluids 25, (1982) 480 Acknowledgement The authors would like to thank Dr. Zhe Gao for fruitful discussions on the short wavelength ITG. 333 

Short Wavelength ITG Modes with Toroidal and Trapped Particle Effects

Abstract

Similar works

Full text

Available Versions

National Institute for Fusion Science (NIFS-Repository)