H. Sugama

T. Kuroda

National Institute for Fusion Science (NIFS-Repository)

§25. lon Temperature Gradient modes and Neoclassical Ripple Transport in Multi-He! icity Fields Kuroda, T., Sugama, H. The ion temperature gradient(ITG) modes have been studied as a cause of the anomalous transport in high-temperature and non-uniform plasmas. In toroidal sys-tems, the properties of lTG modes are significantly af-fected by the magnetic field geometry through the \7 B-curvature drift motion( v D) of particles. In this work, we investigate the linear stability of the electrostatic lTG modes in the multi-helicity field [1], where the magnetic field strength is approximately given by B I Bo = 1 - Et cos() - Eh cos(£() - M () - E- cos[(£ - 1)()- M(]- E+ cos[(£+ 1)B- M(]. (1) Here Bo is the magnitude on the magnetic axis, ()and ( denote the poloidal and toroidal angles, respectively, and M (L) is the toroidal (main poloidal) period number of the helical fields. For the LHD, L = 2 and M = 10. Here, Et ( r) = r I R << 1 ( r: the minor radius, R: the. major ~a­d ius) and Eh ( r) ex: rL are the parameters assocmted with the toroidicity and the main helical component, respec-tively, while E-(r) ex: rL- I and E+(r) ex: rL+I represent sideband helical components. The collisionless gyrokinetic equation is used to de-scribe the ion dynamics while the Boltzmann distribu-tion of electrons is assumed. The dispersion relation is determined by the quasineutrality condition, and the ballooning representation is used to obtain the structure of the electrostatic perturbation ¢ along the magnetic field line. Temporal dependence of ¢ is assumed to be given by ¢ ex: exp(iwt) with a complex-valued frequency w = Wr + i1. Then, the dispersion relation takes a form of an integral eigenvalue equation as ( T ) l+oo d()' 1 + ~ ¢(B) = rrcK(w, (), B')¢(B'), T1. -oo v 21r (2) where the poloidal angle () is used as a parallel coordi-nate variable in the ballooning (or covering) space. The integral kernel K depends on parameters such as TJi = [d(ln Ti)ldr]/[d(ln ni)ldr], En = [d(ln ni)ldr]- 1 I Ro! ~e = TeiTi, and s = (rlq)(dqldr). The boundary conditiOns ¢( () ---+ ±oo) = 0 are used. Figure 1 . shows contours of the normalized growth rate i' = 1 I /oo on the ( E- I Et, E-IEt)-plane obtained by numerically solving Eq.(2) for EhiEt = 1. Here, /oo = 0.183w*e is the growth rate for the case (a) with E+ = E_ = 0, and w*e is elec-tron diamagnetic frequency. Other parameters used here are found in Refs. 1 and 2. In order to compare the effects of the sideband helical components on the lTG mode shown in Fig.1 with their effects on the neo~las­sical transport, contours of the geometrical factor Gneo for the neoclassical ripple transport are shown in Fig.2, where Gneo is normalized such that Gneo = 1 f~r the case (a) with no sideband components. Larger Gneo corre-sponds to larger neoclassical ripple transport. Here, the same parameters as in Fig.1 are used. In the case (b) -2 - 0.25 -1 .5 -1 -0.5 0 0.5 f__IEt Fig.1: Contours of i' a " \ \ \ \ \ \ \ I I . I Xd I : I I : I : I : I I 1. 1.5 2 20 1.5 -0.5 -1 -1.5 -2 -1.5 -1 -0.5 0 0.5 1.5 2 f_ _ IEt Fig.2: Contours of Gneo with (E-IEt, E+ l ct) = ( - 1, -0.4), we find from the pro-file of the magnetic field strength B (B) along the field line that the bottom of the magnetic ripple is nearly constant, which causes smaller neoclassical ripple trans-port, Gneo = 0.177. The profile of k 1. · v D ( ()~ .for the case (b) is unfavorable for the lTG mode stability and gives the maximum growth rate i' = 1.5. On the other hand, both profiles of k1. · vv(B) and B(B) are favorable in the case (c) with (E-IEt,E+ IEt) = (- 0.4, - 2), where a negative lTG growth rate, i' = -0.019, and a neo-classical geometrical factor smaller than for the case (a), Gneo = 0.54, are obtained. This simultaneous realization of favorable profiles of k1. · vv(B) and B(B) may give a clue for optimization of the magnetic field configuration for better plasma confinement. References [1] Kuroda, T. and Sugama, H., to be published in J. Phys. Soc. Jpn. 70 (2001). [2] Kuroda, T., Sugama, H., Kanno, R., and Okamoto, M., J. Phys. Soc. Jpn. 69 (2000) 2485. 201 

Ion Temperature Gradient modes and Neoclassical Ripple Transport in Multi-Helicity Fields

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Ion Temperature Gradient modes and Neoclassical Ripple Transport in Multi-Helicity Fields

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