H. Sugama

T. Kuroda

National Institute for Fusion Science (NIFS-Repository)

§20. Electromagnetic ITG Modes in Helical Systems Kuroda, T., Sugama, H. The ion temperature gradient (ITG) mode is considered to cause the anomalous ion thermal transport in high tem-perature core regions of tokamak plasmas. Recently, heli-cal systems such as the Large Helical Device (LHD) have succeeded in producing high ion temperature plasmas. In addition, experiments to produce higher f3 plasmas in he-lical systems are in progress, and therefore it is important to clarify electromagnetic effects on the ITG mode. In this work, linear properties of the electromagnetic ITG mode in finite-f3 helical systems with the large aspect-ratio mag-netic configuration B / Bo = 1 - Et cos 8 - Eh (L8 - M () are studied, and compared with those in the electrostatic case and in the tokamak case[l]. The temporal dependence of the perturbation terms ¢ (the electrostatic potential) and All (the parallel compo-nent of the vector potential), is assumed to be given by ¢, All ex: exp( -iwt) with a complex frequency w = Wr + iT and time t. The perturbation part is given by 61 = -(qc¢/T)nFM + hexp( -ik~ . p), where p == (B/B) x (v/nB ) is the gyroradius vector, nB = qcB/(mc) is the gyrofrequency, k~ is the wavenumber vector given by the ballooning representation, qc is the charge (qc = e for ions, -e for electrons), n is the equilibrium density, and c is the light speed. The nonadiabatic part of the distribution function h, is determined by the collisionless linear electro-magnetic gyrokinetic equation, [ VII 8 ]-i--+(w-wD) h Rq88 = (w - W'T)JOC~:-L ) FM q~n (~_ V~I All) , (1) where WD = k~ . VD, VD = Ol/(v" + v'ij2)B- 2 B x VB, W*T = w*[{l + TJ(V/VT) - 3/2}]' W* = ckoT/qcBLn' TJ == Ln/ LT, Ln = -(d/dr) In n, and LT = -(d/dr) In T. In order to derive the eigenmode equations, the quasineu-trality condition ni = ne and the Ampere's law VI All = -(47r/c) U;II + j:ll) are used. The number density pertur-bation n = J d3v 61 and the current density perturbation jll = qc J d3 v VII 61 are rewritten in terms of ¢ and All by integrating Eq.(l). Here, we neglect effects of trapped particles and take the lowest-order solution of Eq.(l) in the massless-electron approximation. Derived parameter dependence of the dispersion relation is written as ~ = F(q, s, 8k, 0, ko, TJi, Te/Ti, En, f3i' Te, Eh/Et, L, M), W*e . (2) with the dimensionless function F, the safety factor q, the magnetic shear parameter s = (r / q) ( dq / dr ), the ballooning angle 8k , the field line label 0, the poloidal wavenumber ko, En = Ln/ Ro and f3i = 87rnTd B2. We use the parameters q = 2, s = -1 (negative shear), 8k = 0, ° = 0, kOPTi = 0.65 TJi = TJe = 3, En = 0.3, Te/Ti = 1, Eh/Et = 1, L = 2, M = 10. For the tokamak case, Eh/Et = O. Figure 1 shows the f3i dependence of the real frequency and the growth rate of the ITG mode. For f3i = 0.001% and 0.5%, the real and imaginary parts of the eigenfunctions ¢ and All are plotted in Fig. 2 for the helical system. In the low f3i case (f3i = 0.001 %), The real frequency, the growth rate, and the potential eigenfunction are in good agreement with those in the electrostatic case[2], and the amplitude of All is negligibly small as shown in Fig. 2. o. '0_ --0.. , '0 _ Growth Rate y'ro*c '0, - 0_ - -0. - '0 - -0 - - 0 __ 0- _ 0- _ 0- _ -0- _ -0 __ Or---------~==~------------~ -0.2 -0.4 '--0 - - Y : Tokamak ---- y : Helical .--6--- (Or: Tokamak .-.... -- Wr : Helical ==: = =~: :~:: ~:: ~::t::: -6- - -6- - -4 - -4 _ _ ,, __ ,, __ ,6_ - -b ---0.6 ----. Real Frequency ro/ro*c o 0.005 0.01 0.015 Figure 1: Normalized real frequency wr/w*e and growth rate. In the case of f3i = 0.5%, higher f3 increases magnetic fluc-tuations and gives more oscillatory profiles of eingenfunc-tions, which results from the multiplier effect of the helical magnetic ripples and the coupling to electromagnetic shear Alfven waves. 0.05 (b) ~=O.OOl% 0 -An • . ---- A"i -0.05 1t e -1t 0 1t e 0.05 (d) 13=0.5% :\/ 0 if-Alli'~ -0.05 1t e -1t 0 1t e Figure 2: Normalized eigenfunctions (e/Te)¢ and (evTdcTe)AII in the helical system Thus, the growth rate of the ITG mode for the helical sys-tem decreases with increasing f3i, and keeps smaller values than for the tokamak case. Reference [1] J. Q. Dong, et al.: Nucl. Fusion 39 (1999) 104l. [2] T. Kuroda, et al.: J. Phys. Soc. Jpn. 69 (2000) 2485. [3] T .Kuroda, H.Sugama, to be published in JPFR SERIES 5. 195 

Electromagnetic ITG Modes in Helical Systems

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