H. Sugama

T.-H. Watanabe

W. Horton

National Institute for Fusion Science (NIFS-Repository)

§22. Kinetic and Fluid Simulations of the Collisionless Slab Ion Temperature Gradient Driven Turbulence Sugama, H., Watanabe, T.-H., Horton, W. (lnst. Fusion Studies, Univ. Texas) In recent years, gyrokinetic and gyrofluid (or gyro-Landau-fluid) simulations of plasma turbu-lence driven by microinstabilities such as the ion temperature gradient (ITG) mode have been acti vely done in order to predict the anoma-lous transport coefficients in lnagnetically confined plasmas frOln the first principle. In the gyroflu-id model, smne closure relations are assurned to construct a trucated system of fluid equaitions from the gyrokinetic equation and their validity in nonlinear or turbulent regirnes is not clear be-causc conventional gyrofluid closure models such as the Han1lnett-Perkins (H-P) model1) are origi-nally derived so as to accurately reproduce gyroki-netic dispersion relations for linear lnodcs. In fact, there exist somc cases, in which the gyrokinetic and gyrofluid simulations show disagreements in their nonlinear results such as the saturated fluc-tuation levels and the turbulent transport coeffi-cients. In our previous work,2) we have presented the nondissipative closure model (NCM), which takcs into account the time revcrsal symmetry of the collisionless kinetic equation. The NC1VI rc-lates the parallel heat flux to the temperature and the parallel flow in terms of the real-valued coef-ficients in the unstable wave number space. The NCM was derivcd such that the closure relation is valid both for the unstable normal-rHode solution and its cOInplex-conjugate solution as well as for any linear combination of these solutions. A fluid systeln of equations with the NCM used repro-duce the exact nonlinear kinetic solution of the three-nlode ITG problern3) while the H-P mod-el fails in reprcsenting that solution. Then, the next question is whether the NCrvI can successful-ly describe strongly turbulent states of collision less kinetic SystClllS with a higher number of degrees of freedom. In the present work, in order to an-swer this question, we do both fluid and kinetic silllulations of the two-dimensional slab ITG tur-bulence and investigate how accurately the fluid silnulation using the NCM or the H-P rHodel can reproduce results of the collisionless kinetic simu-lation under the same conditions. Here, in order to avoid the cornplexity brought about by the zonal flow and get finite turbulent transport, \VC arti-ficially suppress the zonal flow cOlllponent of the fluctuations. Figure 1 shows the nOI'lllalized perpendicular heat diffusivity xl (P7vtl Ln) as a function of nor-lllalized tillle Vttl Ln obtained by the kinetic and fluid (NCM, H-P) silllulations. It is found frOlll the kinetic simulation that thc phase relation be-tween the potential and the distribution function for the most unstable mode is different frOIll that predicted by the linear unstable eigenfunction and is better described by the NCl\1 than by the H-P model. This fact explains a rcason for the result shown in Fig.1 that, in the steady turbulence s-tate, the turbulent thermal diffusivity X obtained by the H-P lllodel is significantly larger than X given by the NCM and that thc latter is doser to X found in the kinetic simulation. 25 [ I I . I ! I I i I-i-~ r X 20 t · --- ;. .-") [ (p-VT / L,) ~ 15 r "----~ 10 f.-~ r' ~ 5 !-.HH. L i-t ! i • i • ! i .H ..HHH_NCM -Kinetic -H-P , ! ii, , ! i o~~~~~~~~~~~~~~~ o 100 200 300 400 500 600 VT t / Ln Fig.l. Normalized perpcndicular heat diffusivity X I (P7 vt/ Ln) as a function of nOI'lllalized tirHe Vttl Ln obtained by the kinetic and fluid (NCl\1, H-P) silllulations. References 1) Hammett, G.W., and Perkins, F.W., Phys. Rev. Lett. 64 (1990) 3019. 2) Suganla, H., Watanabe, T.-H., and Horton, 'V. , Phys. Plaslllas 8 (2001) 2617. 3) Watanabe, T.-H., Sugama, H., and Sato, T., Phys. Plaslllas 7 (2000) 984. 197 

Kinetic and Fluid Simulations of the Collisionless Slab Ion Temperature Gradient Driven Turbulence

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