H. Sugama

M. Furukawa

M. Wakatani

W. Horton

National Institute for Fusion Science (NIFS-Repository)

§ 1 5. Dependence of Neoclassical Viscosity and Inertia Force on Radial Electric Field Sugama, H., Furukawa, M., Wakatani, M. (Kyoto Univ.) Horton, W. (lnst. Fusion Studies, Univ. Texas) which gives the plateau parallel viscosity and the inertia force as ( ) Vi VTi B2 (" _ A 2iiO) -2mini ullvE'V B = -nimiR 0 J1EI UO + J1E2-Effects of radial electric fields on the neo- 4 q 5Pi classical viscosity and the inertia force in ax-isymmetric toroidal plasmas are investigated [1]. We use the drift kinetic equation for the perturbed distribution function Il(x, v, e) (e = vlI/ v == cos a: the cosine of the pitch an-gle) given by ( veb. V - ~v(1- e2)b. (VlnB)~ + LE - c) II 2 ae mic 2 2 aIM = ~-v (1 +e)b x (VlnB)· Vr-a 2eB r where C denotes the linearized collision op-erator, and the effect of the radial electric field Er is represented by LE = VE' V + VE%v + eE%f,' with VE == (cEr/B)Vr x b, VE = t(cEr/B)v(I + e2)(V x b) . Vr, and eE = t(cEr/ B)ve(1 - e2 )(V x b) . Vr. Here, effects of the nonlinear inertia term VE . VVE are not considered. The parallel momentum balance equation for the axisymmetric case are derived from the drift kinetic equation (1) as (1) e\I!'(B2 ) . (B,(V'Tr))plateau-2m i ni(ullvE'V B) = cI forhit (2) where ( ... ) denotes the flux-surface average. In Eq.(2), (B . (V . Tr))plateau represents the contribution of ions in the pl~teau region [v < (r/R)-3/2Rqvii] to the surface-averaged parallel ion viscosity [the Pfirsch-Schliiter re-gion (v < Rqvii) is assumed to be negligibly small]. The right-hand side of Eq.(2) repre-sents a driving force for the poloidal rotation due to the orbit loss f orhid= -( cI / eW' (B2) )(B· (V . Tr) )hanana] of ions in the banana region [v > (r/R)-3/2Rqvii]. The inertia force -2mini(ullvE' V B) = mi(B· [V· {niulI(bvE + vEb)}]) results from the LE term in Eq.(I). The approximate analytical solution of Eq.(I) for the plateau regime is obtained, (3) with [ ~rrj ] }1Ej where ~(m{e - Alp(v)}) == 7r- 1 v/[(m{e Mp(V)})2 + v2 ], Mp(v) == cIEr/(w'Bov), and B = Bo[I - Em>1 {Em cos( me) + 8m sin( me)}] are used. These analytical results are in good agreement with the numerical solutions by the D KES code as shown in Fig.I. M p Fig.1. Coefficients jJ,rr and jJ,rr + jJ,E as a func-tion of Mp. They are normalized by the value of jJ,rr for Mp = O. Solid and dashed curves correspond to analytical and nu-merical results, respectively. References 1) Sugama, H., Furukawa, M., Wakatani, M., and Horton, W. : Proceedings of the Joint Varenna-Lausanne International Workshop on Theory of Fusion Plasmas (1999) p.4.55. 199 (4) 

Dependence of Neoclassical Viscosity and Inertia Force on Radial Electric Field

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