M. "Okamoto

N. Nakajima

S. Satake

W." Wang

"Okamoto,  M.

Nakajima,  N.

Satake,  S.

Wang,  W."

NIFS-Repository (National Institute for Fusion Science)

§12. 8f Simulation and the Radial Electric Field Okamoto, M., Nakajima, N., Satake, S. (Grad. U. Advanced Studies), Wang, W. (PPPL) The satndard neoclassical theory does not hold near the magnetic axis since particle orbits near the axis are complicated and different from usual ba-nana and passing particles [1]. The FOW (Finite Orbit Width) effect is important for such a plasma near the axis as well as for the plasma with steep pressure gradients. To take into account the effect of FOW, a 6 f Monte Carlo particle simulation code FORTEC [2] has been developed. The radial elec-tric field has been calculated for the plasma with constant q and no toroidal rotation [3]. Here, we calculate the radial electric field in a rotated tokamak plasma by FORTEC. The rota-tion is modelled by a shifted Maxwellian velocity distribution. The drift kinetic equation for ion distribution function is given, in (c, /-l, x) space, by aaf + ~ aa<I> aaf + (vII + Vd) . V f = C(f, f) (1) t m t c The notations are standard. This drift kinetic equation is solved by the 6f method which employs the two weighting scheme with accurate linear col-lision operator [2]. The shifted Maxwellian distri-bution function has a form of (2) Here, ull is the shifted parallel velocity. It should be noted that vII is a function of c, /-l, r, and (). The equation for the radial electric field becomes (cgs-unit) ( c2) a Er / J 3 ) 1 + vi 8t = -4ne \ d vVdrf (3) Here, Vdr is the radial drift velocity. Eq.(3) is solved with the time step less than the GAM (geodesic acoustic Inode) period WGA~ [4]. If we assume that the temperature is constant in space (VT = 0), we can estimate the radial electric field by a simple analytical model neglecting the collision term C(f, f). From Eqs.(I),(2), and (3), we obtain (4) The factors C1 and C2 can be easily calculated. In the limit of t = 00 (after the GAM damps out), Er = (T/e)(C2 /Cd and we obtain Er = T [vn + 2 (h _ ull dUll)] + T ahull (5) e n Ia dr e Ia where a = 2r/(qRp), ull = ull/Vth, and Ia,h and 12 are integrals containing Gauss function to yield h / Ia ~ 3.3ull and 12/ Ia ~ 0.43. In Fig.l, the calculation results are shown. Three cases of (1) ulla = 0, (2) ulla = +0.1, and (3) ulla = -0.1 are illustrated. Simulation results (solid lines) and analytical estimations (dotted lines) are well in agreement. The agreement can be seen for the case of the plasma with steep pressure gradient. The comparison with an experimental measurement of Er in a rotating plasma is under investigation. 2 0 (2) -2 E ----> -4 6 W -6 -8 ~-----:~ (3) -10 0 0.2 0.4 0.6 0.8 x=r/a Fig. 1 Profiles in a rotating plasma. References [1] S. Satake, H. Sugama, M. Okamoto and M. Wakatani, J. Plasma Fus. Res. 77, 573 (2001). [2] W. X. Wang, N. Nakajima, M. Okamoto and S. Murakami, Plasma Phys. Control. Fusion 41, 1091 (1999). [3] W. X. Wang, F. L. Hinton and S. K. Wong, Phys. Rev. Let. 87 (5), 055002-1 (2001). [4] N. Winsor, J. L. Jhonson and J. M. Dawson, Phys. Fluid 11 (11) ,2448 (1968). 187 

δf Simulation and the Radial Electric Field

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δf Simulation and the Radial Electric Field

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