H" Sugama

M. Okamoto

N. Nakajima

S. "Satake

"Satake,  S.

Okamoto,  M.

Nakajima,  N.

Sugama,  H"

NIFS-Repository (National Institute for Fusion Science)

§2. Neoclassical Transport Simulation by oj Monte-Carlo Method Satake, S., Okamoto, M., Nakajima, N., Sugama, H To study neoclassical(NC) transport with finite-orbit-width (FOW) effect of trapped particle orbits has at-tracted much attention recently. There appear non-standard guiding-center orbits ncar the magnetic axis of tokamak called "potato" orbits[lJ. Typical orbit width of potato particles is as large as (q2p2RO)1/3. The stan-dard NC transport theory constructed in the small-orbit-width (SOW) approximation is not applicable to such cases in which the orbit width is comparable to the back-ground ground gradient scale length or in the near-axis region. We have constructed "a new transport theory which can be applicable to the near-axis region of toka-mak[2J by using a Lagrangian description of the drift-kinetic equation. However, in that theory the effect of radial electric field Er has been neglected. Since the in-trinsic arnbipolarity of neoclassical particle fluxes breaks if the FOW effect is considered, NC transport calculation with consistent ambipolar Er is important in tokamaks as in non-axisymmetric cases. To study the evolution of Er and NC transport with the FOW effect, we have developed a Monte-Carlo trans-port simulation code using the Sf method.[3,4J In this method, the distribution function of plasma is separated into f = fM+sf, where fM is a local Maxwellian and Sf is considered as a small perturbation from f M. We solve the linearized drift-kinetic equation for 51 as follows (1 ) where IC = mv2 /2. G(sf, fM) = GTP is the test-particle collision term implemented by random kicks in the ve-loeity space, and GUM,S!) = PfM is the field-particle collision term defined so that the collision operator sat-isfies the conservation properties (2) In eq. (1), the term Vd . \lsf brings the FOW effect, which is neglected in standard formulation in the SOW limit. The radial electric field develops according to ( C2 ) aEr(r, t) EO 1 + v~ at = -Zie(ri{r, Ero t)), (3) where r i is the ion radial flux and the electron one is neglected. In the time evolution of Erl a rapid oscillation called geodesic acoustic mode (GAM) occurs. It is known[5J that GAM shows a rapid Landau-like damping when q '" 1. But the calculation shown in [5J uses a SOW limit model. Our Sf simulation revealed [6J the global 326 evolution of GAM as shown in Fig. 1. In a reversed-shear configuration with qmin ~ 1 at 1" = 0.5, it can be seen that the fast GAM damping occurred at r = 0.5 also affects the time evolution of Er on both sides of the reso--nance surface. The interference pattern of Er at T > 0.5 is formed because GAM frequency WGAM ~ Vth/ RO is different on each flux surface. These features can be found only by the global simulation. Figure 2 shows the ion heat conductivity Xi compared with the SOW-limit NC theory. The reduction of Xi in the near-axis region haB been predicted in our analysis[2J for a collisionless plasma. By the 51 simulation, we also found that Xi also reduces even in the plateau regime[7J. The difference of Xi from the SOW-limit estimation be-comes larger as collisionality is getting lower since the FOW effect of potato particles is significant in banana regime. 0.4 0.2 Fig. 1 : GAM oscillation in a reversed-shear configuration ~ ~ 10° ........................ . §. ...................... ... >-< -~ -o ~-----------'-- banana ---- plateau 0.5 rIa Fig. 2 : Ion heat conductivity in two collisionality regimes l)Satake, S. et al., 77, 573 (2001). 2)Satake, S. et al., Phys. Plasmas 9, 3946 (2002). 3) Wang W. X. et ai, Plasma Phys. Control. Fusion 41, 1091 (1999). 4) Okamoto M. et ai, Journal. Plasma. Fusion Res. 78, 1344 (2002). 5) Novakovskii S. V. et ai, Phys. Plasmas 4, 4272 (1997). 6) Satake S. and Okamoto M., Bulletin of APS Vol. 48, No.7, LPl-42 (2003). 7) Satake S. et ai, to appear in JPFR Series 6 (accepted). 

Neoclassical Transport Simulation by δf Monte-Carlo Method

Neoclassical Transport Simulation by δf Monte-Carlo Method

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