M. Okamoto

N. Nakajima

S. Murakami

W.X. Wang

National Institute for Fusion Science (NIFS-Repository)

§16. Monte Carlo Collision Operator for Simu-lation of Edge Transport in Torus Wang, W.X. (Grad. Uni. Advanced Studies) Okamoto, M., Nakajima, N., Murakami, S. At the edge region of the torus the presence of large gradients in plasma temperatures and density makes analytical study of neoclassical transport very difficult. Monte Carlo simula-tion, however, may provide an effective way for solving the problem. We are developing a fvionte Carlo simulation code for the purpose of studying neoclassical transports near the edge. Constructing an appropriate Monte Carlo collision operator is an important step in the simulation. In the previous work11•2l, the Monte Carlo scheme which uses Lorentz collision op-erator has a substantial limitation due to lack of momentum conservation. However, the mo-mentum conservation is important since, for ex-ample, it may cancel the contribution of like particle collisions to the particle fi ux. The Monte Carlo collision operator developed here does exactly conserve not only energy but also momentum. The velocity alternation of parti-cle a(ma, v:_, ea) during a collision with particle b(mb, v"b, eb) in a time interval 8.t is determined as follows, !\ ..... - mb ( o1x - 1) ..... uVa - e U ma+mb (1) and small parameter E is given as where i1 = v: - v"b is relative velocity before the collision, ln A is Coulomb logarithm, n is a ran-dom unit vector, and nb, JVb are particle density and model particle number of species b. Its equivalence to Fokker Planck equation of Lan-dau form is proved by keeping the lowest order term in the friction· and diffusion coefficients. In addition, considering each particle collisions with all other particles in the same cell makes 128 the equivalence more reasonable. In order to check the collision model, we perform simula-tions for temperature rela."'<:ation processes in a uniform plasma. The results are shown in Fig.1 and Fig.2. 0.8 h"l~ I I h" ~ 0.6 Analytical result 0.4 Monte Carlo result 0 .2 0.0 c__ __ ___,__ __ _.___ _ ___,_____, 0 .0 0.05 0.1 0.15 Time normalized by rexalation time Fig. 1: The relaxation between ion tempera-ture Ti and electron temperature Te. t.::;~ I ~ 0 h ~ 0.6 0.4 0.2 Monte Carlo result Analytical result 0.0 '-------'----'-----'--_..J 0.0 0.5 1.0 1.5 2.0 Time normalized by rexalation time Fig. 2: The relaxation between longitudinal temperature r,, and transverse temperature Tl_. References 1) Allen H. Boozer and Gioietta Kuo-Petravic, Phys. Fluids 24(1981)851. 2) R. H. Fowler, J. A. Rome and J. F. Lyon, Phys. Fluids 28(1985)338. 

Monte Carlo Collision Operator for Simulation of Edge Transport in Torus

Abstract

Similar works

Full text

Available Versions

National Institute for Fusion Science (NIFS-Repository)