25aE17P
トカマク周辺プラズマにおける不純物の新古典輸送のモデリング
Numerical Modeling of Impurity Neoclassical Transport in Tokamak Edge Plasmas
井上春如1，本間裕貴2，矢本昌平1，畑山明聖1Haruyuki Inoue1, Yuki Homma2, Shohei Yamoto1, and Akiyoshi Hatayama1
慶應義塾大学大学院理工学研究科1，日本原子力研究開発機構2
Graduate School of Science and Technology, Keio University1, Japan Atomic Energy Agency2
1. Introduction
Understanding and control of tungsten impurity
transport is one of the most important issues.
Recently, we have developed a numerical scheme ofimpurity classical/neoclassical transport[1,2,3,4]. The
numerical scheme makes it possible to reproduce not
only the classical transport but also the neoclassicalself-diffusion (NC SD), the neoclassical inward
pinch (NC IWP), and the neoclassical temperaturescreening effect (NC TSE) for impurity ions.
However, impurity transport has been modeled onlyin the case where plasmas are in the Pfirsch-Schluter(PS) regime.
The final goal is to extend our model to wider
range of collisionality regimes, i.e., not only the PS
regime, but also the plateau and banana regimes. In
this study, we focus on the NC SD and the NC IWP.
Some test calculations have been done and comparedwith neoclassical theory.

Carlo Model (BCM)[7] has been used. In the BCM,
after sampling the velocity and density ofbackground ions from the given distribution function,
the velocity change of test impurity ions is calculated
by using random numbers.
In addition to these, so as to simulate theneoclassical transport with the BCM, velocity
distribution of background ions has been modeled asa deformed Maxwellian distribution which includes
the density gradient.
4. Results
By using this scheme, some test calculations
with a simple torus magnetic configuration havebeen done. Some parameter dependence of NC SDand NC IWP have been checked. Figure 1 shows thedependence of NC IWP velocity on safety factor 𝑞
in the case where impurity ions and background ions
are in the plateau regime. Other simulation results
will been shown in the presentation.

2. Impurity Neoclassical Transport[5]Now consider two types of ion denoted bysubscript 1 and 2. Subscript 1 and 2 correspond to
the impurity ions and the background fuel ions,respectively. In the case where background ionshave a radial density gradient, the collisional radial
flux of impurity ions 𝜞𝑟1 is given by(1)𝜞𝑟1 = −𝐷1 ∇𝑟 𝑁1 + 𝑁1 𝑽pinch,
𝑍1 ∇𝑟 𝑁2(2)𝑽≈𝐷,pinch

1𝑍

2

𝑁2

where 𝐷 , 𝑁 , 𝑽pinch , and 𝑍 are the diffusion
coefficient, density, the IWP velocity, and charge
state, respectively. The first term in Eq. (1) denotes
the SD effect relaxing the density gradient ofimpurity ions. The second denotes the IWP effect,
which is in the direction parallel to the density
gradient of the background fuel ions. In neoclassicaltransport theory, the diffusion coefficient 𝐷
depends on the collisionality parameter and has
different characteristics in each collisionality regime.
3. Numerical Scheme
In this study, the trajectory of each impurity ion
in the magnetic field is followed by Boris-Bunemanalgorithm[6]. Furthermore, to calculate the effects ofCoulomb collisions, the Binary Collision Monte-Fig. 1 Dependence of NC IWP on safety factor (in the plateau regime).
References[1] Y. Homma and A. Hatayama: J. Comp. Phys. 231 (2012)3211-3227.
[2] Y. Homma and A. Hatayama: J. Comp. Phys. 250 (2013)206-223.
[3] Y. Sawada et al.: J. Plasma Fusion Res. 63 (2013)353-354.
[4] Y. Homma et al.: Kinetic modeling for neoclassical transport ofhigh-Z impurity particles using Binary Collision Method (to be
published in Nucl. Fusion).
[5] P. Helander and D. J. Sigmar: Collisional Transport in Magnetized
Plasma (Cambridge University Press, New York, 2002).
[6] C.K.Bridsall et al: Physics via Computer Simulation (McGrraw-Hill,NewYork, 1985).
[7] T. Takizuka and H. Abe: J.Comp. Phys. 25 (1977) 205.