24P041-P
The calculations about the Neoclassical diffusion of ions in GAMMA10A-divertor
GAMMA10 A-divertor 中央ミラー部におけるイオンの新古典拡散に関する計算
Shuhei Sato, Isao Katanuma, Shun Masaki, Kazuto Sekiya and Tsuyoshi Imai
佐藤周平, 片沼伊佐夫, 真崎俊, 関谷和人, 今井剛
Plasma Research Center, Tsukuba University
1-1-1 Tennodai, Tsukuba City, Ibaraki 305-0006, Japan筑波大学プラズマ研究センター 305-0005 茨城県つくば市天王台 1-1-1

Previously, Monte Carlo simulation was performed to research the Neoclassical transport in GAMMA10 A-divertor. Theguiding center approximation of ion orbit and the paraxial approximation of magnetic field are used in the simulation. Itwas found that the large transport occurs even in the GAMMA10 A-divertor.

Introduction
approved when |Bx /Bz | ¿ 1, |By /Bz | ¿ 1 and we
GAMMA10 A-divertor is the remodeling device of assume that energy of the particle ε and magnetic moGAMMA10. This device is replaced its nonaxisym- ment µ is conserved. Therefore drift equation is transmetric magnetic field of anchor cell with an axisym- formed into[]
metric divertor configuration. The object of this de∂φ cdψ=− c+ {2ε − µB − 2qφ} κ(2)vice is performing divertor simulation experiments ofdt∂θqlarge torus device. Here, predictable consequence isdθ∂φ cthat the magnitude of the neoclassical transport be=c
+ {2ε − µB − 2qφ} κ„(3)dt∂ψ qcomes altered due to replacing the configuration. There[]122dz
fore, this research aims to show quantitative informa=±{ε − µB − qφ}(4)dt
mtions of the radial transport in GAMMA10 A-divertor
using Monte Carlo method.
Here, κ , κ„ are the component of curvature. The expressions of curvature are2 Calculation model^„ ψ sin 2θκ„ (ψ, θ, z) = κ(5)We omit gyro motion of particle and calculate only
drift motion of guiding center. This drift motion is11
κ (ψ, θ, z) = κ^ (z) − κ^„ (z) cos 2θ
(6)calculated by drift equation. We use the expression
22()
where,c∇φ × B mc v2⊥ + 2vk ∇B × Bv = vk e^k −−[]
B22qB3r20
d2 σ(z)d2 τ(z)κ^„ (z) = −σ(z)− τ(z)(7)(1)2ψdz2
dz2[]
r20
d2 σ(z)d2 τ(z)as drift equation. Here, vk is the component alongκ^ (z) =σ(z)+ τ(z)
(8)
2ψ
dz2
dz2
magnetic field line of velocity, e^k is the unit vector
along magnetic field line and v⊥ is perpendicular veand the expressions of magnetic field line arelocity to magnetic field line. Second term of this equation is E × B component and third term is ∇B andx (ψ, θ, z) = σ(z)r0 cos θ(9)curveture drift component. We define (ψ, θ, z) coory (ψ, θ, z) = τ(z)r0 sin θ(10)dinate system, where z axis is chosenalongmagnetic∫rfield line and B = ∇ψ × ∇θ. ψ = 0 Bz rdr increases
Monte Calro method was used to calculate effects
toward radius direction and θ is increasing toward az- of coulomb collision. A basic equation of collision isimuthal direction. Besides, paraxial approximation is Fokker-Planck equation.
1

[cm]
24.0

Energy of particle：All are 1kev
Pitch angle：All are 11.95°
Dfault position：(15.0cm, 40°, 0cm)
(15.0cm, 60°, 0cm)(15.0cm, 80°, 0cm)
(15.0cm, 100°, 0cm)
(15.0cm, 120°, 0cm)

16.0[cm]40.0

initial energy of particles =1kev
initial real space position(10.0cm, θ, 0cm)
number of particle = 10000
11 -3
density of ﬁeld particle = 1.0 x 10 cm

8.00

20.0

x 0.00
x
0.00

-8.00
-16.0

-20.0
-24.0
-24.0

-16.0

-8.00

0.00

y

8.00

16.0

24.0 [cm]Fig. 1: Banana orbits when initial azimuthal positions are40◦ − 120◦ .

-40.0
-40.0

-20.00.00

y

20.0

40.0 [cm]Fig. 2: Including collision effects. Faster diffusion oc3

curred in the position of banana orbit than other nonresonant particles.

Calculation result and Discussion
We define Poincaré plot of a record of intersection
points of a particle orbit on x-y plane when a particle passes through z = 0. Potential is assumed as
φ = 300 (1 − ψ/ψ0 ) [V/cm], ψ0 is ψ at r = 18cm
∆r2/τ [cm2/ms]
and r is distance from z axis. Circular orbits which
6encircle z−axis were confirmed at most parameters of5ε and µ. However, at some particular parameters ofε, µ, we found the particles drawing banana orbits. If4particle energy was 1keV, the banana orbits were ex3
isting while pitch angle 11.95◦ ± 2.45◦ at z = 0 andwhen we changed initial azimuthal positions, distor2
tion magnitude of banana orbits are altered . Figure 1
1shows each banana orbit when initial azimuthal positions are changed. Even if radial initial position was
012111010changed, the banana orbits still exist.
[cm-3]
fieldFigure 2 shows the particle positions mapped at z =0 when t = 32.310ms, where collision effects are inFig. 3: Diffusion coefficient
cluded. The particles around the positions of banana
orbits begin to diffuse fast rate. This data indicates thatthe banana orbits have an influence on the diffusion.
Figure 3 plots diffusion coefficient as a function of 4 Summary
We confirmed the existence of the banana orbits andcollision frequency. Note, collision frequency depends
thosebanana orbits cause a fast rate diffusion of ions.
on the density of field particles.
The diffusion coefficient changes with the density offield particles.
We would like to calculate detailed profile of diffusion coefficient for our future work.

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