24P141-P
2-D effect of ion dynamics on radial profile of ion temperaturein the edge of magnetized plasma
磁化プラズマ周辺領域のイオン温度分布における	 イオンダイナミクスの2次元的効果	 
Yuki Hayashi1, Naomichi Ezumi1, Hirohiko Tanaka2, Katsuya Okazaki2 and Noriyasu Ohno2
林	  祐貴1, 江角直道1，田中宏彦2，岡崎克哉2，大野哲靖2
12

Nagano National College of Technology, 716 Tokuma, Nagano 381-8550, Japan
Graduated School of engineering, Nagoya University, Furo-cho Chikusa-ku, Nagoya 464-8603, Japan1
長野工業高等専門学校 〒381-8550 長野市徳間716
2
名古屋大学大学院工学研究科 〒464-8603 名古屋市千種区不老町

Ion dynamics in the edge region of magnetized plasmas have been studied by comparing experimentallyobtained radial profiles of ion temperature with analytical ion mean energy profiles based on the ion
Larmor motion. Both radial profiles show the tendency that ion temperature increase at the outside of theplasma column with increasing the radial distance from the plasma center. Two-dimensional model
considering the radial profile of magnetized plasma indicates the importance of high-energy ions whichhave large Larmor radius.

1. Introduction
It is important to understand the edge and thedivertor plasmas in order to operate highperformance plasmas in magnetic confinement
fusion devices. The spatial profiles of ion
temperature Ti, electron temperature Te andelectron density ne are the key parameters forcharacterizing the transport in these boundaryplasmas.
So far, Ti measurements using an Ion Sensitive
Probe (ISP) [1] have been done using a linear
plasma device, Compact Test Plasma device with
Hot Cathode (CTP-HC), in Nagano National
College of Technology. The observed results
showed the tendency that Ti becomes high withincreasing radial position at the outside of theplasma column [2,3]. A simple analysis about theradial profile of Ti also has been done using
one-dimensional (1-D) Ti evaluation model basedon ion Larmor motion [4]. According to the model,a probe put at far from the plasma column measureshigh-energy ions selectively. The analysis model
showed the results consistent with experimentalone.
In this study, in order to check the influence of
two-dimensional (2-D) effect for Ti profile we havemeasured Ti using an ISP in the linear divertor
plasma simulator NAGDIS-II in Nagoya Universityof which plasma diameter is larger than CTP-HC.
The experimental results have compared Ti profiles
with 1-D and 2-D models.

2. Experimental setup
Figure 1 shows a schematic of the ISP
measurement system in NAGDIS-II. Radial
position of the probe can be changed with 2mm inspace resolution. In this study, Helium is used forplasma discharge.
Function
Generator

Ion sensitiveprobePowersupplyRgVoltage
divider

Isolation
amp

Rp
Isolation
amp

Space
resolution:2mmPlasma

AD converter

Fig.1 Schematics of ISP measurement system

3. Analysis model
We consider the behavior of ion which is locatedat P(r,θ) in a cross section of a cylindrical plasma,
where r is the distance from the plasma center andθ is an azimuthal angle as shown in Fig. 2.
Assuming no diffusion process, the ion at P(r,θ)
can reach a probe position rc moving a Larmor
orbit when it has ion energy Ei(r,θ). The distance
between P and rc is represented by l . At theprobe position rc, ions with Larmor radius of l /2
are collected. Ei(r,θ) is ion energy to reach probehead calculated by l and is proportional to squared!
Larmor radius.

!
!

due to lack of some assumptions. One possible
reason is diffusing low temperature plasma aroundplasma column. Another one is the charge exchange
reaction of ions during Larmor motion. Moreover
parallel transport might be taken into account.
The cause of that 2-D analysis show higher Ti
profile than 1-D could be due to considering moreions on the 2-D analysis than the 1-D analysis.

yEi (r,!)P(r,!)
lrrc!

xFig.2 ion Larmor dynamics

This 2-D model indicates ions with large
Larmor radius (higher energy) can reach more
outside of plasma column. Therefore, Ti isexpected to show high temperature with increasingradial position.
Considering the all position for the origin ofion, mean energy at the probe position Ti (rc) isexpressed as follows:

Ti (rc ) =## n(r," )E (r," )F(E )drd"## n(r," )F(E )drd"
ii(1)

i!

Where, n(r,θ) is plasma density. F(Ei) is
Maxwell distribution assuming a Ti in the plasma
column at P(r,θ).
4. Results and discussion
Figure 3 shows the comparison of theexperimentally obtained Ti profile with analyticalresults using Eq. (1). Both analyses assume theexperimental condition of NAGDIS-II for ne profile,gas pressure. Ti in the plasma column is assumed anexponent profile predicted by the experimentalresult.
As shown in Fig.3, the experimental result shows
the tendency that Ti becomes high with increasingradial position like CTP-HC. Both analytical resultsof 1-D and 2-D model also show the same tendency.
Hence, the analytical results are qualitativelyconsistent with the experimental result. However,analytical results show higher Ti profiles than theexperimental result. Furthermore, 2-D analyticalresult shows higher Ti profiles than 1-D analyticalone.
The reason why the difference caused might beFig.3 Comparison of Ti profile obtained by ISP
measurement at the outside of the plasma column withresults of analytical models of 1-D and 2-D

5. Conclusions
In this study, radial profiles of Ti have beenmeasured using an ISP in NAGDIS-II. The
experimental results show the tendency that Ti
becomes high with increasing radial position. Theresults of 1-D and 2-D analyses based on the ion
Larmor motion were compared with theexperimental result. Both analytical results werequalitatively consistent with the experimental result,although the both analytical results showed higher
profiles than the experimental result. Moreover, the2-D analytical result showed higher profile than the
1-D analytical result.
References[1] I. Katsumata, Contrib. Plasma Phys. 36, S, 73 (1996)[2] K. Todoroki and N. Ezumi, 8thIWEP2009, Innsbruck,Austria, 21-23 Sep. (2009).
th[3] N. Ezumi and K. Todoroki, 8 Joint Conference forFusion Energy, Takayama, Japan, 10-11 June
2010, 10B-19p, in Japanese.
[4] N. Ezumi, Y. Hayashi, K. Okazaki, H. Tanaka, N.
Ohno, 27th JSPF Annual Meeting, Hokkaido, Japan,
30 Nov.-3 Dec. 2010, 03P03, in Japanese.