23P052-P
Confinement Analysis of Low Aspect Ratio Tokamak-Stellarator HybridConfigurations
低アスペクト比トカマク‐ステラレーター混成配位の閉じ込め解析
Hidemasa Ozeki1, Kozo Yamazaki1, Hideki Arimoto1, Tetsutarou Oishi1, Tatsuo Shoji1and M.I.Mikhailov2
尾関秀将1, 山﨑耕造1，有本英樹1，大石鉄太郎1，庄司多津男1，M.I.Mikhailov2
1. Nagoya University, Furo-cho, Chikua-ku, Nagoya 464-8603, Japan
2. Russian Research Center ‘‘Kurchatov Institute’’, 123182, Moscow, Russia
1. 名古屋大学 〒464-8603 名古屋市千種区不老町
2. ロシアクルチャトフ研究所 〒123182 モスクワ
We proposed 6 types of low aspect ratio tokamak-stellarator hybrid configurations with a few helical coils
wound on spherical or cylindrical boundary. We call these configurations ‘‘TOKASTAR’’. In this study
these configurations are analyzed by computational simulation and experiment, and the connections
between the parameters of magnetic flux surface and equilibrium beta or confinement capability of single
high-energy particle of TOKASTAR are studied. We found that they can produce low aspect ratio flux
surface with high elongation and the N=1 configuration achieved the highest equilibrium beta value among6 types.

1. Introduction
Fusion reactor has several serious problems tobe overcome for achieving commercial fusion
reactor. It requires low capital cost, steady-state
operation and good confinement capability offusion plasmas. To solve these problems at thesame time a new magnetic configuration concept
is proposed [1], which is a low aspect ratio
tokamak-stellarator hybrid configuration with afew simple helical coils wound on spherical or
cylindrical boundary. We call these configurations‘‘TOKASTAR’’. The coil design concept ofTOKASTAR is shown in Fig. 1 and N in thecaption is the toroidal mode number of helicalcoils. In the previous study the configuration withthe shape of coils shown in Fig. 1 is analyzed interms of magnetic flux surface formation,
confinement capability of single particle andequilibrium beta by computational simulation,and the requirement for optimizing configuration
is suggested [2].
In this study, we proposed 5 new TOKASTAR
configurations shown in Fig. 2 and comparedthem with the previous study from the same view(a) N=1

Fig.1. Concept of N=2 TOKASTAR(b) N=4

point. The aim of this study is to find out theconnections between the parameters of magnetic
flux surface and equilibrium beta or confinement
capability of single high-energy particle ofTOKASTAR.
2. Analysis Methods
2.1 Computation method
We analyzed TOKASTAR configurations bycomputational simulation code. We studied thevacuum magnetic flux surface and the plasma
equilibrium state.
For magnetic flux surface analysis, we used theHSD code. This code traces a magnetic field line
produced by the coils and defines the vacuum
magnetic flux surface. The guiding center orbit ofsingle high-energy particle is also computed in thiscode. This codesolves the particle drift equationrrr
Bm 1 2r(1)v = v // +v ⊥ + v //2  B × ∇ B
3 B qB  2
In this computation, we used filament coil model.
Plasma current and pressure were not consideredwhen we used this code.

(c) N=2 withcentral helix(d) N=2 cylindricalcoil system(e) N=2 withcrescent
cross-section

Fig.2. Concept design of 5 new TOKASTAR configurations

2.2 Experimental methodWe carried out electron confinement experimentin TOKASTAR by impedance method. The details
are going to be presented in the conference.
3. Results of Analysis and experiment
3.1 Result of simulation of magnetic flux surface
We carried out magnetic flux surface analysis for6 types of TOKASTAR with HSD and VMEC
codes and the results are shown in Fig. 3 and Table
I. Figure 3 shows typical last-closed vacuum
magnetic surface of N=2 TOKASTAR. Table I
shows the shape parameters of cross-section of flux
surfaces for 6 types of TOKASTAR. From theseresults we found out TOKASTAR can produce low
aspect ratio configuration with high elongation.

configurations. This beta limit is determined byconvergence condition of VMEC and Shafranov
shift condition: the beta value at which themagnetic axis shifts half way out to the last flux
surface. The result of equilibrium beta limit analysis
is shown in Fig. 4. In this figure, the vertical axis
<β>limit indicates the volume-averaged equilibrium
beta limit and the horizontal axis indicates the valueof rotational transform at the plasma axis producedby plasma current. The radial dependence of theplasma current is assumed(2)ι pl ( s ) = ι pl (0)(1 − s + 1 3 s 2 ) ,where s is normalized toroidal flux and s ~ρ2. InFig. 4 the configuration N=1, which produces flux
surface with the lowest <Ap> in Table I, achieved
the highest equilibrium beta value within 6 types.
30

N=1
N = 2 (previous)
N=4
N = 2 central helix
N = 2 cylindricalN = 2 crescent<β>limit[%]For equilibrium analysis, the VMEC code wasutilized. The finite-beta 3-dimenional equilibrium
was solved with the results of flux surface analysis
by this code. The computational procedure of
VMEC is to minimize the total energy of a plasma
confined in a toroidal domain. The equilibrium
states with finite-beta plasmas and the effects ofplasma current in TOKASTAR configurations wereanalyzed with this code.

2010000.2

0.4

0.6

Fig.4. Equilibrium beta as a function ofcentral rotational transform(a)Vacuum magnetic
field line (HSD code)(b)3-D shape of surface(VMEC code)

Fig.3. Result of magnetic flux surface
analysis of N=2 TOKASTAR.
Table I. Shape Parameters of magnetic flux surface

N =2 ( previous )N =2 with central

Ap(=R/a)< Ap >(=R/√ab)

2.7

1.6

Ellipticity
κ
3.0

2.5

1.4

3.3

5.3

2.6

4.1

helix
N =2 with crescentcross section
N =2 cylindrical coilsystem
N =1

3.3

3.1

1.2

2.3

1.2

3.6

N =4

3.0

1.8

2.8

3.2 Result of simulation of equilibrium
In the equilibrium analysis with VMEC code, we
researched equilibrium beta limit of TOKASTAR

3.3 Result of simulation of particle confinement andexperiment
We analyzed electron and alpha particle
confinement capability with HSD code and wecompared these computational results withexperimental result. The details are going to bepresented in the conference.
4. Summary
We proposed and analyzed 6 types ofTOKASTAR configurations and we found they canproduce low aspect ratio flux surface with highelongation and the N=1 configuration with thelowest <Ap> achieved the highest equilibrium beta.
MHD stability and neoclassical transport of thisTOKASTAR configuration will be clarified in thenear future.
References[1] K.Yamazaki and Y.Abe: Nagoya Research Report
IPPJ-718 (1985).
[2] Y. Taira and K. Yamazaki et al., Plasma and Fusion
Research, Vol.5, S1025 (2010).