22P168-P
LHD-type fusion reactor magnetic configuration with helical coils
winding along geodesic line of a torus
円環の測地線に沿って巻くヘリカルコイルによる
LHD 型核融合炉磁場配位
Tsuguhiro WATANABE渡辺二太
National Institute for Fusion Science,322-6 Oroshi-cho, Toki 509-5292, Japan
核融合科学研究所 〒 509-5292 土岐市下石町 322-6
A new concept, the geodesic winding helical coil system, to satisfy the requirement of the wide blanket
space and the large plasma volume is proposed for the LHD-type fusion reactor. The position of the magneticaxis shift close to the center of the two helical coils. The magnetic well is formed in the core region, and thehigh magnetic shear is present in the peripheral region. The D-shaped to the bean-shaped cross-section of the lastclosed magnetic surface is produced at vertically elongated cross-section. Direct loss of 3.52MeV alpha particles
is reduced by the adoption of a ”winding frame” with oval shaped cross-section.

1. Introduction

LHD-type magnetic configuration (` = 2 Heliotronconfiguration) is produced by continuous helical and vertical coil systems. LHD experiments have achieved an average beta value of 5 % without beta collapse.

The LHD helical coils are wound as θ = pφ+αc sin pφ
on a torus with circular cross section (Rc = 3.9m, ac =0.975m), where p is the helical pitch number (≡ m/` = 5).
The coil pitch parameter γ ≡ (m/`)/(Rc /ac ) = 1.25. The
small pitch modulation of αc = 0.1 was determined by considering the the gap distance between the first wall and thelast closed magnetic surface (LCFS) and the confinement
properties of the high energetic particles [1]. High helicalsymmetry of magnetic surface with elliptic cross-section,and good confinement of high energetic particles of standard LHD configurations have been numerically confirmed[2]. High performance of energetic particle confinement
was experimentally proved by a high energy ion tail which
extended up to 1.6MeV during the long-pulse ICRF heating operation of LHD [3].
In the LHD-type fusion reactor (FFHR) design studies, the balance blanket space and plasma volume become
an important issue. Kozaki have pointed out that the γ dependence of magnetic structure is essential in LHD-typereactors, which is critically sensitive not only for optimizing plasma volume but also for selecting the optimum blanket conditions[4]. Sufficient blanket space is necessary foradequate tritium breeding and for shielding the magnet.
For this purpose, the small γ configuration is preferable,
but this leads to the reduction the plasma volume.
For the compatibility of the sufficient blanket space
and the large plasma volume, we have studied the possibility of the D-shaped cross-section of the LCFS. For
this purpose, we have analyzed numerically the mag-netic configuration produced by the helical coils winding
along a geodesic line of a torus, which we call the torus
as ”winding frame” for the helical coils. The effective
value of the coil pitch parameter γ of the geodesic line
is reduced(increased) inboard(outboard) side of the torus.
Therefore, the enough space between the first wall and theLFCS is reserved, and the position of the magnetic axis
shift close to the center of the two helical coils, and the volume of the LCFS increased and magnetic well is created.
However, when the cross-section of the ”winding frame”
is a circle, the geodesic line is very close to the pitch modulation curve with αc ' 0.532, (Rc = 3.9m, ac = 0.955m).
Helical field produced by large positive pitch modulation
winding law has very poor confinement performance forthe high energetic particles. To recover the confinement
performance for the high energetic particles, we have developed a magnetic configuration with helical coils winding along geodesic line of a ”winding frame” with oval
type cross-section.
In Sec. 2, we describe the helical winding along thegeodesic line on a toroidal oval. Characteristics of themagnetic lines of force produced by the helical coil system is summarized. In Sec. 3, we discuss our results.

2.

Helical winding along the geodesic line ona toroidal oval

To achieve an excellent alpha-particle confinement,
we mitigate the variation of magnetic field intensity distribution in horizontally elongated cross-section (φ = 0)
by introducing a ”winding frame” with oval shaped crosssection as shown in Fig.1(a), given by constant major radius Rc and variable minor radius a(χ). The orbit of thehelical coil center rc is givenrc (φ)= {Rc cos pφ + a(χ) cos(χ − pφ)} i

+ {−Rc sin pφ + a(χ) sin(χ − pφ)} j ,(1)using helical rotating helical coordinate system [2]. Theorbit length L of the helical coil center rc is givens!2
Z π/2p+2π/p
drc
dφ ,
L=(2)
dφ
π/2p
the Euler equation for the geodesic line is reduced to202 dχd  {a(χ) + a (χ) } dφ 
0 = − dφdoRc + a(χ) cos χ n 0a (χ) cos χ − a(χ) sin χ+d!2a0 (χ){a(χ) + a00 (χ)} dχ(3)+ddφs!2dχ
+ {Rc + a(χ) cos χ}2 ,(4)d = {a(χ)2 + a0 (χ)2 }dφFig. 2 Magnetic configuration produced by helical coils, winding along geodesic line of a toroidal oval. Poincaré plotof the lines of force at φ = 0, π/20, π/10 are shown withthe cross-section of helical coils and vacuum vessel.

1.5

ι/ 2π , U / UAX

U / UAXIn the present paper we have adopted the following functional form for the variable minor radius,a(χ) = a0 1 + a2 sin2 χ + a4 sin4 ,(5)with parameters shown in Table.1, with scale corresponding to the LHD.

p55IIIRc (m)3.9
3.9a0 (m)
0.865
0.975

a2
0.4
0.0

a4
0.5
0.0Rax (m)
3.9
3.6

1.0

ι/ 2π

0.50

Table 1 Parameters of ”winding frame” of geodesic winding helical coils(I) and of the LHD helical coils(II).

3.0

3.5

4.0

4.5

5.0R(M)

3Vlcfs (m )
67.0
28.9

VLCFS=67.0 M3

Fig. 3 Distributions of the rotational transform ι/2π and the specific volume U produced by helical coils, winding along
geodesic line of a toroidal oval.

1.0(b)
1.5(a)3.

Z (M)χ / 2π, χ′ / 25

0.80.60.4

χ

1.00.50
3.0

3.5

4.0R (M)

4.5

χ′

0.2

0π/10

2π/103π/10

φ4π/105π/10

Fig. 1 (a): An example of oval shaped cross-section of a ”winding frame” for helical coils. (b): Variation of poloidal
angle χ of geodesic line on the ”winding frame”. One
period of toroidal angle φ for the helical coils is 2π/5,because of p = 5.

Discussion

It is shown that the geodesic winding helical coilmethod satisfies the requirement of the wide blanket space
and the large plasma volume. The magnetic well is formedin the core region, and the high magnetic shear is present in
the peripheral region. In addition, geodesic winding allows
tightening winding of the superconducting wires.
Numerical computations show the 14.0% direct loss
rate of 3.52MeV alpha particles, born uniformly in theregion of ρ/ρlcfs ≤ 0.8, for the case of Rc = 14m andBax = 6T. The direct loss rate of alpha particles of standard
LHD configuration under the same condition is 0.2%
For discussing the geodesic winding helical coil systems, the author thanks the members of the Meeting on
Helical Reactor Design at the National Institute for Fusion
Science.
References

Structure of the magnetic surface is shown in Fig.2
and distributions of the rotational transform ι/2π and thespecific volume U, produced by helical coils winding
along geodesic line of a toroidal oval, is shown in Fig.3.

[1] N. Ohyabu, et.al, Nucl. Fusion, 34, (1994) 387.
[2] T. Watanabe, et.al., Nucl. Fusion 46 (2006) 291.
[3] T. Mutoh, et.al., Nucl. Fusion 47 47 (2007) 1250.
[4] Y. Kozaki et. al., Nucl. Fusion 49 ( 2009) 115011.