23P084-P
Autonomous Plasma Position Controls for Tokamak Disruptions
with 3D Shaped Coils
３次元形状コイルを用いた自律的プラズマ位置制御
Shoichi Hatakeyama1, Soya Masaharu1, Hiroaki Tsutsui1, Shunji Tsuji-Iio1, Ryuichi Shimada1,Tsuhoshi Akiyama2, Yasuhiro Suzuki2, and Kiyomasa Watanabe2
畠山 昭一1, 征矢 正治1，筒井 広明1，飯尾 俊二1，嶋田 隆一1
秋山 毅志2，鈴木 康浩2，渡邊 清政2
1) Tokyo Institute of Technology 2-12-1-N1-11, Ookayama, Meguro-ku, Tokyo 152-8850, Japan
東京工業大学 〒152-8850 東京都目黒区大岡山2-12-1-N1-112) National Institute of Fusion Science 322-6, Oroshi-cho, Toki, Gifu 509-5292, Japan
核融合科学研究所 〒322-6 岐阜県土岐市下石町322-6
3D shaped coils are employed to suppress vertical displacement events (VDEs) which occur in elongatedshaped tokamak plasma. The coils are simplified helical coils which are placed excluding the inner side oftorus. The coils make plasma elongated and stabilize plasma position vertically and holizontally. The twoeffects were investigated by using VMEC code. The plasma with 3D shaped coils have 3-dimentional
geometry and elongated cross-section on average. And it enable us to maintain plasma configuration
horizontally even under a drastic change in hoop force. Experimental demonstration of the stabilizing
effects on a small tokamak is under study.

1. Introduction
It is well known that a good energy confinement
and high β can be achieved in elongated tokamak
plasmas. However, elongated plasmas suffer fromvertical instabilities conventionally. Usually, westabilize vertical modes by shell effects and active
positional control using a feedback system. At a
disruption, however, large eddy currents aregenerated in thermal and current quench phases andthe feedback system fails to keep the plasma at aprescribed position. Then vertical displacement
events (VDEs) are triggered. The contact of plasma
and first wall will lead to the damages of a reactor
by high heat flux and induced electromagneticforces. This event drops the operating ratio of areactor which is very important factor of economy
for power plants. Since it is difficult to avoid
disruptions completely, we must makecountermeasure development to ensure the reactor
safety.
2. 3D shaped coils for the positional stability andelongation
We proposed a 3D shaped coils system. They
have two effects, to make plasma elongated and tostabilize position vertically and horizontally [1,2,3].
Then it avoids an occurrence of VDEs by addition
to a tokamak reactor. Figure 1 shows a schematic
illustration of the coil configuration. The coils aresimplified helical coils which are placed excluding
the inner side of torus to give place to existing coils

vesselrestoringforce
IpBr
Proposed
3D shaped coils

PlasmaFig.1. Schematic illustration of the coil configuration.
The arrows indicate the direction of coil currents. Here,Ip is plasma current, Br is fields made by coils. Add 3D
shaped coils to tokamak. The fields made by coils
stabilize vertical mode and make plasma elongated.

of tokamaks. The directions of coil currents arealternate like stellarator windings. 3D shaped coils
can autonomously control plasma position without
a feedback system. The feature can be advantageous
in reactors, since measurements of plasma condition
will be limited because of high heat and nutron
fluxes.
3. Equilibrium configurations with 3D shaped
coils computed with VMEC code
We analyzed magnetic flux surfaces with theVMEC code with free boundary conditions. Figure 2
shows equilibrium configurations with 3D shapedw/o 3D shaped coilswith 3D shaped coils

Fig.3. Comparison of equilibrium horizontal shift
between with and w/o 3D shaped coils

R: major radius
Z: z direction
ζ: toroidal angle
s: nomalized minor radius
q: safety factor

[m]
0.15

PFC

vacuum closed
magnetic surface

0.0

Fig.2. Equilibrium configurations with 3D shaped coils
computed with VMEC

coils. Six 3D shaped coils are located around the torus
except the inner side. The plasma parameters are R =0.3 [m], a = 0.08 [m], BT = 0.5 [T], Ip = 5 [kA], β =0%. We confirmed that the cross-section is elongated,
whose averaged ellipticity is 1.6. The q-profile
increases with normalized small radius in the same
way as conventional tokamaks.

4. Horizontal plasma shift under a drasticchange in hoop force
We analyzed stabilizing effect of plasma
position. In particular, we focus horizontal plasma
shift by change in hoop force. The hoop force waschanged by an increase in plasma current. Figure 3
shows equilibrium with and without 3D shaped
coils at one poloidal cross-section. The equilibrium
without 3D shaped coils shifts to outside withincreased hoop force. On the other hand,equilibrium with 3D shaped coils remains almost
unchanged in the horizontal direction. Furthermore,
if we use 3D shaped coils, equilibrium can beobtained without poloidal field coils whichtokamaks have normally. We assumed that the coils
stabilize plasma position vertically in the same way
as the horizontal result.
5. Vacuum closed magnetic surface made with
3D shaped coils and poloidal field coils
Furthermore, the proposed coils have another-0.15
0.2

3D shaped coils
0.3

PFC

0.4 [m]Fig.4. Vacuum closed magnetic surface made with 3D
shaped coils in combination with poloidal magnetic fieldcoils

advantage. It can make closed vacuum magnetic
surfaces in combination with poloidal magnetic
field coils. Then it makes plasma breakdown andcurrent drive easy in application of sphericaltokamaks.
6. Summary and future work
We proposed 3D shaped coils for the position
control and plasma elongation. And we analyzed theseeffects with VMEC code. We confirmed that the coils
produces elongated plasma and it has a capability ofmaintaining plasma configuration horizontally evenunder a drastic change in hoop force. We areinvestigating the stabilizing effects experimentally ona small tokamak.
References[1] H. Ikezi, K. F. Schwarzenegger, Phys. Fluids 22,
2009 (1979).
[2] A. Reiman, Phys. Rev. Lett 99, 135007 (2007).
[3] S. Hatakeyama et al., P4.044, EPS2011, Strasbourg,2011