23P103-P
Magnetic Field Line Analysisof Merging Formation Process of a Spherical Torus
プラズマ合体による球状トーラス生成過程の磁力線解析
Keii Gi*, Toru II**, Toshiyuki Umezawa*, Michiaki Inomoto** and Yasushi Ono*
魏 啓為, 伊井 亨，梅澤 俊之，井 通暁，小野 靖*Graduate School of Frontier Science, The University of Tokyo** School of Engineering, The University of Tokyo
2-11-16 Yayoi, Bunkyo-ku, Tokyo, Japan*東京大学大学院新領域創成科学研究科 **東京大学大学院工学系研究科〒113-0032 東京都文京区弥生2-11-16
The Tokyo University Spherical Torus (TS-3 and 4) merging device experiments have demonstrated plasma merging formation of a high-beta spherical torus using two colliding plasma toroids with co-helicity
and counter-helicity. The plasma merging process is analyzed by using magnetic field line tracing method.
In the co-helicity merging, which forms a high-beta Spherical Tokamak (ST), the reconnecting magnetic
field lines show the flux piled-up effect, and the reconnected magnetic field lines offer an overshoot toradial direction. In the counter-helicity merging, which forms a Field-Reversed Configuration (FRC), twodifferent states are introduced. Their different characteristics are influenced by the local Hall effect.

1. Introduction
Plasma merging formation method of ahigh-beta spherical torus [1] has been developedin the Tokyo University Spherical Torus (TS-3/4)
merging device, using two colliding plasma toroids with co-helicity and counter-helicity. In themerging process, especially ions are significantly
heated, and have dramatic transition of magnetic
topology through magnetic reconnection. We
analyze transformation of 3-D magnetic fieldstructure and 3-D shape of the magnetic fieldlines before and after magnetic reconnection.
2.
PlasmaMerging
ExperimentandThree-Dimensional Magnetic Field Line Tracing
In the TS-3 and 4 merging device, two plasma
toroids are created individually by a pair of fluxcore.
They attract with each other due to their parallel
plasma currents, and merge on the midplane (Z = 0)
through magnetic reconnection, relaxing to ahigh-beta spherical torus. A high-beta Spherical
Tokamak (ST) is formed by merging two low-beta
STs with parallel toroidal magnetic fields(co-helicity merging) as shown in Fig. 1(a). An oblate Field-Reversed Configuration (FRC) is formedby merging two spheromaks with equal but opposing toroidal magnetic fields (counter-helicity merging) as shown in Fig. 1(b). Significant ion heating isexperimentally observed in counter-helicity merging, which has been explained as a result of theslingshot effect [1].
Two-dimensional (10 × 9) array of magnetic
probes is located on the R-Z plane in the cylindrical

High-β ST(a) Low-β STs

I t BtIt(b) Spheromaks

ItBt

It

Bt
Slingshot (j×B Force)

I t BtBt

FRCItBt  0Fig. 1 Magnetic field lines of (a) co-helicity mergingand (b) counter-helicity merging.

vacuum vessel of the TS-4 merging device for thepurpose of measuring poloidal and toroidal magnetic fields Bz and Bt. They are used to calculatemagnetic fields, poloidal flux Ψ and toroidal current density jt. Three-dimensional magnetic fieldlines are traced by numerical integration (Dormand-Prince method) of the calculated magnetic
field vectors in a cylindrical coordinate system.
3. Analysis of the Co-Helicity Merging Formation of a STFig. 2(a) shows the two-dimensional contours ofpoloidal flux Ψ and toroidal current density jt
during the co-helicity merging formation of a ST. A
current sheet is formed at the contacting point of thetwo STs with parallel toroidal currents. Magnetic
reconnection progresses with the current sheet dissipation, and the magnetic configuration relaxes toa high-beta ST. Fig. 2(b) shows magnetic field lines

(a)

-0.2

772

Case-I(b)Ψ[Wb]： Contour Spacing 0.002
jt[MA/m2]：

Case-O

0.2

Bt

Bt

Bt

Bt

R [mm]

92-430Z [mm]

430

Fig. 2 (a) R-Z poloidal flux contours Ψ with toroidal
current density jt, (b) top view of magnetic field linesof two initial STs just before magnetic reconnection.

Fig. 3 Two-dimensional illustrations of reconnecting
magnetic field lines in Case-I (left) and Case-O (right)of the counter-helicity merging.
Ψ[Wb]： Contour Spacing 0.002

jt[MA/m2]：-0.2

772

of two initial STs just before reconnection. It
represents their deformation near the midplane.
This fact suggests the flux piled-up effect in thecurrent sheet [2], which contributes to fast magneticreconnection. The reconnected magnetic field linesoffer an overshoot to radial direction (not shownhere), which accelerates particles.
4. Analysis of the Counter-Helicity Merging
Formation of an FRC
The counter-helicity merging has two differentstates (Case-I and Case-O), characterized by sign ofthe toroidal field of the two initial spheromaks, as
shown in Fig. 3 [3]. Our previous experiments indicate that an FRC formed in Case-I has better particle confinement than the other in Case-O. The reconnection (X) point of magnetic field lines is located in the outer current sheet in Case-I, while in
the inner current sheet in Case-O (Fig. 4). These
facts are probably explained by the tilt of reconnection planes with respect to the R-Z plane [3] or current sheet ejection [1], which make reconnection
speed faster than co-helicity merging.
The reconnected magnetic field lines shows theslingshot driven by j×B force. In the vicinity of theX-point, the ion motion is detached from the electron motion, because ion gyroradius is much larger
than electron one. Therefore, electrons are dominant
in the current sheet, and generate the Hall effectwhich is experimentally identified by the sharpbending of the reconnected magnetic field lines [4].
Fig. 5 shows their magnetic field line shapes inthese cases. The slingshot (red arrow) accelerates
particles mainly toward inside of radial direction in
Case-I, while outside in Case-O. It is also observedthat the Hall effect generated by the electron motionin the current sheet (blue arrow) pulls the reconnected field lines toward toroidal direction, tilting
the reconnected plane especially in Case-O.
5. Summary
We analyze the process of plasma merging formation of a ST and an FRC in detail by using
three-dimensional magnetic field line tracing me-0.2

R [mm]

92-430Z [mm]

430-430

Z [mm]

430

Fig. 4 R-Z poloidal flux contours Ψ with toroidal
current density jt during magnetic reconnection in
Case-I (left) and Case-O (right).
(a)

Front View

Side View(b)

Front View

Side View

Fig. 5 Front (left) and Side (right) views of reconnected magnetic field lines in (a) Case-I and (b)Case-O during couter-helicity merging.

thod. In the co-helicity merging, the flux piled-up
effect is identified, which causes fast reconnection.
In the counter-helicity merging, two different statesof the reconnection plane and the reconnection
point offer the two different slingshot motions affected by the local Hall effect, suggesting a cause
and mechanism for the two different particle confinement.
References[1] Y. Ono, M. Inomoto, T. Okazaki, and Y. Ueda: Phys.
Plasmas, 4 (1997) 1953.
[2] Y. Ono, R. Imazawa, H. Imanaka, T. Hayamizu, M.
Inomoto et al.: 21st IAEA Fusion Energy Conference
EX/P7-12 (2006).
[3] M. Inomoto, S. P. Gerhardt, M. Yamada, H. Ji, E.
Belova et al.: Phys. Rev. Lett, 97 (2006) 135002.
[4] K. Gi, T. Ii, Y. Ono: IEEJ Trans. FM, 131 (2011) (tobe published).