23P116-P
Active Stabilization of FRCs by Intermittent Merging ofCounter-Helicity Spheromaks in TS-3 and TS-4 Merging Experiments
TS-3・TS-4装置を用いた異極性スフェロマックの連続合体によるFRCの安定化	 	 
Shizuo Inoue,	  Yasushi Ono, Shingo Ito,	  Michiaki Inomoto,	  Ritoku Horiuchi
井上静雄1, 小野	  靖1, 伊藤慎悟1, 井	  通暁1, 堀内利得2
1: Graduate School of Engineering, The University of Tokyo
2-11-16, Yayoi, Bunkyo-ku, Tokyo 113-0032, Japan
東京大学工学系研究科 〒113-0032	  東京都文京区弥生2-11-16
2: National Institute for Fusion Science, Toki 509-52, Japan
核融合科学研究所	  〒509-52	  岐阜県土岐市下石町322-6
Since 1990, an efficient formation method of a field-reversed configuration (FRC) has been developed in
the TS-3 merging experiment using two merging spheromaks with opposing toroidal field. This counterhelicity reconnection transforms two force-free (β = 5-10%) spheromaks into an oblate FRC with β =70-100%, exploring the oblate FRC in large size-parameter (s) regime (<20). Slingshot and spontaneous
formation of toroidal flow was measured during the FRC merging formation in TS-3 and TS-4 experiments.
We found that this shear-flow produced by the sling-shot motion saturates the n=1 tilt instability for FRCs
by transforming the n = 1 mode into the n = 2 and higher mode. A new method for continuous
sheared-flow generation is proposed for stabilization and heating of the FRCs by the use of intermittent
merging of spheromaks with opposing toroidal field. We will present this concept by comparing our simulations with our TS-4 experiments. We simulated for the first time the FRC plasma with the intermittent
merging of a pair of counterhelicity spheromaks using the MHD code. We will present how the intermittent merging maintains the flow shear as well as the stability of FRCs and then will show initial results in
TS-4 intermittent merging experiment in comparison with the our simulation results.

1. Introduction
Recently, an interest has grown in generating
field reversed configuration (FRCs) with large s(average number of ion gyroradii) for a future
large scale confinement experiment. As the size
and magnetic field of an FRC increase, its the svalue tends to increase significantly, transforming
the FRC stability from the small s kinetic regime
into large s MHD regime. From an engineering
point of view, a large-scale experiment also requires a slow formation of the FRC withhigh-energy efficiency, leading to several newformation technics in the MHD regime. We developed a slow formation method by which was
two force force-free spheromaks with opposing
troidal magnetic field were axially collided andwere transformed into an oblate FRC [1]. And we
also found this merging method generate sheared
flow, leading to stabilization of n=1 (tilt and/orshift) modes [2].
2. Concept of Continuous Merging
Figure 1 shows a basic concept of continuous
merging. Two merging force-free (β = 5-10%)
spheromaks are transformed into an oblate FRC

with β = 70-100%, generating sheared flow by
j × B sling-shot effect. This sheared flow suppress
the n=1 instability, so that the continuously merging

Fig.1. Continuous generation of sheared flow by multiple merging for stability / heating FRC.[]of two counter-helicity spheromaks into oblate FRC
leads to getting possibly improve the stability ofsteady-state FRC against n=1 mode.
This continuous merging technique is useful also
for fuel-feeding and flux-injection not only in FRCs
but also in spherical tokamaks (STs). The continuous merging ST scheme is almost the same as FRC.

Two small co-helicity ST formulated by coaxial
gun or flux core merge a center main ST, supplying
toroidal magnetic flux ( ψ tot = ψ big + 2ψ small ) andparticles to the main ST. It is difficult to provide
toroidal plasma current (poloidal flux) by center
solenoid coil because of narrow space in center
stack of ST device. This continuous merging technique realizes new toroidal current drive of STs
through q-value control by toroidal flux supplying.
3. MHD Simulation Model
We started modeling the continuous merging ofFRCs by use of 2-D MHD simulation code [3]. Itsolves the resistive MHD equations using the explicit finite-difference method with forth-order accuracy both in space and time[3]. The initial condition of MHD simulation is obtained by solving theGrad-Shafranov equation and the two boundary
between the main FRC and two spheromaks areconnected with vacuum magnetic field.
4. First results of continuous merging experiment and simulation
Figure 2 shows the 2-D MHD simulation resultof continuous spheromak merging with the main
FRC. Both sides of spheromaks with counterhelicity merge together with center main FRC at 0 ~ 34
[ TA ], generating toroidal sheared flow by the j × Bforce of the slingshot motion at 38 ~ 42 [ TA ]. The
sheared flow changes its polarity because it is generated by the repeating slingshot motion. This
sheared flow is expected to saturate the n=1 instability and continuously repeating cycle of spheromak merging possibly fully suppress the low-n
FRC’s instability. Since the MHD equation does
not include kinetic or two fluids effect, we are now
arranging the particle code as the next step.
Figure 3 shows time evolution of poloidal flux
contous when one small ST merges with the main
ST after their merging formation side. First, two
STs produced by both sides of flux core, merge together to form one main ST. Next, the 3rd ST collides into the produced main ST, supplying toroidal
flux, plasma particles and generating sheared flow.
These effects will be discussed in poster session indetail.
5. Summary
We numerically and experimentally demonstrated the continuous merging scheme useful for suppressing FRC’s instability or supplying the magnetic flux to ST. We obtained the first numericaland experimental results for this scheme, and in oursession, we will describe these two schemes in deta-

Fig.2 R-Z contours of poloidal flux and toroidal velocity (in color) when two small spheromak merge with thecenter main FRC (the MHD simulation).

Fig. 3 R-Z poloidal flux contous when two ST merges
together and the 3rd ST merge with the produced mainST.

il, and show initial results in TS-4 intermittent
merging experiment in comparison with the simulation results.
References[1] Y. Ono, et al., Phys. Rev. Lett. 76 (1996) 3328.
[2] Y. Ono, et al., Nuclear Fusion, 39 (1999) 2001.
[3] R. Hoiuchi and T. Sato, Phys. Fluids, 1 (1989) 581.