J. Plasma
J.
Plasma Fusion
Fusion Res.
Res. SERIES,SERIES,Vol.
Vol.6 6(2004)(2004)326–328
000–000

Self-Reversal and Sustainment of Magnetic Fields in
Helicity-driven Toroidal Plasmas
NAGATA Masayoshi, TAKAMIYA Tetsuhiro, HASEGAWA Hiroyuki, KAWAMI Kazuhiro,
FUKUMOTO Naoyuki, UYAMA Tadao, MASAMUNE Sadao1 and KATSURAI Makoto2
Himeji Institute of Technology, Hyogo 671-2201, Japan1
Kyoto Institute of Technology, Kyoto 606-8585, Japan
2
University of Tokyo, Tokyo 113-8656, Japan(Received: 9 December 2003 / Accepted: 11 March 2004)

Abstract
In the HIST experiment, self-organizing transition studies between helicity-driven relaxed states of the low-aspectratio toroidal plasmas have been made by means of a rapid reversal of the external toroidal field. Results show thatthe spherical torus (ST) relaxes towards flipped ST states, which is accompanied by spontaneous reversal of plasma
currents. It has been found that an intermittent behavior of the non-flipped region at the outer edge of the flipped ST
plasma plays an important role in its current sustainment by coaxial helicity injection.
Keywords:
self-organization, current reversal, coaxial helicity injection, flipped ST, current sustainment

1. Introduction

electrodes by the shortest path is defined as a non-flipped
region.
From the viewpoint of the CHI current drive, it isconceivable that the F-ST, which consists of only closed flux
surfaces, compares favorably with the N-ST with open fieldlines. It has not yet been verified whether the CHI method
can create enough closed flux surfaces in the N-ST plasmas

Coaxial helicity injection (CHI) using a magnetizedcoaxial plasma gun (MCPG) is expected to be the attractive
non-inductive current-drive method for a spheromak [1] anda spherical tokamak (ST) [2]. The CHI current drive basedon Taylor relaxation theory provides us with broad interests
concerning magnetic reconnection, magnetohydrodynamic(MHD) relaxation and self-organization. In the Helicity
Injected Spherical Torus (HIST) experiment, we haveinvestigated dynamics of self-organizing toroidal plasmas
during the helicity injection process [3,4].
The relaxed toroidal plasmas in the driven system, as
well as in the closed one, are described by the force-freeequilibrium equation, ∇×B = λ B, where the force-freeparameter λ = µ0 J·B/B2 = const [5,6]. The relaxed states intoroidal systems are characterized by the strength and sign ofthe external toroidal field (TF), and the value of λ determinedby coupling to a helicity source. Figure 1 illustrates
comparison of poloidal flux topologies between relaxed
configurations with “open” magnetic field lines penetrating
the boundaries in both the cases of positive and negative TF
with λ < λ en, where λ en is the lowest eigenvalue. There areclear differences in magnetic topology between “normal” ST(N-ST) and “flipped” ST (F-ST). It should be noted that theopen flux no longer surrounds the closed flux in the F-ST
since the toroidal current is in the opposite direction although
the gun bias flux Ψbias and the gun current Igun are applied in
the same direction. The open flux that directly joins the gunFCBt

Bt

BpMCPG

Non-flippedregion

ItfFig. 1

Corresponding author’s e-mail: nagata@elct.eng.himeji-tech.ac.jp1326-Bt-BpItfλ < λe Ψt.e > 0λ < λe Ψt.e < 0(a) Normal ST(b) Flipped ST

Comparison of poloidal flux topologies between twokinds of relaxed states (ST (a) and F-ST (b)) in driventoroidal systems which depend on the direction of theexternal toroidal flux Ψt.e.

©2004 by The Japan Society of Plasma
Science and Nuclear Fusion Research

Nagata M. et al., Self-Reversal and Sustainment of Magnetic Fields in Helicity-driven Toroidal Plasmas

or not. Accordingly, it is interesting and worthwhile toinvestigate how the F-ST plasma is sustained, although it isisolated from the gun electrodes working as a helicity source.

HISTSurface Magnetic Probe (B t,Bp)

Magnetic Probe(Br ,Bφ ,Bz)

Spherical FluxConserver

171915222. Experimental setup
The HIST device (a major radius R = 0.30 m, a minorradius a = 0.24 m and an aspect ratio A = 1.25) produces
low-aspect-ratio torus plasmas by utilizing the variation of theTF coil current Itf from zero to maximally 0.25 MAturns.
Figure 2 depicts a schematic diagram of HIST anddiagnostics. The detail experimental description concerning
the HIST devise is presented in ref. [3].
In this experiment, the ST plasmas with a peak toroidal
current It of 60–80 kA are initially produced by CHI and thenthe reversed-TF circuit is triggered at t = 0.16–0.35 ms during
the current ramp-down phase. The Igun and gun voltage Vgun
are ≈ 25–30 kA, and ≤ 0.8 kV respectively and the bias flux
Ψbias produced around the MCPG muzzle is 0.8–1.1 mWb inthis experiment. The TF-coil current Itf is varied from +20
kAturns to 0 ~ –60 kAturns. The time scale over which Itfchanges is quite slow (≈ 0.5 ms) compared with an Alfvéntime.
A three axis magnetic probe (9 channels each for Br, Bφ ,Bz ) is located in the plasma at a distance of z = –0.75 m fromthe midplane (z = 0 m) of the flux conserver (FC). Magnetic
pick up coils (26 channels each for Bp, Bt ) are located in thepoloidal direction along the inner surface of the FC tocalculate the total toroidal current It. Note that the It measured
by the surface magnetic coils includes not only the flipped
region but also the non-flipped region. A fast framing camera
measurement was performed in order to investigate dynamics
of current reversal.

CentralConductor

261510812

ToroidalField Coil
Magnetized Coaxial
Plasma Gun (MCPG)
Fig. 2The schematic drawing of the HIST device anddiagnostics.

(kG)

(kG)

t=0.157 (ms)

0.4

0.4
0.2
0-0.2
-0.4
-0.6
-0.8
0ST

0.2
0Bt
Bz
Br
Vacuum Bt.v

-0.2
-0.4
00.1 0.2 0.3 0.4 0.5

t=0.600 (ms)Flipped ST

0.1 0.2 0.3 0.4 0.5

R (m)

#9086
Toroidal Current

STIt (kA)

6040200-200R (m)abcd e f

Flipped ST
0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9(kG)t = 0.440 (ms)Time (ms)

3. Experimental results
Experimental results showed that the ST plasma becomes
unstable when I tf decreases by –4 kAturns because of
violation of the Kruskal-Shafranov stability condition andafterward its toroidal current starts to drop suddenly andreverse its sign as shown in Fig. 3. The F-ST plasma decays
resistively after the reversal. Internal magnetic measurements
indicated that toroidal and poloidal magnetic field profiles
reverse sign and the relaxation to the F-ST magnetic fieldstructures takes place. Figure 3 (a–f) implies a nonaxisymmetric topological change of magnetic field lines
during the transition. Fast camera image in Fig. 3 shows thehelical deformation of plasma around the central conductor
at the initial growth time (a, b, c) of the reversal. Threedimensional MHD numerical simulations succeeded indemonstrating the formation of the flipped ST and
substantially enabled us to understand the non-linear dynamic
field-reversal mechanisms [7]. The simulation results indicatethat a large helical distortion of the open flux and thefollowing magnetic reconnection between open and closed
field lines play a major role in the self-reversal process. The
experimental results are almost in good agreement with thoseof simulation (see Fig. 2 C in ref. [7]).

(kG)

t = 0.400 (ms)

1
Br
0.8
Bt.v
0.6
0.4
0.2
0-0.2
Bt-0.4Bz-0.6
0 0.1 0.2 0.3 0.4 0.5

a(kG)

1
0.8
0.6
0.4
0.2
0-0.2
-0.4
-0.6

(kG)

(kG) t = 0.540 (ms)bR (m)

R (m)(kG) t = 0.460 (ms)

10.8
0.6
0.4
0.2
0-0.2
-0.4
-0.6
0 0.1 0.2 0.3 0.4 0.5

dR (m)

Fig. 32327

t = 0.420 (ms)

1
0.8
0.6
0.4
0.2
0-0.2
-0.4
-0.6
0 0.1 0.2 0.3 0.4 0.5

0 0.1 0.2 0.3 0.4 0.5

R (m)t = 0.500 (ms)

1
0.8
0.6
0.4
0.2
0-0.2
-0.4
-0.6
0 0.1 0.2 0.3 0.4 0.5

eR (m)

c1
0.8
0.6
0.4
0.2
0-0.2
-0.4
-0.6

f0 0.1 0.2 0.3 0.4 0.5

R (m)Time evolution of toroidal current, and the radial profile
of magnetic fields of ST, F-ST, and during the transition
process from ST to F-ST. Fast framing camera image
corresponds to the magnetic field profile of (a, b, c).

Nagata M. et al., Self-Reversal and Sustainment of Magnetic Fields in Helicity-driven Toroidal Plasmas

Fig. 5 Time evolutions of F-ST plasmas sustained by helicity injection.
Fig. 4

Dependence of the axial length Zof the non-flipped (non-reversal)
region on the reversed-TF coilcurrent –Itf .

The helicity-driven relaxed theory [5,6] indicates that
there exists a non-flipped region in the F-ST configuration asshown in Fig. 1. We have experimentally verified theexistence of the non-flipped region near the gun. Figure 4
shows the axial length of the non-flipped region as a functionof the reversed TF coil current –Itf . We can see that the nonflipped region shrinks towards the gun electrodes and theflipped region becomes dominant in the FC as –Itf increases.
This is because the Lorentz force by Ig is reduced by theincrease in –Itf . The condition of |–Itf | < Ig for continuous orintermittent ejection of plasma with helicity from the gun
should be satisfied for the successful sustainment of the F-STplasmas.
At present, we have successfully demonstrated thesustainment of the F-ST plasmas by adjusting –Itf . Figure 5
shows that the toroidal current in the F-ST is maintained for
longer time (≈ 2 ms) than a resistive decay time (≈ 0.2–
0.3 ms) after the quiescence phase (≈ 0.25 ms). The nonflipped (non-reversal) region starts to extend gradually
towards the midplane of the FC from t = 1.2–1.3 ms because|–Itf | decreases from the peak value in time. Note that theamount of |+It | in the non-flipped region is comparable with|–It | in the flipped region after t = 1.7 ms, so we haveobserved that the measured It oscillates regularly around zero.
The boundary magnetic probe signals show interesting
behaviors. There are almost no regular magnetic fluctuationsin the inboard side. In the other hand, signals in the outboard
side show intermittent fluctuations in the same period as theoscillation of It. The observations suggest that the fluctuations
at the outboard side are related to the current drive.

ST plasmas tend to self-organize to the flipped states while
reversing the direction of TF. The observation of the selfreversal phenomena suggests strongly that the sign ofmagnetic helicity K = cΨpΨt (1 < c < 2), where c depends on
the plasma shape and current profile, is conserved withresistive loss in the magnitude during the transition process,namely when Ψ t in the flipped plasma region becomes
negative, then Ψp must also be so. A quantitative proof of thehelicity conservation is an important work in our future
experiments and numerical simulations. The reversal
mechanism is closely associated with the kinking behavior of
the open field lines around the central conductor. We havebeen able to maintain successfully the F-ST configuration byCHI, although the mechanism has not been understoodadequately. We are considering the possibility that thehelically kinked magnetic flux of the non-flipped region
causes fluctuations at the outer edge region of the F-ST andthe following magnetic reconnection transports intermittentlyhelicity from the gun to the F-ST plasma interior.

References
[1]
[2]
[3]
[4]
[5]

H.S. McLean et al., Phys. Rev. Lett. 88, 125004 (2002).
R. Raman et al., Phys. Rev. Lett. 90, 075005 (2003).
M. Nagata et al., Phys. Plasmas 10, 2932 (2003).
M. Nagata et al., Phys. Rev. Lett. 90, 225001 (2003).
J.B. Taylor and M.F. Turner, Nucl. Fusion 29, 219(1989).
[6] P.K. Browning et al., Plasma Phys. Control. Fusion 35,1563 (1993).
[7] Y. Kagei et al., Plasma Phys. Control. Fusion 45, L17(2003).

4. SummaryThe most interesting finding of this experiment is that3328