Proceedings of ITC/ISHW2007

Spatial Distribution of Toroidal Flowin a Field-Reversed Configuration
T. Asai1), T. Matsuzawa1), N. Yamamoto1), K. Sakuraba1), T. Kiguchi1), K. Kishi1), T. Takahashi1),
S. Hiromori1), T. Ikeyama1), Y. Nogi1) and T. Takahashi2)
1)

College of Science and Technology, Nihon University, 1-8 Kanda-Surugadai, Tokyo 101-8308, Japan
2)

Dept. of Electronic Engineering, Gunma University,1-5-1 Tenjin-cho, Kiryu 376-8515, Japan

A radial profile of toroidal flow in a field-reversed configuration plasma has been measured with a newly built ion
Doppler spectroscopy system with a line-spectrum of impurity carbon (CV: 227.2nm). With this system, radial profile oftoroidal flow was observed preliminary on the theta-pinch FRC plsma. The toroidal flow inside the separatrix starts tospin-up just after the formation and the flow velocity is gradually increased. The velocity is comparable with an ion
diamagnetic velocity at 25µs from the formation. However, the flow velocity out side the separatrix keeps small value orsettled. It indicates the existence of flow shear in vicinity of the separatrix. The observed results were also compared with anumerical calculation by newly proposed toroidal spin-up mechanism which employs direct conversion of the kinetic
angular momentum from the magnetic flux [T. Takahashi, et al., Plasma Fusion Res. 2 (2007) 008]. The calculated results
are consistent with the presented experimental results.
Keywords: field-reversed configuration, n = 2 mode rotational Instability, toroidal flow, flow shear, toroidal
spin-up

1. Inroduction
Rotational instability with toroidal mode number n =2 is the only destructive instability in a field-reversed
configuration (FRC) plasma. Also, the toroidal velocity
shear potentially has a stabilization effect on aninterchange instability with highr toroidal mode numbersn ≥ 3. Therefore, investigation of mechanism of toroidal
spin-up and its spatial structure are longstanding
problems in the FRC research to improve confinement
and stability property. The toroidal plasma current justafter formation is primarily carried by electrons, whileions are approximately at rest [1]. The ions, however,gradually gain angular momentum in the direction with
the ion diamagnetic before the onset of the n = 2
deformation due to rotational instability. The mechanismof toroidal spin-up has been discussed theoretically withseveral possible mechanisms of selective loss of ions[2-4], end-shorting [5-8], and both [9]. However, only afew experimental investigations have been performed sofar.
In this work, radial velocity profile of toroidal flow
in a FRC plasma has been measured with a newly built
ion Doppler spectroscopy (IDS) system in detail. Fromthe ion Doppler shift measurement of impurity ions,radial profile of toroidal flow and its time evolution areobserved preliminary on the theta-pinch FRC plasma.
The experimental observation will also becompared with the newly proposed toroidal spin-up
mechanism, which employs direct conversion of theauthor’s e-mail: asai@phys.cst.nihon-u.ac.jp

kinetic angular momentum from the magnetic flux [10].

2. Experimental Apparatus and Diagnostic
Figure 1 shows a schematic view of experimental
apparatus and diagnostic. The FRC plasma is formed by anegative-biased theta-pinch method in the Nihon
University Compact Torus Experiment (NUCTE) –III
device.
The device has a 1.5m one-turn solenoidal
theta-pinch coil. It consists a center confinement coil witha diameter of 0.34m and a length of 1.0m and a mirror
coil with a diameter of 0.30m and a length of 0.25m at
the both end. A ratio of the passive mirror is about 1.22.
A slow bank with 5kV-1980µF and a first bank with
32kV-67.5µF are connected with the theta pinch coilthrough a collector plate. The coil produces a bias fieldup to 0.064T with a rising time of 90ms and aFig.1Toroidal section of NUCTE-III device andarrangement of collimators for IDS.

Proceedings of ITC/ISHW2007
confinement field up to 0.6T with a rising time of 4ms
and a decay time of 120µs. The transparent fused silica
discharge tube with a diameter of 0.256m and a length of
2.0m is evacuated to about 1.5×10-4 Pa using a turbo
molecular pump. A 10mTorr of deuterium gas is filled
and pre-ionized by a z-discharge method.
An axial separatrix profile (rs(z)) is observed by anexcluded flux measurement. An averaged electron density( n e ) is estimated by a line integrated electron density,
which is measured by a quadrature 3.39µm He-Ne laserinterferometer on the midplane (z = 0). A total plasma
temperature (Tt = Ti + Te : sum of a ion and electron
temperature), is calculated from a radial pressure and anaxial force balances,!

Tt = (1" 0.5(rs rw ) 2 )Be2 2µ0 n e .

!

A poloidal flux and its time evolution can also be estimatedby the equation," p = 0.32#rs (0) 2 Be rw!

(1)

(2)

which is given by the assumption of a rigid rotor profile
equilibrium model.
The IDS system consists of a collector with f = 100
convex-plane lens, a quartz optical fiber tube with 5m oflength, a Czerny-Turner grating monochrometer, and a 16Fig.2

Time evolution of toroidal flow velocity
measured by the IDS measurement.

Fig. 3Time evolution of radial profile oftoroidal angular velocity.

channels photo-multiplier tube (PMT). Dispersed light ismagnified by a cylindrical lens with a diameter of 5 mm
and detected on the PMT. An impurity line intensity of CV(227.1nm) emitted from the FRC plasma is collected by
the collector and transferred to the IDS system through theoptical fiber tube. Wavelength resolution and sensitivity
between channels are calibrated by Hg line spectrum of254 nm. The optical resolution per channel is about 0.05
nm in the system. From the obtained shift and broadeningof the line spectrum, ion temperature and ion flow velocity.
To confirm a motion of the FRC plasma andreproducibility of FRC formation, a visible lightmulti-channel optical detector is arrayed in the x-direction
at the same toroidal cross section with the IDS.
3. Experimental Results
Typical FRC plasma parameters of this experiment atequilibrium phase (t = 20 µs) are n e : 2×1021 m-3, Tt: 190
eV, rs(0): 0.06 m, Trapped poloidal flux: 0.5 mWb, particle
confinement time: 80 µs and decay time of poloidal flux:
100 µs.
! evolution of the toroidal flow
Figure 2 shows the time
velocity at the midplane along the chords (x = - 4.5, -3, 0, 3,4.5 and 6 cm) measured by the IDS system. The rotation
velocity already has a finite value just after formation
period of field-reversal phase. The velocity of CV ion isincreased gradually during the equilibrium phase. Therotation velocity at 20 µs is approximately 10 km/s at x =±4.5 cm. The measured velocity and direction are
corresponded to the ion diamagnetic drift. Flow velocity on
the chord at x = 0 is almost at rest during the discharge.
The time evolution of radial profile of toroidal flow isshown in Fig.3. The radial profile of toroidal velocity isalmost flat in the very early phase of FRC discharge pulse.
However, the rotation velocity outside of the separatrix is
not accelerated compared to the rotation inside of theseparatrix. It indicates the existence of velocity shear near
the separtrix. The stability effect of this observed shear on
higher toroidal mode number of interchange instability
could be a reason why the higher mode of toroidal
deformation predicted in the theoretical works has neverbeen observed in the FRC experiments. In Table 1, theresults of these toroidal flow measurements aresummarized.

Fig. 4

Time evolution of the flux decay andnumerically calculated troidal flow
velocity.

Proceedings of ITC/ISHW2007
Table 1 Summary of experimental results
Position

Rotation direction

Inside of Separatrix

Diamagnetic

Outside ofSeparatrix

No rotation

Radial profile
Uniform (like rigidbody)-Table 2 Summary of past theoretical predictions
Mechanism

Plasmarotation

Ion flow(inside)Ion flow(outside)

Particle loss

Diamagnetic

Diamagnetic

Paramagnetic

End-shorting

Diamagnetic

Diamagnetic

Diamagnetic

4. Discussion
The past proposed theoretical predictions are
summarized in Table 2. The presented experimental results
show faster spin-up of the plasma column inside theseparatrix. Also directions of the toroidal flow are samewith ion diamagnetic direction. It is not consistent withpast theoretical prediction of toroidal ion spin-up shown in
Table 2. Recently, some of the authors have proposed newmechanism of toroidal spin-up [10]. In the scenario, flux
decay is directly converted toroidal momentum of ions.
Under the assumtion of axisymmetry and canonicalmomentum conservation, every ion gains angularmomentum in the ion diamagnetic direction when thepolodial flux decays. While the flux is decreasing, changeof ion trajectory type, i.e. figure-8 shape trajectory changes
into betatron one results in increment of the toridal angularmomentum. Inductive electric field by the poloidal flux
decay is also a possible cause of the rotation.
To compare the experimental result with the newtheory, particle simulation has been performed taking into
account of these possible sources of ion spin-up for theplasma parameter in the presented experiment. Figure 4
indicates the calculated time evolution of the flux decay
and the toroidal flow velocity. The time, the toloidal flow
velocity and the decay flux are normalized by Alfven time

Fig. 5Time evolution of the poloidal flux
estimated under the assumption of rigid rotor
profile model.

Fig. 4 Time evolution of poloidal flux

tA0, Alfven velocity vA0 and the magnetic flux at coil wall
ΨW, respectively. In this calculation, toroidal flow velocity
is shown as a function of the amount of change in thepoloidal flux ΔΨ. In this experiment, Alfven velocity andAlfven time are about 140 km/s and 1.2 µs. Figure 5 shows
the time evolution of the poloidal flux which is obtained
experimentally on the NUCTE-III FRC. In Fig. 3, thedecayed flux can be estimated about 0.31mWb. Also
decayed flux in the experiment is about 0.12mWb for 40µsof equilibrium phase. The normalized toroidal flow
velocities in the experiment and the calculation at 35 tA0 are
0.15 v A0 and 0.25 v A0, respectively. The calculation isconsistent with the presented experiment results. It will be
expanded to discuss the radial profile of flow.
5. Summary
Investigation of the toroidal flow profile and its time
evolution has been started with both methods ofexperiments and numerical approach. Experimentallyobserved flow profile is not consistent with past theoreticalpredictions. Then the experimental results are comparedwith the newly proposed theory and it is shown that thecalculated result agrees with the experimental result.
Detailed flow profile measurements and confirmation of
the new theory will be continued.
This work was partially supported by a Grant-in-Aidfor Science Research from the Ministry of Education,
Culture, Sports, Science and Technology of Japan (MEXT),a Nihon University Research Grant, and NIFS
collaborative Research Program (NIFS06KDBD003) and(NIFS06KKMP003).

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