J. Plasma
J.
Plasma Fusion
Fusion Res.
Res. SERIES,SERIES,Vol.
Vol.6 6(2004)(2004)179–182
000–000

Formation of Toroidal Plasma Flowin an Internal Conductor Trap
SAITOH Haruhiko, YOSHIDA Zensho, HIMURA Haruhiko, MORIKAWA Junji1,
FUKAO Masayuki1 and WAKABAYASHI Hidenori
Graduate School of Frontier Sciences, University of Tokyo, Tokyo, 113-0032, Japan
1
High Temperature Plasma Center, University of Tokyo, Tokyo, 113-0032, Japan(Received: 10 December 2003 / Accepted: 20 February 2004)

Abstract
The effects of electrode biasing and electron injection into a plasma were examined in an internal conductor
device Proto-RT. By using a negatively biased ring electrode, radial electric field of up to ~2 kV·m-1 was generated ina broad region between the vessel wall and the electrode. The corresponding toroidal E × B drift speed ~105 m·s-1 iscomparable to ion sound speed. In contrast, when electrons were injected into a plasma from an electron gun, potential
gradient was not effectively generated, due to electron loss.
Keywords:
plasma flow, radial electric field, electrode biasing, electron injection, internal conductor device,dipole magnetic field, double Beltrami fields

1. Introduction
A relaxation theory of plasmas including the effects ofion flow has recently been proposed. The equilibrium state of
two fluid plasmas is represented by double Beltrami fields[1] and it provides a condition for the flow velocity v and β
value of the plasmas to satisfy β + (v/vA)2/2 = const., wherev A is Alfvén velocity. When the plasma has fast flow
comparable to vA, ultra-high β (possibly β > 1) state will be
realized due to the effects of the dynamic pressure of theplasmas. In search for the new relaxation states of the flowing
plasmas, toroidal trap devices equipping normal-conducting
or superconducting internal coils have been constructed andfundamental researches are being carried out [2,3]. Formationof internal electric field and flow is one of the essential
subjects in these studies. For the generation of radial electricfields in plasmas, several techniques might be used, such as
non-neutralization of plasmas by the orbit loss of high-energy
electrons or electron injection, or application of external
electric fields. In this work, we studied the potential structuresof RF plasmas under the influence of a ring electrode andelectron injection from a gun using a LaB6 cathode.

Fig. 1

Schematic view of the Proto-RT and magnetic surfaces
generated by an internal ring coil and external verticalfield coils (not seen).

magnetic field strength is of the order of 10-2 T. In the current
experiments, plasmas are generated by RF electric field witha frequency of 13.56 MHz and an input power of ~200 W,
supplied via an inductively coupled loop antenna locatedinside the chamber. Hydrogen pressure used was 4 × 10-4 Torr.
Inside the chamber, a torus-shaped electrode on the ring
conductor and a LaB6 cathode electron gun are installed. The

2. Potential formation in Proto-RT
Proto-RT [2,3] (cross-sectional view is shown in Fig. 1)
is a prototype ring trap device with a normal-conducting
internal conductor (IC). The combination of dipole, vertical,
and toroidal magnetic fields provides a variety of static
magnetic field configurations for the confinement. The typicalCorresponding author’s e-mail: saito@plasma.q.t.u-tokyo.ac.jp1179©2004 by The Japan Society of Plasma
Science and Nuclear Fusion ResearchSaitoh H. et al., Formation of Toroidal Plasma Flow in an Internal Conductor TrapFig. 22-d potential profiles of plasmas (floating potentials of emissive Langmuir probes) when the IC electrode was (a) positivelybiased: VIC = +600 V and (b) negatively biased: VIC = –600 V. Thin lines show the magnetic surfaces.

Fig. 4

Fig. 3

IC electrode current vs bias voltage. Decrease of thecurrent when VIC < –200 V is due to the difficulty of RFmatching.

Radial potential profiles of plasmas at Z = 0, in thevariation of IC electrode bias voltage VIC from –600 to+600 V.

potential profiles of plasmas were measured by emissive
Langmuir probes. Because the electron temperature is low(Te ~ 5 eV) and also the variation of Te is small throughout
the experiments, the gradient of the measured floating
potential will give a good approximation of the electric field
in plasmas. Double probes for the electron density andelectron temperature measurements were also employed.
Fig. 5 Radial electron density profiles.

2.1 Electrode biasing
The potential structures of plasmas under the influenceof a positively or negatively biased ring electrode are shownin Figs. 2 and 3. Potential contours almost coincide with theflux surfaces of poloidal magnetic fields and the electric fieldis generated in the radial direction of the toroidal plasmas.
When the electrode was negatively biased, internal electricfield of up to 2 kV·m -1 was produced in a broad region
between the electrode and the vessel wall. The corresponding
toroidal E × B rotational speed is ~105 m·s-1. In contrast,
when VIC > 0, potential gradient was observed in a very
limited region near the electrode, and internal electric field
was not generated. A current between the IC electrode andvessel wall, IIC, in Fig. 4 also shows the strong asymmetry of
the response of plasmas against the polarity of the electrodevoltage. In the radial distributions of electron density in Fig.
5, a density gap is formed around the IC electrode when theIC electrode is positively biased. It leads to limit the current
IIC and also results in the observed flat potential profiles when
VIC > 0.
In the current 13.56 MHz RF experiments, typicalelectron number density is ne = 5 × 1013 m-3 and typicalelectron temperature is Te = 5 eV. With the applied magnetic
field strength B ~ 0.01 T, neutral gas density nn = 1.4 ×
10 19 m -3, and estimated hydrogen ion temperature T i =0.5 eV, plasma parameters are calculated to be Debye length
λD = 2 mm, Larmor radii for electrons and ions rLe = 1 mm
and rLi = 10 mm, ion sound speed cs = 2 × 104 m·s-1, Alfvén2180

Saitoh H. et al., Formation of Toroidal Plasma Flow in an Internal Conductor Trap

velocity vA = 3 × 107 m·s-1.
In the above parameter region, electromagnetic forces
and the effects of collisions with neutral atoms are dominant
in the motion of charged particles [4] and because theexperiments were carried out in a pure poloidal magnetic
field, radial electric field is sustained only by the toroidal
rotation of the plasma. In a steady state, the motions of ionsand electrons are approximated asvk⊥ =q νnk
E× B
E+ 2 ,2mkω ckB

radial electric fields and the electrode current are explained
as the transport due to the collisions with neutral atoms.

2.2 Electron injection
Figure 7 shows a potential profile of a plasma whenelectrons are injected into the plasma with an acceleration
voltage of 1 kV and beam current of 0.2 A. Although a small
potential gradient was formed near the electron gun, thepotential drop saturated around zero and the generated radial
electric field remained less than 50 V·m-1. The increase of
the acceleration voltage of the electron gun or the heating
current of the cathode (electron beam current of up to ~0.5 A
and acceleration voltage of up tp 1.3 kV) does not contributeto form a large potential well inside the plasma.
Assuming that the observed potential drop of ~30 V isdue to the injected electrons, the charge of the injected andtrapped electrons is of the order of 10-7 C. From the injectedbeam current of ~1 A, the confinement time of electrons isestimated to be τe ~ 0.1 µs. In pure electron experiments inProto-RT, obtained maximum electron confinement time isτpe ~ 100 ms and it is much larger than τe . Generated spacepotential of the plasma and the potential of the IC electrode,when electrons are injected into a vacuum (no RF plasmas)(1)

because cyclotron frequency ωck exceeds collision frequency
22/v nk>> 1. In the magnetic and electric configuration
vnk: ω ck
of the Proto-RT device, the first term corresponds to the radial
motion of charged particles across the magnetic surfaces dueto the radial electric field and collisions with neutral atoms,
and the second term is the E × B drift motion in the toroidal
direction due to the poloidal magnetic field and the radial
electric field Er. Figure 6 shows a single ion orbits in DC
electric and magnetic fields in Proto-RT without the effectsof collisions with neutral atoms. The relation between Er andradial current density jr is given by⎛ νν ⎞
jr = | q | (ni vi + ne ve ) = q 2 ne ⎜ in 2 + en 2 ⎟ Er .
ωmmeω ce ⎠⎝ i ci(2)Because the first term is dominant, the radial current acrossthe magnetic surfaces is mainly transported by ions:jr ~–q 2νin ne
Er ~ 3 × 10−5 Er .
miω ci2(3)Because the RF coupling and density distribution of theplasmas are modified according to the magnetic field strength
or background neutral density, it was not straightforward to
obtain the parameter dependence of the radial electric field
Er and the radial current IIC between the IC electrode and thevessel wall. However, with the surface area of the IC electrode
SIC = 0.59 m 2 and by assuming the radial symmetry ofplasmas around the IC electrode, the observed Er ~ 5 kV·m-1
near the IC electrode and IIC ~ 0.3 A generally agree with therelation between Er and IIC in Eq. (3), indicating the observed

Fig. 7

Potential profiles in the Proto-RT, with and without theelectron injection. The gun is located at R = 50 cm andZ = 0.

Fig. 8(a) Electrostatic potentials generated by an electron gun
as functions of background pressure and (b) the drain
and beam current of the electron gun, without thegeneration of RF plasmas.

z (m)

y (m)
x (m)
Fig. 6

The typical orbit of a hydrogen ion in the magnetic andelectric field configuration in the Proto-RT.

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Saitoh H. et al., Formation of Toroidal Plasma Flow in an Internal Conductor Trap

generated in the plasma in the Proto-RT, the obtained plasma
parameters still remain in an electrostatic range in the present
experiments. The Alfvén velocity is two order of magnitudelarger than the obtained drift speed of the plasma, v, and thus
the effect of the dynamic pressure of plasma flow on β value
is negligibly small. An increase in the plasma density,
possibly by means of another plasma generation method, will
reduce the Alfvén velocity (e.g. plasma density ne = 1017 m-3
give a more realistic value of vA ~ 106 m·s-1) and would makeit possible to test the effects of plasma flow on the equilibria
in future experiments.

vessel, are shown in Fig. 8. In the pressure range of above
P0 = 6 × 10-5 Torr, electron cloud does not formed and also
the increase of the gun current was observed due to thecollisions of electrons with neutral atoms. However, when RFplasmas were generated in the hydrogen pressure of 4 × 10-5Torr (< P0), the generated potential reduced to around zero,suggesting the electrons loss is caused by a diffusion via RF
plasmas.

3. Conclusion
The effects of electrode biasing and electron injection
into a plasma were examined in an internal conductor device
Proto-RT. When the ring electrode was biased, both theelectrode current and internal electric fields of the plasmas
showed a strong asymmetry according to the polarity of theelectrode bias voltage. By using a negatively biased ring
electrode, radial electric field of up to ~2 kV·m -1 wasgenerated, and it is consistent with the radial current due tothe transport of ions by the collisions with neutral atoms. The
corresponding E × B toroidal drift speed is comparable to theion sound speed. In the current experiments of electron
injection, potential gradient was not effectively generated dueto the electron loss via RF plasmas.
Although electric field or flow was successfully

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